Research Article Predicting Erosion-Induced Water Inrush of Karst Collapse Pillars Using Inverse Velocity Theory Banghua Yao, 1,2,3 Zhongwei Chen , 2,4 Jianping Wei, 1,3 Tianhang Bai, 4 and Shumin Liu 1 1 School of Safety Science and Engineering, Henan Polytechnic University, Jiaozuo, Henan 454000, China 2 State Key Laboratory of Mining Disaster Prevention and Control Co-Founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Shandong 266590, China 3 Collaborative Innovation Center of Coal Work Safety, Henan Province, Jiaozuo 454000, China 4 School of Mechanical and Mining Engineering, e University of Queensland, Brisbane, QLD 4072, Australia Correspondence should be addressed to Zhongwei Chen; [email protected] Received 28 July 2017; Accepted 16 November 2017; Published 28 January 2018 Academic Editor: Tianchyi Yeh Copyright © 2018 Banghua Yao et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Although the impact of Karst Collapse Pillars (KCPs) on water inrush has been widely recognized and studied, few have investigated the fluid-solid interaction, the particles migration inside KCPs, and the evolution feature of water inrush channels. Moreover, an effective approach to reliably predict the water inrush time has yet to be developed. In this work, a suite of fully coupled governing equations considering the processes of water flow, fracture erosion, and the change of rock permeability due to erosion were presented. e inverse velocity theory was then introduced to predict the water inrush time under different geological and flow conditions. e impact of four different controlling factors on the fracture geometry change, water flow, and inrush time was discussed in detail. e results showed that the inverse velocity theory was capable of predicting the occurrences of water inrush under different conditions, and the time of water inrush had a power relationship with the rock heterogeneity, water pressure, and initial particle concentration and an exponential relationship with the initial fracture apertures. e general approach developed in this work can be extended to other engineering applications such as the tunneling and tailing dam erosion. 1. Introduction Groundwater inrush in coal mines has caused thousands of fatalities across many countries, such as the USA, Russia, Poland, Canada, Australia, Germany, Great Britain, India, and especially China [1]. As mining activities progress further deeper underground, there have been an increasing number of water outburst incidents occurring annually largely due to the impact of some key geological structures such as Karst Collapse Pillars (KCPs), as illustrated in Figure 1 [2, 3]. As a special geological structure, KCPs commonly exist at more than twenty coal fields in the northern China, such as Shanxi province (see Figure 2) [4]. e existence of the geological structure usually functions as an underground water flow path, thus posing a great threat to the mining production safety [3, 5]. According to the statistics, the most serious water disasters in Chinese coal mines were all directly caused by water inrushes associated with the KCPs under the Permo-Carboniferous coal seams located at northern China [6, 7]. Take Fangezhuang coal mine of Kuiluan Group, for instance, during the accident in 1984, the maximum water inflow associated with KCPs reached 2,053 m 3 /min, resulting in the mine and other three neighboring mines submerged in a very short time, and caused a direct capital loss of around US$90 million [8]. us, better understanding of the mechanism of water inrush has both economic and safety benefits. Significant number of investigations have been per- formed to explore water inrush mechanism of KCPs using single or combined methods of theoretical analysis and numerical simulation as well as experimental studies. For instance, based on the elastic thick plate theory, Tang et al. [4] developed a mechanical model for water inrush of KCPs. Bai et al. [9] established a mechanical model-plug model, which was used to describe the behavior of water seepage flow in coal-seam-floor containing KCPs. Furthermore, the variable Hindawi Geofluids Volume 2018, Article ID 2090584, 18 pages https://doi.org/10.1155/2018/2090584
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Research ArticlePredicting Erosion-Induced Water Inrush of Karst CollapsePillars Using Inverse Velocity Theory
Banghua Yao123 Zhongwei Chen 24 Jianping Wei13 Tianhang Bai4 and Shumin Liu1
1School of Safety Science and Engineering Henan Polytechnic University Jiaozuo Henan 454000 China2State Key Laboratory of Mining Disaster Prevention and Control Co-Founded by Shandong Provinceand the Ministry of Science and Technology Shandong University of Science and Technology Shandong 266590 China3Collaborative Innovation Center of Coal Work Safety Henan Province Jiaozuo 454000 China4School of Mechanical and Mining Engineering The University of Queensland Brisbane QLD 4072 Australia
Correspondence should be addressed to Zhongwei Chen zhongweichenuqeduau
Received 28 July 2017 Accepted 16 November 2017 Published 28 January 2018
Academic Editor Tianchyi Yeh
Copyright copy 2018 Banghua Yao et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Although the impact of Karst Collapse Pillars (KCPs) onwater inrush has beenwidely recognized and studied few have investigatedthe fluid-solid interaction the particles migration inside KCPs and the evolution feature of water inrush channels Moreover aneffective approach to reliably predict the water inrush time has yet to be developed In this work a suite of fully coupled governingequations considering the processes of water flow fracture erosion and the change of rock permeability due to erosion werepresented The inverse velocity theory was then introduced to predict the water inrush time under different geological and flowconditions The impact of four different controlling factors on the fracture geometry change water flow and inrush time wasdiscussed in detail The results showed that the inverse velocity theory was capable of predicting the occurrences of water inrushunder different conditions and the time of water inrush had a power relationship with the rock heterogeneity water pressure andinitial particle concentration and an exponential relationship with the initial fracture apertures The general approach developedin this work can be extended to other engineering applications such as the tunneling and tailing dam erosion
1 Introduction
Groundwater inrush in coal mines has caused thousands offatalities across many countries such as the USA RussiaPoland Canada Australia Germany Great Britain Indiaand especially China [1] Asmining activities progress furtherdeeper underground there have been an increasing numberof water outburst incidents occurring annually largely due tothe impact of some key geological structures such as KarstCollapse Pillars (KCPs) as illustrated in Figure 1 [2 3] As aspecial geological structure KCPs commonly exist at morethan twenty coal fields in the northern China such as Shanxiprovince (see Figure 2) [4]
The existence of the geological structure usually functionsas an underground water flow path thus posing a great threatto the mining production safety [3 5] According to thestatistics the most serious water disasters in Chinese coalmines were all directly caused by water inrushes associated
with the KCPs under the Permo-Carboniferous coal seamslocated at northern China [6 7] Take Fangezhuang coalmine of Kuiluan Group for instance during the accidentin 1984 the maximum water inflow associated with KCPsreached 2053m3min resulting in the mine and other threeneighboring mines submerged in a very short time andcaused a direct capital loss of aroundUS$90million [8]Thusbetter understanding of the mechanism of water inrush hasboth economic and safety benefits
Significant number of investigations have been per-formed to explore water inrush mechanism of KCPs usingsingle or combined methods of theoretical analysis andnumerical simulation as well as experimental studies Forinstance based on the elastic thick plate theory Tang et al [4]developed a mechanical model for water inrush of KCPs Baiet al [9] established a mechanical model-plug model whichwas used to describe the behavior of water seepage flow incoal-seam-floor containing KCPs Furthermore the variable
HindawiGeofluidsVolume 2018 Article ID 2090584 18 pageshttpsdoiorg10115520182090584
2 Geofluids
Rock strata
Coal seam
K
C
P
Rock strata
Working face
Figure 1 Illustration of aKarst Collapse Pillar front viewof a typicalcone shaped KCP (not to scale) [23] and different shapes of rocklayers represent different types of rocks
mass dynamics and nonlinear dynamics were introducedand the seepage properties of KCPs associated with particlesmigration were investigated using numerical simulation [3]Ma and Bai [10] numerically studied the impacts of mining-induced damage on KCPs and the surrounding rocks andon the formation of the fracture zone and analyzed mining-induced KCP groundwater inrush risk This work was laterextended to study the effect of coal mining operations onKCPs related groundwater inrush using FLAC3D and theshear stress damage zone and their effects on seepage fielddevelopmentwere also discussed [11] Yao [12] experimentallystudied the evolution of the crushed rock mass seepageproperties under different particle sizes and stresses and ana-lyzed particle migration feature and the KCPs water inrushmechanism Moreover there are also some experimentalstudies focused on the permeability change of the KCPs toinvestigate water inrush mechanisms [13ndash15]
Recent studies on the water inrush mechanism of KCPshave consistently revealed that complex interactions existbetween the evolution of fractures and porosity in solidswater transport and rock solid particles migration whichaccompanies the erosion phenomenon [3 12] Significantprogress on the understanding of this complex process hasbeen made For example the reaction of aqueous solutionsmineral components and its impact on water flow wereinvestigated and amodel for porosity change was established[16] Vardoulakis et al [17] studied the piping and surfaceerosion effects based on mass balance particles migrationand Darcyrsquos law The dissolution of fracture surfaces due towater-rock interactions with variable fracture apertures overtimewas also studied and a depth-averagedmodel of fractureflow and reactive transport that explicitly calculated localdissolution-induced alterations in fracture apertures werepresented [18] Habib et al [19] numerically investigated theerosion rate correlations of a pipe protruding from an abruptpipe contraction problem
Despite the significant progress in understanding KCPswater inrush mechanism and water prevention technologyover the past several decades [20ndash22] most investigationswere carried out with respect to structure failure and fewhave investigated this issue by integrating the solid-fluidinteraction and particles migration due to erosion Waterinflow rate as probably the only direct measuring data in thefield has yet to be directly used in the literature to predict theprecise time of water inrush An effective method to predictwater inrush does not appear to be available neither In thiswork a set of fully coupled governing equations for KCPswater inrush will be developed by incorporating the fracturesand porosity evolution for KCPs particles migration andwater seepage process The governing equations will thenbe implemented into COMSOL Multiphysics software Theheterogeneity of rocks in KCPs will be determined using theWeibull distribution and the parameters including porosityseepage particle concentration and water inflow as well asseepage channels evolution law will be obtained accordinglyThis numerical model will be then used to investigate thewater flow characteristics with erosion Based on the inversevelocity theory the corresponding water inrush times fordifferent flow conditions will also be discussed in detail
2 Development of a Fully CoupledTheoretical Model
21 Selection of Microstructure Model of KCPs A KCPtypically consists of three parts solid rock matrix fluidsand infilling particles The intact rock blocks form a rockmass which is filled with fluids for example water andinfilling materials such as solid particles (Figure 3) As thepermeability of rock blocks is generally very low the interrockfractures provide the main passages for water flow Thisstructure matches the characteristics of the dual porositymodel where the rocks are considered as consisting ofmatrixes and fractures A numbers of different dual porositymodels have been developed including the Warren-RootKazemi et al and de Swaanmodels [24ndash26] but theWarren-Root model as shown in Figure 4 was widely accepted asa proper model to represent such rock structure As suchin this work the Warren-Root model is selected to examinethe processes of particle migration and the evolution of thefractures aperture and porosity
22 Governing Equations
221 Assumptions In order to establish a fully coupledtheoreticalmodel that integrates particlesmigration seepageand fracture and porosity evolution in KCPs under erosioneffects the following assumptions have been made
(1) The fluid and particles in KCPs are incompressible
(2) The suspended particles share the velocity field withthe fluid
(3) As the internal structure of KCPs is generally veryloose and the rock mass surrounding the KCPs is
Geofluids 3
N Datong
Shuozhou
TaiyuanYangquan
Jincheng
Huozhou
Yuncheng
Tuanbai
Main coal mine
Tuanbai coal mineCoal field in Shanxi
BeijingCity
Figure 2 The distribution of major coal mines in China and the coal fields in Shanxi province
Figure 3 Rock and infilling material (particles) in a KCP
Fractures
Matrix
Figure 4 Sketch of the Warren-Root Model [24]
generally competent the impact of the change in theeffective stress on KCPrsquos permeability is insignificant
(4) The impact of erosion on the permeability change isin proportion to the change of particle concentrationin the fluid
Half fracture
Matrix block
Water Particles
a
a + b
Figure 5 Sketch of a representative element of a typical KCP
222 Definition Based on the aforementioned assumptionsa representative element for a typical KCP microstructure isshown in Figure 5 The length 119871 (m) and volume 119881 (m3) ofthe element are expressed as
119871 = 119886 + 119887119881 = (119886 + 119887)3 (1)
where 119886 (m) is the length of the matrix and 119887 (m) is theaperture of the fracture
The total voidage 120593 () of an element is written as [28]
120593 = (119886 + 119887)3 minus 1198863(119886 + 119887)3 + 120601 cong 3119887
119886 + 120601 (2)
where 120601 () is the matrix porosity It should be noted that119887 ≪ 119886
4 Geofluids
o a + b
a + b
x3
x2
x1
(M1 + N1) L2
(M2 + N2) L2
(M1 +M1
x1
L) L2 + (N1 +N1
x1
L) L2
(M2 +M2
x2
L) L2 + ((N2 +N2
x2
L) L2
Figure 6 Illustration of a three-dimensional characteristic element in a KCP 119872119894 and 119873119894 are mass change of solids due to convection anddiffusion respectively defined as 119872119894 = 119862120588119904119902119894 119873119894 = minus119863(120597(119862120593120588119904)120597119909119894)
223 Mass Conservation Equations for Particles In order tostudy the migration characteristics of the infilling particlesthe dynamic mass conservation equations for particles werecalculated based on a three-dimensional representative ele-ment as illustrated in Figure 6
Infilling particles migration inside a representative ele-ment under erosion effects is affected by both convection andprocesses The average seepage velocity of an element can bedefined as997888rarr119902 119894 (ms) For the convection and diffusion processin the direction of 119909119894 (119894 = 1 2 3) the mass losses of particlesflowing out of the element in a unit time can be calculated by(3) and (4) respectively
120597 (119862120588119904119902119894)120597119909119894 119881 (3)
minus 120597120597119909119894 [119863 120597 (119862120593120588119904)120597119909119894 ] 119881 (4)
where 119862 () is the particle concentration (ie particlesaturation) 120588119904 (kgm3) denotes the density of solid particlesand 119863 (m2s) illustrates the particles diffusion coefficient
In the direction of 119909119894 the mass flowing into the elementdue to the convection-diffusion should be expressed as
120597119872119894120597119909119894 119881 + 120597119873119894120597119909119894 119881 (119894 = 1 2 3) (5)
For the element the total mass flowing can be expressedas the summation of the three directions
3sum119894=1
( 120597119872119894120597119909119894 119881 + 120597119873119894120597119909119894 119881) (6)
Under the effects of erosion the mass loss of the elementin a unit time can be summarized as
minus 120597120597119905 (119862120593120588119904) 119881 + 119881 (7)
where (kgm3s) is the particle mass that migrates into thefluid from a unit element in a unit time and is written as
= 120597120593120597119905 120588119904 (8)
According to the mass conservation law for the unit ele-ment (6) and (7) are equivalent giving themass conservationequation for particles as
minus 120597120597119905 (119862120593120588119904) 119881 + 119881 = 3sum
119894=1
( 120597119872119894120597119909119894 119881 + 120597119873119894120597119909119894 119881) (9)
Substituting (2) into (9) yields
[ 3119886
120597 (119887119862)120597119905 + 120597 (119862120601)
120597119905 ] + nabla sdot (119862997888rarr119902 ) minus nabla
sdot 119863nabla sdot [119862 ( 3119887119886 + 120601)] = ( 3
119886120597119887120597119905 + 120597120601
120597119905 ) (10)
As particle sizes are normally several orders of magnitudesmaller than the fracture aperture the diffusion effect can beneglected Equation (10) can therefore be simplified into
[ 3119886
120597 (119887119862)120597119905 + 120597 (119862120601)
120597119905 ] + nabla sdot (119862997888rarr119902 ) = ( 3119886
120597119887120597119905 + 120597120601
120597119905 ) (11)
224 Water Mass Conservation Equations For the waterflow the mass flowing out of the element in the direction of119909119894 (119894 = 1 2 3) can be expressed as
120597 [(1 minus 119862) 120588119891119902119894]120597119909119894 119881 (119894 = 1 2 3) (12)
where 120588119891 (kgm3) denotes the density of the fluid The massloss of the fluid in the element in a unit time can be calculatedas
minus 120597120597119905 [(1 minus 119862) 120593120588119891] 119881 (13)
By combining (2) (3) (12) and (13) the mass conserva-tion equation for water flow can be derived as
3119886
120597 [119887 (1 minus 119862)]120597119905 + 120597 [(1 minus 119862) 120601]
120597119905 + nabla sdot [(1 minus 119862) 997888rarr119902 ]= 0
(14)
Geofluids 5
225 Evolution of the Fracture Aperture and Porosity Rockporosity plays an important role in determining rock per-meability so full understanding of its evolution is essentialto study the seepage characteristics of KCPs Sakthivadiveland Irmay [29] investigated the erosion problem for porousmedia by using both experimental and theoretical methodsVardoulakis et al [17] summarized the studies on porousmedia erosion and according to that study the evolutionof fracture aperture and permeability was affected by theporosity and particles concentration as well as the seepagevelocity The following equations have been developed todetermine the evolution of fracture aperture and porosity[17]
120597119887120597119905 = 1205821120588119904 (119887max minus 119887) 119862 10038161003816100381610038161199021003816100381610038161003816 120597120601120597119905 = 1205822120588119904 (120601max minus 120601) 119862 10038161003816100381610038161199021003816100381610038161003816
(15)
where 1205821 and 1205822 are constant |119902| = radic11990221 + 11990222 + 11990223 is theabsolute value of the seepage velocity (ms) and 119887max and120601max illustrate the maximum value that fracture aperture andporosity can reach under fluid erosion
Equations (15) indicate that the porosity evolution isproportional to the particle concentration as well as theseepage velocity
226 Water Seepage Fluid transport in porous media isnormally described by Darcyrsquos law which is derived (a) frombalance of momentum for the fluid phase and (b) from aconstitutive equation for the fluid-solid interaction force (iethe seepage force) [30] In general the balance of linearmomentum for the fluid phase has the form [31]
minus 120597119901120597119909119894 = minus 120578
119896 119902119894 + 120588119891 120597120597119905 ( 119902119894120593 ) (16)
where 119901 denotes the pore pressure (Pa) 120578 is the dynamicviscosity of the fluid (Pasdots) and 119896 illustrates the permeabilityof the volumetric element (m2) For this study the flowvelocity is relatively low thereby the acceleration term canbe neglected giving
997888rarr119902 = minus 119896120578 (nabla119901 + 120588119891119892nabla119911) (17)
where 997888rarr119902 is the Darcy velocity (ms) and nabla119911 is the unit vectorin the direction of gravity For fractured porous media 119896 isthe sum of fracture permeability and porosity permeability(m2) which can be expressed as [32]
119896 = 119896119898 + 119896119891 = 1198961198980 ( 1206011198981206011198980)3 ( 1 minus 12060111989801 minus 120601119898 )2 + 1198873
12119886 (18)
in which 119896119898 = 1198961198980(1206011198981206011198980)3((1 minus 1206011198980)(1 minus 120601119898))2 and119896119891 = 119887312119886 represent the porosity permeability and fracturepermeability respectively
Equations (2) (11) (14) (15) and (17) together with (18)compose the coupled processes of water transport of KCPs
Waterseepage
Particlestransport
Fractureporosityevolution
KCP
C
C
q
q
b b
Figure 7 Coupling process among each physics
under erosion effects as illustrated in Figure 7 The abovegoverning equations will be implemented into COMSOLMultiphysics next to understand water inrush mechanism inKCPs to evaluate water inrush risks and to predict waterinrush time under different rock and flow conditions Thereare six unknowns with equations so the set of governingequations can provide a unique solution
In petroleum engineering generally there is a criticalvelocity associated with sand production in oil and gasreservoirs However for the particle movements in KCPs thecritical velocitywas not considered because (1) the sizes of theinfilling particles are significantly smaller than the fractureapertures (120583m versus mm) (2) the movement of the erodedmaterials does not require a critical pressure gradient (or flowvelocity) for most KCP infilling materials are soluble to waterforming diluted solution and (3) the fluid flow inside KCPsis generally much greater than the critical velocity of around0ndash77mms for the particle size of 1ndash10 120583m [33 34]
23 Inverse Velocity Theory The inverse velocity theory wasoriginally proposed by Fukuzono [35] based on experimentalstudies This theory was initially used to predict the failuretime of a solid material that experiences slow continuousdeformation (ie creep) When the reciprocal of the defor-mation velocity (ie the inverse velocity) is plotted as afunction of time its value approaches zero as the velocityincreases asymptotically towards failureThe trend line of theinverse velocity intersects with the abscissa which representstime and the intersectional point can predict the time offailure There are three types of trend line namely concavelinear and convex as shown in Figure 8
The following equation is used to define the envelope
119881minus1 = [119860 (120572 minus 1)]1(120572minus1) (119905119891 minus 119905)1(120572minus1) (19)
where 119881 is the inverse velocity (ms) 119860 and 120572 are constants119905119891 is the time of failure and 119905 is the time of cutoff or the mostrecent time of themonitoring dataThe inverse velocity curveis concave when 120572 lt 2 and it is linear when 120572 = 2 while it isconvex when 120572 gt 2 Fukuzono [35] indicated that a linear fitcould provide a reasonable prediction of failure time
The inverse velocity theory has been successfully used insoils rocks and other materials and has been proved to be
6 Geofluids
Time
Failure
a gt2 (convex)a = 2 (linear)
a lt 2 (concave)
Inve
rse v
eloci
ty (1
V)
Figure 8 Inverse velocity trend lines to predict the time of failure[27]
Water flowInverse velocityLinear fitting
0
200
400
600
800
1000
1200
1400
1600
Flow
rate
(Ｇ3h
)
0
0002
0004
0006
0008
001
0012
0014
0016
0018
002In
vers
e velo
city
(hＧ
3)
5 10 15 200Time (h)
Water inrush point
Figure 9 Verification of the inverse velocity theory in predictingwater inrush
reliable in estimating the failure time using the linear fittingcurve [36 37]Therefore in thiswork this theory (ie inversefluid flow velocity) is adopted as the first attempt to predictwater inrush in KCPs
In order to verify the applicability of theory to waterinrush the field monitoring data from Yao et al [38] and Bai[39] was used and the comparison of inrush time betweenreal data and predicted time using inverse velocity theorywas conducted The results were plotted in Figure 9 It can beseen that the predicted inrush time matches the actual waterinrush time very well which proves that this theory can beused to predict water inrush for KCPs
3 Numerical Model Implementation
31 Background of the Coal Mine In this section a case studywas conducted based on the hydrogeological conditions of
Goaf
Hau
lage
rise
Coal haulage roadway
Ventilation roadway
Miningadvance
KCP
Railw
ay ri
se
KCP
Figure 10 Illustration of number 10-106 longwall panel and KCP inTuanbai coal mine of Shanxi province China
the Tuanbai Coalmine which is affiliatedwithHuozhouCoalElectricity Group of China The mine is located in TuanbaiCounty Linfen City Shanxi Province as marked in blue inFigure 2 The mining operation is current extracting number10 coal seam at approximately 300m depth To date 97 KCPshave been found during the mining operations at this seamThese KCPs included rock blocks of different sizes and inmost cases mud infillings and sizes of KCPs varied from tensto hundreds of meters In addition some had low level ofcompaction and cementation and relatively high infiltrationcapabilities
Since the distance between number 10 coal seam and theOrdovician limestone was only about 35m (as illustrated inFigure 13(a)) themining operation is being carried out underpressure from the Ordovician limestone water of the floorThe water pressure was found to be about 2MPa This minehas suffered a number of water inrush accidents associatedwith the KCPs For instance one accident occurred on thebelt roadway of the first longwall panel in 2007 with a waterflow rate of nearly 470m3h In addition there were a numberof water inrush accidents on longwall panels such as 10-106 asshown in Figure 10 10-112 and 10-114 at a rate of range from40m3h to 150m3h in 2010 resulting in the submergenceof the longwall panels Later investigation of these incidentsrevealed that all were directly caused by the KCPs whichacted as water channels with the confined water serving asthe source
32 Characterisation of the Infilling Materials In KCPs thecomposition of the infillings and their particle size distri-bution (PSD) have been found to be highly relevant to themigration of the particles For this reason two samples (iesample 1 and sample 2) were collected from the Tuanbai coalmine and the X-ray diffraction phase analysis (compositionanalysis) was carried out on the infillingmaterials of theKCPsas well as the PSD characteristics The results are shown inFigures 11 and 12
The composition analysis (as shown in Figure 11) indi-cated that the infilling materials mainly included kaolin-ites quartz illite smectite mixed layers small quantities offeldspars montmorillonites chlorites calcites siderites and
Geofluids 7
402
281
93
108
14
4231
05 05
19
KaoliniteQuartzIlliteIllite-smectiteSmectite
ChloriteFeldsparCalciteSideriteOthers
(a)
465
198
137
125
24
00
1304
19
15
KaoliniteQuartzIlliteIllite-smectiteSmectite
ChloriteFeldsparCalciteSideriteOthers
(b)
Figure 11 (a) Mineral components of infilling materials for Sample 1 and (b) mineral components of infilling materials for Sample 2
0
20
40
60
80
100
Cum
ulat
ive (
)
0
5
10
15
20
25
30
35
40
Freq
uenc
y (
)
001 01 1 100001Size (mm)
FrequencyCumulative
(a)
FrequencyCumulative
0
20
40
60
80
100
Cum
ulat
ive (
)
0
5
10
15
20
25
30
35
40
Freq
uenc
y (
)
001 01 1 100001Size (mm)
(b)
Figure 12 Particle size distribution (PSD) of infilling materials (a) Sample 1 (b) Sample 2
other mineral compositions The PSD results (Figure 12)showed that the particle sizes varied from 1 120583m to a few mmfor both Samples 1 and 2 with majority spanning from 10120583m to 1mm This could be a result of long-term weatheringbut the weak and unfavorable rock properties observed inthe field indicate that KCPs are very fractured and loose instructure with low strength high permeability being proneto water erosion and the water inrush risks
33 Numerical Model Setup Although diverse in geometryKCPs are usually presented similarly to a dome shape [9]Each of these approximates a 3D axisymmetric model whichcan be simplified as a 2D symmetrical model
In this work according to the lithology of the mine thebottom diameter top diameter and height are 15m 10m and20m respectively (as shown in Figure 13) The pressure atthe water inlet on the lower boundary was 20MPa and the
8 Geofluids
Description LithologyThickness (m)
11 coal
Limestone
Mudstone
Fine sandstone
Aquifer
10 coal
Limestone
Mudstone
30
25
73
33
46
200
358
Mudstone
9 coal
89
05
96
(a) (b) (c)
times10minus4
05
06
07
08
09
1
11
12
13
14
Figure 13 Model geometry and setup (a) illustration of KCP and rock strata (b) 2D simulation model and (c) distribution of apertureopening based on Weibull function
pressure at the water outlet on the top was 01MPa initialwater pressure in the model was 01MPa initial particle vol-ume concentration was 001 initial average fracture aperture1198870 was 01mm and initial porosity 1206010 was 10 The mainparameters of the model were all determined according tothe relevant references [3 12] in which the studies wereconducted on the same seam Other used parameters arelisted in Table 1Themodel was divided into 5000 grids usingmapped mesh method embedded in the COMSOL softwareThe shape of the grids is rectangular
Heterogeneity has been determined to be a prominentfeature of rock There are currently various approaches toobtaining the characteristics of the heterogeneous distribu-tion of rock materials For example digital core techniquesand mathematical statistics methods have both been utilizedPrevious studies have shown that the heterogeneity of rockcan be described by the Weibull distribution [40ndash42] Thusthe Weibull distribution was selected in this study due to itseffectiveness and great simplicity to obtain the heterogeneousdistribution of fracture apertures of the KCPs The distribu-tion probability density equation was as follows
119891 (119887) = 1198981198870 ( 119887
1198870)119898minus1
exp [minus ( 1198871198870)119898] (20)
where 119887 indicates the fracture aperture 1198870 denotes the initialfracture aperture and 119898 is the uniformity index The larger119898 represents the higher level of uniformity The fractureaperture distribution obtained by the numerical generationmethod is shown in Figure 13(c)
Based on thismodel geometry (9) (11) (14) (15) (17) and(18) will be solved simultaneously to investigate the dynamicchange of water flow behaviors and the associated inrush riskunder different flow conditions
4 Results and Analysis
In order to analyze the characteristics of seepage at differenttimes in this study six different moments were selected (ie14 times 103 15 times 103 16 times 103 17 times 103 175 times 103 and 18 times 103 s)The specific results will be discussed below
41 Distribution of the Fracture Apertures Figure 14 illus-trates the spatial changes of the fracture apertures at differenttimes Figure 15 shows the evolution of fracture aperturesalong O-O10158401015840 and O1015840-A1015840 lines as marked in Figure 13(b)and the average fracture aperture-time curve was plotted inFigure 16 The results show the following(1) The fracture aperture gradually increases under theeffects of the erosion However the increase rate is higherin the upper part of the model than in the lower part Thisis likely because the upper outlet boundary is narrower thanthe bottom inlet boundary giving rise to higher flow velocitySuch higher velocity causes more significant erosion andconsequently the fracture aperture change is faster(2) As the infiltration continues the average fractureaperture increases by approximately 200 from 01mm tonearly 03mm (Figure 16) At the initial stage the fracture issubject to random distribution with minor difference in theapertures However the variation diverges under the effectsof the erosion The fractures with smaller initial aperturesbecome slowly enlarged by approximately 20 while thosewith larger apertures continuously increase by more than200 As the fractures gradually dilate and interconnectwith each other a number of dominant seepage channels areformed as illustrated in Figure 14(f)
42 Distribution of Water Seepage Velocity The seepagevelocities (ie Darcy velocity) in the model domain andalong O-O10158401015840 and O1015840-A1015840 lines were shown in Figures 17 and
Geofluids 9
Table 1 Input parameters for the numerical simulation
120588119904(kgm3) 120578(Pasdots) 1198961198980(m2) 1206010 1198870(m) 119886 1205821(mminus1) 1205822(mminus1) 119898 11986202000 10minus3 10minus12 01 00001 001 001 001 6 001
1
2
3
4
5
6
7
(a) 14000 s
1
2
3
4
5
6
7
(b) 15000 s
1
2
3
4
5
6
7
(c) 16000 s
1
2
3
4
5
6
7
(d) 17000 s
1
2
3
4
5
6
7
(e) 17500 s
1
2
3
4
5
6
7
(f) 18000 s
Figure 14 The spatial distribution of aperture 119887 (10minus4m ) at different times
18 respectively The predicted failure time using the inversevelocity theory was plotted in Figure 19The key observationsinclude the following(1) As shown in Figure 17 the changes in the flowvelocity are consistent with the distribution of the fractures(Figure 14) and more fracture aperture changes are observedat the locations where higher seepage velocities take place Asshown in Figure 18 at 14times 104 s theminimumandmaximumseepage velocities were approximately 35 times 10minus6ms and 411times 10minus5ms At 18 times 104 s these two figures increased by 20and 200 to 42 times 10minus6ms and 125 times 10minus3ms respectively(2)Therewas a continuous increase in flow rate at the out-let from approximately 37m3 h initially to approximately100m3 h at 18times 104 s increased by nearly 30 times Howeverits increase showed a nonlinear trend likely due to the fact
that the increase rate was relatively slow in the initial stagebut accelerated gradually until the water inrush occurredFigure 19 was generated according to the inverse velocitytheory and the results showed that the water inrush wouldoccur at 185 times 104 s for this particular flow condition Thetrend has been reflected by the change in flow velocity shownin Figure 17 The figure shows that shortly before the inrushthe flow channels rapidly connected together and formed amain channel resulting in a surge in water flow
43 Distribution of the Particle Concentrations Particle con-centration is directly related to the erosion rate Higherparticle concentration indicates more severe erosion whichis more likely to result in greater fracture aperture change
10 Geofluids
05
15
25
35
45
55
65Fr
actu
re ap
ertu
reb
(times10
minus4
m)
5 10 15 200z (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
(a)
1 2 3 4 5 6 70r (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
05
15
25
35
45
55
65
Frac
ture
aper
ture
b(times
10minus4
m)
(b)
Figure 15 Evolution of fracture aperture along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
1
15
2
25
3
Frac
ture
aper
ture
b(times
10minus4
m)
5 10 15 200Time (times103 s)
Figure 16 Change of average fracture aperture with time
Figure 20 shows the evolution of the average particleconcentration along O-O10158401015840 and O1015840-A1015840 lines The averageparticle concentration and particle loss rate was plotted inFigure 21
Figure 20 plots the spatial distribution of the particleconcentrations for the wholemodel at different times Resultsshow that the particle concentration gradually increasesfrom the bottom upwards This is because under the effectsof the erosion increasing amount of particles migratedinto the water and gradually moved upwards through thefractures and pores This is consistent with the change inthe particle concentration at different locations as shown inFigure 21
Results in Figure 22 are well in line with the results shownin Figure 18 For example at the beginning the particle lossrate is relatively low however the rate constantly increasesover time and culminates at the inrushThis is due to the fact
that along with the increases in the seepage velocities theerosion effects on the solid particles are constantly intensifiedwhich results in frequent migration and substantial particleloss
44 Sensitivity Analyses The outburst processes wereaffected or controlled by various factors including thespatial heterogeneity of lithology of the KCPs waterpressure absolute aperture and distribution of the fracturesdistribution law of concentration of the karst particlesand their sensitivity to water erosion Based on the newlydeveloped coupling model this work further examined thewater and particle migration characteristics in the KCPsunder different hydrological and geological conditionsas well as the variations in the inrush occurrences Thescenarios to be studied are summarized in Table 2
Geofluids 11
2
16
12
08
04
0(a) 14000 s
2
16
12
08
04
0(b) 15000 s
2
16
12
08
04
0(c) 16000 s
2
16
12
08
04
0(d) 17000 s
2
16
12
08
04
0(e) 17500 s
2
16
12
08
04
0(f) 18000 s
Figure 17 The change of seepage velocity (10minus3ms) in a KCP
14000 s15000 s16000 s
17000 s17500 s18000 s
r (m)
1 2 3 4 5 6 70
Velo
city
(10minus
3m
s)
14
12
1
08
06
04
02
0
(a)
14000 s15000 s16000 s
17000 s17500 s18000 s
50 10z (m)
15 20
Velo
city
(10minus
3m
s)
14
12
1
08
06
04
02
0
(b)
Figure 18 Evolution of seepage velocity along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
12 Geofluids
Inverse velocityLinear fitting
0
20
40
60
80
100
Flow
rate
(m3h
)
0
5
10
15
20
25
30
Inve
rse v
eloci
ty (h
m)
5 10 15 200Time (times103 s)
Q
Figure 19 Water flow rate along the bottom surface of the numerical model
025
02
03
015
01
005
0(a) 14000 s
025
02
03
015
01
005
0(b) 15000 s
025
02
03
015
01
005
0(c) 16000 s
025
02
03
015
01
005
0(d) 17000 s
025
02
03
015
01
005
0(e) 17500 s
025
02
03
015
01
005
0(f) 18000 s
Figure 20 Change of particles concentration in a KCP
Geofluids 13
0
005
01
015
02
025
03
035C
once
ntra
tion
1 2 3 4 5 6 70r (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
(a)
105 15 200z (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
0
005
01
015
02
025
03
035
Con
cent
ratio
n (b)
Figure 21 Evolution of particle concentration along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
ConcentrationLoss rate
0
005
01
015
Con
cent
ratio
n
5 10 15 200Time (times103 s)
0
5
10
15
20
25
Part
icle
loss
rate
Qp
(m3h
)
Figure 22 Evolution of average particle volumetric concentrationand particle loss rate
441 Impact of Heterogeneity on Fractures Evolution Fig-ure 23 illustrates the distribution law of the fractures seepagevelocities and particle volume concentrations under identicalflow pressures but different fracture distribution conditionsat 175 times 103 seconds The results show that more intercon-nected fractures are developed along with the increase in mvalues For example when119898 = 4 there are only two intercon-nected fractures However asm value increases an increasingnumber of fractures were generated and interconnected Inthe fourth case (119898 = 10) three interconnected fractures weregenerated This finding indicates that the homogeneity canaccelerate the propagation of the fractures An increase in
Table 2 List of simulation scenarios
Parameter Value
Weibull distribution coefficient (-)
119898 = 4119898 = 6119898 = 8
119898 = 10
Water pressure (MPa)
119901 = 10119901 = 20119901 = 30119901 = 40
Initial particle concentration ()
1198620 = 00051198620 = 0011198620 = 0021198620 = 005
Fracture aperture (times10minus4m)
119887 = 075119887 = 10
119887 = 125119887 = 15
flow velocity and particle concentration with increasing mvalues was also observed as shown in Figures 23(b) and 23(c)
442 Prediction of Water Inrush under Different ConditionsThe analysis and prediction of the occurrences of waterinrush in KCPs based on the changes in seepage are essentialfor the safety of mining processes Some researchers haveadopted catastrophe theories to predict the occurrences ofwater inrush However an approach that can be used topredict water inrush based on water flow has yet to be foundin the literature This study presents the first attempt toresolve this challenge by applying the inverse velocity theory
14 Geofluids
m = 4 m = 6 m = 8 m = 10
1
2
3
4
5
6
7
(a) Distribution of aperture 119887 (times10minus4m )
m = 4 m = 6 m = 8 m = 10
2
16
12
08
04
0
(b) Distribution of seepage velocity (times10minus3ms)
m = 4 m = 6 m = 8 m = 10
025
02
03
015
01
005
0
(c) Distribution of particles concentration
Figure 23 Distribution of fracture seepage velocity and particle concentration at different Weibull distribution conditions (a) Impact ofWeibull distribution on fractures evolution (b) impact of Weibull distribution on water velocity evolution (c) impact of Weibull distributionon particle concentration evolution
Geofluids 15
5 10 15 200Time (times103 s)
m = 4
m = 6 m = 10
m = 8
0
20
40
60
80
100
120Fl
ow ra
te (m
3h
)
(a)
205
21
215
22
225
23
Wat
er in
rush
tim
e (times10
3s)
4 6 8 102Weibull coefficient m
y = 25699xminus0089
R2 = 09825
(b)
Figure 24 Impact of heterogeneity on water flow rate (a) and inrush time (b)
0
20
40
60
80
100
120
140
160
180
200
Flow
rate
(m3h
)
5 10 15 200Time (times103 s)
p = 1MPap = 2MPa
p = 3MPap = 4MPa
(a)
y = 41733xminus1001
R2 = 09992
1 2 3 4 50Water pressure (MPa)
0
5
10
15
20
25
30
35
40
45
Wat
er in
rush
tim
e (times10
3s)
(b)
Figure 25 Impact of aquifer water pressure on water flow rate (a) and inrush time (b)
which has been widely approved effective in many fields suchas slope stability predictionThe relevant results and analysesare shown in Figure 24ndashFigure 27
As shown in Figure 24 water flow rate exhibits a non-linear increase and as the value of m increases the seepagerate accelerates gradually For example at 119905 = 15 times 104 s theseepage rate was approximately 15m3h for 119898 = 4 while itjumped to 25m3h for 119898 = 10 Results from Figure 24(b)show that water inrush occurs sooner for a greater 119898 valueIn other words the inrush occurs earlier as the heterogeneityincreases The water inrush time follows the power functionThis is due to the fact that the water is more prone to flowingthrough the existing fractures (which indicates a higher
permeability) in the heterogeneous structure Neverthelessdue to the heterogeneous distribution of the aperture thefractures cannot be easily interconnected which hampers theformation of the seepage channels In regard to the homo-geneous rock strata since the flow of water was dominantlycontrolled by the pressure gradient the fractures generatedduring the process of erosion could be easily interconnectedand as a result the water inrush occurredsooner
Figure 25 illustrates the impact of the initial KCPrsquos waterpressure on the flow rates and water inrush time It can beseen that as the pressure increases the changes in the flowrates accelerate For example for119901 = 2MPa the flow rate wasonly approximately 5m3h and it increased to 30m3h when
16 Geofluids
0
20
40
60
80
100
120
140
160
180
200Fl
ow ra
te (m
3h
)
5 10 15 20 250Time (times103 s)
c = 0005
c = 001
c = 002
c = 005
(a)
0
5
10
15
20
25
30
35
Wat
er in
rush
tim
e (times10
3s)
001 002 003 004 0050Initial particle concentration
y = 13554xminus0591
R2 = 09975
(b)
Figure 26 Impact of initial particle concentration on water flow rate (a) and inrush time (b)
0
20
40
60
80
100
120
140
160
180
200
Flow
rate
(m3h
)
5 10 15 200Time (times103 s)
075E minus 4m100E minus 4m
125E minus 4m150E minus 4m
(a)
y = 31027eminus286x
R2 = 09503
09 11 13 1507Fracture aperture (times10minus4 m)
0
5
10
15
20
25
30
35
40
Wat
er in
rush
tim
e (times10
3s)
(b)
Figure 27 Impact of absolute aperture on water flow rate (a) and inrush time (b)
119901 = 3MPa In addition with increasing the aquifer waterpressure the water inrush time was also brought forward asshown in Figure 25(a) The outburst time was approximately119905 = 40 times 104 s for p = 1MPa while only 10 times 104 s for119901 = 4MPa The relationship between the time of the inrushoccurrences and the aquifer water pressure follows the powerfunction as illustrated in Figure 25
For varying initial particle concentrations the evolutionof both the water flow rate change and the water inrushtime shows a similar trend to that of different aquifer waterpressures The flow rate accelerates with increasing initialparticle concentration and consequently the water inrushoccurs earlier as shown in Figure 26The outburst times alsoshow a power function to the initial particle concentration
The initial average fracture aperture also shows significantimpact on water flow behavior For instance results fromFigure 27 clearly illustrate that the flow rate increases withincreasing initial average fracture aperture Please note thatthe inrush time follows an exponential function to the initialaverage fracture aperture
These numerical results can be explained by the factthat the initial seepage velocity is expected to be higher forthe modelling cases with the higher initial aquifer pressureinitial fracture aperture andor initial particle concentrationThe higher flow velocity would intensify the erosion of thefractures enhance the permeability and thereby acceleratethe migration of the particles and interconnection of seepagechannels which causes water inrush
Geofluids 17
5 Conclusions
In this study a systematic approach was established to inves-tigate the impact of controlling factors onwater flow behaviorfor KCPs and to predict water inrush time by introducing theinverse velocity theory In this approach a suite of governingequations was developed to couple all the physics involvedin this complex process including water flow rock erosionand change in rock microstructure These equations werethen implemented into a finite element software COMSOLMultiphysics to simulate the fully coupled process Basedon this numerical model a series of sensitivity studies wereconducted and some important findings have been drawn
(i) Water flow rate increases with increasing aquiferpressure initial particle concentration and fractureopening This results in an increase in the permeabil-ity and finally an acceleration of the migration of theparticles and interconnection of the seepage channelsThis finding suggests the grouting of the KCPs couldbe an effective measure to mitigate water inrush risk
(ii) The inverse velocity theory was successfully appliedto analyze the occurrences of water inrush underdifferent conditions The results show that the timeof inrush has a power relationship to the rock het-erogeneity water pressure and initial particle concen-tration and follows an exponential relationship to theinitial fracture apertures
The framework developed from this work not only helpsenhance coal mining operations safety by better under-standing and predicting water inrush risks so that propermitigation measures can be put in place timely It canalso be extended to other fields such as tunneling backfillpaste piping tailing dam erosion and other engineeringapplications which are likely to encounter time-dependenterosion or deformation or water inrush issues
Please be noted that there are a number of other stochasticmethods available in the literature that can be used to illus-trate rock heterogeneity such as the Monte-Carlo methodor First-Order approach The differences of these methodson the results of water inrush prediction may be worthcomparing in the near future
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This project is supported by the National Natural ScienceFoundation of China (nos 51304072 51774110) the Programfor Innovative Research Team in University of Ministryof Education of China (IRT 16R22) and the PostdoctoralScience Foundation of China (2017M612398)
References
[1] DMa XMiao H Bai et al ldquoEffect of mining on shear sidewallgroundwater inrush hazard caused by seepage instability of the
penetrated karst collapse pillarrdquo Natural Hazards vol 82 no 1pp 73ndash93 2016
[2] H Keqiang Y Guangming and L Yaoru ldquoPalaeo-karst collapsepillars in northern China and their damage to the geologicalenvironmentsrdquo Environmental Geology vol 58 no 5 pp 1029ndash1040 2009
[3] B Yao J Wei D Wang D Ma and Z Chen ldquoNumericalstudy on seepage property of karst collapse columns underparticle migrationrdquo CMES Computer Modeling in Engineeringamp Sciences vol 91 no 2 pp 81ndash100 2013
[4] J Tang H Bai B Yao and Y Wu ldquoTheoretical analysis onwater-inrush mechanism of concealed collapse pillars in floorrdquoMining Science and Technology vol 21 no 1 pp 57ndash60 2011
[5] Y Chen M Yi C Chen and C Yu ldquoBernstein polynomialsmethod for fractional convection-diffusion equation with vari-able coefficientsrdquoComputerModeling in Engineering amp Sciencesvol 83 no 6 pp 639ndash653 2012
[6] J Zhang and B Shen ldquoCoal mining under aquifers in China Acase studyrdquo International Journal of Rock Mechanics and MiningSciences vol 41 no 4 pp 629ndash639 2004
[7] D Ma H Bai X Miao H Pu B Jiang and Z ChenldquoCompaction and seepage properties of crushed limestoneparticle mixture an experimental investigation for Ordoviciankarst collapse pillar groundwater inrushrdquo Environmental EarthSciences vol 75 no 1 article 11 p 14 2016
[8] S Yin J Zhang and D Liu ldquoA study of mine water inrushesby measurements of in situ stress and rock failuresrdquo NaturalHazards vol 79 no 3 pp 1961ndash1979 2015
[9] H Bai D Ma and Z Chen ldquoMechanical behavior of ground-water seepage in karst collapse pillarsrdquo Engineering Geology vol164 pp 101ndash106 2013
[10] D Ma and H Bai ldquoGroundwater inflow prediction model ofkarst collapse pillar a case study for mining-induced ground-water inrush riskrdquoNatural Hazards vol 76 no 2 pp 1319ndash13342015
[11] D Ma H Bai and Y Wang ldquoMechanical behavior of a coalseam penetrated by a karst collapse pillar mining-inducedgroundwater inrush riskrdquo Natural Hazards vol 75 no 3 pp2137ndash2151 2015
[12] B Yao Research on variable mass fluid-solid coupling dynamictheory of broken rockmass and application China Univeristy ofMining and Technology Xuzhou China 2012
[13] D Ma X Miao H Bai et al ldquoImpact of particle transfer onflow properties of crushed mudstonesrdquo Environmental EarthSciences vol 75 no 7 article 593 2016
[14] DMa H Bai Z Chen andH Pu ldquoEffect of particlemixture onseepage properties of crushed mudstonesrdquo Transport in PorousMedia vol 108 no 2 pp 257ndash277 2015
[15] B Zhang H Bai and K Zhang ldquoSeepage characteristics ofcollapse columnfillingsrdquo International Journal ofMining Scienceand Technology 2015
[16] P Ortoleva J Chadam E Merino and A Sen ldquoGeochemicalself-organization II the reactive-infiltration instabilityrdquo Ameri-can Journal of Science vol 287 no 10 pp 1008ndash1040 1987
[17] I Vardoulakis M Stavropoulou and P Papanastasiou ldquoHydro-mechanical aspects of the sand production problemrdquo Transportin Porous Media vol 22 no 2 pp 225ndash244 1996
[18] R L Detwiler and H Rajaram ldquoPredicting dissolution patternsin variable aperture fractures Evaluation of an enhanced depth-averaged computational modelrdquoWater Resources Research vol43 no 4 Article IDW04403 2007
18 Geofluids
[19] M A Habib H M Badr R Ben-Mansour and M E KabirldquoErosion rate correlations of a pipe protruded in an abrupt pipecontractionrdquo International Journal of Impact Engineering vol34 no 8 pp 1350ndash1369 2007
[20] H T Xiao and H Y Xu ldquoIn situ permeability measurementsto establish the influence of slice mining on floor rocksrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 37 no 5 pp 855ndash860 2000
[21] H Guo D P Adhikary and M S Craig ldquoSimulation of minewater inflow and gas emission during longwall miningrdquo RockMechanics and Rock Engineering vol 42 no 1 pp 25ndash51 2009
[22] R Zhang Z JiangH ZhouC Yang and S Xiao ldquoGroundwateroutbursts from faults above a confined aquifer in the coalminingrdquo Natural Hazards vol 71 no 3 pp 1861ndash1872 2014
[23] B Yao F Du E Li and X Wang ldquoMechanical model of karstcollapse columns water inrush and its applicationrdquo ElectronicJournal of Geotechnical Engineering vol 19 pp 1665ndash1675 2014
[24] J Warren and P Root ldquoThe behavior of naturally fracturedreservoirsrdquo SPE Journal vol 3 no 3 pp 245ndash255 2013
[25] H KazemiM S Seth andGWThomas ldquoThe interpretation ofinterference tests in naturally fractured reservoirs with uniformfracture distributionrdquo SPE Journal vol 9 no 4 pp 463ndash4721969
[26] A de Swaan O ldquoAnalytical solutions for determining naturallyfractured reservoir properties by well testingrdquo SPE Journal vol16 no 3 pp 117ndash122 1976
[27] N D Rose and O Hungr ldquoForecasting potential rock slopefailure in open pit mines using the inverse-velocity methodrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 2 pp 308ndash320 2007
[28] J R Fanchi Petroleum Engineering Handbook Volume 1 Gen-eral Engineering Society of Petroleum Engineers 2006
[29] R Sakthivadivel and S Irmay A Review of Filtration TheoriesHydraulic Engineering Laboratory College of EngineeringUniversity of California Berkeley Calif USA 1996
[30] C Wang P Zhai Z Chen J Liu L Wang and J XieldquoExperimental study of coal matrix-cleat interaction underconstant volume boundary conditionrdquo International Journal ofCoal Geology vol 181 pp 124ndash132 2017
[31] S Irmay ldquoOn the theoretical derivation of Darcy and Forch-heimer formulasrdquo Eos Transactions American GeophysicalUnion vol 39 no 4 pp 702ndash707 1958
[32] CH Lee and IW Farmer ldquoA simplemethod of estimating rockmass porosity and permeabilityrdquo International Journal ofMiningand Geological Engineering vol 8 no 1 pp 57ndash65 1990
[33] C Nalluri A K El-Zaemey and H L Chan ldquoSedimenttransport over fixed deposited beds in sewers - An appraisal ofexisting modelsrdquoWater Science and Technology vol 36 no 8-9pp 123ndash128 1997
[34] P Novak and C Nalluri ldquoSediment transport in smooth fixedbed channelsrdquo Journal of the Hydraulics Division vol 101 no 9pp 1139ndash1154 1975
[35] T Fukuzono ldquoA newmethod for predicting the failure time of asloperdquo in Proceedings of the In 4th International Conference andField Workshop on Landslides Tokyo Japan 1985
[36] C R J Kilburn andDN Petley ldquoForecasting giant catastrophicslope collapse lessons from Vajont Northern Italyrdquo Geomor-phology vol 54 no 1-2 pp 21ndash32 2003
[37] B Voight ldquoA method for prediction of volcanic eruptionsrdquoNature vol 332 no 6160 pp 125ndash130 1988
[38] B Yao X Mao J Wei and D Wang ldquoStudy on coupled fluid-solid model for collapse columns considering the effect ofparticle transportrdquo Zhongguo Kuangye Daxue XuebaoJournalof China University of Mining and Technology vol 43 no 1 pp30ndash35 2014
[39] H Bai Seepage Characteristics of Top Stratum of OrdovicianSystem and Its Application Study as Key Aquifuge ChinaUniversity of Mining amp Technology Xuzhou China 2008
[40] C A Tang L G Tham P K K Lee T H Yang and L CLi ldquoCoupled analysis of flow stress and damage (FSD) in rockfailurerdquo International Journal of Rock Mechanics and MiningSciences vol 39 no 4 pp 477ndash489 2002
[41] W C Zhu and C A Tang ldquoMicromechanical model forsimulating the fracture process of rockrdquo Rock Mechanics andRock Engineering vol 37 no 1 pp 25ndash56 2004
[42] T H Yang L G Tham C A Tang Z Z Liang and YTsui ldquoInfluence of heterogeneity of mechanical properties onhydraulic fracturing in permeable rocksrdquo Rock Mechanics andRock Engineering vol 37 no 4 pp 251ndash275 2004
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Submit your manuscripts atwwwhindawicom
2 Geofluids
Rock strata
Coal seam
K
C
P
Rock strata
Working face
Figure 1 Illustration of aKarst Collapse Pillar front viewof a typicalcone shaped KCP (not to scale) [23] and different shapes of rocklayers represent different types of rocks
mass dynamics and nonlinear dynamics were introducedand the seepage properties of KCPs associated with particlesmigration were investigated using numerical simulation [3]Ma and Bai [10] numerically studied the impacts of mining-induced damage on KCPs and the surrounding rocks andon the formation of the fracture zone and analyzed mining-induced KCP groundwater inrush risk This work was laterextended to study the effect of coal mining operations onKCPs related groundwater inrush using FLAC3D and theshear stress damage zone and their effects on seepage fielddevelopmentwere also discussed [11] Yao [12] experimentallystudied the evolution of the crushed rock mass seepageproperties under different particle sizes and stresses and ana-lyzed particle migration feature and the KCPs water inrushmechanism Moreover there are also some experimentalstudies focused on the permeability change of the KCPs toinvestigate water inrush mechanisms [13ndash15]
Recent studies on the water inrush mechanism of KCPshave consistently revealed that complex interactions existbetween the evolution of fractures and porosity in solidswater transport and rock solid particles migration whichaccompanies the erosion phenomenon [3 12] Significantprogress on the understanding of this complex process hasbeen made For example the reaction of aqueous solutionsmineral components and its impact on water flow wereinvestigated and amodel for porosity change was established[16] Vardoulakis et al [17] studied the piping and surfaceerosion effects based on mass balance particles migrationand Darcyrsquos law The dissolution of fracture surfaces due towater-rock interactions with variable fracture apertures overtimewas also studied and a depth-averagedmodel of fractureflow and reactive transport that explicitly calculated localdissolution-induced alterations in fracture apertures werepresented [18] Habib et al [19] numerically investigated theerosion rate correlations of a pipe protruding from an abruptpipe contraction problem
Despite the significant progress in understanding KCPswater inrush mechanism and water prevention technologyover the past several decades [20ndash22] most investigationswere carried out with respect to structure failure and fewhave investigated this issue by integrating the solid-fluidinteraction and particles migration due to erosion Waterinflow rate as probably the only direct measuring data in thefield has yet to be directly used in the literature to predict theprecise time of water inrush An effective method to predictwater inrush does not appear to be available neither In thiswork a set of fully coupled governing equations for KCPswater inrush will be developed by incorporating the fracturesand porosity evolution for KCPs particles migration andwater seepage process The governing equations will thenbe implemented into COMSOL Multiphysics software Theheterogeneity of rocks in KCPs will be determined using theWeibull distribution and the parameters including porosityseepage particle concentration and water inflow as well asseepage channels evolution law will be obtained accordinglyThis numerical model will be then used to investigate thewater flow characteristics with erosion Based on the inversevelocity theory the corresponding water inrush times fordifferent flow conditions will also be discussed in detail
2 Development of a Fully CoupledTheoretical Model
21 Selection of Microstructure Model of KCPs A KCPtypically consists of three parts solid rock matrix fluidsand infilling particles The intact rock blocks form a rockmass which is filled with fluids for example water andinfilling materials such as solid particles (Figure 3) As thepermeability of rock blocks is generally very low the interrockfractures provide the main passages for water flow Thisstructure matches the characteristics of the dual porositymodel where the rocks are considered as consisting ofmatrixes and fractures A numbers of different dual porositymodels have been developed including the Warren-RootKazemi et al and de Swaanmodels [24ndash26] but theWarren-Root model as shown in Figure 4 was widely accepted asa proper model to represent such rock structure As suchin this work the Warren-Root model is selected to examinethe processes of particle migration and the evolution of thefractures aperture and porosity
22 Governing Equations
221 Assumptions In order to establish a fully coupledtheoreticalmodel that integrates particlesmigration seepageand fracture and porosity evolution in KCPs under erosioneffects the following assumptions have been made
(1) The fluid and particles in KCPs are incompressible
(2) The suspended particles share the velocity field withthe fluid
(3) As the internal structure of KCPs is generally veryloose and the rock mass surrounding the KCPs is
Geofluids 3
N Datong
Shuozhou
TaiyuanYangquan
Jincheng
Huozhou
Yuncheng
Tuanbai
Main coal mine
Tuanbai coal mineCoal field in Shanxi
BeijingCity
Figure 2 The distribution of major coal mines in China and the coal fields in Shanxi province
Figure 3 Rock and infilling material (particles) in a KCP
Fractures
Matrix
Figure 4 Sketch of the Warren-Root Model [24]
generally competent the impact of the change in theeffective stress on KCPrsquos permeability is insignificant
(4) The impact of erosion on the permeability change isin proportion to the change of particle concentrationin the fluid
Half fracture
Matrix block
Water Particles
a
a + b
Figure 5 Sketch of a representative element of a typical KCP
222 Definition Based on the aforementioned assumptionsa representative element for a typical KCP microstructure isshown in Figure 5 The length 119871 (m) and volume 119881 (m3) ofthe element are expressed as
119871 = 119886 + 119887119881 = (119886 + 119887)3 (1)
where 119886 (m) is the length of the matrix and 119887 (m) is theaperture of the fracture
The total voidage 120593 () of an element is written as [28]
120593 = (119886 + 119887)3 minus 1198863(119886 + 119887)3 + 120601 cong 3119887
119886 + 120601 (2)
where 120601 () is the matrix porosity It should be noted that119887 ≪ 119886
4 Geofluids
o a + b
a + b
x3
x2
x1
(M1 + N1) L2
(M2 + N2) L2
(M1 +M1
x1
L) L2 + (N1 +N1
x1
L) L2
(M2 +M2
x2
L) L2 + ((N2 +N2
x2
L) L2
Figure 6 Illustration of a three-dimensional characteristic element in a KCP 119872119894 and 119873119894 are mass change of solids due to convection anddiffusion respectively defined as 119872119894 = 119862120588119904119902119894 119873119894 = minus119863(120597(119862120593120588119904)120597119909119894)
223 Mass Conservation Equations for Particles In order tostudy the migration characteristics of the infilling particlesthe dynamic mass conservation equations for particles werecalculated based on a three-dimensional representative ele-ment as illustrated in Figure 6
Infilling particles migration inside a representative ele-ment under erosion effects is affected by both convection andprocesses The average seepage velocity of an element can bedefined as997888rarr119902 119894 (ms) For the convection and diffusion processin the direction of 119909119894 (119894 = 1 2 3) the mass losses of particlesflowing out of the element in a unit time can be calculated by(3) and (4) respectively
120597 (119862120588119904119902119894)120597119909119894 119881 (3)
minus 120597120597119909119894 [119863 120597 (119862120593120588119904)120597119909119894 ] 119881 (4)
where 119862 () is the particle concentration (ie particlesaturation) 120588119904 (kgm3) denotes the density of solid particlesand 119863 (m2s) illustrates the particles diffusion coefficient
In the direction of 119909119894 the mass flowing into the elementdue to the convection-diffusion should be expressed as
120597119872119894120597119909119894 119881 + 120597119873119894120597119909119894 119881 (119894 = 1 2 3) (5)
For the element the total mass flowing can be expressedas the summation of the three directions
3sum119894=1
( 120597119872119894120597119909119894 119881 + 120597119873119894120597119909119894 119881) (6)
Under the effects of erosion the mass loss of the elementin a unit time can be summarized as
minus 120597120597119905 (119862120593120588119904) 119881 + 119881 (7)
where (kgm3s) is the particle mass that migrates into thefluid from a unit element in a unit time and is written as
= 120597120593120597119905 120588119904 (8)
According to the mass conservation law for the unit ele-ment (6) and (7) are equivalent giving themass conservationequation for particles as
minus 120597120597119905 (119862120593120588119904) 119881 + 119881 = 3sum
119894=1
( 120597119872119894120597119909119894 119881 + 120597119873119894120597119909119894 119881) (9)
Substituting (2) into (9) yields
[ 3119886
120597 (119887119862)120597119905 + 120597 (119862120601)
120597119905 ] + nabla sdot (119862997888rarr119902 ) minus nabla
sdot 119863nabla sdot [119862 ( 3119887119886 + 120601)] = ( 3
119886120597119887120597119905 + 120597120601
120597119905 ) (10)
As particle sizes are normally several orders of magnitudesmaller than the fracture aperture the diffusion effect can beneglected Equation (10) can therefore be simplified into
[ 3119886
120597 (119887119862)120597119905 + 120597 (119862120601)
120597119905 ] + nabla sdot (119862997888rarr119902 ) = ( 3119886
120597119887120597119905 + 120597120601
120597119905 ) (11)
224 Water Mass Conservation Equations For the waterflow the mass flowing out of the element in the direction of119909119894 (119894 = 1 2 3) can be expressed as
120597 [(1 minus 119862) 120588119891119902119894]120597119909119894 119881 (119894 = 1 2 3) (12)
where 120588119891 (kgm3) denotes the density of the fluid The massloss of the fluid in the element in a unit time can be calculatedas
minus 120597120597119905 [(1 minus 119862) 120593120588119891] 119881 (13)
By combining (2) (3) (12) and (13) the mass conserva-tion equation for water flow can be derived as
3119886
120597 [119887 (1 minus 119862)]120597119905 + 120597 [(1 minus 119862) 120601]
120597119905 + nabla sdot [(1 minus 119862) 997888rarr119902 ]= 0
(14)
Geofluids 5
225 Evolution of the Fracture Aperture and Porosity Rockporosity plays an important role in determining rock per-meability so full understanding of its evolution is essentialto study the seepage characteristics of KCPs Sakthivadiveland Irmay [29] investigated the erosion problem for porousmedia by using both experimental and theoretical methodsVardoulakis et al [17] summarized the studies on porousmedia erosion and according to that study the evolutionof fracture aperture and permeability was affected by theporosity and particles concentration as well as the seepagevelocity The following equations have been developed todetermine the evolution of fracture aperture and porosity[17]
120597119887120597119905 = 1205821120588119904 (119887max minus 119887) 119862 10038161003816100381610038161199021003816100381610038161003816 120597120601120597119905 = 1205822120588119904 (120601max minus 120601) 119862 10038161003816100381610038161199021003816100381610038161003816
(15)
where 1205821 and 1205822 are constant |119902| = radic11990221 + 11990222 + 11990223 is theabsolute value of the seepage velocity (ms) and 119887max and120601max illustrate the maximum value that fracture aperture andporosity can reach under fluid erosion
Equations (15) indicate that the porosity evolution isproportional to the particle concentration as well as theseepage velocity
226 Water Seepage Fluid transport in porous media isnormally described by Darcyrsquos law which is derived (a) frombalance of momentum for the fluid phase and (b) from aconstitutive equation for the fluid-solid interaction force (iethe seepage force) [30] In general the balance of linearmomentum for the fluid phase has the form [31]
minus 120597119901120597119909119894 = minus 120578
119896 119902119894 + 120588119891 120597120597119905 ( 119902119894120593 ) (16)
where 119901 denotes the pore pressure (Pa) 120578 is the dynamicviscosity of the fluid (Pasdots) and 119896 illustrates the permeabilityof the volumetric element (m2) For this study the flowvelocity is relatively low thereby the acceleration term canbe neglected giving
997888rarr119902 = minus 119896120578 (nabla119901 + 120588119891119892nabla119911) (17)
where 997888rarr119902 is the Darcy velocity (ms) and nabla119911 is the unit vectorin the direction of gravity For fractured porous media 119896 isthe sum of fracture permeability and porosity permeability(m2) which can be expressed as [32]
119896 = 119896119898 + 119896119891 = 1198961198980 ( 1206011198981206011198980)3 ( 1 minus 12060111989801 minus 120601119898 )2 + 1198873
12119886 (18)
in which 119896119898 = 1198961198980(1206011198981206011198980)3((1 minus 1206011198980)(1 minus 120601119898))2 and119896119891 = 119887312119886 represent the porosity permeability and fracturepermeability respectively
Equations (2) (11) (14) (15) and (17) together with (18)compose the coupled processes of water transport of KCPs
Waterseepage
Particlestransport
Fractureporosityevolution
KCP
C
C
q
q
b b
Figure 7 Coupling process among each physics
under erosion effects as illustrated in Figure 7 The abovegoverning equations will be implemented into COMSOLMultiphysics next to understand water inrush mechanism inKCPs to evaluate water inrush risks and to predict waterinrush time under different rock and flow conditions Thereare six unknowns with equations so the set of governingequations can provide a unique solution
In petroleum engineering generally there is a criticalvelocity associated with sand production in oil and gasreservoirs However for the particle movements in KCPs thecritical velocitywas not considered because (1) the sizes of theinfilling particles are significantly smaller than the fractureapertures (120583m versus mm) (2) the movement of the erodedmaterials does not require a critical pressure gradient (or flowvelocity) for most KCP infilling materials are soluble to waterforming diluted solution and (3) the fluid flow inside KCPsis generally much greater than the critical velocity of around0ndash77mms for the particle size of 1ndash10 120583m [33 34]
23 Inverse Velocity Theory The inverse velocity theory wasoriginally proposed by Fukuzono [35] based on experimentalstudies This theory was initially used to predict the failuretime of a solid material that experiences slow continuousdeformation (ie creep) When the reciprocal of the defor-mation velocity (ie the inverse velocity) is plotted as afunction of time its value approaches zero as the velocityincreases asymptotically towards failureThe trend line of theinverse velocity intersects with the abscissa which representstime and the intersectional point can predict the time offailure There are three types of trend line namely concavelinear and convex as shown in Figure 8
The following equation is used to define the envelope
119881minus1 = [119860 (120572 minus 1)]1(120572minus1) (119905119891 minus 119905)1(120572minus1) (19)
where 119881 is the inverse velocity (ms) 119860 and 120572 are constants119905119891 is the time of failure and 119905 is the time of cutoff or the mostrecent time of themonitoring dataThe inverse velocity curveis concave when 120572 lt 2 and it is linear when 120572 = 2 while it isconvex when 120572 gt 2 Fukuzono [35] indicated that a linear fitcould provide a reasonable prediction of failure time
The inverse velocity theory has been successfully used insoils rocks and other materials and has been proved to be
6 Geofluids
Time
Failure
a gt2 (convex)a = 2 (linear)
a lt 2 (concave)
Inve
rse v
eloci
ty (1
V)
Figure 8 Inverse velocity trend lines to predict the time of failure[27]
Water flowInverse velocityLinear fitting
0
200
400
600
800
1000
1200
1400
1600
Flow
rate
(Ｇ3h
)
0
0002
0004
0006
0008
001
0012
0014
0016
0018
002In
vers
e velo
city
(hＧ
3)
5 10 15 200Time (h)
Water inrush point
Figure 9 Verification of the inverse velocity theory in predictingwater inrush
reliable in estimating the failure time using the linear fittingcurve [36 37]Therefore in thiswork this theory (ie inversefluid flow velocity) is adopted as the first attempt to predictwater inrush in KCPs
In order to verify the applicability of theory to waterinrush the field monitoring data from Yao et al [38] and Bai[39] was used and the comparison of inrush time betweenreal data and predicted time using inverse velocity theorywas conducted The results were plotted in Figure 9 It can beseen that the predicted inrush time matches the actual waterinrush time very well which proves that this theory can beused to predict water inrush for KCPs
3 Numerical Model Implementation
31 Background of the Coal Mine In this section a case studywas conducted based on the hydrogeological conditions of
Goaf
Hau
lage
rise
Coal haulage roadway
Ventilation roadway
Miningadvance
KCP
Railw
ay ri
se
KCP
Figure 10 Illustration of number 10-106 longwall panel and KCP inTuanbai coal mine of Shanxi province China
the Tuanbai Coalmine which is affiliatedwithHuozhouCoalElectricity Group of China The mine is located in TuanbaiCounty Linfen City Shanxi Province as marked in blue inFigure 2 The mining operation is current extracting number10 coal seam at approximately 300m depth To date 97 KCPshave been found during the mining operations at this seamThese KCPs included rock blocks of different sizes and inmost cases mud infillings and sizes of KCPs varied from tensto hundreds of meters In addition some had low level ofcompaction and cementation and relatively high infiltrationcapabilities
Since the distance between number 10 coal seam and theOrdovician limestone was only about 35m (as illustrated inFigure 13(a)) themining operation is being carried out underpressure from the Ordovician limestone water of the floorThe water pressure was found to be about 2MPa This minehas suffered a number of water inrush accidents associatedwith the KCPs For instance one accident occurred on thebelt roadway of the first longwall panel in 2007 with a waterflow rate of nearly 470m3h In addition there were a numberof water inrush accidents on longwall panels such as 10-106 asshown in Figure 10 10-112 and 10-114 at a rate of range from40m3h to 150m3h in 2010 resulting in the submergenceof the longwall panels Later investigation of these incidentsrevealed that all were directly caused by the KCPs whichacted as water channels with the confined water serving asthe source
32 Characterisation of the Infilling Materials In KCPs thecomposition of the infillings and their particle size distri-bution (PSD) have been found to be highly relevant to themigration of the particles For this reason two samples (iesample 1 and sample 2) were collected from the Tuanbai coalmine and the X-ray diffraction phase analysis (compositionanalysis) was carried out on the infillingmaterials of theKCPsas well as the PSD characteristics The results are shown inFigures 11 and 12
The composition analysis (as shown in Figure 11) indi-cated that the infilling materials mainly included kaolin-ites quartz illite smectite mixed layers small quantities offeldspars montmorillonites chlorites calcites siderites and
Geofluids 7
402
281
93
108
14
4231
05 05
19
KaoliniteQuartzIlliteIllite-smectiteSmectite
ChloriteFeldsparCalciteSideriteOthers
(a)
465
198
137
125
24
00
1304
19
15
KaoliniteQuartzIlliteIllite-smectiteSmectite
ChloriteFeldsparCalciteSideriteOthers
(b)
Figure 11 (a) Mineral components of infilling materials for Sample 1 and (b) mineral components of infilling materials for Sample 2
0
20
40
60
80
100
Cum
ulat
ive (
)
0
5
10
15
20
25
30
35
40
Freq
uenc
y (
)
001 01 1 100001Size (mm)
FrequencyCumulative
(a)
FrequencyCumulative
0
20
40
60
80
100
Cum
ulat
ive (
)
0
5
10
15
20
25
30
35
40
Freq
uenc
y (
)
001 01 1 100001Size (mm)
(b)
Figure 12 Particle size distribution (PSD) of infilling materials (a) Sample 1 (b) Sample 2
other mineral compositions The PSD results (Figure 12)showed that the particle sizes varied from 1 120583m to a few mmfor both Samples 1 and 2 with majority spanning from 10120583m to 1mm This could be a result of long-term weatheringbut the weak and unfavorable rock properties observed inthe field indicate that KCPs are very fractured and loose instructure with low strength high permeability being proneto water erosion and the water inrush risks
33 Numerical Model Setup Although diverse in geometryKCPs are usually presented similarly to a dome shape [9]Each of these approximates a 3D axisymmetric model whichcan be simplified as a 2D symmetrical model
In this work according to the lithology of the mine thebottom diameter top diameter and height are 15m 10m and20m respectively (as shown in Figure 13) The pressure atthe water inlet on the lower boundary was 20MPa and the
8 Geofluids
Description LithologyThickness (m)
11 coal
Limestone
Mudstone
Fine sandstone
Aquifer
10 coal
Limestone
Mudstone
30
25
73
33
46
200
358
Mudstone
9 coal
89
05
96
(a) (b) (c)
times10minus4
05
06
07
08
09
1
11
12
13
14
Figure 13 Model geometry and setup (a) illustration of KCP and rock strata (b) 2D simulation model and (c) distribution of apertureopening based on Weibull function
pressure at the water outlet on the top was 01MPa initialwater pressure in the model was 01MPa initial particle vol-ume concentration was 001 initial average fracture aperture1198870 was 01mm and initial porosity 1206010 was 10 The mainparameters of the model were all determined according tothe relevant references [3 12] in which the studies wereconducted on the same seam Other used parameters arelisted in Table 1Themodel was divided into 5000 grids usingmapped mesh method embedded in the COMSOL softwareThe shape of the grids is rectangular
Heterogeneity has been determined to be a prominentfeature of rock There are currently various approaches toobtaining the characteristics of the heterogeneous distribu-tion of rock materials For example digital core techniquesand mathematical statistics methods have both been utilizedPrevious studies have shown that the heterogeneity of rockcan be described by the Weibull distribution [40ndash42] Thusthe Weibull distribution was selected in this study due to itseffectiveness and great simplicity to obtain the heterogeneousdistribution of fracture apertures of the KCPs The distribu-tion probability density equation was as follows
119891 (119887) = 1198981198870 ( 119887
1198870)119898minus1
exp [minus ( 1198871198870)119898] (20)
where 119887 indicates the fracture aperture 1198870 denotes the initialfracture aperture and 119898 is the uniformity index The larger119898 represents the higher level of uniformity The fractureaperture distribution obtained by the numerical generationmethod is shown in Figure 13(c)
Based on thismodel geometry (9) (11) (14) (15) (17) and(18) will be solved simultaneously to investigate the dynamicchange of water flow behaviors and the associated inrush riskunder different flow conditions
4 Results and Analysis
In order to analyze the characteristics of seepage at differenttimes in this study six different moments were selected (ie14 times 103 15 times 103 16 times 103 17 times 103 175 times 103 and 18 times 103 s)The specific results will be discussed below
41 Distribution of the Fracture Apertures Figure 14 illus-trates the spatial changes of the fracture apertures at differenttimes Figure 15 shows the evolution of fracture aperturesalong O-O10158401015840 and O1015840-A1015840 lines as marked in Figure 13(b)and the average fracture aperture-time curve was plotted inFigure 16 The results show the following(1) The fracture aperture gradually increases under theeffects of the erosion However the increase rate is higherin the upper part of the model than in the lower part Thisis likely because the upper outlet boundary is narrower thanthe bottom inlet boundary giving rise to higher flow velocitySuch higher velocity causes more significant erosion andconsequently the fracture aperture change is faster(2) As the infiltration continues the average fractureaperture increases by approximately 200 from 01mm tonearly 03mm (Figure 16) At the initial stage the fracture issubject to random distribution with minor difference in theapertures However the variation diverges under the effectsof the erosion The fractures with smaller initial aperturesbecome slowly enlarged by approximately 20 while thosewith larger apertures continuously increase by more than200 As the fractures gradually dilate and interconnectwith each other a number of dominant seepage channels areformed as illustrated in Figure 14(f)
42 Distribution of Water Seepage Velocity The seepagevelocities (ie Darcy velocity) in the model domain andalong O-O10158401015840 and O1015840-A1015840 lines were shown in Figures 17 and
Geofluids 9
Table 1 Input parameters for the numerical simulation
120588119904(kgm3) 120578(Pasdots) 1198961198980(m2) 1206010 1198870(m) 119886 1205821(mminus1) 1205822(mminus1) 119898 11986202000 10minus3 10minus12 01 00001 001 001 001 6 001
1
2
3
4
5
6
7
(a) 14000 s
1
2
3
4
5
6
7
(b) 15000 s
1
2
3
4
5
6
7
(c) 16000 s
1
2
3
4
5
6
7
(d) 17000 s
1
2
3
4
5
6
7
(e) 17500 s
1
2
3
4
5
6
7
(f) 18000 s
Figure 14 The spatial distribution of aperture 119887 (10minus4m ) at different times
18 respectively The predicted failure time using the inversevelocity theory was plotted in Figure 19The key observationsinclude the following(1) As shown in Figure 17 the changes in the flowvelocity are consistent with the distribution of the fractures(Figure 14) and more fracture aperture changes are observedat the locations where higher seepage velocities take place Asshown in Figure 18 at 14times 104 s theminimumandmaximumseepage velocities were approximately 35 times 10minus6ms and 411times 10minus5ms At 18 times 104 s these two figures increased by 20and 200 to 42 times 10minus6ms and 125 times 10minus3ms respectively(2)Therewas a continuous increase in flow rate at the out-let from approximately 37m3 h initially to approximately100m3 h at 18times 104 s increased by nearly 30 times Howeverits increase showed a nonlinear trend likely due to the fact
that the increase rate was relatively slow in the initial stagebut accelerated gradually until the water inrush occurredFigure 19 was generated according to the inverse velocitytheory and the results showed that the water inrush wouldoccur at 185 times 104 s for this particular flow condition Thetrend has been reflected by the change in flow velocity shownin Figure 17 The figure shows that shortly before the inrushthe flow channels rapidly connected together and formed amain channel resulting in a surge in water flow
43 Distribution of the Particle Concentrations Particle con-centration is directly related to the erosion rate Higherparticle concentration indicates more severe erosion whichis more likely to result in greater fracture aperture change
10 Geofluids
05
15
25
35
45
55
65Fr
actu
re ap
ertu
reb
(times10
minus4
m)
5 10 15 200z (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
(a)
1 2 3 4 5 6 70r (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
05
15
25
35
45
55
65
Frac
ture
aper
ture
b(times
10minus4
m)
(b)
Figure 15 Evolution of fracture aperture along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
1
15
2
25
3
Frac
ture
aper
ture
b(times
10minus4
m)
5 10 15 200Time (times103 s)
Figure 16 Change of average fracture aperture with time
Figure 20 shows the evolution of the average particleconcentration along O-O10158401015840 and O1015840-A1015840 lines The averageparticle concentration and particle loss rate was plotted inFigure 21
Figure 20 plots the spatial distribution of the particleconcentrations for the wholemodel at different times Resultsshow that the particle concentration gradually increasesfrom the bottom upwards This is because under the effectsof the erosion increasing amount of particles migratedinto the water and gradually moved upwards through thefractures and pores This is consistent with the change inthe particle concentration at different locations as shown inFigure 21
Results in Figure 22 are well in line with the results shownin Figure 18 For example at the beginning the particle lossrate is relatively low however the rate constantly increasesover time and culminates at the inrushThis is due to the fact
that along with the increases in the seepage velocities theerosion effects on the solid particles are constantly intensifiedwhich results in frequent migration and substantial particleloss
44 Sensitivity Analyses The outburst processes wereaffected or controlled by various factors including thespatial heterogeneity of lithology of the KCPs waterpressure absolute aperture and distribution of the fracturesdistribution law of concentration of the karst particlesand their sensitivity to water erosion Based on the newlydeveloped coupling model this work further examined thewater and particle migration characteristics in the KCPsunder different hydrological and geological conditionsas well as the variations in the inrush occurrences Thescenarios to be studied are summarized in Table 2
Geofluids 11
2
16
12
08
04
0(a) 14000 s
2
16
12
08
04
0(b) 15000 s
2
16
12
08
04
0(c) 16000 s
2
16
12
08
04
0(d) 17000 s
2
16
12
08
04
0(e) 17500 s
2
16
12
08
04
0(f) 18000 s
Figure 17 The change of seepage velocity (10minus3ms) in a KCP
14000 s15000 s16000 s
17000 s17500 s18000 s
r (m)
1 2 3 4 5 6 70
Velo
city
(10minus
3m
s)
14
12
1
08
06
04
02
0
(a)
14000 s15000 s16000 s
17000 s17500 s18000 s
50 10z (m)
15 20
Velo
city
(10minus
3m
s)
14
12
1
08
06
04
02
0
(b)
Figure 18 Evolution of seepage velocity along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
12 Geofluids
Inverse velocityLinear fitting
0
20
40
60
80
100
Flow
rate
(m3h
)
0
5
10
15
20
25
30
Inve
rse v
eloci
ty (h
m)
5 10 15 200Time (times103 s)
Q
Figure 19 Water flow rate along the bottom surface of the numerical model
025
02
03
015
01
005
0(a) 14000 s
025
02
03
015
01
005
0(b) 15000 s
025
02
03
015
01
005
0(c) 16000 s
025
02
03
015
01
005
0(d) 17000 s
025
02
03
015
01
005
0(e) 17500 s
025
02
03
015
01
005
0(f) 18000 s
Figure 20 Change of particles concentration in a KCP
Geofluids 13
0
005
01
015
02
025
03
035C
once
ntra
tion
1 2 3 4 5 6 70r (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
(a)
105 15 200z (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
0
005
01
015
02
025
03
035
Con
cent
ratio
n (b)
Figure 21 Evolution of particle concentration along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
ConcentrationLoss rate
0
005
01
015
Con
cent
ratio
n
5 10 15 200Time (times103 s)
0
5
10
15
20
25
Part
icle
loss
rate
Qp
(m3h
)
Figure 22 Evolution of average particle volumetric concentrationand particle loss rate
441 Impact of Heterogeneity on Fractures Evolution Fig-ure 23 illustrates the distribution law of the fractures seepagevelocities and particle volume concentrations under identicalflow pressures but different fracture distribution conditionsat 175 times 103 seconds The results show that more intercon-nected fractures are developed along with the increase in mvalues For example when119898 = 4 there are only two intercon-nected fractures However asm value increases an increasingnumber of fractures were generated and interconnected Inthe fourth case (119898 = 10) three interconnected fractures weregenerated This finding indicates that the homogeneity canaccelerate the propagation of the fractures An increase in
Table 2 List of simulation scenarios
Parameter Value
Weibull distribution coefficient (-)
119898 = 4119898 = 6119898 = 8
119898 = 10
Water pressure (MPa)
119901 = 10119901 = 20119901 = 30119901 = 40
Initial particle concentration ()
1198620 = 00051198620 = 0011198620 = 0021198620 = 005
Fracture aperture (times10minus4m)
119887 = 075119887 = 10
119887 = 125119887 = 15
flow velocity and particle concentration with increasing mvalues was also observed as shown in Figures 23(b) and 23(c)
442 Prediction of Water Inrush under Different ConditionsThe analysis and prediction of the occurrences of waterinrush in KCPs based on the changes in seepage are essentialfor the safety of mining processes Some researchers haveadopted catastrophe theories to predict the occurrences ofwater inrush However an approach that can be used topredict water inrush based on water flow has yet to be foundin the literature This study presents the first attempt toresolve this challenge by applying the inverse velocity theory
14 Geofluids
m = 4 m = 6 m = 8 m = 10
1
2
3
4
5
6
7
(a) Distribution of aperture 119887 (times10minus4m )
m = 4 m = 6 m = 8 m = 10
2
16
12
08
04
0
(b) Distribution of seepage velocity (times10minus3ms)
m = 4 m = 6 m = 8 m = 10
025
02
03
015
01
005
0
(c) Distribution of particles concentration
Figure 23 Distribution of fracture seepage velocity and particle concentration at different Weibull distribution conditions (a) Impact ofWeibull distribution on fractures evolution (b) impact of Weibull distribution on water velocity evolution (c) impact of Weibull distributionon particle concentration evolution
Geofluids 15
5 10 15 200Time (times103 s)
m = 4
m = 6 m = 10
m = 8
0
20
40
60
80
100
120Fl
ow ra
te (m
3h
)
(a)
205
21
215
22
225
23
Wat
er in
rush
tim
e (times10
3s)
4 6 8 102Weibull coefficient m
y = 25699xminus0089
R2 = 09825
(b)
Figure 24 Impact of heterogeneity on water flow rate (a) and inrush time (b)
0
20
40
60
80
100
120
140
160
180
200
Flow
rate
(m3h
)
5 10 15 200Time (times103 s)
p = 1MPap = 2MPa
p = 3MPap = 4MPa
(a)
y = 41733xminus1001
R2 = 09992
1 2 3 4 50Water pressure (MPa)
0
5
10
15
20
25
30
35
40
45
Wat
er in
rush
tim
e (times10
3s)
(b)
Figure 25 Impact of aquifer water pressure on water flow rate (a) and inrush time (b)
which has been widely approved effective in many fields suchas slope stability predictionThe relevant results and analysesare shown in Figure 24ndashFigure 27
As shown in Figure 24 water flow rate exhibits a non-linear increase and as the value of m increases the seepagerate accelerates gradually For example at 119905 = 15 times 104 s theseepage rate was approximately 15m3h for 119898 = 4 while itjumped to 25m3h for 119898 = 10 Results from Figure 24(b)show that water inrush occurs sooner for a greater 119898 valueIn other words the inrush occurs earlier as the heterogeneityincreases The water inrush time follows the power functionThis is due to the fact that the water is more prone to flowingthrough the existing fractures (which indicates a higher
permeability) in the heterogeneous structure Neverthelessdue to the heterogeneous distribution of the aperture thefractures cannot be easily interconnected which hampers theformation of the seepage channels In regard to the homo-geneous rock strata since the flow of water was dominantlycontrolled by the pressure gradient the fractures generatedduring the process of erosion could be easily interconnectedand as a result the water inrush occurredsooner
Figure 25 illustrates the impact of the initial KCPrsquos waterpressure on the flow rates and water inrush time It can beseen that as the pressure increases the changes in the flowrates accelerate For example for119901 = 2MPa the flow rate wasonly approximately 5m3h and it increased to 30m3h when
16 Geofluids
0
20
40
60
80
100
120
140
160
180
200Fl
ow ra
te (m
3h
)
5 10 15 20 250Time (times103 s)
c = 0005
c = 001
c = 002
c = 005
(a)
0
5
10
15
20
25
30
35
Wat
er in
rush
tim
e (times10
3s)
001 002 003 004 0050Initial particle concentration
y = 13554xminus0591
R2 = 09975
(b)
Figure 26 Impact of initial particle concentration on water flow rate (a) and inrush time (b)
0
20
40
60
80
100
120
140
160
180
200
Flow
rate
(m3h
)
5 10 15 200Time (times103 s)
075E minus 4m100E minus 4m
125E minus 4m150E minus 4m
(a)
y = 31027eminus286x
R2 = 09503
09 11 13 1507Fracture aperture (times10minus4 m)
0
5
10
15
20
25
30
35
40
Wat
er in
rush
tim
e (times10
3s)
(b)
Figure 27 Impact of absolute aperture on water flow rate (a) and inrush time (b)
119901 = 3MPa In addition with increasing the aquifer waterpressure the water inrush time was also brought forward asshown in Figure 25(a) The outburst time was approximately119905 = 40 times 104 s for p = 1MPa while only 10 times 104 s for119901 = 4MPa The relationship between the time of the inrushoccurrences and the aquifer water pressure follows the powerfunction as illustrated in Figure 25
For varying initial particle concentrations the evolutionof both the water flow rate change and the water inrushtime shows a similar trend to that of different aquifer waterpressures The flow rate accelerates with increasing initialparticle concentration and consequently the water inrushoccurs earlier as shown in Figure 26The outburst times alsoshow a power function to the initial particle concentration
The initial average fracture aperture also shows significantimpact on water flow behavior For instance results fromFigure 27 clearly illustrate that the flow rate increases withincreasing initial average fracture aperture Please note thatthe inrush time follows an exponential function to the initialaverage fracture aperture
These numerical results can be explained by the factthat the initial seepage velocity is expected to be higher forthe modelling cases with the higher initial aquifer pressureinitial fracture aperture andor initial particle concentrationThe higher flow velocity would intensify the erosion of thefractures enhance the permeability and thereby acceleratethe migration of the particles and interconnection of seepagechannels which causes water inrush
Geofluids 17
5 Conclusions
In this study a systematic approach was established to inves-tigate the impact of controlling factors onwater flow behaviorfor KCPs and to predict water inrush time by introducing theinverse velocity theory In this approach a suite of governingequations was developed to couple all the physics involvedin this complex process including water flow rock erosionand change in rock microstructure These equations werethen implemented into a finite element software COMSOLMultiphysics to simulate the fully coupled process Basedon this numerical model a series of sensitivity studies wereconducted and some important findings have been drawn
(i) Water flow rate increases with increasing aquiferpressure initial particle concentration and fractureopening This results in an increase in the permeabil-ity and finally an acceleration of the migration of theparticles and interconnection of the seepage channelsThis finding suggests the grouting of the KCPs couldbe an effective measure to mitigate water inrush risk
(ii) The inverse velocity theory was successfully appliedto analyze the occurrences of water inrush underdifferent conditions The results show that the timeof inrush has a power relationship to the rock het-erogeneity water pressure and initial particle concen-tration and follows an exponential relationship to theinitial fracture apertures
The framework developed from this work not only helpsenhance coal mining operations safety by better under-standing and predicting water inrush risks so that propermitigation measures can be put in place timely It canalso be extended to other fields such as tunneling backfillpaste piping tailing dam erosion and other engineeringapplications which are likely to encounter time-dependenterosion or deformation or water inrush issues
Please be noted that there are a number of other stochasticmethods available in the literature that can be used to illus-trate rock heterogeneity such as the Monte-Carlo methodor First-Order approach The differences of these methodson the results of water inrush prediction may be worthcomparing in the near future
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This project is supported by the National Natural ScienceFoundation of China (nos 51304072 51774110) the Programfor Innovative Research Team in University of Ministryof Education of China (IRT 16R22) and the PostdoctoralScience Foundation of China (2017M612398)
References
[1] DMa XMiao H Bai et al ldquoEffect of mining on shear sidewallgroundwater inrush hazard caused by seepage instability of the
penetrated karst collapse pillarrdquo Natural Hazards vol 82 no 1pp 73ndash93 2016
[2] H Keqiang Y Guangming and L Yaoru ldquoPalaeo-karst collapsepillars in northern China and their damage to the geologicalenvironmentsrdquo Environmental Geology vol 58 no 5 pp 1029ndash1040 2009
[3] B Yao J Wei D Wang D Ma and Z Chen ldquoNumericalstudy on seepage property of karst collapse columns underparticle migrationrdquo CMES Computer Modeling in Engineeringamp Sciences vol 91 no 2 pp 81ndash100 2013
[4] J Tang H Bai B Yao and Y Wu ldquoTheoretical analysis onwater-inrush mechanism of concealed collapse pillars in floorrdquoMining Science and Technology vol 21 no 1 pp 57ndash60 2011
[5] Y Chen M Yi C Chen and C Yu ldquoBernstein polynomialsmethod for fractional convection-diffusion equation with vari-able coefficientsrdquoComputerModeling in Engineering amp Sciencesvol 83 no 6 pp 639ndash653 2012
[6] J Zhang and B Shen ldquoCoal mining under aquifers in China Acase studyrdquo International Journal of Rock Mechanics and MiningSciences vol 41 no 4 pp 629ndash639 2004
[7] D Ma H Bai X Miao H Pu B Jiang and Z ChenldquoCompaction and seepage properties of crushed limestoneparticle mixture an experimental investigation for Ordoviciankarst collapse pillar groundwater inrushrdquo Environmental EarthSciences vol 75 no 1 article 11 p 14 2016
[8] S Yin J Zhang and D Liu ldquoA study of mine water inrushesby measurements of in situ stress and rock failuresrdquo NaturalHazards vol 79 no 3 pp 1961ndash1979 2015
[9] H Bai D Ma and Z Chen ldquoMechanical behavior of ground-water seepage in karst collapse pillarsrdquo Engineering Geology vol164 pp 101ndash106 2013
[10] D Ma and H Bai ldquoGroundwater inflow prediction model ofkarst collapse pillar a case study for mining-induced ground-water inrush riskrdquoNatural Hazards vol 76 no 2 pp 1319ndash13342015
[11] D Ma H Bai and Y Wang ldquoMechanical behavior of a coalseam penetrated by a karst collapse pillar mining-inducedgroundwater inrush riskrdquo Natural Hazards vol 75 no 3 pp2137ndash2151 2015
[12] B Yao Research on variable mass fluid-solid coupling dynamictheory of broken rockmass and application China Univeristy ofMining and Technology Xuzhou China 2012
[13] D Ma X Miao H Bai et al ldquoImpact of particle transfer onflow properties of crushed mudstonesrdquo Environmental EarthSciences vol 75 no 7 article 593 2016
[14] DMa H Bai Z Chen andH Pu ldquoEffect of particlemixture onseepage properties of crushed mudstonesrdquo Transport in PorousMedia vol 108 no 2 pp 257ndash277 2015
[15] B Zhang H Bai and K Zhang ldquoSeepage characteristics ofcollapse columnfillingsrdquo International Journal ofMining Scienceand Technology 2015
[16] P Ortoleva J Chadam E Merino and A Sen ldquoGeochemicalself-organization II the reactive-infiltration instabilityrdquo Ameri-can Journal of Science vol 287 no 10 pp 1008ndash1040 1987
[17] I Vardoulakis M Stavropoulou and P Papanastasiou ldquoHydro-mechanical aspects of the sand production problemrdquo Transportin Porous Media vol 22 no 2 pp 225ndash244 1996
[18] R L Detwiler and H Rajaram ldquoPredicting dissolution patternsin variable aperture fractures Evaluation of an enhanced depth-averaged computational modelrdquoWater Resources Research vol43 no 4 Article IDW04403 2007
18 Geofluids
[19] M A Habib H M Badr R Ben-Mansour and M E KabirldquoErosion rate correlations of a pipe protruded in an abrupt pipecontractionrdquo International Journal of Impact Engineering vol34 no 8 pp 1350ndash1369 2007
[20] H T Xiao and H Y Xu ldquoIn situ permeability measurementsto establish the influence of slice mining on floor rocksrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 37 no 5 pp 855ndash860 2000
[21] H Guo D P Adhikary and M S Craig ldquoSimulation of minewater inflow and gas emission during longwall miningrdquo RockMechanics and Rock Engineering vol 42 no 1 pp 25ndash51 2009
[22] R Zhang Z JiangH ZhouC Yang and S Xiao ldquoGroundwateroutbursts from faults above a confined aquifer in the coalminingrdquo Natural Hazards vol 71 no 3 pp 1861ndash1872 2014
[23] B Yao F Du E Li and X Wang ldquoMechanical model of karstcollapse columns water inrush and its applicationrdquo ElectronicJournal of Geotechnical Engineering vol 19 pp 1665ndash1675 2014
[24] J Warren and P Root ldquoThe behavior of naturally fracturedreservoirsrdquo SPE Journal vol 3 no 3 pp 245ndash255 2013
[25] H KazemiM S Seth andGWThomas ldquoThe interpretation ofinterference tests in naturally fractured reservoirs with uniformfracture distributionrdquo SPE Journal vol 9 no 4 pp 463ndash4721969
[26] A de Swaan O ldquoAnalytical solutions for determining naturallyfractured reservoir properties by well testingrdquo SPE Journal vol16 no 3 pp 117ndash122 1976
[27] N D Rose and O Hungr ldquoForecasting potential rock slopefailure in open pit mines using the inverse-velocity methodrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 2 pp 308ndash320 2007
[28] J R Fanchi Petroleum Engineering Handbook Volume 1 Gen-eral Engineering Society of Petroleum Engineers 2006
[29] R Sakthivadivel and S Irmay A Review of Filtration TheoriesHydraulic Engineering Laboratory College of EngineeringUniversity of California Berkeley Calif USA 1996
[30] C Wang P Zhai Z Chen J Liu L Wang and J XieldquoExperimental study of coal matrix-cleat interaction underconstant volume boundary conditionrdquo International Journal ofCoal Geology vol 181 pp 124ndash132 2017
[31] S Irmay ldquoOn the theoretical derivation of Darcy and Forch-heimer formulasrdquo Eos Transactions American GeophysicalUnion vol 39 no 4 pp 702ndash707 1958
[32] CH Lee and IW Farmer ldquoA simplemethod of estimating rockmass porosity and permeabilityrdquo International Journal ofMiningand Geological Engineering vol 8 no 1 pp 57ndash65 1990
[33] C Nalluri A K El-Zaemey and H L Chan ldquoSedimenttransport over fixed deposited beds in sewers - An appraisal ofexisting modelsrdquoWater Science and Technology vol 36 no 8-9pp 123ndash128 1997
[34] P Novak and C Nalluri ldquoSediment transport in smooth fixedbed channelsrdquo Journal of the Hydraulics Division vol 101 no 9pp 1139ndash1154 1975
[35] T Fukuzono ldquoA newmethod for predicting the failure time of asloperdquo in Proceedings of the In 4th International Conference andField Workshop on Landslides Tokyo Japan 1985
[36] C R J Kilburn andDN Petley ldquoForecasting giant catastrophicslope collapse lessons from Vajont Northern Italyrdquo Geomor-phology vol 54 no 1-2 pp 21ndash32 2003
[37] B Voight ldquoA method for prediction of volcanic eruptionsrdquoNature vol 332 no 6160 pp 125ndash130 1988
[38] B Yao X Mao J Wei and D Wang ldquoStudy on coupled fluid-solid model for collapse columns considering the effect ofparticle transportrdquo Zhongguo Kuangye Daxue XuebaoJournalof China University of Mining and Technology vol 43 no 1 pp30ndash35 2014
[39] H Bai Seepage Characteristics of Top Stratum of OrdovicianSystem and Its Application Study as Key Aquifuge ChinaUniversity of Mining amp Technology Xuzhou China 2008
[40] C A Tang L G Tham P K K Lee T H Yang and L CLi ldquoCoupled analysis of flow stress and damage (FSD) in rockfailurerdquo International Journal of Rock Mechanics and MiningSciences vol 39 no 4 pp 477ndash489 2002
[41] W C Zhu and C A Tang ldquoMicromechanical model forsimulating the fracture process of rockrdquo Rock Mechanics andRock Engineering vol 37 no 1 pp 25ndash56 2004
[42] T H Yang L G Tham C A Tang Z Z Liang and YTsui ldquoInfluence of heterogeneity of mechanical properties onhydraulic fracturing in permeable rocksrdquo Rock Mechanics andRock Engineering vol 37 no 4 pp 251ndash275 2004
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Submit your manuscripts atwwwhindawicom
Geofluids 3
N Datong
Shuozhou
TaiyuanYangquan
Jincheng
Huozhou
Yuncheng
Tuanbai
Main coal mine
Tuanbai coal mineCoal field in Shanxi
BeijingCity
Figure 2 The distribution of major coal mines in China and the coal fields in Shanxi province
Figure 3 Rock and infilling material (particles) in a KCP
Fractures
Matrix
Figure 4 Sketch of the Warren-Root Model [24]
generally competent the impact of the change in theeffective stress on KCPrsquos permeability is insignificant
(4) The impact of erosion on the permeability change isin proportion to the change of particle concentrationin the fluid
Half fracture
Matrix block
Water Particles
a
a + b
Figure 5 Sketch of a representative element of a typical KCP
222 Definition Based on the aforementioned assumptionsa representative element for a typical KCP microstructure isshown in Figure 5 The length 119871 (m) and volume 119881 (m3) ofthe element are expressed as
119871 = 119886 + 119887119881 = (119886 + 119887)3 (1)
where 119886 (m) is the length of the matrix and 119887 (m) is theaperture of the fracture
The total voidage 120593 () of an element is written as [28]
120593 = (119886 + 119887)3 minus 1198863(119886 + 119887)3 + 120601 cong 3119887
119886 + 120601 (2)
where 120601 () is the matrix porosity It should be noted that119887 ≪ 119886
4 Geofluids
o a + b
a + b
x3
x2
x1
(M1 + N1) L2
(M2 + N2) L2
(M1 +M1
x1
L) L2 + (N1 +N1
x1
L) L2
(M2 +M2
x2
L) L2 + ((N2 +N2
x2
L) L2
Figure 6 Illustration of a three-dimensional characteristic element in a KCP 119872119894 and 119873119894 are mass change of solids due to convection anddiffusion respectively defined as 119872119894 = 119862120588119904119902119894 119873119894 = minus119863(120597(119862120593120588119904)120597119909119894)
223 Mass Conservation Equations for Particles In order tostudy the migration characteristics of the infilling particlesthe dynamic mass conservation equations for particles werecalculated based on a three-dimensional representative ele-ment as illustrated in Figure 6
Infilling particles migration inside a representative ele-ment under erosion effects is affected by both convection andprocesses The average seepage velocity of an element can bedefined as997888rarr119902 119894 (ms) For the convection and diffusion processin the direction of 119909119894 (119894 = 1 2 3) the mass losses of particlesflowing out of the element in a unit time can be calculated by(3) and (4) respectively
120597 (119862120588119904119902119894)120597119909119894 119881 (3)
minus 120597120597119909119894 [119863 120597 (119862120593120588119904)120597119909119894 ] 119881 (4)
where 119862 () is the particle concentration (ie particlesaturation) 120588119904 (kgm3) denotes the density of solid particlesand 119863 (m2s) illustrates the particles diffusion coefficient
In the direction of 119909119894 the mass flowing into the elementdue to the convection-diffusion should be expressed as
120597119872119894120597119909119894 119881 + 120597119873119894120597119909119894 119881 (119894 = 1 2 3) (5)
For the element the total mass flowing can be expressedas the summation of the three directions
3sum119894=1
( 120597119872119894120597119909119894 119881 + 120597119873119894120597119909119894 119881) (6)
Under the effects of erosion the mass loss of the elementin a unit time can be summarized as
minus 120597120597119905 (119862120593120588119904) 119881 + 119881 (7)
where (kgm3s) is the particle mass that migrates into thefluid from a unit element in a unit time and is written as
= 120597120593120597119905 120588119904 (8)
According to the mass conservation law for the unit ele-ment (6) and (7) are equivalent giving themass conservationequation for particles as
minus 120597120597119905 (119862120593120588119904) 119881 + 119881 = 3sum
119894=1
( 120597119872119894120597119909119894 119881 + 120597119873119894120597119909119894 119881) (9)
Substituting (2) into (9) yields
[ 3119886
120597 (119887119862)120597119905 + 120597 (119862120601)
120597119905 ] + nabla sdot (119862997888rarr119902 ) minus nabla
sdot 119863nabla sdot [119862 ( 3119887119886 + 120601)] = ( 3
119886120597119887120597119905 + 120597120601
120597119905 ) (10)
As particle sizes are normally several orders of magnitudesmaller than the fracture aperture the diffusion effect can beneglected Equation (10) can therefore be simplified into
[ 3119886
120597 (119887119862)120597119905 + 120597 (119862120601)
120597119905 ] + nabla sdot (119862997888rarr119902 ) = ( 3119886
120597119887120597119905 + 120597120601
120597119905 ) (11)
224 Water Mass Conservation Equations For the waterflow the mass flowing out of the element in the direction of119909119894 (119894 = 1 2 3) can be expressed as
120597 [(1 minus 119862) 120588119891119902119894]120597119909119894 119881 (119894 = 1 2 3) (12)
where 120588119891 (kgm3) denotes the density of the fluid The massloss of the fluid in the element in a unit time can be calculatedas
minus 120597120597119905 [(1 minus 119862) 120593120588119891] 119881 (13)
By combining (2) (3) (12) and (13) the mass conserva-tion equation for water flow can be derived as
3119886
120597 [119887 (1 minus 119862)]120597119905 + 120597 [(1 minus 119862) 120601]
120597119905 + nabla sdot [(1 minus 119862) 997888rarr119902 ]= 0
(14)
Geofluids 5
225 Evolution of the Fracture Aperture and Porosity Rockporosity plays an important role in determining rock per-meability so full understanding of its evolution is essentialto study the seepage characteristics of KCPs Sakthivadiveland Irmay [29] investigated the erosion problem for porousmedia by using both experimental and theoretical methodsVardoulakis et al [17] summarized the studies on porousmedia erosion and according to that study the evolutionof fracture aperture and permeability was affected by theporosity and particles concentration as well as the seepagevelocity The following equations have been developed todetermine the evolution of fracture aperture and porosity[17]
120597119887120597119905 = 1205821120588119904 (119887max minus 119887) 119862 10038161003816100381610038161199021003816100381610038161003816 120597120601120597119905 = 1205822120588119904 (120601max minus 120601) 119862 10038161003816100381610038161199021003816100381610038161003816
(15)
where 1205821 and 1205822 are constant |119902| = radic11990221 + 11990222 + 11990223 is theabsolute value of the seepage velocity (ms) and 119887max and120601max illustrate the maximum value that fracture aperture andporosity can reach under fluid erosion
Equations (15) indicate that the porosity evolution isproportional to the particle concentration as well as theseepage velocity
226 Water Seepage Fluid transport in porous media isnormally described by Darcyrsquos law which is derived (a) frombalance of momentum for the fluid phase and (b) from aconstitutive equation for the fluid-solid interaction force (iethe seepage force) [30] In general the balance of linearmomentum for the fluid phase has the form [31]
minus 120597119901120597119909119894 = minus 120578
119896 119902119894 + 120588119891 120597120597119905 ( 119902119894120593 ) (16)
where 119901 denotes the pore pressure (Pa) 120578 is the dynamicviscosity of the fluid (Pasdots) and 119896 illustrates the permeabilityof the volumetric element (m2) For this study the flowvelocity is relatively low thereby the acceleration term canbe neglected giving
997888rarr119902 = minus 119896120578 (nabla119901 + 120588119891119892nabla119911) (17)
where 997888rarr119902 is the Darcy velocity (ms) and nabla119911 is the unit vectorin the direction of gravity For fractured porous media 119896 isthe sum of fracture permeability and porosity permeability(m2) which can be expressed as [32]
119896 = 119896119898 + 119896119891 = 1198961198980 ( 1206011198981206011198980)3 ( 1 minus 12060111989801 minus 120601119898 )2 + 1198873
12119886 (18)
in which 119896119898 = 1198961198980(1206011198981206011198980)3((1 minus 1206011198980)(1 minus 120601119898))2 and119896119891 = 119887312119886 represent the porosity permeability and fracturepermeability respectively
Equations (2) (11) (14) (15) and (17) together with (18)compose the coupled processes of water transport of KCPs
Waterseepage
Particlestransport
Fractureporosityevolution
KCP
C
C
q
q
b b
Figure 7 Coupling process among each physics
under erosion effects as illustrated in Figure 7 The abovegoverning equations will be implemented into COMSOLMultiphysics next to understand water inrush mechanism inKCPs to evaluate water inrush risks and to predict waterinrush time under different rock and flow conditions Thereare six unknowns with equations so the set of governingequations can provide a unique solution
In petroleum engineering generally there is a criticalvelocity associated with sand production in oil and gasreservoirs However for the particle movements in KCPs thecritical velocitywas not considered because (1) the sizes of theinfilling particles are significantly smaller than the fractureapertures (120583m versus mm) (2) the movement of the erodedmaterials does not require a critical pressure gradient (or flowvelocity) for most KCP infilling materials are soluble to waterforming diluted solution and (3) the fluid flow inside KCPsis generally much greater than the critical velocity of around0ndash77mms for the particle size of 1ndash10 120583m [33 34]
23 Inverse Velocity Theory The inverse velocity theory wasoriginally proposed by Fukuzono [35] based on experimentalstudies This theory was initially used to predict the failuretime of a solid material that experiences slow continuousdeformation (ie creep) When the reciprocal of the defor-mation velocity (ie the inverse velocity) is plotted as afunction of time its value approaches zero as the velocityincreases asymptotically towards failureThe trend line of theinverse velocity intersects with the abscissa which representstime and the intersectional point can predict the time offailure There are three types of trend line namely concavelinear and convex as shown in Figure 8
The following equation is used to define the envelope
119881minus1 = [119860 (120572 minus 1)]1(120572minus1) (119905119891 minus 119905)1(120572minus1) (19)
where 119881 is the inverse velocity (ms) 119860 and 120572 are constants119905119891 is the time of failure and 119905 is the time of cutoff or the mostrecent time of themonitoring dataThe inverse velocity curveis concave when 120572 lt 2 and it is linear when 120572 = 2 while it isconvex when 120572 gt 2 Fukuzono [35] indicated that a linear fitcould provide a reasonable prediction of failure time
The inverse velocity theory has been successfully used insoils rocks and other materials and has been proved to be
6 Geofluids
Time
Failure
a gt2 (convex)a = 2 (linear)
a lt 2 (concave)
Inve
rse v
eloci
ty (1
V)
Figure 8 Inverse velocity trend lines to predict the time of failure[27]
Water flowInverse velocityLinear fitting
0
200
400
600
800
1000
1200
1400
1600
Flow
rate
(Ｇ3h
)
0
0002
0004
0006
0008
001
0012
0014
0016
0018
002In
vers
e velo
city
(hＧ
3)
5 10 15 200Time (h)
Water inrush point
Figure 9 Verification of the inverse velocity theory in predictingwater inrush
reliable in estimating the failure time using the linear fittingcurve [36 37]Therefore in thiswork this theory (ie inversefluid flow velocity) is adopted as the first attempt to predictwater inrush in KCPs
In order to verify the applicability of theory to waterinrush the field monitoring data from Yao et al [38] and Bai[39] was used and the comparison of inrush time betweenreal data and predicted time using inverse velocity theorywas conducted The results were plotted in Figure 9 It can beseen that the predicted inrush time matches the actual waterinrush time very well which proves that this theory can beused to predict water inrush for KCPs
3 Numerical Model Implementation
31 Background of the Coal Mine In this section a case studywas conducted based on the hydrogeological conditions of
Goaf
Hau
lage
rise
Coal haulage roadway
Ventilation roadway
Miningadvance
KCP
Railw
ay ri
se
KCP
Figure 10 Illustration of number 10-106 longwall panel and KCP inTuanbai coal mine of Shanxi province China
the Tuanbai Coalmine which is affiliatedwithHuozhouCoalElectricity Group of China The mine is located in TuanbaiCounty Linfen City Shanxi Province as marked in blue inFigure 2 The mining operation is current extracting number10 coal seam at approximately 300m depth To date 97 KCPshave been found during the mining operations at this seamThese KCPs included rock blocks of different sizes and inmost cases mud infillings and sizes of KCPs varied from tensto hundreds of meters In addition some had low level ofcompaction and cementation and relatively high infiltrationcapabilities
Since the distance between number 10 coal seam and theOrdovician limestone was only about 35m (as illustrated inFigure 13(a)) themining operation is being carried out underpressure from the Ordovician limestone water of the floorThe water pressure was found to be about 2MPa This minehas suffered a number of water inrush accidents associatedwith the KCPs For instance one accident occurred on thebelt roadway of the first longwall panel in 2007 with a waterflow rate of nearly 470m3h In addition there were a numberof water inrush accidents on longwall panels such as 10-106 asshown in Figure 10 10-112 and 10-114 at a rate of range from40m3h to 150m3h in 2010 resulting in the submergenceof the longwall panels Later investigation of these incidentsrevealed that all were directly caused by the KCPs whichacted as water channels with the confined water serving asthe source
32 Characterisation of the Infilling Materials In KCPs thecomposition of the infillings and their particle size distri-bution (PSD) have been found to be highly relevant to themigration of the particles For this reason two samples (iesample 1 and sample 2) were collected from the Tuanbai coalmine and the X-ray diffraction phase analysis (compositionanalysis) was carried out on the infillingmaterials of theKCPsas well as the PSD characteristics The results are shown inFigures 11 and 12
The composition analysis (as shown in Figure 11) indi-cated that the infilling materials mainly included kaolin-ites quartz illite smectite mixed layers small quantities offeldspars montmorillonites chlorites calcites siderites and
Geofluids 7
402
281
93
108
14
4231
05 05
19
KaoliniteQuartzIlliteIllite-smectiteSmectite
ChloriteFeldsparCalciteSideriteOthers
(a)
465
198
137
125
24
00
1304
19
15
KaoliniteQuartzIlliteIllite-smectiteSmectite
ChloriteFeldsparCalciteSideriteOthers
(b)
Figure 11 (a) Mineral components of infilling materials for Sample 1 and (b) mineral components of infilling materials for Sample 2
0
20
40
60
80
100
Cum
ulat
ive (
)
0
5
10
15
20
25
30
35
40
Freq
uenc
y (
)
001 01 1 100001Size (mm)
FrequencyCumulative
(a)
FrequencyCumulative
0
20
40
60
80
100
Cum
ulat
ive (
)
0
5
10
15
20
25
30
35
40
Freq
uenc
y (
)
001 01 1 100001Size (mm)
(b)
Figure 12 Particle size distribution (PSD) of infilling materials (a) Sample 1 (b) Sample 2
other mineral compositions The PSD results (Figure 12)showed that the particle sizes varied from 1 120583m to a few mmfor both Samples 1 and 2 with majority spanning from 10120583m to 1mm This could be a result of long-term weatheringbut the weak and unfavorable rock properties observed inthe field indicate that KCPs are very fractured and loose instructure with low strength high permeability being proneto water erosion and the water inrush risks
33 Numerical Model Setup Although diverse in geometryKCPs are usually presented similarly to a dome shape [9]Each of these approximates a 3D axisymmetric model whichcan be simplified as a 2D symmetrical model
In this work according to the lithology of the mine thebottom diameter top diameter and height are 15m 10m and20m respectively (as shown in Figure 13) The pressure atthe water inlet on the lower boundary was 20MPa and the
8 Geofluids
Description LithologyThickness (m)
11 coal
Limestone
Mudstone
Fine sandstone
Aquifer
10 coal
Limestone
Mudstone
30
25
73
33
46
200
358
Mudstone
9 coal
89
05
96
(a) (b) (c)
times10minus4
05
06
07
08
09
1
11
12
13
14
Figure 13 Model geometry and setup (a) illustration of KCP and rock strata (b) 2D simulation model and (c) distribution of apertureopening based on Weibull function
pressure at the water outlet on the top was 01MPa initialwater pressure in the model was 01MPa initial particle vol-ume concentration was 001 initial average fracture aperture1198870 was 01mm and initial porosity 1206010 was 10 The mainparameters of the model were all determined according tothe relevant references [3 12] in which the studies wereconducted on the same seam Other used parameters arelisted in Table 1Themodel was divided into 5000 grids usingmapped mesh method embedded in the COMSOL softwareThe shape of the grids is rectangular
Heterogeneity has been determined to be a prominentfeature of rock There are currently various approaches toobtaining the characteristics of the heterogeneous distribu-tion of rock materials For example digital core techniquesand mathematical statistics methods have both been utilizedPrevious studies have shown that the heterogeneity of rockcan be described by the Weibull distribution [40ndash42] Thusthe Weibull distribution was selected in this study due to itseffectiveness and great simplicity to obtain the heterogeneousdistribution of fracture apertures of the KCPs The distribu-tion probability density equation was as follows
119891 (119887) = 1198981198870 ( 119887
1198870)119898minus1
exp [minus ( 1198871198870)119898] (20)
where 119887 indicates the fracture aperture 1198870 denotes the initialfracture aperture and 119898 is the uniformity index The larger119898 represents the higher level of uniformity The fractureaperture distribution obtained by the numerical generationmethod is shown in Figure 13(c)
Based on thismodel geometry (9) (11) (14) (15) (17) and(18) will be solved simultaneously to investigate the dynamicchange of water flow behaviors and the associated inrush riskunder different flow conditions
4 Results and Analysis
In order to analyze the characteristics of seepage at differenttimes in this study six different moments were selected (ie14 times 103 15 times 103 16 times 103 17 times 103 175 times 103 and 18 times 103 s)The specific results will be discussed below
41 Distribution of the Fracture Apertures Figure 14 illus-trates the spatial changes of the fracture apertures at differenttimes Figure 15 shows the evolution of fracture aperturesalong O-O10158401015840 and O1015840-A1015840 lines as marked in Figure 13(b)and the average fracture aperture-time curve was plotted inFigure 16 The results show the following(1) The fracture aperture gradually increases under theeffects of the erosion However the increase rate is higherin the upper part of the model than in the lower part Thisis likely because the upper outlet boundary is narrower thanthe bottom inlet boundary giving rise to higher flow velocitySuch higher velocity causes more significant erosion andconsequently the fracture aperture change is faster(2) As the infiltration continues the average fractureaperture increases by approximately 200 from 01mm tonearly 03mm (Figure 16) At the initial stage the fracture issubject to random distribution with minor difference in theapertures However the variation diverges under the effectsof the erosion The fractures with smaller initial aperturesbecome slowly enlarged by approximately 20 while thosewith larger apertures continuously increase by more than200 As the fractures gradually dilate and interconnectwith each other a number of dominant seepage channels areformed as illustrated in Figure 14(f)
42 Distribution of Water Seepage Velocity The seepagevelocities (ie Darcy velocity) in the model domain andalong O-O10158401015840 and O1015840-A1015840 lines were shown in Figures 17 and
Geofluids 9
Table 1 Input parameters for the numerical simulation
120588119904(kgm3) 120578(Pasdots) 1198961198980(m2) 1206010 1198870(m) 119886 1205821(mminus1) 1205822(mminus1) 119898 11986202000 10minus3 10minus12 01 00001 001 001 001 6 001
1
2
3
4
5
6
7
(a) 14000 s
1
2
3
4
5
6
7
(b) 15000 s
1
2
3
4
5
6
7
(c) 16000 s
1
2
3
4
5
6
7
(d) 17000 s
1
2
3
4
5
6
7
(e) 17500 s
1
2
3
4
5
6
7
(f) 18000 s
Figure 14 The spatial distribution of aperture 119887 (10minus4m ) at different times
18 respectively The predicted failure time using the inversevelocity theory was plotted in Figure 19The key observationsinclude the following(1) As shown in Figure 17 the changes in the flowvelocity are consistent with the distribution of the fractures(Figure 14) and more fracture aperture changes are observedat the locations where higher seepage velocities take place Asshown in Figure 18 at 14times 104 s theminimumandmaximumseepage velocities were approximately 35 times 10minus6ms and 411times 10minus5ms At 18 times 104 s these two figures increased by 20and 200 to 42 times 10minus6ms and 125 times 10minus3ms respectively(2)Therewas a continuous increase in flow rate at the out-let from approximately 37m3 h initially to approximately100m3 h at 18times 104 s increased by nearly 30 times Howeverits increase showed a nonlinear trend likely due to the fact
that the increase rate was relatively slow in the initial stagebut accelerated gradually until the water inrush occurredFigure 19 was generated according to the inverse velocitytheory and the results showed that the water inrush wouldoccur at 185 times 104 s for this particular flow condition Thetrend has been reflected by the change in flow velocity shownin Figure 17 The figure shows that shortly before the inrushthe flow channels rapidly connected together and formed amain channel resulting in a surge in water flow
43 Distribution of the Particle Concentrations Particle con-centration is directly related to the erosion rate Higherparticle concentration indicates more severe erosion whichis more likely to result in greater fracture aperture change
10 Geofluids
05
15
25
35
45
55
65Fr
actu
re ap
ertu
reb
(times10
minus4
m)
5 10 15 200z (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
(a)
1 2 3 4 5 6 70r (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
05
15
25
35
45
55
65
Frac
ture
aper
ture
b(times
10minus4
m)
(b)
Figure 15 Evolution of fracture aperture along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
1
15
2
25
3
Frac
ture
aper
ture
b(times
10minus4
m)
5 10 15 200Time (times103 s)
Figure 16 Change of average fracture aperture with time
Figure 20 shows the evolution of the average particleconcentration along O-O10158401015840 and O1015840-A1015840 lines The averageparticle concentration and particle loss rate was plotted inFigure 21
Figure 20 plots the spatial distribution of the particleconcentrations for the wholemodel at different times Resultsshow that the particle concentration gradually increasesfrom the bottom upwards This is because under the effectsof the erosion increasing amount of particles migratedinto the water and gradually moved upwards through thefractures and pores This is consistent with the change inthe particle concentration at different locations as shown inFigure 21
Results in Figure 22 are well in line with the results shownin Figure 18 For example at the beginning the particle lossrate is relatively low however the rate constantly increasesover time and culminates at the inrushThis is due to the fact
that along with the increases in the seepage velocities theerosion effects on the solid particles are constantly intensifiedwhich results in frequent migration and substantial particleloss
44 Sensitivity Analyses The outburst processes wereaffected or controlled by various factors including thespatial heterogeneity of lithology of the KCPs waterpressure absolute aperture and distribution of the fracturesdistribution law of concentration of the karst particlesand their sensitivity to water erosion Based on the newlydeveloped coupling model this work further examined thewater and particle migration characteristics in the KCPsunder different hydrological and geological conditionsas well as the variations in the inrush occurrences Thescenarios to be studied are summarized in Table 2
Geofluids 11
2
16
12
08
04
0(a) 14000 s
2
16
12
08
04
0(b) 15000 s
2
16
12
08
04
0(c) 16000 s
2
16
12
08
04
0(d) 17000 s
2
16
12
08
04
0(e) 17500 s
2
16
12
08
04
0(f) 18000 s
Figure 17 The change of seepage velocity (10minus3ms) in a KCP
14000 s15000 s16000 s
17000 s17500 s18000 s
r (m)
1 2 3 4 5 6 70
Velo
city
(10minus
3m
s)
14
12
1
08
06
04
02
0
(a)
14000 s15000 s16000 s
17000 s17500 s18000 s
50 10z (m)
15 20
Velo
city
(10minus
3m
s)
14
12
1
08
06
04
02
0
(b)
Figure 18 Evolution of seepage velocity along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
12 Geofluids
Inverse velocityLinear fitting
0
20
40
60
80
100
Flow
rate
(m3h
)
0
5
10
15
20
25
30
Inve
rse v
eloci
ty (h
m)
5 10 15 200Time (times103 s)
Q
Figure 19 Water flow rate along the bottom surface of the numerical model
025
02
03
015
01
005
0(a) 14000 s
025
02
03
015
01
005
0(b) 15000 s
025
02
03
015
01
005
0(c) 16000 s
025
02
03
015
01
005
0(d) 17000 s
025
02
03
015
01
005
0(e) 17500 s
025
02
03
015
01
005
0(f) 18000 s
Figure 20 Change of particles concentration in a KCP
Geofluids 13
0
005
01
015
02
025
03
035C
once
ntra
tion
1 2 3 4 5 6 70r (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
(a)
105 15 200z (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
0
005
01
015
02
025
03
035
Con
cent
ratio
n (b)
Figure 21 Evolution of particle concentration along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
ConcentrationLoss rate
0
005
01
015
Con
cent
ratio
n
5 10 15 200Time (times103 s)
0
5
10
15
20
25
Part
icle
loss
rate
Qp
(m3h
)
Figure 22 Evolution of average particle volumetric concentrationand particle loss rate
441 Impact of Heterogeneity on Fractures Evolution Fig-ure 23 illustrates the distribution law of the fractures seepagevelocities and particle volume concentrations under identicalflow pressures but different fracture distribution conditionsat 175 times 103 seconds The results show that more intercon-nected fractures are developed along with the increase in mvalues For example when119898 = 4 there are only two intercon-nected fractures However asm value increases an increasingnumber of fractures were generated and interconnected Inthe fourth case (119898 = 10) three interconnected fractures weregenerated This finding indicates that the homogeneity canaccelerate the propagation of the fractures An increase in
Table 2 List of simulation scenarios
Parameter Value
Weibull distribution coefficient (-)
119898 = 4119898 = 6119898 = 8
119898 = 10
Water pressure (MPa)
119901 = 10119901 = 20119901 = 30119901 = 40
Initial particle concentration ()
1198620 = 00051198620 = 0011198620 = 0021198620 = 005
Fracture aperture (times10minus4m)
119887 = 075119887 = 10
119887 = 125119887 = 15
flow velocity and particle concentration with increasing mvalues was also observed as shown in Figures 23(b) and 23(c)
442 Prediction of Water Inrush under Different ConditionsThe analysis and prediction of the occurrences of waterinrush in KCPs based on the changes in seepage are essentialfor the safety of mining processes Some researchers haveadopted catastrophe theories to predict the occurrences ofwater inrush However an approach that can be used topredict water inrush based on water flow has yet to be foundin the literature This study presents the first attempt toresolve this challenge by applying the inverse velocity theory
14 Geofluids
m = 4 m = 6 m = 8 m = 10
1
2
3
4
5
6
7
(a) Distribution of aperture 119887 (times10minus4m )
m = 4 m = 6 m = 8 m = 10
2
16
12
08
04
0
(b) Distribution of seepage velocity (times10minus3ms)
m = 4 m = 6 m = 8 m = 10
025
02
03
015
01
005
0
(c) Distribution of particles concentration
Figure 23 Distribution of fracture seepage velocity and particle concentration at different Weibull distribution conditions (a) Impact ofWeibull distribution on fractures evolution (b) impact of Weibull distribution on water velocity evolution (c) impact of Weibull distributionon particle concentration evolution
Geofluids 15
5 10 15 200Time (times103 s)
m = 4
m = 6 m = 10
m = 8
0
20
40
60
80
100
120Fl
ow ra
te (m
3h
)
(a)
205
21
215
22
225
23
Wat
er in
rush
tim
e (times10
3s)
4 6 8 102Weibull coefficient m
y = 25699xminus0089
R2 = 09825
(b)
Figure 24 Impact of heterogeneity on water flow rate (a) and inrush time (b)
0
20
40
60
80
100
120
140
160
180
200
Flow
rate
(m3h
)
5 10 15 200Time (times103 s)
p = 1MPap = 2MPa
p = 3MPap = 4MPa
(a)
y = 41733xminus1001
R2 = 09992
1 2 3 4 50Water pressure (MPa)
0
5
10
15
20
25
30
35
40
45
Wat
er in
rush
tim
e (times10
3s)
(b)
Figure 25 Impact of aquifer water pressure on water flow rate (a) and inrush time (b)
which has been widely approved effective in many fields suchas slope stability predictionThe relevant results and analysesare shown in Figure 24ndashFigure 27
As shown in Figure 24 water flow rate exhibits a non-linear increase and as the value of m increases the seepagerate accelerates gradually For example at 119905 = 15 times 104 s theseepage rate was approximately 15m3h for 119898 = 4 while itjumped to 25m3h for 119898 = 10 Results from Figure 24(b)show that water inrush occurs sooner for a greater 119898 valueIn other words the inrush occurs earlier as the heterogeneityincreases The water inrush time follows the power functionThis is due to the fact that the water is more prone to flowingthrough the existing fractures (which indicates a higher
permeability) in the heterogeneous structure Neverthelessdue to the heterogeneous distribution of the aperture thefractures cannot be easily interconnected which hampers theformation of the seepage channels In regard to the homo-geneous rock strata since the flow of water was dominantlycontrolled by the pressure gradient the fractures generatedduring the process of erosion could be easily interconnectedand as a result the water inrush occurredsooner
Figure 25 illustrates the impact of the initial KCPrsquos waterpressure on the flow rates and water inrush time It can beseen that as the pressure increases the changes in the flowrates accelerate For example for119901 = 2MPa the flow rate wasonly approximately 5m3h and it increased to 30m3h when
16 Geofluids
0
20
40
60
80
100
120
140
160
180
200Fl
ow ra
te (m
3h
)
5 10 15 20 250Time (times103 s)
c = 0005
c = 001
c = 002
c = 005
(a)
0
5
10
15
20
25
30
35
Wat
er in
rush
tim
e (times10
3s)
001 002 003 004 0050Initial particle concentration
y = 13554xminus0591
R2 = 09975
(b)
Figure 26 Impact of initial particle concentration on water flow rate (a) and inrush time (b)
0
20
40
60
80
100
120
140
160
180
200
Flow
rate
(m3h
)
5 10 15 200Time (times103 s)
075E minus 4m100E minus 4m
125E minus 4m150E minus 4m
(a)
y = 31027eminus286x
R2 = 09503
09 11 13 1507Fracture aperture (times10minus4 m)
0
5
10
15
20
25
30
35
40
Wat
er in
rush
tim
e (times10
3s)
(b)
Figure 27 Impact of absolute aperture on water flow rate (a) and inrush time (b)
119901 = 3MPa In addition with increasing the aquifer waterpressure the water inrush time was also brought forward asshown in Figure 25(a) The outburst time was approximately119905 = 40 times 104 s for p = 1MPa while only 10 times 104 s for119901 = 4MPa The relationship between the time of the inrushoccurrences and the aquifer water pressure follows the powerfunction as illustrated in Figure 25
For varying initial particle concentrations the evolutionof both the water flow rate change and the water inrushtime shows a similar trend to that of different aquifer waterpressures The flow rate accelerates with increasing initialparticle concentration and consequently the water inrushoccurs earlier as shown in Figure 26The outburst times alsoshow a power function to the initial particle concentration
The initial average fracture aperture also shows significantimpact on water flow behavior For instance results fromFigure 27 clearly illustrate that the flow rate increases withincreasing initial average fracture aperture Please note thatthe inrush time follows an exponential function to the initialaverage fracture aperture
These numerical results can be explained by the factthat the initial seepage velocity is expected to be higher forthe modelling cases with the higher initial aquifer pressureinitial fracture aperture andor initial particle concentrationThe higher flow velocity would intensify the erosion of thefractures enhance the permeability and thereby acceleratethe migration of the particles and interconnection of seepagechannels which causes water inrush
Geofluids 17
5 Conclusions
In this study a systematic approach was established to inves-tigate the impact of controlling factors onwater flow behaviorfor KCPs and to predict water inrush time by introducing theinverse velocity theory In this approach a suite of governingequations was developed to couple all the physics involvedin this complex process including water flow rock erosionand change in rock microstructure These equations werethen implemented into a finite element software COMSOLMultiphysics to simulate the fully coupled process Basedon this numerical model a series of sensitivity studies wereconducted and some important findings have been drawn
(i) Water flow rate increases with increasing aquiferpressure initial particle concentration and fractureopening This results in an increase in the permeabil-ity and finally an acceleration of the migration of theparticles and interconnection of the seepage channelsThis finding suggests the grouting of the KCPs couldbe an effective measure to mitigate water inrush risk
(ii) The inverse velocity theory was successfully appliedto analyze the occurrences of water inrush underdifferent conditions The results show that the timeof inrush has a power relationship to the rock het-erogeneity water pressure and initial particle concen-tration and follows an exponential relationship to theinitial fracture apertures
The framework developed from this work not only helpsenhance coal mining operations safety by better under-standing and predicting water inrush risks so that propermitigation measures can be put in place timely It canalso be extended to other fields such as tunneling backfillpaste piping tailing dam erosion and other engineeringapplications which are likely to encounter time-dependenterosion or deformation or water inrush issues
Please be noted that there are a number of other stochasticmethods available in the literature that can be used to illus-trate rock heterogeneity such as the Monte-Carlo methodor First-Order approach The differences of these methodson the results of water inrush prediction may be worthcomparing in the near future
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This project is supported by the National Natural ScienceFoundation of China (nos 51304072 51774110) the Programfor Innovative Research Team in University of Ministryof Education of China (IRT 16R22) and the PostdoctoralScience Foundation of China (2017M612398)
References
[1] DMa XMiao H Bai et al ldquoEffect of mining on shear sidewallgroundwater inrush hazard caused by seepage instability of the
penetrated karst collapse pillarrdquo Natural Hazards vol 82 no 1pp 73ndash93 2016
[2] H Keqiang Y Guangming and L Yaoru ldquoPalaeo-karst collapsepillars in northern China and their damage to the geologicalenvironmentsrdquo Environmental Geology vol 58 no 5 pp 1029ndash1040 2009
[3] B Yao J Wei D Wang D Ma and Z Chen ldquoNumericalstudy on seepage property of karst collapse columns underparticle migrationrdquo CMES Computer Modeling in Engineeringamp Sciences vol 91 no 2 pp 81ndash100 2013
[4] J Tang H Bai B Yao and Y Wu ldquoTheoretical analysis onwater-inrush mechanism of concealed collapse pillars in floorrdquoMining Science and Technology vol 21 no 1 pp 57ndash60 2011
[5] Y Chen M Yi C Chen and C Yu ldquoBernstein polynomialsmethod for fractional convection-diffusion equation with vari-able coefficientsrdquoComputerModeling in Engineering amp Sciencesvol 83 no 6 pp 639ndash653 2012
[6] J Zhang and B Shen ldquoCoal mining under aquifers in China Acase studyrdquo International Journal of Rock Mechanics and MiningSciences vol 41 no 4 pp 629ndash639 2004
[7] D Ma H Bai X Miao H Pu B Jiang and Z ChenldquoCompaction and seepage properties of crushed limestoneparticle mixture an experimental investigation for Ordoviciankarst collapse pillar groundwater inrushrdquo Environmental EarthSciences vol 75 no 1 article 11 p 14 2016
[8] S Yin J Zhang and D Liu ldquoA study of mine water inrushesby measurements of in situ stress and rock failuresrdquo NaturalHazards vol 79 no 3 pp 1961ndash1979 2015
[9] H Bai D Ma and Z Chen ldquoMechanical behavior of ground-water seepage in karst collapse pillarsrdquo Engineering Geology vol164 pp 101ndash106 2013
[10] D Ma and H Bai ldquoGroundwater inflow prediction model ofkarst collapse pillar a case study for mining-induced ground-water inrush riskrdquoNatural Hazards vol 76 no 2 pp 1319ndash13342015
[11] D Ma H Bai and Y Wang ldquoMechanical behavior of a coalseam penetrated by a karst collapse pillar mining-inducedgroundwater inrush riskrdquo Natural Hazards vol 75 no 3 pp2137ndash2151 2015
[12] B Yao Research on variable mass fluid-solid coupling dynamictheory of broken rockmass and application China Univeristy ofMining and Technology Xuzhou China 2012
[13] D Ma X Miao H Bai et al ldquoImpact of particle transfer onflow properties of crushed mudstonesrdquo Environmental EarthSciences vol 75 no 7 article 593 2016
[14] DMa H Bai Z Chen andH Pu ldquoEffect of particlemixture onseepage properties of crushed mudstonesrdquo Transport in PorousMedia vol 108 no 2 pp 257ndash277 2015
[15] B Zhang H Bai and K Zhang ldquoSeepage characteristics ofcollapse columnfillingsrdquo International Journal ofMining Scienceand Technology 2015
[16] P Ortoleva J Chadam E Merino and A Sen ldquoGeochemicalself-organization II the reactive-infiltration instabilityrdquo Ameri-can Journal of Science vol 287 no 10 pp 1008ndash1040 1987
[17] I Vardoulakis M Stavropoulou and P Papanastasiou ldquoHydro-mechanical aspects of the sand production problemrdquo Transportin Porous Media vol 22 no 2 pp 225ndash244 1996
[18] R L Detwiler and H Rajaram ldquoPredicting dissolution patternsin variable aperture fractures Evaluation of an enhanced depth-averaged computational modelrdquoWater Resources Research vol43 no 4 Article IDW04403 2007
18 Geofluids
[19] M A Habib H M Badr R Ben-Mansour and M E KabirldquoErosion rate correlations of a pipe protruded in an abrupt pipecontractionrdquo International Journal of Impact Engineering vol34 no 8 pp 1350ndash1369 2007
[20] H T Xiao and H Y Xu ldquoIn situ permeability measurementsto establish the influence of slice mining on floor rocksrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 37 no 5 pp 855ndash860 2000
[21] H Guo D P Adhikary and M S Craig ldquoSimulation of minewater inflow and gas emission during longwall miningrdquo RockMechanics and Rock Engineering vol 42 no 1 pp 25ndash51 2009
[22] R Zhang Z JiangH ZhouC Yang and S Xiao ldquoGroundwateroutbursts from faults above a confined aquifer in the coalminingrdquo Natural Hazards vol 71 no 3 pp 1861ndash1872 2014
[23] B Yao F Du E Li and X Wang ldquoMechanical model of karstcollapse columns water inrush and its applicationrdquo ElectronicJournal of Geotechnical Engineering vol 19 pp 1665ndash1675 2014
[24] J Warren and P Root ldquoThe behavior of naturally fracturedreservoirsrdquo SPE Journal vol 3 no 3 pp 245ndash255 2013
[25] H KazemiM S Seth andGWThomas ldquoThe interpretation ofinterference tests in naturally fractured reservoirs with uniformfracture distributionrdquo SPE Journal vol 9 no 4 pp 463ndash4721969
[26] A de Swaan O ldquoAnalytical solutions for determining naturallyfractured reservoir properties by well testingrdquo SPE Journal vol16 no 3 pp 117ndash122 1976
[27] N D Rose and O Hungr ldquoForecasting potential rock slopefailure in open pit mines using the inverse-velocity methodrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 2 pp 308ndash320 2007
[28] J R Fanchi Petroleum Engineering Handbook Volume 1 Gen-eral Engineering Society of Petroleum Engineers 2006
[29] R Sakthivadivel and S Irmay A Review of Filtration TheoriesHydraulic Engineering Laboratory College of EngineeringUniversity of California Berkeley Calif USA 1996
[30] C Wang P Zhai Z Chen J Liu L Wang and J XieldquoExperimental study of coal matrix-cleat interaction underconstant volume boundary conditionrdquo International Journal ofCoal Geology vol 181 pp 124ndash132 2017
[31] S Irmay ldquoOn the theoretical derivation of Darcy and Forch-heimer formulasrdquo Eos Transactions American GeophysicalUnion vol 39 no 4 pp 702ndash707 1958
[32] CH Lee and IW Farmer ldquoA simplemethod of estimating rockmass porosity and permeabilityrdquo International Journal ofMiningand Geological Engineering vol 8 no 1 pp 57ndash65 1990
[33] C Nalluri A K El-Zaemey and H L Chan ldquoSedimenttransport over fixed deposited beds in sewers - An appraisal ofexisting modelsrdquoWater Science and Technology vol 36 no 8-9pp 123ndash128 1997
[34] P Novak and C Nalluri ldquoSediment transport in smooth fixedbed channelsrdquo Journal of the Hydraulics Division vol 101 no 9pp 1139ndash1154 1975
[35] T Fukuzono ldquoA newmethod for predicting the failure time of asloperdquo in Proceedings of the In 4th International Conference andField Workshop on Landslides Tokyo Japan 1985
[36] C R J Kilburn andDN Petley ldquoForecasting giant catastrophicslope collapse lessons from Vajont Northern Italyrdquo Geomor-phology vol 54 no 1-2 pp 21ndash32 2003
[37] B Voight ldquoA method for prediction of volcanic eruptionsrdquoNature vol 332 no 6160 pp 125ndash130 1988
[38] B Yao X Mao J Wei and D Wang ldquoStudy on coupled fluid-solid model for collapse columns considering the effect ofparticle transportrdquo Zhongguo Kuangye Daxue XuebaoJournalof China University of Mining and Technology vol 43 no 1 pp30ndash35 2014
[39] H Bai Seepage Characteristics of Top Stratum of OrdovicianSystem and Its Application Study as Key Aquifuge ChinaUniversity of Mining amp Technology Xuzhou China 2008
[40] C A Tang L G Tham P K K Lee T H Yang and L CLi ldquoCoupled analysis of flow stress and damage (FSD) in rockfailurerdquo International Journal of Rock Mechanics and MiningSciences vol 39 no 4 pp 477ndash489 2002
[41] W C Zhu and C A Tang ldquoMicromechanical model forsimulating the fracture process of rockrdquo Rock Mechanics andRock Engineering vol 37 no 1 pp 25ndash56 2004
[42] T H Yang L G Tham C A Tang Z Z Liang and YTsui ldquoInfluence of heterogeneity of mechanical properties onhydraulic fracturing in permeable rocksrdquo Rock Mechanics andRock Engineering vol 37 no 4 pp 251ndash275 2004
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Submit your manuscripts atwwwhindawicom
4 Geofluids
o a + b
a + b
x3
x2
x1
(M1 + N1) L2
(M2 + N2) L2
(M1 +M1
x1
L) L2 + (N1 +N1
x1
L) L2
(M2 +M2
x2
L) L2 + ((N2 +N2
x2
L) L2
Figure 6 Illustration of a three-dimensional characteristic element in a KCP 119872119894 and 119873119894 are mass change of solids due to convection anddiffusion respectively defined as 119872119894 = 119862120588119904119902119894 119873119894 = minus119863(120597(119862120593120588119904)120597119909119894)
223 Mass Conservation Equations for Particles In order tostudy the migration characteristics of the infilling particlesthe dynamic mass conservation equations for particles werecalculated based on a three-dimensional representative ele-ment as illustrated in Figure 6
Infilling particles migration inside a representative ele-ment under erosion effects is affected by both convection andprocesses The average seepage velocity of an element can bedefined as997888rarr119902 119894 (ms) For the convection and diffusion processin the direction of 119909119894 (119894 = 1 2 3) the mass losses of particlesflowing out of the element in a unit time can be calculated by(3) and (4) respectively
120597 (119862120588119904119902119894)120597119909119894 119881 (3)
minus 120597120597119909119894 [119863 120597 (119862120593120588119904)120597119909119894 ] 119881 (4)
where 119862 () is the particle concentration (ie particlesaturation) 120588119904 (kgm3) denotes the density of solid particlesand 119863 (m2s) illustrates the particles diffusion coefficient
In the direction of 119909119894 the mass flowing into the elementdue to the convection-diffusion should be expressed as
120597119872119894120597119909119894 119881 + 120597119873119894120597119909119894 119881 (119894 = 1 2 3) (5)
For the element the total mass flowing can be expressedas the summation of the three directions
3sum119894=1
( 120597119872119894120597119909119894 119881 + 120597119873119894120597119909119894 119881) (6)
Under the effects of erosion the mass loss of the elementin a unit time can be summarized as
minus 120597120597119905 (119862120593120588119904) 119881 + 119881 (7)
where (kgm3s) is the particle mass that migrates into thefluid from a unit element in a unit time and is written as
= 120597120593120597119905 120588119904 (8)
According to the mass conservation law for the unit ele-ment (6) and (7) are equivalent giving themass conservationequation for particles as
minus 120597120597119905 (119862120593120588119904) 119881 + 119881 = 3sum
119894=1
( 120597119872119894120597119909119894 119881 + 120597119873119894120597119909119894 119881) (9)
Substituting (2) into (9) yields
[ 3119886
120597 (119887119862)120597119905 + 120597 (119862120601)
120597119905 ] + nabla sdot (119862997888rarr119902 ) minus nabla
sdot 119863nabla sdot [119862 ( 3119887119886 + 120601)] = ( 3
119886120597119887120597119905 + 120597120601
120597119905 ) (10)
As particle sizes are normally several orders of magnitudesmaller than the fracture aperture the diffusion effect can beneglected Equation (10) can therefore be simplified into
[ 3119886
120597 (119887119862)120597119905 + 120597 (119862120601)
120597119905 ] + nabla sdot (119862997888rarr119902 ) = ( 3119886
120597119887120597119905 + 120597120601
120597119905 ) (11)
224 Water Mass Conservation Equations For the waterflow the mass flowing out of the element in the direction of119909119894 (119894 = 1 2 3) can be expressed as
120597 [(1 minus 119862) 120588119891119902119894]120597119909119894 119881 (119894 = 1 2 3) (12)
where 120588119891 (kgm3) denotes the density of the fluid The massloss of the fluid in the element in a unit time can be calculatedas
minus 120597120597119905 [(1 minus 119862) 120593120588119891] 119881 (13)
By combining (2) (3) (12) and (13) the mass conserva-tion equation for water flow can be derived as
3119886
120597 [119887 (1 minus 119862)]120597119905 + 120597 [(1 minus 119862) 120601]
120597119905 + nabla sdot [(1 minus 119862) 997888rarr119902 ]= 0
(14)
Geofluids 5
225 Evolution of the Fracture Aperture and Porosity Rockporosity plays an important role in determining rock per-meability so full understanding of its evolution is essentialto study the seepage characteristics of KCPs Sakthivadiveland Irmay [29] investigated the erosion problem for porousmedia by using both experimental and theoretical methodsVardoulakis et al [17] summarized the studies on porousmedia erosion and according to that study the evolutionof fracture aperture and permeability was affected by theporosity and particles concentration as well as the seepagevelocity The following equations have been developed todetermine the evolution of fracture aperture and porosity[17]
120597119887120597119905 = 1205821120588119904 (119887max minus 119887) 119862 10038161003816100381610038161199021003816100381610038161003816 120597120601120597119905 = 1205822120588119904 (120601max minus 120601) 119862 10038161003816100381610038161199021003816100381610038161003816
(15)
where 1205821 and 1205822 are constant |119902| = radic11990221 + 11990222 + 11990223 is theabsolute value of the seepage velocity (ms) and 119887max and120601max illustrate the maximum value that fracture aperture andporosity can reach under fluid erosion
Equations (15) indicate that the porosity evolution isproportional to the particle concentration as well as theseepage velocity
226 Water Seepage Fluid transport in porous media isnormally described by Darcyrsquos law which is derived (a) frombalance of momentum for the fluid phase and (b) from aconstitutive equation for the fluid-solid interaction force (iethe seepage force) [30] In general the balance of linearmomentum for the fluid phase has the form [31]
minus 120597119901120597119909119894 = minus 120578
119896 119902119894 + 120588119891 120597120597119905 ( 119902119894120593 ) (16)
where 119901 denotes the pore pressure (Pa) 120578 is the dynamicviscosity of the fluid (Pasdots) and 119896 illustrates the permeabilityof the volumetric element (m2) For this study the flowvelocity is relatively low thereby the acceleration term canbe neglected giving
997888rarr119902 = minus 119896120578 (nabla119901 + 120588119891119892nabla119911) (17)
where 997888rarr119902 is the Darcy velocity (ms) and nabla119911 is the unit vectorin the direction of gravity For fractured porous media 119896 isthe sum of fracture permeability and porosity permeability(m2) which can be expressed as [32]
119896 = 119896119898 + 119896119891 = 1198961198980 ( 1206011198981206011198980)3 ( 1 minus 12060111989801 minus 120601119898 )2 + 1198873
12119886 (18)
in which 119896119898 = 1198961198980(1206011198981206011198980)3((1 minus 1206011198980)(1 minus 120601119898))2 and119896119891 = 119887312119886 represent the porosity permeability and fracturepermeability respectively
Equations (2) (11) (14) (15) and (17) together with (18)compose the coupled processes of water transport of KCPs
Waterseepage
Particlestransport
Fractureporosityevolution
KCP
C
C
q
q
b b
Figure 7 Coupling process among each physics
under erosion effects as illustrated in Figure 7 The abovegoverning equations will be implemented into COMSOLMultiphysics next to understand water inrush mechanism inKCPs to evaluate water inrush risks and to predict waterinrush time under different rock and flow conditions Thereare six unknowns with equations so the set of governingequations can provide a unique solution
In petroleum engineering generally there is a criticalvelocity associated with sand production in oil and gasreservoirs However for the particle movements in KCPs thecritical velocitywas not considered because (1) the sizes of theinfilling particles are significantly smaller than the fractureapertures (120583m versus mm) (2) the movement of the erodedmaterials does not require a critical pressure gradient (or flowvelocity) for most KCP infilling materials are soluble to waterforming diluted solution and (3) the fluid flow inside KCPsis generally much greater than the critical velocity of around0ndash77mms for the particle size of 1ndash10 120583m [33 34]
23 Inverse Velocity Theory The inverse velocity theory wasoriginally proposed by Fukuzono [35] based on experimentalstudies This theory was initially used to predict the failuretime of a solid material that experiences slow continuousdeformation (ie creep) When the reciprocal of the defor-mation velocity (ie the inverse velocity) is plotted as afunction of time its value approaches zero as the velocityincreases asymptotically towards failureThe trend line of theinverse velocity intersects with the abscissa which representstime and the intersectional point can predict the time offailure There are three types of trend line namely concavelinear and convex as shown in Figure 8
The following equation is used to define the envelope
119881minus1 = [119860 (120572 minus 1)]1(120572minus1) (119905119891 minus 119905)1(120572minus1) (19)
where 119881 is the inverse velocity (ms) 119860 and 120572 are constants119905119891 is the time of failure and 119905 is the time of cutoff or the mostrecent time of themonitoring dataThe inverse velocity curveis concave when 120572 lt 2 and it is linear when 120572 = 2 while it isconvex when 120572 gt 2 Fukuzono [35] indicated that a linear fitcould provide a reasonable prediction of failure time
The inverse velocity theory has been successfully used insoils rocks and other materials and has been proved to be
6 Geofluids
Time
Failure
a gt2 (convex)a = 2 (linear)
a lt 2 (concave)
Inve
rse v
eloci
ty (1
V)
Figure 8 Inverse velocity trend lines to predict the time of failure[27]
Water flowInverse velocityLinear fitting
0
200
400
600
800
1000
1200
1400
1600
Flow
rate
(Ｇ3h
)
0
0002
0004
0006
0008
001
0012
0014
0016
0018
002In
vers
e velo
city
(hＧ
3)
5 10 15 200Time (h)
Water inrush point
Figure 9 Verification of the inverse velocity theory in predictingwater inrush
reliable in estimating the failure time using the linear fittingcurve [36 37]Therefore in thiswork this theory (ie inversefluid flow velocity) is adopted as the first attempt to predictwater inrush in KCPs
In order to verify the applicability of theory to waterinrush the field monitoring data from Yao et al [38] and Bai[39] was used and the comparison of inrush time betweenreal data and predicted time using inverse velocity theorywas conducted The results were plotted in Figure 9 It can beseen that the predicted inrush time matches the actual waterinrush time very well which proves that this theory can beused to predict water inrush for KCPs
3 Numerical Model Implementation
31 Background of the Coal Mine In this section a case studywas conducted based on the hydrogeological conditions of
Goaf
Hau
lage
rise
Coal haulage roadway
Ventilation roadway
Miningadvance
KCP
Railw
ay ri
se
KCP
Figure 10 Illustration of number 10-106 longwall panel and KCP inTuanbai coal mine of Shanxi province China
the Tuanbai Coalmine which is affiliatedwithHuozhouCoalElectricity Group of China The mine is located in TuanbaiCounty Linfen City Shanxi Province as marked in blue inFigure 2 The mining operation is current extracting number10 coal seam at approximately 300m depth To date 97 KCPshave been found during the mining operations at this seamThese KCPs included rock blocks of different sizes and inmost cases mud infillings and sizes of KCPs varied from tensto hundreds of meters In addition some had low level ofcompaction and cementation and relatively high infiltrationcapabilities
Since the distance between number 10 coal seam and theOrdovician limestone was only about 35m (as illustrated inFigure 13(a)) themining operation is being carried out underpressure from the Ordovician limestone water of the floorThe water pressure was found to be about 2MPa This minehas suffered a number of water inrush accidents associatedwith the KCPs For instance one accident occurred on thebelt roadway of the first longwall panel in 2007 with a waterflow rate of nearly 470m3h In addition there were a numberof water inrush accidents on longwall panels such as 10-106 asshown in Figure 10 10-112 and 10-114 at a rate of range from40m3h to 150m3h in 2010 resulting in the submergenceof the longwall panels Later investigation of these incidentsrevealed that all were directly caused by the KCPs whichacted as water channels with the confined water serving asthe source
32 Characterisation of the Infilling Materials In KCPs thecomposition of the infillings and their particle size distri-bution (PSD) have been found to be highly relevant to themigration of the particles For this reason two samples (iesample 1 and sample 2) were collected from the Tuanbai coalmine and the X-ray diffraction phase analysis (compositionanalysis) was carried out on the infillingmaterials of theKCPsas well as the PSD characteristics The results are shown inFigures 11 and 12
The composition analysis (as shown in Figure 11) indi-cated that the infilling materials mainly included kaolin-ites quartz illite smectite mixed layers small quantities offeldspars montmorillonites chlorites calcites siderites and
Geofluids 7
402
281
93
108
14
4231
05 05
19
KaoliniteQuartzIlliteIllite-smectiteSmectite
ChloriteFeldsparCalciteSideriteOthers
(a)
465
198
137
125
24
00
1304
19
15
KaoliniteQuartzIlliteIllite-smectiteSmectite
ChloriteFeldsparCalciteSideriteOthers
(b)
Figure 11 (a) Mineral components of infilling materials for Sample 1 and (b) mineral components of infilling materials for Sample 2
0
20
40
60
80
100
Cum
ulat
ive (
)
0
5
10
15
20
25
30
35
40
Freq
uenc
y (
)
001 01 1 100001Size (mm)
FrequencyCumulative
(a)
FrequencyCumulative
0
20
40
60
80
100
Cum
ulat
ive (
)
0
5
10
15
20
25
30
35
40
Freq
uenc
y (
)
001 01 1 100001Size (mm)
(b)
Figure 12 Particle size distribution (PSD) of infilling materials (a) Sample 1 (b) Sample 2
other mineral compositions The PSD results (Figure 12)showed that the particle sizes varied from 1 120583m to a few mmfor both Samples 1 and 2 with majority spanning from 10120583m to 1mm This could be a result of long-term weatheringbut the weak and unfavorable rock properties observed inthe field indicate that KCPs are very fractured and loose instructure with low strength high permeability being proneto water erosion and the water inrush risks
33 Numerical Model Setup Although diverse in geometryKCPs are usually presented similarly to a dome shape [9]Each of these approximates a 3D axisymmetric model whichcan be simplified as a 2D symmetrical model
In this work according to the lithology of the mine thebottom diameter top diameter and height are 15m 10m and20m respectively (as shown in Figure 13) The pressure atthe water inlet on the lower boundary was 20MPa and the
8 Geofluids
Description LithologyThickness (m)
11 coal
Limestone
Mudstone
Fine sandstone
Aquifer
10 coal
Limestone
Mudstone
30
25
73
33
46
200
358
Mudstone
9 coal
89
05
96
(a) (b) (c)
times10minus4
05
06
07
08
09
1
11
12
13
14
Figure 13 Model geometry and setup (a) illustration of KCP and rock strata (b) 2D simulation model and (c) distribution of apertureopening based on Weibull function
pressure at the water outlet on the top was 01MPa initialwater pressure in the model was 01MPa initial particle vol-ume concentration was 001 initial average fracture aperture1198870 was 01mm and initial porosity 1206010 was 10 The mainparameters of the model were all determined according tothe relevant references [3 12] in which the studies wereconducted on the same seam Other used parameters arelisted in Table 1Themodel was divided into 5000 grids usingmapped mesh method embedded in the COMSOL softwareThe shape of the grids is rectangular
Heterogeneity has been determined to be a prominentfeature of rock There are currently various approaches toobtaining the characteristics of the heterogeneous distribu-tion of rock materials For example digital core techniquesand mathematical statistics methods have both been utilizedPrevious studies have shown that the heterogeneity of rockcan be described by the Weibull distribution [40ndash42] Thusthe Weibull distribution was selected in this study due to itseffectiveness and great simplicity to obtain the heterogeneousdistribution of fracture apertures of the KCPs The distribu-tion probability density equation was as follows
119891 (119887) = 1198981198870 ( 119887
1198870)119898minus1
exp [minus ( 1198871198870)119898] (20)
where 119887 indicates the fracture aperture 1198870 denotes the initialfracture aperture and 119898 is the uniformity index The larger119898 represents the higher level of uniformity The fractureaperture distribution obtained by the numerical generationmethod is shown in Figure 13(c)
Based on thismodel geometry (9) (11) (14) (15) (17) and(18) will be solved simultaneously to investigate the dynamicchange of water flow behaviors and the associated inrush riskunder different flow conditions
4 Results and Analysis
In order to analyze the characteristics of seepage at differenttimes in this study six different moments were selected (ie14 times 103 15 times 103 16 times 103 17 times 103 175 times 103 and 18 times 103 s)The specific results will be discussed below
41 Distribution of the Fracture Apertures Figure 14 illus-trates the spatial changes of the fracture apertures at differenttimes Figure 15 shows the evolution of fracture aperturesalong O-O10158401015840 and O1015840-A1015840 lines as marked in Figure 13(b)and the average fracture aperture-time curve was plotted inFigure 16 The results show the following(1) The fracture aperture gradually increases under theeffects of the erosion However the increase rate is higherin the upper part of the model than in the lower part Thisis likely because the upper outlet boundary is narrower thanthe bottom inlet boundary giving rise to higher flow velocitySuch higher velocity causes more significant erosion andconsequently the fracture aperture change is faster(2) As the infiltration continues the average fractureaperture increases by approximately 200 from 01mm tonearly 03mm (Figure 16) At the initial stage the fracture issubject to random distribution with minor difference in theapertures However the variation diverges under the effectsof the erosion The fractures with smaller initial aperturesbecome slowly enlarged by approximately 20 while thosewith larger apertures continuously increase by more than200 As the fractures gradually dilate and interconnectwith each other a number of dominant seepage channels areformed as illustrated in Figure 14(f)
42 Distribution of Water Seepage Velocity The seepagevelocities (ie Darcy velocity) in the model domain andalong O-O10158401015840 and O1015840-A1015840 lines were shown in Figures 17 and
Geofluids 9
Table 1 Input parameters for the numerical simulation
120588119904(kgm3) 120578(Pasdots) 1198961198980(m2) 1206010 1198870(m) 119886 1205821(mminus1) 1205822(mminus1) 119898 11986202000 10minus3 10minus12 01 00001 001 001 001 6 001
1
2
3
4
5
6
7
(a) 14000 s
1
2
3
4
5
6
7
(b) 15000 s
1
2
3
4
5
6
7
(c) 16000 s
1
2
3
4
5
6
7
(d) 17000 s
1
2
3
4
5
6
7
(e) 17500 s
1
2
3
4
5
6
7
(f) 18000 s
Figure 14 The spatial distribution of aperture 119887 (10minus4m ) at different times
18 respectively The predicted failure time using the inversevelocity theory was plotted in Figure 19The key observationsinclude the following(1) As shown in Figure 17 the changes in the flowvelocity are consistent with the distribution of the fractures(Figure 14) and more fracture aperture changes are observedat the locations where higher seepage velocities take place Asshown in Figure 18 at 14times 104 s theminimumandmaximumseepage velocities were approximately 35 times 10minus6ms and 411times 10minus5ms At 18 times 104 s these two figures increased by 20and 200 to 42 times 10minus6ms and 125 times 10minus3ms respectively(2)Therewas a continuous increase in flow rate at the out-let from approximately 37m3 h initially to approximately100m3 h at 18times 104 s increased by nearly 30 times Howeverits increase showed a nonlinear trend likely due to the fact
that the increase rate was relatively slow in the initial stagebut accelerated gradually until the water inrush occurredFigure 19 was generated according to the inverse velocitytheory and the results showed that the water inrush wouldoccur at 185 times 104 s for this particular flow condition Thetrend has been reflected by the change in flow velocity shownin Figure 17 The figure shows that shortly before the inrushthe flow channels rapidly connected together and formed amain channel resulting in a surge in water flow
43 Distribution of the Particle Concentrations Particle con-centration is directly related to the erosion rate Higherparticle concentration indicates more severe erosion whichis more likely to result in greater fracture aperture change
10 Geofluids
05
15
25
35
45
55
65Fr
actu
re ap
ertu
reb
(times10
minus4
m)
5 10 15 200z (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
(a)
1 2 3 4 5 6 70r (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
05
15
25
35
45
55
65
Frac
ture
aper
ture
b(times
10minus4
m)
(b)
Figure 15 Evolution of fracture aperture along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
1
15
2
25
3
Frac
ture
aper
ture
b(times
10minus4
m)
5 10 15 200Time (times103 s)
Figure 16 Change of average fracture aperture with time
Figure 20 shows the evolution of the average particleconcentration along O-O10158401015840 and O1015840-A1015840 lines The averageparticle concentration and particle loss rate was plotted inFigure 21
Figure 20 plots the spatial distribution of the particleconcentrations for the wholemodel at different times Resultsshow that the particle concentration gradually increasesfrom the bottom upwards This is because under the effectsof the erosion increasing amount of particles migratedinto the water and gradually moved upwards through thefractures and pores This is consistent with the change inthe particle concentration at different locations as shown inFigure 21
Results in Figure 22 are well in line with the results shownin Figure 18 For example at the beginning the particle lossrate is relatively low however the rate constantly increasesover time and culminates at the inrushThis is due to the fact
that along with the increases in the seepage velocities theerosion effects on the solid particles are constantly intensifiedwhich results in frequent migration and substantial particleloss
44 Sensitivity Analyses The outburst processes wereaffected or controlled by various factors including thespatial heterogeneity of lithology of the KCPs waterpressure absolute aperture and distribution of the fracturesdistribution law of concentration of the karst particlesand their sensitivity to water erosion Based on the newlydeveloped coupling model this work further examined thewater and particle migration characteristics in the KCPsunder different hydrological and geological conditionsas well as the variations in the inrush occurrences Thescenarios to be studied are summarized in Table 2
Geofluids 11
2
16
12
08
04
0(a) 14000 s
2
16
12
08
04
0(b) 15000 s
2
16
12
08
04
0(c) 16000 s
2
16
12
08
04
0(d) 17000 s
2
16
12
08
04
0(e) 17500 s
2
16
12
08
04
0(f) 18000 s
Figure 17 The change of seepage velocity (10minus3ms) in a KCP
14000 s15000 s16000 s
17000 s17500 s18000 s
r (m)
1 2 3 4 5 6 70
Velo
city
(10minus
3m
s)
14
12
1
08
06
04
02
0
(a)
14000 s15000 s16000 s
17000 s17500 s18000 s
50 10z (m)
15 20
Velo
city
(10minus
3m
s)
14
12
1
08
06
04
02
0
(b)
Figure 18 Evolution of seepage velocity along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
12 Geofluids
Inverse velocityLinear fitting
0
20
40
60
80
100
Flow
rate
(m3h
)
0
5
10
15
20
25
30
Inve
rse v
eloci
ty (h
m)
5 10 15 200Time (times103 s)
Q
Figure 19 Water flow rate along the bottom surface of the numerical model
025
02
03
015
01
005
0(a) 14000 s
025
02
03
015
01
005
0(b) 15000 s
025
02
03
015
01
005
0(c) 16000 s
025
02
03
015
01
005
0(d) 17000 s
025
02
03
015
01
005
0(e) 17500 s
025
02
03
015
01
005
0(f) 18000 s
Figure 20 Change of particles concentration in a KCP
Geofluids 13
0
005
01
015
02
025
03
035C
once
ntra
tion
1 2 3 4 5 6 70r (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
(a)
105 15 200z (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
0
005
01
015
02
025
03
035
Con
cent
ratio
n (b)
Figure 21 Evolution of particle concentration along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
ConcentrationLoss rate
0
005
01
015
Con
cent
ratio
n
5 10 15 200Time (times103 s)
0
5
10
15
20
25
Part
icle
loss
rate
Qp
(m3h
)
Figure 22 Evolution of average particle volumetric concentrationand particle loss rate
441 Impact of Heterogeneity on Fractures Evolution Fig-ure 23 illustrates the distribution law of the fractures seepagevelocities and particle volume concentrations under identicalflow pressures but different fracture distribution conditionsat 175 times 103 seconds The results show that more intercon-nected fractures are developed along with the increase in mvalues For example when119898 = 4 there are only two intercon-nected fractures However asm value increases an increasingnumber of fractures were generated and interconnected Inthe fourth case (119898 = 10) three interconnected fractures weregenerated This finding indicates that the homogeneity canaccelerate the propagation of the fractures An increase in
Table 2 List of simulation scenarios
Parameter Value
Weibull distribution coefficient (-)
119898 = 4119898 = 6119898 = 8
119898 = 10
Water pressure (MPa)
119901 = 10119901 = 20119901 = 30119901 = 40
Initial particle concentration ()
1198620 = 00051198620 = 0011198620 = 0021198620 = 005
Fracture aperture (times10minus4m)
119887 = 075119887 = 10
119887 = 125119887 = 15
flow velocity and particle concentration with increasing mvalues was also observed as shown in Figures 23(b) and 23(c)
442 Prediction of Water Inrush under Different ConditionsThe analysis and prediction of the occurrences of waterinrush in KCPs based on the changes in seepage are essentialfor the safety of mining processes Some researchers haveadopted catastrophe theories to predict the occurrences ofwater inrush However an approach that can be used topredict water inrush based on water flow has yet to be foundin the literature This study presents the first attempt toresolve this challenge by applying the inverse velocity theory
14 Geofluids
m = 4 m = 6 m = 8 m = 10
1
2
3
4
5
6
7
(a) Distribution of aperture 119887 (times10minus4m )
m = 4 m = 6 m = 8 m = 10
2
16
12
08
04
0
(b) Distribution of seepage velocity (times10minus3ms)
m = 4 m = 6 m = 8 m = 10
025
02
03
015
01
005
0
(c) Distribution of particles concentration
Figure 23 Distribution of fracture seepage velocity and particle concentration at different Weibull distribution conditions (a) Impact ofWeibull distribution on fractures evolution (b) impact of Weibull distribution on water velocity evolution (c) impact of Weibull distributionon particle concentration evolution
Geofluids 15
5 10 15 200Time (times103 s)
m = 4
m = 6 m = 10
m = 8
0
20
40
60
80
100
120Fl
ow ra
te (m
3h
)
(a)
205
21
215
22
225
23
Wat
er in
rush
tim
e (times10
3s)
4 6 8 102Weibull coefficient m
y = 25699xminus0089
R2 = 09825
(b)
Figure 24 Impact of heterogeneity on water flow rate (a) and inrush time (b)
0
20
40
60
80
100
120
140
160
180
200
Flow
rate
(m3h
)
5 10 15 200Time (times103 s)
p = 1MPap = 2MPa
p = 3MPap = 4MPa
(a)
y = 41733xminus1001
R2 = 09992
1 2 3 4 50Water pressure (MPa)
0
5
10
15
20
25
30
35
40
45
Wat
er in
rush
tim
e (times10
3s)
(b)
Figure 25 Impact of aquifer water pressure on water flow rate (a) and inrush time (b)
which has been widely approved effective in many fields suchas slope stability predictionThe relevant results and analysesare shown in Figure 24ndashFigure 27
As shown in Figure 24 water flow rate exhibits a non-linear increase and as the value of m increases the seepagerate accelerates gradually For example at 119905 = 15 times 104 s theseepage rate was approximately 15m3h for 119898 = 4 while itjumped to 25m3h for 119898 = 10 Results from Figure 24(b)show that water inrush occurs sooner for a greater 119898 valueIn other words the inrush occurs earlier as the heterogeneityincreases The water inrush time follows the power functionThis is due to the fact that the water is more prone to flowingthrough the existing fractures (which indicates a higher
permeability) in the heterogeneous structure Neverthelessdue to the heterogeneous distribution of the aperture thefractures cannot be easily interconnected which hampers theformation of the seepage channels In regard to the homo-geneous rock strata since the flow of water was dominantlycontrolled by the pressure gradient the fractures generatedduring the process of erosion could be easily interconnectedand as a result the water inrush occurredsooner
Figure 25 illustrates the impact of the initial KCPrsquos waterpressure on the flow rates and water inrush time It can beseen that as the pressure increases the changes in the flowrates accelerate For example for119901 = 2MPa the flow rate wasonly approximately 5m3h and it increased to 30m3h when
16 Geofluids
0
20
40
60
80
100
120
140
160
180
200Fl
ow ra
te (m
3h
)
5 10 15 20 250Time (times103 s)
c = 0005
c = 001
c = 002
c = 005
(a)
0
5
10
15
20
25
30
35
Wat
er in
rush
tim
e (times10
3s)
001 002 003 004 0050Initial particle concentration
y = 13554xminus0591
R2 = 09975
(b)
Figure 26 Impact of initial particle concentration on water flow rate (a) and inrush time (b)
0
20
40
60
80
100
120
140
160
180
200
Flow
rate
(m3h
)
5 10 15 200Time (times103 s)
075E minus 4m100E minus 4m
125E minus 4m150E minus 4m
(a)
y = 31027eminus286x
R2 = 09503
09 11 13 1507Fracture aperture (times10minus4 m)
0
5
10
15
20
25
30
35
40
Wat
er in
rush
tim
e (times10
3s)
(b)
Figure 27 Impact of absolute aperture on water flow rate (a) and inrush time (b)
119901 = 3MPa In addition with increasing the aquifer waterpressure the water inrush time was also brought forward asshown in Figure 25(a) The outburst time was approximately119905 = 40 times 104 s for p = 1MPa while only 10 times 104 s for119901 = 4MPa The relationship between the time of the inrushoccurrences and the aquifer water pressure follows the powerfunction as illustrated in Figure 25
For varying initial particle concentrations the evolutionof both the water flow rate change and the water inrushtime shows a similar trend to that of different aquifer waterpressures The flow rate accelerates with increasing initialparticle concentration and consequently the water inrushoccurs earlier as shown in Figure 26The outburst times alsoshow a power function to the initial particle concentration
The initial average fracture aperture also shows significantimpact on water flow behavior For instance results fromFigure 27 clearly illustrate that the flow rate increases withincreasing initial average fracture aperture Please note thatthe inrush time follows an exponential function to the initialaverage fracture aperture
These numerical results can be explained by the factthat the initial seepage velocity is expected to be higher forthe modelling cases with the higher initial aquifer pressureinitial fracture aperture andor initial particle concentrationThe higher flow velocity would intensify the erosion of thefractures enhance the permeability and thereby acceleratethe migration of the particles and interconnection of seepagechannels which causes water inrush
Geofluids 17
5 Conclusions
In this study a systematic approach was established to inves-tigate the impact of controlling factors onwater flow behaviorfor KCPs and to predict water inrush time by introducing theinverse velocity theory In this approach a suite of governingequations was developed to couple all the physics involvedin this complex process including water flow rock erosionand change in rock microstructure These equations werethen implemented into a finite element software COMSOLMultiphysics to simulate the fully coupled process Basedon this numerical model a series of sensitivity studies wereconducted and some important findings have been drawn
(i) Water flow rate increases with increasing aquiferpressure initial particle concentration and fractureopening This results in an increase in the permeabil-ity and finally an acceleration of the migration of theparticles and interconnection of the seepage channelsThis finding suggests the grouting of the KCPs couldbe an effective measure to mitigate water inrush risk
(ii) The inverse velocity theory was successfully appliedto analyze the occurrences of water inrush underdifferent conditions The results show that the timeof inrush has a power relationship to the rock het-erogeneity water pressure and initial particle concen-tration and follows an exponential relationship to theinitial fracture apertures
The framework developed from this work not only helpsenhance coal mining operations safety by better under-standing and predicting water inrush risks so that propermitigation measures can be put in place timely It canalso be extended to other fields such as tunneling backfillpaste piping tailing dam erosion and other engineeringapplications which are likely to encounter time-dependenterosion or deformation or water inrush issues
Please be noted that there are a number of other stochasticmethods available in the literature that can be used to illus-trate rock heterogeneity such as the Monte-Carlo methodor First-Order approach The differences of these methodson the results of water inrush prediction may be worthcomparing in the near future
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This project is supported by the National Natural ScienceFoundation of China (nos 51304072 51774110) the Programfor Innovative Research Team in University of Ministryof Education of China (IRT 16R22) and the PostdoctoralScience Foundation of China (2017M612398)
References
[1] DMa XMiao H Bai et al ldquoEffect of mining on shear sidewallgroundwater inrush hazard caused by seepage instability of the
penetrated karst collapse pillarrdquo Natural Hazards vol 82 no 1pp 73ndash93 2016
[2] H Keqiang Y Guangming and L Yaoru ldquoPalaeo-karst collapsepillars in northern China and their damage to the geologicalenvironmentsrdquo Environmental Geology vol 58 no 5 pp 1029ndash1040 2009
[3] B Yao J Wei D Wang D Ma and Z Chen ldquoNumericalstudy on seepage property of karst collapse columns underparticle migrationrdquo CMES Computer Modeling in Engineeringamp Sciences vol 91 no 2 pp 81ndash100 2013
[4] J Tang H Bai B Yao and Y Wu ldquoTheoretical analysis onwater-inrush mechanism of concealed collapse pillars in floorrdquoMining Science and Technology vol 21 no 1 pp 57ndash60 2011
[5] Y Chen M Yi C Chen and C Yu ldquoBernstein polynomialsmethod for fractional convection-diffusion equation with vari-able coefficientsrdquoComputerModeling in Engineering amp Sciencesvol 83 no 6 pp 639ndash653 2012
[6] J Zhang and B Shen ldquoCoal mining under aquifers in China Acase studyrdquo International Journal of Rock Mechanics and MiningSciences vol 41 no 4 pp 629ndash639 2004
[7] D Ma H Bai X Miao H Pu B Jiang and Z ChenldquoCompaction and seepage properties of crushed limestoneparticle mixture an experimental investigation for Ordoviciankarst collapse pillar groundwater inrushrdquo Environmental EarthSciences vol 75 no 1 article 11 p 14 2016
[8] S Yin J Zhang and D Liu ldquoA study of mine water inrushesby measurements of in situ stress and rock failuresrdquo NaturalHazards vol 79 no 3 pp 1961ndash1979 2015
[9] H Bai D Ma and Z Chen ldquoMechanical behavior of ground-water seepage in karst collapse pillarsrdquo Engineering Geology vol164 pp 101ndash106 2013
[10] D Ma and H Bai ldquoGroundwater inflow prediction model ofkarst collapse pillar a case study for mining-induced ground-water inrush riskrdquoNatural Hazards vol 76 no 2 pp 1319ndash13342015
[11] D Ma H Bai and Y Wang ldquoMechanical behavior of a coalseam penetrated by a karst collapse pillar mining-inducedgroundwater inrush riskrdquo Natural Hazards vol 75 no 3 pp2137ndash2151 2015
[12] B Yao Research on variable mass fluid-solid coupling dynamictheory of broken rockmass and application China Univeristy ofMining and Technology Xuzhou China 2012
[13] D Ma X Miao H Bai et al ldquoImpact of particle transfer onflow properties of crushed mudstonesrdquo Environmental EarthSciences vol 75 no 7 article 593 2016
[14] DMa H Bai Z Chen andH Pu ldquoEffect of particlemixture onseepage properties of crushed mudstonesrdquo Transport in PorousMedia vol 108 no 2 pp 257ndash277 2015
[15] B Zhang H Bai and K Zhang ldquoSeepage characteristics ofcollapse columnfillingsrdquo International Journal ofMining Scienceand Technology 2015
[16] P Ortoleva J Chadam E Merino and A Sen ldquoGeochemicalself-organization II the reactive-infiltration instabilityrdquo Ameri-can Journal of Science vol 287 no 10 pp 1008ndash1040 1987
[17] I Vardoulakis M Stavropoulou and P Papanastasiou ldquoHydro-mechanical aspects of the sand production problemrdquo Transportin Porous Media vol 22 no 2 pp 225ndash244 1996
[18] R L Detwiler and H Rajaram ldquoPredicting dissolution patternsin variable aperture fractures Evaluation of an enhanced depth-averaged computational modelrdquoWater Resources Research vol43 no 4 Article IDW04403 2007
18 Geofluids
[19] M A Habib H M Badr R Ben-Mansour and M E KabirldquoErosion rate correlations of a pipe protruded in an abrupt pipecontractionrdquo International Journal of Impact Engineering vol34 no 8 pp 1350ndash1369 2007
[20] H T Xiao and H Y Xu ldquoIn situ permeability measurementsto establish the influence of slice mining on floor rocksrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 37 no 5 pp 855ndash860 2000
[21] H Guo D P Adhikary and M S Craig ldquoSimulation of minewater inflow and gas emission during longwall miningrdquo RockMechanics and Rock Engineering vol 42 no 1 pp 25ndash51 2009
[22] R Zhang Z JiangH ZhouC Yang and S Xiao ldquoGroundwateroutbursts from faults above a confined aquifer in the coalminingrdquo Natural Hazards vol 71 no 3 pp 1861ndash1872 2014
[23] B Yao F Du E Li and X Wang ldquoMechanical model of karstcollapse columns water inrush and its applicationrdquo ElectronicJournal of Geotechnical Engineering vol 19 pp 1665ndash1675 2014
[24] J Warren and P Root ldquoThe behavior of naturally fracturedreservoirsrdquo SPE Journal vol 3 no 3 pp 245ndash255 2013
[25] H KazemiM S Seth andGWThomas ldquoThe interpretation ofinterference tests in naturally fractured reservoirs with uniformfracture distributionrdquo SPE Journal vol 9 no 4 pp 463ndash4721969
[26] A de Swaan O ldquoAnalytical solutions for determining naturallyfractured reservoir properties by well testingrdquo SPE Journal vol16 no 3 pp 117ndash122 1976
[27] N D Rose and O Hungr ldquoForecasting potential rock slopefailure in open pit mines using the inverse-velocity methodrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 2 pp 308ndash320 2007
[28] J R Fanchi Petroleum Engineering Handbook Volume 1 Gen-eral Engineering Society of Petroleum Engineers 2006
[29] R Sakthivadivel and S Irmay A Review of Filtration TheoriesHydraulic Engineering Laboratory College of EngineeringUniversity of California Berkeley Calif USA 1996
[30] C Wang P Zhai Z Chen J Liu L Wang and J XieldquoExperimental study of coal matrix-cleat interaction underconstant volume boundary conditionrdquo International Journal ofCoal Geology vol 181 pp 124ndash132 2017
[31] S Irmay ldquoOn the theoretical derivation of Darcy and Forch-heimer formulasrdquo Eos Transactions American GeophysicalUnion vol 39 no 4 pp 702ndash707 1958
[32] CH Lee and IW Farmer ldquoA simplemethod of estimating rockmass porosity and permeabilityrdquo International Journal ofMiningand Geological Engineering vol 8 no 1 pp 57ndash65 1990
[33] C Nalluri A K El-Zaemey and H L Chan ldquoSedimenttransport over fixed deposited beds in sewers - An appraisal ofexisting modelsrdquoWater Science and Technology vol 36 no 8-9pp 123ndash128 1997
[34] P Novak and C Nalluri ldquoSediment transport in smooth fixedbed channelsrdquo Journal of the Hydraulics Division vol 101 no 9pp 1139ndash1154 1975
[35] T Fukuzono ldquoA newmethod for predicting the failure time of asloperdquo in Proceedings of the In 4th International Conference andField Workshop on Landslides Tokyo Japan 1985
[36] C R J Kilburn andDN Petley ldquoForecasting giant catastrophicslope collapse lessons from Vajont Northern Italyrdquo Geomor-phology vol 54 no 1-2 pp 21ndash32 2003
[37] B Voight ldquoA method for prediction of volcanic eruptionsrdquoNature vol 332 no 6160 pp 125ndash130 1988
[38] B Yao X Mao J Wei and D Wang ldquoStudy on coupled fluid-solid model for collapse columns considering the effect ofparticle transportrdquo Zhongguo Kuangye Daxue XuebaoJournalof China University of Mining and Technology vol 43 no 1 pp30ndash35 2014
[39] H Bai Seepage Characteristics of Top Stratum of OrdovicianSystem and Its Application Study as Key Aquifuge ChinaUniversity of Mining amp Technology Xuzhou China 2008
[40] C A Tang L G Tham P K K Lee T H Yang and L CLi ldquoCoupled analysis of flow stress and damage (FSD) in rockfailurerdquo International Journal of Rock Mechanics and MiningSciences vol 39 no 4 pp 477ndash489 2002
[41] W C Zhu and C A Tang ldquoMicromechanical model forsimulating the fracture process of rockrdquo Rock Mechanics andRock Engineering vol 37 no 1 pp 25ndash56 2004
[42] T H Yang L G Tham C A Tang Z Z Liang and YTsui ldquoInfluence of heterogeneity of mechanical properties onhydraulic fracturing in permeable rocksrdquo Rock Mechanics andRock Engineering vol 37 no 4 pp 251ndash275 2004
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Geofluids 5
225 Evolution of the Fracture Aperture and Porosity Rockporosity plays an important role in determining rock per-meability so full understanding of its evolution is essentialto study the seepage characteristics of KCPs Sakthivadiveland Irmay [29] investigated the erosion problem for porousmedia by using both experimental and theoretical methodsVardoulakis et al [17] summarized the studies on porousmedia erosion and according to that study the evolutionof fracture aperture and permeability was affected by theporosity and particles concentration as well as the seepagevelocity The following equations have been developed todetermine the evolution of fracture aperture and porosity[17]
120597119887120597119905 = 1205821120588119904 (119887max minus 119887) 119862 10038161003816100381610038161199021003816100381610038161003816 120597120601120597119905 = 1205822120588119904 (120601max minus 120601) 119862 10038161003816100381610038161199021003816100381610038161003816
(15)
where 1205821 and 1205822 are constant |119902| = radic11990221 + 11990222 + 11990223 is theabsolute value of the seepage velocity (ms) and 119887max and120601max illustrate the maximum value that fracture aperture andporosity can reach under fluid erosion
Equations (15) indicate that the porosity evolution isproportional to the particle concentration as well as theseepage velocity
226 Water Seepage Fluid transport in porous media isnormally described by Darcyrsquos law which is derived (a) frombalance of momentum for the fluid phase and (b) from aconstitutive equation for the fluid-solid interaction force (iethe seepage force) [30] In general the balance of linearmomentum for the fluid phase has the form [31]
minus 120597119901120597119909119894 = minus 120578
119896 119902119894 + 120588119891 120597120597119905 ( 119902119894120593 ) (16)
where 119901 denotes the pore pressure (Pa) 120578 is the dynamicviscosity of the fluid (Pasdots) and 119896 illustrates the permeabilityof the volumetric element (m2) For this study the flowvelocity is relatively low thereby the acceleration term canbe neglected giving
997888rarr119902 = minus 119896120578 (nabla119901 + 120588119891119892nabla119911) (17)
where 997888rarr119902 is the Darcy velocity (ms) and nabla119911 is the unit vectorin the direction of gravity For fractured porous media 119896 isthe sum of fracture permeability and porosity permeability(m2) which can be expressed as [32]
119896 = 119896119898 + 119896119891 = 1198961198980 ( 1206011198981206011198980)3 ( 1 minus 12060111989801 minus 120601119898 )2 + 1198873
12119886 (18)
in which 119896119898 = 1198961198980(1206011198981206011198980)3((1 minus 1206011198980)(1 minus 120601119898))2 and119896119891 = 119887312119886 represent the porosity permeability and fracturepermeability respectively
Equations (2) (11) (14) (15) and (17) together with (18)compose the coupled processes of water transport of KCPs
Waterseepage
Particlestransport
Fractureporosityevolution
KCP
C
C
q
q
b b
Figure 7 Coupling process among each physics
under erosion effects as illustrated in Figure 7 The abovegoverning equations will be implemented into COMSOLMultiphysics next to understand water inrush mechanism inKCPs to evaluate water inrush risks and to predict waterinrush time under different rock and flow conditions Thereare six unknowns with equations so the set of governingequations can provide a unique solution
In petroleum engineering generally there is a criticalvelocity associated with sand production in oil and gasreservoirs However for the particle movements in KCPs thecritical velocitywas not considered because (1) the sizes of theinfilling particles are significantly smaller than the fractureapertures (120583m versus mm) (2) the movement of the erodedmaterials does not require a critical pressure gradient (or flowvelocity) for most KCP infilling materials are soluble to waterforming diluted solution and (3) the fluid flow inside KCPsis generally much greater than the critical velocity of around0ndash77mms for the particle size of 1ndash10 120583m [33 34]
23 Inverse Velocity Theory The inverse velocity theory wasoriginally proposed by Fukuzono [35] based on experimentalstudies This theory was initially used to predict the failuretime of a solid material that experiences slow continuousdeformation (ie creep) When the reciprocal of the defor-mation velocity (ie the inverse velocity) is plotted as afunction of time its value approaches zero as the velocityincreases asymptotically towards failureThe trend line of theinverse velocity intersects with the abscissa which representstime and the intersectional point can predict the time offailure There are three types of trend line namely concavelinear and convex as shown in Figure 8
The following equation is used to define the envelope
119881minus1 = [119860 (120572 minus 1)]1(120572minus1) (119905119891 minus 119905)1(120572minus1) (19)
where 119881 is the inverse velocity (ms) 119860 and 120572 are constants119905119891 is the time of failure and 119905 is the time of cutoff or the mostrecent time of themonitoring dataThe inverse velocity curveis concave when 120572 lt 2 and it is linear when 120572 = 2 while it isconvex when 120572 gt 2 Fukuzono [35] indicated that a linear fitcould provide a reasonable prediction of failure time
The inverse velocity theory has been successfully used insoils rocks and other materials and has been proved to be
6 Geofluids
Time
Failure
a gt2 (convex)a = 2 (linear)
a lt 2 (concave)
Inve
rse v
eloci
ty (1
V)
Figure 8 Inverse velocity trend lines to predict the time of failure[27]
Water flowInverse velocityLinear fitting
0
200
400
600
800
1000
1200
1400
1600
Flow
rate
(Ｇ3h
)
0
0002
0004
0006
0008
001
0012
0014
0016
0018
002In
vers
e velo
city
(hＧ
3)
5 10 15 200Time (h)
Water inrush point
Figure 9 Verification of the inverse velocity theory in predictingwater inrush
reliable in estimating the failure time using the linear fittingcurve [36 37]Therefore in thiswork this theory (ie inversefluid flow velocity) is adopted as the first attempt to predictwater inrush in KCPs
In order to verify the applicability of theory to waterinrush the field monitoring data from Yao et al [38] and Bai[39] was used and the comparison of inrush time betweenreal data and predicted time using inverse velocity theorywas conducted The results were plotted in Figure 9 It can beseen that the predicted inrush time matches the actual waterinrush time very well which proves that this theory can beused to predict water inrush for KCPs
3 Numerical Model Implementation
31 Background of the Coal Mine In this section a case studywas conducted based on the hydrogeological conditions of
Goaf
Hau
lage
rise
Coal haulage roadway
Ventilation roadway
Miningadvance
KCP
Railw
ay ri
se
KCP
Figure 10 Illustration of number 10-106 longwall panel and KCP inTuanbai coal mine of Shanxi province China
the Tuanbai Coalmine which is affiliatedwithHuozhouCoalElectricity Group of China The mine is located in TuanbaiCounty Linfen City Shanxi Province as marked in blue inFigure 2 The mining operation is current extracting number10 coal seam at approximately 300m depth To date 97 KCPshave been found during the mining operations at this seamThese KCPs included rock blocks of different sizes and inmost cases mud infillings and sizes of KCPs varied from tensto hundreds of meters In addition some had low level ofcompaction and cementation and relatively high infiltrationcapabilities
Since the distance between number 10 coal seam and theOrdovician limestone was only about 35m (as illustrated inFigure 13(a)) themining operation is being carried out underpressure from the Ordovician limestone water of the floorThe water pressure was found to be about 2MPa This minehas suffered a number of water inrush accidents associatedwith the KCPs For instance one accident occurred on thebelt roadway of the first longwall panel in 2007 with a waterflow rate of nearly 470m3h In addition there were a numberof water inrush accidents on longwall panels such as 10-106 asshown in Figure 10 10-112 and 10-114 at a rate of range from40m3h to 150m3h in 2010 resulting in the submergenceof the longwall panels Later investigation of these incidentsrevealed that all were directly caused by the KCPs whichacted as water channels with the confined water serving asthe source
32 Characterisation of the Infilling Materials In KCPs thecomposition of the infillings and their particle size distri-bution (PSD) have been found to be highly relevant to themigration of the particles For this reason two samples (iesample 1 and sample 2) were collected from the Tuanbai coalmine and the X-ray diffraction phase analysis (compositionanalysis) was carried out on the infillingmaterials of theKCPsas well as the PSD characteristics The results are shown inFigures 11 and 12
The composition analysis (as shown in Figure 11) indi-cated that the infilling materials mainly included kaolin-ites quartz illite smectite mixed layers small quantities offeldspars montmorillonites chlorites calcites siderites and
Geofluids 7
402
281
93
108
14
4231
05 05
19
KaoliniteQuartzIlliteIllite-smectiteSmectite
ChloriteFeldsparCalciteSideriteOthers
(a)
465
198
137
125
24
00
1304
19
15
KaoliniteQuartzIlliteIllite-smectiteSmectite
ChloriteFeldsparCalciteSideriteOthers
(b)
Figure 11 (a) Mineral components of infilling materials for Sample 1 and (b) mineral components of infilling materials for Sample 2
0
20
40
60
80
100
Cum
ulat
ive (
)
0
5
10
15
20
25
30
35
40
Freq
uenc
y (
)
001 01 1 100001Size (mm)
FrequencyCumulative
(a)
FrequencyCumulative
0
20
40
60
80
100
Cum
ulat
ive (
)
0
5
10
15
20
25
30
35
40
Freq
uenc
y (
)
001 01 1 100001Size (mm)
(b)
Figure 12 Particle size distribution (PSD) of infilling materials (a) Sample 1 (b) Sample 2
other mineral compositions The PSD results (Figure 12)showed that the particle sizes varied from 1 120583m to a few mmfor both Samples 1 and 2 with majority spanning from 10120583m to 1mm This could be a result of long-term weatheringbut the weak and unfavorable rock properties observed inthe field indicate that KCPs are very fractured and loose instructure with low strength high permeability being proneto water erosion and the water inrush risks
33 Numerical Model Setup Although diverse in geometryKCPs are usually presented similarly to a dome shape [9]Each of these approximates a 3D axisymmetric model whichcan be simplified as a 2D symmetrical model
In this work according to the lithology of the mine thebottom diameter top diameter and height are 15m 10m and20m respectively (as shown in Figure 13) The pressure atthe water inlet on the lower boundary was 20MPa and the
8 Geofluids
Description LithologyThickness (m)
11 coal
Limestone
Mudstone
Fine sandstone
Aquifer
10 coal
Limestone
Mudstone
30
25
73
33
46
200
358
Mudstone
9 coal
89
05
96
(a) (b) (c)
times10minus4
05
06
07
08
09
1
11
12
13
14
Figure 13 Model geometry and setup (a) illustration of KCP and rock strata (b) 2D simulation model and (c) distribution of apertureopening based on Weibull function
pressure at the water outlet on the top was 01MPa initialwater pressure in the model was 01MPa initial particle vol-ume concentration was 001 initial average fracture aperture1198870 was 01mm and initial porosity 1206010 was 10 The mainparameters of the model were all determined according tothe relevant references [3 12] in which the studies wereconducted on the same seam Other used parameters arelisted in Table 1Themodel was divided into 5000 grids usingmapped mesh method embedded in the COMSOL softwareThe shape of the grids is rectangular
Heterogeneity has been determined to be a prominentfeature of rock There are currently various approaches toobtaining the characteristics of the heterogeneous distribu-tion of rock materials For example digital core techniquesand mathematical statistics methods have both been utilizedPrevious studies have shown that the heterogeneity of rockcan be described by the Weibull distribution [40ndash42] Thusthe Weibull distribution was selected in this study due to itseffectiveness and great simplicity to obtain the heterogeneousdistribution of fracture apertures of the KCPs The distribu-tion probability density equation was as follows
119891 (119887) = 1198981198870 ( 119887
1198870)119898minus1
exp [minus ( 1198871198870)119898] (20)
where 119887 indicates the fracture aperture 1198870 denotes the initialfracture aperture and 119898 is the uniformity index The larger119898 represents the higher level of uniformity The fractureaperture distribution obtained by the numerical generationmethod is shown in Figure 13(c)
Based on thismodel geometry (9) (11) (14) (15) (17) and(18) will be solved simultaneously to investigate the dynamicchange of water flow behaviors and the associated inrush riskunder different flow conditions
4 Results and Analysis
In order to analyze the characteristics of seepage at differenttimes in this study six different moments were selected (ie14 times 103 15 times 103 16 times 103 17 times 103 175 times 103 and 18 times 103 s)The specific results will be discussed below
41 Distribution of the Fracture Apertures Figure 14 illus-trates the spatial changes of the fracture apertures at differenttimes Figure 15 shows the evolution of fracture aperturesalong O-O10158401015840 and O1015840-A1015840 lines as marked in Figure 13(b)and the average fracture aperture-time curve was plotted inFigure 16 The results show the following(1) The fracture aperture gradually increases under theeffects of the erosion However the increase rate is higherin the upper part of the model than in the lower part Thisis likely because the upper outlet boundary is narrower thanthe bottom inlet boundary giving rise to higher flow velocitySuch higher velocity causes more significant erosion andconsequently the fracture aperture change is faster(2) As the infiltration continues the average fractureaperture increases by approximately 200 from 01mm tonearly 03mm (Figure 16) At the initial stage the fracture issubject to random distribution with minor difference in theapertures However the variation diverges under the effectsof the erosion The fractures with smaller initial aperturesbecome slowly enlarged by approximately 20 while thosewith larger apertures continuously increase by more than200 As the fractures gradually dilate and interconnectwith each other a number of dominant seepage channels areformed as illustrated in Figure 14(f)
42 Distribution of Water Seepage Velocity The seepagevelocities (ie Darcy velocity) in the model domain andalong O-O10158401015840 and O1015840-A1015840 lines were shown in Figures 17 and
Geofluids 9
Table 1 Input parameters for the numerical simulation
120588119904(kgm3) 120578(Pasdots) 1198961198980(m2) 1206010 1198870(m) 119886 1205821(mminus1) 1205822(mminus1) 119898 11986202000 10minus3 10minus12 01 00001 001 001 001 6 001
1
2
3
4
5
6
7
(a) 14000 s
1
2
3
4
5
6
7
(b) 15000 s
1
2
3
4
5
6
7
(c) 16000 s
1
2
3
4
5
6
7
(d) 17000 s
1
2
3
4
5
6
7
(e) 17500 s
1
2
3
4
5
6
7
(f) 18000 s
Figure 14 The spatial distribution of aperture 119887 (10minus4m ) at different times
18 respectively The predicted failure time using the inversevelocity theory was plotted in Figure 19The key observationsinclude the following(1) As shown in Figure 17 the changes in the flowvelocity are consistent with the distribution of the fractures(Figure 14) and more fracture aperture changes are observedat the locations where higher seepage velocities take place Asshown in Figure 18 at 14times 104 s theminimumandmaximumseepage velocities were approximately 35 times 10minus6ms and 411times 10minus5ms At 18 times 104 s these two figures increased by 20and 200 to 42 times 10minus6ms and 125 times 10minus3ms respectively(2)Therewas a continuous increase in flow rate at the out-let from approximately 37m3 h initially to approximately100m3 h at 18times 104 s increased by nearly 30 times Howeverits increase showed a nonlinear trend likely due to the fact
that the increase rate was relatively slow in the initial stagebut accelerated gradually until the water inrush occurredFigure 19 was generated according to the inverse velocitytheory and the results showed that the water inrush wouldoccur at 185 times 104 s for this particular flow condition Thetrend has been reflected by the change in flow velocity shownin Figure 17 The figure shows that shortly before the inrushthe flow channels rapidly connected together and formed amain channel resulting in a surge in water flow
43 Distribution of the Particle Concentrations Particle con-centration is directly related to the erosion rate Higherparticle concentration indicates more severe erosion whichis more likely to result in greater fracture aperture change
10 Geofluids
05
15
25
35
45
55
65Fr
actu
re ap
ertu
reb
(times10
minus4
m)
5 10 15 200z (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
(a)
1 2 3 4 5 6 70r (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
05
15
25
35
45
55
65
Frac
ture
aper
ture
b(times
10minus4
m)
(b)
Figure 15 Evolution of fracture aperture along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
1
15
2
25
3
Frac
ture
aper
ture
b(times
10minus4
m)
5 10 15 200Time (times103 s)
Figure 16 Change of average fracture aperture with time
Figure 20 shows the evolution of the average particleconcentration along O-O10158401015840 and O1015840-A1015840 lines The averageparticle concentration and particle loss rate was plotted inFigure 21
Figure 20 plots the spatial distribution of the particleconcentrations for the wholemodel at different times Resultsshow that the particle concentration gradually increasesfrom the bottom upwards This is because under the effectsof the erosion increasing amount of particles migratedinto the water and gradually moved upwards through thefractures and pores This is consistent with the change inthe particle concentration at different locations as shown inFigure 21
Results in Figure 22 are well in line with the results shownin Figure 18 For example at the beginning the particle lossrate is relatively low however the rate constantly increasesover time and culminates at the inrushThis is due to the fact
that along with the increases in the seepage velocities theerosion effects on the solid particles are constantly intensifiedwhich results in frequent migration and substantial particleloss
44 Sensitivity Analyses The outburst processes wereaffected or controlled by various factors including thespatial heterogeneity of lithology of the KCPs waterpressure absolute aperture and distribution of the fracturesdistribution law of concentration of the karst particlesand their sensitivity to water erosion Based on the newlydeveloped coupling model this work further examined thewater and particle migration characteristics in the KCPsunder different hydrological and geological conditionsas well as the variations in the inrush occurrences Thescenarios to be studied are summarized in Table 2
Geofluids 11
2
16
12
08
04
0(a) 14000 s
2
16
12
08
04
0(b) 15000 s
2
16
12
08
04
0(c) 16000 s
2
16
12
08
04
0(d) 17000 s
2
16
12
08
04
0(e) 17500 s
2
16
12
08
04
0(f) 18000 s
Figure 17 The change of seepage velocity (10minus3ms) in a KCP
14000 s15000 s16000 s
17000 s17500 s18000 s
r (m)
1 2 3 4 5 6 70
Velo
city
(10minus
3m
s)
14
12
1
08
06
04
02
0
(a)
14000 s15000 s16000 s
17000 s17500 s18000 s
50 10z (m)
15 20
Velo
city
(10minus
3m
s)
14
12
1
08
06
04
02
0
(b)
Figure 18 Evolution of seepage velocity along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
12 Geofluids
Inverse velocityLinear fitting
0
20
40
60
80
100
Flow
rate
(m3h
)
0
5
10
15
20
25
30
Inve
rse v
eloci
ty (h
m)
5 10 15 200Time (times103 s)
Q
Figure 19 Water flow rate along the bottom surface of the numerical model
025
02
03
015
01
005
0(a) 14000 s
025
02
03
015
01
005
0(b) 15000 s
025
02
03
015
01
005
0(c) 16000 s
025
02
03
015
01
005
0(d) 17000 s
025
02
03
015
01
005
0(e) 17500 s
025
02
03
015
01
005
0(f) 18000 s
Figure 20 Change of particles concentration in a KCP
Geofluids 13
0
005
01
015
02
025
03
035C
once
ntra
tion
1 2 3 4 5 6 70r (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
(a)
105 15 200z (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
0
005
01
015
02
025
03
035
Con
cent
ratio
n (b)
Figure 21 Evolution of particle concentration along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
ConcentrationLoss rate
0
005
01
015
Con
cent
ratio
n
5 10 15 200Time (times103 s)
0
5
10
15
20
25
Part
icle
loss
rate
Qp
(m3h
)
Figure 22 Evolution of average particle volumetric concentrationand particle loss rate
441 Impact of Heterogeneity on Fractures Evolution Fig-ure 23 illustrates the distribution law of the fractures seepagevelocities and particle volume concentrations under identicalflow pressures but different fracture distribution conditionsat 175 times 103 seconds The results show that more intercon-nected fractures are developed along with the increase in mvalues For example when119898 = 4 there are only two intercon-nected fractures However asm value increases an increasingnumber of fractures were generated and interconnected Inthe fourth case (119898 = 10) three interconnected fractures weregenerated This finding indicates that the homogeneity canaccelerate the propagation of the fractures An increase in
Table 2 List of simulation scenarios
Parameter Value
Weibull distribution coefficient (-)
119898 = 4119898 = 6119898 = 8
119898 = 10
Water pressure (MPa)
119901 = 10119901 = 20119901 = 30119901 = 40
Initial particle concentration ()
1198620 = 00051198620 = 0011198620 = 0021198620 = 005
Fracture aperture (times10minus4m)
119887 = 075119887 = 10
119887 = 125119887 = 15
flow velocity and particle concentration with increasing mvalues was also observed as shown in Figures 23(b) and 23(c)
442 Prediction of Water Inrush under Different ConditionsThe analysis and prediction of the occurrences of waterinrush in KCPs based on the changes in seepage are essentialfor the safety of mining processes Some researchers haveadopted catastrophe theories to predict the occurrences ofwater inrush However an approach that can be used topredict water inrush based on water flow has yet to be foundin the literature This study presents the first attempt toresolve this challenge by applying the inverse velocity theory
14 Geofluids
m = 4 m = 6 m = 8 m = 10
1
2
3
4
5
6
7
(a) Distribution of aperture 119887 (times10minus4m )
m = 4 m = 6 m = 8 m = 10
2
16
12
08
04
0
(b) Distribution of seepage velocity (times10minus3ms)
m = 4 m = 6 m = 8 m = 10
025
02
03
015
01
005
0
(c) Distribution of particles concentration
Figure 23 Distribution of fracture seepage velocity and particle concentration at different Weibull distribution conditions (a) Impact ofWeibull distribution on fractures evolution (b) impact of Weibull distribution on water velocity evolution (c) impact of Weibull distributionon particle concentration evolution
Geofluids 15
5 10 15 200Time (times103 s)
m = 4
m = 6 m = 10
m = 8
0
20
40
60
80
100
120Fl
ow ra
te (m
3h
)
(a)
205
21
215
22
225
23
Wat
er in
rush
tim
e (times10
3s)
4 6 8 102Weibull coefficient m
y = 25699xminus0089
R2 = 09825
(b)
Figure 24 Impact of heterogeneity on water flow rate (a) and inrush time (b)
0
20
40
60
80
100
120
140
160
180
200
Flow
rate
(m3h
)
5 10 15 200Time (times103 s)
p = 1MPap = 2MPa
p = 3MPap = 4MPa
(a)
y = 41733xminus1001
R2 = 09992
1 2 3 4 50Water pressure (MPa)
0
5
10
15
20
25
30
35
40
45
Wat
er in
rush
tim
e (times10
3s)
(b)
Figure 25 Impact of aquifer water pressure on water flow rate (a) and inrush time (b)
which has been widely approved effective in many fields suchas slope stability predictionThe relevant results and analysesare shown in Figure 24ndashFigure 27
As shown in Figure 24 water flow rate exhibits a non-linear increase and as the value of m increases the seepagerate accelerates gradually For example at 119905 = 15 times 104 s theseepage rate was approximately 15m3h for 119898 = 4 while itjumped to 25m3h for 119898 = 10 Results from Figure 24(b)show that water inrush occurs sooner for a greater 119898 valueIn other words the inrush occurs earlier as the heterogeneityincreases The water inrush time follows the power functionThis is due to the fact that the water is more prone to flowingthrough the existing fractures (which indicates a higher
permeability) in the heterogeneous structure Neverthelessdue to the heterogeneous distribution of the aperture thefractures cannot be easily interconnected which hampers theformation of the seepage channels In regard to the homo-geneous rock strata since the flow of water was dominantlycontrolled by the pressure gradient the fractures generatedduring the process of erosion could be easily interconnectedand as a result the water inrush occurredsooner
Figure 25 illustrates the impact of the initial KCPrsquos waterpressure on the flow rates and water inrush time It can beseen that as the pressure increases the changes in the flowrates accelerate For example for119901 = 2MPa the flow rate wasonly approximately 5m3h and it increased to 30m3h when
16 Geofluids
0
20
40
60
80
100
120
140
160
180
200Fl
ow ra
te (m
3h
)
5 10 15 20 250Time (times103 s)
c = 0005
c = 001
c = 002
c = 005
(a)
0
5
10
15
20
25
30
35
Wat
er in
rush
tim
e (times10
3s)
001 002 003 004 0050Initial particle concentration
y = 13554xminus0591
R2 = 09975
(b)
Figure 26 Impact of initial particle concentration on water flow rate (a) and inrush time (b)
0
20
40
60
80
100
120
140
160
180
200
Flow
rate
(m3h
)
5 10 15 200Time (times103 s)
075E minus 4m100E minus 4m
125E minus 4m150E minus 4m
(a)
y = 31027eminus286x
R2 = 09503
09 11 13 1507Fracture aperture (times10minus4 m)
0
5
10
15
20
25
30
35
40
Wat
er in
rush
tim
e (times10
3s)
(b)
Figure 27 Impact of absolute aperture on water flow rate (a) and inrush time (b)
119901 = 3MPa In addition with increasing the aquifer waterpressure the water inrush time was also brought forward asshown in Figure 25(a) The outburst time was approximately119905 = 40 times 104 s for p = 1MPa while only 10 times 104 s for119901 = 4MPa The relationship between the time of the inrushoccurrences and the aquifer water pressure follows the powerfunction as illustrated in Figure 25
For varying initial particle concentrations the evolutionof both the water flow rate change and the water inrushtime shows a similar trend to that of different aquifer waterpressures The flow rate accelerates with increasing initialparticle concentration and consequently the water inrushoccurs earlier as shown in Figure 26The outburst times alsoshow a power function to the initial particle concentration
The initial average fracture aperture also shows significantimpact on water flow behavior For instance results fromFigure 27 clearly illustrate that the flow rate increases withincreasing initial average fracture aperture Please note thatthe inrush time follows an exponential function to the initialaverage fracture aperture
These numerical results can be explained by the factthat the initial seepage velocity is expected to be higher forthe modelling cases with the higher initial aquifer pressureinitial fracture aperture andor initial particle concentrationThe higher flow velocity would intensify the erosion of thefractures enhance the permeability and thereby acceleratethe migration of the particles and interconnection of seepagechannels which causes water inrush
Geofluids 17
5 Conclusions
In this study a systematic approach was established to inves-tigate the impact of controlling factors onwater flow behaviorfor KCPs and to predict water inrush time by introducing theinverse velocity theory In this approach a suite of governingequations was developed to couple all the physics involvedin this complex process including water flow rock erosionand change in rock microstructure These equations werethen implemented into a finite element software COMSOLMultiphysics to simulate the fully coupled process Basedon this numerical model a series of sensitivity studies wereconducted and some important findings have been drawn
(i) Water flow rate increases with increasing aquiferpressure initial particle concentration and fractureopening This results in an increase in the permeabil-ity and finally an acceleration of the migration of theparticles and interconnection of the seepage channelsThis finding suggests the grouting of the KCPs couldbe an effective measure to mitigate water inrush risk
(ii) The inverse velocity theory was successfully appliedto analyze the occurrences of water inrush underdifferent conditions The results show that the timeof inrush has a power relationship to the rock het-erogeneity water pressure and initial particle concen-tration and follows an exponential relationship to theinitial fracture apertures
The framework developed from this work not only helpsenhance coal mining operations safety by better under-standing and predicting water inrush risks so that propermitigation measures can be put in place timely It canalso be extended to other fields such as tunneling backfillpaste piping tailing dam erosion and other engineeringapplications which are likely to encounter time-dependenterosion or deformation or water inrush issues
Please be noted that there are a number of other stochasticmethods available in the literature that can be used to illus-trate rock heterogeneity such as the Monte-Carlo methodor First-Order approach The differences of these methodson the results of water inrush prediction may be worthcomparing in the near future
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This project is supported by the National Natural ScienceFoundation of China (nos 51304072 51774110) the Programfor Innovative Research Team in University of Ministryof Education of China (IRT 16R22) and the PostdoctoralScience Foundation of China (2017M612398)
References
[1] DMa XMiao H Bai et al ldquoEffect of mining on shear sidewallgroundwater inrush hazard caused by seepage instability of the
penetrated karst collapse pillarrdquo Natural Hazards vol 82 no 1pp 73ndash93 2016
[2] H Keqiang Y Guangming and L Yaoru ldquoPalaeo-karst collapsepillars in northern China and their damage to the geologicalenvironmentsrdquo Environmental Geology vol 58 no 5 pp 1029ndash1040 2009
[3] B Yao J Wei D Wang D Ma and Z Chen ldquoNumericalstudy on seepage property of karst collapse columns underparticle migrationrdquo CMES Computer Modeling in Engineeringamp Sciences vol 91 no 2 pp 81ndash100 2013
[4] J Tang H Bai B Yao and Y Wu ldquoTheoretical analysis onwater-inrush mechanism of concealed collapse pillars in floorrdquoMining Science and Technology vol 21 no 1 pp 57ndash60 2011
[5] Y Chen M Yi C Chen and C Yu ldquoBernstein polynomialsmethod for fractional convection-diffusion equation with vari-able coefficientsrdquoComputerModeling in Engineering amp Sciencesvol 83 no 6 pp 639ndash653 2012
[6] J Zhang and B Shen ldquoCoal mining under aquifers in China Acase studyrdquo International Journal of Rock Mechanics and MiningSciences vol 41 no 4 pp 629ndash639 2004
[7] D Ma H Bai X Miao H Pu B Jiang and Z ChenldquoCompaction and seepage properties of crushed limestoneparticle mixture an experimental investigation for Ordoviciankarst collapse pillar groundwater inrushrdquo Environmental EarthSciences vol 75 no 1 article 11 p 14 2016
[8] S Yin J Zhang and D Liu ldquoA study of mine water inrushesby measurements of in situ stress and rock failuresrdquo NaturalHazards vol 79 no 3 pp 1961ndash1979 2015
[9] H Bai D Ma and Z Chen ldquoMechanical behavior of ground-water seepage in karst collapse pillarsrdquo Engineering Geology vol164 pp 101ndash106 2013
[10] D Ma and H Bai ldquoGroundwater inflow prediction model ofkarst collapse pillar a case study for mining-induced ground-water inrush riskrdquoNatural Hazards vol 76 no 2 pp 1319ndash13342015
[11] D Ma H Bai and Y Wang ldquoMechanical behavior of a coalseam penetrated by a karst collapse pillar mining-inducedgroundwater inrush riskrdquo Natural Hazards vol 75 no 3 pp2137ndash2151 2015
[12] B Yao Research on variable mass fluid-solid coupling dynamictheory of broken rockmass and application China Univeristy ofMining and Technology Xuzhou China 2012
[13] D Ma X Miao H Bai et al ldquoImpact of particle transfer onflow properties of crushed mudstonesrdquo Environmental EarthSciences vol 75 no 7 article 593 2016
[14] DMa H Bai Z Chen andH Pu ldquoEffect of particlemixture onseepage properties of crushed mudstonesrdquo Transport in PorousMedia vol 108 no 2 pp 257ndash277 2015
[15] B Zhang H Bai and K Zhang ldquoSeepage characteristics ofcollapse columnfillingsrdquo International Journal ofMining Scienceand Technology 2015
[16] P Ortoleva J Chadam E Merino and A Sen ldquoGeochemicalself-organization II the reactive-infiltration instabilityrdquo Ameri-can Journal of Science vol 287 no 10 pp 1008ndash1040 1987
[17] I Vardoulakis M Stavropoulou and P Papanastasiou ldquoHydro-mechanical aspects of the sand production problemrdquo Transportin Porous Media vol 22 no 2 pp 225ndash244 1996
[18] R L Detwiler and H Rajaram ldquoPredicting dissolution patternsin variable aperture fractures Evaluation of an enhanced depth-averaged computational modelrdquoWater Resources Research vol43 no 4 Article IDW04403 2007
18 Geofluids
[19] M A Habib H M Badr R Ben-Mansour and M E KabirldquoErosion rate correlations of a pipe protruded in an abrupt pipecontractionrdquo International Journal of Impact Engineering vol34 no 8 pp 1350ndash1369 2007
[20] H T Xiao and H Y Xu ldquoIn situ permeability measurementsto establish the influence of slice mining on floor rocksrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 37 no 5 pp 855ndash860 2000
[21] H Guo D P Adhikary and M S Craig ldquoSimulation of minewater inflow and gas emission during longwall miningrdquo RockMechanics and Rock Engineering vol 42 no 1 pp 25ndash51 2009
[22] R Zhang Z JiangH ZhouC Yang and S Xiao ldquoGroundwateroutbursts from faults above a confined aquifer in the coalminingrdquo Natural Hazards vol 71 no 3 pp 1861ndash1872 2014
[23] B Yao F Du E Li and X Wang ldquoMechanical model of karstcollapse columns water inrush and its applicationrdquo ElectronicJournal of Geotechnical Engineering vol 19 pp 1665ndash1675 2014
[24] J Warren and P Root ldquoThe behavior of naturally fracturedreservoirsrdquo SPE Journal vol 3 no 3 pp 245ndash255 2013
[25] H KazemiM S Seth andGWThomas ldquoThe interpretation ofinterference tests in naturally fractured reservoirs with uniformfracture distributionrdquo SPE Journal vol 9 no 4 pp 463ndash4721969
[26] A de Swaan O ldquoAnalytical solutions for determining naturallyfractured reservoir properties by well testingrdquo SPE Journal vol16 no 3 pp 117ndash122 1976
[27] N D Rose and O Hungr ldquoForecasting potential rock slopefailure in open pit mines using the inverse-velocity methodrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 2 pp 308ndash320 2007
[28] J R Fanchi Petroleum Engineering Handbook Volume 1 Gen-eral Engineering Society of Petroleum Engineers 2006
[29] R Sakthivadivel and S Irmay A Review of Filtration TheoriesHydraulic Engineering Laboratory College of EngineeringUniversity of California Berkeley Calif USA 1996
[30] C Wang P Zhai Z Chen J Liu L Wang and J XieldquoExperimental study of coal matrix-cleat interaction underconstant volume boundary conditionrdquo International Journal ofCoal Geology vol 181 pp 124ndash132 2017
[31] S Irmay ldquoOn the theoretical derivation of Darcy and Forch-heimer formulasrdquo Eos Transactions American GeophysicalUnion vol 39 no 4 pp 702ndash707 1958
[32] CH Lee and IW Farmer ldquoA simplemethod of estimating rockmass porosity and permeabilityrdquo International Journal ofMiningand Geological Engineering vol 8 no 1 pp 57ndash65 1990
[33] C Nalluri A K El-Zaemey and H L Chan ldquoSedimenttransport over fixed deposited beds in sewers - An appraisal ofexisting modelsrdquoWater Science and Technology vol 36 no 8-9pp 123ndash128 1997
[34] P Novak and C Nalluri ldquoSediment transport in smooth fixedbed channelsrdquo Journal of the Hydraulics Division vol 101 no 9pp 1139ndash1154 1975
[35] T Fukuzono ldquoA newmethod for predicting the failure time of asloperdquo in Proceedings of the In 4th International Conference andField Workshop on Landslides Tokyo Japan 1985
[36] C R J Kilburn andDN Petley ldquoForecasting giant catastrophicslope collapse lessons from Vajont Northern Italyrdquo Geomor-phology vol 54 no 1-2 pp 21ndash32 2003
[37] B Voight ldquoA method for prediction of volcanic eruptionsrdquoNature vol 332 no 6160 pp 125ndash130 1988
[38] B Yao X Mao J Wei and D Wang ldquoStudy on coupled fluid-solid model for collapse columns considering the effect ofparticle transportrdquo Zhongguo Kuangye Daxue XuebaoJournalof China University of Mining and Technology vol 43 no 1 pp30ndash35 2014
[39] H Bai Seepage Characteristics of Top Stratum of OrdovicianSystem and Its Application Study as Key Aquifuge ChinaUniversity of Mining amp Technology Xuzhou China 2008
[40] C A Tang L G Tham P K K Lee T H Yang and L CLi ldquoCoupled analysis of flow stress and damage (FSD) in rockfailurerdquo International Journal of Rock Mechanics and MiningSciences vol 39 no 4 pp 477ndash489 2002
[41] W C Zhu and C A Tang ldquoMicromechanical model forsimulating the fracture process of rockrdquo Rock Mechanics andRock Engineering vol 37 no 1 pp 25ndash56 2004
[42] T H Yang L G Tham C A Tang Z Z Liang and YTsui ldquoInfluence of heterogeneity of mechanical properties onhydraulic fracturing in permeable rocksrdquo Rock Mechanics andRock Engineering vol 37 no 4 pp 251ndash275 2004
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Submit your manuscripts atwwwhindawicom
6 Geofluids
Time
Failure
a gt2 (convex)a = 2 (linear)
a lt 2 (concave)
Inve
rse v
eloci
ty (1
V)
Figure 8 Inverse velocity trend lines to predict the time of failure[27]
Water flowInverse velocityLinear fitting
0
200
400
600
800
1000
1200
1400
1600
Flow
rate
(Ｇ3h
)
0
0002
0004
0006
0008
001
0012
0014
0016
0018
002In
vers
e velo
city
(hＧ
3)
5 10 15 200Time (h)
Water inrush point
Figure 9 Verification of the inverse velocity theory in predictingwater inrush
reliable in estimating the failure time using the linear fittingcurve [36 37]Therefore in thiswork this theory (ie inversefluid flow velocity) is adopted as the first attempt to predictwater inrush in KCPs
In order to verify the applicability of theory to waterinrush the field monitoring data from Yao et al [38] and Bai[39] was used and the comparison of inrush time betweenreal data and predicted time using inverse velocity theorywas conducted The results were plotted in Figure 9 It can beseen that the predicted inrush time matches the actual waterinrush time very well which proves that this theory can beused to predict water inrush for KCPs
3 Numerical Model Implementation
31 Background of the Coal Mine In this section a case studywas conducted based on the hydrogeological conditions of
Goaf
Hau
lage
rise
Coal haulage roadway
Ventilation roadway
Miningadvance
KCP
Railw
ay ri
se
KCP
Figure 10 Illustration of number 10-106 longwall panel and KCP inTuanbai coal mine of Shanxi province China
the Tuanbai Coalmine which is affiliatedwithHuozhouCoalElectricity Group of China The mine is located in TuanbaiCounty Linfen City Shanxi Province as marked in blue inFigure 2 The mining operation is current extracting number10 coal seam at approximately 300m depth To date 97 KCPshave been found during the mining operations at this seamThese KCPs included rock blocks of different sizes and inmost cases mud infillings and sizes of KCPs varied from tensto hundreds of meters In addition some had low level ofcompaction and cementation and relatively high infiltrationcapabilities
Since the distance between number 10 coal seam and theOrdovician limestone was only about 35m (as illustrated inFigure 13(a)) themining operation is being carried out underpressure from the Ordovician limestone water of the floorThe water pressure was found to be about 2MPa This minehas suffered a number of water inrush accidents associatedwith the KCPs For instance one accident occurred on thebelt roadway of the first longwall panel in 2007 with a waterflow rate of nearly 470m3h In addition there were a numberof water inrush accidents on longwall panels such as 10-106 asshown in Figure 10 10-112 and 10-114 at a rate of range from40m3h to 150m3h in 2010 resulting in the submergenceof the longwall panels Later investigation of these incidentsrevealed that all were directly caused by the KCPs whichacted as water channels with the confined water serving asthe source
32 Characterisation of the Infilling Materials In KCPs thecomposition of the infillings and their particle size distri-bution (PSD) have been found to be highly relevant to themigration of the particles For this reason two samples (iesample 1 and sample 2) were collected from the Tuanbai coalmine and the X-ray diffraction phase analysis (compositionanalysis) was carried out on the infillingmaterials of theKCPsas well as the PSD characteristics The results are shown inFigures 11 and 12
The composition analysis (as shown in Figure 11) indi-cated that the infilling materials mainly included kaolin-ites quartz illite smectite mixed layers small quantities offeldspars montmorillonites chlorites calcites siderites and
Geofluids 7
402
281
93
108
14
4231
05 05
19
KaoliniteQuartzIlliteIllite-smectiteSmectite
ChloriteFeldsparCalciteSideriteOthers
(a)
465
198
137
125
24
00
1304
19
15
KaoliniteQuartzIlliteIllite-smectiteSmectite
ChloriteFeldsparCalciteSideriteOthers
(b)
Figure 11 (a) Mineral components of infilling materials for Sample 1 and (b) mineral components of infilling materials for Sample 2
0
20
40
60
80
100
Cum
ulat
ive (
)
0
5
10
15
20
25
30
35
40
Freq
uenc
y (
)
001 01 1 100001Size (mm)
FrequencyCumulative
(a)
FrequencyCumulative
0
20
40
60
80
100
Cum
ulat
ive (
)
0
5
10
15
20
25
30
35
40
Freq
uenc
y (
)
001 01 1 100001Size (mm)
(b)
Figure 12 Particle size distribution (PSD) of infilling materials (a) Sample 1 (b) Sample 2
other mineral compositions The PSD results (Figure 12)showed that the particle sizes varied from 1 120583m to a few mmfor both Samples 1 and 2 with majority spanning from 10120583m to 1mm This could be a result of long-term weatheringbut the weak and unfavorable rock properties observed inthe field indicate that KCPs are very fractured and loose instructure with low strength high permeability being proneto water erosion and the water inrush risks
33 Numerical Model Setup Although diverse in geometryKCPs are usually presented similarly to a dome shape [9]Each of these approximates a 3D axisymmetric model whichcan be simplified as a 2D symmetrical model
In this work according to the lithology of the mine thebottom diameter top diameter and height are 15m 10m and20m respectively (as shown in Figure 13) The pressure atthe water inlet on the lower boundary was 20MPa and the
8 Geofluids
Description LithologyThickness (m)
11 coal
Limestone
Mudstone
Fine sandstone
Aquifer
10 coal
Limestone
Mudstone
30
25
73
33
46
200
358
Mudstone
9 coal
89
05
96
(a) (b) (c)
times10minus4
05
06
07
08
09
1
11
12
13
14
Figure 13 Model geometry and setup (a) illustration of KCP and rock strata (b) 2D simulation model and (c) distribution of apertureopening based on Weibull function
pressure at the water outlet on the top was 01MPa initialwater pressure in the model was 01MPa initial particle vol-ume concentration was 001 initial average fracture aperture1198870 was 01mm and initial porosity 1206010 was 10 The mainparameters of the model were all determined according tothe relevant references [3 12] in which the studies wereconducted on the same seam Other used parameters arelisted in Table 1Themodel was divided into 5000 grids usingmapped mesh method embedded in the COMSOL softwareThe shape of the grids is rectangular
Heterogeneity has been determined to be a prominentfeature of rock There are currently various approaches toobtaining the characteristics of the heterogeneous distribu-tion of rock materials For example digital core techniquesand mathematical statistics methods have both been utilizedPrevious studies have shown that the heterogeneity of rockcan be described by the Weibull distribution [40ndash42] Thusthe Weibull distribution was selected in this study due to itseffectiveness and great simplicity to obtain the heterogeneousdistribution of fracture apertures of the KCPs The distribu-tion probability density equation was as follows
119891 (119887) = 1198981198870 ( 119887
1198870)119898minus1
exp [minus ( 1198871198870)119898] (20)
where 119887 indicates the fracture aperture 1198870 denotes the initialfracture aperture and 119898 is the uniformity index The larger119898 represents the higher level of uniformity The fractureaperture distribution obtained by the numerical generationmethod is shown in Figure 13(c)
Based on thismodel geometry (9) (11) (14) (15) (17) and(18) will be solved simultaneously to investigate the dynamicchange of water flow behaviors and the associated inrush riskunder different flow conditions
4 Results and Analysis
In order to analyze the characteristics of seepage at differenttimes in this study six different moments were selected (ie14 times 103 15 times 103 16 times 103 17 times 103 175 times 103 and 18 times 103 s)The specific results will be discussed below
41 Distribution of the Fracture Apertures Figure 14 illus-trates the spatial changes of the fracture apertures at differenttimes Figure 15 shows the evolution of fracture aperturesalong O-O10158401015840 and O1015840-A1015840 lines as marked in Figure 13(b)and the average fracture aperture-time curve was plotted inFigure 16 The results show the following(1) The fracture aperture gradually increases under theeffects of the erosion However the increase rate is higherin the upper part of the model than in the lower part Thisis likely because the upper outlet boundary is narrower thanthe bottom inlet boundary giving rise to higher flow velocitySuch higher velocity causes more significant erosion andconsequently the fracture aperture change is faster(2) As the infiltration continues the average fractureaperture increases by approximately 200 from 01mm tonearly 03mm (Figure 16) At the initial stage the fracture issubject to random distribution with minor difference in theapertures However the variation diverges under the effectsof the erosion The fractures with smaller initial aperturesbecome slowly enlarged by approximately 20 while thosewith larger apertures continuously increase by more than200 As the fractures gradually dilate and interconnectwith each other a number of dominant seepage channels areformed as illustrated in Figure 14(f)
42 Distribution of Water Seepage Velocity The seepagevelocities (ie Darcy velocity) in the model domain andalong O-O10158401015840 and O1015840-A1015840 lines were shown in Figures 17 and
Geofluids 9
Table 1 Input parameters for the numerical simulation
120588119904(kgm3) 120578(Pasdots) 1198961198980(m2) 1206010 1198870(m) 119886 1205821(mminus1) 1205822(mminus1) 119898 11986202000 10minus3 10minus12 01 00001 001 001 001 6 001
1
2
3
4
5
6
7
(a) 14000 s
1
2
3
4
5
6
7
(b) 15000 s
1
2
3
4
5
6
7
(c) 16000 s
1
2
3
4
5
6
7
(d) 17000 s
1
2
3
4
5
6
7
(e) 17500 s
1
2
3
4
5
6
7
(f) 18000 s
Figure 14 The spatial distribution of aperture 119887 (10minus4m ) at different times
18 respectively The predicted failure time using the inversevelocity theory was plotted in Figure 19The key observationsinclude the following(1) As shown in Figure 17 the changes in the flowvelocity are consistent with the distribution of the fractures(Figure 14) and more fracture aperture changes are observedat the locations where higher seepage velocities take place Asshown in Figure 18 at 14times 104 s theminimumandmaximumseepage velocities were approximately 35 times 10minus6ms and 411times 10minus5ms At 18 times 104 s these two figures increased by 20and 200 to 42 times 10minus6ms and 125 times 10minus3ms respectively(2)Therewas a continuous increase in flow rate at the out-let from approximately 37m3 h initially to approximately100m3 h at 18times 104 s increased by nearly 30 times Howeverits increase showed a nonlinear trend likely due to the fact
that the increase rate was relatively slow in the initial stagebut accelerated gradually until the water inrush occurredFigure 19 was generated according to the inverse velocitytheory and the results showed that the water inrush wouldoccur at 185 times 104 s for this particular flow condition Thetrend has been reflected by the change in flow velocity shownin Figure 17 The figure shows that shortly before the inrushthe flow channels rapidly connected together and formed amain channel resulting in a surge in water flow
43 Distribution of the Particle Concentrations Particle con-centration is directly related to the erosion rate Higherparticle concentration indicates more severe erosion whichis more likely to result in greater fracture aperture change
10 Geofluids
05
15
25
35
45
55
65Fr
actu
re ap
ertu
reb
(times10
minus4
m)
5 10 15 200z (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
(a)
1 2 3 4 5 6 70r (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
05
15
25
35
45
55
65
Frac
ture
aper
ture
b(times
10minus4
m)
(b)
Figure 15 Evolution of fracture aperture along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
1
15
2
25
3
Frac
ture
aper
ture
b(times
10minus4
m)
5 10 15 200Time (times103 s)
Figure 16 Change of average fracture aperture with time
Figure 20 shows the evolution of the average particleconcentration along O-O10158401015840 and O1015840-A1015840 lines The averageparticle concentration and particle loss rate was plotted inFigure 21
Figure 20 plots the spatial distribution of the particleconcentrations for the wholemodel at different times Resultsshow that the particle concentration gradually increasesfrom the bottom upwards This is because under the effectsof the erosion increasing amount of particles migratedinto the water and gradually moved upwards through thefractures and pores This is consistent with the change inthe particle concentration at different locations as shown inFigure 21
Results in Figure 22 are well in line with the results shownin Figure 18 For example at the beginning the particle lossrate is relatively low however the rate constantly increasesover time and culminates at the inrushThis is due to the fact
that along with the increases in the seepage velocities theerosion effects on the solid particles are constantly intensifiedwhich results in frequent migration and substantial particleloss
44 Sensitivity Analyses The outburst processes wereaffected or controlled by various factors including thespatial heterogeneity of lithology of the KCPs waterpressure absolute aperture and distribution of the fracturesdistribution law of concentration of the karst particlesand their sensitivity to water erosion Based on the newlydeveloped coupling model this work further examined thewater and particle migration characteristics in the KCPsunder different hydrological and geological conditionsas well as the variations in the inrush occurrences Thescenarios to be studied are summarized in Table 2
Geofluids 11
2
16
12
08
04
0(a) 14000 s
2
16
12
08
04
0(b) 15000 s
2
16
12
08
04
0(c) 16000 s
2
16
12
08
04
0(d) 17000 s
2
16
12
08
04
0(e) 17500 s
2
16
12
08
04
0(f) 18000 s
Figure 17 The change of seepage velocity (10minus3ms) in a KCP
14000 s15000 s16000 s
17000 s17500 s18000 s
r (m)
1 2 3 4 5 6 70
Velo
city
(10minus
3m
s)
14
12
1
08
06
04
02
0
(a)
14000 s15000 s16000 s
17000 s17500 s18000 s
50 10z (m)
15 20
Velo
city
(10minus
3m
s)
14
12
1
08
06
04
02
0
(b)
Figure 18 Evolution of seepage velocity along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
12 Geofluids
Inverse velocityLinear fitting
0
20
40
60
80
100
Flow
rate
(m3h
)
0
5
10
15
20
25
30
Inve
rse v
eloci
ty (h
m)
5 10 15 200Time (times103 s)
Q
Figure 19 Water flow rate along the bottom surface of the numerical model
025
02
03
015
01
005
0(a) 14000 s
025
02
03
015
01
005
0(b) 15000 s
025
02
03
015
01
005
0(c) 16000 s
025
02
03
015
01
005
0(d) 17000 s
025
02
03
015
01
005
0(e) 17500 s
025
02
03
015
01
005
0(f) 18000 s
Figure 20 Change of particles concentration in a KCP
Geofluids 13
0
005
01
015
02
025
03
035C
once
ntra
tion
1 2 3 4 5 6 70r (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
(a)
105 15 200z (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
0
005
01
015
02
025
03
035
Con
cent
ratio
n (b)
Figure 21 Evolution of particle concentration along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
ConcentrationLoss rate
0
005
01
015
Con
cent
ratio
n
5 10 15 200Time (times103 s)
0
5
10
15
20
25
Part
icle
loss
rate
Qp
(m3h
)
Figure 22 Evolution of average particle volumetric concentrationand particle loss rate
441 Impact of Heterogeneity on Fractures Evolution Fig-ure 23 illustrates the distribution law of the fractures seepagevelocities and particle volume concentrations under identicalflow pressures but different fracture distribution conditionsat 175 times 103 seconds The results show that more intercon-nected fractures are developed along with the increase in mvalues For example when119898 = 4 there are only two intercon-nected fractures However asm value increases an increasingnumber of fractures were generated and interconnected Inthe fourth case (119898 = 10) three interconnected fractures weregenerated This finding indicates that the homogeneity canaccelerate the propagation of the fractures An increase in
Table 2 List of simulation scenarios
Parameter Value
Weibull distribution coefficient (-)
119898 = 4119898 = 6119898 = 8
119898 = 10
Water pressure (MPa)
119901 = 10119901 = 20119901 = 30119901 = 40
Initial particle concentration ()
1198620 = 00051198620 = 0011198620 = 0021198620 = 005
Fracture aperture (times10minus4m)
119887 = 075119887 = 10
119887 = 125119887 = 15
flow velocity and particle concentration with increasing mvalues was also observed as shown in Figures 23(b) and 23(c)
442 Prediction of Water Inrush under Different ConditionsThe analysis and prediction of the occurrences of waterinrush in KCPs based on the changes in seepage are essentialfor the safety of mining processes Some researchers haveadopted catastrophe theories to predict the occurrences ofwater inrush However an approach that can be used topredict water inrush based on water flow has yet to be foundin the literature This study presents the first attempt toresolve this challenge by applying the inverse velocity theory
14 Geofluids
m = 4 m = 6 m = 8 m = 10
1
2
3
4
5
6
7
(a) Distribution of aperture 119887 (times10minus4m )
m = 4 m = 6 m = 8 m = 10
2
16
12
08
04
0
(b) Distribution of seepage velocity (times10minus3ms)
m = 4 m = 6 m = 8 m = 10
025
02
03
015
01
005
0
(c) Distribution of particles concentration
Figure 23 Distribution of fracture seepage velocity and particle concentration at different Weibull distribution conditions (a) Impact ofWeibull distribution on fractures evolution (b) impact of Weibull distribution on water velocity evolution (c) impact of Weibull distributionon particle concentration evolution
Geofluids 15
5 10 15 200Time (times103 s)
m = 4
m = 6 m = 10
m = 8
0
20
40
60
80
100
120Fl
ow ra
te (m
3h
)
(a)
205
21
215
22
225
23
Wat
er in
rush
tim
e (times10
3s)
4 6 8 102Weibull coefficient m
y = 25699xminus0089
R2 = 09825
(b)
Figure 24 Impact of heterogeneity on water flow rate (a) and inrush time (b)
0
20
40
60
80
100
120
140
160
180
200
Flow
rate
(m3h
)
5 10 15 200Time (times103 s)
p = 1MPap = 2MPa
p = 3MPap = 4MPa
(a)
y = 41733xminus1001
R2 = 09992
1 2 3 4 50Water pressure (MPa)
0
5
10
15
20
25
30
35
40
45
Wat
er in
rush
tim
e (times10
3s)
(b)
Figure 25 Impact of aquifer water pressure on water flow rate (a) and inrush time (b)
which has been widely approved effective in many fields suchas slope stability predictionThe relevant results and analysesare shown in Figure 24ndashFigure 27
As shown in Figure 24 water flow rate exhibits a non-linear increase and as the value of m increases the seepagerate accelerates gradually For example at 119905 = 15 times 104 s theseepage rate was approximately 15m3h for 119898 = 4 while itjumped to 25m3h for 119898 = 10 Results from Figure 24(b)show that water inrush occurs sooner for a greater 119898 valueIn other words the inrush occurs earlier as the heterogeneityincreases The water inrush time follows the power functionThis is due to the fact that the water is more prone to flowingthrough the existing fractures (which indicates a higher
permeability) in the heterogeneous structure Neverthelessdue to the heterogeneous distribution of the aperture thefractures cannot be easily interconnected which hampers theformation of the seepage channels In regard to the homo-geneous rock strata since the flow of water was dominantlycontrolled by the pressure gradient the fractures generatedduring the process of erosion could be easily interconnectedand as a result the water inrush occurredsooner
Figure 25 illustrates the impact of the initial KCPrsquos waterpressure on the flow rates and water inrush time It can beseen that as the pressure increases the changes in the flowrates accelerate For example for119901 = 2MPa the flow rate wasonly approximately 5m3h and it increased to 30m3h when
16 Geofluids
0
20
40
60
80
100
120
140
160
180
200Fl
ow ra
te (m
3h
)
5 10 15 20 250Time (times103 s)
c = 0005
c = 001
c = 002
c = 005
(a)
0
5
10
15
20
25
30
35
Wat
er in
rush
tim
e (times10
3s)
001 002 003 004 0050Initial particle concentration
y = 13554xminus0591
R2 = 09975
(b)
Figure 26 Impact of initial particle concentration on water flow rate (a) and inrush time (b)
0
20
40
60
80
100
120
140
160
180
200
Flow
rate
(m3h
)
5 10 15 200Time (times103 s)
075E minus 4m100E minus 4m
125E minus 4m150E minus 4m
(a)
y = 31027eminus286x
R2 = 09503
09 11 13 1507Fracture aperture (times10minus4 m)
0
5
10
15
20
25
30
35
40
Wat
er in
rush
tim
e (times10
3s)
(b)
Figure 27 Impact of absolute aperture on water flow rate (a) and inrush time (b)
119901 = 3MPa In addition with increasing the aquifer waterpressure the water inrush time was also brought forward asshown in Figure 25(a) The outburst time was approximately119905 = 40 times 104 s for p = 1MPa while only 10 times 104 s for119901 = 4MPa The relationship between the time of the inrushoccurrences and the aquifer water pressure follows the powerfunction as illustrated in Figure 25
For varying initial particle concentrations the evolutionof both the water flow rate change and the water inrushtime shows a similar trend to that of different aquifer waterpressures The flow rate accelerates with increasing initialparticle concentration and consequently the water inrushoccurs earlier as shown in Figure 26The outburst times alsoshow a power function to the initial particle concentration
The initial average fracture aperture also shows significantimpact on water flow behavior For instance results fromFigure 27 clearly illustrate that the flow rate increases withincreasing initial average fracture aperture Please note thatthe inrush time follows an exponential function to the initialaverage fracture aperture
These numerical results can be explained by the factthat the initial seepage velocity is expected to be higher forthe modelling cases with the higher initial aquifer pressureinitial fracture aperture andor initial particle concentrationThe higher flow velocity would intensify the erosion of thefractures enhance the permeability and thereby acceleratethe migration of the particles and interconnection of seepagechannels which causes water inrush
Geofluids 17
5 Conclusions
In this study a systematic approach was established to inves-tigate the impact of controlling factors onwater flow behaviorfor KCPs and to predict water inrush time by introducing theinverse velocity theory In this approach a suite of governingequations was developed to couple all the physics involvedin this complex process including water flow rock erosionand change in rock microstructure These equations werethen implemented into a finite element software COMSOLMultiphysics to simulate the fully coupled process Basedon this numerical model a series of sensitivity studies wereconducted and some important findings have been drawn
(i) Water flow rate increases with increasing aquiferpressure initial particle concentration and fractureopening This results in an increase in the permeabil-ity and finally an acceleration of the migration of theparticles and interconnection of the seepage channelsThis finding suggests the grouting of the KCPs couldbe an effective measure to mitigate water inrush risk
(ii) The inverse velocity theory was successfully appliedto analyze the occurrences of water inrush underdifferent conditions The results show that the timeof inrush has a power relationship to the rock het-erogeneity water pressure and initial particle concen-tration and follows an exponential relationship to theinitial fracture apertures
The framework developed from this work not only helpsenhance coal mining operations safety by better under-standing and predicting water inrush risks so that propermitigation measures can be put in place timely It canalso be extended to other fields such as tunneling backfillpaste piping tailing dam erosion and other engineeringapplications which are likely to encounter time-dependenterosion or deformation or water inrush issues
Please be noted that there are a number of other stochasticmethods available in the literature that can be used to illus-trate rock heterogeneity such as the Monte-Carlo methodor First-Order approach The differences of these methodson the results of water inrush prediction may be worthcomparing in the near future
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This project is supported by the National Natural ScienceFoundation of China (nos 51304072 51774110) the Programfor Innovative Research Team in University of Ministryof Education of China (IRT 16R22) and the PostdoctoralScience Foundation of China (2017M612398)
References
[1] DMa XMiao H Bai et al ldquoEffect of mining on shear sidewallgroundwater inrush hazard caused by seepage instability of the
penetrated karst collapse pillarrdquo Natural Hazards vol 82 no 1pp 73ndash93 2016
[2] H Keqiang Y Guangming and L Yaoru ldquoPalaeo-karst collapsepillars in northern China and their damage to the geologicalenvironmentsrdquo Environmental Geology vol 58 no 5 pp 1029ndash1040 2009
[3] B Yao J Wei D Wang D Ma and Z Chen ldquoNumericalstudy on seepage property of karst collapse columns underparticle migrationrdquo CMES Computer Modeling in Engineeringamp Sciences vol 91 no 2 pp 81ndash100 2013
[4] J Tang H Bai B Yao and Y Wu ldquoTheoretical analysis onwater-inrush mechanism of concealed collapse pillars in floorrdquoMining Science and Technology vol 21 no 1 pp 57ndash60 2011
[5] Y Chen M Yi C Chen and C Yu ldquoBernstein polynomialsmethod for fractional convection-diffusion equation with vari-able coefficientsrdquoComputerModeling in Engineering amp Sciencesvol 83 no 6 pp 639ndash653 2012
[6] J Zhang and B Shen ldquoCoal mining under aquifers in China Acase studyrdquo International Journal of Rock Mechanics and MiningSciences vol 41 no 4 pp 629ndash639 2004
[7] D Ma H Bai X Miao H Pu B Jiang and Z ChenldquoCompaction and seepage properties of crushed limestoneparticle mixture an experimental investigation for Ordoviciankarst collapse pillar groundwater inrushrdquo Environmental EarthSciences vol 75 no 1 article 11 p 14 2016
[8] S Yin J Zhang and D Liu ldquoA study of mine water inrushesby measurements of in situ stress and rock failuresrdquo NaturalHazards vol 79 no 3 pp 1961ndash1979 2015
[9] H Bai D Ma and Z Chen ldquoMechanical behavior of ground-water seepage in karst collapse pillarsrdquo Engineering Geology vol164 pp 101ndash106 2013
[10] D Ma and H Bai ldquoGroundwater inflow prediction model ofkarst collapse pillar a case study for mining-induced ground-water inrush riskrdquoNatural Hazards vol 76 no 2 pp 1319ndash13342015
[11] D Ma H Bai and Y Wang ldquoMechanical behavior of a coalseam penetrated by a karst collapse pillar mining-inducedgroundwater inrush riskrdquo Natural Hazards vol 75 no 3 pp2137ndash2151 2015
[12] B Yao Research on variable mass fluid-solid coupling dynamictheory of broken rockmass and application China Univeristy ofMining and Technology Xuzhou China 2012
[13] D Ma X Miao H Bai et al ldquoImpact of particle transfer onflow properties of crushed mudstonesrdquo Environmental EarthSciences vol 75 no 7 article 593 2016
[14] DMa H Bai Z Chen andH Pu ldquoEffect of particlemixture onseepage properties of crushed mudstonesrdquo Transport in PorousMedia vol 108 no 2 pp 257ndash277 2015
[15] B Zhang H Bai and K Zhang ldquoSeepage characteristics ofcollapse columnfillingsrdquo International Journal ofMining Scienceand Technology 2015
[16] P Ortoleva J Chadam E Merino and A Sen ldquoGeochemicalself-organization II the reactive-infiltration instabilityrdquo Ameri-can Journal of Science vol 287 no 10 pp 1008ndash1040 1987
[17] I Vardoulakis M Stavropoulou and P Papanastasiou ldquoHydro-mechanical aspects of the sand production problemrdquo Transportin Porous Media vol 22 no 2 pp 225ndash244 1996
[18] R L Detwiler and H Rajaram ldquoPredicting dissolution patternsin variable aperture fractures Evaluation of an enhanced depth-averaged computational modelrdquoWater Resources Research vol43 no 4 Article IDW04403 2007
18 Geofluids
[19] M A Habib H M Badr R Ben-Mansour and M E KabirldquoErosion rate correlations of a pipe protruded in an abrupt pipecontractionrdquo International Journal of Impact Engineering vol34 no 8 pp 1350ndash1369 2007
[20] H T Xiao and H Y Xu ldquoIn situ permeability measurementsto establish the influence of slice mining on floor rocksrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 37 no 5 pp 855ndash860 2000
[21] H Guo D P Adhikary and M S Craig ldquoSimulation of minewater inflow and gas emission during longwall miningrdquo RockMechanics and Rock Engineering vol 42 no 1 pp 25ndash51 2009
[22] R Zhang Z JiangH ZhouC Yang and S Xiao ldquoGroundwateroutbursts from faults above a confined aquifer in the coalminingrdquo Natural Hazards vol 71 no 3 pp 1861ndash1872 2014
[23] B Yao F Du E Li and X Wang ldquoMechanical model of karstcollapse columns water inrush and its applicationrdquo ElectronicJournal of Geotechnical Engineering vol 19 pp 1665ndash1675 2014
[24] J Warren and P Root ldquoThe behavior of naturally fracturedreservoirsrdquo SPE Journal vol 3 no 3 pp 245ndash255 2013
[25] H KazemiM S Seth andGWThomas ldquoThe interpretation ofinterference tests in naturally fractured reservoirs with uniformfracture distributionrdquo SPE Journal vol 9 no 4 pp 463ndash4721969
[26] A de Swaan O ldquoAnalytical solutions for determining naturallyfractured reservoir properties by well testingrdquo SPE Journal vol16 no 3 pp 117ndash122 1976
[27] N D Rose and O Hungr ldquoForecasting potential rock slopefailure in open pit mines using the inverse-velocity methodrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 2 pp 308ndash320 2007
[28] J R Fanchi Petroleum Engineering Handbook Volume 1 Gen-eral Engineering Society of Petroleum Engineers 2006
[29] R Sakthivadivel and S Irmay A Review of Filtration TheoriesHydraulic Engineering Laboratory College of EngineeringUniversity of California Berkeley Calif USA 1996
[30] C Wang P Zhai Z Chen J Liu L Wang and J XieldquoExperimental study of coal matrix-cleat interaction underconstant volume boundary conditionrdquo International Journal ofCoal Geology vol 181 pp 124ndash132 2017
[31] S Irmay ldquoOn the theoretical derivation of Darcy and Forch-heimer formulasrdquo Eos Transactions American GeophysicalUnion vol 39 no 4 pp 702ndash707 1958
[32] CH Lee and IW Farmer ldquoA simplemethod of estimating rockmass porosity and permeabilityrdquo International Journal ofMiningand Geological Engineering vol 8 no 1 pp 57ndash65 1990
[33] C Nalluri A K El-Zaemey and H L Chan ldquoSedimenttransport over fixed deposited beds in sewers - An appraisal ofexisting modelsrdquoWater Science and Technology vol 36 no 8-9pp 123ndash128 1997
[34] P Novak and C Nalluri ldquoSediment transport in smooth fixedbed channelsrdquo Journal of the Hydraulics Division vol 101 no 9pp 1139ndash1154 1975
[35] T Fukuzono ldquoA newmethod for predicting the failure time of asloperdquo in Proceedings of the In 4th International Conference andField Workshop on Landslides Tokyo Japan 1985
[36] C R J Kilburn andDN Petley ldquoForecasting giant catastrophicslope collapse lessons from Vajont Northern Italyrdquo Geomor-phology vol 54 no 1-2 pp 21ndash32 2003
[37] B Voight ldquoA method for prediction of volcanic eruptionsrdquoNature vol 332 no 6160 pp 125ndash130 1988
[38] B Yao X Mao J Wei and D Wang ldquoStudy on coupled fluid-solid model for collapse columns considering the effect ofparticle transportrdquo Zhongguo Kuangye Daxue XuebaoJournalof China University of Mining and Technology vol 43 no 1 pp30ndash35 2014
[39] H Bai Seepage Characteristics of Top Stratum of OrdovicianSystem and Its Application Study as Key Aquifuge ChinaUniversity of Mining amp Technology Xuzhou China 2008
[40] C A Tang L G Tham P K K Lee T H Yang and L CLi ldquoCoupled analysis of flow stress and damage (FSD) in rockfailurerdquo International Journal of Rock Mechanics and MiningSciences vol 39 no 4 pp 477ndash489 2002
[41] W C Zhu and C A Tang ldquoMicromechanical model forsimulating the fracture process of rockrdquo Rock Mechanics andRock Engineering vol 37 no 1 pp 25ndash56 2004
[42] T H Yang L G Tham C A Tang Z Z Liang and YTsui ldquoInfluence of heterogeneity of mechanical properties onhydraulic fracturing in permeable rocksrdquo Rock Mechanics andRock Engineering vol 37 no 4 pp 251ndash275 2004
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Submit your manuscripts atwwwhindawicom
Geofluids 7
402
281
93
108
14
4231
05 05
19
KaoliniteQuartzIlliteIllite-smectiteSmectite
ChloriteFeldsparCalciteSideriteOthers
(a)
465
198
137
125
24
00
1304
19
15
KaoliniteQuartzIlliteIllite-smectiteSmectite
ChloriteFeldsparCalciteSideriteOthers
(b)
Figure 11 (a) Mineral components of infilling materials for Sample 1 and (b) mineral components of infilling materials for Sample 2
0
20
40
60
80
100
Cum
ulat
ive (
)
0
5
10
15
20
25
30
35
40
Freq
uenc
y (
)
001 01 1 100001Size (mm)
FrequencyCumulative
(a)
FrequencyCumulative
0
20
40
60
80
100
Cum
ulat
ive (
)
0
5
10
15
20
25
30
35
40
Freq
uenc
y (
)
001 01 1 100001Size (mm)
(b)
Figure 12 Particle size distribution (PSD) of infilling materials (a) Sample 1 (b) Sample 2
other mineral compositions The PSD results (Figure 12)showed that the particle sizes varied from 1 120583m to a few mmfor both Samples 1 and 2 with majority spanning from 10120583m to 1mm This could be a result of long-term weatheringbut the weak and unfavorable rock properties observed inthe field indicate that KCPs are very fractured and loose instructure with low strength high permeability being proneto water erosion and the water inrush risks
33 Numerical Model Setup Although diverse in geometryKCPs are usually presented similarly to a dome shape [9]Each of these approximates a 3D axisymmetric model whichcan be simplified as a 2D symmetrical model
In this work according to the lithology of the mine thebottom diameter top diameter and height are 15m 10m and20m respectively (as shown in Figure 13) The pressure atthe water inlet on the lower boundary was 20MPa and the
8 Geofluids
Description LithologyThickness (m)
11 coal
Limestone
Mudstone
Fine sandstone
Aquifer
10 coal
Limestone
Mudstone
30
25
73
33
46
200
358
Mudstone
9 coal
89
05
96
(a) (b) (c)
times10minus4
05
06
07
08
09
1
11
12
13
14
Figure 13 Model geometry and setup (a) illustration of KCP and rock strata (b) 2D simulation model and (c) distribution of apertureopening based on Weibull function
pressure at the water outlet on the top was 01MPa initialwater pressure in the model was 01MPa initial particle vol-ume concentration was 001 initial average fracture aperture1198870 was 01mm and initial porosity 1206010 was 10 The mainparameters of the model were all determined according tothe relevant references [3 12] in which the studies wereconducted on the same seam Other used parameters arelisted in Table 1Themodel was divided into 5000 grids usingmapped mesh method embedded in the COMSOL softwareThe shape of the grids is rectangular
Heterogeneity has been determined to be a prominentfeature of rock There are currently various approaches toobtaining the characteristics of the heterogeneous distribu-tion of rock materials For example digital core techniquesand mathematical statistics methods have both been utilizedPrevious studies have shown that the heterogeneity of rockcan be described by the Weibull distribution [40ndash42] Thusthe Weibull distribution was selected in this study due to itseffectiveness and great simplicity to obtain the heterogeneousdistribution of fracture apertures of the KCPs The distribu-tion probability density equation was as follows
119891 (119887) = 1198981198870 ( 119887
1198870)119898minus1
exp [minus ( 1198871198870)119898] (20)
where 119887 indicates the fracture aperture 1198870 denotes the initialfracture aperture and 119898 is the uniformity index The larger119898 represents the higher level of uniformity The fractureaperture distribution obtained by the numerical generationmethod is shown in Figure 13(c)
Based on thismodel geometry (9) (11) (14) (15) (17) and(18) will be solved simultaneously to investigate the dynamicchange of water flow behaviors and the associated inrush riskunder different flow conditions
4 Results and Analysis
In order to analyze the characteristics of seepage at differenttimes in this study six different moments were selected (ie14 times 103 15 times 103 16 times 103 17 times 103 175 times 103 and 18 times 103 s)The specific results will be discussed below
41 Distribution of the Fracture Apertures Figure 14 illus-trates the spatial changes of the fracture apertures at differenttimes Figure 15 shows the evolution of fracture aperturesalong O-O10158401015840 and O1015840-A1015840 lines as marked in Figure 13(b)and the average fracture aperture-time curve was plotted inFigure 16 The results show the following(1) The fracture aperture gradually increases under theeffects of the erosion However the increase rate is higherin the upper part of the model than in the lower part Thisis likely because the upper outlet boundary is narrower thanthe bottom inlet boundary giving rise to higher flow velocitySuch higher velocity causes more significant erosion andconsequently the fracture aperture change is faster(2) As the infiltration continues the average fractureaperture increases by approximately 200 from 01mm tonearly 03mm (Figure 16) At the initial stage the fracture issubject to random distribution with minor difference in theapertures However the variation diverges under the effectsof the erosion The fractures with smaller initial aperturesbecome slowly enlarged by approximately 20 while thosewith larger apertures continuously increase by more than200 As the fractures gradually dilate and interconnectwith each other a number of dominant seepage channels areformed as illustrated in Figure 14(f)
42 Distribution of Water Seepage Velocity The seepagevelocities (ie Darcy velocity) in the model domain andalong O-O10158401015840 and O1015840-A1015840 lines were shown in Figures 17 and
Geofluids 9
Table 1 Input parameters for the numerical simulation
120588119904(kgm3) 120578(Pasdots) 1198961198980(m2) 1206010 1198870(m) 119886 1205821(mminus1) 1205822(mminus1) 119898 11986202000 10minus3 10minus12 01 00001 001 001 001 6 001
1
2
3
4
5
6
7
(a) 14000 s
1
2
3
4
5
6
7
(b) 15000 s
1
2
3
4
5
6
7
(c) 16000 s
1
2
3
4
5
6
7
(d) 17000 s
1
2
3
4
5
6
7
(e) 17500 s
1
2
3
4
5
6
7
(f) 18000 s
Figure 14 The spatial distribution of aperture 119887 (10minus4m ) at different times
18 respectively The predicted failure time using the inversevelocity theory was plotted in Figure 19The key observationsinclude the following(1) As shown in Figure 17 the changes in the flowvelocity are consistent with the distribution of the fractures(Figure 14) and more fracture aperture changes are observedat the locations where higher seepage velocities take place Asshown in Figure 18 at 14times 104 s theminimumandmaximumseepage velocities were approximately 35 times 10minus6ms and 411times 10minus5ms At 18 times 104 s these two figures increased by 20and 200 to 42 times 10minus6ms and 125 times 10minus3ms respectively(2)Therewas a continuous increase in flow rate at the out-let from approximately 37m3 h initially to approximately100m3 h at 18times 104 s increased by nearly 30 times Howeverits increase showed a nonlinear trend likely due to the fact
that the increase rate was relatively slow in the initial stagebut accelerated gradually until the water inrush occurredFigure 19 was generated according to the inverse velocitytheory and the results showed that the water inrush wouldoccur at 185 times 104 s for this particular flow condition Thetrend has been reflected by the change in flow velocity shownin Figure 17 The figure shows that shortly before the inrushthe flow channels rapidly connected together and formed amain channel resulting in a surge in water flow
43 Distribution of the Particle Concentrations Particle con-centration is directly related to the erosion rate Higherparticle concentration indicates more severe erosion whichis more likely to result in greater fracture aperture change
10 Geofluids
05
15
25
35
45
55
65Fr
actu
re ap
ertu
reb
(times10
minus4
m)
5 10 15 200z (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
(a)
1 2 3 4 5 6 70r (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
05
15
25
35
45
55
65
Frac
ture
aper
ture
b(times
10minus4
m)
(b)
Figure 15 Evolution of fracture aperture along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
1
15
2
25
3
Frac
ture
aper
ture
b(times
10minus4
m)
5 10 15 200Time (times103 s)
Figure 16 Change of average fracture aperture with time
Figure 20 shows the evolution of the average particleconcentration along O-O10158401015840 and O1015840-A1015840 lines The averageparticle concentration and particle loss rate was plotted inFigure 21
Figure 20 plots the spatial distribution of the particleconcentrations for the wholemodel at different times Resultsshow that the particle concentration gradually increasesfrom the bottom upwards This is because under the effectsof the erosion increasing amount of particles migratedinto the water and gradually moved upwards through thefractures and pores This is consistent with the change inthe particle concentration at different locations as shown inFigure 21
Results in Figure 22 are well in line with the results shownin Figure 18 For example at the beginning the particle lossrate is relatively low however the rate constantly increasesover time and culminates at the inrushThis is due to the fact
that along with the increases in the seepage velocities theerosion effects on the solid particles are constantly intensifiedwhich results in frequent migration and substantial particleloss
44 Sensitivity Analyses The outburst processes wereaffected or controlled by various factors including thespatial heterogeneity of lithology of the KCPs waterpressure absolute aperture and distribution of the fracturesdistribution law of concentration of the karst particlesand their sensitivity to water erosion Based on the newlydeveloped coupling model this work further examined thewater and particle migration characteristics in the KCPsunder different hydrological and geological conditionsas well as the variations in the inrush occurrences Thescenarios to be studied are summarized in Table 2
Geofluids 11
2
16
12
08
04
0(a) 14000 s
2
16
12
08
04
0(b) 15000 s
2
16
12
08
04
0(c) 16000 s
2
16
12
08
04
0(d) 17000 s
2
16
12
08
04
0(e) 17500 s
2
16
12
08
04
0(f) 18000 s
Figure 17 The change of seepage velocity (10minus3ms) in a KCP
14000 s15000 s16000 s
17000 s17500 s18000 s
r (m)
1 2 3 4 5 6 70
Velo
city
(10minus
3m
s)
14
12
1
08
06
04
02
0
(a)
14000 s15000 s16000 s
17000 s17500 s18000 s
50 10z (m)
15 20
Velo
city
(10minus
3m
s)
14
12
1
08
06
04
02
0
(b)
Figure 18 Evolution of seepage velocity along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
12 Geofluids
Inverse velocityLinear fitting
0
20
40
60
80
100
Flow
rate
(m3h
)
0
5
10
15
20
25
30
Inve
rse v
eloci
ty (h
m)
5 10 15 200Time (times103 s)
Q
Figure 19 Water flow rate along the bottom surface of the numerical model
025
02
03
015
01
005
0(a) 14000 s
025
02
03
015
01
005
0(b) 15000 s
025
02
03
015
01
005
0(c) 16000 s
025
02
03
015
01
005
0(d) 17000 s
025
02
03
015
01
005
0(e) 17500 s
025
02
03
015
01
005
0(f) 18000 s
Figure 20 Change of particles concentration in a KCP
Geofluids 13
0
005
01
015
02
025
03
035C
once
ntra
tion
1 2 3 4 5 6 70r (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
(a)
105 15 200z (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
0
005
01
015
02
025
03
035
Con
cent
ratio
n (b)
Figure 21 Evolution of particle concentration along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
ConcentrationLoss rate
0
005
01
015
Con
cent
ratio
n
5 10 15 200Time (times103 s)
0
5
10
15
20
25
Part
icle
loss
rate
Qp
(m3h
)
Figure 22 Evolution of average particle volumetric concentrationand particle loss rate
441 Impact of Heterogeneity on Fractures Evolution Fig-ure 23 illustrates the distribution law of the fractures seepagevelocities and particle volume concentrations under identicalflow pressures but different fracture distribution conditionsat 175 times 103 seconds The results show that more intercon-nected fractures are developed along with the increase in mvalues For example when119898 = 4 there are only two intercon-nected fractures However asm value increases an increasingnumber of fractures were generated and interconnected Inthe fourth case (119898 = 10) three interconnected fractures weregenerated This finding indicates that the homogeneity canaccelerate the propagation of the fractures An increase in
Table 2 List of simulation scenarios
Parameter Value
Weibull distribution coefficient (-)
119898 = 4119898 = 6119898 = 8
119898 = 10
Water pressure (MPa)
119901 = 10119901 = 20119901 = 30119901 = 40
Initial particle concentration ()
1198620 = 00051198620 = 0011198620 = 0021198620 = 005
Fracture aperture (times10minus4m)
119887 = 075119887 = 10
119887 = 125119887 = 15
flow velocity and particle concentration with increasing mvalues was also observed as shown in Figures 23(b) and 23(c)
442 Prediction of Water Inrush under Different ConditionsThe analysis and prediction of the occurrences of waterinrush in KCPs based on the changes in seepage are essentialfor the safety of mining processes Some researchers haveadopted catastrophe theories to predict the occurrences ofwater inrush However an approach that can be used topredict water inrush based on water flow has yet to be foundin the literature This study presents the first attempt toresolve this challenge by applying the inverse velocity theory
14 Geofluids
m = 4 m = 6 m = 8 m = 10
1
2
3
4
5
6
7
(a) Distribution of aperture 119887 (times10minus4m )
m = 4 m = 6 m = 8 m = 10
2
16
12
08
04
0
(b) Distribution of seepage velocity (times10minus3ms)
m = 4 m = 6 m = 8 m = 10
025
02
03
015
01
005
0
(c) Distribution of particles concentration
Figure 23 Distribution of fracture seepage velocity and particle concentration at different Weibull distribution conditions (a) Impact ofWeibull distribution on fractures evolution (b) impact of Weibull distribution on water velocity evolution (c) impact of Weibull distributionon particle concentration evolution
Geofluids 15
5 10 15 200Time (times103 s)
m = 4
m = 6 m = 10
m = 8
0
20
40
60
80
100
120Fl
ow ra
te (m
3h
)
(a)
205
21
215
22
225
23
Wat
er in
rush
tim
e (times10
3s)
4 6 8 102Weibull coefficient m
y = 25699xminus0089
R2 = 09825
(b)
Figure 24 Impact of heterogeneity on water flow rate (a) and inrush time (b)
0
20
40
60
80
100
120
140
160
180
200
Flow
rate
(m3h
)
5 10 15 200Time (times103 s)
p = 1MPap = 2MPa
p = 3MPap = 4MPa
(a)
y = 41733xminus1001
R2 = 09992
1 2 3 4 50Water pressure (MPa)
0
5
10
15
20
25
30
35
40
45
Wat
er in
rush
tim
e (times10
3s)
(b)
Figure 25 Impact of aquifer water pressure on water flow rate (a) and inrush time (b)
which has been widely approved effective in many fields suchas slope stability predictionThe relevant results and analysesare shown in Figure 24ndashFigure 27
As shown in Figure 24 water flow rate exhibits a non-linear increase and as the value of m increases the seepagerate accelerates gradually For example at 119905 = 15 times 104 s theseepage rate was approximately 15m3h for 119898 = 4 while itjumped to 25m3h for 119898 = 10 Results from Figure 24(b)show that water inrush occurs sooner for a greater 119898 valueIn other words the inrush occurs earlier as the heterogeneityincreases The water inrush time follows the power functionThis is due to the fact that the water is more prone to flowingthrough the existing fractures (which indicates a higher
permeability) in the heterogeneous structure Neverthelessdue to the heterogeneous distribution of the aperture thefractures cannot be easily interconnected which hampers theformation of the seepage channels In regard to the homo-geneous rock strata since the flow of water was dominantlycontrolled by the pressure gradient the fractures generatedduring the process of erosion could be easily interconnectedand as a result the water inrush occurredsooner
Figure 25 illustrates the impact of the initial KCPrsquos waterpressure on the flow rates and water inrush time It can beseen that as the pressure increases the changes in the flowrates accelerate For example for119901 = 2MPa the flow rate wasonly approximately 5m3h and it increased to 30m3h when
16 Geofluids
0
20
40
60
80
100
120
140
160
180
200Fl
ow ra
te (m
3h
)
5 10 15 20 250Time (times103 s)
c = 0005
c = 001
c = 002
c = 005
(a)
0
5
10
15
20
25
30
35
Wat
er in
rush
tim
e (times10
3s)
001 002 003 004 0050Initial particle concentration
y = 13554xminus0591
R2 = 09975
(b)
Figure 26 Impact of initial particle concentration on water flow rate (a) and inrush time (b)
0
20
40
60
80
100
120
140
160
180
200
Flow
rate
(m3h
)
5 10 15 200Time (times103 s)
075E minus 4m100E minus 4m
125E minus 4m150E minus 4m
(a)
y = 31027eminus286x
R2 = 09503
09 11 13 1507Fracture aperture (times10minus4 m)
0
5
10
15
20
25
30
35
40
Wat
er in
rush
tim
e (times10
3s)
(b)
Figure 27 Impact of absolute aperture on water flow rate (a) and inrush time (b)
119901 = 3MPa In addition with increasing the aquifer waterpressure the water inrush time was also brought forward asshown in Figure 25(a) The outburst time was approximately119905 = 40 times 104 s for p = 1MPa while only 10 times 104 s for119901 = 4MPa The relationship between the time of the inrushoccurrences and the aquifer water pressure follows the powerfunction as illustrated in Figure 25
For varying initial particle concentrations the evolutionof both the water flow rate change and the water inrushtime shows a similar trend to that of different aquifer waterpressures The flow rate accelerates with increasing initialparticle concentration and consequently the water inrushoccurs earlier as shown in Figure 26The outburst times alsoshow a power function to the initial particle concentration
The initial average fracture aperture also shows significantimpact on water flow behavior For instance results fromFigure 27 clearly illustrate that the flow rate increases withincreasing initial average fracture aperture Please note thatthe inrush time follows an exponential function to the initialaverage fracture aperture
These numerical results can be explained by the factthat the initial seepage velocity is expected to be higher forthe modelling cases with the higher initial aquifer pressureinitial fracture aperture andor initial particle concentrationThe higher flow velocity would intensify the erosion of thefractures enhance the permeability and thereby acceleratethe migration of the particles and interconnection of seepagechannels which causes water inrush
Geofluids 17
5 Conclusions
In this study a systematic approach was established to inves-tigate the impact of controlling factors onwater flow behaviorfor KCPs and to predict water inrush time by introducing theinverse velocity theory In this approach a suite of governingequations was developed to couple all the physics involvedin this complex process including water flow rock erosionand change in rock microstructure These equations werethen implemented into a finite element software COMSOLMultiphysics to simulate the fully coupled process Basedon this numerical model a series of sensitivity studies wereconducted and some important findings have been drawn
(i) Water flow rate increases with increasing aquiferpressure initial particle concentration and fractureopening This results in an increase in the permeabil-ity and finally an acceleration of the migration of theparticles and interconnection of the seepage channelsThis finding suggests the grouting of the KCPs couldbe an effective measure to mitigate water inrush risk
(ii) The inverse velocity theory was successfully appliedto analyze the occurrences of water inrush underdifferent conditions The results show that the timeof inrush has a power relationship to the rock het-erogeneity water pressure and initial particle concen-tration and follows an exponential relationship to theinitial fracture apertures
The framework developed from this work not only helpsenhance coal mining operations safety by better under-standing and predicting water inrush risks so that propermitigation measures can be put in place timely It canalso be extended to other fields such as tunneling backfillpaste piping tailing dam erosion and other engineeringapplications which are likely to encounter time-dependenterosion or deformation or water inrush issues
Please be noted that there are a number of other stochasticmethods available in the literature that can be used to illus-trate rock heterogeneity such as the Monte-Carlo methodor First-Order approach The differences of these methodson the results of water inrush prediction may be worthcomparing in the near future
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This project is supported by the National Natural ScienceFoundation of China (nos 51304072 51774110) the Programfor Innovative Research Team in University of Ministryof Education of China (IRT 16R22) and the PostdoctoralScience Foundation of China (2017M612398)
References
[1] DMa XMiao H Bai et al ldquoEffect of mining on shear sidewallgroundwater inrush hazard caused by seepage instability of the
penetrated karst collapse pillarrdquo Natural Hazards vol 82 no 1pp 73ndash93 2016
[2] H Keqiang Y Guangming and L Yaoru ldquoPalaeo-karst collapsepillars in northern China and their damage to the geologicalenvironmentsrdquo Environmental Geology vol 58 no 5 pp 1029ndash1040 2009
[3] B Yao J Wei D Wang D Ma and Z Chen ldquoNumericalstudy on seepage property of karst collapse columns underparticle migrationrdquo CMES Computer Modeling in Engineeringamp Sciences vol 91 no 2 pp 81ndash100 2013
[4] J Tang H Bai B Yao and Y Wu ldquoTheoretical analysis onwater-inrush mechanism of concealed collapse pillars in floorrdquoMining Science and Technology vol 21 no 1 pp 57ndash60 2011
[5] Y Chen M Yi C Chen and C Yu ldquoBernstein polynomialsmethod for fractional convection-diffusion equation with vari-able coefficientsrdquoComputerModeling in Engineering amp Sciencesvol 83 no 6 pp 639ndash653 2012
[6] J Zhang and B Shen ldquoCoal mining under aquifers in China Acase studyrdquo International Journal of Rock Mechanics and MiningSciences vol 41 no 4 pp 629ndash639 2004
[7] D Ma H Bai X Miao H Pu B Jiang and Z ChenldquoCompaction and seepage properties of crushed limestoneparticle mixture an experimental investigation for Ordoviciankarst collapse pillar groundwater inrushrdquo Environmental EarthSciences vol 75 no 1 article 11 p 14 2016
[8] S Yin J Zhang and D Liu ldquoA study of mine water inrushesby measurements of in situ stress and rock failuresrdquo NaturalHazards vol 79 no 3 pp 1961ndash1979 2015
[9] H Bai D Ma and Z Chen ldquoMechanical behavior of ground-water seepage in karst collapse pillarsrdquo Engineering Geology vol164 pp 101ndash106 2013
[10] D Ma and H Bai ldquoGroundwater inflow prediction model ofkarst collapse pillar a case study for mining-induced ground-water inrush riskrdquoNatural Hazards vol 76 no 2 pp 1319ndash13342015
[11] D Ma H Bai and Y Wang ldquoMechanical behavior of a coalseam penetrated by a karst collapse pillar mining-inducedgroundwater inrush riskrdquo Natural Hazards vol 75 no 3 pp2137ndash2151 2015
[12] B Yao Research on variable mass fluid-solid coupling dynamictheory of broken rockmass and application China Univeristy ofMining and Technology Xuzhou China 2012
[13] D Ma X Miao H Bai et al ldquoImpact of particle transfer onflow properties of crushed mudstonesrdquo Environmental EarthSciences vol 75 no 7 article 593 2016
[14] DMa H Bai Z Chen andH Pu ldquoEffect of particlemixture onseepage properties of crushed mudstonesrdquo Transport in PorousMedia vol 108 no 2 pp 257ndash277 2015
[15] B Zhang H Bai and K Zhang ldquoSeepage characteristics ofcollapse columnfillingsrdquo International Journal ofMining Scienceand Technology 2015
[16] P Ortoleva J Chadam E Merino and A Sen ldquoGeochemicalself-organization II the reactive-infiltration instabilityrdquo Ameri-can Journal of Science vol 287 no 10 pp 1008ndash1040 1987
[17] I Vardoulakis M Stavropoulou and P Papanastasiou ldquoHydro-mechanical aspects of the sand production problemrdquo Transportin Porous Media vol 22 no 2 pp 225ndash244 1996
[18] R L Detwiler and H Rajaram ldquoPredicting dissolution patternsin variable aperture fractures Evaluation of an enhanced depth-averaged computational modelrdquoWater Resources Research vol43 no 4 Article IDW04403 2007
18 Geofluids
[19] M A Habib H M Badr R Ben-Mansour and M E KabirldquoErosion rate correlations of a pipe protruded in an abrupt pipecontractionrdquo International Journal of Impact Engineering vol34 no 8 pp 1350ndash1369 2007
[20] H T Xiao and H Y Xu ldquoIn situ permeability measurementsto establish the influence of slice mining on floor rocksrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 37 no 5 pp 855ndash860 2000
[21] H Guo D P Adhikary and M S Craig ldquoSimulation of minewater inflow and gas emission during longwall miningrdquo RockMechanics and Rock Engineering vol 42 no 1 pp 25ndash51 2009
[22] R Zhang Z JiangH ZhouC Yang and S Xiao ldquoGroundwateroutbursts from faults above a confined aquifer in the coalminingrdquo Natural Hazards vol 71 no 3 pp 1861ndash1872 2014
[23] B Yao F Du E Li and X Wang ldquoMechanical model of karstcollapse columns water inrush and its applicationrdquo ElectronicJournal of Geotechnical Engineering vol 19 pp 1665ndash1675 2014
[24] J Warren and P Root ldquoThe behavior of naturally fracturedreservoirsrdquo SPE Journal vol 3 no 3 pp 245ndash255 2013
[25] H KazemiM S Seth andGWThomas ldquoThe interpretation ofinterference tests in naturally fractured reservoirs with uniformfracture distributionrdquo SPE Journal vol 9 no 4 pp 463ndash4721969
[26] A de Swaan O ldquoAnalytical solutions for determining naturallyfractured reservoir properties by well testingrdquo SPE Journal vol16 no 3 pp 117ndash122 1976
[27] N D Rose and O Hungr ldquoForecasting potential rock slopefailure in open pit mines using the inverse-velocity methodrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 2 pp 308ndash320 2007
[28] J R Fanchi Petroleum Engineering Handbook Volume 1 Gen-eral Engineering Society of Petroleum Engineers 2006
[29] R Sakthivadivel and S Irmay A Review of Filtration TheoriesHydraulic Engineering Laboratory College of EngineeringUniversity of California Berkeley Calif USA 1996
[30] C Wang P Zhai Z Chen J Liu L Wang and J XieldquoExperimental study of coal matrix-cleat interaction underconstant volume boundary conditionrdquo International Journal ofCoal Geology vol 181 pp 124ndash132 2017
[31] S Irmay ldquoOn the theoretical derivation of Darcy and Forch-heimer formulasrdquo Eos Transactions American GeophysicalUnion vol 39 no 4 pp 702ndash707 1958
[32] CH Lee and IW Farmer ldquoA simplemethod of estimating rockmass porosity and permeabilityrdquo International Journal ofMiningand Geological Engineering vol 8 no 1 pp 57ndash65 1990
[33] C Nalluri A K El-Zaemey and H L Chan ldquoSedimenttransport over fixed deposited beds in sewers - An appraisal ofexisting modelsrdquoWater Science and Technology vol 36 no 8-9pp 123ndash128 1997
[34] P Novak and C Nalluri ldquoSediment transport in smooth fixedbed channelsrdquo Journal of the Hydraulics Division vol 101 no 9pp 1139ndash1154 1975
[35] T Fukuzono ldquoA newmethod for predicting the failure time of asloperdquo in Proceedings of the In 4th International Conference andField Workshop on Landslides Tokyo Japan 1985
[36] C R J Kilburn andDN Petley ldquoForecasting giant catastrophicslope collapse lessons from Vajont Northern Italyrdquo Geomor-phology vol 54 no 1-2 pp 21ndash32 2003
[37] B Voight ldquoA method for prediction of volcanic eruptionsrdquoNature vol 332 no 6160 pp 125ndash130 1988
[38] B Yao X Mao J Wei and D Wang ldquoStudy on coupled fluid-solid model for collapse columns considering the effect ofparticle transportrdquo Zhongguo Kuangye Daxue XuebaoJournalof China University of Mining and Technology vol 43 no 1 pp30ndash35 2014
[39] H Bai Seepage Characteristics of Top Stratum of OrdovicianSystem and Its Application Study as Key Aquifuge ChinaUniversity of Mining amp Technology Xuzhou China 2008
[40] C A Tang L G Tham P K K Lee T H Yang and L CLi ldquoCoupled analysis of flow stress and damage (FSD) in rockfailurerdquo International Journal of Rock Mechanics and MiningSciences vol 39 no 4 pp 477ndash489 2002
[41] W C Zhu and C A Tang ldquoMicromechanical model forsimulating the fracture process of rockrdquo Rock Mechanics andRock Engineering vol 37 no 1 pp 25ndash56 2004
[42] T H Yang L G Tham C A Tang Z Z Liang and YTsui ldquoInfluence of heterogeneity of mechanical properties onhydraulic fracturing in permeable rocksrdquo Rock Mechanics andRock Engineering vol 37 no 4 pp 251ndash275 2004
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Submit your manuscripts atwwwhindawicom
8 Geofluids
Description LithologyThickness (m)
11 coal
Limestone
Mudstone
Fine sandstone
Aquifer
10 coal
Limestone
Mudstone
30
25
73
33
46
200
358
Mudstone
9 coal
89
05
96
(a) (b) (c)
times10minus4
05
06
07
08
09
1
11
12
13
14
Figure 13 Model geometry and setup (a) illustration of KCP and rock strata (b) 2D simulation model and (c) distribution of apertureopening based on Weibull function
pressure at the water outlet on the top was 01MPa initialwater pressure in the model was 01MPa initial particle vol-ume concentration was 001 initial average fracture aperture1198870 was 01mm and initial porosity 1206010 was 10 The mainparameters of the model were all determined according tothe relevant references [3 12] in which the studies wereconducted on the same seam Other used parameters arelisted in Table 1Themodel was divided into 5000 grids usingmapped mesh method embedded in the COMSOL softwareThe shape of the grids is rectangular
Heterogeneity has been determined to be a prominentfeature of rock There are currently various approaches toobtaining the characteristics of the heterogeneous distribu-tion of rock materials For example digital core techniquesand mathematical statistics methods have both been utilizedPrevious studies have shown that the heterogeneity of rockcan be described by the Weibull distribution [40ndash42] Thusthe Weibull distribution was selected in this study due to itseffectiveness and great simplicity to obtain the heterogeneousdistribution of fracture apertures of the KCPs The distribu-tion probability density equation was as follows
119891 (119887) = 1198981198870 ( 119887
1198870)119898minus1
exp [minus ( 1198871198870)119898] (20)
where 119887 indicates the fracture aperture 1198870 denotes the initialfracture aperture and 119898 is the uniformity index The larger119898 represents the higher level of uniformity The fractureaperture distribution obtained by the numerical generationmethod is shown in Figure 13(c)
Based on thismodel geometry (9) (11) (14) (15) (17) and(18) will be solved simultaneously to investigate the dynamicchange of water flow behaviors and the associated inrush riskunder different flow conditions
4 Results and Analysis
In order to analyze the characteristics of seepage at differenttimes in this study six different moments were selected (ie14 times 103 15 times 103 16 times 103 17 times 103 175 times 103 and 18 times 103 s)The specific results will be discussed below
41 Distribution of the Fracture Apertures Figure 14 illus-trates the spatial changes of the fracture apertures at differenttimes Figure 15 shows the evolution of fracture aperturesalong O-O10158401015840 and O1015840-A1015840 lines as marked in Figure 13(b)and the average fracture aperture-time curve was plotted inFigure 16 The results show the following(1) The fracture aperture gradually increases under theeffects of the erosion However the increase rate is higherin the upper part of the model than in the lower part Thisis likely because the upper outlet boundary is narrower thanthe bottom inlet boundary giving rise to higher flow velocitySuch higher velocity causes more significant erosion andconsequently the fracture aperture change is faster(2) As the infiltration continues the average fractureaperture increases by approximately 200 from 01mm tonearly 03mm (Figure 16) At the initial stage the fracture issubject to random distribution with minor difference in theapertures However the variation diverges under the effectsof the erosion The fractures with smaller initial aperturesbecome slowly enlarged by approximately 20 while thosewith larger apertures continuously increase by more than200 As the fractures gradually dilate and interconnectwith each other a number of dominant seepage channels areformed as illustrated in Figure 14(f)
42 Distribution of Water Seepage Velocity The seepagevelocities (ie Darcy velocity) in the model domain andalong O-O10158401015840 and O1015840-A1015840 lines were shown in Figures 17 and
Geofluids 9
Table 1 Input parameters for the numerical simulation
120588119904(kgm3) 120578(Pasdots) 1198961198980(m2) 1206010 1198870(m) 119886 1205821(mminus1) 1205822(mminus1) 119898 11986202000 10minus3 10minus12 01 00001 001 001 001 6 001
1
2
3
4
5
6
7
(a) 14000 s
1
2
3
4
5
6
7
(b) 15000 s
1
2
3
4
5
6
7
(c) 16000 s
1
2
3
4
5
6
7
(d) 17000 s
1
2
3
4
5
6
7
(e) 17500 s
1
2
3
4
5
6
7
(f) 18000 s
Figure 14 The spatial distribution of aperture 119887 (10minus4m ) at different times
18 respectively The predicted failure time using the inversevelocity theory was plotted in Figure 19The key observationsinclude the following(1) As shown in Figure 17 the changes in the flowvelocity are consistent with the distribution of the fractures(Figure 14) and more fracture aperture changes are observedat the locations where higher seepage velocities take place Asshown in Figure 18 at 14times 104 s theminimumandmaximumseepage velocities were approximately 35 times 10minus6ms and 411times 10minus5ms At 18 times 104 s these two figures increased by 20and 200 to 42 times 10minus6ms and 125 times 10minus3ms respectively(2)Therewas a continuous increase in flow rate at the out-let from approximately 37m3 h initially to approximately100m3 h at 18times 104 s increased by nearly 30 times Howeverits increase showed a nonlinear trend likely due to the fact
that the increase rate was relatively slow in the initial stagebut accelerated gradually until the water inrush occurredFigure 19 was generated according to the inverse velocitytheory and the results showed that the water inrush wouldoccur at 185 times 104 s for this particular flow condition Thetrend has been reflected by the change in flow velocity shownin Figure 17 The figure shows that shortly before the inrushthe flow channels rapidly connected together and formed amain channel resulting in a surge in water flow
43 Distribution of the Particle Concentrations Particle con-centration is directly related to the erosion rate Higherparticle concentration indicates more severe erosion whichis more likely to result in greater fracture aperture change
10 Geofluids
05
15
25
35
45
55
65Fr
actu
re ap
ertu
reb
(times10
minus4
m)
5 10 15 200z (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
(a)
1 2 3 4 5 6 70r (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
05
15
25
35
45
55
65
Frac
ture
aper
ture
b(times
10minus4
m)
(b)
Figure 15 Evolution of fracture aperture along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
1
15
2
25
3
Frac
ture
aper
ture
b(times
10minus4
m)
5 10 15 200Time (times103 s)
Figure 16 Change of average fracture aperture with time
Figure 20 shows the evolution of the average particleconcentration along O-O10158401015840 and O1015840-A1015840 lines The averageparticle concentration and particle loss rate was plotted inFigure 21
Figure 20 plots the spatial distribution of the particleconcentrations for the wholemodel at different times Resultsshow that the particle concentration gradually increasesfrom the bottom upwards This is because under the effectsof the erosion increasing amount of particles migratedinto the water and gradually moved upwards through thefractures and pores This is consistent with the change inthe particle concentration at different locations as shown inFigure 21
Results in Figure 22 are well in line with the results shownin Figure 18 For example at the beginning the particle lossrate is relatively low however the rate constantly increasesover time and culminates at the inrushThis is due to the fact
that along with the increases in the seepage velocities theerosion effects on the solid particles are constantly intensifiedwhich results in frequent migration and substantial particleloss
44 Sensitivity Analyses The outburst processes wereaffected or controlled by various factors including thespatial heterogeneity of lithology of the KCPs waterpressure absolute aperture and distribution of the fracturesdistribution law of concentration of the karst particlesand their sensitivity to water erosion Based on the newlydeveloped coupling model this work further examined thewater and particle migration characteristics in the KCPsunder different hydrological and geological conditionsas well as the variations in the inrush occurrences Thescenarios to be studied are summarized in Table 2
Geofluids 11
2
16
12
08
04
0(a) 14000 s
2
16
12
08
04
0(b) 15000 s
2
16
12
08
04
0(c) 16000 s
2
16
12
08
04
0(d) 17000 s
2
16
12
08
04
0(e) 17500 s
2
16
12
08
04
0(f) 18000 s
Figure 17 The change of seepage velocity (10minus3ms) in a KCP
14000 s15000 s16000 s
17000 s17500 s18000 s
r (m)
1 2 3 4 5 6 70
Velo
city
(10minus
3m
s)
14
12
1
08
06
04
02
0
(a)
14000 s15000 s16000 s
17000 s17500 s18000 s
50 10z (m)
15 20
Velo
city
(10minus
3m
s)
14
12
1
08
06
04
02
0
(b)
Figure 18 Evolution of seepage velocity along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
12 Geofluids
Inverse velocityLinear fitting
0
20
40
60
80
100
Flow
rate
(m3h
)
0
5
10
15
20
25
30
Inve
rse v
eloci
ty (h
m)
5 10 15 200Time (times103 s)
Q
Figure 19 Water flow rate along the bottom surface of the numerical model
025
02
03
015
01
005
0(a) 14000 s
025
02
03
015
01
005
0(b) 15000 s
025
02
03
015
01
005
0(c) 16000 s
025
02
03
015
01
005
0(d) 17000 s
025
02
03
015
01
005
0(e) 17500 s
025
02
03
015
01
005
0(f) 18000 s
Figure 20 Change of particles concentration in a KCP
Geofluids 13
0
005
01
015
02
025
03
035C
once
ntra
tion
1 2 3 4 5 6 70r (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
(a)
105 15 200z (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
0
005
01
015
02
025
03
035
Con
cent
ratio
n (b)
Figure 21 Evolution of particle concentration along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
ConcentrationLoss rate
0
005
01
015
Con
cent
ratio
n
5 10 15 200Time (times103 s)
0
5
10
15
20
25
Part
icle
loss
rate
Qp
(m3h
)
Figure 22 Evolution of average particle volumetric concentrationand particle loss rate
441 Impact of Heterogeneity on Fractures Evolution Fig-ure 23 illustrates the distribution law of the fractures seepagevelocities and particle volume concentrations under identicalflow pressures but different fracture distribution conditionsat 175 times 103 seconds The results show that more intercon-nected fractures are developed along with the increase in mvalues For example when119898 = 4 there are only two intercon-nected fractures However asm value increases an increasingnumber of fractures were generated and interconnected Inthe fourth case (119898 = 10) three interconnected fractures weregenerated This finding indicates that the homogeneity canaccelerate the propagation of the fractures An increase in
Table 2 List of simulation scenarios
Parameter Value
Weibull distribution coefficient (-)
119898 = 4119898 = 6119898 = 8
119898 = 10
Water pressure (MPa)
119901 = 10119901 = 20119901 = 30119901 = 40
Initial particle concentration ()
1198620 = 00051198620 = 0011198620 = 0021198620 = 005
Fracture aperture (times10minus4m)
119887 = 075119887 = 10
119887 = 125119887 = 15
flow velocity and particle concentration with increasing mvalues was also observed as shown in Figures 23(b) and 23(c)
442 Prediction of Water Inrush under Different ConditionsThe analysis and prediction of the occurrences of waterinrush in KCPs based on the changes in seepage are essentialfor the safety of mining processes Some researchers haveadopted catastrophe theories to predict the occurrences ofwater inrush However an approach that can be used topredict water inrush based on water flow has yet to be foundin the literature This study presents the first attempt toresolve this challenge by applying the inverse velocity theory
14 Geofluids
m = 4 m = 6 m = 8 m = 10
1
2
3
4
5
6
7
(a) Distribution of aperture 119887 (times10minus4m )
m = 4 m = 6 m = 8 m = 10
2
16
12
08
04
0
(b) Distribution of seepage velocity (times10minus3ms)
m = 4 m = 6 m = 8 m = 10
025
02
03
015
01
005
0
(c) Distribution of particles concentration
Figure 23 Distribution of fracture seepage velocity and particle concentration at different Weibull distribution conditions (a) Impact ofWeibull distribution on fractures evolution (b) impact of Weibull distribution on water velocity evolution (c) impact of Weibull distributionon particle concentration evolution
Geofluids 15
5 10 15 200Time (times103 s)
m = 4
m = 6 m = 10
m = 8
0
20
40
60
80
100
120Fl
ow ra
te (m
3h
)
(a)
205
21
215
22
225
23
Wat
er in
rush
tim
e (times10
3s)
4 6 8 102Weibull coefficient m
y = 25699xminus0089
R2 = 09825
(b)
Figure 24 Impact of heterogeneity on water flow rate (a) and inrush time (b)
0
20
40
60
80
100
120
140
160
180
200
Flow
rate
(m3h
)
5 10 15 200Time (times103 s)
p = 1MPap = 2MPa
p = 3MPap = 4MPa
(a)
y = 41733xminus1001
R2 = 09992
1 2 3 4 50Water pressure (MPa)
0
5
10
15
20
25
30
35
40
45
Wat
er in
rush
tim
e (times10
3s)
(b)
Figure 25 Impact of aquifer water pressure on water flow rate (a) and inrush time (b)
which has been widely approved effective in many fields suchas slope stability predictionThe relevant results and analysesare shown in Figure 24ndashFigure 27
As shown in Figure 24 water flow rate exhibits a non-linear increase and as the value of m increases the seepagerate accelerates gradually For example at 119905 = 15 times 104 s theseepage rate was approximately 15m3h for 119898 = 4 while itjumped to 25m3h for 119898 = 10 Results from Figure 24(b)show that water inrush occurs sooner for a greater 119898 valueIn other words the inrush occurs earlier as the heterogeneityincreases The water inrush time follows the power functionThis is due to the fact that the water is more prone to flowingthrough the existing fractures (which indicates a higher
permeability) in the heterogeneous structure Neverthelessdue to the heterogeneous distribution of the aperture thefractures cannot be easily interconnected which hampers theformation of the seepage channels In regard to the homo-geneous rock strata since the flow of water was dominantlycontrolled by the pressure gradient the fractures generatedduring the process of erosion could be easily interconnectedand as a result the water inrush occurredsooner
Figure 25 illustrates the impact of the initial KCPrsquos waterpressure on the flow rates and water inrush time It can beseen that as the pressure increases the changes in the flowrates accelerate For example for119901 = 2MPa the flow rate wasonly approximately 5m3h and it increased to 30m3h when
16 Geofluids
0
20
40
60
80
100
120
140
160
180
200Fl
ow ra
te (m
3h
)
5 10 15 20 250Time (times103 s)
c = 0005
c = 001
c = 002
c = 005
(a)
0
5
10
15
20
25
30
35
Wat
er in
rush
tim
e (times10
3s)
001 002 003 004 0050Initial particle concentration
y = 13554xminus0591
R2 = 09975
(b)
Figure 26 Impact of initial particle concentration on water flow rate (a) and inrush time (b)
0
20
40
60
80
100
120
140
160
180
200
Flow
rate
(m3h
)
5 10 15 200Time (times103 s)
075E minus 4m100E minus 4m
125E minus 4m150E minus 4m
(a)
y = 31027eminus286x
R2 = 09503
09 11 13 1507Fracture aperture (times10minus4 m)
0
5
10
15
20
25
30
35
40
Wat
er in
rush
tim
e (times10
3s)
(b)
Figure 27 Impact of absolute aperture on water flow rate (a) and inrush time (b)
119901 = 3MPa In addition with increasing the aquifer waterpressure the water inrush time was also brought forward asshown in Figure 25(a) The outburst time was approximately119905 = 40 times 104 s for p = 1MPa while only 10 times 104 s for119901 = 4MPa The relationship between the time of the inrushoccurrences and the aquifer water pressure follows the powerfunction as illustrated in Figure 25
For varying initial particle concentrations the evolutionof both the water flow rate change and the water inrushtime shows a similar trend to that of different aquifer waterpressures The flow rate accelerates with increasing initialparticle concentration and consequently the water inrushoccurs earlier as shown in Figure 26The outburst times alsoshow a power function to the initial particle concentration
The initial average fracture aperture also shows significantimpact on water flow behavior For instance results fromFigure 27 clearly illustrate that the flow rate increases withincreasing initial average fracture aperture Please note thatthe inrush time follows an exponential function to the initialaverage fracture aperture
These numerical results can be explained by the factthat the initial seepage velocity is expected to be higher forthe modelling cases with the higher initial aquifer pressureinitial fracture aperture andor initial particle concentrationThe higher flow velocity would intensify the erosion of thefractures enhance the permeability and thereby acceleratethe migration of the particles and interconnection of seepagechannels which causes water inrush
Geofluids 17
5 Conclusions
In this study a systematic approach was established to inves-tigate the impact of controlling factors onwater flow behaviorfor KCPs and to predict water inrush time by introducing theinverse velocity theory In this approach a suite of governingequations was developed to couple all the physics involvedin this complex process including water flow rock erosionand change in rock microstructure These equations werethen implemented into a finite element software COMSOLMultiphysics to simulate the fully coupled process Basedon this numerical model a series of sensitivity studies wereconducted and some important findings have been drawn
(i) Water flow rate increases with increasing aquiferpressure initial particle concentration and fractureopening This results in an increase in the permeabil-ity and finally an acceleration of the migration of theparticles and interconnection of the seepage channelsThis finding suggests the grouting of the KCPs couldbe an effective measure to mitigate water inrush risk
(ii) The inverse velocity theory was successfully appliedto analyze the occurrences of water inrush underdifferent conditions The results show that the timeof inrush has a power relationship to the rock het-erogeneity water pressure and initial particle concen-tration and follows an exponential relationship to theinitial fracture apertures
The framework developed from this work not only helpsenhance coal mining operations safety by better under-standing and predicting water inrush risks so that propermitigation measures can be put in place timely It canalso be extended to other fields such as tunneling backfillpaste piping tailing dam erosion and other engineeringapplications which are likely to encounter time-dependenterosion or deformation or water inrush issues
Please be noted that there are a number of other stochasticmethods available in the literature that can be used to illus-trate rock heterogeneity such as the Monte-Carlo methodor First-Order approach The differences of these methodson the results of water inrush prediction may be worthcomparing in the near future
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This project is supported by the National Natural ScienceFoundation of China (nos 51304072 51774110) the Programfor Innovative Research Team in University of Ministryof Education of China (IRT 16R22) and the PostdoctoralScience Foundation of China (2017M612398)
References
[1] DMa XMiao H Bai et al ldquoEffect of mining on shear sidewallgroundwater inrush hazard caused by seepage instability of the
penetrated karst collapse pillarrdquo Natural Hazards vol 82 no 1pp 73ndash93 2016
[2] H Keqiang Y Guangming and L Yaoru ldquoPalaeo-karst collapsepillars in northern China and their damage to the geologicalenvironmentsrdquo Environmental Geology vol 58 no 5 pp 1029ndash1040 2009
[3] B Yao J Wei D Wang D Ma and Z Chen ldquoNumericalstudy on seepage property of karst collapse columns underparticle migrationrdquo CMES Computer Modeling in Engineeringamp Sciences vol 91 no 2 pp 81ndash100 2013
[4] J Tang H Bai B Yao and Y Wu ldquoTheoretical analysis onwater-inrush mechanism of concealed collapse pillars in floorrdquoMining Science and Technology vol 21 no 1 pp 57ndash60 2011
[5] Y Chen M Yi C Chen and C Yu ldquoBernstein polynomialsmethod for fractional convection-diffusion equation with vari-able coefficientsrdquoComputerModeling in Engineering amp Sciencesvol 83 no 6 pp 639ndash653 2012
[6] J Zhang and B Shen ldquoCoal mining under aquifers in China Acase studyrdquo International Journal of Rock Mechanics and MiningSciences vol 41 no 4 pp 629ndash639 2004
[7] D Ma H Bai X Miao H Pu B Jiang and Z ChenldquoCompaction and seepage properties of crushed limestoneparticle mixture an experimental investigation for Ordoviciankarst collapse pillar groundwater inrushrdquo Environmental EarthSciences vol 75 no 1 article 11 p 14 2016
[8] S Yin J Zhang and D Liu ldquoA study of mine water inrushesby measurements of in situ stress and rock failuresrdquo NaturalHazards vol 79 no 3 pp 1961ndash1979 2015
[9] H Bai D Ma and Z Chen ldquoMechanical behavior of ground-water seepage in karst collapse pillarsrdquo Engineering Geology vol164 pp 101ndash106 2013
[10] D Ma and H Bai ldquoGroundwater inflow prediction model ofkarst collapse pillar a case study for mining-induced ground-water inrush riskrdquoNatural Hazards vol 76 no 2 pp 1319ndash13342015
[11] D Ma H Bai and Y Wang ldquoMechanical behavior of a coalseam penetrated by a karst collapse pillar mining-inducedgroundwater inrush riskrdquo Natural Hazards vol 75 no 3 pp2137ndash2151 2015
[12] B Yao Research on variable mass fluid-solid coupling dynamictheory of broken rockmass and application China Univeristy ofMining and Technology Xuzhou China 2012
[13] D Ma X Miao H Bai et al ldquoImpact of particle transfer onflow properties of crushed mudstonesrdquo Environmental EarthSciences vol 75 no 7 article 593 2016
[14] DMa H Bai Z Chen andH Pu ldquoEffect of particlemixture onseepage properties of crushed mudstonesrdquo Transport in PorousMedia vol 108 no 2 pp 257ndash277 2015
[15] B Zhang H Bai and K Zhang ldquoSeepage characteristics ofcollapse columnfillingsrdquo International Journal ofMining Scienceand Technology 2015
[16] P Ortoleva J Chadam E Merino and A Sen ldquoGeochemicalself-organization II the reactive-infiltration instabilityrdquo Ameri-can Journal of Science vol 287 no 10 pp 1008ndash1040 1987
[17] I Vardoulakis M Stavropoulou and P Papanastasiou ldquoHydro-mechanical aspects of the sand production problemrdquo Transportin Porous Media vol 22 no 2 pp 225ndash244 1996
[18] R L Detwiler and H Rajaram ldquoPredicting dissolution patternsin variable aperture fractures Evaluation of an enhanced depth-averaged computational modelrdquoWater Resources Research vol43 no 4 Article IDW04403 2007
18 Geofluids
[19] M A Habib H M Badr R Ben-Mansour and M E KabirldquoErosion rate correlations of a pipe protruded in an abrupt pipecontractionrdquo International Journal of Impact Engineering vol34 no 8 pp 1350ndash1369 2007
[20] H T Xiao and H Y Xu ldquoIn situ permeability measurementsto establish the influence of slice mining on floor rocksrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 37 no 5 pp 855ndash860 2000
[21] H Guo D P Adhikary and M S Craig ldquoSimulation of minewater inflow and gas emission during longwall miningrdquo RockMechanics and Rock Engineering vol 42 no 1 pp 25ndash51 2009
[22] R Zhang Z JiangH ZhouC Yang and S Xiao ldquoGroundwateroutbursts from faults above a confined aquifer in the coalminingrdquo Natural Hazards vol 71 no 3 pp 1861ndash1872 2014
[23] B Yao F Du E Li and X Wang ldquoMechanical model of karstcollapse columns water inrush and its applicationrdquo ElectronicJournal of Geotechnical Engineering vol 19 pp 1665ndash1675 2014
[24] J Warren and P Root ldquoThe behavior of naturally fracturedreservoirsrdquo SPE Journal vol 3 no 3 pp 245ndash255 2013
[25] H KazemiM S Seth andGWThomas ldquoThe interpretation ofinterference tests in naturally fractured reservoirs with uniformfracture distributionrdquo SPE Journal vol 9 no 4 pp 463ndash4721969
[26] A de Swaan O ldquoAnalytical solutions for determining naturallyfractured reservoir properties by well testingrdquo SPE Journal vol16 no 3 pp 117ndash122 1976
[27] N D Rose and O Hungr ldquoForecasting potential rock slopefailure in open pit mines using the inverse-velocity methodrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 2 pp 308ndash320 2007
[28] J R Fanchi Petroleum Engineering Handbook Volume 1 Gen-eral Engineering Society of Petroleum Engineers 2006
[29] R Sakthivadivel and S Irmay A Review of Filtration TheoriesHydraulic Engineering Laboratory College of EngineeringUniversity of California Berkeley Calif USA 1996
[30] C Wang P Zhai Z Chen J Liu L Wang and J XieldquoExperimental study of coal matrix-cleat interaction underconstant volume boundary conditionrdquo International Journal ofCoal Geology vol 181 pp 124ndash132 2017
[31] S Irmay ldquoOn the theoretical derivation of Darcy and Forch-heimer formulasrdquo Eos Transactions American GeophysicalUnion vol 39 no 4 pp 702ndash707 1958
[32] CH Lee and IW Farmer ldquoA simplemethod of estimating rockmass porosity and permeabilityrdquo International Journal ofMiningand Geological Engineering vol 8 no 1 pp 57ndash65 1990
[33] C Nalluri A K El-Zaemey and H L Chan ldquoSedimenttransport over fixed deposited beds in sewers - An appraisal ofexisting modelsrdquoWater Science and Technology vol 36 no 8-9pp 123ndash128 1997
[34] P Novak and C Nalluri ldquoSediment transport in smooth fixedbed channelsrdquo Journal of the Hydraulics Division vol 101 no 9pp 1139ndash1154 1975
[35] T Fukuzono ldquoA newmethod for predicting the failure time of asloperdquo in Proceedings of the In 4th International Conference andField Workshop on Landslides Tokyo Japan 1985
[36] C R J Kilburn andDN Petley ldquoForecasting giant catastrophicslope collapse lessons from Vajont Northern Italyrdquo Geomor-phology vol 54 no 1-2 pp 21ndash32 2003
[37] B Voight ldquoA method for prediction of volcanic eruptionsrdquoNature vol 332 no 6160 pp 125ndash130 1988
[38] B Yao X Mao J Wei and D Wang ldquoStudy on coupled fluid-solid model for collapse columns considering the effect ofparticle transportrdquo Zhongguo Kuangye Daxue XuebaoJournalof China University of Mining and Technology vol 43 no 1 pp30ndash35 2014
[39] H Bai Seepage Characteristics of Top Stratum of OrdovicianSystem and Its Application Study as Key Aquifuge ChinaUniversity of Mining amp Technology Xuzhou China 2008
[40] C A Tang L G Tham P K K Lee T H Yang and L CLi ldquoCoupled analysis of flow stress and damage (FSD) in rockfailurerdquo International Journal of Rock Mechanics and MiningSciences vol 39 no 4 pp 477ndash489 2002
[41] W C Zhu and C A Tang ldquoMicromechanical model forsimulating the fracture process of rockrdquo Rock Mechanics andRock Engineering vol 37 no 1 pp 25ndash56 2004
[42] T H Yang L G Tham C A Tang Z Z Liang and YTsui ldquoInfluence of heterogeneity of mechanical properties onhydraulic fracturing in permeable rocksrdquo Rock Mechanics andRock Engineering vol 37 no 4 pp 251ndash275 2004
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Submit your manuscripts atwwwhindawicom
Geofluids 9
Table 1 Input parameters for the numerical simulation
120588119904(kgm3) 120578(Pasdots) 1198961198980(m2) 1206010 1198870(m) 119886 1205821(mminus1) 1205822(mminus1) 119898 11986202000 10minus3 10minus12 01 00001 001 001 001 6 001
1
2
3
4
5
6
7
(a) 14000 s
1
2
3
4
5
6
7
(b) 15000 s
1
2
3
4
5
6
7
(c) 16000 s
1
2
3
4
5
6
7
(d) 17000 s
1
2
3
4
5
6
7
(e) 17500 s
1
2
3
4
5
6
7
(f) 18000 s
Figure 14 The spatial distribution of aperture 119887 (10minus4m ) at different times
18 respectively The predicted failure time using the inversevelocity theory was plotted in Figure 19The key observationsinclude the following(1) As shown in Figure 17 the changes in the flowvelocity are consistent with the distribution of the fractures(Figure 14) and more fracture aperture changes are observedat the locations where higher seepage velocities take place Asshown in Figure 18 at 14times 104 s theminimumandmaximumseepage velocities were approximately 35 times 10minus6ms and 411times 10minus5ms At 18 times 104 s these two figures increased by 20and 200 to 42 times 10minus6ms and 125 times 10minus3ms respectively(2)Therewas a continuous increase in flow rate at the out-let from approximately 37m3 h initially to approximately100m3 h at 18times 104 s increased by nearly 30 times Howeverits increase showed a nonlinear trend likely due to the fact
that the increase rate was relatively slow in the initial stagebut accelerated gradually until the water inrush occurredFigure 19 was generated according to the inverse velocitytheory and the results showed that the water inrush wouldoccur at 185 times 104 s for this particular flow condition Thetrend has been reflected by the change in flow velocity shownin Figure 17 The figure shows that shortly before the inrushthe flow channels rapidly connected together and formed amain channel resulting in a surge in water flow
43 Distribution of the Particle Concentrations Particle con-centration is directly related to the erosion rate Higherparticle concentration indicates more severe erosion whichis more likely to result in greater fracture aperture change
10 Geofluids
05
15
25
35
45
55
65Fr
actu
re ap
ertu
reb
(times10
minus4
m)
5 10 15 200z (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
(a)
1 2 3 4 5 6 70r (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
05
15
25
35
45
55
65
Frac
ture
aper
ture
b(times
10minus4
m)
(b)
Figure 15 Evolution of fracture aperture along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
1
15
2
25
3
Frac
ture
aper
ture
b(times
10minus4
m)
5 10 15 200Time (times103 s)
Figure 16 Change of average fracture aperture with time
Figure 20 shows the evolution of the average particleconcentration along O-O10158401015840 and O1015840-A1015840 lines The averageparticle concentration and particle loss rate was plotted inFigure 21
Figure 20 plots the spatial distribution of the particleconcentrations for the wholemodel at different times Resultsshow that the particle concentration gradually increasesfrom the bottom upwards This is because under the effectsof the erosion increasing amount of particles migratedinto the water and gradually moved upwards through thefractures and pores This is consistent with the change inthe particle concentration at different locations as shown inFigure 21
Results in Figure 22 are well in line with the results shownin Figure 18 For example at the beginning the particle lossrate is relatively low however the rate constantly increasesover time and culminates at the inrushThis is due to the fact
that along with the increases in the seepage velocities theerosion effects on the solid particles are constantly intensifiedwhich results in frequent migration and substantial particleloss
44 Sensitivity Analyses The outburst processes wereaffected or controlled by various factors including thespatial heterogeneity of lithology of the KCPs waterpressure absolute aperture and distribution of the fracturesdistribution law of concentration of the karst particlesand their sensitivity to water erosion Based on the newlydeveloped coupling model this work further examined thewater and particle migration characteristics in the KCPsunder different hydrological and geological conditionsas well as the variations in the inrush occurrences Thescenarios to be studied are summarized in Table 2
Geofluids 11
2
16
12
08
04
0(a) 14000 s
2
16
12
08
04
0(b) 15000 s
2
16
12
08
04
0(c) 16000 s
2
16
12
08
04
0(d) 17000 s
2
16
12
08
04
0(e) 17500 s
2
16
12
08
04
0(f) 18000 s
Figure 17 The change of seepage velocity (10minus3ms) in a KCP
14000 s15000 s16000 s
17000 s17500 s18000 s
r (m)
1 2 3 4 5 6 70
Velo
city
(10minus
3m
s)
14
12
1
08
06
04
02
0
(a)
14000 s15000 s16000 s
17000 s17500 s18000 s
50 10z (m)
15 20
Velo
city
(10minus
3m
s)
14
12
1
08
06
04
02
0
(b)
Figure 18 Evolution of seepage velocity along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
12 Geofluids
Inverse velocityLinear fitting
0
20
40
60
80
100
Flow
rate
(m3h
)
0
5
10
15
20
25
30
Inve
rse v
eloci
ty (h
m)
5 10 15 200Time (times103 s)
Q
Figure 19 Water flow rate along the bottom surface of the numerical model
025
02
03
015
01
005
0(a) 14000 s
025
02
03
015
01
005
0(b) 15000 s
025
02
03
015
01
005
0(c) 16000 s
025
02
03
015
01
005
0(d) 17000 s
025
02
03
015
01
005
0(e) 17500 s
025
02
03
015
01
005
0(f) 18000 s
Figure 20 Change of particles concentration in a KCP
Geofluids 13
0
005
01
015
02
025
03
035C
once
ntra
tion
1 2 3 4 5 6 70r (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
(a)
105 15 200z (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
0
005
01
015
02
025
03
035
Con
cent
ratio
n (b)
Figure 21 Evolution of particle concentration along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
ConcentrationLoss rate
0
005
01
015
Con
cent
ratio
n
5 10 15 200Time (times103 s)
0
5
10
15
20
25
Part
icle
loss
rate
Qp
(m3h
)
Figure 22 Evolution of average particle volumetric concentrationand particle loss rate
441 Impact of Heterogeneity on Fractures Evolution Fig-ure 23 illustrates the distribution law of the fractures seepagevelocities and particle volume concentrations under identicalflow pressures but different fracture distribution conditionsat 175 times 103 seconds The results show that more intercon-nected fractures are developed along with the increase in mvalues For example when119898 = 4 there are only two intercon-nected fractures However asm value increases an increasingnumber of fractures were generated and interconnected Inthe fourth case (119898 = 10) three interconnected fractures weregenerated This finding indicates that the homogeneity canaccelerate the propagation of the fractures An increase in
Table 2 List of simulation scenarios
Parameter Value
Weibull distribution coefficient (-)
119898 = 4119898 = 6119898 = 8
119898 = 10
Water pressure (MPa)
119901 = 10119901 = 20119901 = 30119901 = 40
Initial particle concentration ()
1198620 = 00051198620 = 0011198620 = 0021198620 = 005
Fracture aperture (times10minus4m)
119887 = 075119887 = 10
119887 = 125119887 = 15
flow velocity and particle concentration with increasing mvalues was also observed as shown in Figures 23(b) and 23(c)
442 Prediction of Water Inrush under Different ConditionsThe analysis and prediction of the occurrences of waterinrush in KCPs based on the changes in seepage are essentialfor the safety of mining processes Some researchers haveadopted catastrophe theories to predict the occurrences ofwater inrush However an approach that can be used topredict water inrush based on water flow has yet to be foundin the literature This study presents the first attempt toresolve this challenge by applying the inverse velocity theory
14 Geofluids
m = 4 m = 6 m = 8 m = 10
1
2
3
4
5
6
7
(a) Distribution of aperture 119887 (times10minus4m )
m = 4 m = 6 m = 8 m = 10
2
16
12
08
04
0
(b) Distribution of seepage velocity (times10minus3ms)
m = 4 m = 6 m = 8 m = 10
025
02
03
015
01
005
0
(c) Distribution of particles concentration
Figure 23 Distribution of fracture seepage velocity and particle concentration at different Weibull distribution conditions (a) Impact ofWeibull distribution on fractures evolution (b) impact of Weibull distribution on water velocity evolution (c) impact of Weibull distributionon particle concentration evolution
Geofluids 15
5 10 15 200Time (times103 s)
m = 4
m = 6 m = 10
m = 8
0
20
40
60
80
100
120Fl
ow ra
te (m
3h
)
(a)
205
21
215
22
225
23
Wat
er in
rush
tim
e (times10
3s)
4 6 8 102Weibull coefficient m
y = 25699xminus0089
R2 = 09825
(b)
Figure 24 Impact of heterogeneity on water flow rate (a) and inrush time (b)
0
20
40
60
80
100
120
140
160
180
200
Flow
rate
(m3h
)
5 10 15 200Time (times103 s)
p = 1MPap = 2MPa
p = 3MPap = 4MPa
(a)
y = 41733xminus1001
R2 = 09992
1 2 3 4 50Water pressure (MPa)
0
5
10
15
20
25
30
35
40
45
Wat
er in
rush
tim
e (times10
3s)
(b)
Figure 25 Impact of aquifer water pressure on water flow rate (a) and inrush time (b)
which has been widely approved effective in many fields suchas slope stability predictionThe relevant results and analysesare shown in Figure 24ndashFigure 27
As shown in Figure 24 water flow rate exhibits a non-linear increase and as the value of m increases the seepagerate accelerates gradually For example at 119905 = 15 times 104 s theseepage rate was approximately 15m3h for 119898 = 4 while itjumped to 25m3h for 119898 = 10 Results from Figure 24(b)show that water inrush occurs sooner for a greater 119898 valueIn other words the inrush occurs earlier as the heterogeneityincreases The water inrush time follows the power functionThis is due to the fact that the water is more prone to flowingthrough the existing fractures (which indicates a higher
permeability) in the heterogeneous structure Neverthelessdue to the heterogeneous distribution of the aperture thefractures cannot be easily interconnected which hampers theformation of the seepage channels In regard to the homo-geneous rock strata since the flow of water was dominantlycontrolled by the pressure gradient the fractures generatedduring the process of erosion could be easily interconnectedand as a result the water inrush occurredsooner
Figure 25 illustrates the impact of the initial KCPrsquos waterpressure on the flow rates and water inrush time It can beseen that as the pressure increases the changes in the flowrates accelerate For example for119901 = 2MPa the flow rate wasonly approximately 5m3h and it increased to 30m3h when
16 Geofluids
0
20
40
60
80
100
120
140
160
180
200Fl
ow ra
te (m
3h
)
5 10 15 20 250Time (times103 s)
c = 0005
c = 001
c = 002
c = 005
(a)
0
5
10
15
20
25
30
35
Wat
er in
rush
tim
e (times10
3s)
001 002 003 004 0050Initial particle concentration
y = 13554xminus0591
R2 = 09975
(b)
Figure 26 Impact of initial particle concentration on water flow rate (a) and inrush time (b)
0
20
40
60
80
100
120
140
160
180
200
Flow
rate
(m3h
)
5 10 15 200Time (times103 s)
075E minus 4m100E minus 4m
125E minus 4m150E minus 4m
(a)
y = 31027eminus286x
R2 = 09503
09 11 13 1507Fracture aperture (times10minus4 m)
0
5
10
15
20
25
30
35
40
Wat
er in
rush
tim
e (times10
3s)
(b)
Figure 27 Impact of absolute aperture on water flow rate (a) and inrush time (b)
119901 = 3MPa In addition with increasing the aquifer waterpressure the water inrush time was also brought forward asshown in Figure 25(a) The outburst time was approximately119905 = 40 times 104 s for p = 1MPa while only 10 times 104 s for119901 = 4MPa The relationship between the time of the inrushoccurrences and the aquifer water pressure follows the powerfunction as illustrated in Figure 25
For varying initial particle concentrations the evolutionof both the water flow rate change and the water inrushtime shows a similar trend to that of different aquifer waterpressures The flow rate accelerates with increasing initialparticle concentration and consequently the water inrushoccurs earlier as shown in Figure 26The outburst times alsoshow a power function to the initial particle concentration
The initial average fracture aperture also shows significantimpact on water flow behavior For instance results fromFigure 27 clearly illustrate that the flow rate increases withincreasing initial average fracture aperture Please note thatthe inrush time follows an exponential function to the initialaverage fracture aperture
These numerical results can be explained by the factthat the initial seepage velocity is expected to be higher forthe modelling cases with the higher initial aquifer pressureinitial fracture aperture andor initial particle concentrationThe higher flow velocity would intensify the erosion of thefractures enhance the permeability and thereby acceleratethe migration of the particles and interconnection of seepagechannels which causes water inrush
Geofluids 17
5 Conclusions
In this study a systematic approach was established to inves-tigate the impact of controlling factors onwater flow behaviorfor KCPs and to predict water inrush time by introducing theinverse velocity theory In this approach a suite of governingequations was developed to couple all the physics involvedin this complex process including water flow rock erosionand change in rock microstructure These equations werethen implemented into a finite element software COMSOLMultiphysics to simulate the fully coupled process Basedon this numerical model a series of sensitivity studies wereconducted and some important findings have been drawn
(i) Water flow rate increases with increasing aquiferpressure initial particle concentration and fractureopening This results in an increase in the permeabil-ity and finally an acceleration of the migration of theparticles and interconnection of the seepage channelsThis finding suggests the grouting of the KCPs couldbe an effective measure to mitigate water inrush risk
(ii) The inverse velocity theory was successfully appliedto analyze the occurrences of water inrush underdifferent conditions The results show that the timeof inrush has a power relationship to the rock het-erogeneity water pressure and initial particle concen-tration and follows an exponential relationship to theinitial fracture apertures
The framework developed from this work not only helpsenhance coal mining operations safety by better under-standing and predicting water inrush risks so that propermitigation measures can be put in place timely It canalso be extended to other fields such as tunneling backfillpaste piping tailing dam erosion and other engineeringapplications which are likely to encounter time-dependenterosion or deformation or water inrush issues
Please be noted that there are a number of other stochasticmethods available in the literature that can be used to illus-trate rock heterogeneity such as the Monte-Carlo methodor First-Order approach The differences of these methodson the results of water inrush prediction may be worthcomparing in the near future
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This project is supported by the National Natural ScienceFoundation of China (nos 51304072 51774110) the Programfor Innovative Research Team in University of Ministryof Education of China (IRT 16R22) and the PostdoctoralScience Foundation of China (2017M612398)
References
[1] DMa XMiao H Bai et al ldquoEffect of mining on shear sidewallgroundwater inrush hazard caused by seepage instability of the
penetrated karst collapse pillarrdquo Natural Hazards vol 82 no 1pp 73ndash93 2016
[2] H Keqiang Y Guangming and L Yaoru ldquoPalaeo-karst collapsepillars in northern China and their damage to the geologicalenvironmentsrdquo Environmental Geology vol 58 no 5 pp 1029ndash1040 2009
[3] B Yao J Wei D Wang D Ma and Z Chen ldquoNumericalstudy on seepage property of karst collapse columns underparticle migrationrdquo CMES Computer Modeling in Engineeringamp Sciences vol 91 no 2 pp 81ndash100 2013
[4] J Tang H Bai B Yao and Y Wu ldquoTheoretical analysis onwater-inrush mechanism of concealed collapse pillars in floorrdquoMining Science and Technology vol 21 no 1 pp 57ndash60 2011
[5] Y Chen M Yi C Chen and C Yu ldquoBernstein polynomialsmethod for fractional convection-diffusion equation with vari-able coefficientsrdquoComputerModeling in Engineering amp Sciencesvol 83 no 6 pp 639ndash653 2012
[6] J Zhang and B Shen ldquoCoal mining under aquifers in China Acase studyrdquo International Journal of Rock Mechanics and MiningSciences vol 41 no 4 pp 629ndash639 2004
[7] D Ma H Bai X Miao H Pu B Jiang and Z ChenldquoCompaction and seepage properties of crushed limestoneparticle mixture an experimental investigation for Ordoviciankarst collapse pillar groundwater inrushrdquo Environmental EarthSciences vol 75 no 1 article 11 p 14 2016
[8] S Yin J Zhang and D Liu ldquoA study of mine water inrushesby measurements of in situ stress and rock failuresrdquo NaturalHazards vol 79 no 3 pp 1961ndash1979 2015
[9] H Bai D Ma and Z Chen ldquoMechanical behavior of ground-water seepage in karst collapse pillarsrdquo Engineering Geology vol164 pp 101ndash106 2013
[10] D Ma and H Bai ldquoGroundwater inflow prediction model ofkarst collapse pillar a case study for mining-induced ground-water inrush riskrdquoNatural Hazards vol 76 no 2 pp 1319ndash13342015
[11] D Ma H Bai and Y Wang ldquoMechanical behavior of a coalseam penetrated by a karst collapse pillar mining-inducedgroundwater inrush riskrdquo Natural Hazards vol 75 no 3 pp2137ndash2151 2015
[12] B Yao Research on variable mass fluid-solid coupling dynamictheory of broken rockmass and application China Univeristy ofMining and Technology Xuzhou China 2012
[13] D Ma X Miao H Bai et al ldquoImpact of particle transfer onflow properties of crushed mudstonesrdquo Environmental EarthSciences vol 75 no 7 article 593 2016
[14] DMa H Bai Z Chen andH Pu ldquoEffect of particlemixture onseepage properties of crushed mudstonesrdquo Transport in PorousMedia vol 108 no 2 pp 257ndash277 2015
[15] B Zhang H Bai and K Zhang ldquoSeepage characteristics ofcollapse columnfillingsrdquo International Journal ofMining Scienceand Technology 2015
[16] P Ortoleva J Chadam E Merino and A Sen ldquoGeochemicalself-organization II the reactive-infiltration instabilityrdquo Ameri-can Journal of Science vol 287 no 10 pp 1008ndash1040 1987
[17] I Vardoulakis M Stavropoulou and P Papanastasiou ldquoHydro-mechanical aspects of the sand production problemrdquo Transportin Porous Media vol 22 no 2 pp 225ndash244 1996
[18] R L Detwiler and H Rajaram ldquoPredicting dissolution patternsin variable aperture fractures Evaluation of an enhanced depth-averaged computational modelrdquoWater Resources Research vol43 no 4 Article IDW04403 2007
18 Geofluids
[19] M A Habib H M Badr R Ben-Mansour and M E KabirldquoErosion rate correlations of a pipe protruded in an abrupt pipecontractionrdquo International Journal of Impact Engineering vol34 no 8 pp 1350ndash1369 2007
[20] H T Xiao and H Y Xu ldquoIn situ permeability measurementsto establish the influence of slice mining on floor rocksrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 37 no 5 pp 855ndash860 2000
[21] H Guo D P Adhikary and M S Craig ldquoSimulation of minewater inflow and gas emission during longwall miningrdquo RockMechanics and Rock Engineering vol 42 no 1 pp 25ndash51 2009
[22] R Zhang Z JiangH ZhouC Yang and S Xiao ldquoGroundwateroutbursts from faults above a confined aquifer in the coalminingrdquo Natural Hazards vol 71 no 3 pp 1861ndash1872 2014
[23] B Yao F Du E Li and X Wang ldquoMechanical model of karstcollapse columns water inrush and its applicationrdquo ElectronicJournal of Geotechnical Engineering vol 19 pp 1665ndash1675 2014
[24] J Warren and P Root ldquoThe behavior of naturally fracturedreservoirsrdquo SPE Journal vol 3 no 3 pp 245ndash255 2013
[25] H KazemiM S Seth andGWThomas ldquoThe interpretation ofinterference tests in naturally fractured reservoirs with uniformfracture distributionrdquo SPE Journal vol 9 no 4 pp 463ndash4721969
[26] A de Swaan O ldquoAnalytical solutions for determining naturallyfractured reservoir properties by well testingrdquo SPE Journal vol16 no 3 pp 117ndash122 1976
[27] N D Rose and O Hungr ldquoForecasting potential rock slopefailure in open pit mines using the inverse-velocity methodrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 2 pp 308ndash320 2007
[28] J R Fanchi Petroleum Engineering Handbook Volume 1 Gen-eral Engineering Society of Petroleum Engineers 2006
[29] R Sakthivadivel and S Irmay A Review of Filtration TheoriesHydraulic Engineering Laboratory College of EngineeringUniversity of California Berkeley Calif USA 1996
[30] C Wang P Zhai Z Chen J Liu L Wang and J XieldquoExperimental study of coal matrix-cleat interaction underconstant volume boundary conditionrdquo International Journal ofCoal Geology vol 181 pp 124ndash132 2017
[31] S Irmay ldquoOn the theoretical derivation of Darcy and Forch-heimer formulasrdquo Eos Transactions American GeophysicalUnion vol 39 no 4 pp 702ndash707 1958
[32] CH Lee and IW Farmer ldquoA simplemethod of estimating rockmass porosity and permeabilityrdquo International Journal ofMiningand Geological Engineering vol 8 no 1 pp 57ndash65 1990
[33] C Nalluri A K El-Zaemey and H L Chan ldquoSedimenttransport over fixed deposited beds in sewers - An appraisal ofexisting modelsrdquoWater Science and Technology vol 36 no 8-9pp 123ndash128 1997
[34] P Novak and C Nalluri ldquoSediment transport in smooth fixedbed channelsrdquo Journal of the Hydraulics Division vol 101 no 9pp 1139ndash1154 1975
[35] T Fukuzono ldquoA newmethod for predicting the failure time of asloperdquo in Proceedings of the In 4th International Conference andField Workshop on Landslides Tokyo Japan 1985
[36] C R J Kilburn andDN Petley ldquoForecasting giant catastrophicslope collapse lessons from Vajont Northern Italyrdquo Geomor-phology vol 54 no 1-2 pp 21ndash32 2003
[37] B Voight ldquoA method for prediction of volcanic eruptionsrdquoNature vol 332 no 6160 pp 125ndash130 1988
[38] B Yao X Mao J Wei and D Wang ldquoStudy on coupled fluid-solid model for collapse columns considering the effect ofparticle transportrdquo Zhongguo Kuangye Daxue XuebaoJournalof China University of Mining and Technology vol 43 no 1 pp30ndash35 2014
[39] H Bai Seepage Characteristics of Top Stratum of OrdovicianSystem and Its Application Study as Key Aquifuge ChinaUniversity of Mining amp Technology Xuzhou China 2008
[40] C A Tang L G Tham P K K Lee T H Yang and L CLi ldquoCoupled analysis of flow stress and damage (FSD) in rockfailurerdquo International Journal of Rock Mechanics and MiningSciences vol 39 no 4 pp 477ndash489 2002
[41] W C Zhu and C A Tang ldquoMicromechanical model forsimulating the fracture process of rockrdquo Rock Mechanics andRock Engineering vol 37 no 1 pp 25ndash56 2004
[42] T H Yang L G Tham C A Tang Z Z Liang and YTsui ldquoInfluence of heterogeneity of mechanical properties onhydraulic fracturing in permeable rocksrdquo Rock Mechanics andRock Engineering vol 37 no 4 pp 251ndash275 2004
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Submit your manuscripts atwwwhindawicom
10 Geofluids
05
15
25
35
45
55
65Fr
actu
re ap
ertu
reb
(times10
minus4
m)
5 10 15 200z (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
(a)
1 2 3 4 5 6 70r (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
05
15
25
35
45
55
65
Frac
ture
aper
ture
b(times
10minus4
m)
(b)
Figure 15 Evolution of fracture aperture along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
1
15
2
25
3
Frac
ture
aper
ture
b(times
10minus4
m)
5 10 15 200Time (times103 s)
Figure 16 Change of average fracture aperture with time
Figure 20 shows the evolution of the average particleconcentration along O-O10158401015840 and O1015840-A1015840 lines The averageparticle concentration and particle loss rate was plotted inFigure 21
Figure 20 plots the spatial distribution of the particleconcentrations for the wholemodel at different times Resultsshow that the particle concentration gradually increasesfrom the bottom upwards This is because under the effectsof the erosion increasing amount of particles migratedinto the water and gradually moved upwards through thefractures and pores This is consistent with the change inthe particle concentration at different locations as shown inFigure 21
Results in Figure 22 are well in line with the results shownin Figure 18 For example at the beginning the particle lossrate is relatively low however the rate constantly increasesover time and culminates at the inrushThis is due to the fact
that along with the increases in the seepage velocities theerosion effects on the solid particles are constantly intensifiedwhich results in frequent migration and substantial particleloss
44 Sensitivity Analyses The outburst processes wereaffected or controlled by various factors including thespatial heterogeneity of lithology of the KCPs waterpressure absolute aperture and distribution of the fracturesdistribution law of concentration of the karst particlesand their sensitivity to water erosion Based on the newlydeveloped coupling model this work further examined thewater and particle migration characteristics in the KCPsunder different hydrological and geological conditionsas well as the variations in the inrush occurrences Thescenarios to be studied are summarized in Table 2
Geofluids 11
2
16
12
08
04
0(a) 14000 s
2
16
12
08
04
0(b) 15000 s
2
16
12
08
04
0(c) 16000 s
2
16
12
08
04
0(d) 17000 s
2
16
12
08
04
0(e) 17500 s
2
16
12
08
04
0(f) 18000 s
Figure 17 The change of seepage velocity (10minus3ms) in a KCP
14000 s15000 s16000 s
17000 s17500 s18000 s
r (m)
1 2 3 4 5 6 70
Velo
city
(10minus
3m
s)
14
12
1
08
06
04
02
0
(a)
14000 s15000 s16000 s
17000 s17500 s18000 s
50 10z (m)
15 20
Velo
city
(10minus
3m
s)
14
12
1
08
06
04
02
0
(b)
Figure 18 Evolution of seepage velocity along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
12 Geofluids
Inverse velocityLinear fitting
0
20
40
60
80
100
Flow
rate
(m3h
)
0
5
10
15
20
25
30
Inve
rse v
eloci
ty (h
m)
5 10 15 200Time (times103 s)
Q
Figure 19 Water flow rate along the bottom surface of the numerical model
025
02
03
015
01
005
0(a) 14000 s
025
02
03
015
01
005
0(b) 15000 s
025
02
03
015
01
005
0(c) 16000 s
025
02
03
015
01
005
0(d) 17000 s
025
02
03
015
01
005
0(e) 17500 s
025
02
03
015
01
005
0(f) 18000 s
Figure 20 Change of particles concentration in a KCP
Geofluids 13
0
005
01
015
02
025
03
035C
once
ntra
tion
1 2 3 4 5 6 70r (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
(a)
105 15 200z (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
0
005
01
015
02
025
03
035
Con
cent
ratio
n (b)
Figure 21 Evolution of particle concentration along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
ConcentrationLoss rate
0
005
01
015
Con
cent
ratio
n
5 10 15 200Time (times103 s)
0
5
10
15
20
25
Part
icle
loss
rate
Qp
(m3h
)
Figure 22 Evolution of average particle volumetric concentrationand particle loss rate
441 Impact of Heterogeneity on Fractures Evolution Fig-ure 23 illustrates the distribution law of the fractures seepagevelocities and particle volume concentrations under identicalflow pressures but different fracture distribution conditionsat 175 times 103 seconds The results show that more intercon-nected fractures are developed along with the increase in mvalues For example when119898 = 4 there are only two intercon-nected fractures However asm value increases an increasingnumber of fractures were generated and interconnected Inthe fourth case (119898 = 10) three interconnected fractures weregenerated This finding indicates that the homogeneity canaccelerate the propagation of the fractures An increase in
Table 2 List of simulation scenarios
Parameter Value
Weibull distribution coefficient (-)
119898 = 4119898 = 6119898 = 8
119898 = 10
Water pressure (MPa)
119901 = 10119901 = 20119901 = 30119901 = 40
Initial particle concentration ()
1198620 = 00051198620 = 0011198620 = 0021198620 = 005
Fracture aperture (times10minus4m)
119887 = 075119887 = 10
119887 = 125119887 = 15
flow velocity and particle concentration with increasing mvalues was also observed as shown in Figures 23(b) and 23(c)
442 Prediction of Water Inrush under Different ConditionsThe analysis and prediction of the occurrences of waterinrush in KCPs based on the changes in seepage are essentialfor the safety of mining processes Some researchers haveadopted catastrophe theories to predict the occurrences ofwater inrush However an approach that can be used topredict water inrush based on water flow has yet to be foundin the literature This study presents the first attempt toresolve this challenge by applying the inverse velocity theory
14 Geofluids
m = 4 m = 6 m = 8 m = 10
1
2
3
4
5
6
7
(a) Distribution of aperture 119887 (times10minus4m )
m = 4 m = 6 m = 8 m = 10
2
16
12
08
04
0
(b) Distribution of seepage velocity (times10minus3ms)
m = 4 m = 6 m = 8 m = 10
025
02
03
015
01
005
0
(c) Distribution of particles concentration
Figure 23 Distribution of fracture seepage velocity and particle concentration at different Weibull distribution conditions (a) Impact ofWeibull distribution on fractures evolution (b) impact of Weibull distribution on water velocity evolution (c) impact of Weibull distributionon particle concentration evolution
Geofluids 15
5 10 15 200Time (times103 s)
m = 4
m = 6 m = 10
m = 8
0
20
40
60
80
100
120Fl
ow ra
te (m
3h
)
(a)
205
21
215
22
225
23
Wat
er in
rush
tim
e (times10
3s)
4 6 8 102Weibull coefficient m
y = 25699xminus0089
R2 = 09825
(b)
Figure 24 Impact of heterogeneity on water flow rate (a) and inrush time (b)
0
20
40
60
80
100
120
140
160
180
200
Flow
rate
(m3h
)
5 10 15 200Time (times103 s)
p = 1MPap = 2MPa
p = 3MPap = 4MPa
(a)
y = 41733xminus1001
R2 = 09992
1 2 3 4 50Water pressure (MPa)
0
5
10
15
20
25
30
35
40
45
Wat
er in
rush
tim
e (times10
3s)
(b)
Figure 25 Impact of aquifer water pressure on water flow rate (a) and inrush time (b)
which has been widely approved effective in many fields suchas slope stability predictionThe relevant results and analysesare shown in Figure 24ndashFigure 27
As shown in Figure 24 water flow rate exhibits a non-linear increase and as the value of m increases the seepagerate accelerates gradually For example at 119905 = 15 times 104 s theseepage rate was approximately 15m3h for 119898 = 4 while itjumped to 25m3h for 119898 = 10 Results from Figure 24(b)show that water inrush occurs sooner for a greater 119898 valueIn other words the inrush occurs earlier as the heterogeneityincreases The water inrush time follows the power functionThis is due to the fact that the water is more prone to flowingthrough the existing fractures (which indicates a higher
permeability) in the heterogeneous structure Neverthelessdue to the heterogeneous distribution of the aperture thefractures cannot be easily interconnected which hampers theformation of the seepage channels In regard to the homo-geneous rock strata since the flow of water was dominantlycontrolled by the pressure gradient the fractures generatedduring the process of erosion could be easily interconnectedand as a result the water inrush occurredsooner
Figure 25 illustrates the impact of the initial KCPrsquos waterpressure on the flow rates and water inrush time It can beseen that as the pressure increases the changes in the flowrates accelerate For example for119901 = 2MPa the flow rate wasonly approximately 5m3h and it increased to 30m3h when
16 Geofluids
0
20
40
60
80
100
120
140
160
180
200Fl
ow ra
te (m
3h
)
5 10 15 20 250Time (times103 s)
c = 0005
c = 001
c = 002
c = 005
(a)
0
5
10
15
20
25
30
35
Wat
er in
rush
tim
e (times10
3s)
001 002 003 004 0050Initial particle concentration
y = 13554xminus0591
R2 = 09975
(b)
Figure 26 Impact of initial particle concentration on water flow rate (a) and inrush time (b)
0
20
40
60
80
100
120
140
160
180
200
Flow
rate
(m3h
)
5 10 15 200Time (times103 s)
075E minus 4m100E minus 4m
125E minus 4m150E minus 4m
(a)
y = 31027eminus286x
R2 = 09503
09 11 13 1507Fracture aperture (times10minus4 m)
0
5
10
15
20
25
30
35
40
Wat
er in
rush
tim
e (times10
3s)
(b)
Figure 27 Impact of absolute aperture on water flow rate (a) and inrush time (b)
119901 = 3MPa In addition with increasing the aquifer waterpressure the water inrush time was also brought forward asshown in Figure 25(a) The outburst time was approximately119905 = 40 times 104 s for p = 1MPa while only 10 times 104 s for119901 = 4MPa The relationship between the time of the inrushoccurrences and the aquifer water pressure follows the powerfunction as illustrated in Figure 25
For varying initial particle concentrations the evolutionof both the water flow rate change and the water inrushtime shows a similar trend to that of different aquifer waterpressures The flow rate accelerates with increasing initialparticle concentration and consequently the water inrushoccurs earlier as shown in Figure 26The outburst times alsoshow a power function to the initial particle concentration
The initial average fracture aperture also shows significantimpact on water flow behavior For instance results fromFigure 27 clearly illustrate that the flow rate increases withincreasing initial average fracture aperture Please note thatthe inrush time follows an exponential function to the initialaverage fracture aperture
These numerical results can be explained by the factthat the initial seepage velocity is expected to be higher forthe modelling cases with the higher initial aquifer pressureinitial fracture aperture andor initial particle concentrationThe higher flow velocity would intensify the erosion of thefractures enhance the permeability and thereby acceleratethe migration of the particles and interconnection of seepagechannels which causes water inrush
Geofluids 17
5 Conclusions
In this study a systematic approach was established to inves-tigate the impact of controlling factors onwater flow behaviorfor KCPs and to predict water inrush time by introducing theinverse velocity theory In this approach a suite of governingequations was developed to couple all the physics involvedin this complex process including water flow rock erosionand change in rock microstructure These equations werethen implemented into a finite element software COMSOLMultiphysics to simulate the fully coupled process Basedon this numerical model a series of sensitivity studies wereconducted and some important findings have been drawn
(i) Water flow rate increases with increasing aquiferpressure initial particle concentration and fractureopening This results in an increase in the permeabil-ity and finally an acceleration of the migration of theparticles and interconnection of the seepage channelsThis finding suggests the grouting of the KCPs couldbe an effective measure to mitigate water inrush risk
(ii) The inverse velocity theory was successfully appliedto analyze the occurrences of water inrush underdifferent conditions The results show that the timeof inrush has a power relationship to the rock het-erogeneity water pressure and initial particle concen-tration and follows an exponential relationship to theinitial fracture apertures
The framework developed from this work not only helpsenhance coal mining operations safety by better under-standing and predicting water inrush risks so that propermitigation measures can be put in place timely It canalso be extended to other fields such as tunneling backfillpaste piping tailing dam erosion and other engineeringapplications which are likely to encounter time-dependenterosion or deformation or water inrush issues
Please be noted that there are a number of other stochasticmethods available in the literature that can be used to illus-trate rock heterogeneity such as the Monte-Carlo methodor First-Order approach The differences of these methodson the results of water inrush prediction may be worthcomparing in the near future
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This project is supported by the National Natural ScienceFoundation of China (nos 51304072 51774110) the Programfor Innovative Research Team in University of Ministryof Education of China (IRT 16R22) and the PostdoctoralScience Foundation of China (2017M612398)
References
[1] DMa XMiao H Bai et al ldquoEffect of mining on shear sidewallgroundwater inrush hazard caused by seepage instability of the
penetrated karst collapse pillarrdquo Natural Hazards vol 82 no 1pp 73ndash93 2016
[2] H Keqiang Y Guangming and L Yaoru ldquoPalaeo-karst collapsepillars in northern China and their damage to the geologicalenvironmentsrdquo Environmental Geology vol 58 no 5 pp 1029ndash1040 2009
[3] B Yao J Wei D Wang D Ma and Z Chen ldquoNumericalstudy on seepage property of karst collapse columns underparticle migrationrdquo CMES Computer Modeling in Engineeringamp Sciences vol 91 no 2 pp 81ndash100 2013
[4] J Tang H Bai B Yao and Y Wu ldquoTheoretical analysis onwater-inrush mechanism of concealed collapse pillars in floorrdquoMining Science and Technology vol 21 no 1 pp 57ndash60 2011
[5] Y Chen M Yi C Chen and C Yu ldquoBernstein polynomialsmethod for fractional convection-diffusion equation with vari-able coefficientsrdquoComputerModeling in Engineering amp Sciencesvol 83 no 6 pp 639ndash653 2012
[6] J Zhang and B Shen ldquoCoal mining under aquifers in China Acase studyrdquo International Journal of Rock Mechanics and MiningSciences vol 41 no 4 pp 629ndash639 2004
[7] D Ma H Bai X Miao H Pu B Jiang and Z ChenldquoCompaction and seepage properties of crushed limestoneparticle mixture an experimental investigation for Ordoviciankarst collapse pillar groundwater inrushrdquo Environmental EarthSciences vol 75 no 1 article 11 p 14 2016
[8] S Yin J Zhang and D Liu ldquoA study of mine water inrushesby measurements of in situ stress and rock failuresrdquo NaturalHazards vol 79 no 3 pp 1961ndash1979 2015
[9] H Bai D Ma and Z Chen ldquoMechanical behavior of ground-water seepage in karst collapse pillarsrdquo Engineering Geology vol164 pp 101ndash106 2013
[10] D Ma and H Bai ldquoGroundwater inflow prediction model ofkarst collapse pillar a case study for mining-induced ground-water inrush riskrdquoNatural Hazards vol 76 no 2 pp 1319ndash13342015
[11] D Ma H Bai and Y Wang ldquoMechanical behavior of a coalseam penetrated by a karst collapse pillar mining-inducedgroundwater inrush riskrdquo Natural Hazards vol 75 no 3 pp2137ndash2151 2015
[12] B Yao Research on variable mass fluid-solid coupling dynamictheory of broken rockmass and application China Univeristy ofMining and Technology Xuzhou China 2012
[13] D Ma X Miao H Bai et al ldquoImpact of particle transfer onflow properties of crushed mudstonesrdquo Environmental EarthSciences vol 75 no 7 article 593 2016
[14] DMa H Bai Z Chen andH Pu ldquoEffect of particlemixture onseepage properties of crushed mudstonesrdquo Transport in PorousMedia vol 108 no 2 pp 257ndash277 2015
[15] B Zhang H Bai and K Zhang ldquoSeepage characteristics ofcollapse columnfillingsrdquo International Journal ofMining Scienceand Technology 2015
[16] P Ortoleva J Chadam E Merino and A Sen ldquoGeochemicalself-organization II the reactive-infiltration instabilityrdquo Ameri-can Journal of Science vol 287 no 10 pp 1008ndash1040 1987
[17] I Vardoulakis M Stavropoulou and P Papanastasiou ldquoHydro-mechanical aspects of the sand production problemrdquo Transportin Porous Media vol 22 no 2 pp 225ndash244 1996
[18] R L Detwiler and H Rajaram ldquoPredicting dissolution patternsin variable aperture fractures Evaluation of an enhanced depth-averaged computational modelrdquoWater Resources Research vol43 no 4 Article IDW04403 2007
18 Geofluids
[19] M A Habib H M Badr R Ben-Mansour and M E KabirldquoErosion rate correlations of a pipe protruded in an abrupt pipecontractionrdquo International Journal of Impact Engineering vol34 no 8 pp 1350ndash1369 2007
[20] H T Xiao and H Y Xu ldquoIn situ permeability measurementsto establish the influence of slice mining on floor rocksrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 37 no 5 pp 855ndash860 2000
[21] H Guo D P Adhikary and M S Craig ldquoSimulation of minewater inflow and gas emission during longwall miningrdquo RockMechanics and Rock Engineering vol 42 no 1 pp 25ndash51 2009
[22] R Zhang Z JiangH ZhouC Yang and S Xiao ldquoGroundwateroutbursts from faults above a confined aquifer in the coalminingrdquo Natural Hazards vol 71 no 3 pp 1861ndash1872 2014
[23] B Yao F Du E Li and X Wang ldquoMechanical model of karstcollapse columns water inrush and its applicationrdquo ElectronicJournal of Geotechnical Engineering vol 19 pp 1665ndash1675 2014
[24] J Warren and P Root ldquoThe behavior of naturally fracturedreservoirsrdquo SPE Journal vol 3 no 3 pp 245ndash255 2013
[25] H KazemiM S Seth andGWThomas ldquoThe interpretation ofinterference tests in naturally fractured reservoirs with uniformfracture distributionrdquo SPE Journal vol 9 no 4 pp 463ndash4721969
[26] A de Swaan O ldquoAnalytical solutions for determining naturallyfractured reservoir properties by well testingrdquo SPE Journal vol16 no 3 pp 117ndash122 1976
[27] N D Rose and O Hungr ldquoForecasting potential rock slopefailure in open pit mines using the inverse-velocity methodrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 2 pp 308ndash320 2007
[28] J R Fanchi Petroleum Engineering Handbook Volume 1 Gen-eral Engineering Society of Petroleum Engineers 2006
[29] R Sakthivadivel and S Irmay A Review of Filtration TheoriesHydraulic Engineering Laboratory College of EngineeringUniversity of California Berkeley Calif USA 1996
[30] C Wang P Zhai Z Chen J Liu L Wang and J XieldquoExperimental study of coal matrix-cleat interaction underconstant volume boundary conditionrdquo International Journal ofCoal Geology vol 181 pp 124ndash132 2017
[31] S Irmay ldquoOn the theoretical derivation of Darcy and Forch-heimer formulasrdquo Eos Transactions American GeophysicalUnion vol 39 no 4 pp 702ndash707 1958
[32] CH Lee and IW Farmer ldquoA simplemethod of estimating rockmass porosity and permeabilityrdquo International Journal ofMiningand Geological Engineering vol 8 no 1 pp 57ndash65 1990
[33] C Nalluri A K El-Zaemey and H L Chan ldquoSedimenttransport over fixed deposited beds in sewers - An appraisal ofexisting modelsrdquoWater Science and Technology vol 36 no 8-9pp 123ndash128 1997
[34] P Novak and C Nalluri ldquoSediment transport in smooth fixedbed channelsrdquo Journal of the Hydraulics Division vol 101 no 9pp 1139ndash1154 1975
[35] T Fukuzono ldquoA newmethod for predicting the failure time of asloperdquo in Proceedings of the In 4th International Conference andField Workshop on Landslides Tokyo Japan 1985
[36] C R J Kilburn andDN Petley ldquoForecasting giant catastrophicslope collapse lessons from Vajont Northern Italyrdquo Geomor-phology vol 54 no 1-2 pp 21ndash32 2003
[37] B Voight ldquoA method for prediction of volcanic eruptionsrdquoNature vol 332 no 6160 pp 125ndash130 1988
[38] B Yao X Mao J Wei and D Wang ldquoStudy on coupled fluid-solid model for collapse columns considering the effect ofparticle transportrdquo Zhongguo Kuangye Daxue XuebaoJournalof China University of Mining and Technology vol 43 no 1 pp30ndash35 2014
[39] H Bai Seepage Characteristics of Top Stratum of OrdovicianSystem and Its Application Study as Key Aquifuge ChinaUniversity of Mining amp Technology Xuzhou China 2008
[40] C A Tang L G Tham P K K Lee T H Yang and L CLi ldquoCoupled analysis of flow stress and damage (FSD) in rockfailurerdquo International Journal of Rock Mechanics and MiningSciences vol 39 no 4 pp 477ndash489 2002
[41] W C Zhu and C A Tang ldquoMicromechanical model forsimulating the fracture process of rockrdquo Rock Mechanics andRock Engineering vol 37 no 1 pp 25ndash56 2004
[42] T H Yang L G Tham C A Tang Z Z Liang and YTsui ldquoInfluence of heterogeneity of mechanical properties onhydraulic fracturing in permeable rocksrdquo Rock Mechanics andRock Engineering vol 37 no 4 pp 251ndash275 2004
Hindawiwwwhindawicom Volume 2018
Journal of
ChemistryArchaeaHindawiwwwhindawicom Volume 2018
Marine BiologyJournal of
Hindawiwwwhindawicom Volume 2018
BiodiversityInternational Journal of
Hindawiwwwhindawicom Volume 2018
EcologyInternational Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Applied ampEnvironmentalSoil Science
Volume 2018
Forestry ResearchInternational Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
International Journal of
Geophysics
Environmental and Public Health
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
International Journal of
Microbiology
Hindawiwwwhindawicom Volume 2018
Public Health Advances in
AgricultureAdvances in
Hindawiwwwhindawicom Volume 2018
Agronomy
Hindawiwwwhindawicom Volume 2018
International Journal of
Hindawiwwwhindawicom Volume 2018
MeteorologyAdvances in
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018Hindawiwwwhindawicom Volume 2018
ChemistryAdvances in
ScienticaHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Geological ResearchJournal of
Analytical ChemistryInternational Journal of
Hindawiwwwhindawicom Volume 2018
Submit your manuscripts atwwwhindawicom
Geofluids 11
2
16
12
08
04
0(a) 14000 s
2
16
12
08
04
0(b) 15000 s
2
16
12
08
04
0(c) 16000 s
2
16
12
08
04
0(d) 17000 s
2
16
12
08
04
0(e) 17500 s
2
16
12
08
04
0(f) 18000 s
Figure 17 The change of seepage velocity (10minus3ms) in a KCP
14000 s15000 s16000 s
17000 s17500 s18000 s
r (m)
1 2 3 4 5 6 70
Velo
city
(10minus
3m
s)
14
12
1
08
06
04
02
0
(a)
14000 s15000 s16000 s
17000 s17500 s18000 s
50 10z (m)
15 20
Velo
city
(10minus
3m
s)
14
12
1
08
06
04
02
0
(b)
Figure 18 Evolution of seepage velocity along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
12 Geofluids
Inverse velocityLinear fitting
0
20
40
60
80
100
Flow
rate
(m3h
)
0
5
10
15
20
25
30
Inve
rse v
eloci
ty (h
m)
5 10 15 200Time (times103 s)
Q
Figure 19 Water flow rate along the bottom surface of the numerical model
025
02
03
015
01
005
0(a) 14000 s
025
02
03
015
01
005
0(b) 15000 s
025
02
03
015
01
005
0(c) 16000 s
025
02
03
015
01
005
0(d) 17000 s
025
02
03
015
01
005
0(e) 17500 s
025
02
03
015
01
005
0(f) 18000 s
Figure 20 Change of particles concentration in a KCP
Geofluids 13
0
005
01
015
02
025
03
035C
once
ntra
tion
1 2 3 4 5 6 70r (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
(a)
105 15 200z (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
0
005
01
015
02
025
03
035
Con
cent
ratio
n (b)
Figure 21 Evolution of particle concentration along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
ConcentrationLoss rate
0
005
01
015
Con
cent
ratio
n
5 10 15 200Time (times103 s)
0
5
10
15
20
25
Part
icle
loss
rate
Qp
(m3h
)
Figure 22 Evolution of average particle volumetric concentrationand particle loss rate
441 Impact of Heterogeneity on Fractures Evolution Fig-ure 23 illustrates the distribution law of the fractures seepagevelocities and particle volume concentrations under identicalflow pressures but different fracture distribution conditionsat 175 times 103 seconds The results show that more intercon-nected fractures are developed along with the increase in mvalues For example when119898 = 4 there are only two intercon-nected fractures However asm value increases an increasingnumber of fractures were generated and interconnected Inthe fourth case (119898 = 10) three interconnected fractures weregenerated This finding indicates that the homogeneity canaccelerate the propagation of the fractures An increase in
Table 2 List of simulation scenarios
Parameter Value
Weibull distribution coefficient (-)
119898 = 4119898 = 6119898 = 8
119898 = 10
Water pressure (MPa)
119901 = 10119901 = 20119901 = 30119901 = 40
Initial particle concentration ()
1198620 = 00051198620 = 0011198620 = 0021198620 = 005
Fracture aperture (times10minus4m)
119887 = 075119887 = 10
119887 = 125119887 = 15
flow velocity and particle concentration with increasing mvalues was also observed as shown in Figures 23(b) and 23(c)
442 Prediction of Water Inrush under Different ConditionsThe analysis and prediction of the occurrences of waterinrush in KCPs based on the changes in seepage are essentialfor the safety of mining processes Some researchers haveadopted catastrophe theories to predict the occurrences ofwater inrush However an approach that can be used topredict water inrush based on water flow has yet to be foundin the literature This study presents the first attempt toresolve this challenge by applying the inverse velocity theory
14 Geofluids
m = 4 m = 6 m = 8 m = 10
1
2
3
4
5
6
7
(a) Distribution of aperture 119887 (times10minus4m )
m = 4 m = 6 m = 8 m = 10
2
16
12
08
04
0
(b) Distribution of seepage velocity (times10minus3ms)
m = 4 m = 6 m = 8 m = 10
025
02
03
015
01
005
0
(c) Distribution of particles concentration
Figure 23 Distribution of fracture seepage velocity and particle concentration at different Weibull distribution conditions (a) Impact ofWeibull distribution on fractures evolution (b) impact of Weibull distribution on water velocity evolution (c) impact of Weibull distributionon particle concentration evolution
Geofluids 15
5 10 15 200Time (times103 s)
m = 4
m = 6 m = 10
m = 8
0
20
40
60
80
100
120Fl
ow ra
te (m
3h
)
(a)
205
21
215
22
225
23
Wat
er in
rush
tim
e (times10
3s)
4 6 8 102Weibull coefficient m
y = 25699xminus0089
R2 = 09825
(b)
Figure 24 Impact of heterogeneity on water flow rate (a) and inrush time (b)
0
20
40
60
80
100
120
140
160
180
200
Flow
rate
(m3h
)
5 10 15 200Time (times103 s)
p = 1MPap = 2MPa
p = 3MPap = 4MPa
(a)
y = 41733xminus1001
R2 = 09992
1 2 3 4 50Water pressure (MPa)
0
5
10
15
20
25
30
35
40
45
Wat
er in
rush
tim
e (times10
3s)
(b)
Figure 25 Impact of aquifer water pressure on water flow rate (a) and inrush time (b)
which has been widely approved effective in many fields suchas slope stability predictionThe relevant results and analysesare shown in Figure 24ndashFigure 27
As shown in Figure 24 water flow rate exhibits a non-linear increase and as the value of m increases the seepagerate accelerates gradually For example at 119905 = 15 times 104 s theseepage rate was approximately 15m3h for 119898 = 4 while itjumped to 25m3h for 119898 = 10 Results from Figure 24(b)show that water inrush occurs sooner for a greater 119898 valueIn other words the inrush occurs earlier as the heterogeneityincreases The water inrush time follows the power functionThis is due to the fact that the water is more prone to flowingthrough the existing fractures (which indicates a higher
permeability) in the heterogeneous structure Neverthelessdue to the heterogeneous distribution of the aperture thefractures cannot be easily interconnected which hampers theformation of the seepage channels In regard to the homo-geneous rock strata since the flow of water was dominantlycontrolled by the pressure gradient the fractures generatedduring the process of erosion could be easily interconnectedand as a result the water inrush occurredsooner
Figure 25 illustrates the impact of the initial KCPrsquos waterpressure on the flow rates and water inrush time It can beseen that as the pressure increases the changes in the flowrates accelerate For example for119901 = 2MPa the flow rate wasonly approximately 5m3h and it increased to 30m3h when
16 Geofluids
0
20
40
60
80
100
120
140
160
180
200Fl
ow ra
te (m
3h
)
5 10 15 20 250Time (times103 s)
c = 0005
c = 001
c = 002
c = 005
(a)
0
5
10
15
20
25
30
35
Wat
er in
rush
tim
e (times10
3s)
001 002 003 004 0050Initial particle concentration
y = 13554xminus0591
R2 = 09975
(b)
Figure 26 Impact of initial particle concentration on water flow rate (a) and inrush time (b)
0
20
40
60
80
100
120
140
160
180
200
Flow
rate
(m3h
)
5 10 15 200Time (times103 s)
075E minus 4m100E minus 4m
125E minus 4m150E minus 4m
(a)
y = 31027eminus286x
R2 = 09503
09 11 13 1507Fracture aperture (times10minus4 m)
0
5
10
15
20
25
30
35
40
Wat
er in
rush
tim
e (times10
3s)
(b)
Figure 27 Impact of absolute aperture on water flow rate (a) and inrush time (b)
119901 = 3MPa In addition with increasing the aquifer waterpressure the water inrush time was also brought forward asshown in Figure 25(a) The outburst time was approximately119905 = 40 times 104 s for p = 1MPa while only 10 times 104 s for119901 = 4MPa The relationship between the time of the inrushoccurrences and the aquifer water pressure follows the powerfunction as illustrated in Figure 25
For varying initial particle concentrations the evolutionof both the water flow rate change and the water inrushtime shows a similar trend to that of different aquifer waterpressures The flow rate accelerates with increasing initialparticle concentration and consequently the water inrushoccurs earlier as shown in Figure 26The outburst times alsoshow a power function to the initial particle concentration
The initial average fracture aperture also shows significantimpact on water flow behavior For instance results fromFigure 27 clearly illustrate that the flow rate increases withincreasing initial average fracture aperture Please note thatthe inrush time follows an exponential function to the initialaverage fracture aperture
These numerical results can be explained by the factthat the initial seepage velocity is expected to be higher forthe modelling cases with the higher initial aquifer pressureinitial fracture aperture andor initial particle concentrationThe higher flow velocity would intensify the erosion of thefractures enhance the permeability and thereby acceleratethe migration of the particles and interconnection of seepagechannels which causes water inrush
Geofluids 17
5 Conclusions
In this study a systematic approach was established to inves-tigate the impact of controlling factors onwater flow behaviorfor KCPs and to predict water inrush time by introducing theinverse velocity theory In this approach a suite of governingequations was developed to couple all the physics involvedin this complex process including water flow rock erosionand change in rock microstructure These equations werethen implemented into a finite element software COMSOLMultiphysics to simulate the fully coupled process Basedon this numerical model a series of sensitivity studies wereconducted and some important findings have been drawn
(i) Water flow rate increases with increasing aquiferpressure initial particle concentration and fractureopening This results in an increase in the permeabil-ity and finally an acceleration of the migration of theparticles and interconnection of the seepage channelsThis finding suggests the grouting of the KCPs couldbe an effective measure to mitigate water inrush risk
(ii) The inverse velocity theory was successfully appliedto analyze the occurrences of water inrush underdifferent conditions The results show that the timeof inrush has a power relationship to the rock het-erogeneity water pressure and initial particle concen-tration and follows an exponential relationship to theinitial fracture apertures
The framework developed from this work not only helpsenhance coal mining operations safety by better under-standing and predicting water inrush risks so that propermitigation measures can be put in place timely It canalso be extended to other fields such as tunneling backfillpaste piping tailing dam erosion and other engineeringapplications which are likely to encounter time-dependenterosion or deformation or water inrush issues
Please be noted that there are a number of other stochasticmethods available in the literature that can be used to illus-trate rock heterogeneity such as the Monte-Carlo methodor First-Order approach The differences of these methodson the results of water inrush prediction may be worthcomparing in the near future
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This project is supported by the National Natural ScienceFoundation of China (nos 51304072 51774110) the Programfor Innovative Research Team in University of Ministryof Education of China (IRT 16R22) and the PostdoctoralScience Foundation of China (2017M612398)
References
[1] DMa XMiao H Bai et al ldquoEffect of mining on shear sidewallgroundwater inrush hazard caused by seepage instability of the
penetrated karst collapse pillarrdquo Natural Hazards vol 82 no 1pp 73ndash93 2016
[2] H Keqiang Y Guangming and L Yaoru ldquoPalaeo-karst collapsepillars in northern China and their damage to the geologicalenvironmentsrdquo Environmental Geology vol 58 no 5 pp 1029ndash1040 2009
[3] B Yao J Wei D Wang D Ma and Z Chen ldquoNumericalstudy on seepage property of karst collapse columns underparticle migrationrdquo CMES Computer Modeling in Engineeringamp Sciences vol 91 no 2 pp 81ndash100 2013
[4] J Tang H Bai B Yao and Y Wu ldquoTheoretical analysis onwater-inrush mechanism of concealed collapse pillars in floorrdquoMining Science and Technology vol 21 no 1 pp 57ndash60 2011
[5] Y Chen M Yi C Chen and C Yu ldquoBernstein polynomialsmethod for fractional convection-diffusion equation with vari-able coefficientsrdquoComputerModeling in Engineering amp Sciencesvol 83 no 6 pp 639ndash653 2012
[6] J Zhang and B Shen ldquoCoal mining under aquifers in China Acase studyrdquo International Journal of Rock Mechanics and MiningSciences vol 41 no 4 pp 629ndash639 2004
[7] D Ma H Bai X Miao H Pu B Jiang and Z ChenldquoCompaction and seepage properties of crushed limestoneparticle mixture an experimental investigation for Ordoviciankarst collapse pillar groundwater inrushrdquo Environmental EarthSciences vol 75 no 1 article 11 p 14 2016
[8] S Yin J Zhang and D Liu ldquoA study of mine water inrushesby measurements of in situ stress and rock failuresrdquo NaturalHazards vol 79 no 3 pp 1961ndash1979 2015
[9] H Bai D Ma and Z Chen ldquoMechanical behavior of ground-water seepage in karst collapse pillarsrdquo Engineering Geology vol164 pp 101ndash106 2013
[10] D Ma and H Bai ldquoGroundwater inflow prediction model ofkarst collapse pillar a case study for mining-induced ground-water inrush riskrdquoNatural Hazards vol 76 no 2 pp 1319ndash13342015
[11] D Ma H Bai and Y Wang ldquoMechanical behavior of a coalseam penetrated by a karst collapse pillar mining-inducedgroundwater inrush riskrdquo Natural Hazards vol 75 no 3 pp2137ndash2151 2015
[12] B Yao Research on variable mass fluid-solid coupling dynamictheory of broken rockmass and application China Univeristy ofMining and Technology Xuzhou China 2012
[13] D Ma X Miao H Bai et al ldquoImpact of particle transfer onflow properties of crushed mudstonesrdquo Environmental EarthSciences vol 75 no 7 article 593 2016
[14] DMa H Bai Z Chen andH Pu ldquoEffect of particlemixture onseepage properties of crushed mudstonesrdquo Transport in PorousMedia vol 108 no 2 pp 257ndash277 2015
[15] B Zhang H Bai and K Zhang ldquoSeepage characteristics ofcollapse columnfillingsrdquo International Journal ofMining Scienceand Technology 2015
[16] P Ortoleva J Chadam E Merino and A Sen ldquoGeochemicalself-organization II the reactive-infiltration instabilityrdquo Ameri-can Journal of Science vol 287 no 10 pp 1008ndash1040 1987
[17] I Vardoulakis M Stavropoulou and P Papanastasiou ldquoHydro-mechanical aspects of the sand production problemrdquo Transportin Porous Media vol 22 no 2 pp 225ndash244 1996
[18] R L Detwiler and H Rajaram ldquoPredicting dissolution patternsin variable aperture fractures Evaluation of an enhanced depth-averaged computational modelrdquoWater Resources Research vol43 no 4 Article IDW04403 2007
18 Geofluids
[19] M A Habib H M Badr R Ben-Mansour and M E KabirldquoErosion rate correlations of a pipe protruded in an abrupt pipecontractionrdquo International Journal of Impact Engineering vol34 no 8 pp 1350ndash1369 2007
[20] H T Xiao and H Y Xu ldquoIn situ permeability measurementsto establish the influence of slice mining on floor rocksrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 37 no 5 pp 855ndash860 2000
[21] H Guo D P Adhikary and M S Craig ldquoSimulation of minewater inflow and gas emission during longwall miningrdquo RockMechanics and Rock Engineering vol 42 no 1 pp 25ndash51 2009
[22] R Zhang Z JiangH ZhouC Yang and S Xiao ldquoGroundwateroutbursts from faults above a confined aquifer in the coalminingrdquo Natural Hazards vol 71 no 3 pp 1861ndash1872 2014
[23] B Yao F Du E Li and X Wang ldquoMechanical model of karstcollapse columns water inrush and its applicationrdquo ElectronicJournal of Geotechnical Engineering vol 19 pp 1665ndash1675 2014
[24] J Warren and P Root ldquoThe behavior of naturally fracturedreservoirsrdquo SPE Journal vol 3 no 3 pp 245ndash255 2013
[25] H KazemiM S Seth andGWThomas ldquoThe interpretation ofinterference tests in naturally fractured reservoirs with uniformfracture distributionrdquo SPE Journal vol 9 no 4 pp 463ndash4721969
[26] A de Swaan O ldquoAnalytical solutions for determining naturallyfractured reservoir properties by well testingrdquo SPE Journal vol16 no 3 pp 117ndash122 1976
[27] N D Rose and O Hungr ldquoForecasting potential rock slopefailure in open pit mines using the inverse-velocity methodrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 2 pp 308ndash320 2007
[28] J R Fanchi Petroleum Engineering Handbook Volume 1 Gen-eral Engineering Society of Petroleum Engineers 2006
[29] R Sakthivadivel and S Irmay A Review of Filtration TheoriesHydraulic Engineering Laboratory College of EngineeringUniversity of California Berkeley Calif USA 1996
[30] C Wang P Zhai Z Chen J Liu L Wang and J XieldquoExperimental study of coal matrix-cleat interaction underconstant volume boundary conditionrdquo International Journal ofCoal Geology vol 181 pp 124ndash132 2017
[31] S Irmay ldquoOn the theoretical derivation of Darcy and Forch-heimer formulasrdquo Eos Transactions American GeophysicalUnion vol 39 no 4 pp 702ndash707 1958
[32] CH Lee and IW Farmer ldquoA simplemethod of estimating rockmass porosity and permeabilityrdquo International Journal ofMiningand Geological Engineering vol 8 no 1 pp 57ndash65 1990
[33] C Nalluri A K El-Zaemey and H L Chan ldquoSedimenttransport over fixed deposited beds in sewers - An appraisal ofexisting modelsrdquoWater Science and Technology vol 36 no 8-9pp 123ndash128 1997
[34] P Novak and C Nalluri ldquoSediment transport in smooth fixedbed channelsrdquo Journal of the Hydraulics Division vol 101 no 9pp 1139ndash1154 1975
[35] T Fukuzono ldquoA newmethod for predicting the failure time of asloperdquo in Proceedings of the In 4th International Conference andField Workshop on Landslides Tokyo Japan 1985
[36] C R J Kilburn andDN Petley ldquoForecasting giant catastrophicslope collapse lessons from Vajont Northern Italyrdquo Geomor-phology vol 54 no 1-2 pp 21ndash32 2003
[37] B Voight ldquoA method for prediction of volcanic eruptionsrdquoNature vol 332 no 6160 pp 125ndash130 1988
[38] B Yao X Mao J Wei and D Wang ldquoStudy on coupled fluid-solid model for collapse columns considering the effect ofparticle transportrdquo Zhongguo Kuangye Daxue XuebaoJournalof China University of Mining and Technology vol 43 no 1 pp30ndash35 2014
[39] H Bai Seepage Characteristics of Top Stratum of OrdovicianSystem and Its Application Study as Key Aquifuge ChinaUniversity of Mining amp Technology Xuzhou China 2008
[40] C A Tang L G Tham P K K Lee T H Yang and L CLi ldquoCoupled analysis of flow stress and damage (FSD) in rockfailurerdquo International Journal of Rock Mechanics and MiningSciences vol 39 no 4 pp 477ndash489 2002
[41] W C Zhu and C A Tang ldquoMicromechanical model forsimulating the fracture process of rockrdquo Rock Mechanics andRock Engineering vol 37 no 1 pp 25ndash56 2004
[42] T H Yang L G Tham C A Tang Z Z Liang and YTsui ldquoInfluence of heterogeneity of mechanical properties onhydraulic fracturing in permeable rocksrdquo Rock Mechanics andRock Engineering vol 37 no 4 pp 251ndash275 2004
Hindawiwwwhindawicom Volume 2018
Journal of
ChemistryArchaeaHindawiwwwhindawicom Volume 2018
Marine BiologyJournal of
Hindawiwwwhindawicom Volume 2018
BiodiversityInternational Journal of
Hindawiwwwhindawicom Volume 2018
EcologyInternational Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Applied ampEnvironmentalSoil Science
Volume 2018
Forestry ResearchInternational Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
International Journal of
Geophysics
Environmental and Public Health
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
International Journal of
Microbiology
Hindawiwwwhindawicom Volume 2018
Public Health Advances in
AgricultureAdvances in
Hindawiwwwhindawicom Volume 2018
Agronomy
Hindawiwwwhindawicom Volume 2018
International Journal of
Hindawiwwwhindawicom Volume 2018
MeteorologyAdvances in
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018Hindawiwwwhindawicom Volume 2018
ChemistryAdvances in
ScienticaHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Geological ResearchJournal of
Analytical ChemistryInternational Journal of
Hindawiwwwhindawicom Volume 2018
Submit your manuscripts atwwwhindawicom
12 Geofluids
Inverse velocityLinear fitting
0
20
40
60
80
100
Flow
rate
(m3h
)
0
5
10
15
20
25
30
Inve
rse v
eloci
ty (h
m)
5 10 15 200Time (times103 s)
Q
Figure 19 Water flow rate along the bottom surface of the numerical model
025
02
03
015
01
005
0(a) 14000 s
025
02
03
015
01
005
0(b) 15000 s
025
02
03
015
01
005
0(c) 16000 s
025
02
03
015
01
005
0(d) 17000 s
025
02
03
015
01
005
0(e) 17500 s
025
02
03
015
01
005
0(f) 18000 s
Figure 20 Change of particles concentration in a KCP
Geofluids 13
0
005
01
015
02
025
03
035C
once
ntra
tion
1 2 3 4 5 6 70r (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
(a)
105 15 200z (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
0
005
01
015
02
025
03
035
Con
cent
ratio
n (b)
Figure 21 Evolution of particle concentration along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
ConcentrationLoss rate
0
005
01
015
Con
cent
ratio
n
5 10 15 200Time (times103 s)
0
5
10
15
20
25
Part
icle
loss
rate
Qp
(m3h
)
Figure 22 Evolution of average particle volumetric concentrationand particle loss rate
441 Impact of Heterogeneity on Fractures Evolution Fig-ure 23 illustrates the distribution law of the fractures seepagevelocities and particle volume concentrations under identicalflow pressures but different fracture distribution conditionsat 175 times 103 seconds The results show that more intercon-nected fractures are developed along with the increase in mvalues For example when119898 = 4 there are only two intercon-nected fractures However asm value increases an increasingnumber of fractures were generated and interconnected Inthe fourth case (119898 = 10) three interconnected fractures weregenerated This finding indicates that the homogeneity canaccelerate the propagation of the fractures An increase in
Table 2 List of simulation scenarios
Parameter Value
Weibull distribution coefficient (-)
119898 = 4119898 = 6119898 = 8
119898 = 10
Water pressure (MPa)
119901 = 10119901 = 20119901 = 30119901 = 40
Initial particle concentration ()
1198620 = 00051198620 = 0011198620 = 0021198620 = 005
Fracture aperture (times10minus4m)
119887 = 075119887 = 10
119887 = 125119887 = 15
flow velocity and particle concentration with increasing mvalues was also observed as shown in Figures 23(b) and 23(c)
442 Prediction of Water Inrush under Different ConditionsThe analysis and prediction of the occurrences of waterinrush in KCPs based on the changes in seepage are essentialfor the safety of mining processes Some researchers haveadopted catastrophe theories to predict the occurrences ofwater inrush However an approach that can be used topredict water inrush based on water flow has yet to be foundin the literature This study presents the first attempt toresolve this challenge by applying the inverse velocity theory
14 Geofluids
m = 4 m = 6 m = 8 m = 10
1
2
3
4
5
6
7
(a) Distribution of aperture 119887 (times10minus4m )
m = 4 m = 6 m = 8 m = 10
2
16
12
08
04
0
(b) Distribution of seepage velocity (times10minus3ms)
m = 4 m = 6 m = 8 m = 10
025
02
03
015
01
005
0
(c) Distribution of particles concentration
Figure 23 Distribution of fracture seepage velocity and particle concentration at different Weibull distribution conditions (a) Impact ofWeibull distribution on fractures evolution (b) impact of Weibull distribution on water velocity evolution (c) impact of Weibull distributionon particle concentration evolution
Geofluids 15
5 10 15 200Time (times103 s)
m = 4
m = 6 m = 10
m = 8
0
20
40
60
80
100
120Fl
ow ra
te (m
3h
)
(a)
205
21
215
22
225
23
Wat
er in
rush
tim
e (times10
3s)
4 6 8 102Weibull coefficient m
y = 25699xminus0089
R2 = 09825
(b)
Figure 24 Impact of heterogeneity on water flow rate (a) and inrush time (b)
0
20
40
60
80
100
120
140
160
180
200
Flow
rate
(m3h
)
5 10 15 200Time (times103 s)
p = 1MPap = 2MPa
p = 3MPap = 4MPa
(a)
y = 41733xminus1001
R2 = 09992
1 2 3 4 50Water pressure (MPa)
0
5
10
15
20
25
30
35
40
45
Wat
er in
rush
tim
e (times10
3s)
(b)
Figure 25 Impact of aquifer water pressure on water flow rate (a) and inrush time (b)
which has been widely approved effective in many fields suchas slope stability predictionThe relevant results and analysesare shown in Figure 24ndashFigure 27
As shown in Figure 24 water flow rate exhibits a non-linear increase and as the value of m increases the seepagerate accelerates gradually For example at 119905 = 15 times 104 s theseepage rate was approximately 15m3h for 119898 = 4 while itjumped to 25m3h for 119898 = 10 Results from Figure 24(b)show that water inrush occurs sooner for a greater 119898 valueIn other words the inrush occurs earlier as the heterogeneityincreases The water inrush time follows the power functionThis is due to the fact that the water is more prone to flowingthrough the existing fractures (which indicates a higher
permeability) in the heterogeneous structure Neverthelessdue to the heterogeneous distribution of the aperture thefractures cannot be easily interconnected which hampers theformation of the seepage channels In regard to the homo-geneous rock strata since the flow of water was dominantlycontrolled by the pressure gradient the fractures generatedduring the process of erosion could be easily interconnectedand as a result the water inrush occurredsooner
Figure 25 illustrates the impact of the initial KCPrsquos waterpressure on the flow rates and water inrush time It can beseen that as the pressure increases the changes in the flowrates accelerate For example for119901 = 2MPa the flow rate wasonly approximately 5m3h and it increased to 30m3h when
16 Geofluids
0
20
40
60
80
100
120
140
160
180
200Fl
ow ra
te (m
3h
)
5 10 15 20 250Time (times103 s)
c = 0005
c = 001
c = 002
c = 005
(a)
0
5
10
15
20
25
30
35
Wat
er in
rush
tim
e (times10
3s)
001 002 003 004 0050Initial particle concentration
y = 13554xminus0591
R2 = 09975
(b)
Figure 26 Impact of initial particle concentration on water flow rate (a) and inrush time (b)
0
20
40
60
80
100
120
140
160
180
200
Flow
rate
(m3h
)
5 10 15 200Time (times103 s)
075E minus 4m100E minus 4m
125E minus 4m150E minus 4m
(a)
y = 31027eminus286x
R2 = 09503
09 11 13 1507Fracture aperture (times10minus4 m)
0
5
10
15
20
25
30
35
40
Wat
er in
rush
tim
e (times10
3s)
(b)
Figure 27 Impact of absolute aperture on water flow rate (a) and inrush time (b)
119901 = 3MPa In addition with increasing the aquifer waterpressure the water inrush time was also brought forward asshown in Figure 25(a) The outburst time was approximately119905 = 40 times 104 s for p = 1MPa while only 10 times 104 s for119901 = 4MPa The relationship between the time of the inrushoccurrences and the aquifer water pressure follows the powerfunction as illustrated in Figure 25
For varying initial particle concentrations the evolutionof both the water flow rate change and the water inrushtime shows a similar trend to that of different aquifer waterpressures The flow rate accelerates with increasing initialparticle concentration and consequently the water inrushoccurs earlier as shown in Figure 26The outburst times alsoshow a power function to the initial particle concentration
The initial average fracture aperture also shows significantimpact on water flow behavior For instance results fromFigure 27 clearly illustrate that the flow rate increases withincreasing initial average fracture aperture Please note thatthe inrush time follows an exponential function to the initialaverage fracture aperture
These numerical results can be explained by the factthat the initial seepage velocity is expected to be higher forthe modelling cases with the higher initial aquifer pressureinitial fracture aperture andor initial particle concentrationThe higher flow velocity would intensify the erosion of thefractures enhance the permeability and thereby acceleratethe migration of the particles and interconnection of seepagechannels which causes water inrush
Geofluids 17
5 Conclusions
In this study a systematic approach was established to inves-tigate the impact of controlling factors onwater flow behaviorfor KCPs and to predict water inrush time by introducing theinverse velocity theory In this approach a suite of governingequations was developed to couple all the physics involvedin this complex process including water flow rock erosionand change in rock microstructure These equations werethen implemented into a finite element software COMSOLMultiphysics to simulate the fully coupled process Basedon this numerical model a series of sensitivity studies wereconducted and some important findings have been drawn
(i) Water flow rate increases with increasing aquiferpressure initial particle concentration and fractureopening This results in an increase in the permeabil-ity and finally an acceleration of the migration of theparticles and interconnection of the seepage channelsThis finding suggests the grouting of the KCPs couldbe an effective measure to mitigate water inrush risk
(ii) The inverse velocity theory was successfully appliedto analyze the occurrences of water inrush underdifferent conditions The results show that the timeof inrush has a power relationship to the rock het-erogeneity water pressure and initial particle concen-tration and follows an exponential relationship to theinitial fracture apertures
The framework developed from this work not only helpsenhance coal mining operations safety by better under-standing and predicting water inrush risks so that propermitigation measures can be put in place timely It canalso be extended to other fields such as tunneling backfillpaste piping tailing dam erosion and other engineeringapplications which are likely to encounter time-dependenterosion or deformation or water inrush issues
Please be noted that there are a number of other stochasticmethods available in the literature that can be used to illus-trate rock heterogeneity such as the Monte-Carlo methodor First-Order approach The differences of these methodson the results of water inrush prediction may be worthcomparing in the near future
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This project is supported by the National Natural ScienceFoundation of China (nos 51304072 51774110) the Programfor Innovative Research Team in University of Ministryof Education of China (IRT 16R22) and the PostdoctoralScience Foundation of China (2017M612398)
References
[1] DMa XMiao H Bai et al ldquoEffect of mining on shear sidewallgroundwater inrush hazard caused by seepage instability of the
penetrated karst collapse pillarrdquo Natural Hazards vol 82 no 1pp 73ndash93 2016
[2] H Keqiang Y Guangming and L Yaoru ldquoPalaeo-karst collapsepillars in northern China and their damage to the geologicalenvironmentsrdquo Environmental Geology vol 58 no 5 pp 1029ndash1040 2009
[3] B Yao J Wei D Wang D Ma and Z Chen ldquoNumericalstudy on seepage property of karst collapse columns underparticle migrationrdquo CMES Computer Modeling in Engineeringamp Sciences vol 91 no 2 pp 81ndash100 2013
[4] J Tang H Bai B Yao and Y Wu ldquoTheoretical analysis onwater-inrush mechanism of concealed collapse pillars in floorrdquoMining Science and Technology vol 21 no 1 pp 57ndash60 2011
[5] Y Chen M Yi C Chen and C Yu ldquoBernstein polynomialsmethod for fractional convection-diffusion equation with vari-able coefficientsrdquoComputerModeling in Engineering amp Sciencesvol 83 no 6 pp 639ndash653 2012
[6] J Zhang and B Shen ldquoCoal mining under aquifers in China Acase studyrdquo International Journal of Rock Mechanics and MiningSciences vol 41 no 4 pp 629ndash639 2004
[7] D Ma H Bai X Miao H Pu B Jiang and Z ChenldquoCompaction and seepage properties of crushed limestoneparticle mixture an experimental investigation for Ordoviciankarst collapse pillar groundwater inrushrdquo Environmental EarthSciences vol 75 no 1 article 11 p 14 2016
[8] S Yin J Zhang and D Liu ldquoA study of mine water inrushesby measurements of in situ stress and rock failuresrdquo NaturalHazards vol 79 no 3 pp 1961ndash1979 2015
[9] H Bai D Ma and Z Chen ldquoMechanical behavior of ground-water seepage in karst collapse pillarsrdquo Engineering Geology vol164 pp 101ndash106 2013
[10] D Ma and H Bai ldquoGroundwater inflow prediction model ofkarst collapse pillar a case study for mining-induced ground-water inrush riskrdquoNatural Hazards vol 76 no 2 pp 1319ndash13342015
[11] D Ma H Bai and Y Wang ldquoMechanical behavior of a coalseam penetrated by a karst collapse pillar mining-inducedgroundwater inrush riskrdquo Natural Hazards vol 75 no 3 pp2137ndash2151 2015
[12] B Yao Research on variable mass fluid-solid coupling dynamictheory of broken rockmass and application China Univeristy ofMining and Technology Xuzhou China 2012
[13] D Ma X Miao H Bai et al ldquoImpact of particle transfer onflow properties of crushed mudstonesrdquo Environmental EarthSciences vol 75 no 7 article 593 2016
[14] DMa H Bai Z Chen andH Pu ldquoEffect of particlemixture onseepage properties of crushed mudstonesrdquo Transport in PorousMedia vol 108 no 2 pp 257ndash277 2015
[15] B Zhang H Bai and K Zhang ldquoSeepage characteristics ofcollapse columnfillingsrdquo International Journal ofMining Scienceand Technology 2015
[16] P Ortoleva J Chadam E Merino and A Sen ldquoGeochemicalself-organization II the reactive-infiltration instabilityrdquo Ameri-can Journal of Science vol 287 no 10 pp 1008ndash1040 1987
[17] I Vardoulakis M Stavropoulou and P Papanastasiou ldquoHydro-mechanical aspects of the sand production problemrdquo Transportin Porous Media vol 22 no 2 pp 225ndash244 1996
[18] R L Detwiler and H Rajaram ldquoPredicting dissolution patternsin variable aperture fractures Evaluation of an enhanced depth-averaged computational modelrdquoWater Resources Research vol43 no 4 Article IDW04403 2007
18 Geofluids
[19] M A Habib H M Badr R Ben-Mansour and M E KabirldquoErosion rate correlations of a pipe protruded in an abrupt pipecontractionrdquo International Journal of Impact Engineering vol34 no 8 pp 1350ndash1369 2007
[20] H T Xiao and H Y Xu ldquoIn situ permeability measurementsto establish the influence of slice mining on floor rocksrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 37 no 5 pp 855ndash860 2000
[21] H Guo D P Adhikary and M S Craig ldquoSimulation of minewater inflow and gas emission during longwall miningrdquo RockMechanics and Rock Engineering vol 42 no 1 pp 25ndash51 2009
[22] R Zhang Z JiangH ZhouC Yang and S Xiao ldquoGroundwateroutbursts from faults above a confined aquifer in the coalminingrdquo Natural Hazards vol 71 no 3 pp 1861ndash1872 2014
[23] B Yao F Du E Li and X Wang ldquoMechanical model of karstcollapse columns water inrush and its applicationrdquo ElectronicJournal of Geotechnical Engineering vol 19 pp 1665ndash1675 2014
[24] J Warren and P Root ldquoThe behavior of naturally fracturedreservoirsrdquo SPE Journal vol 3 no 3 pp 245ndash255 2013
[25] H KazemiM S Seth andGWThomas ldquoThe interpretation ofinterference tests in naturally fractured reservoirs with uniformfracture distributionrdquo SPE Journal vol 9 no 4 pp 463ndash4721969
[26] A de Swaan O ldquoAnalytical solutions for determining naturallyfractured reservoir properties by well testingrdquo SPE Journal vol16 no 3 pp 117ndash122 1976
[27] N D Rose and O Hungr ldquoForecasting potential rock slopefailure in open pit mines using the inverse-velocity methodrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 2 pp 308ndash320 2007
[28] J R Fanchi Petroleum Engineering Handbook Volume 1 Gen-eral Engineering Society of Petroleum Engineers 2006
[29] R Sakthivadivel and S Irmay A Review of Filtration TheoriesHydraulic Engineering Laboratory College of EngineeringUniversity of California Berkeley Calif USA 1996
[30] C Wang P Zhai Z Chen J Liu L Wang and J XieldquoExperimental study of coal matrix-cleat interaction underconstant volume boundary conditionrdquo International Journal ofCoal Geology vol 181 pp 124ndash132 2017
[31] S Irmay ldquoOn the theoretical derivation of Darcy and Forch-heimer formulasrdquo Eos Transactions American GeophysicalUnion vol 39 no 4 pp 702ndash707 1958
[32] CH Lee and IW Farmer ldquoA simplemethod of estimating rockmass porosity and permeabilityrdquo International Journal ofMiningand Geological Engineering vol 8 no 1 pp 57ndash65 1990
[33] C Nalluri A K El-Zaemey and H L Chan ldquoSedimenttransport over fixed deposited beds in sewers - An appraisal ofexisting modelsrdquoWater Science and Technology vol 36 no 8-9pp 123ndash128 1997
[34] P Novak and C Nalluri ldquoSediment transport in smooth fixedbed channelsrdquo Journal of the Hydraulics Division vol 101 no 9pp 1139ndash1154 1975
[35] T Fukuzono ldquoA newmethod for predicting the failure time of asloperdquo in Proceedings of the In 4th International Conference andField Workshop on Landslides Tokyo Japan 1985
[36] C R J Kilburn andDN Petley ldquoForecasting giant catastrophicslope collapse lessons from Vajont Northern Italyrdquo Geomor-phology vol 54 no 1-2 pp 21ndash32 2003
[37] B Voight ldquoA method for prediction of volcanic eruptionsrdquoNature vol 332 no 6160 pp 125ndash130 1988
[38] B Yao X Mao J Wei and D Wang ldquoStudy on coupled fluid-solid model for collapse columns considering the effect ofparticle transportrdquo Zhongguo Kuangye Daxue XuebaoJournalof China University of Mining and Technology vol 43 no 1 pp30ndash35 2014
[39] H Bai Seepage Characteristics of Top Stratum of OrdovicianSystem and Its Application Study as Key Aquifuge ChinaUniversity of Mining amp Technology Xuzhou China 2008
[40] C A Tang L G Tham P K K Lee T H Yang and L CLi ldquoCoupled analysis of flow stress and damage (FSD) in rockfailurerdquo International Journal of Rock Mechanics and MiningSciences vol 39 no 4 pp 477ndash489 2002
[41] W C Zhu and C A Tang ldquoMicromechanical model forsimulating the fracture process of rockrdquo Rock Mechanics andRock Engineering vol 37 no 1 pp 25ndash56 2004
[42] T H Yang L G Tham C A Tang Z Z Liang and YTsui ldquoInfluence of heterogeneity of mechanical properties onhydraulic fracturing in permeable rocksrdquo Rock Mechanics andRock Engineering vol 37 no 4 pp 251ndash275 2004
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Geological ResearchJournal of
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Submit your manuscripts atwwwhindawicom
Geofluids 13
0
005
01
015
02
025
03
035C
once
ntra
tion
1 2 3 4 5 6 70r (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
(a)
105 15 200z (m)
14000 s15000 s16000 s
17000 s17500 s18000 s
0
005
01
015
02
025
03
035
Con
cent
ratio
n (b)
Figure 21 Evolution of particle concentration along the lines of (a) O-O10158401015840 axis and (b) O1015840-A1015840 axis
ConcentrationLoss rate
0
005
01
015
Con
cent
ratio
n
5 10 15 200Time (times103 s)
0
5
10
15
20
25
Part
icle
loss
rate
Qp
(m3h
)
Figure 22 Evolution of average particle volumetric concentrationand particle loss rate
441 Impact of Heterogeneity on Fractures Evolution Fig-ure 23 illustrates the distribution law of the fractures seepagevelocities and particle volume concentrations under identicalflow pressures but different fracture distribution conditionsat 175 times 103 seconds The results show that more intercon-nected fractures are developed along with the increase in mvalues For example when119898 = 4 there are only two intercon-nected fractures However asm value increases an increasingnumber of fractures were generated and interconnected Inthe fourth case (119898 = 10) three interconnected fractures weregenerated This finding indicates that the homogeneity canaccelerate the propagation of the fractures An increase in
Table 2 List of simulation scenarios
Parameter Value
Weibull distribution coefficient (-)
119898 = 4119898 = 6119898 = 8
119898 = 10
Water pressure (MPa)
119901 = 10119901 = 20119901 = 30119901 = 40
Initial particle concentration ()
1198620 = 00051198620 = 0011198620 = 0021198620 = 005
Fracture aperture (times10minus4m)
119887 = 075119887 = 10
119887 = 125119887 = 15
flow velocity and particle concentration with increasing mvalues was also observed as shown in Figures 23(b) and 23(c)
442 Prediction of Water Inrush under Different ConditionsThe analysis and prediction of the occurrences of waterinrush in KCPs based on the changes in seepage are essentialfor the safety of mining processes Some researchers haveadopted catastrophe theories to predict the occurrences ofwater inrush However an approach that can be used topredict water inrush based on water flow has yet to be foundin the literature This study presents the first attempt toresolve this challenge by applying the inverse velocity theory
14 Geofluids
m = 4 m = 6 m = 8 m = 10
1
2
3
4
5
6
7
(a) Distribution of aperture 119887 (times10minus4m )
m = 4 m = 6 m = 8 m = 10
2
16
12
08
04
0
(b) Distribution of seepage velocity (times10minus3ms)
m = 4 m = 6 m = 8 m = 10
025
02
03
015
01
005
0
(c) Distribution of particles concentration
Figure 23 Distribution of fracture seepage velocity and particle concentration at different Weibull distribution conditions (a) Impact ofWeibull distribution on fractures evolution (b) impact of Weibull distribution on water velocity evolution (c) impact of Weibull distributionon particle concentration evolution
Geofluids 15
5 10 15 200Time (times103 s)
m = 4
m = 6 m = 10
m = 8
0
20
40
60
80
100
120Fl
ow ra
te (m
3h
)
(a)
205
21
215
22
225
23
Wat
er in
rush
tim
e (times10
3s)
4 6 8 102Weibull coefficient m
y = 25699xminus0089
R2 = 09825
(b)
Figure 24 Impact of heterogeneity on water flow rate (a) and inrush time (b)
0
20
40
60
80
100
120
140
160
180
200
Flow
rate
(m3h
)
5 10 15 200Time (times103 s)
p = 1MPap = 2MPa
p = 3MPap = 4MPa
(a)
y = 41733xminus1001
R2 = 09992
1 2 3 4 50Water pressure (MPa)
0
5
10
15
20
25
30
35
40
45
Wat
er in
rush
tim
e (times10
3s)
(b)
Figure 25 Impact of aquifer water pressure on water flow rate (a) and inrush time (b)
which has been widely approved effective in many fields suchas slope stability predictionThe relevant results and analysesare shown in Figure 24ndashFigure 27
As shown in Figure 24 water flow rate exhibits a non-linear increase and as the value of m increases the seepagerate accelerates gradually For example at 119905 = 15 times 104 s theseepage rate was approximately 15m3h for 119898 = 4 while itjumped to 25m3h for 119898 = 10 Results from Figure 24(b)show that water inrush occurs sooner for a greater 119898 valueIn other words the inrush occurs earlier as the heterogeneityincreases The water inrush time follows the power functionThis is due to the fact that the water is more prone to flowingthrough the existing fractures (which indicates a higher
permeability) in the heterogeneous structure Neverthelessdue to the heterogeneous distribution of the aperture thefractures cannot be easily interconnected which hampers theformation of the seepage channels In regard to the homo-geneous rock strata since the flow of water was dominantlycontrolled by the pressure gradient the fractures generatedduring the process of erosion could be easily interconnectedand as a result the water inrush occurredsooner
Figure 25 illustrates the impact of the initial KCPrsquos waterpressure on the flow rates and water inrush time It can beseen that as the pressure increases the changes in the flowrates accelerate For example for119901 = 2MPa the flow rate wasonly approximately 5m3h and it increased to 30m3h when
16 Geofluids
0
20
40
60
80
100
120
140
160
180
200Fl
ow ra
te (m
3h
)
5 10 15 20 250Time (times103 s)
c = 0005
c = 001
c = 002
c = 005
(a)
0
5
10
15
20
25
30
35
Wat
er in
rush
tim
e (times10
3s)
001 002 003 004 0050Initial particle concentration
y = 13554xminus0591
R2 = 09975
(b)
Figure 26 Impact of initial particle concentration on water flow rate (a) and inrush time (b)
0
20
40
60
80
100
120
140
160
180
200
Flow
rate
(m3h
)
5 10 15 200Time (times103 s)
075E minus 4m100E minus 4m
125E minus 4m150E minus 4m
(a)
y = 31027eminus286x
R2 = 09503
09 11 13 1507Fracture aperture (times10minus4 m)
0
5
10
15
20
25
30
35
40
Wat
er in
rush
tim
e (times10
3s)
(b)
Figure 27 Impact of absolute aperture on water flow rate (a) and inrush time (b)
119901 = 3MPa In addition with increasing the aquifer waterpressure the water inrush time was also brought forward asshown in Figure 25(a) The outburst time was approximately119905 = 40 times 104 s for p = 1MPa while only 10 times 104 s for119901 = 4MPa The relationship between the time of the inrushoccurrences and the aquifer water pressure follows the powerfunction as illustrated in Figure 25
For varying initial particle concentrations the evolutionof both the water flow rate change and the water inrushtime shows a similar trend to that of different aquifer waterpressures The flow rate accelerates with increasing initialparticle concentration and consequently the water inrushoccurs earlier as shown in Figure 26The outburst times alsoshow a power function to the initial particle concentration
The initial average fracture aperture also shows significantimpact on water flow behavior For instance results fromFigure 27 clearly illustrate that the flow rate increases withincreasing initial average fracture aperture Please note thatthe inrush time follows an exponential function to the initialaverage fracture aperture
These numerical results can be explained by the factthat the initial seepage velocity is expected to be higher forthe modelling cases with the higher initial aquifer pressureinitial fracture aperture andor initial particle concentrationThe higher flow velocity would intensify the erosion of thefractures enhance the permeability and thereby acceleratethe migration of the particles and interconnection of seepagechannels which causes water inrush
Geofluids 17
5 Conclusions
In this study a systematic approach was established to inves-tigate the impact of controlling factors onwater flow behaviorfor KCPs and to predict water inrush time by introducing theinverse velocity theory In this approach a suite of governingequations was developed to couple all the physics involvedin this complex process including water flow rock erosionand change in rock microstructure These equations werethen implemented into a finite element software COMSOLMultiphysics to simulate the fully coupled process Basedon this numerical model a series of sensitivity studies wereconducted and some important findings have been drawn
(i) Water flow rate increases with increasing aquiferpressure initial particle concentration and fractureopening This results in an increase in the permeabil-ity and finally an acceleration of the migration of theparticles and interconnection of the seepage channelsThis finding suggests the grouting of the KCPs couldbe an effective measure to mitigate water inrush risk
(ii) The inverse velocity theory was successfully appliedto analyze the occurrences of water inrush underdifferent conditions The results show that the timeof inrush has a power relationship to the rock het-erogeneity water pressure and initial particle concen-tration and follows an exponential relationship to theinitial fracture apertures
The framework developed from this work not only helpsenhance coal mining operations safety by better under-standing and predicting water inrush risks so that propermitigation measures can be put in place timely It canalso be extended to other fields such as tunneling backfillpaste piping tailing dam erosion and other engineeringapplications which are likely to encounter time-dependenterosion or deformation or water inrush issues
Please be noted that there are a number of other stochasticmethods available in the literature that can be used to illus-trate rock heterogeneity such as the Monte-Carlo methodor First-Order approach The differences of these methodson the results of water inrush prediction may be worthcomparing in the near future
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This project is supported by the National Natural ScienceFoundation of China (nos 51304072 51774110) the Programfor Innovative Research Team in University of Ministryof Education of China (IRT 16R22) and the PostdoctoralScience Foundation of China (2017M612398)
References
[1] DMa XMiao H Bai et al ldquoEffect of mining on shear sidewallgroundwater inrush hazard caused by seepage instability of the
penetrated karst collapse pillarrdquo Natural Hazards vol 82 no 1pp 73ndash93 2016
[2] H Keqiang Y Guangming and L Yaoru ldquoPalaeo-karst collapsepillars in northern China and their damage to the geologicalenvironmentsrdquo Environmental Geology vol 58 no 5 pp 1029ndash1040 2009
[3] B Yao J Wei D Wang D Ma and Z Chen ldquoNumericalstudy on seepage property of karst collapse columns underparticle migrationrdquo CMES Computer Modeling in Engineeringamp Sciences vol 91 no 2 pp 81ndash100 2013
[4] J Tang H Bai B Yao and Y Wu ldquoTheoretical analysis onwater-inrush mechanism of concealed collapse pillars in floorrdquoMining Science and Technology vol 21 no 1 pp 57ndash60 2011
[5] Y Chen M Yi C Chen and C Yu ldquoBernstein polynomialsmethod for fractional convection-diffusion equation with vari-able coefficientsrdquoComputerModeling in Engineering amp Sciencesvol 83 no 6 pp 639ndash653 2012
[6] J Zhang and B Shen ldquoCoal mining under aquifers in China Acase studyrdquo International Journal of Rock Mechanics and MiningSciences vol 41 no 4 pp 629ndash639 2004
[7] D Ma H Bai X Miao H Pu B Jiang and Z ChenldquoCompaction and seepage properties of crushed limestoneparticle mixture an experimental investigation for Ordoviciankarst collapse pillar groundwater inrushrdquo Environmental EarthSciences vol 75 no 1 article 11 p 14 2016
[8] S Yin J Zhang and D Liu ldquoA study of mine water inrushesby measurements of in situ stress and rock failuresrdquo NaturalHazards vol 79 no 3 pp 1961ndash1979 2015
[9] H Bai D Ma and Z Chen ldquoMechanical behavior of ground-water seepage in karst collapse pillarsrdquo Engineering Geology vol164 pp 101ndash106 2013
[10] D Ma and H Bai ldquoGroundwater inflow prediction model ofkarst collapse pillar a case study for mining-induced ground-water inrush riskrdquoNatural Hazards vol 76 no 2 pp 1319ndash13342015
[11] D Ma H Bai and Y Wang ldquoMechanical behavior of a coalseam penetrated by a karst collapse pillar mining-inducedgroundwater inrush riskrdquo Natural Hazards vol 75 no 3 pp2137ndash2151 2015
[12] B Yao Research on variable mass fluid-solid coupling dynamictheory of broken rockmass and application China Univeristy ofMining and Technology Xuzhou China 2012
[13] D Ma X Miao H Bai et al ldquoImpact of particle transfer onflow properties of crushed mudstonesrdquo Environmental EarthSciences vol 75 no 7 article 593 2016
[14] DMa H Bai Z Chen andH Pu ldquoEffect of particlemixture onseepage properties of crushed mudstonesrdquo Transport in PorousMedia vol 108 no 2 pp 257ndash277 2015
[15] B Zhang H Bai and K Zhang ldquoSeepage characteristics ofcollapse columnfillingsrdquo International Journal ofMining Scienceand Technology 2015
[16] P Ortoleva J Chadam E Merino and A Sen ldquoGeochemicalself-organization II the reactive-infiltration instabilityrdquo Ameri-can Journal of Science vol 287 no 10 pp 1008ndash1040 1987
[17] I Vardoulakis M Stavropoulou and P Papanastasiou ldquoHydro-mechanical aspects of the sand production problemrdquo Transportin Porous Media vol 22 no 2 pp 225ndash244 1996
[18] R L Detwiler and H Rajaram ldquoPredicting dissolution patternsin variable aperture fractures Evaluation of an enhanced depth-averaged computational modelrdquoWater Resources Research vol43 no 4 Article IDW04403 2007
18 Geofluids
[19] M A Habib H M Badr R Ben-Mansour and M E KabirldquoErosion rate correlations of a pipe protruded in an abrupt pipecontractionrdquo International Journal of Impact Engineering vol34 no 8 pp 1350ndash1369 2007
[20] H T Xiao and H Y Xu ldquoIn situ permeability measurementsto establish the influence of slice mining on floor rocksrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 37 no 5 pp 855ndash860 2000
[21] H Guo D P Adhikary and M S Craig ldquoSimulation of minewater inflow and gas emission during longwall miningrdquo RockMechanics and Rock Engineering vol 42 no 1 pp 25ndash51 2009
[22] R Zhang Z JiangH ZhouC Yang and S Xiao ldquoGroundwateroutbursts from faults above a confined aquifer in the coalminingrdquo Natural Hazards vol 71 no 3 pp 1861ndash1872 2014
[23] B Yao F Du E Li and X Wang ldquoMechanical model of karstcollapse columns water inrush and its applicationrdquo ElectronicJournal of Geotechnical Engineering vol 19 pp 1665ndash1675 2014
[24] J Warren and P Root ldquoThe behavior of naturally fracturedreservoirsrdquo SPE Journal vol 3 no 3 pp 245ndash255 2013
[25] H KazemiM S Seth andGWThomas ldquoThe interpretation ofinterference tests in naturally fractured reservoirs with uniformfracture distributionrdquo SPE Journal vol 9 no 4 pp 463ndash4721969
[26] A de Swaan O ldquoAnalytical solutions for determining naturallyfractured reservoir properties by well testingrdquo SPE Journal vol16 no 3 pp 117ndash122 1976
[27] N D Rose and O Hungr ldquoForecasting potential rock slopefailure in open pit mines using the inverse-velocity methodrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 2 pp 308ndash320 2007
[28] J R Fanchi Petroleum Engineering Handbook Volume 1 Gen-eral Engineering Society of Petroleum Engineers 2006
[29] R Sakthivadivel and S Irmay A Review of Filtration TheoriesHydraulic Engineering Laboratory College of EngineeringUniversity of California Berkeley Calif USA 1996
[30] C Wang P Zhai Z Chen J Liu L Wang and J XieldquoExperimental study of coal matrix-cleat interaction underconstant volume boundary conditionrdquo International Journal ofCoal Geology vol 181 pp 124ndash132 2017
[31] S Irmay ldquoOn the theoretical derivation of Darcy and Forch-heimer formulasrdquo Eos Transactions American GeophysicalUnion vol 39 no 4 pp 702ndash707 1958
[32] CH Lee and IW Farmer ldquoA simplemethod of estimating rockmass porosity and permeabilityrdquo International Journal ofMiningand Geological Engineering vol 8 no 1 pp 57ndash65 1990
[33] C Nalluri A K El-Zaemey and H L Chan ldquoSedimenttransport over fixed deposited beds in sewers - An appraisal ofexisting modelsrdquoWater Science and Technology vol 36 no 8-9pp 123ndash128 1997
[34] P Novak and C Nalluri ldquoSediment transport in smooth fixedbed channelsrdquo Journal of the Hydraulics Division vol 101 no 9pp 1139ndash1154 1975
[35] T Fukuzono ldquoA newmethod for predicting the failure time of asloperdquo in Proceedings of the In 4th International Conference andField Workshop on Landslides Tokyo Japan 1985
[36] C R J Kilburn andDN Petley ldquoForecasting giant catastrophicslope collapse lessons from Vajont Northern Italyrdquo Geomor-phology vol 54 no 1-2 pp 21ndash32 2003
[37] B Voight ldquoA method for prediction of volcanic eruptionsrdquoNature vol 332 no 6160 pp 125ndash130 1988
[38] B Yao X Mao J Wei and D Wang ldquoStudy on coupled fluid-solid model for collapse columns considering the effect ofparticle transportrdquo Zhongguo Kuangye Daxue XuebaoJournalof China University of Mining and Technology vol 43 no 1 pp30ndash35 2014
[39] H Bai Seepage Characteristics of Top Stratum of OrdovicianSystem and Its Application Study as Key Aquifuge ChinaUniversity of Mining amp Technology Xuzhou China 2008
[40] C A Tang L G Tham P K K Lee T H Yang and L CLi ldquoCoupled analysis of flow stress and damage (FSD) in rockfailurerdquo International Journal of Rock Mechanics and MiningSciences vol 39 no 4 pp 477ndash489 2002
[41] W C Zhu and C A Tang ldquoMicromechanical model forsimulating the fracture process of rockrdquo Rock Mechanics andRock Engineering vol 37 no 1 pp 25ndash56 2004
[42] T H Yang L G Tham C A Tang Z Z Liang and YTsui ldquoInfluence of heterogeneity of mechanical properties onhydraulic fracturing in permeable rocksrdquo Rock Mechanics andRock Engineering vol 37 no 4 pp 251ndash275 2004
Hindawiwwwhindawicom Volume 2018
Journal of
ChemistryArchaeaHindawiwwwhindawicom Volume 2018
Marine BiologyJournal of
Hindawiwwwhindawicom Volume 2018
BiodiversityInternational Journal of
Hindawiwwwhindawicom Volume 2018
EcologyInternational Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Applied ampEnvironmentalSoil Science
Volume 2018
Forestry ResearchInternational Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
International Journal of
Geophysics
Environmental and Public Health
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
International Journal of
Microbiology
Hindawiwwwhindawicom Volume 2018
Public Health Advances in
AgricultureAdvances in
Hindawiwwwhindawicom Volume 2018
Agronomy
Hindawiwwwhindawicom Volume 2018
International Journal of
Hindawiwwwhindawicom Volume 2018
MeteorologyAdvances in
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018Hindawiwwwhindawicom Volume 2018
ChemistryAdvances in
ScienticaHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Geological ResearchJournal of
Analytical ChemistryInternational Journal of
Hindawiwwwhindawicom Volume 2018
Submit your manuscripts atwwwhindawicom
14 Geofluids
m = 4 m = 6 m = 8 m = 10
1
2
3
4
5
6
7
(a) Distribution of aperture 119887 (times10minus4m )
m = 4 m = 6 m = 8 m = 10
2
16
12
08
04
0
(b) Distribution of seepage velocity (times10minus3ms)
m = 4 m = 6 m = 8 m = 10
025
02
03
015
01
005
0
(c) Distribution of particles concentration
Figure 23 Distribution of fracture seepage velocity and particle concentration at different Weibull distribution conditions (a) Impact ofWeibull distribution on fractures evolution (b) impact of Weibull distribution on water velocity evolution (c) impact of Weibull distributionon particle concentration evolution
Geofluids 15
5 10 15 200Time (times103 s)
m = 4
m = 6 m = 10
m = 8
0
20
40
60
80
100
120Fl
ow ra
te (m
3h
)
(a)
205
21
215
22
225
23
Wat
er in
rush
tim
e (times10
3s)
4 6 8 102Weibull coefficient m
y = 25699xminus0089
R2 = 09825
(b)
Figure 24 Impact of heterogeneity on water flow rate (a) and inrush time (b)
0
20
40
60
80
100
120
140
160
180
200
Flow
rate
(m3h
)
5 10 15 200Time (times103 s)
p = 1MPap = 2MPa
p = 3MPap = 4MPa
(a)
y = 41733xminus1001
R2 = 09992
1 2 3 4 50Water pressure (MPa)
0
5
10
15
20
25
30
35
40
45
Wat
er in
rush
tim
e (times10
3s)
(b)
Figure 25 Impact of aquifer water pressure on water flow rate (a) and inrush time (b)
which has been widely approved effective in many fields suchas slope stability predictionThe relevant results and analysesare shown in Figure 24ndashFigure 27
As shown in Figure 24 water flow rate exhibits a non-linear increase and as the value of m increases the seepagerate accelerates gradually For example at 119905 = 15 times 104 s theseepage rate was approximately 15m3h for 119898 = 4 while itjumped to 25m3h for 119898 = 10 Results from Figure 24(b)show that water inrush occurs sooner for a greater 119898 valueIn other words the inrush occurs earlier as the heterogeneityincreases The water inrush time follows the power functionThis is due to the fact that the water is more prone to flowingthrough the existing fractures (which indicates a higher
permeability) in the heterogeneous structure Neverthelessdue to the heterogeneous distribution of the aperture thefractures cannot be easily interconnected which hampers theformation of the seepage channels In regard to the homo-geneous rock strata since the flow of water was dominantlycontrolled by the pressure gradient the fractures generatedduring the process of erosion could be easily interconnectedand as a result the water inrush occurredsooner
Figure 25 illustrates the impact of the initial KCPrsquos waterpressure on the flow rates and water inrush time It can beseen that as the pressure increases the changes in the flowrates accelerate For example for119901 = 2MPa the flow rate wasonly approximately 5m3h and it increased to 30m3h when
16 Geofluids
0
20
40
60
80
100
120
140
160
180
200Fl
ow ra
te (m
3h
)
5 10 15 20 250Time (times103 s)
c = 0005
c = 001
c = 002
c = 005
(a)
0
5
10
15
20
25
30
35
Wat
er in
rush
tim
e (times10
3s)
001 002 003 004 0050Initial particle concentration
y = 13554xminus0591
R2 = 09975
(b)
Figure 26 Impact of initial particle concentration on water flow rate (a) and inrush time (b)
0
20
40
60
80
100
120
140
160
180
200
Flow
rate
(m3h
)
5 10 15 200Time (times103 s)
075E minus 4m100E minus 4m
125E minus 4m150E minus 4m
(a)
y = 31027eminus286x
R2 = 09503
09 11 13 1507Fracture aperture (times10minus4 m)
0
5
10
15
20
25
30
35
40
Wat
er in
rush
tim
e (times10
3s)
(b)
Figure 27 Impact of absolute aperture on water flow rate (a) and inrush time (b)
119901 = 3MPa In addition with increasing the aquifer waterpressure the water inrush time was also brought forward asshown in Figure 25(a) The outburst time was approximately119905 = 40 times 104 s for p = 1MPa while only 10 times 104 s for119901 = 4MPa The relationship between the time of the inrushoccurrences and the aquifer water pressure follows the powerfunction as illustrated in Figure 25
For varying initial particle concentrations the evolutionof both the water flow rate change and the water inrushtime shows a similar trend to that of different aquifer waterpressures The flow rate accelerates with increasing initialparticle concentration and consequently the water inrushoccurs earlier as shown in Figure 26The outburst times alsoshow a power function to the initial particle concentration
The initial average fracture aperture also shows significantimpact on water flow behavior For instance results fromFigure 27 clearly illustrate that the flow rate increases withincreasing initial average fracture aperture Please note thatthe inrush time follows an exponential function to the initialaverage fracture aperture
These numerical results can be explained by the factthat the initial seepage velocity is expected to be higher forthe modelling cases with the higher initial aquifer pressureinitial fracture aperture andor initial particle concentrationThe higher flow velocity would intensify the erosion of thefractures enhance the permeability and thereby acceleratethe migration of the particles and interconnection of seepagechannels which causes water inrush
Geofluids 17
5 Conclusions
In this study a systematic approach was established to inves-tigate the impact of controlling factors onwater flow behaviorfor KCPs and to predict water inrush time by introducing theinverse velocity theory In this approach a suite of governingequations was developed to couple all the physics involvedin this complex process including water flow rock erosionand change in rock microstructure These equations werethen implemented into a finite element software COMSOLMultiphysics to simulate the fully coupled process Basedon this numerical model a series of sensitivity studies wereconducted and some important findings have been drawn
(i) Water flow rate increases with increasing aquiferpressure initial particle concentration and fractureopening This results in an increase in the permeabil-ity and finally an acceleration of the migration of theparticles and interconnection of the seepage channelsThis finding suggests the grouting of the KCPs couldbe an effective measure to mitigate water inrush risk
(ii) The inverse velocity theory was successfully appliedto analyze the occurrences of water inrush underdifferent conditions The results show that the timeof inrush has a power relationship to the rock het-erogeneity water pressure and initial particle concen-tration and follows an exponential relationship to theinitial fracture apertures
The framework developed from this work not only helpsenhance coal mining operations safety by better under-standing and predicting water inrush risks so that propermitigation measures can be put in place timely It canalso be extended to other fields such as tunneling backfillpaste piping tailing dam erosion and other engineeringapplications which are likely to encounter time-dependenterosion or deformation or water inrush issues
Please be noted that there are a number of other stochasticmethods available in the literature that can be used to illus-trate rock heterogeneity such as the Monte-Carlo methodor First-Order approach The differences of these methodson the results of water inrush prediction may be worthcomparing in the near future
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This project is supported by the National Natural ScienceFoundation of China (nos 51304072 51774110) the Programfor Innovative Research Team in University of Ministryof Education of China (IRT 16R22) and the PostdoctoralScience Foundation of China (2017M612398)
References
[1] DMa XMiao H Bai et al ldquoEffect of mining on shear sidewallgroundwater inrush hazard caused by seepage instability of the
penetrated karst collapse pillarrdquo Natural Hazards vol 82 no 1pp 73ndash93 2016
[2] H Keqiang Y Guangming and L Yaoru ldquoPalaeo-karst collapsepillars in northern China and their damage to the geologicalenvironmentsrdquo Environmental Geology vol 58 no 5 pp 1029ndash1040 2009
[3] B Yao J Wei D Wang D Ma and Z Chen ldquoNumericalstudy on seepage property of karst collapse columns underparticle migrationrdquo CMES Computer Modeling in Engineeringamp Sciences vol 91 no 2 pp 81ndash100 2013
[4] J Tang H Bai B Yao and Y Wu ldquoTheoretical analysis onwater-inrush mechanism of concealed collapse pillars in floorrdquoMining Science and Technology vol 21 no 1 pp 57ndash60 2011
[5] Y Chen M Yi C Chen and C Yu ldquoBernstein polynomialsmethod for fractional convection-diffusion equation with vari-able coefficientsrdquoComputerModeling in Engineering amp Sciencesvol 83 no 6 pp 639ndash653 2012
[6] J Zhang and B Shen ldquoCoal mining under aquifers in China Acase studyrdquo International Journal of Rock Mechanics and MiningSciences vol 41 no 4 pp 629ndash639 2004
[7] D Ma H Bai X Miao H Pu B Jiang and Z ChenldquoCompaction and seepage properties of crushed limestoneparticle mixture an experimental investigation for Ordoviciankarst collapse pillar groundwater inrushrdquo Environmental EarthSciences vol 75 no 1 article 11 p 14 2016
[8] S Yin J Zhang and D Liu ldquoA study of mine water inrushesby measurements of in situ stress and rock failuresrdquo NaturalHazards vol 79 no 3 pp 1961ndash1979 2015
[9] H Bai D Ma and Z Chen ldquoMechanical behavior of ground-water seepage in karst collapse pillarsrdquo Engineering Geology vol164 pp 101ndash106 2013
[10] D Ma and H Bai ldquoGroundwater inflow prediction model ofkarst collapse pillar a case study for mining-induced ground-water inrush riskrdquoNatural Hazards vol 76 no 2 pp 1319ndash13342015
[11] D Ma H Bai and Y Wang ldquoMechanical behavior of a coalseam penetrated by a karst collapse pillar mining-inducedgroundwater inrush riskrdquo Natural Hazards vol 75 no 3 pp2137ndash2151 2015
[12] B Yao Research on variable mass fluid-solid coupling dynamictheory of broken rockmass and application China Univeristy ofMining and Technology Xuzhou China 2012
[13] D Ma X Miao H Bai et al ldquoImpact of particle transfer onflow properties of crushed mudstonesrdquo Environmental EarthSciences vol 75 no 7 article 593 2016
[14] DMa H Bai Z Chen andH Pu ldquoEffect of particlemixture onseepage properties of crushed mudstonesrdquo Transport in PorousMedia vol 108 no 2 pp 257ndash277 2015
[15] B Zhang H Bai and K Zhang ldquoSeepage characteristics ofcollapse columnfillingsrdquo International Journal ofMining Scienceand Technology 2015
[16] P Ortoleva J Chadam E Merino and A Sen ldquoGeochemicalself-organization II the reactive-infiltration instabilityrdquo Ameri-can Journal of Science vol 287 no 10 pp 1008ndash1040 1987
[17] I Vardoulakis M Stavropoulou and P Papanastasiou ldquoHydro-mechanical aspects of the sand production problemrdquo Transportin Porous Media vol 22 no 2 pp 225ndash244 1996
[18] R L Detwiler and H Rajaram ldquoPredicting dissolution patternsin variable aperture fractures Evaluation of an enhanced depth-averaged computational modelrdquoWater Resources Research vol43 no 4 Article IDW04403 2007
18 Geofluids
[19] M A Habib H M Badr R Ben-Mansour and M E KabirldquoErosion rate correlations of a pipe protruded in an abrupt pipecontractionrdquo International Journal of Impact Engineering vol34 no 8 pp 1350ndash1369 2007
[20] H T Xiao and H Y Xu ldquoIn situ permeability measurementsto establish the influence of slice mining on floor rocksrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 37 no 5 pp 855ndash860 2000
[21] H Guo D P Adhikary and M S Craig ldquoSimulation of minewater inflow and gas emission during longwall miningrdquo RockMechanics and Rock Engineering vol 42 no 1 pp 25ndash51 2009
[22] R Zhang Z JiangH ZhouC Yang and S Xiao ldquoGroundwateroutbursts from faults above a confined aquifer in the coalminingrdquo Natural Hazards vol 71 no 3 pp 1861ndash1872 2014
[23] B Yao F Du E Li and X Wang ldquoMechanical model of karstcollapse columns water inrush and its applicationrdquo ElectronicJournal of Geotechnical Engineering vol 19 pp 1665ndash1675 2014
[24] J Warren and P Root ldquoThe behavior of naturally fracturedreservoirsrdquo SPE Journal vol 3 no 3 pp 245ndash255 2013
[25] H KazemiM S Seth andGWThomas ldquoThe interpretation ofinterference tests in naturally fractured reservoirs with uniformfracture distributionrdquo SPE Journal vol 9 no 4 pp 463ndash4721969
[26] A de Swaan O ldquoAnalytical solutions for determining naturallyfractured reservoir properties by well testingrdquo SPE Journal vol16 no 3 pp 117ndash122 1976
[27] N D Rose and O Hungr ldquoForecasting potential rock slopefailure in open pit mines using the inverse-velocity methodrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 2 pp 308ndash320 2007
[28] J R Fanchi Petroleum Engineering Handbook Volume 1 Gen-eral Engineering Society of Petroleum Engineers 2006
[29] R Sakthivadivel and S Irmay A Review of Filtration TheoriesHydraulic Engineering Laboratory College of EngineeringUniversity of California Berkeley Calif USA 1996
[30] C Wang P Zhai Z Chen J Liu L Wang and J XieldquoExperimental study of coal matrix-cleat interaction underconstant volume boundary conditionrdquo International Journal ofCoal Geology vol 181 pp 124ndash132 2017
[31] S Irmay ldquoOn the theoretical derivation of Darcy and Forch-heimer formulasrdquo Eos Transactions American GeophysicalUnion vol 39 no 4 pp 702ndash707 1958
[32] CH Lee and IW Farmer ldquoA simplemethod of estimating rockmass porosity and permeabilityrdquo International Journal ofMiningand Geological Engineering vol 8 no 1 pp 57ndash65 1990
[33] C Nalluri A K El-Zaemey and H L Chan ldquoSedimenttransport over fixed deposited beds in sewers - An appraisal ofexisting modelsrdquoWater Science and Technology vol 36 no 8-9pp 123ndash128 1997
[34] P Novak and C Nalluri ldquoSediment transport in smooth fixedbed channelsrdquo Journal of the Hydraulics Division vol 101 no 9pp 1139ndash1154 1975
[35] T Fukuzono ldquoA newmethod for predicting the failure time of asloperdquo in Proceedings of the In 4th International Conference andField Workshop on Landslides Tokyo Japan 1985
[36] C R J Kilburn andDN Petley ldquoForecasting giant catastrophicslope collapse lessons from Vajont Northern Italyrdquo Geomor-phology vol 54 no 1-2 pp 21ndash32 2003
[37] B Voight ldquoA method for prediction of volcanic eruptionsrdquoNature vol 332 no 6160 pp 125ndash130 1988
[38] B Yao X Mao J Wei and D Wang ldquoStudy on coupled fluid-solid model for collapse columns considering the effect ofparticle transportrdquo Zhongguo Kuangye Daxue XuebaoJournalof China University of Mining and Technology vol 43 no 1 pp30ndash35 2014
[39] H Bai Seepage Characteristics of Top Stratum of OrdovicianSystem and Its Application Study as Key Aquifuge ChinaUniversity of Mining amp Technology Xuzhou China 2008
[40] C A Tang L G Tham P K K Lee T H Yang and L CLi ldquoCoupled analysis of flow stress and damage (FSD) in rockfailurerdquo International Journal of Rock Mechanics and MiningSciences vol 39 no 4 pp 477ndash489 2002
[41] W C Zhu and C A Tang ldquoMicromechanical model forsimulating the fracture process of rockrdquo Rock Mechanics andRock Engineering vol 37 no 1 pp 25ndash56 2004
[42] T H Yang L G Tham C A Tang Z Z Liang and YTsui ldquoInfluence of heterogeneity of mechanical properties onhydraulic fracturing in permeable rocksrdquo Rock Mechanics andRock Engineering vol 37 no 4 pp 251ndash275 2004
Hindawiwwwhindawicom Volume 2018
Journal of
ChemistryArchaeaHindawiwwwhindawicom Volume 2018
Marine BiologyJournal of
Hindawiwwwhindawicom Volume 2018
BiodiversityInternational Journal of
Hindawiwwwhindawicom Volume 2018
EcologyInternational Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Applied ampEnvironmentalSoil Science
Volume 2018
Forestry ResearchInternational Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
International Journal of
Geophysics
Environmental and Public Health
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
International Journal of
Microbiology
Hindawiwwwhindawicom Volume 2018
Public Health Advances in
AgricultureAdvances in
Hindawiwwwhindawicom Volume 2018
Agronomy
Hindawiwwwhindawicom Volume 2018
International Journal of
Hindawiwwwhindawicom Volume 2018
MeteorologyAdvances in
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018Hindawiwwwhindawicom Volume 2018
ChemistryAdvances in
ScienticaHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Geological ResearchJournal of
Analytical ChemistryInternational Journal of
Hindawiwwwhindawicom Volume 2018
Submit your manuscripts atwwwhindawicom
Geofluids 15
5 10 15 200Time (times103 s)
m = 4
m = 6 m = 10
m = 8
0
20
40
60
80
100
120Fl
ow ra
te (m
3h
)
(a)
205
21
215
22
225
23
Wat
er in
rush
tim
e (times10
3s)
4 6 8 102Weibull coefficient m
y = 25699xminus0089
R2 = 09825
(b)
Figure 24 Impact of heterogeneity on water flow rate (a) and inrush time (b)
0
20
40
60
80
100
120
140
160
180
200
Flow
rate
(m3h
)
5 10 15 200Time (times103 s)
p = 1MPap = 2MPa
p = 3MPap = 4MPa
(a)
y = 41733xminus1001
R2 = 09992
1 2 3 4 50Water pressure (MPa)
0
5
10
15
20
25
30
35
40
45
Wat
er in
rush
tim
e (times10
3s)
(b)
Figure 25 Impact of aquifer water pressure on water flow rate (a) and inrush time (b)
which has been widely approved effective in many fields suchas slope stability predictionThe relevant results and analysesare shown in Figure 24ndashFigure 27
As shown in Figure 24 water flow rate exhibits a non-linear increase and as the value of m increases the seepagerate accelerates gradually For example at 119905 = 15 times 104 s theseepage rate was approximately 15m3h for 119898 = 4 while itjumped to 25m3h for 119898 = 10 Results from Figure 24(b)show that water inrush occurs sooner for a greater 119898 valueIn other words the inrush occurs earlier as the heterogeneityincreases The water inrush time follows the power functionThis is due to the fact that the water is more prone to flowingthrough the existing fractures (which indicates a higher
permeability) in the heterogeneous structure Neverthelessdue to the heterogeneous distribution of the aperture thefractures cannot be easily interconnected which hampers theformation of the seepage channels In regard to the homo-geneous rock strata since the flow of water was dominantlycontrolled by the pressure gradient the fractures generatedduring the process of erosion could be easily interconnectedand as a result the water inrush occurredsooner
Figure 25 illustrates the impact of the initial KCPrsquos waterpressure on the flow rates and water inrush time It can beseen that as the pressure increases the changes in the flowrates accelerate For example for119901 = 2MPa the flow rate wasonly approximately 5m3h and it increased to 30m3h when
16 Geofluids
0
20
40
60
80
100
120
140
160
180
200Fl
ow ra
te (m
3h
)
5 10 15 20 250Time (times103 s)
c = 0005
c = 001
c = 002
c = 005
(a)
0
5
10
15
20
25
30
35
Wat
er in
rush
tim
e (times10
3s)
001 002 003 004 0050Initial particle concentration
y = 13554xminus0591
R2 = 09975
(b)
Figure 26 Impact of initial particle concentration on water flow rate (a) and inrush time (b)
0
20
40
60
80
100
120
140
160
180
200
Flow
rate
(m3h
)
5 10 15 200Time (times103 s)
075E minus 4m100E minus 4m
125E minus 4m150E minus 4m
(a)
y = 31027eminus286x
R2 = 09503
09 11 13 1507Fracture aperture (times10minus4 m)
0
5
10
15
20
25
30
35
40
Wat
er in
rush
tim
e (times10
3s)
(b)
Figure 27 Impact of absolute aperture on water flow rate (a) and inrush time (b)
119901 = 3MPa In addition with increasing the aquifer waterpressure the water inrush time was also brought forward asshown in Figure 25(a) The outburst time was approximately119905 = 40 times 104 s for p = 1MPa while only 10 times 104 s for119901 = 4MPa The relationship between the time of the inrushoccurrences and the aquifer water pressure follows the powerfunction as illustrated in Figure 25
For varying initial particle concentrations the evolutionof both the water flow rate change and the water inrushtime shows a similar trend to that of different aquifer waterpressures The flow rate accelerates with increasing initialparticle concentration and consequently the water inrushoccurs earlier as shown in Figure 26The outburst times alsoshow a power function to the initial particle concentration
The initial average fracture aperture also shows significantimpact on water flow behavior For instance results fromFigure 27 clearly illustrate that the flow rate increases withincreasing initial average fracture aperture Please note thatthe inrush time follows an exponential function to the initialaverage fracture aperture
These numerical results can be explained by the factthat the initial seepage velocity is expected to be higher forthe modelling cases with the higher initial aquifer pressureinitial fracture aperture andor initial particle concentrationThe higher flow velocity would intensify the erosion of thefractures enhance the permeability and thereby acceleratethe migration of the particles and interconnection of seepagechannels which causes water inrush
Geofluids 17
5 Conclusions
In this study a systematic approach was established to inves-tigate the impact of controlling factors onwater flow behaviorfor KCPs and to predict water inrush time by introducing theinverse velocity theory In this approach a suite of governingequations was developed to couple all the physics involvedin this complex process including water flow rock erosionand change in rock microstructure These equations werethen implemented into a finite element software COMSOLMultiphysics to simulate the fully coupled process Basedon this numerical model a series of sensitivity studies wereconducted and some important findings have been drawn
(i) Water flow rate increases with increasing aquiferpressure initial particle concentration and fractureopening This results in an increase in the permeabil-ity and finally an acceleration of the migration of theparticles and interconnection of the seepage channelsThis finding suggests the grouting of the KCPs couldbe an effective measure to mitigate water inrush risk
(ii) The inverse velocity theory was successfully appliedto analyze the occurrences of water inrush underdifferent conditions The results show that the timeof inrush has a power relationship to the rock het-erogeneity water pressure and initial particle concen-tration and follows an exponential relationship to theinitial fracture apertures
The framework developed from this work not only helpsenhance coal mining operations safety by better under-standing and predicting water inrush risks so that propermitigation measures can be put in place timely It canalso be extended to other fields such as tunneling backfillpaste piping tailing dam erosion and other engineeringapplications which are likely to encounter time-dependenterosion or deformation or water inrush issues
Please be noted that there are a number of other stochasticmethods available in the literature that can be used to illus-trate rock heterogeneity such as the Monte-Carlo methodor First-Order approach The differences of these methodson the results of water inrush prediction may be worthcomparing in the near future
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This project is supported by the National Natural ScienceFoundation of China (nos 51304072 51774110) the Programfor Innovative Research Team in University of Ministryof Education of China (IRT 16R22) and the PostdoctoralScience Foundation of China (2017M612398)
References
[1] DMa XMiao H Bai et al ldquoEffect of mining on shear sidewallgroundwater inrush hazard caused by seepage instability of the
penetrated karst collapse pillarrdquo Natural Hazards vol 82 no 1pp 73ndash93 2016
[2] H Keqiang Y Guangming and L Yaoru ldquoPalaeo-karst collapsepillars in northern China and their damage to the geologicalenvironmentsrdquo Environmental Geology vol 58 no 5 pp 1029ndash1040 2009
[3] B Yao J Wei D Wang D Ma and Z Chen ldquoNumericalstudy on seepage property of karst collapse columns underparticle migrationrdquo CMES Computer Modeling in Engineeringamp Sciences vol 91 no 2 pp 81ndash100 2013
[4] J Tang H Bai B Yao and Y Wu ldquoTheoretical analysis onwater-inrush mechanism of concealed collapse pillars in floorrdquoMining Science and Technology vol 21 no 1 pp 57ndash60 2011
[5] Y Chen M Yi C Chen and C Yu ldquoBernstein polynomialsmethod for fractional convection-diffusion equation with vari-able coefficientsrdquoComputerModeling in Engineering amp Sciencesvol 83 no 6 pp 639ndash653 2012
[6] J Zhang and B Shen ldquoCoal mining under aquifers in China Acase studyrdquo International Journal of Rock Mechanics and MiningSciences vol 41 no 4 pp 629ndash639 2004
[7] D Ma H Bai X Miao H Pu B Jiang and Z ChenldquoCompaction and seepage properties of crushed limestoneparticle mixture an experimental investigation for Ordoviciankarst collapse pillar groundwater inrushrdquo Environmental EarthSciences vol 75 no 1 article 11 p 14 2016
[8] S Yin J Zhang and D Liu ldquoA study of mine water inrushesby measurements of in situ stress and rock failuresrdquo NaturalHazards vol 79 no 3 pp 1961ndash1979 2015
[9] H Bai D Ma and Z Chen ldquoMechanical behavior of ground-water seepage in karst collapse pillarsrdquo Engineering Geology vol164 pp 101ndash106 2013
[10] D Ma and H Bai ldquoGroundwater inflow prediction model ofkarst collapse pillar a case study for mining-induced ground-water inrush riskrdquoNatural Hazards vol 76 no 2 pp 1319ndash13342015
[11] D Ma H Bai and Y Wang ldquoMechanical behavior of a coalseam penetrated by a karst collapse pillar mining-inducedgroundwater inrush riskrdquo Natural Hazards vol 75 no 3 pp2137ndash2151 2015
[12] B Yao Research on variable mass fluid-solid coupling dynamictheory of broken rockmass and application China Univeristy ofMining and Technology Xuzhou China 2012
[13] D Ma X Miao H Bai et al ldquoImpact of particle transfer onflow properties of crushed mudstonesrdquo Environmental EarthSciences vol 75 no 7 article 593 2016
[14] DMa H Bai Z Chen andH Pu ldquoEffect of particlemixture onseepage properties of crushed mudstonesrdquo Transport in PorousMedia vol 108 no 2 pp 257ndash277 2015
[15] B Zhang H Bai and K Zhang ldquoSeepage characteristics ofcollapse columnfillingsrdquo International Journal ofMining Scienceand Technology 2015
[16] P Ortoleva J Chadam E Merino and A Sen ldquoGeochemicalself-organization II the reactive-infiltration instabilityrdquo Ameri-can Journal of Science vol 287 no 10 pp 1008ndash1040 1987
[17] I Vardoulakis M Stavropoulou and P Papanastasiou ldquoHydro-mechanical aspects of the sand production problemrdquo Transportin Porous Media vol 22 no 2 pp 225ndash244 1996
[18] R L Detwiler and H Rajaram ldquoPredicting dissolution patternsin variable aperture fractures Evaluation of an enhanced depth-averaged computational modelrdquoWater Resources Research vol43 no 4 Article IDW04403 2007
18 Geofluids
[19] M A Habib H M Badr R Ben-Mansour and M E KabirldquoErosion rate correlations of a pipe protruded in an abrupt pipecontractionrdquo International Journal of Impact Engineering vol34 no 8 pp 1350ndash1369 2007
[20] H T Xiao and H Y Xu ldquoIn situ permeability measurementsto establish the influence of slice mining on floor rocksrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 37 no 5 pp 855ndash860 2000
[21] H Guo D P Adhikary and M S Craig ldquoSimulation of minewater inflow and gas emission during longwall miningrdquo RockMechanics and Rock Engineering vol 42 no 1 pp 25ndash51 2009
[22] R Zhang Z JiangH ZhouC Yang and S Xiao ldquoGroundwateroutbursts from faults above a confined aquifer in the coalminingrdquo Natural Hazards vol 71 no 3 pp 1861ndash1872 2014
[23] B Yao F Du E Li and X Wang ldquoMechanical model of karstcollapse columns water inrush and its applicationrdquo ElectronicJournal of Geotechnical Engineering vol 19 pp 1665ndash1675 2014
[24] J Warren and P Root ldquoThe behavior of naturally fracturedreservoirsrdquo SPE Journal vol 3 no 3 pp 245ndash255 2013
[25] H KazemiM S Seth andGWThomas ldquoThe interpretation ofinterference tests in naturally fractured reservoirs with uniformfracture distributionrdquo SPE Journal vol 9 no 4 pp 463ndash4721969
[26] A de Swaan O ldquoAnalytical solutions for determining naturallyfractured reservoir properties by well testingrdquo SPE Journal vol16 no 3 pp 117ndash122 1976
[27] N D Rose and O Hungr ldquoForecasting potential rock slopefailure in open pit mines using the inverse-velocity methodrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 2 pp 308ndash320 2007
[28] J R Fanchi Petroleum Engineering Handbook Volume 1 Gen-eral Engineering Society of Petroleum Engineers 2006
[29] R Sakthivadivel and S Irmay A Review of Filtration TheoriesHydraulic Engineering Laboratory College of EngineeringUniversity of California Berkeley Calif USA 1996
[30] C Wang P Zhai Z Chen J Liu L Wang and J XieldquoExperimental study of coal matrix-cleat interaction underconstant volume boundary conditionrdquo International Journal ofCoal Geology vol 181 pp 124ndash132 2017
[31] S Irmay ldquoOn the theoretical derivation of Darcy and Forch-heimer formulasrdquo Eos Transactions American GeophysicalUnion vol 39 no 4 pp 702ndash707 1958
[32] CH Lee and IW Farmer ldquoA simplemethod of estimating rockmass porosity and permeabilityrdquo International Journal ofMiningand Geological Engineering vol 8 no 1 pp 57ndash65 1990
[33] C Nalluri A K El-Zaemey and H L Chan ldquoSedimenttransport over fixed deposited beds in sewers - An appraisal ofexisting modelsrdquoWater Science and Technology vol 36 no 8-9pp 123ndash128 1997
[34] P Novak and C Nalluri ldquoSediment transport in smooth fixedbed channelsrdquo Journal of the Hydraulics Division vol 101 no 9pp 1139ndash1154 1975
[35] T Fukuzono ldquoA newmethod for predicting the failure time of asloperdquo in Proceedings of the In 4th International Conference andField Workshop on Landslides Tokyo Japan 1985
[36] C R J Kilburn andDN Petley ldquoForecasting giant catastrophicslope collapse lessons from Vajont Northern Italyrdquo Geomor-phology vol 54 no 1-2 pp 21ndash32 2003
[37] B Voight ldquoA method for prediction of volcanic eruptionsrdquoNature vol 332 no 6160 pp 125ndash130 1988
[38] B Yao X Mao J Wei and D Wang ldquoStudy on coupled fluid-solid model for collapse columns considering the effect ofparticle transportrdquo Zhongguo Kuangye Daxue XuebaoJournalof China University of Mining and Technology vol 43 no 1 pp30ndash35 2014
[39] H Bai Seepage Characteristics of Top Stratum of OrdovicianSystem and Its Application Study as Key Aquifuge ChinaUniversity of Mining amp Technology Xuzhou China 2008
[40] C A Tang L G Tham P K K Lee T H Yang and L CLi ldquoCoupled analysis of flow stress and damage (FSD) in rockfailurerdquo International Journal of Rock Mechanics and MiningSciences vol 39 no 4 pp 477ndash489 2002
[41] W C Zhu and C A Tang ldquoMicromechanical model forsimulating the fracture process of rockrdquo Rock Mechanics andRock Engineering vol 37 no 1 pp 25ndash56 2004
[42] T H Yang L G Tham C A Tang Z Z Liang and YTsui ldquoInfluence of heterogeneity of mechanical properties onhydraulic fracturing in permeable rocksrdquo Rock Mechanics andRock Engineering vol 37 no 4 pp 251ndash275 2004
Hindawiwwwhindawicom Volume 2018
Journal of
ChemistryArchaeaHindawiwwwhindawicom Volume 2018
Marine BiologyJournal of
Hindawiwwwhindawicom Volume 2018
BiodiversityInternational Journal of
Hindawiwwwhindawicom Volume 2018
EcologyInternational Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Applied ampEnvironmentalSoil Science
Volume 2018
Forestry ResearchInternational Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
International Journal of
Geophysics
Environmental and Public Health
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
International Journal of
Microbiology
Hindawiwwwhindawicom Volume 2018
Public Health Advances in
AgricultureAdvances in
Hindawiwwwhindawicom Volume 2018
Agronomy
Hindawiwwwhindawicom Volume 2018
International Journal of
Hindawiwwwhindawicom Volume 2018
MeteorologyAdvances in
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018Hindawiwwwhindawicom Volume 2018
ChemistryAdvances in
ScienticaHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Geological ResearchJournal of
Analytical ChemistryInternational Journal of
Hindawiwwwhindawicom Volume 2018
Submit your manuscripts atwwwhindawicom
16 Geofluids
0
20
40
60
80
100
120
140
160
180
200Fl
ow ra
te (m
3h
)
5 10 15 20 250Time (times103 s)
c = 0005
c = 001
c = 002
c = 005
(a)
0
5
10
15
20
25
30
35
Wat
er in
rush
tim
e (times10
3s)
001 002 003 004 0050Initial particle concentration
y = 13554xminus0591
R2 = 09975
(b)
Figure 26 Impact of initial particle concentration on water flow rate (a) and inrush time (b)
0
20
40
60
80
100
120
140
160
180
200
Flow
rate
(m3h
)
5 10 15 200Time (times103 s)
075E minus 4m100E minus 4m
125E minus 4m150E minus 4m
(a)
y = 31027eminus286x
R2 = 09503
09 11 13 1507Fracture aperture (times10minus4 m)
0
5
10
15
20
25
30
35
40
Wat
er in
rush
tim
e (times10
3s)
(b)
Figure 27 Impact of absolute aperture on water flow rate (a) and inrush time (b)
119901 = 3MPa In addition with increasing the aquifer waterpressure the water inrush time was also brought forward asshown in Figure 25(a) The outburst time was approximately119905 = 40 times 104 s for p = 1MPa while only 10 times 104 s for119901 = 4MPa The relationship between the time of the inrushoccurrences and the aquifer water pressure follows the powerfunction as illustrated in Figure 25
For varying initial particle concentrations the evolutionof both the water flow rate change and the water inrushtime shows a similar trend to that of different aquifer waterpressures The flow rate accelerates with increasing initialparticle concentration and consequently the water inrushoccurs earlier as shown in Figure 26The outburst times alsoshow a power function to the initial particle concentration
The initial average fracture aperture also shows significantimpact on water flow behavior For instance results fromFigure 27 clearly illustrate that the flow rate increases withincreasing initial average fracture aperture Please note thatthe inrush time follows an exponential function to the initialaverage fracture aperture
These numerical results can be explained by the factthat the initial seepage velocity is expected to be higher forthe modelling cases with the higher initial aquifer pressureinitial fracture aperture andor initial particle concentrationThe higher flow velocity would intensify the erosion of thefractures enhance the permeability and thereby acceleratethe migration of the particles and interconnection of seepagechannels which causes water inrush
Geofluids 17
5 Conclusions
In this study a systematic approach was established to inves-tigate the impact of controlling factors onwater flow behaviorfor KCPs and to predict water inrush time by introducing theinverse velocity theory In this approach a suite of governingequations was developed to couple all the physics involvedin this complex process including water flow rock erosionand change in rock microstructure These equations werethen implemented into a finite element software COMSOLMultiphysics to simulate the fully coupled process Basedon this numerical model a series of sensitivity studies wereconducted and some important findings have been drawn
(i) Water flow rate increases with increasing aquiferpressure initial particle concentration and fractureopening This results in an increase in the permeabil-ity and finally an acceleration of the migration of theparticles and interconnection of the seepage channelsThis finding suggests the grouting of the KCPs couldbe an effective measure to mitigate water inrush risk
(ii) The inverse velocity theory was successfully appliedto analyze the occurrences of water inrush underdifferent conditions The results show that the timeof inrush has a power relationship to the rock het-erogeneity water pressure and initial particle concen-tration and follows an exponential relationship to theinitial fracture apertures
The framework developed from this work not only helpsenhance coal mining operations safety by better under-standing and predicting water inrush risks so that propermitigation measures can be put in place timely It canalso be extended to other fields such as tunneling backfillpaste piping tailing dam erosion and other engineeringapplications which are likely to encounter time-dependenterosion or deformation or water inrush issues
Please be noted that there are a number of other stochasticmethods available in the literature that can be used to illus-trate rock heterogeneity such as the Monte-Carlo methodor First-Order approach The differences of these methodson the results of water inrush prediction may be worthcomparing in the near future
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This project is supported by the National Natural ScienceFoundation of China (nos 51304072 51774110) the Programfor Innovative Research Team in University of Ministryof Education of China (IRT 16R22) and the PostdoctoralScience Foundation of China (2017M612398)
References
[1] DMa XMiao H Bai et al ldquoEffect of mining on shear sidewallgroundwater inrush hazard caused by seepage instability of the
penetrated karst collapse pillarrdquo Natural Hazards vol 82 no 1pp 73ndash93 2016
[2] H Keqiang Y Guangming and L Yaoru ldquoPalaeo-karst collapsepillars in northern China and their damage to the geologicalenvironmentsrdquo Environmental Geology vol 58 no 5 pp 1029ndash1040 2009
[3] B Yao J Wei D Wang D Ma and Z Chen ldquoNumericalstudy on seepage property of karst collapse columns underparticle migrationrdquo CMES Computer Modeling in Engineeringamp Sciences vol 91 no 2 pp 81ndash100 2013
[4] J Tang H Bai B Yao and Y Wu ldquoTheoretical analysis onwater-inrush mechanism of concealed collapse pillars in floorrdquoMining Science and Technology vol 21 no 1 pp 57ndash60 2011
[5] Y Chen M Yi C Chen and C Yu ldquoBernstein polynomialsmethod for fractional convection-diffusion equation with vari-able coefficientsrdquoComputerModeling in Engineering amp Sciencesvol 83 no 6 pp 639ndash653 2012
[6] J Zhang and B Shen ldquoCoal mining under aquifers in China Acase studyrdquo International Journal of Rock Mechanics and MiningSciences vol 41 no 4 pp 629ndash639 2004
[7] D Ma H Bai X Miao H Pu B Jiang and Z ChenldquoCompaction and seepage properties of crushed limestoneparticle mixture an experimental investigation for Ordoviciankarst collapse pillar groundwater inrushrdquo Environmental EarthSciences vol 75 no 1 article 11 p 14 2016
[8] S Yin J Zhang and D Liu ldquoA study of mine water inrushesby measurements of in situ stress and rock failuresrdquo NaturalHazards vol 79 no 3 pp 1961ndash1979 2015
[9] H Bai D Ma and Z Chen ldquoMechanical behavior of ground-water seepage in karst collapse pillarsrdquo Engineering Geology vol164 pp 101ndash106 2013
[10] D Ma and H Bai ldquoGroundwater inflow prediction model ofkarst collapse pillar a case study for mining-induced ground-water inrush riskrdquoNatural Hazards vol 76 no 2 pp 1319ndash13342015
[11] D Ma H Bai and Y Wang ldquoMechanical behavior of a coalseam penetrated by a karst collapse pillar mining-inducedgroundwater inrush riskrdquo Natural Hazards vol 75 no 3 pp2137ndash2151 2015
[12] B Yao Research on variable mass fluid-solid coupling dynamictheory of broken rockmass and application China Univeristy ofMining and Technology Xuzhou China 2012
[13] D Ma X Miao H Bai et al ldquoImpact of particle transfer onflow properties of crushed mudstonesrdquo Environmental EarthSciences vol 75 no 7 article 593 2016
[14] DMa H Bai Z Chen andH Pu ldquoEffect of particlemixture onseepage properties of crushed mudstonesrdquo Transport in PorousMedia vol 108 no 2 pp 257ndash277 2015
[15] B Zhang H Bai and K Zhang ldquoSeepage characteristics ofcollapse columnfillingsrdquo International Journal ofMining Scienceand Technology 2015
[16] P Ortoleva J Chadam E Merino and A Sen ldquoGeochemicalself-organization II the reactive-infiltration instabilityrdquo Ameri-can Journal of Science vol 287 no 10 pp 1008ndash1040 1987
[17] I Vardoulakis M Stavropoulou and P Papanastasiou ldquoHydro-mechanical aspects of the sand production problemrdquo Transportin Porous Media vol 22 no 2 pp 225ndash244 1996
[18] R L Detwiler and H Rajaram ldquoPredicting dissolution patternsin variable aperture fractures Evaluation of an enhanced depth-averaged computational modelrdquoWater Resources Research vol43 no 4 Article IDW04403 2007
18 Geofluids
[19] M A Habib H M Badr R Ben-Mansour and M E KabirldquoErosion rate correlations of a pipe protruded in an abrupt pipecontractionrdquo International Journal of Impact Engineering vol34 no 8 pp 1350ndash1369 2007
[20] H T Xiao and H Y Xu ldquoIn situ permeability measurementsto establish the influence of slice mining on floor rocksrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 37 no 5 pp 855ndash860 2000
[21] H Guo D P Adhikary and M S Craig ldquoSimulation of minewater inflow and gas emission during longwall miningrdquo RockMechanics and Rock Engineering vol 42 no 1 pp 25ndash51 2009
[22] R Zhang Z JiangH ZhouC Yang and S Xiao ldquoGroundwateroutbursts from faults above a confined aquifer in the coalminingrdquo Natural Hazards vol 71 no 3 pp 1861ndash1872 2014
[23] B Yao F Du E Li and X Wang ldquoMechanical model of karstcollapse columns water inrush and its applicationrdquo ElectronicJournal of Geotechnical Engineering vol 19 pp 1665ndash1675 2014
[24] J Warren and P Root ldquoThe behavior of naturally fracturedreservoirsrdquo SPE Journal vol 3 no 3 pp 245ndash255 2013
[25] H KazemiM S Seth andGWThomas ldquoThe interpretation ofinterference tests in naturally fractured reservoirs with uniformfracture distributionrdquo SPE Journal vol 9 no 4 pp 463ndash4721969
[26] A de Swaan O ldquoAnalytical solutions for determining naturallyfractured reservoir properties by well testingrdquo SPE Journal vol16 no 3 pp 117ndash122 1976
[27] N D Rose and O Hungr ldquoForecasting potential rock slopefailure in open pit mines using the inverse-velocity methodrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 2 pp 308ndash320 2007
[28] J R Fanchi Petroleum Engineering Handbook Volume 1 Gen-eral Engineering Society of Petroleum Engineers 2006
[29] R Sakthivadivel and S Irmay A Review of Filtration TheoriesHydraulic Engineering Laboratory College of EngineeringUniversity of California Berkeley Calif USA 1996
[30] C Wang P Zhai Z Chen J Liu L Wang and J XieldquoExperimental study of coal matrix-cleat interaction underconstant volume boundary conditionrdquo International Journal ofCoal Geology vol 181 pp 124ndash132 2017
[31] S Irmay ldquoOn the theoretical derivation of Darcy and Forch-heimer formulasrdquo Eos Transactions American GeophysicalUnion vol 39 no 4 pp 702ndash707 1958
[32] CH Lee and IW Farmer ldquoA simplemethod of estimating rockmass porosity and permeabilityrdquo International Journal ofMiningand Geological Engineering vol 8 no 1 pp 57ndash65 1990
[33] C Nalluri A K El-Zaemey and H L Chan ldquoSedimenttransport over fixed deposited beds in sewers - An appraisal ofexisting modelsrdquoWater Science and Technology vol 36 no 8-9pp 123ndash128 1997
[34] P Novak and C Nalluri ldquoSediment transport in smooth fixedbed channelsrdquo Journal of the Hydraulics Division vol 101 no 9pp 1139ndash1154 1975
[35] T Fukuzono ldquoA newmethod for predicting the failure time of asloperdquo in Proceedings of the In 4th International Conference andField Workshop on Landslides Tokyo Japan 1985
[36] C R J Kilburn andDN Petley ldquoForecasting giant catastrophicslope collapse lessons from Vajont Northern Italyrdquo Geomor-phology vol 54 no 1-2 pp 21ndash32 2003
[37] B Voight ldquoA method for prediction of volcanic eruptionsrdquoNature vol 332 no 6160 pp 125ndash130 1988
[38] B Yao X Mao J Wei and D Wang ldquoStudy on coupled fluid-solid model for collapse columns considering the effect ofparticle transportrdquo Zhongguo Kuangye Daxue XuebaoJournalof China University of Mining and Technology vol 43 no 1 pp30ndash35 2014
[39] H Bai Seepage Characteristics of Top Stratum of OrdovicianSystem and Its Application Study as Key Aquifuge ChinaUniversity of Mining amp Technology Xuzhou China 2008
[40] C A Tang L G Tham P K K Lee T H Yang and L CLi ldquoCoupled analysis of flow stress and damage (FSD) in rockfailurerdquo International Journal of Rock Mechanics and MiningSciences vol 39 no 4 pp 477ndash489 2002
[41] W C Zhu and C A Tang ldquoMicromechanical model forsimulating the fracture process of rockrdquo Rock Mechanics andRock Engineering vol 37 no 1 pp 25ndash56 2004
[42] T H Yang L G Tham C A Tang Z Z Liang and YTsui ldquoInfluence of heterogeneity of mechanical properties onhydraulic fracturing in permeable rocksrdquo Rock Mechanics andRock Engineering vol 37 no 4 pp 251ndash275 2004
Hindawiwwwhindawicom Volume 2018
Journal of
ChemistryArchaeaHindawiwwwhindawicom Volume 2018
Marine BiologyJournal of
Hindawiwwwhindawicom Volume 2018
BiodiversityInternational Journal of
Hindawiwwwhindawicom Volume 2018
EcologyInternational Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Applied ampEnvironmentalSoil Science
Volume 2018
Forestry ResearchInternational Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
International Journal of
Geophysics
Environmental and Public Health
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
International Journal of
Microbiology
Hindawiwwwhindawicom Volume 2018
Public Health Advances in
AgricultureAdvances in
Hindawiwwwhindawicom Volume 2018
Agronomy
Hindawiwwwhindawicom Volume 2018
International Journal of
Hindawiwwwhindawicom Volume 2018
MeteorologyAdvances in
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018Hindawiwwwhindawicom Volume 2018
ChemistryAdvances in
ScienticaHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Geological ResearchJournal of
Analytical ChemistryInternational Journal of
Hindawiwwwhindawicom Volume 2018
Submit your manuscripts atwwwhindawicom
Geofluids 17
5 Conclusions
In this study a systematic approach was established to inves-tigate the impact of controlling factors onwater flow behaviorfor KCPs and to predict water inrush time by introducing theinverse velocity theory In this approach a suite of governingequations was developed to couple all the physics involvedin this complex process including water flow rock erosionand change in rock microstructure These equations werethen implemented into a finite element software COMSOLMultiphysics to simulate the fully coupled process Basedon this numerical model a series of sensitivity studies wereconducted and some important findings have been drawn
(i) Water flow rate increases with increasing aquiferpressure initial particle concentration and fractureopening This results in an increase in the permeabil-ity and finally an acceleration of the migration of theparticles and interconnection of the seepage channelsThis finding suggests the grouting of the KCPs couldbe an effective measure to mitigate water inrush risk
(ii) The inverse velocity theory was successfully appliedto analyze the occurrences of water inrush underdifferent conditions The results show that the timeof inrush has a power relationship to the rock het-erogeneity water pressure and initial particle concen-tration and follows an exponential relationship to theinitial fracture apertures
The framework developed from this work not only helpsenhance coal mining operations safety by better under-standing and predicting water inrush risks so that propermitigation measures can be put in place timely It canalso be extended to other fields such as tunneling backfillpaste piping tailing dam erosion and other engineeringapplications which are likely to encounter time-dependenterosion or deformation or water inrush issues
Please be noted that there are a number of other stochasticmethods available in the literature that can be used to illus-trate rock heterogeneity such as the Monte-Carlo methodor First-Order approach The differences of these methodson the results of water inrush prediction may be worthcomparing in the near future
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
This project is supported by the National Natural ScienceFoundation of China (nos 51304072 51774110) the Programfor Innovative Research Team in University of Ministryof Education of China (IRT 16R22) and the PostdoctoralScience Foundation of China (2017M612398)
References
[1] DMa XMiao H Bai et al ldquoEffect of mining on shear sidewallgroundwater inrush hazard caused by seepage instability of the
penetrated karst collapse pillarrdquo Natural Hazards vol 82 no 1pp 73ndash93 2016
[2] H Keqiang Y Guangming and L Yaoru ldquoPalaeo-karst collapsepillars in northern China and their damage to the geologicalenvironmentsrdquo Environmental Geology vol 58 no 5 pp 1029ndash1040 2009
[3] B Yao J Wei D Wang D Ma and Z Chen ldquoNumericalstudy on seepage property of karst collapse columns underparticle migrationrdquo CMES Computer Modeling in Engineeringamp Sciences vol 91 no 2 pp 81ndash100 2013
[4] J Tang H Bai B Yao and Y Wu ldquoTheoretical analysis onwater-inrush mechanism of concealed collapse pillars in floorrdquoMining Science and Technology vol 21 no 1 pp 57ndash60 2011
[5] Y Chen M Yi C Chen and C Yu ldquoBernstein polynomialsmethod for fractional convection-diffusion equation with vari-able coefficientsrdquoComputerModeling in Engineering amp Sciencesvol 83 no 6 pp 639ndash653 2012
[6] J Zhang and B Shen ldquoCoal mining under aquifers in China Acase studyrdquo International Journal of Rock Mechanics and MiningSciences vol 41 no 4 pp 629ndash639 2004
[7] D Ma H Bai X Miao H Pu B Jiang and Z ChenldquoCompaction and seepage properties of crushed limestoneparticle mixture an experimental investigation for Ordoviciankarst collapse pillar groundwater inrushrdquo Environmental EarthSciences vol 75 no 1 article 11 p 14 2016
[8] S Yin J Zhang and D Liu ldquoA study of mine water inrushesby measurements of in situ stress and rock failuresrdquo NaturalHazards vol 79 no 3 pp 1961ndash1979 2015
[9] H Bai D Ma and Z Chen ldquoMechanical behavior of ground-water seepage in karst collapse pillarsrdquo Engineering Geology vol164 pp 101ndash106 2013
[10] D Ma and H Bai ldquoGroundwater inflow prediction model ofkarst collapse pillar a case study for mining-induced ground-water inrush riskrdquoNatural Hazards vol 76 no 2 pp 1319ndash13342015
[11] D Ma H Bai and Y Wang ldquoMechanical behavior of a coalseam penetrated by a karst collapse pillar mining-inducedgroundwater inrush riskrdquo Natural Hazards vol 75 no 3 pp2137ndash2151 2015
[12] B Yao Research on variable mass fluid-solid coupling dynamictheory of broken rockmass and application China Univeristy ofMining and Technology Xuzhou China 2012
[13] D Ma X Miao H Bai et al ldquoImpact of particle transfer onflow properties of crushed mudstonesrdquo Environmental EarthSciences vol 75 no 7 article 593 2016
[14] DMa H Bai Z Chen andH Pu ldquoEffect of particlemixture onseepage properties of crushed mudstonesrdquo Transport in PorousMedia vol 108 no 2 pp 257ndash277 2015
[15] B Zhang H Bai and K Zhang ldquoSeepage characteristics ofcollapse columnfillingsrdquo International Journal ofMining Scienceand Technology 2015
[16] P Ortoleva J Chadam E Merino and A Sen ldquoGeochemicalself-organization II the reactive-infiltration instabilityrdquo Ameri-can Journal of Science vol 287 no 10 pp 1008ndash1040 1987
[17] I Vardoulakis M Stavropoulou and P Papanastasiou ldquoHydro-mechanical aspects of the sand production problemrdquo Transportin Porous Media vol 22 no 2 pp 225ndash244 1996
[18] R L Detwiler and H Rajaram ldquoPredicting dissolution patternsin variable aperture fractures Evaluation of an enhanced depth-averaged computational modelrdquoWater Resources Research vol43 no 4 Article IDW04403 2007
18 Geofluids
[19] M A Habib H M Badr R Ben-Mansour and M E KabirldquoErosion rate correlations of a pipe protruded in an abrupt pipecontractionrdquo International Journal of Impact Engineering vol34 no 8 pp 1350ndash1369 2007
[20] H T Xiao and H Y Xu ldquoIn situ permeability measurementsto establish the influence of slice mining on floor rocksrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 37 no 5 pp 855ndash860 2000
[21] H Guo D P Adhikary and M S Craig ldquoSimulation of minewater inflow and gas emission during longwall miningrdquo RockMechanics and Rock Engineering vol 42 no 1 pp 25ndash51 2009
[22] R Zhang Z JiangH ZhouC Yang and S Xiao ldquoGroundwateroutbursts from faults above a confined aquifer in the coalminingrdquo Natural Hazards vol 71 no 3 pp 1861ndash1872 2014
[23] B Yao F Du E Li and X Wang ldquoMechanical model of karstcollapse columns water inrush and its applicationrdquo ElectronicJournal of Geotechnical Engineering vol 19 pp 1665ndash1675 2014
[24] J Warren and P Root ldquoThe behavior of naturally fracturedreservoirsrdquo SPE Journal vol 3 no 3 pp 245ndash255 2013
[25] H KazemiM S Seth andGWThomas ldquoThe interpretation ofinterference tests in naturally fractured reservoirs with uniformfracture distributionrdquo SPE Journal vol 9 no 4 pp 463ndash4721969
[26] A de Swaan O ldquoAnalytical solutions for determining naturallyfractured reservoir properties by well testingrdquo SPE Journal vol16 no 3 pp 117ndash122 1976
[27] N D Rose and O Hungr ldquoForecasting potential rock slopefailure in open pit mines using the inverse-velocity methodrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 2 pp 308ndash320 2007
[28] J R Fanchi Petroleum Engineering Handbook Volume 1 Gen-eral Engineering Society of Petroleum Engineers 2006
[29] R Sakthivadivel and S Irmay A Review of Filtration TheoriesHydraulic Engineering Laboratory College of EngineeringUniversity of California Berkeley Calif USA 1996
[30] C Wang P Zhai Z Chen J Liu L Wang and J XieldquoExperimental study of coal matrix-cleat interaction underconstant volume boundary conditionrdquo International Journal ofCoal Geology vol 181 pp 124ndash132 2017
[31] S Irmay ldquoOn the theoretical derivation of Darcy and Forch-heimer formulasrdquo Eos Transactions American GeophysicalUnion vol 39 no 4 pp 702ndash707 1958
[32] CH Lee and IW Farmer ldquoA simplemethod of estimating rockmass porosity and permeabilityrdquo International Journal ofMiningand Geological Engineering vol 8 no 1 pp 57ndash65 1990
[33] C Nalluri A K El-Zaemey and H L Chan ldquoSedimenttransport over fixed deposited beds in sewers - An appraisal ofexisting modelsrdquoWater Science and Technology vol 36 no 8-9pp 123ndash128 1997
[34] P Novak and C Nalluri ldquoSediment transport in smooth fixedbed channelsrdquo Journal of the Hydraulics Division vol 101 no 9pp 1139ndash1154 1975
[35] T Fukuzono ldquoA newmethod for predicting the failure time of asloperdquo in Proceedings of the In 4th International Conference andField Workshop on Landslides Tokyo Japan 1985
[36] C R J Kilburn andDN Petley ldquoForecasting giant catastrophicslope collapse lessons from Vajont Northern Italyrdquo Geomor-phology vol 54 no 1-2 pp 21ndash32 2003
[37] B Voight ldquoA method for prediction of volcanic eruptionsrdquoNature vol 332 no 6160 pp 125ndash130 1988
[38] B Yao X Mao J Wei and D Wang ldquoStudy on coupled fluid-solid model for collapse columns considering the effect ofparticle transportrdquo Zhongguo Kuangye Daxue XuebaoJournalof China University of Mining and Technology vol 43 no 1 pp30ndash35 2014
[39] H Bai Seepage Characteristics of Top Stratum of OrdovicianSystem and Its Application Study as Key Aquifuge ChinaUniversity of Mining amp Technology Xuzhou China 2008
[40] C A Tang L G Tham P K K Lee T H Yang and L CLi ldquoCoupled analysis of flow stress and damage (FSD) in rockfailurerdquo International Journal of Rock Mechanics and MiningSciences vol 39 no 4 pp 477ndash489 2002
[41] W C Zhu and C A Tang ldquoMicromechanical model forsimulating the fracture process of rockrdquo Rock Mechanics andRock Engineering vol 37 no 1 pp 25ndash56 2004
[42] T H Yang L G Tham C A Tang Z Z Liang and YTsui ldquoInfluence of heterogeneity of mechanical properties onhydraulic fracturing in permeable rocksrdquo Rock Mechanics andRock Engineering vol 37 no 4 pp 251ndash275 2004
Hindawiwwwhindawicom Volume 2018
Journal of
ChemistryArchaeaHindawiwwwhindawicom Volume 2018
Marine BiologyJournal of
Hindawiwwwhindawicom Volume 2018
BiodiversityInternational Journal of
Hindawiwwwhindawicom Volume 2018
EcologyInternational Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Applied ampEnvironmentalSoil Science
Volume 2018
Forestry ResearchInternational Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
International Journal of
Geophysics
Environmental and Public Health
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
International Journal of
Microbiology
Hindawiwwwhindawicom Volume 2018
Public Health Advances in
AgricultureAdvances in
Hindawiwwwhindawicom Volume 2018
Agronomy
Hindawiwwwhindawicom Volume 2018
International Journal of
Hindawiwwwhindawicom Volume 2018
MeteorologyAdvances in
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018Hindawiwwwhindawicom Volume 2018
ChemistryAdvances in
ScienticaHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Geological ResearchJournal of
Analytical ChemistryInternational Journal of
Hindawiwwwhindawicom Volume 2018
Submit your manuscripts atwwwhindawicom
18 Geofluids
[19] M A Habib H M Badr R Ben-Mansour and M E KabirldquoErosion rate correlations of a pipe protruded in an abrupt pipecontractionrdquo International Journal of Impact Engineering vol34 no 8 pp 1350ndash1369 2007
[20] H T Xiao and H Y Xu ldquoIn situ permeability measurementsto establish the influence of slice mining on floor rocksrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 37 no 5 pp 855ndash860 2000
[21] H Guo D P Adhikary and M S Craig ldquoSimulation of minewater inflow and gas emission during longwall miningrdquo RockMechanics and Rock Engineering vol 42 no 1 pp 25ndash51 2009
[22] R Zhang Z JiangH ZhouC Yang and S Xiao ldquoGroundwateroutbursts from faults above a confined aquifer in the coalminingrdquo Natural Hazards vol 71 no 3 pp 1861ndash1872 2014
[23] B Yao F Du E Li and X Wang ldquoMechanical model of karstcollapse columns water inrush and its applicationrdquo ElectronicJournal of Geotechnical Engineering vol 19 pp 1665ndash1675 2014
[24] J Warren and P Root ldquoThe behavior of naturally fracturedreservoirsrdquo SPE Journal vol 3 no 3 pp 245ndash255 2013
[25] H KazemiM S Seth andGWThomas ldquoThe interpretation ofinterference tests in naturally fractured reservoirs with uniformfracture distributionrdquo SPE Journal vol 9 no 4 pp 463ndash4721969
[26] A de Swaan O ldquoAnalytical solutions for determining naturallyfractured reservoir properties by well testingrdquo SPE Journal vol16 no 3 pp 117ndash122 1976
[27] N D Rose and O Hungr ldquoForecasting potential rock slopefailure in open pit mines using the inverse-velocity methodrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 2 pp 308ndash320 2007
[28] J R Fanchi Petroleum Engineering Handbook Volume 1 Gen-eral Engineering Society of Petroleum Engineers 2006
[29] R Sakthivadivel and S Irmay A Review of Filtration TheoriesHydraulic Engineering Laboratory College of EngineeringUniversity of California Berkeley Calif USA 1996
[30] C Wang P Zhai Z Chen J Liu L Wang and J XieldquoExperimental study of coal matrix-cleat interaction underconstant volume boundary conditionrdquo International Journal ofCoal Geology vol 181 pp 124ndash132 2017
[31] S Irmay ldquoOn the theoretical derivation of Darcy and Forch-heimer formulasrdquo Eos Transactions American GeophysicalUnion vol 39 no 4 pp 702ndash707 1958
[32] CH Lee and IW Farmer ldquoA simplemethod of estimating rockmass porosity and permeabilityrdquo International Journal ofMiningand Geological Engineering vol 8 no 1 pp 57ndash65 1990
[33] C Nalluri A K El-Zaemey and H L Chan ldquoSedimenttransport over fixed deposited beds in sewers - An appraisal ofexisting modelsrdquoWater Science and Technology vol 36 no 8-9pp 123ndash128 1997
[34] P Novak and C Nalluri ldquoSediment transport in smooth fixedbed channelsrdquo Journal of the Hydraulics Division vol 101 no 9pp 1139ndash1154 1975
[35] T Fukuzono ldquoA newmethod for predicting the failure time of asloperdquo in Proceedings of the In 4th International Conference andField Workshop on Landslides Tokyo Japan 1985
[36] C R J Kilburn andDN Petley ldquoForecasting giant catastrophicslope collapse lessons from Vajont Northern Italyrdquo Geomor-phology vol 54 no 1-2 pp 21ndash32 2003
[37] B Voight ldquoA method for prediction of volcanic eruptionsrdquoNature vol 332 no 6160 pp 125ndash130 1988
[38] B Yao X Mao J Wei and D Wang ldquoStudy on coupled fluid-solid model for collapse columns considering the effect ofparticle transportrdquo Zhongguo Kuangye Daxue XuebaoJournalof China University of Mining and Technology vol 43 no 1 pp30ndash35 2014
[39] H Bai Seepage Characteristics of Top Stratum of OrdovicianSystem and Its Application Study as Key Aquifuge ChinaUniversity of Mining amp Technology Xuzhou China 2008
[40] C A Tang L G Tham P K K Lee T H Yang and L CLi ldquoCoupled analysis of flow stress and damage (FSD) in rockfailurerdquo International Journal of Rock Mechanics and MiningSciences vol 39 no 4 pp 477ndash489 2002
[41] W C Zhu and C A Tang ldquoMicromechanical model forsimulating the fracture process of rockrdquo Rock Mechanics andRock Engineering vol 37 no 1 pp 25ndash56 2004
[42] T H Yang L G Tham C A Tang Z Z Liang and YTsui ldquoInfluence of heterogeneity of mechanical properties onhydraulic fracturing in permeable rocksrdquo Rock Mechanics andRock Engineering vol 37 no 4 pp 251ndash275 2004
Hindawiwwwhindawicom Volume 2018
Journal of
ChemistryArchaeaHindawiwwwhindawicom Volume 2018
Marine BiologyJournal of
Hindawiwwwhindawicom Volume 2018
BiodiversityInternational Journal of
Hindawiwwwhindawicom Volume 2018
EcologyInternational Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Applied ampEnvironmentalSoil Science
Volume 2018
Forestry ResearchInternational Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
International Journal of
Geophysics
Environmental and Public Health
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
International Journal of
Microbiology
Hindawiwwwhindawicom Volume 2018
Public Health Advances in
AgricultureAdvances in
Hindawiwwwhindawicom Volume 2018
Agronomy
Hindawiwwwhindawicom Volume 2018
International Journal of
Hindawiwwwhindawicom Volume 2018
MeteorologyAdvances in
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018Hindawiwwwhindawicom Volume 2018
ChemistryAdvances in
ScienticaHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Geological ResearchJournal of
Analytical ChemistryInternational Journal of
Hindawiwwwhindawicom Volume 2018
Submit your manuscripts atwwwhindawicom
Hindawiwwwhindawicom Volume 2018
Journal of
ChemistryArchaeaHindawiwwwhindawicom Volume 2018
Marine BiologyJournal of
Hindawiwwwhindawicom Volume 2018
BiodiversityInternational Journal of
Hindawiwwwhindawicom Volume 2018
EcologyInternational Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Applied ampEnvironmentalSoil Science
Volume 2018
Forestry ResearchInternational Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
International Journal of
Geophysics
Environmental and Public Health
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
International Journal of
Microbiology
Hindawiwwwhindawicom Volume 2018
Public Health Advances in
AgricultureAdvances in
Hindawiwwwhindawicom Volume 2018
Agronomy
Hindawiwwwhindawicom Volume 2018
International Journal of
Hindawiwwwhindawicom Volume 2018
MeteorologyAdvances in
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018Hindawiwwwhindawicom Volume 2018
ChemistryAdvances in
ScienticaHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Geological ResearchJournal of
Analytical ChemistryInternational Journal of
Hindawiwwwhindawicom Volume 2018
Submit your manuscripts atwwwhindawicom
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