Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556. 1 Role of Rock Mass Fabric and Faulting in the Development of Block Caving Induced Surface Subsidence Vyazmensky A. 1 , Elmo D. 2 , Stead D. 3 (1) Senior Geotechnical Engineer, Copper Projects Group, Rio Tinto Ltd., Vancouver, Canada Mailing address: Dr. Alexander Vyazmensky. Rio Tinto Ltd. Copper Projects. 354-200 Granville St., Vancouver, BC, Canada, V6C 1S4 E-mail: [email protected](alt. [email protected]) (2) Rock Mechanics Specialist, Golder Associates Ltd., Mining Division, Vancouver, Canada (3) Professor, Department of Earth Science, Simon Fraser University, Vancouver, Canada Abstract: Extraction of a large volume of ore during block caving can lead to the formation of significant surface subsidence. Current knowledge of the mechanisms that control subsidence development is limited as are our subsidence prediction capabilities. Mining experience suggests that, among other contributing factors, geological structures play a particularly important role in subsidence development. A conceptual modeling study has been undertaken to evaluate the significance of geological structure on surface subsidence. A hybrid finite/discrete element technique incorporating a coupled elasto-plastic fracture mechanics constitutive criterion is adopted; this allows physically realistic modeling of block caving through simulation of the transition from a continuum to a discontinuum. Numerical experiments presented emphasize the importance of joint orientation and fault location on mechanisms of subsidence development and the governing role of geological structure in defining the degree of surface subsidence asymmetry. Keywords: surface subsidence; rock mass fabric; faulting; block caving; numerical modeling; FEM/DEM-DFN
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Role of rock mass fabric and faulting in the development of block caving induced surface subsidence
Extraction of a large volume of ore during block caving can lead to the formation of significant surface subsidence. Current knowledge of the mechanisms that control subsidence development is limited as are our subsidence prediction capabilities. Mining experience suggests that, among other contributing factors, geological structures play a particularly important role in subsidence development. A conceptual modeling study has been undertaken to evaluate the significance of geological structure on surface subsidence. A hybrid finite/discrete element technique incorporating a coupled elasto-plastic fracture mechanics constitutive criterion is adopted; this allows physically realistic modeling of block caving through simulation of the transition from a continuum to a discontinuum. Numerical experiments presented emphasize the importance of joint orientation and fault location on mechanisms of subsidence development and the governing role of geological structure in defining the degree of surface subsidence asymmetry.
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Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556.
1
Role of Rock Mass Fabric and Faulting in the Development of Block Caving Induced Surface Subsidence
translational failure and full disintegration of the fault hanging wall and a gradual
failure of the fault footwall. By the end of ore extraction the fault is almost fully
consumed by the caving. Observed surface subsidence deformations are largely
symmetrical with respect to the block centre vertical axis. The minimum angle
delineating the extent of major (10cm) surface displacements is 73°, which is
only 2° higher than for the same model but without a fault (Base Case, Fig. 5a).
For the model with a fault located 100m from the block centre vertical axis (F2,
Figs. 12b and 13b) a notably different subsidence development mechanism is
observed. Only a minor undercuting of the fault coupled with caving induced
unloading triggers translational failure of major hanging wall segments along the
fault interface, eventually resulting in the hanging wall “sagging” into the cave.
The fault footwall withstood the caving sustaining only minor damage. Surface
subsidence is clearly asymmetrical in a direction towards the fault. The minimum
angle delineating the extent of major surface displacement is 61°, which is 10°
less than for the Base Case model (Fig. 5a). A fault positioned outside the caving
boundaries, at 150m from the block centre vertical axis (F3, Figs. 12c and 13c),
has no significant influence on the simulated surface subsidence. As seen in Fig.
14, the presence of a steeply dipping fault in a vertical/horizontal jointed rock
mass, located at 50m (F1) and 150m (F3) from the block centre vertical axis has
negligible effect on the extent of the zone of major surface displacements. In
contrast, a fault located at 100m (F2) has been shown to increase the extent of
major vertical and horizontal displacements zone by approximately 20%,
primarily in a direction towards the fault.
Subsidence development mechanisms for the F4 and F5 models, which assume
steeply/gently dipping (70°/20°) joints, are illustrated in Figs. 12(d,e) and show
similar observed trends as previously discussed for the F2 and F3 models. Final
surface subsidence deformation at 100% ore extraction for models F4 and F5 is
Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556.
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given in Fig. 13(d,e). Comparing the models where a fault is intersecting the
block (F2, F4), it can be noted that the change of joint orientation does not affect
the extent of major surface deformation, which is limited by the fault. For models,
where the fault does not intersect the block (F3, F5), subsidence is primarily
governed by jointing. Comparing the F3 (Fig. 13c) and Base Case (Fig. 5a)
models, increased tensile fracturing can be noted in the hanging wall in the
vicinity of the caving boundary indicating the weakening effect of the fault on the
hanging wall rock mass. The J2 (Fig. 5c) and F5 (Fig. 13e) models illustrate the
limiting effect of the fault on rock mass mobilization, clearly indicating that the
fault prevents mobilization of the rock mass in the footwall, increasing the limiting
angle from 53° to 59°. According to Fig. 15, the presence of a fault in
steeply/gently dipping (70°/20°) joint settings located at 100m and 150m from the
block centre vertical axis decreased the zone of major surface horizontal
displacements by 13% and 9%, respectively, in the direction towards the fault.
Figs. 16 and 17 illustrate far-field displacements for models based on
vertical/horizontal and inclined joint sets, respectively. For models with
vertical/horizontal joints, faults generally increased the magnitude and extent of
the far-field displacement. The largest increase is observed for the model with a
fault located 150m from the block centre vertical axis (F3), where horizontal
displacements in excess of 1cm are observed as far as 200m from the caving
boundary, which is twice the extent simulated in the model without a fault (Base
case). For models with inclined joints the opposite trend is observed, the
presence of a fault limiting both the magnitude and extent of far-field
displacement. Irrespective of joint set orientation horizontal displacements are
predominant.
Caving induced unloading of the hanging wall results in the formation of a
topographical step where the fault daylights. Fig. 18 compares differential XY
displacements along fault surfaces with continuous ore extraction for all
simulations. Depending on the fault location with respect to the block centre,
movements at the fault surface may vary significantly. For the models F1, F2 and
Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556.
17
F4, where a fault intersects the block, movements in the order of metres are
observed, whereas for models F3 and F5, where a fault does not intersect the
block, movements limited to several centimetres are noted. Inclination of the joint
sets affects these movements, such that larger XY displacements, which develop
more rapidly, are observed for models with inclined joints.
6.2 Effect of Fault Inclination
The effect of fault inclination on the development of surface subsidence was
evaluated based on six modelling scenarios, for a fault partially intersecting the
block. Three different fault inclinations and two different joint set conditions were
considered, as summarized in Table 5.
Figs. 12b, 19a and 19b illustrate the development of surface subsidence at 35,
50 and 60% ore extraction, and, Figs. 13b and 20(a,b) show resultant
subsidence deformations at 100% ore extraction for models F2, F6 and F7,
assuming vertical/horizontal joints. Figs. 12d, 19c and 19d present surface
subsidence development at 35, 50 and 60% ore extraction and Figs. 13d and
20(c,d) show the resultant subsidence deformation at 100% ore extraction for
models F4, F8 and F9, assuming steeply/gently dipping joints. Comparing
subsidence deformation development for varying fault inclinations and varying
joint set orientations it should be noted that, for all assumed inclinations, faults
affect the development of subsidence deformation. Irrespective of jointing
orientation caving induced failure is predominantly controlled by the plane of
weakness provided by the fault. Continuous ore extraction leads to full
mobilization of the entire hanging wall and its disintegration into segments. The
mode of hanging wall segmentation appears to be controlled by joint orientation.
Failure of the hanging wall leads to formation of a crater wall along the footwall of
the exposed fault; particularly pronounced for the 75° and 60° faults. For the 75°
fault models (F7, F9, Fig. 20(b,d)) exposure of a steep footwall by the caving
causes its partial failure, the magnitude of this failure is strongly controlled by the
jointing.
Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556.
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Vertical/horizontal jointing contributes to formation of a nearly vertical wall,
whereas inclined joint sets favour kinematic instability of major near surface rock
mass blocks. For the 60° faults (F2, F4, Fig. 13(b,d)), the moderately inclined
footwall was more limited in exposure and the passive support provided by the
muck pile prevented development of major internal instability. Here it should be
noted that removal of this support will likely trigger further footwall damage,
particularly for the case with inclined joints. For the 45° faults (F6, F8, Fig.
20(a,c)), the footwall sustained only minor damage. It appears that for the
simulated jointing conditions development of major instability in a 45° footwall
slope even with continuous ore extraction is highly unlikely.
Inclination of the fault significantly alters the extent of the caving influence. For
the 45° and 60° faults, irrespective of the assumed joint set conditions, the extent
of major surface deformation toward the fault was determined by the fault
inclination, so that the angular limits of major (10cm) surface displacements are
equal or nearly equal to the fault inclination. For the 75° faults the extent of major
surface deformation is a function of the stability of the exposed footwall. For the
model with vertical/horizontal joints the limiting angle is 75, whereas for the
model with inclined joints it is 59.
Comparison of the extent of major surface displacements for the models with
vertical/horizontal joints without a fault (Base Case) and with fault dips of 75
(F6), 60 (F2) and 45 (F7) is presented in Fig. 21. This figure shows that faults
with inclinations of 60 and 45 extended the total zones of major displacement
by about 20 and 60%, respectively. In the direction towards the fault, for 60 and
45 dipping faults, the zone of influence was increased by 40 and 120%,
respectively, i.e. a decrease in fault inclination by 15 extended the zone of major
surface displacements by 80%. The fault with 75 inclination had only a minor
influence on the observed extent of major surface displacements. Comparison of
the extent of major surface displacements for the models with inclined joints
without a fault (J2) and with a fault of 75 (F9), 60 (F4) and 45 (F8) inclination is
Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556.
19
given in Fig. 22. As can be inferred from this figure for faults with inclinations of
60 and 75 the extent of the zone of major surface displacement towards the
fault was reduced by as much as 50%. The surface outcrop location of the 45
fault coincided approximately with the extent of major displacements for the
model without a fault (see Figs. 5c and 20d), hence no major influence was
observed. Interestingly models with 45 and 75 dipping faults exhibit increased
zones of influence in an eastward direction from the block centre vertical axis.
Far-field displacements for models with vertical/horizontal and inclined joints are
presented in Figs. 23 and 24, respectively. It can be inferred from these figures
that, in the direction towards the fault, the extent of the far-field displacements is
a function of fault inclination. A shallower fault inclination resulted in a larger area
mobilized by the caving. Conversely, steeper faults limit such an area. Within the
failing hanging wall higher deformation magnitudes were observed for models
with vertical/horizontal joints. Depending on the fault inclination the amount of
differential displacement at the surface outcrop of the fault varies, higher
displacements being observed for models with steeper faults (see Fig. 25).
7. Results Synthesis and Conclusions
The adopted modelling methodology has allowed physically realistic simulation of
subsidence deformation mechanisms, from caving initiation to the final
subsidence topography. It thereby has provided quantitative support for the
observational-based conceptual model of subsidence development proposed by
Abel and Lee (1980). The 2D FEM/DEM-DFN modelling offers a convenient
framework for future quantitative analysis of block caving induced surface
subsidence and has significant potential for improving subsidence prediction
capabilities. Vyazmensky et al. (2009) have applied this approach to the analysis
of a block caving induced large open pit slope failure at the Palabora mine and
illustrated that the 2D FEM/DEM-DFN modelling methodology can be
successfully applied to the analysis of complex industrial scale problems.
Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556.
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The program of 2D FEM/DEM with fracture simulations presented in this paper is
the most comprehensive of its kind to date constituting a significant advance in
the 2D simulation of fracture and subsidence associated with block caving. New
and valuable insights were gained into the complex mechanisms governing
caving induced rock mass deformations and associated subsidence
development. The numerical experiments presented in this paper have
highlighted the importance of both joint set orientation and fault location and
inclination, in determining the mechanisms of subsidence development; in
addition their governing role in defining the degree of surface subsidence
asymmetry has been demonstrated. Key model observations are summarized in
Table 6. Based on the modelling analyses a preliminary classification of the
influence of major geological discontinuities on surface subsidence is proposed,
Table 7. Further analysis should consider a range of stochastically generated
DFN realisations. It should be noted that presented modelling results represent
only a small part of a larger study investigating factors governing block cave
subsidence development (Vyazmensky, 2009).
While 3D analysis of geomechanical problems is preferred, the simulation of
block caving related subsidence in 3D has to date almost exclusively involved
continuum modelling. This choice is primarily driven by the higher computational
efficiency of continuum codes for large scale modelling. It should be recognized
that these continuum codes are unable to simulate explicitly important
mechanisms for block caving subsidence development such as brittle fracture
and failure kinematics and therefore may not be applicable in all cases. As
illustrated by Stead et al. (2007) applications of discontinuum codes for detailed
block caving analysis face extreme computational challenges. Detailed and
realistic mine scale block caving modelling in 3D has yet to be achieved.
In the authors' opinion FEM/DEM-DFN modeling provides an important
alternative to traditional modelling approaches and represents a new and
valuable tool in the rock engineer’s geotechnical modelling toolbox. The initial
applications of this technique are very encouraging. As the requisite computing
Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556.
21
power becomes available and the existing FEM/DEM codes are adapted to
maximize the use of 64 bit architectures and parallel processing facilities
FEM/DEM-DFN technique will be adopted to mine scale 3D modelling, allowing
physically realistic simulation of the block caving process, including caving
initiation, fragmentation, mass flow and resultant surface subsidence.
Acknowledgements
The authors would like to acknowledge research funding provided by Rio Tinto and Natural Sciences and Engineering Research Council of Canada. We would also like to acknowledge research collaboration with Allan Moss and Andre van As (Rio Tinto), Erik Eberhardt, Scott Dunbar and Malcolm Scoble (University of British Columbia). Technical support of Rockfield Technology Ltd. (UK) is gratefully appreciated.
Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556.
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References
Abel JF, Lee TF (1980) Subsidence Potential in Shale and Crystalline Rocks. U.S. Geological Survey Open File Report 80-1072. 49pp.
Barton N, Lien R, Lunde J (1974) Engineering classification of rock masses for design of tunnel support. Rock Mech. 6(4): 189–236.
Bieniawski ZT (1989) Engineering Rock Mass Classifications. Wiley. 272 pp.
Crane WR (1929) Subsidence and Ground Movement in the Copper and Iron Mines of the Upper Peninsula, Michigan. USBM Bulletin 285. 66pp.
Elmo D (2006) Evaluation of a hybrid FEM/DEM approach for determination of rock mass strength using a combination of discontinuity mapping and fracture mechanics modelling, with particular emphasis on modelling of jointed pillars. PhD Thesis. Camborne School of Mines, University of Exeter, UK.
Elmo D, Vyazmensky A, Stead D, Rance JR (2008) A hybrid FEM/DEM approach to model the interaction between open pit and underground block caving mining. Proc. 1st Canada-U.S. Rock Mechanics Symposium, Vol 2, 1287-94pp.
Elmo D, Stead D (2009) An integrated numerical modelling - discrete fracture network approach applied to the characterisation of rock mass strength of naturally fractured pillars. Rock Mechanics and Rock Engineering, DOI 10.1007/s00603-009-0027-3.
Flores G, Karzulovic A (2002) Geotechnical guidelines for a transition from open pit to undeground mining. Benchmarking Report for ICSII. Task 4. 91 pp.
Golder Associates (2007) FracMan Technology Group. Home page at: http://www.fracman.golder.com
Hoek ET, Kaiser PK, Bawden WF (1995) Support of underground excavations in hard rock. A.A. Balkena. Rotterdam. 300pp.
Klerck PA (2000) The finite element modelling of discrete fracture in quasi-brittle materials. Ph.D. thesis, University of Wales, Swansea.
Laubscher DH (1990) A geomechanics classification system for the rating of rock mass in mine design. J. S. Atr. Inst. Min. Metall. 90(1): 257-293.
Mahtab MA, Bolstad DD, Kendorski FS (1973) Analysis of the geometry of fractures in San Manuel copper mine, Arizona. Bureau of Mines. Technical report RI 7715.
Munjiza A, Owen DRJ, Bicanic N (1995). A combined finite/discrete element method in transient dynamics of fracturing solids. Int. J. Engng Comput. 12(2): 145–174.
Munjiza A (2004) The combined finite-discrete element method. Chichester: J. Wiley & Sons. 348pp.
Owen DRJ, Feng YT, de Souza Neto EA, Cottrell M G,Wang F, Andrade Pires FM, Yu J. (2004) The modelling of multi-fracturing solids and particulate media. Int. J. Num. Meth. Eng. 60(1): 317-339.
Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556.
23
Panek LA (1984) Subsidence in undercut - cave operations, subsidence resulting from limited extraction of two neighboring cave operations. In: Geomechanical Applications in Hard Rock Mining. (ed. Pariseau, W.G.) pp 225-240.
Pine RJ, Owen DRJ, Coggan JS, Rance JM (2007) A new discrete modelling approach for rock masses. Geotechnique. 57(9): 757-766.
Pine RJ, Coggan JS, Flynn ZN, Elmo D (2006) The development of a new numerical modelling approach for naturally fractured rock masses. Rock Mech. Rock Engng. 39(5): 395-419.
Rance JM, van As A, Owen DRJ, Feng YT, Pine RJ (2007) Computational modelling of multiple fragmentation in rock masses with application to block caving. Proc. 1st Canada-U.S. Rock Mechanics Symposium. Vancouver Vol 1: 477-484pp
Rockfield Software Ltd (2007) ELFEN user manual, Swansea, UK. Home page at: http://www.rockfield.co.uk
Stacey TR, Swart AH (2001) Practical rock engineering practice for practice for shallow and opencast mines. SIMRAC The safety of mines research advisory committee, 66pp.
Stead D, Coggan JS, Eberhardt E (2004) Realistic simulation of rock slope failure mechanisms: The need to incorporate principles of fracture mechanics. SINOROCK 2004: Special Issue of Int. Journal of Rock Mechanics. 41(3). 6pp.
Stead D, Coggan JS, Elmo D, Yan M (2007) Modelling brittle fracture in rock slopes: experience gained and lessons learned. In Proc. Int. Symp. on Rock Slope Stability in Open Pit Mining and Civil Engineering. Perth. pp. 239-252.
van As A, Davison J, Moss A (2003) Subsidence Definitions for Block Caving Mines. Technical report. 59pp.
Vyazmensky A, Elmo D, Stead D, Rance JR (2007) Combined finite-discrete element modelling of surface subsidence associated with block caving mining. In Proc. 1st Canada-U.S. Rock Mechanics Symposium. Vancouver Vol 1: 467-475.
Vyazmensky A (2008) Numerical modelling of surface subsidence associated with block cave mining using a finite element / discrete element approach. PhD thesis. Simon Fraser University, Canada.
Vyazmensky A, Stead D, Elmo D, Moss A (2009) Numerical Analysis of Block Caving-Induced Instability in Large Open Pit Slopes: A Finite Element/Discrete Element Approach. Rock Mechanics and Rock Engineering, DOI 10.1007/s00603-009-0035-3
Wilson ED (1958) Geologic Factors Related to Block Caving at San Manuel Copper Mine, Pinal County, Arizona. Progress Report, April 1956-1958. Bureau of Mines Rept. of Inv. 5336. 40pp.
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Table 1 Influence of geological structure on block caving surface subsidence development
Geological structure
Influence on block caving subsidence Reference
Joints In the absence of faults and dykes, joint dip governs the angle of break. Angle of break for a mine should be equal to the dip of the most prominent joint set.
Crane (1929), Wilson (1958)
Faults
When a mining face encounters a significant discontinuity, such as a fault, with moderate to steep dip, movement will occur on the fault regardless of the cave angle through intact rock. A stepped crack will result where the fault daylights at surface. If mining is only on the hanging wall side of the fault there will only be surface movements on the one side. If the fault dip is steeper than the cave angle the extent of surface subsidence will be reduced, conversely, if the fault dip is less than the cave angle the extent of surface subsidence will be increased.
Abel and Lee (1980),
Stacey and Swart (2001),
van As et al. (2003)
Table 2 Modelling input parameters
Parameter Unit Value Parameter Unit Value
Rock mass Discontinuities
Young’s Modulus, E GPa 18 Fracture cohesion, cf MPa 0
Poisson’s ratio, 0.25 Fracture friction, f degrees 35
Density, ρ kgm-3 2600 Normal stiffness GPa/m 2
Tensile strength, t MPa 1 Shear stiffness GPa/m 0.2
Fracture energy, Gf Jm-2 60
Cohesion, ci MPa 4.7 Stress level
Friction, i degrees 45 In-situ stress ratio, K 1
Dilation, ψ degrees 5
Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556.
25
Table 3 Modelling scenarios for analysis of the effect of joint orientation
Scenario Number of sets
Joint sets dips, °
Description
Base Case (BC)
Two sets 90/0 Orthogonal sets, vertical/horizontal
J1 Two sets 80/10 Orthogonal sets, sub-vertical/sub-horizontal
J2 Two sets 70/20 Orthogonal sets, steeply dipping/gently dipping
J3 Two sets 70/0 Orthogonal sets, steeply dipping/horizontal
J4 Three sets 70/20/90 Orthogonal sets, steeply dipping/gently dipping/vertical
Table 4 Modelling scenarios for analysis of the effect of fault location
Scenario Joint set dips, ° Fault dip, ° Fault location with respect to block centre axis, m
Figure
F1
90/0
60
50 10(a)
F2 100 10(b)
F3 150 10(c)
F4 70/20
100 10(d)
F5 150 10(e)
Table 5 Modelling scenarios for analysis of the effect of fault inclination
Scenario Joint set dips, ° Fault dip, ° Figure
F6
90/0
45 10(f)
F2 60 10(b)
F7 75 10(h)
F8
70/20
45 10(g)
F4 60 10(c)
F9 75 10(i)
Table 6 Summary of modelling findings
Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556.
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Influence on block caving subsidence
Jo
int
orienta
tion
Well defined, vertical to steeply dipping joints govern the direction of cave propagation and the mechanism of near surface rock mass mobilization. The shallower the dip of these joints the more inclined from vertical the cave propagation direction is and the more asymmetrical the surface deformation with respect to the block centre vertical axis. In cases where multiple well defined and persistent steeply dipping joint sets are present, the steepest set will generally have the predominant influence.
Significant subsidence asymmetry is observed in the dip direction of the sub-vertical/steeply dipping set. Where joints are inclined towards the cave, the rock mass fails through a combination of block-flexural and block toppling and the detachment and sliding of major rock segments. Where a sub-vertical joint set is dipping into the cave, the surface deformation direction is controlled by the dip of the sub-vertical joint set. In this case the rock mass fails predominantly through block toppling and sliding along the sub-vertical joints.
The orientation of well defined, gently dipping joints influences the extent of the rock mass mobilized by the failure and the degree of subsidence asymmetry.
Fau
lts in
clin
atio
n a
nd
loca
tion
Unequivocally, the inclination of the fault partially intersecting the caving area controls the extent of surface subsidence deformations. Low dipping faults will extend and steeply dipping faults will decrease the area of surface subsidence.
For faults daylighting into the cave, failure of the hanging wall is likely inevitable. For the assumed hard rock mass conditions in the current modelling, the stability of the exposed footwall is dependent on its slope, the amount of passive support provided by the muck pile and the orientation and persistence of jointing within the footwall. The presence of well defined steeply/gently dipping joint set approaching perpendicular orientation with relation to the fault will increase the kinematic potential for failure of major near surface footwall segments. In such circumstances a model combining the fault/jointing system is extremely important.
Steeply dipping faults, daylighting into the cave and located within an area of imminent caving are likely to be caved and therefore are unlikely to play any major role in the resultant subsidence.
Faults partially intersecting the caving area may create unfavourable conditions with potential for failure of the entire hanging wall.
Depending on rock mass fabric, faults located in the vicinity of the caving zone may have a minimal influence or decrease the extent of the area of subsidence deformation. The former behaviour was observed in models with horizontal/vertical joint sets and the latter for orthogonal steeply/gently dipping joints.
A topographical step in the surface profile is formed where the fault daylights at the surface. Significant movements should be anticipated if the fault daylights into the cave.
Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556.
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Table 7 Preliminary classification of the influence of major geological discontinuities on caving induced surface subsidence
Degree of influence Typical subsidence deformations Description
I. Low to Moderate
I(a)
fault
highly
disturbed torubblizedrock mass
intact
rock mass
disturbed
rock mass
2H
W=H
I(b)
fault
I(a) fault located at distances exceeding 0.5H from the caving boundary
fault may act as a displacement barrier limiting rock mass movements in the far-field
I(b) more than 2/3 of the fault near surface segment is located within the caving zone
in both cases the extent of surface subsidence and subsidence asymmetry will be governed by fault inclination
Note: this classification is based on the modelling that assumed rock mass corresponding to ~ MRMR 55-60, uniform ore extraction and block depth 2H (where H is block height).
Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556.
28
Fig. 1 Schematic illustration of block cave mining and associated surface subsidence (modified after block caving animation (Sandvik Group 2004)).
Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556.
Legend: rotational failure; translational failure; active rock mass movement;
developing rock mass failure; centre of surface depression
Fig. 3 Subsidence crater formation for BC (a), J1 (b), J2 (c), J3 (d) & J4 (e) models
31
Fig. 4 Variation of vertical stress (Pa) contours with caving at 5% ore extraction for Base Case and J2 models
32
0-100 -50-150-200-250 10050 150 200 250 300-300
(a)
BC
(b)
J1
(c)
J2
(d)
J3
(e)
J4
Fig. 5 Subsidence at 100% ore extraction for BC (a), J1 (b), J2 (c), J3 (d) & J4 (e) models
90°
0°
80°
10°
70°
20°
70°
0°
0°
70°
20°
10cm displ. contours
vertical
horizontal
Legend:
angle
of fracture
initiation
71°
70°
53°
61°
59°
71°
76°
73°
74°
74°
72°
MRV = 28114m3
AI = 0.93
MRV = 30762m3
AI = 0.96
MRV = 34990m3
AI = 0.72
MRV = 35250m3
AI = 0.82
MRV = 30836m3
AI = 0.82
33
-80
-70
-60
-50
-40
-30
-20
-10
0
-350 -250 -150 -50 50 150 250 350
Vert
ical d
isp
lacem
en
ts,
m
Distance from block centre, m
Base case
J1
J2
J3
J4
0, -55
9.4, -49.6
28.6, -41
9.4, -44.5
10, -50
Lowest point coordinates, m
Fig. 5 Surface profiles at the end of ore extraction for BC, J1, J2, J3 and J4 models
207234
268 269245
100%
113%
129%
130%
118%
0
50
100
150
200
250
300
350
0
50
100
150
200
250
300
350
To
tal exte
nt o
f 10cm
vert
ical
su
rface d
isp
lacem
en
ts
no
rmalized
b
y B
ase C
ase, %
To
tal e
xte
nt o
f 10cm
vert
ical
su
rface d
isp
lacem
en
ts,
m
BC J1 J2 J3 J4
218235
308
269290
100%
108% 141%
123%
133%
0
50
100
150
200
250
300
350
0
50
100
150
200
250
300
350
To
tal exte
nt o
f 10cm
ho
riz.
su
rface d
isp
lacem
en
ts
no
rmalized
b
y B
ase C
ase, %
To
tal e
xte
nt o
f 10cm
ho
riz.
su
rface d
isp
lacem
en
ts,
m
BC J1 J2 J3 J4
-112
95
-123
111
-161
107
-161
108
-132
113119%
132%
114%
144%
113%
144%
117%
110%
100%
100%
-300 -200 -100 0 100 200 300
-250 -200 -150 -100 -50 0 50 100 150 200 250
Extent of 10cm surface vertical displacements in relation to block centre, normalized by Base Case, %
Extent of 10cm surface vertical dispacements in relation to block centre, m
BCJ1J2J3J4
BCJ1J2J3J4
-118
100
-123
112
-201
107
-161
108
-173
117117%
147%
108%
136%
107%
170%
116%
104%
100%
100%
-300 -200 -100 0 100 200 300
-250 -200 -150 -100 -50 0 50 100 150 200 250
Extent of 10cm surface horizontal displacements in relation to block centre, normalized by Base Case, %
Extent of 10cm surface horizontal displacements in relation to block centre, m
BCJ1J2J3J4
BCJ1J2J3J4
Fig. 7 Subsidence characterization for Base Case, J1, J2, J3 and J4 models Total extent of 10cm vertical (a) and horiz. (b) surface displacement; extent of 10cm surface vertical (c) and horiz. (d) displacement in relation to centre axis of the block, in m
(c) (d)
(a) (b)
34
0
10
20
30
40
50
60
70
80
90
100
-250 -200 -150 -100 -50 0 50 100 150 200 250
Ore
extr
acti
on
, %
Extent of 10cm surface deformations, m
YY
XX
0
10
20
30
40
50
60
70
80
90
100
-250 -200 -150 -100 -50 0 50 100 150 200 250
Ore
extr
acti
on
, %
Extent of 10cm surface deformations, m
YY
XX
Fig. 8 Evolution of zone of major (≥10cm) vertical (YY) and horizontal (XX) surface deformation with continuous ore extraction for Base Case (a), J1 (b), J2 (c), J3 (d) and J4 (e) models
Fig. 9 Rate of growth of 10cm surface displacement zone west of the block centre vertical axis with continuous ore extraction for Base Case, J1, J2, J3 and J4 models (a) vertical displacement, (b) horizontal displacement
0
10
20
30
40
50
60
70
80
90
100
-250 -200 -150 -100 -50 0 50 100 150 200 250
Ore
extr
acti
on
, %
Extent of 10cm surface deformations, m
YY
XX
0
10
20
30
40
50
60
70
80
90
100
-250 -200 -150 -100 -50 0 50 100 150 200 250
Ore
extr
acti
on
, %
Extent of 10cm surface deformations, m
YY
XX
0
10
20
30
40
50
60
70
80
90
100
-250 -200 -150 -100 -50 0 50 100 150 200 250
Ore
extr
acti
on
, %
Extent of 10cm surface deformations, m
YY
XX
0
20
40
60
80
100
120
0 20 40 60 80 100 120
exte
nt
of
vert
ical
10cm
su
rface
dis
pla
cem
en
ts,
%
Ore extraction, %
BC_YY
J1_YY
J2_YY
J3_YY
J4_YY
0
20
40
60
80
100
120
0 20 40 60 80 100 120
exte
nt
of
ho
rizo
nta
l 10cm
su
rface
dis
pla
cem
en
ts,
%
Ore extraction, %
BC_XX
J1_XX
J2_XX
J3_XX
J4_XX
(d) J3
(e) J4
(b) J1 (a) BC
(c) J2
(a) (b)
35
J2 J3
J4
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
-300 -250 -200 -150 150 200 250 300
Vert
ical d
isp
lacem
en
ts,
m
Distance from block centre, m
-0.38 -2.1
J2
J3
BC
BC BC
J1
J1
J1J2
J2
J2
J2
J3
J3
J3
J3
J4
J4
J4
0
0.05
0.1
0.15
0.2
0.25
0.3
-300 -250 -200 -150 150 200 250 300
Ho
rizo
nta
l dis
pla
cem
en
ts, m
Distance from block centre, m
0.9 3.8
Fig. 10 Total vertical (a) and horizontal (b) surface displacement at the end of ore extraction at different distances from block centre for Base Case, J1, J2, J3 and J4 models
(a)
(b)
36
0-100 -50-150-200-250 10050 150 200 250 300-300
(a) F1
(b) F2
(c) F4
(d) F3
(e) F5
(f) F6
(g) F8
(h) F7
(i) F9
Fig. 11 Assumed fracture orientations and fault positions for F1 to F9 models
90°
0°
70°
20°
90°
0°
70°
20°
90°
0°
90°
0°
70°
20°
90°
0°
70°
20°
fault
60°
50m
60°
100m
60°
150m
45°
75°
37
(a) (b) (c) (d) (e)
Legend: rotational failure; translational failure; fault location prior to failure
active rock mass movement; developing rock mass failure
Fig. 12 Subsidence crater formation for F1 (a), F2 (b), F3 (c), F4 (d) and F5 (e) models
fault fault fault fault fault
38
0-100 -50-150-200-250 10050 150 200 250 300-300
(a)
F1
(b)
F2
(c)
F3
(d)
F4
(e)
F5
Fig. 13 Subsidence at 100% ore extraction for F1, F2, F3, F4 and F5 model
fault location prior
to caving
90°
0°
73°
10cm displ. contours
vertical
horizontal
Legend:
angle
of fracture
initiation
73°
73° MRV = 30154m3
AI = 1.0
90°
0°
61° 76° MRV = 32207m3
AI = 0.80
90°
0°
73° 74° MRV = 27519m3
AI = 0.99
70°
20°
61° 74° MRV = 34630m3
AI = 0.82
70°
20°
59° 74° MRV = 35602m3
AI = 0.80
39
207 202
255
212
100%
98% 123%
102%
0
50
100
150
200
250
300
350
0
50
100
150
200
250
300
350
To
tal e
xte
nt o
f 10cm
vert
ical
su
rface d
isp
lacem
en
ts
no
rmalized
by B
ase C
ase, %
To
tal e
xte
nt o
f 10cm
vert
ical
su
rface d
isp
lacem
en
ts,
m
BC F1 F2 F3
218 220
258
220
100%
101%
118%
101%
0
50
100
150
200
250
300
350
0
50
100
150
200
250
300
350
To
tal e
xte
nt o
f 10cm
vert
ical
su
rface d
isp
lacem
en
ts
no
rmalized
by B
ase C
ase, %
To
tal e
xte
nt o
f 10cm
ho
riz.
su
rface d
isp
lacem
en
ts,
m
BC F1 F2 F3
-112
95
-110
92
-160
95
-112
100105%
100%
100%
143%
97%
98%
100%
100%
-300 -200 -100 0 100 200 300
-250 -200 -150 -100 -50 0 50 100 150 200 250
Extent of 10cm surface vertical displacements in relation to block centre, normalized by Base Case, %
Extent of 10cm surface vertical dispacements in relation to block centre, m
BC
F1
F2
F3
BC
F1
F2
F3
-118
100
-110
110
-160
98
-112
108108%
95%
98%
136%
110%
93%
100%
100%
-300 -200 -100 0 100 200 300
-250 -200 -150 -100 -50 0 50 100 150 200 250
Extent of 10cm surface horizontal displacements in relation to block centre, normalized by Base Case, %
Extent of 10cm surface horizontal displacements in relation to block centre, m
BC
F1
F2
F3
BC
F1
F2
F3
Fig. 14 Subsidence characterization for Base case, F1, F2 and F3 Total extent of major (≥10cm) vertical (a) and horizontal (b) surface displacement in m and in % of Base case value; extent of 10cm surface vertical (c) and horizontal (d) displacement in relation to centre axis of the block, in m
(a) (b)
(c) (d)
40
268 269 275
100%
100%
103%
0
50
100
150
200
250
300
350
0
50
100
150
200
250
300
350
To
tal exte
nt o
f 10cm
vert
ical
su
rface d
isp
lacem
en
ts
no
rmalized
b
y J
2, %
To
tal e
xte
nt o
f 10cm
vert
ical
su
rface d
isp
lacem
en
ts,
m
J2 F4 F5
308
268
279
100%
87%
91%
0
50
100
150
200
250
300
350
240
250
260
270
280
290
300
310
320
To
tal exte
nt o
f 10cm
vert
ical
su
rface d
isp
lacem
en
ts
no
rmalized
b
y J
2, %
To
tal e
xte
nt o
f 10cm
ho
riz.
su
rface d
isp
lacem
en
ts,
m
J2 F4 F5
-161
107
-161
108
-167
108101%
104%
101%
100%
100%
100%
-300 -200 -100 0 100 200 300
-250 -200 -150 -100 -50 0 50 100 150 200 250
Extent of 10cm surface vertical displacements in relation to block centre, normalized by J2, %
Extent of 10cm surface vertical dispacements in relation to block centre, m
J2
F4
F5
J2
F4
F5
-201
107
-160
108
-171
108101%
85%
101%
80%
100%
100%
-300 -200 -100 0 100 200 300
-250 -200 -150 -100 -50 0 50 100 150 200 250
Extent of 10cm surface horizontal displacements in relation to block centre, normalized by J2, %
Extent of 10cm surface horizontal displacements in relation to block centre, m
J2
F4
F5
J2
F4
F5
Fig. 15 Subsidence characterization for J2, F4 and F5 Total extent of major (≥10cm) vertical (a) and horizontal (b) surface displacement in m and in % of J2 value; extent of 10cm surface vertical (c) and horizontal (d) displacement in relation to central axis of the block, in m
(a) (b)
(c) (d)
41
F3
F3
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
-300 -250 -200 -150 150 200 250 300
Vert
ical d
isp
lacem
en
ts,
m
Distance from block centre, m
-2
F2
B
C BCF
1
F1
F1
F2
F2
F3 F3
F3
F3
0
0.05
0.1
0.15
0.2
0.25
0.3
-300 -250 -200 -150 150 200 250 300
Ho
rizo
nta
l dis
pla
cem
en
ts, m
Distance from block centre, m
1.2
Fig. 16 Total vertical (a) and horizontal (b) surface displacement at the end of ore extraction at different distances from block centre for Base Case, F1, F2 and F3 models
J2
J2
F4
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
-300 -250 -200 -150 150 200 250 300
Vert
ical d
isp
lacem
en
ts,
m
Distance from block centre, m
-0.4
F5
-3.2
J2
J2
J2
J2F4
F4
F4F5
F5
F5
0
0.05
0.1
0.15
0.2
0.25
0.3
-300 -250 -200 -150 150 200 250 300
Ho
rizo
nta
l d
isp
lacem
en
ts, m
Distance from block centre, m
1.20.8
Fig. 17 Total vertical (a) and horizontal (b) surface displacement at the end of ore extraction at different distances from block centre for J2, F4 and F5 models
(a)
(b)
(a)
(b)
42
Fig. 18 Differential XY displacement for surface points on the fault hanging and footwalls: (a) F1, F2 and F3; (b) F4 and F5 models
footwall
hanging
wall
differential
XY displacement
-4.31m
-2.37m
-0.02m
-5
-4
-3
-2
-1
0
0 10 20 30 40 50 60 70 80 90 100
Dif
fere
nti
al
XY
d
isp
lac
em
en
ts, m
Ore extraction, %
F1
F2
F3
-3.73m
-5
-4
-3
-2
-1
0
0 10 20 30 40 50 60 70 80 90 100
Dif
fere
nti
al
XY
d
isp
lac
em
en
ts, m
Ore extraction, %
F4
F5
-0.07m
hangingwall disintegrated
(b)
(a)
90°
0°
70°
20°
43
(a) (b) (c) (d)
Legend: rotational failure; translational failure; fault location prior to failure
active rock mass movement; developing rock mass failure
Fig. 19 Subsidence crater formation for F6 (a), F7 (b), F8 (c) and F9 (d) models
fault fault fault fault
44
0-100 -50-150-200-250 10050 150 200 250 300-300
(a)
F6
(b)
F7
(c)
F8
(d)
F9
Fig. 20 Subsidence at 100% ore extraction for F6, F7, F8 and F9 models
90°
0°
70°
20°
fault location prior
to caving
70°
20°
46°
71°
46°
59°
10cm displ. contours
vertical
horizontal
Legend:
angle
of fracture
initiation
46°
75°
75°
66°
67°
90°
0°
MRV = 40798m3
AI = 0.61
MRV = 29594m3
AI = 0.95
MRV = 43319m3
AI = 0.70
MRV = 33922m3
AI = 0.88
45
207 204
255
331
100%
102% 125% 161%
0
50
100
150
200
250
300
350
0
50
100
150
200
250
300
350
To
tal exte
nt o
f 10cm
vert
ical
su
rface d
isp
lacem
en
ts
no
rmalized
b
y B
ase C
ase, %
To
tal e
xte
nt o
f 10cm
vert
ical
su
rface d
isp
lacem
en
ts,
m
BC F7 F2 F6
218 222
258
350
100%
102%
118% 161%
0
50
100
150
200
250
300
350
0
50
100
150
200
250
300
350
To
tal exte
nt o
f 10cm
vert
ical
su
rface d
isp
lacem
en
ts
no
rmalized
b
y B
ase C
ase, %
To
tal e
xte
nt o
f 10cm
ho
riz.
su
rface d
isp
lacem
en
ts,
m
BC F7 F2 F6
-112
95
-102
102
-160
95
-245
8691%
219%
100%
143%
107%
91%
100%
100%
-300 -200 -100 0 100 200 300
-250 -200 -150 -100 -50 0 50 100 150 200 250
Extent of 10cm surface vertical displacements in relation to block centre, normalized by Base Case, %
Extent of 10cm surface vertical dispacements in relation to block centre, m
BC
F7
F2
F6
BC
F7
F2
F6
-118
100
-102
120
-160
98
-245
105105%
208%
98%
136%
120%
86%
100%
100%
-300 -200 -100 0 100 200 300
-250 -200 -150 -100 -50 0 50 100 150 200 250
Extent of 10cm surface horizontal displacements in relation to block centre, normalized by Base Case, %
Extent of 10cm surface horizontal displacements in relation to block centre, m
BC
F7
F2
F6
BC
F7
F2
F6
Fig. 21 Subsidence characterization for BC, F2, F6 and F7 models Total extent of major (≥10cm) vertical (a) and horizontal (b) surface displacement in m and in % of Base Case value; extent of 10cm surface vertical (c) and horizontal (d) displacement in relation to centre axis of the block, in m
(a) (b)
(c) (d)
46
268254
269
100%
95%
100% 1
40%
0
50
100
150
200
250
300
350
0
50
100
150
200
250
300
350
To
tal e
xte
nt o
f 10cm
vert
ical
su
rface d
isp
lacem
en
ts
no
rmalized
by J
2, %
To
tal e
xte
nt o
f 10cm
vert
ical
su
rface d
isp
lacem
en
ts,
m
375
J2 F9 F4 F8
308 305
268
100%
99%
87% 125%
0
50
100
150
200
250
300
350
0
50
100
150
200
250
300
350
To
tal e
xte
nt o
f 10cm
vert
ical
su
rface d
isp
lacem
en
ts
no
rmalized
by J
2, %
To
tal e
xte
nt o
f 10cm
ho
riz.
su
rface d
isp
lacem
en
ts,
m
J2 F9 F4 F8
384
-161
107
-126
128
-161
108
-245
130151%
100%
126%
66%
149%
51%
100%
100%
-350 -250 -150 -50 50 150 250 350
-250 -200 -150 -100 -50 0 50 100 150 200 250
Extent of 10cm surface vertical displacements in relation to block centre, normalized by J2, %
Extent of 10cm surface vertical dispacements in relation to block centre, m
J2
F9
F4
F8
J2
F9
F4
F8
-245
105
-169
136
-160
108
-245
139132%
100%
103%
65%
130%
69%
100%
100%
-300 -200 -100 0 100 200 300
-250 -200 -150 -100 -50 0 50 100 150 200 250
Extent of 10cm surface horizontal displacements in relation to block centre, normalized by J2, %
Extent of 10cm surface horizontal displacements in relation to block centre, m
J2
F9
F4
F8
J2
F9
F4
F8
Fig. 22 Subsidence characterization for J2, F4, F8 and F9 models Total extent of major (≥10cm) vertical (a) and horizontal (b) surface displacement in m and in % of J2 value; extent of 10cm surface vertical (c) and horizontal (d) displacement in relation to centre axis of the block, in m
(a) (b)
(c) (d)
47
F6
F6
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
-300 -250 -200 -150 150 200 250 300
Vert
ical d
isp
lacem
en
ts,
m
Distance from block centre, m
-2
F2
-0.8-0.8
BC BC
F7 F7
F2
F2
F6 F6
F6
0
0.05
0.1
0.15
0.2
0.25
0.3
-300 -250 -200 -150 150 200 250 300
Ho
rizo
nta
l d
isp
lacem
en
ts, m
Distance from block centre, m
1.20.8 0.8
Fig. 23 Total vertical (a) and horizontal (b) surface displacement at the end of ore extraction at different distances from block centre for Base Case, F2, F6 and F7 models
J2
J2
F9 F4
F8
F8
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
-300 -250 -200 -150 150 200 250 300
Vert
ical d
isp
lacem
en
ts,
m
Distance from block centre, m
-0.4
J2
J2
J2
J2F9
F9
F9
F4
F4
F4F8
F8
F8
F8
0
0.05
0.1
0.15
0.2
0.25
0.3
-300 -250 -200 -150 150 200 250 300
Ho
rizo
nta
l d
isp
lacem
en
ts, m
Distance from block centre, m
0.450.8
Fig. 24 Total vertical (a) and horizontal (b) surface displacement at the end of ore extraction at different distances from block centre for J2, F4, F8 and F9 models
(a)
(b)
(a)
(b)
48
Fig. 25 Differential XY displacement for surface points on the fault hanging and foot walls for F2, F6 and F7 models