8/10/2019 (Phd Thesis) a Model for Cave Propagation and Subsidence Assessment in Jointed Rock Masses http://slidepdf.com/reader/full/phd-thesis-a-model-for-cave-propagation-and-subsidence-assessment-in-jointed 1/300 A MODEL FOR CAVE PROPAGATION AND SUBSIDENCE ASSESSMENT IN JOINTED ROCK MASSES Bre-Anne Sainsbury B.E. (Geological Engineering) Royal Melbourne Institute of Technology M.E. (Mining) The University of New South Wales A Thesis submitted to The University of New South Wales in fulfilment of the requirements for the degree Doctor of Philosophy August 2012
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(Phd Thesis) a Model for Cave Propagation and Subsidence Assessment in Jointed Rock Masses
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8/10/2019 (Phd Thesis) a Model for Cave Propagation and Subsidence Assessment in Jointed Rock Masses
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6.1 Rock Mass Density ..................... ..................... ....................... ...................... ...................... ............ 130
6.2 Rock Mass Dilation ....................... ...................... ....................... ........................ .................... ........ 132
Implementation of Non-Constant Dilation in the Cave Demonstration6.2.1
Model .........................................................................................................................................136
CASE STUDY VALIDATION: CAVING INDUCED FAILURE OF THE PALABORA11
OPEN PIT .................................................................................................................................................... 210
11.4 Production History ....................... ......................... ........................ ....................... .................... ..... 214
ixA Model for Cave Propagation and Subsidence Assessment in Jointed Rock Masses
Figure 18. Development of a discrete element model to study cave propagation
(a) particle clusters early in the caving process with superimposed
contact force chains (after Lorig et al., 1995). (b) particle clusters after
significant cave propagation showing internal fractures of blocks in the
caving zone chains (after Lorig et al., 1995). (c) forces arching around
the unstable rock mass (after Brown, 2003). .................................... ........................ . 32
Figure 19. Large-scale (mine-wide) discrete element modelling of caving and
subsidence phenomena in three-dimensions. Cross section of
subsidence mass movement from block caving and simulated synthetic
rock mass triaxial test of PFC material (after Gilbride et al., 2005). ................. 34
Figure 20. Large-scale discrete element modelling of caving and subsidence
phenomena in three-dimensions. (after Sharrock et al., 2011). ......................... 35
Figure 21. Three-dimensional strain-softening, continuum models for cave
propagation (a) logic sequence to simulate caving (b) typical
simulation results (after Pierce and Lorig, 1998). ........................... ....................... .. 37Figure 22. Simulation of production draw from large-scale, three-dimensional
strain-softening continuum models based on velocities. ........................ .............. 38
Figure 23. Large-scale back-analysis of cave propagation behaviour at the
Figure 26. Measured rock strength-scale effect including large size specimens of
in situ test (after Pratt et al., 1972). ................................................................................ 44Figure 27. Applicability of the Hoek-Brown empirical rock mass strength
criterion at different scales (after Li et al., 2008). ...................................... .............. 45
Figure 28. Development of equivalent Mohr-Coulomb property estimates from a
fit to the Hoek-Brown curve. ............................................................................................. 47
Figure 29. Idealised stress-strain curves representing different material
behaviour used in numerical modelling. ......................... ........................ ..................... 48
Figure 30. Stages of damage within a three-dimensional, strain-softening
Figure 31. Summary of FLAC 3D critical strain relation and data points used for
fitting. .......................................................................................................................................... 51Figure 32. Post-peak response as a function of zone resolution controlled by
Figure 34. Development of equivalent linear Mohr-Coulomb strength parameters
based on a fit to the Hoek-Brown strength envelope. ....................... ...................... 60
Figure 35. Schematic diagram of the mobilisation of the strength components
cohesion and friction (a) in the laboratory (b) around an underground
opening (after Hajiabdolmajid, Kaiser and Martin, 2002). ........................ ........... 61
Figure 36. Implementation of the CWFS model in a two-dimensional numericalmodel of a tunnel failure (after Barton and Pandey, 2011). ......................... ........ 62
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Figure 40. Three-dimensional response of a synthetic rock mass sample tested in
three-opposing directions under unconfined compression; (after
Sainsbury et al., 2009). ......................................................................................................... 70
Figure 41. Stress-path dependent Synthetic Rock Mass approach (a) stress path,
fitted peak-strength envelope (b) estimates of brittleness obtained
from SRM testing (after Pierce et al., 2006). ......................... ....................... ............. 72
Figure 42. Validation of Synthetic Rock Mass response based on observed and
measured fracture modes and fragmentation (after Pierce et al., 2006)........ 73
Figure 43. Development of a large-scale caving model using stress-path
dependent Synthetic Rock Mass strengths (after Mas Ivars et al., 2011). ...... 75Figure 44. Research methodology plan. ........................ ....................... ...................... ...................... 84
Figure 45. Development of a numerical demonstration model: geomechanical
Figure 47. Empirical estimates of rock mass caveability for four rock mass
domains simulated in the numerical demonstration model. ......................... ...... 88
Figure 48. Predicted cave propagation behaviour for variable peak strength rock
masses in the numerical demonstration model. .......................... ........................ ..... 89Figure 49. Simulated variable post-peak softening responses for the same peak
strength rock mass................................................................................................................. 91
Figure 50. Variation in cave propagation behaviour based on variable post-peak
softening rates simulated in the numerical cave propagation model. ............. 92
Figure 51. Hoek-Brown curves and equivalent bi-linear Mohr-Coulomb property
estimates for varying mi values........................................................................................ 93
Figure 52. Effect of estimates of mi on predicted cave propagation behaviour in
the numerical demonstration model. ........................... ..................... ........................ ..... 94
Figure 53. Cave propagation results for increasing stress /depth in the numerical
demonstration model. ....................... ...................... ....................... ....................... ............. 96Figure 54. Subiquitous constitutive model in FLA3D; assignment of matrix and
Figure 58. Examples of (a) poor (b) low and (c) good mesh resolution required
for large-scale analysis of cave propagation. ......................... ........................ ...........104Figure 59. Discontinuity shear strength in a triaxial cell (after Brady and Brown,
Figure 65. Calibrated UJRM: SRM results at 5 MPa confinement for each lithology
at Palabora in three testing directions. .......................................................................115Figure 66. UJRM UCS results for the carbonatite domain at Palabora compared to
SRM results at three different sample sizes in three loading directions. ...... 116
Figure 67. Calibrated stress-strain curves within PFC for three rock mass
Mas Ivars and Darcel, 2008). ......................................... ....................... ........................ ... 122Figure 71. Quantification of GSI chart (after Cai et al., 2007). ...................... ....................... ....123
Figure 72. Domain 1 SRM test results and UJRM response represented in FLAC 3D :
1 MPa triaxial tests (after Sainsbury, Mas Ivars and Darcel, 2008). ............... 124
Figure 73. Domain 2 SRM test results and UJRM response represented in FLAC 3D :
1 MPa triaxial tests (after Sainsbury, Mas Ivars and Darcel, 2008). ............... 125
Figure 74. Domain 3 SRM test results and UJRM response represented in FLAC 3D: 1
MPa triaxial tests (after Sainsbury, Mas Ivars and Darcel, 2008). ................... 125
Figure 75. Cave propagation behaviour for varying joint orientations simulated in
the numerical demonstration model. ........................... ...................... ....................... ... 127
Figure 76. Simulated porosity profile during propagation of a block cave. ....................... 130Figure 77. Conceptual diagram of dilation associated with sliding along micro-
cracks and particles (after Zhao and Cai, 2010). ........................... ....................... ... 132
Figure 78. Typical stress-strain curve for uniaxial compression of brittle,
crystalline rock (after Rudnicki and Rice, 1975)....................... ....................... ....... 132
Figure 79. Evolution of peak dilation estimate on a rock mass during cave
propagation using the Alejano and Alonso relation. ....................... .......................136
Figure 80. Implementation of a non-constant dilation relation and its impact on
cave propagation behaviour in the numerical demonstration model
compared to the simulation of a constant dilation angle.......................... ........... 137
Figure 81. Schematic linear relationship for rock mass deformation modulusreduction based on Pierce et al. (2006) relation. ......................... ....................... ....139
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Figure 89. Terminology used to describe subsidence features for block- and
panel-cave mines (modified after van As et al., 2003). ......................... ................ 148
Figure 90. Conceptual model of the development of block caving subsidence
(after Sainsbury and Lorig, 2005). ........................... ...................... ....................... ........ 151
Figure 91. Conceptual model of chimney cave development (Betourney et al.,
1994), b) surface expression of a chimney pipe in a kimberlite caving
operation (after van As et al., 2003). ......................... ........................ ....................... .... 152
Figure 92. Plug subsidence mechanism at the Athens Mine in Michigan USA (after
Obert and Duvall, 1967). ...................................................................................................153Figure 93. Geometry of Lift 1 cave a) before and b) after plug caving (after Pierce,
Figure 97. Simplified subsurface erosion mechanism (after Van der Merwe 1999). .... 159
Figure 98. Photos of subsurface erosion pot holes (after Van der Merwe, 1999)........... 160Figure 99. Photo of sinkhole located outside the limit of large-scale cracking at
the abandoned Grace Mine (after Sainsbury and Lorig, 2005). ........................ 160
Figure 100. Schematic diagram of how crater shape can be modified by major
geological structure (after Stacey and Swart, 2001). ........................................ .... 162
Figure 101. Conceptual development of surface subsidence at the San Manuel Mine
Figure 103. Photos showing cave propagation controlled by weak vertical fault at
the Ridgeway Mine (Brunton, 2009). ......................... ....................... ........................ ... 166Figure 104. Photo of Goathill Crater at the Questa Mine (after Gilbride et al., 2005). ..... 167
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Figure 111. Simulated direct shear test; normal stress 10 MPa using ubiquitous
joints in FLAC 3D. ...................................................................................................................... 174Figure 112. Ubiquitous joint faults used to simulate faults within a cave-scale
Figure 114. Schematic diagram showing interface logic and how it can be used to
represent a discontinuity in a numerical model of caving. .................................177
Figure 115. Cross-section of mobilised zone (2m displacement) – explicit, interface
approach used to simulate conceptual discontinuity surfaces......................... . 179
Figure 116. Plan view of subsidence limits at the Grace Mine determined byobservations. .......................................................................................................................... 182
Figure 117. Effect of draw strategy on the caveability of a rock mass in the
Figure 121. Identification of perimeter gridpoints for production draw simulationin a numerical mesh. .......................................... ........................ ....................... .................. 189
Figure 122. Simulated large-scale laboratory tests at different applied loading
velocities and the impact on the sample strength response. ............................. 190
Figure 123. Impact of selection of draw velocity on cave propagation behaviour in
the numerical demonstration model. ........................... ..................... ........................ ... 191
Figure 124. Schematic diagram of the mass-based production draw algorithm
Figure 140. Estimated in situ stress orientation and magnitude at Palabora based
on back-analysis of pit slope failure and stress measurement testing. ......... 213Figure 141. Historical mining record at the Palabora block cave mine. ....................... ......... 214
Figure 142. Observed seismicity at the Palabora Mine during cave initiation and
Figure 146. (a) Cave profiles at the Palabora Mine; April 2002 to December 2003
(after Glazer, 2006) compared to the simulated cave profile (b). .................... 219
Figure 147. Numerical simulation – north wall failure during Q4 2004. ........................ ...... 220Figure 148. North wall failure: observed versus simulated limits. ................... ...................... . 221
Figure 149. Development of the pit slope failure mechanism at the Palabora Mine
at various stages of production. .............................. ....................... ........................ ........ 222
Figure 150. Development of the Palabora block cave between 2003 and 2004 in
relation to fault structure. .................................................................................................223
Figure 151. Cross section of the Henderson Mine (after Rech, 2001). ..................... .............. 225
Figure 152. Geological domains at the Henderson Mine a) plan view of weak
contact; b) 7210 Level yield zone during December 2007. ...................... .......... 226
Figure 153. Development of the numerical model of the Henderson Mine a)
regional extents of model; b) existing cave volumes. ................... ........................ . 227Figure 154. Interface used to simulate the weak Seriate contact at the Henderson
xviiA Model for Cave Propagation and Subsidence Assessment in Jointed Rock Masses
TABLE OF TABLES
Table 1. Documented yield zone propagation rates from caving operations
around the world (after Sainsbury and Sainsbury, 2010). ................................... 17Table 2. Cave height as a function of brittleness (after Lorig, 2000). ......................... ....... 54
Table 3. Estimate of Hoek-Brown and equivalent Mohr-Coulomb rock mass
strength properties for four simulated domains in the numerical
Table 4. Mean target intact rock block properties for the lithology at Palabora. ....... 109
Table 5. Measured joint frequencies and persistence from mapping at Palabora
(after Mas Ivars et al., 2008) ....................... ....................... ........................ ...................... 109
Table 6. Estimated joint properties for the rock mass domains at Palabora
(after Mas Ivars et al., 2008). ............................ ..................... ........................ .................. 112
Table 7. SRM-derived strengths for the rock mass domains at Palabora - triaxial5-MPa confinement (after Mas Ivars et al., 2008)...................................................112
Table 8. Calibrated UJRM properties for the rock mass domains at Palabora. ............ 114
Table 9. Summary of laboratory test results for three rock mass domains. ................. 118
Table 10. Calibrated PFC micro-properties for three rock mass domains (after
Sainsbury, Mas Ivars and Darcel, 2008). ...................... ........................ .......................120
Table 11. Calibrated intact foliation strength properties in PFC 3D (after
Sainsbury, Mas Ivars and Darcel, 2008). ....................... ....................... ....................... 120
Table 12. Estimated open joint strength properties for simulation of joints in
SRM sample (after Sainsbury, Mas Ivars and Darcel, 2008). .......................... .... 121
Table 13. Calibrated continuum material properties for seven rock massdomains. ................................................................................................................................... 124
Table 14. Dilation angle in large-scale triaxial tests on rock fill material (after
Marachi et al., 1972) ......................... ....................... ....................... ........................ ............. 134
Table 15. Summary of terminology used to define discontinuous subsidence
(after Flores and Karzolovic, 2004). .......................... ..................... ....................... ....... 147
Table 16. Observed residual subsidence duration over longwall mines (after
Table 17. Conceptual fault shear strength and stiffness parameters represented
in numerical demonstration model. ....................... ........................ ....................... ....... 173
Table 18. Example of gridpoint velocity scaling based on variable productiondraw. ..........................................................................................................................................190
Table 19. Rock mass properties used for the representation of the granite
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INTRODUCTION1
1.1 Cave Mining Method
Caving is a mass mining method, capable of high and sustained production rates
and is relatively low cost per tonne when compared to other mining methods. In
general, a uniform grade distribution and rock mass strength is required to assure
that the maximum potential of a deposit is achieved (Brady and Brown, 2006).
Presently, there are approximately twenty operating cave mines around the world
and many more in the planning stage. Figure 1 provides the locations of the most
notable caving mines that have been, or are currently in operation.
Figure 1. Location of some historical and currently operating caving mines around theworld.
The caving process involves undercutting (blasting a horizon of in situ rock mass)
and extraction of the broken rock from drawpoints on a production horizonlocated at depth. When the plan area of the undercut footprint/active area reaches
a large enough dimension a self-sustained propagating cave will develop so long as
the ore is continued to be withdrawn. This is generally described as the critical
Hydraulic Radius (HR) which can be calculated through the ratio of the
undercut/active footprint area (m2) to the cumulative undercut/active footprint
perimeter length (m).
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Cave mines require extensive infrastructure to be in place prior to any production.
Infrastructure usually includes access through a decline or shaft to an undercut
level and an extraction level that is located approximately 15-20 m below that.
Extraction level infrastructure must be designed to be stable throughout the life of
mine, often without previous experience of the large-scale rock mass response.
The three-dimensional nature of typical extraction level geometries, together with
the complex stress-redistribution around a propagating cave make completing an
accurate assessment of cave propagation and subsidence behaviour difficult. A
schematic diagram of a typical block cave mine layout is provided in Figure 2.
Figure 2. Schematic representation of a typical block cave mine (modified after AtlasCopco, 2011).
There are three variations to the cave mining method that include block, panel and
sub-level caving. In block and panel caving operations, the ore is withdrawn from a
single mining horizon (extraction level). The transition of the ore from an in situ
rock mass to a fully fragmented cave material is achieved without drilling and
blasting after the initial undercut development. The fragmentation of the rockmass is controlled by natural processes that include the in situ fracturing of the
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Laubscher 1987, Laubscher 1990, 1994, 2000) that are further discussed in
Section 2.1.2. In the case of South African diamond mining, effective caving is
enabled without dilution problems by the contrast in strength between the weak
kimberlitic diamond pipe and the comparatively strong host rock mass.
As a result of the continued success of the cave mining method in coal, iron ore and
kimberlite operations and in a number of strong, (UCS, greater than 80 MPa and
GSI, greater than 50) jointed rock masses (e.g. Urad Mine, Colorado, USA; 1914-
1960; Philex Padcal Mine, Philippines, 1959-current and El Teniente, Chile,
1920’s-current), during the mid-1990’s a caving mine was planned at Rio Tinto’s
Northparkes E26 Lift 1 Orebody. Feasibility studies for the mine were carried outusing Laubscher’s empirically derived caveability chart and the orebody was
predicted to fall well within the Caving Zone (Ross and van As, 2005). Production
from the block cave commenced in 1996 and cave initiation followed. However,
once the undercut development was completed, the cave stalled at a height of 95
m. Figure 3 provides a chart showing the initial estimate of caveability at the E26
5A Model for Cave Propagation and Subsidence Assessment in Jointed Rock Masses
Increased production rates failed to induce further caving of the orebody and an
air-gap developed. In order to stimulate cave growth, a hydraulic fracturing
campaign was conducted. Boundary weakening (blasting a sub-vertical slot on the
south-western boundary of the cave) methods were also employed. After a
significant amount of effort over a two year period, caving once again
recommenced. However, on Wednesday, 24th November, 1999, the cave back
advanced rapidly through to the ground surface and generated a wind-blast
through the underground workings. Four workers were killed. It is estimated that
a total amount of 13 MTonnes of material came down in this collapse - a column
height of 200 m. At the time of the accident, the air-gap was in excess of 180 m
(Ross and van As, 2005).
As a result of the unexpected stall and then rapid failure and air-blast at the
Northparkes E26 Lift 1 Mine, the International Caving Study (ICS 1997-2004) and
Mass Mining Technology (MMT I 2005-2008 and MMT II 2009-2012) projects
were initiated. These industry funded research projects have made significant
contributions to the advance of rock mechanics understanding associated with
cave mining methods in hard, jointed rock masses. The following section providesa review of the current state-of-the-art engineering for cave propagation and
subsidence assessment in hard, jointed rock masses.
1.3 Caving Mechanics
It is commonly understood that all rock masses must cave if they are undercut over
a significant enough area. Caving can occur as a result of two influences – gravity
and stress. The mechanism of caving will depend on the relationship between
induced stresses, geometry of the cave footprint, strength of the rock mass and
joint fabric (Brown, 2003).
Stress caving occurs when the induced stresses in the cave back exceed the
strength of the rock mass causing yielding and fragmentation of the rock mass into
a caved rock state. Gravity caving is characterised by low mining induced stresses
and is often analysed by knowledge of the joint fabric and simple kinematics.
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Gravity induced unravelling can be expected to occur in the cave back (roof) as a
tensile failure mechanism under low stress conditions. Failure can occur through
slip along pre-existing joints as the rock is unconfined from below, or through
bending/deflection of the rock layers (voussoir beam theory). Gravity caving
usually results in coarser drawpoint fragmentation since little damage is induced
to the rock mass during its mobilisation. Primary fragmentation in this case, is
usually close to the in situ block size. Example stress-paths for both stress and
gravity caving mechanisms are presented in Figure 4. The disintegration and
mobilisation of a rock mass resulting from yield in the compressive regime is
called stress caving. In the tensile regime, it is gravity caving.
Figure 4. Typical caving stress-paths representing stress and gravity cavingmechanisms.
Self-sustained propagation of the cave stalls when a stable arch develops in the
advancing back. In this case, the induced stresses do not exceed the strength of the
intact rock bridges and/or is unable to induce failure along pre-existing joints.Time-dependent processes (i.e., stress corrosion, ground water etc.) may
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Mobilised Zone – This zone gives an estimate of portion of the orebody
that has moved in response to the production draw and may be
recoverable. Although the specific location of the cave back is difficult to
predict precisely, it is estimated to be rock that has experienced a
displacement greater than or equal to 1-2 m (after Pierce et al., 2006). The
reduction in rock block size (compared to the primary fragmentation state)
is described as secondary fragmentation. Secondary fragmentation is
affected by draw height and internal caving stresses (Laubscher, 1994).
Cave propagation behaviour and subsidence are closely linked geomechanical
processes. The surface projection of a cave after break-through can be describedby similar terminology as the underground regions. A conceptual schematic model
of the surface subsidence domains compared to the underground cave domains are
presented in Figure 7.
Figure 7. Conceptual schematic diagram showing the main behavioural regions of acave that has propagated through to the ground surface.
The characteristics of each region are described below.
A crater is a common surface feature of many caving mines; it also is
referred to as the zone of active movement (van As et al., 2003). The crater
consists of irregular blocks of rock, ranging in size from millimetres to
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Through a number of recent published case studies, these assumptions have been
shown to be incorrect. At the Ridgeway Deeps Mine in NSW, Australia, Beck et al.
(2011) documented a scenario in which cave initiation did not occur in a portion of
the undercut footprint. Carlson and Golden Jr. (2008) describe a situation at the
Henderson Mine in which migration of the propagating cave beyond the undercut
footprint was observed along a weak intrusive contact. And, at Northparkes Lift 1
Mine, Ross and van As (2005) have described in detail the highly variable caving
rate during cave initiation, propagation, stalling and rapid plug failure at this
operation.
The documentation of cave propagation rates at numerous operating minesaround the world also shows significant variability. The propagation rate has been
assessed by the ratio of the yield zone height to the average production draw
height measured in solid rock drawn. A summary is provided in Table 1.
Documented yield zone propagation rates from caving operations around theTable 1.world (after Sainsbury and Sainsbury, 2010).
Yield
PropagationOperation Method Rate Reference
El Teniente, Chile Panel 5: 1 Villegas (2008)
Henderson Mine, Colorado, USA Panel 7: 1 Board et al. (2009)
Grace Mine, Pennsylvania, USA Panel 8.2: 1 Sainsbury et al. (2005)Australian Coal Mine Longwall 8.9: 1 Hebblewhite (1995)
DOZ Mine, Indonesia Block 6-10: 1 Szwedzicki et al. (2006)
Kimberley Mines, South Africa Block 6 - 12: 1 Guest (2009)Lakeshore Mine, Arizona, USA Block 10: 1 Panek (1984)
Questa Mine, New Mexico, USA Block 10: 1 Gilbride et al. (2005)
San Manuel Mine, Arizona, USA Panel 10: 1 Gilbride et al. (2005)
Athens Mine, Michigan, USA Block 14: 1 Boyum (1961)
Palabora Mine, South Africa Block 15: 1 Sainsbury et al. (2008)
Northparkes Lift 2, Australia Block 20: 1 Pierce et al. (2006)Chinese Coal Mine Longwall 31.3: 1 Liu (1981)
Caving rates in the order of 5:1 up to 31:1 have previously been documented. This
variability can be attributed to variations in the in situ geomechanical conditions
and cave mining method. Based on the values presented in Table 1 it can be seen
that a longwall mining method provides the greatest documented propagation
rate, followed by block caving and then panel caving methods. The ability to
predict and represent this variation in propagation rates between caving methods
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Figure 10. Empirical method for predicting caveability: Extended Mathews StabilityChart (after Trueman and Mawdesley, 2003).
Although the development of this method extended the application of the existingempirical approach to stronger rock masses, by necessity, the method is still
limited by the dataset that it was developed from. Additional limitations of
Laubscher’s and Trueman and Mawdesley’s empirical approaches have previously
been documented by Brown (2003) and suggest that the approaches are only
satisfactory for footprint length to width ratios of three or less. Beyond this, the
technique is unable to account for variations in three-dimensional stress
redistribution around rectangular undercut footprints. In addition the influence ofonly one joint set orientation can be analysed. Experience suggests that the critical
joint set orientation may vary around the undercut footprint as the principal stress
direction changes during undercutting and cave propagation. Milne et al. (1998)
also suggest that the determination of adjustment factors can be ambiguous and
subject to personal experience. This means, for the same rock mass data set,
different caving behaviour may be interpreted.
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2.1.3.1 Two-Dimensiona l Elasti c Models
Soon after the introduction of the Finite Element Method (FEM) for the numerical
analysis of stresses and displacements in continuous structures by Clough (1960),
Palma and Agarwal (1973) developed the first known two-dimensional, elastic,
finite element model to study cave propagation behaviour at the El Teniente Mine
in Chile. During this study, they identified the need to consider the nature of the in
situ rock mass fracture network and the impact of principal stress direction in
relation to the undercut dimensions on the cave propagation behaviour.
The high level of fracturing in the El Teniente rock mass was represented by
assigning zero tensile strength to all zones within the model. Although not many
details of the modelling methodology are provided, it is clear that yielding of the
rock mass immediately above the simulated undercut was assumed to propagate
when a tensile stress component was identified within a zone. Figure 11 presents
the results that clearly show the simulated impact of cave height based on in situ
stress and orientation of the undercut footprint.
Figure 11. Impact of principal stress orientation in relation to an undercut as definedby two-dimensional numerical modelling (after Palma and Agarwal 1973).
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could deform and become stressed infinitely without failing. This basic assumption
may be appropriate for some mining methods in very strong, massive rocks but
can lead to highly misleading results in weaker rock masses when there is the
potential for shear failure of the rock mass and redistribution of stresses.
2.1.3.2 Two-Dimensional Plasticity Models
Through the application of two-dimensional FEM simulations at the Grace Mine,
located in Pennsylvania, USA, Barla et al. (1980) introduced a softening material
model to represent the degradation of the in situ rock mass strength to a fully
weakened and bulked state during cave propagation. The use of such a material
model highlighted the limitations of elastic modelling completed by Palma and
Agarwal (1973) and the development in understanding that caving may not only
occur due to a gravity mechanism, but also a stress mechanism – as discussed in
Section 1.3.
The softening behaviour in the model was simulated through a periodic review of
the failure states in the numerical mesh. If a zone failed via a compressional or
tensile mechanism, then the strength, density and stiffness were reduced to a
residual value. Production draw was simulated through a force application in the
undercut roof. Figure 13 provides a schematic representation of their modelling
methodology.
The simulations conducted by Barla et al. (1980) do not only account for a
softening material model, but also represent the changes in deformation modulus
and density during cave propagation. In addition, they identified the importance
in being able to accurately represent the mining process within the numericalmodel in order to predict the most realistic rock mass response. However no
correlation was made regarding the amount of material withdrawn.
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Figure 13. Development of two-dimensional numerical modelling approaches for cave propagation analysis. (a) Model mesh (b) section through the mining geometry (c) simulated undercutting process (d) contours of resultantmobilised strength – the shaded area represents a fully softened/caved rockmass (after Barla et al., 1980).
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During the early 1990’s, Rech and Lorig (1992) conducted two-dimensional, finite
difference analyses in order to reproduce the existing cave conditions at the
Henderson Mine in Colorado, USA and predict the expected cave propagation
behaviour. These are the first simulations that attempted to correlate the
production schedule with the simulated cave propagation behaviour.
The cave zone was initialised within the model through a number of incremental
undercut expansions that corresponded to the historical and planned production
schedule. Vertical draw and a bulking factor were assumed based on the
volumetric equations outlined by Panek (1984). Stresses were reset to zero within
the cave mass and the rock mass properties were reduced to those consistent witha fully-bulked rock mass. Simulation of residual rock mass properties and reduced
vertical stress conditions within the caved mass ensured that the mining induced
stress magnitude and directions were accurately captured. However, by manually
initialising the caved rock mass within the model, a true and spontaneous cave
initiation could not be predicted. In addition, by artificially reducing stresses
within the cave, mass and energy were not conserved within the system. As a
result of this, the representation of the exact production tonnage simulated withinthe model could not be gauged and the real caving induced stress-damage may
have been under-estimated.
The algorithm used by Rech and Lorig to model the undercutting and mining
advance sequence is provided in Figure 14.
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Figure 15. Determination of the Cave Propagation Factor at Northparkes E26 Lift
1 (after Karzulovic and Flores 2003). Here a 480 m block height, and arock mass of fair to good geotechnical quality, (HC = 480 m, B = 180 m,K = 1.50) has been assessed. The chart indicates that the caving will not
propagate through the 480 m block.
Based upon stress redistribution around an imposed cave shape, a Cave
Propagation Factor (CPF) was used to determine if caving is ‘Problematic’,
‘Transitional’ or ‘Self-Sustained’ - much like Laubscher’s ‘Caving’, ‘Transitional’ and
‘Stable’ Zones. The CPF has been defined by Karzulovic and Flores as the ratio
between the average deviatoric stress acting on the cave back and the maximum
deviatoric stress that the rock mass can sustain. The equations used to determine
the value are presented in Figure 15.
Although simple assumptions were used in the representation of geometry, stress
redistribution (two-dimensional), rock mass plasticity and post-peak rock mass
behaviour, assessment of the CPF at the Northparkes Lift 1 Mine provided good
correlation with the actual performance of the cave that stalled in 1999 – as shown
in Figure 15b.
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However, the methodology is unable to account for the time-dependent nature of
the stable arch that developed at Northparkes Lift 1 and the subsequent plug-
failure. Limitations associated with the two-dimensional nature of the modelling
and the assumptions regarding cave shape and the propagation window (defined
by W=0.1B in Figure 15a) also make it difficult for the technique to accurately
predict three-dimensional, self-sustained cave propagation, and the cave
behavioural regions presented in Figure 6. In addition, only vertical cave
propagation and homogeneous rock mass properties can be considered which
limits its applicability.
2.1.3.3
Axis-Symmetr ic Str ai n-softenin g Models
In an attempt to include a better representation of the three-dimensional shape of
the propagating cave and surrounding induced stress field, Lorig (2000) (also
reported in Brown 2003) conducted sensitivity simulations in axis-symmetric
models. A cylindrical undercut located at increasing depths was considered. The
initial state of stress within the model was assumed to be lithostatic and stress
boundaries (a support pressure) were imposed at the excavated undercut level to
ensure initial stability. To simulate production draw, the support pressure wasmonotonically reduced in the roof of the undercut (similar to the approach of Barla
and Boshcov, 1980) and the extension of the yielded rock mass (represented by a
strain-softening material model) was assessed.
A schematic representation of the modelling methodology used to simulate
production draw from these axis-symmetric models is provided in Figure 16.
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Figure 16. Development of axis-symmetric numerical methods for cave propagation (a)axis-symmetric concept (b) evolution of the undercut pressure and height (c)
stepwise reduction of undercut pressure (d) details of the pressure evolutionwith a simulated reduction step (after Brown, 2003).
Through this approach, even though the true three-dimensional geometry and
stress tensor were not accurately represented, Lorig (2000) was able to predict a
hydraulic radius associated with cave initiation that compared well to Laubscher’s
empirical cave stability chart over a range of MRMR values. This technique is
considered to be an advancement on the CPF method proposed by Karzulovic and
Flores (2003) since failure was not limited to a window of rock mass in the cave
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back (dictated by the undercut width), but allowed to evolve based on the rock
mass properties and stress state in the model.
Using this axis-symmetric approach, Lorig completed an analysis of theNorthparkes Lift 1 cave using the same parameters as Karzulovic and Flores
(2003). The displacement vector (a) and cohesion (b) results are illustrated in
Figure 17.
Figure 17. Development of cave geometry resulting from a two dimensional strain- softening numerical simulation, hydraulic radius 42.5m (a) displacementvectors (b) cohesion softening ; green represents no softening, red represents
fully softened rock mass(after Lorig, 2000).
For an incrementally expanding undercut size, the resulting cave yield height was
assessed in the numerical model. A hydraulic radius of 42.5 m was required to
reproduce the observed stalled yield zone height at Northparkes of 95 m. This is
consistent with the documented stalled undercut geometry by Ross and van As
(2005). However, although the cave yield height was reproduced, it is clear that the
shape of the yielded rock mass volume is not necessarily realistic when the results
are compared to the conceptual model of a cave. It is simulated with a flat back.
The modelling results of Lorig showed that a strain-softening model could be used
with confidence to predict rock mass damage and cave propagation. However, a
model that was able to simulate the failure mechanisms in the back of the cave in
more detail was required to ensure the flat back shape was addressed.
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2.1.3.4 Two-Dimensional Disti nct Element Models
Two dimensional, Distinct Element Models (DEM) were developed by Lorig et al.
(1995) within the PFC 2D code (Itasca, 1995) to provide a greater understanding of
the fracturing of the in situ rock mass and an improved cave back shape based on
the models shown in Figure 17. Conceptual models of cave propagation behaviour
in a high initial stress state were developed and two fundamental failure
mechanisms associated with cave propagation were identified that included; intact
rock block failure and slip along pre-existing joints. The model results are
presented in Figure 18a and Figure 18b. Brown (2003) reports on the extension of
the two-dimensional DEM simulations to three-dimensional axis-symmetric
models which are presented in Figure 18c.
Figure 18. Development of a discrete element model to study cave propagation (a) particle clusters early in the caving process with superimposed contact forcechains (after Lorig et al., 1995). (b) particle clusters after significant cave
propagation showing internal fractures of blocks in the caving zone chains(after Lorig et al., 1995). (c) forces arching around the unstable rock mass(after Brown, 2003).
Within these models, each intact rock block is represented by particles that are
glued together. Upon initiation of the undercut, the bonds between the particles
are broken if the induced force is greater than the bond strength (stress caving).
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Figure 19. Large-scale (mine-wide) discrete element modelling of caving and subsidence phenomena in three-dimensions. Cross section of subsidence mass movement from block caving and simulated synthetic rock mass triaxial test of PFC
material (after Gilbride et al., 2005).
Since there is no comparison between actual field data, or presentation of the data
used for the calibration, it is difficult to determine the accuracy of the model
results.
Sharrock et al. (2011) calibrated a response through large-scale observations of
surface subsidence, as presented in Figure 20.
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Figure 20. Large-scale (mine-wide) discrete element modelling of caving and subsidence phenomena in three-dimensions. Plan view cave zones: measured (blue) andsimulated (red) (after Sharrock et al., 2011).
In this case, there is significant difference between the model result and the
subsidence observations on the eastern limits of the crater.
It seems in each case, computational inefficiency of the DEM technique, has limited
the particle size within the models to 13-24 m, and thus restricted the size of the
physical phenomena that can be resolved. As a result of this, the small-scale
cracking / dislocation of the rock mass achieved by Lorig et al. (1995) was unableto be reproduced with such a large-scale model due to the minimum particle size
required to achieve this scale of model.
As shown by Gilbride et al. (2005) and Sharrock et al. (2011), at present, it is not
practical to simulate the complex large-scale mining/geological processes in DEM
codes due to the computational intensity of the numerical technique. It seems at
the current time, computational constraints continue to limit application of DEM
simulations to small-scale (e.g. <100 m) boundary value problems in densely
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jointed rock. As a result of this, continuum methods continue to be used to ensure
that the regional mine scale changes can be captured in the one model.
2.1.3.6
Thr ee-Dim ensional Conti nuum Methods
Based on computational limitations of simulating the large-scale caving process in
DEM codes, Pierce & Lorig (1998) describe an improved methodology developed
in a three-dimensional continuum code compared to the axis-symmetric approach
reported by Brown (2003). In this model, sequential undercuts of constant width
were simulated to reproduce the increasing undercut hydraulic radius during cave
initiation. Production draw was simulated by monotonically reducing stresses at
the undercut level using the same methodology presented in Figure 16. For each
undercut increment, the model was stepped to equilibrium before subsequent
undercut expansions were simulated. In addition to the dynamic nature of the
undercut expansion, Pierce & Lorig implemented a user-defined function that
modified material properties and stresses based on plasticity state and strain
within the numerical model. Through this approach, the point at which self-
sustained propagation (the critical HR) could be determined based on the actual
three-dimensional stresses distributing around the undercut. A diagram thatrepresents the modelling methodology is provided in Figure 21a along with typical
model results (Figure 21b). It can be seen that the modelling methodology
generally still results in a flat cave back - Figure 21B-7.
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The numerical model was able to accurately predict the rate and shape of the
mobilised and yielded rock mass zones through a large-scale application.
Similar to this approach, Beck et al. (2007) developed a methodology for theassessment of cave propagation behaviour using the numerical modelling package
ABAQUS (Simulia, 2011). An example of some of the results from one of these
models is provided in Figure 24.
Figure 24. Example of a mine-wide, three-dimensional, multi-scale simulation (afterBeck et al., 2011).
An attempt was made to review the caving approach that has been developed in
Abaqus based on a number of publications (Beck et al., 2006; Beck et al., 2011).
However, at the present time there are insufficient details provided in these (and
associated) publications to allow for a detailed critical review. As a result of this, it
was not possible to comment on the appropriateness of the underlying
methodology, constitutive behaviours and associated assumptions for simulating
caving using Abaqus.
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failure criterion to determine the initiation of new cracks within the continuum
mesh.
In addition, the hybrid finite element / distinct element modelling methodology iscurrently limited to two-dimensions. Numerical modelling conducted by Palma
and Argawal (1973) have already shown that cave propagation is a three-
dimensional problem. The two-dimensional plane strain nature of the ELFEN
model, and the over simplified production draw simulation routine (i.e., uniform
draw over the entire footprint) can over-estimate the influence of major structures
and is not well suited to studying the potential for cave propagation to stall, as it
does not allow for the three-dimensional concentration of stresses in the caveback. Significant research has been conducted that demonstrates that a three-
dimensional analysis is required to accurately account for the influence of the
major principal stress orientation, undercut advance orientation, (Palma an
Agarwal, 1973) and three-dimensional structure (faults and joints) orientation and
persistence during cave propagation (Phillips and Hellewell, 1994).
Although many conceptual block cave models have been documented (Rogers et
al., 2010; Pine et al., 2007 and Vyazmensky et al., 2007) this approach has not
been validated against observed behaviour at an existing mine.
Summary2.1.4
The understanding of failure and deformation of jointed rock masses surrounding
underground and surface excavations has been a problem for centuries. However,
it was only during the 1970’s and 80’s and the rapid development of computer
technology that enabled numerical methods in rock mechanics to explore these
issues.
As a result of the low cost nature of the cave mining method, very large caving
operations are currently being planned around the world and the empirical caving
design methods which have long served the industry are no longer adequate for
the assessment of complex rock failure and deformation processes expected at
these locations. In addition, these empirical techniques do not satisfy the
increasingly stringent risk-based criteria for approving the large capital
expenditure in caving mines prior to production.
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Linear Elastic-Perfectly Plastic - An assumption is made by an elastic-perfectly
plastic relationship that the stress - strain response can be represented by two
straight lines that describe an initial linear elastic stiffness and the yield stress or
strength at failure during plastic straining. Rock behaves elastically for stresses
less than the yield stress, then deforms without limit at the yield stress. A rock that
exhibits such a response can be considered perfectly ductile.
Perfectly Brittle - Rock that exhibit a stress-strain response similar to Figure 29E
are called perfectly brittle materials. For a brittle rock, the stress strain curve is
nearly linear at all stress levels, up to and including the final fracture stress. Brittle
failure is the process by which sudden loss in strength occurs. During brittlefailure the strength of the rock mass reduces to a residual value instantaneously.
Strain-softening - When stress has exceeded the elastic limit, the rock mass
begins to yield. It continues to yield until the peak strength is reached before
reducing to a residual value.
Strain-softening behaviour best describes a rock mass response during caving
since it is able to represent the progressive nature of the strength reduction. A
strain-softening model has previously been used by Pierce et al. (2006) to simulate
the complex process of the progressive failure and disintegration of a rock mass
from an intact, jointed material to a bulked rock mass during the caving process.
An example of simulated strain-softening behaviour in is provided in Figure 30. In
this instance, both the intact and joint response is considered during simulated
sample straining.
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values ranging from 0 to 98. The value may be scaled with respect to edge length
by Equation [3].
[3]
Where z is the element width or edge length of zone in model.
The values derived from this relation are consistent with the typical stress-
strain relations provided by Hoek and Brown (1997) for strain-softening rock
masses which show that rock masses with higher GSI values are more brittle than
rock masses with a lower GSI.
Since the development of the relation by Cundall et al. (2005), additional case
studies have been completed as part of this research (presented in Sections 11, 12,
13 and 14) and are provided as the red data points in Figure 31. A new linear
relation [4] is proposed to determine a value that fits the combined datasets
and is valid for all GSI values from 0 to 100.
[4]
In the case of caving, softening of the tension and cohesion at this rate should be
applied to ensure the rock mass in its post-peak state is represented with the
greatest accuracy.
2.2.2.3 Mesh Dependency
Trueman and Mawdesley (2003) suggest that numerical methods that use a strain-
softening approach are not robust since the post-peak response is highly sensitiveto mesh size. This is true, if mesh dependency is not accounted for in the
development of material property responses.
There are at least two methods that can be used to alleviate the problem of mesh
dependency as outlined by Dawson and Cundall (1995). They include Cosserat
Theory and the Standard Regularisation Method.
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Where s is the softening slope, is the change in material property value and
is the change in displacement.
In order to obtain mesh-independent results, a scaled softening slope can be inputsuch that the slope is dependent on the element width as shown in Equation [7].
[7]
Where is constant and relates to Equation [4] and, in the case is
independent of and can be re-written as Equation [8].
[8]
Using this relationship, for example, if the zone size is doubled, then the critical
strain must be halved for comparable results.
Through this approach Lorig (2000) showed that cave simulation results are
repeatable with different sized meshes. His results are provided in Table 2.
Cave height as a function of brittleness (after Lorig, 2000).Table 2.
Critical Plastic Strain Cave Height
Grid ( ps
crit
ps
crit) (m)
Coarse 0.1 160
Fine 0.02 150Coarse 0.005 200
Fine 0.01 205
Coarse 0.0025 225
Fine 0.005 250
This scaling approach has also been used by other researchers to account for mesh
dependency in the numerical simulation of other geomechanical processes (Crook
et al., 2003).
Scale-Dependent Brittleness2.2.2.3.3
It can be shown that for the same numerical zone size, increasing the size of a test
sample will result in a more brittle post-peak response. This is shown in Figure 32
where Unconfined Compressive Strength (UCS) testing has been conducted on a
strain-softening material. The zone size and critical strain have remained
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Localisation and Bifurcation2.2.2.3.4
Zones of localised deformation (shear bands) are a common feature of brittle
jointed rock masses that have failed in compression, both in the laboratory and
naturally as earth faults (Rudnicki and Rice, 1975).
Localisation refers to the “occurrence of strong strain gradients in specific areas of a
material that finally become discontinuities” (Varas et al., 2005). The possibility of
localisation occurs when one or more stress components in an element are able to
decrease with increasing strain. Cundall (1991) suggests that there are three
possible ways that stress in an element can decrease with increasing strain:
large geometrical distortions (i.e., buckling of a thin beam)
material softening in which the intrinsic material becomes weaker (i.e.,
dilatant material becomes looser and hence weaker), or a
change in stress state such that at least one stress component decreases.
It is the latter two of these possibilities that are expected to occur during caving.
Localisation has been shown to occur by Santarelli (1989) and Besuelle (2001) at
stresses levels of between 60% and 90% the peak strength. However, shear bands
are already in place by the time that the material softening commences. The
development of shear bands is triggered by very small local variations in the initial
conditions of the problem – known as bifurcation. Bifurcation is well known in
laboratory settings, where, for example, in a simple shear test, a sample may either
deform uniformly or develop shear bands. Within numerical modelling codes,
bifurcation entails the occurrence of multiple solutions compatible with
equilibrium equations and boundary conditions.
In a previous study, Cundall (1991) shows that the process of shear band
formation is one of crack coalescence rather than propagation. When the
numerical simulation is run for a long time, bands are seen to coalesce, grow both
in length and intensity and finally become dormant. Furthermore, Cundall (1991)
also shows that the formation of one band will inhibit the formation of anotherlaterally nearby, i.e., two bands cannot form close together. The inhibiting effect
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Figure 33. Schematic diagram of a tensile failure mechanism that does not affectcohesive strength.
This phenomenon has previously been described by Pine et al. (2007). “Crack
growth orthogonal to the direction of dilation in a compressive stress field does not
immediately produce a mechanical instability, as observed in tensile fields…It is thisstable fracture process in compression that results in large differences between
tensile and compressive strengths.”
Palma and Agarwal (1973) have previously considered this mechanism of
independent tensile softening in an analysis of caving at the El Teniente Mine
through a continuous sampling of stresses within a numerical model. The same
approach is proposed for the numerical model of cave propagation. In addition to
softening tension and cohesion at the same rate based on plastic strain (discussed
in Section 2.2.2.2), tension should be allowed to soften independent of cohesion in
the instance of a tensile yield state within the model. This will ensure that a
gravitational mode of caving can accurately be represented within the model and
develop independently of a stress caving mechanism.
The implementation of such a relation suggests that a rock mass is perfectly brittle
in tension. Previous investigations by Cai (2010) suggest that this is a reasonable
assumption.
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Hajiabdolmajid, Kaiser and Martin (2002) have explored this concept in relation to
failure in laboratory specimens and around underground openings. They relate
the mobilisation of the cohesion and frictional strength components to
accumulated plastic strain. A sketch showing their conceptual model is presented
in Figure 35.
Figure 35. Schematic diagram of the mobilisation of the strength components cohesionand friction (a) in the laboratory (b) around an underground opening; c i andc r and ε c
p and ε f p represent the plastic strain components when the friction
and cohesion strength components have reached ultimate values (afterHajiabdolmajid, Kaiser and Martin, 2002).
The simplest Cohesion Weakening Friction Strengthening (CWFS) model has
previously been described by Ettema et al. (1989) as a bi-linear function. “One
(friction) value is taken at the peak of the stress-strain curve … Its value is affected by
initial porosity and confining pressure prior to shearing. The other value is taken
after considerable straining … when further straining occurs without significant
change in either porosity or confining pressure.” This is known as the constant or
residual friction angle. Pierce et al. (2006) have previously reported residual
values of 43-45 degrees for jointed rock masses.
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A CWFS model has successfully been used in the back-analysis of two breakouts in
different rock types at the Underground Research Laboratory (Hajiabdolmajiod et
al., 2002) as well as in two slope failures in jointed rock (Hajiabdolmajiod and
Kaiser, 2003; Eberhardt et al., 2002). However, it is noted that in a numerical
back-analysis of one of the tunnel break-outs presented in Hajiabdolmajiod and
Kaiser (2002), the non-uniformity of the mesh (i.e., not aspect ratio zones) and no
discussion of critical strain scaling may be affecting the simulation results.
Pierce et al. (2006) have modelled friction as a strain-softening value whereby the
peak value has been estimated by a linear Mohr-Coulomb fit to the Hoek-Brown
curve. Friction is modified to a residual value in response to plastic shear strain (atthe same rate as cohesion) and volumetric strain. Barton and Pandey (2011)
developed a similar approach; however, their friction value is dynamic and has
been calibrated based on the application at two case study locations.
In order to account for the CWFS behaviour of a rock mass, it is proposed that the
peak friction angle/s be estimated by the bi-linear technique described in Section
2.2.2. The values should be modified to a residual value of 43-45 degrees after a
fully bulked rock mass state is achieved and/or at the same softening rate as
cohesion.
A fully bulked rock mass state (or maximum volumetric strain achievable) can be
estimated based on the maximum porosity (η) of a rock mass previously
determined by Pierce et al. (2006) to be approximately 0.4. Based on this, a
volumetric strain cut-off, , of approximately 66% can be determined by
Equation [11].
[11]
Where η is the rock mass porosity. In this instance, the fully bulked rock mass will
have properties consistent with gravel e.g., frictional strength only.
2.2.2.6 Summary
It is generally accepted by the geotechnical engineering community that the Hoek-
Brown Failure Criterion, is the most widely adopted standard for expressing the
strength of a jointed rock mass. It is therefore considered the starting point for the
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representation of rock mass strength for a cave propagation and subsidence
assessment.
As a result of this, a bi-linear CWFS constitutive relation is proposed for thenumerical model of cave propagation. Initial cohesion and friction values are
determined from a bi-liner Mohr-Coulomb fit to the Hoek-Brown curve.
Cohesion and tension should be softened to a residual strength of zero in relation
to which can be determined from Equation [4]. In addition, tension softening
must be allowed to occur independently of cohesion softening through the
constant querying of plasticity states. A residual friction angle of 43-45 degrees is
simulated once a maximum volumetric strain is exceeded and/or at the same rate
as cohesion. This maximum value can be determined by Equation [11].
Provided mesh dependency is accounted for within the calibrated rock mass
response, the simulated laboratory response of a bi-linear, strain-softening rock
mass under uniaxial compression and triaxial compression loading conditions
(illustrated in Figure 37) provides the general elastic, peak strength, post-peak
softening and dilatancy mechanisms expected in an isotropic rock mass asconfinement is increased.
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developed (Pierce et al., 2006) to allow for the detailed consideration of the rock
mass joint fabric in the determination of rock mass response at large scales – i.e. 10
to 100 m. The SRM methodology uses PFC 3D (Itasca, 2007) to explicitly represent a
Discrete Fracture Network (DFN) embedded within an intact rock matrix.
The intact rock matrix is simulated using the Bonded Particle Model (BPM). The
BPM represents the rock as rigid particles (grains) glued together at their contacts
by parallel bonds that represent a normal and shear stiffness. As a result of these
bonds, the BPM does not impose theoretical assumptions and limitations on
macroscopic material behaviour, as continuum models do. Micro-cracks are able
to form, interact, and coalesce into macroscopic fractures according to localconditions. In this manner, macroscopic material behaviours not encompassed by
current continuum theories can be investigated. The BPM has a demonstrated
ability to reproduce many features of rock behaviour, including elasticity,
fracturing, acoustic emission, and damage accumulation producing material
anisotropy, hysteresis, dilation, post-peak softening, and strength increase with
confinement (Mas Ivars et al., 2011); all of which have been validated based on
instrumented laboratory tests. The micro-properties of the intact rock in SRMsamples are chosen via a calibration process based on matching laboratory test
results (intact rock UCS, Young’s modulus, and Poisson’s ratio).
Discontinuities within the rock mass samples are represented via the Smooth Joint
contact Model (SJM) which allows the simulation of a smooth interface between
particles regardless of the local particle contact orientations along the alignment as
shown in Figure 38.
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Figure 38. The Smooth Joint Contact Model. (a) Graphical representation of how thesmooth joint contact model can be used to realign the default contactorientation to one that honours a macroscopic joint orientation. (b) Byusing the smooth joint contact model to reorient all contacts lying along themacroscopic joint plane, sliding along a smooth planar feature can be moreaccurately simulated (after Mas Ivars et al., 2011).
With the SJM, macroscopic joints with a given dimension and orientation can be
embedded within the assembly and can experience shearing in the manner of a
smooth, frictional surface without resorting to particle size refinement or particle
relocation along the joint surface (Mas Ivars et al., 2011). It has been demonstrated
that the model can be used to reproduce the extension and coalescence of multiple,
isolated, embedded flaws observed in laboratory experiments (Deisman et al.,
2008).
A SRM sample can explicitly account for the presence of intact rock bridges
between terminating fractures – similar to in situ rock mass conditions. Through
simulated testing of the synthetic samples, it is possible to derive large-scale rock
mass failure mechanisms and properties such as deformation modulus, strength
and brittleness. An example SRM composite sample is presented in Figure 39.
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Figure 39. Components of a Synthetic Rock Mass sample. (a) Three-dimensionalDFN, (b) the corresponding three-dimensional synthetic rock mass sample,and (c) synthetic rock mass basic components. The colours in (b) and (c)denote intact rock blocks bounded by joints. Notice the internal non- through-going jointing in the ‘‘intact’’ rock blocks (after Mas Ivars et al.,2011).
Simulations of uniaxial compression testing on a SRM sample are presented in
Figure 40. For each of the tests, the full stress-strain curve and the percentage of
bond breakages versus total initial bonds have been recorded (percent damage).
These parameters provide an estimate of the pre-peak and post-peak behaviour of
the rock mass along with an estimate of the amount of intact damage occurring
within the sample during loading.
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Figure 40. Three-dimensional response of a synthetic rock mass sample tested in three- opposing directions under unconfined compression; testing directions east- west, north-south and vertical (after Sainsbury et al., 2009).
The potential power of SRM is that it allows for site-specific consideration of joint
fabric, loading conditions and material property variations. This may be
particularly useful in cases where the joint fabric is highly anisotropic (as shown in
Figure 40) or where the problem is sensitive to post-peak strength. In addition,
large-scale samples can be tested in significant detail – ensuring an accurate failure
mechanism is represented.
Based on a review of the SRM technology, Hoek and Martin (2010) believe that
“there is no doubt that the tools assembled in the SRM approach are the most
advanced available to us today ” and that they “believe the physics in the SRM
approach is sound ”. In addition they go on to say that “we believe very strongly that
the Bonded Particle Model (BPM), the modelling foundation for the SRM, is the only
commercially available code that can be used to properly capture the behaviour of
intact rock. Sufficient published and independent research using the BPM has been
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As a result of this, the more generalised SRM testing methodology (described by
Mas Ivars et al. 2008) is considered more universally appropriate for
implementation in caving models. Mas Ivars et al. (2008) describe how the SRM
methodology has been developed to allow testing of a rock mass in all three
opposing loading directions and at a number of different scales. Three industry-
standard tests, (direct tensile test, uniaxial compressive-strength test and triaxial
test) were selected to provide measures of rock-mass tensile strength (),
unconfined compressive strength () and compressive strength at several
confinement levels (σ3i , σ3ii , etc). This ensures that the material constitutive
properties derived from this technique are not specific to one particular stress
path, and they may be applied to a number of different large-scale
mining/geological processes.
2.2.3.2 Summary
Based upon the limitations of empirical techniques to consider, strength
anisotropy and scale effects, the SRM technique is considered an advancement in
the determination of rock mass behaviour when compared to the Hoek-Brown
approach. A review of SRM technology (Hoek and Martin, 2010) has provided apositive response and their assessment concludes the SRM provides “(the best)
representation of the processes that are active in a yielding discontinuous rock mass”.
However, the application of three-dimensional SRMs to large-scale (e.g. >100 m)
boundary value problems in densely jointed rock has been relatively limited to
date. Current limitations of the technique include computational constraints that
continue to restrict application of the technique to smaller-scale boundary value
problems. Pierce et al. (2006) have previously shown how a continuum
constitutive model can be calibrated to SRM strength responses. Cave propagation
analyses conducted using this technique provided numerical results that match
well with the observed conditions during cave propagation at the Northparkes E26
Lift 2 Mine. However their responses were limited to a specific application and a
more generalised calibrated continuum response is required.
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is non-linear in nature. A thorough review of published laboratory test data
associated with granular material is required to develop a relationship between
volumetric strain and deformation modulus for use in the numerical model of cave
and subsidence assessment.
3.2.1.4 Simulat ion of Large-Scale Discont in ui ti es
The influence of large-scale discontinuities on subsidence and cave propagation is
recognised to be important by many researchers. In situ observations have shown
that the impact of structure can be varied based on persistence, strength and
orientation relative to the undercut footprint and major principal stress direction.
There are various numerical techniques available to simulate large-scale
discontinuities within a three-dimensional numerical model. A thorough
investigation of all approaches is required to ensure the most accurate method is
implemented within the numerical model of cave propagation and subsidence
assessment.
Production Draw Simulation3.2.2
The development and implementation of state-of-the-art numerical techniques for
a more accurate and adaptable production draw simulation is implemented within
the numerical model of cave propagation and subsidence assessment.
3.2.2.1 Mass-Based Pr oducti on Draw Algor it hm
The rate of production draw and shape of the undercut footprint has previously
been identified by Laubscher (1990, 1994) to impact the caveability of a rock mass.
Evolution of the footprint shape and evolving hydraulic radius can be simulatedthrough the constant updating of the active production area in the model. At the
current time, most of the methodologies control production draw by a Height of
Draw (HOD) schedule that is estimated based on a pre-determined bulking factor
for the in situ rock mass.
A mass-based production draw algorithm is required to ensure the production
schedule is accurately represented in the numerical model of cave propagation.
This is most important during cave initiation when the production tonnes are low
and caving rates will be at their maximum. By allowing a cave to develop as a
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Figure 44. Research methodology plan. Red tasks indicate developments that considerrock mass behaviour and its impact on caving. Green tasks indicatedevelopments that are associated with numerical modelling techniquesrequired to simulate caving.
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4.3 Cave Propagation Sensitivity Studies
Effect of Rock Mass Peak Strength on Cave Propagation4.3.1
The effect that rock mass strength has on propagation behaviour has been
explored in the Cave Demonstration Model. Four different strength rock masses
have been defined (RM1, RM2, RM3 and RM4) and bi-linear, strain-softening
material responses have been developed for each property set based on the
methodology described in Section 2.2.2. A summary of the measurable material
properties and Mohr-Coulomb strength estimates for each of the rock masses are
provided in Table 3 based on a minor principal stress fit of 15 MPa.
Estimate of Hoek-Brown and equivalent Mohr-Coulomb rock mass strengthTable 3. properties for four simulated domains in the numerical demonstration model.
Seg. 1 Seg. 2
UCS Erm Tens. Coh. Coh.
(MPa) GSI MRMR mi (GPa) (MPa) (MPa) (Deg.) (MPa) (Deg.)
RM1 120 48 52 12 8.9 0.25 0.2 1.7 50 5.8 35
RM2 120 55 58 14 13.3 0.25 0.3 2.2 52 6.8 38
RM3 145 59 65 16 16.7 0.25 0.4 3.0 54 8.1 42
RM4 170 70 75 20 31.6 0.25 0.9 5.2 57 11.4 47
The Hoek-Brown failure envelopes for each of the rock masses and stress-strain
material responses at different confinement levels are provided in Figure 46.
Figure 46. Hoek-Brown failure envelopes and simulated rock mass stress-strain curves for the rock mass domains in the numerical demonstration model.
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The empirical estimates of caveability (after Laubscher, 2000) for each of the rock
masses are provided in Figure 47 for a HR of 30. Each of the rock masses are
classified as having a different caveability potential based on their MRMR values
ranging from ‘caving’ to ‘stable’.
Figure 47. Empirical estimates of rock mass caveability for four rock mass domainssimulated in the numerical demonstration model.
The RM4 rock mass falls within the ‘Stable’ region which suggests that cave
initiation and propagation may be problematic. Caving in the RM1 and RM2 rock
masses is not expected to be problematic. The caveability of RM3 is unable to be
determined since it falls within the ‘Transitional Zone’. The numerical simulationresults are provided in Figure 48. Propagation rates for both the mobilised and
yield zones have been calculated based on their simulated height above the
undercut level and the simulated HOD.
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It can be seen that as the rock mass strength increases, the propagation rate
decreases (from 18:1 in the case of RM1 to 1:1 in the case of RM4). Self-sustained
cave propagation in the lower strength RM1 and RM2 rock masses is predicted.
Stalling is seen in the simulation of caving in RM3 (depicted by the co-incident cave
and yield zones in Figure 48A) at a height of approximately 25 m above the
undercut. The cave fails to initiate in the strong rock mass RM4.
The evolution of the bulked caved mass for each rock mass is also presented for
each of the rock mass strengths through a review of the evolving rock mass
density. It can be seen that bulking is not uniform within the caved mass. Higher
bulking (lower densities) can be seen at the edges of the cave. Results of the RM4model provide a full-bulked caved rock across the entire undercut footprint, while
the RM1 and RM2 rock masses only reach a maximum bulked rock mass density
around the cave periphery - where the shearing stress is at a maximum. These
numerical results are considered to represent more closely the actual response of a
rock mass during caving than assuming a constant reduced density for production
calculations (such as Beck et al., 2011)
Maximum principal stress magnitudes in the mining abutments of the lower
strength RM1 and RM2 rock masses reach larger values than the higher strength
RM3 and RM4. This shows that minimal stress redistribution has occurred in the
high strength cases. It is expected with the additional simulation of production
draw, abutments stresses will continue to increase in the RM1 and RM2 models
until the cave intersects the ground surface.
The Damage Threshold (
) values plotted for each of the rock masses provide
two important pieces of information that include if damage is occurring in the rock
mass; and where this damage is occurring. This is important in understanding the
ongoing caveability of the rock mass and where the cave is likely to evolve.
The simulation of caving in each of the rock mass types agrees with the initial
estimates of caveability based on the Laubscher (2000) caveability chart. In
addition, in the case of RM4 the inability of the cave to initiate and problematic
caving was predicted in the case of RM4 and RM3 respectively are a significant
result.
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the demonstration model have been simulated. The results are provided in Figure
50.
Figure 50. Variation in cave propagation behaviour based on variable post-peaksoftening rates simulated in the numerical cave propagation model.
It can be seen that the cave propagation rate is strongly influenced by the post-
peak response of the rock mass. Problematic cave initiation and propagation is
simulated with a ductile post-peak response. Similar propagation rates aresimulated for the Average and Brittle post-peak responses, however, it can been
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Figure 53. Cave propagation results for increasing stress /depth in the numericaldemonstration model. Significant increases are seen between the 600m –650m simulations as the in situ stress at the extraction level approaches therock mass peak strength.
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Figure 59. Discontinuity shear strength in a triaxial cell (after Brady and Brown,2006).
It is clear from Figure 59a, that if relative shear displacement of the two parts of
the sample is to occur, there must be lateral as well as axial relative translation.
Laboratory testing is often conducted with spherical seats (Figure 59b and Figure
59c) which can cause rotation of the sample during loading. An alternative end-
condition involves the use of lubricated discs, as illustrated in Figure 20d. This
laboratory technique allows the lateral component of translation to freely occur,
however, this unrestrained end-condition is not encountered in situ.
In reality, laboratory UCS tests conducted on intact samples are performed by
loading the sample between two steel platens. These platens provide a small
amount of confinement to the test specimen due to frictional resistance. In anumerical sample loading conditions may be modelled by (a) allowing the sample
ends to move in all directions perpendicular to the loading direction, (b) fixing the
sample ends in all directions, or (c) modelling the steel platens above and below
the sample, and installing an interface between the two materials that is assigned a
stiffness and frictional resistance. The effect of each of these loading conditions on
the sample response is shown in Figure 60.
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5.2 Calibration of UJRM Response
The following section outlines the methodology for the selection of the input
parameters for calibration of a UJRM to SRM responses. The methodology has
been based on four rock mass units detailed in Mas Ivars et al. (2008).
For the calibration of UJRM samples, it is assumed that all input properties can be
estimated based on measurable rock mass parameters. By modifying the input
strength parameters (defined in Figure 54), the calibration of deformation
modulus, unconfined compressive strength (UCS), tensile strength and the
softening behaviour of different sample sizes and in different loading directions
can be completed. In addition, SRM failure mechanisms are also honoured through
the monitoring of progressive matrix degradation, joint slip and joint dislocation
within the sample during failure.
Summary of SRM Responses5.2.1
As discussed in Section 2.2.3, the SRM methodology has been developed to define
generalised stress-strain curves of a large-scale sample of a rock mass in three
opposing loading directions, and at a number of different scales. This ensures that
the material properties derived from the technique are not specific to one
particular stress path (as in the case of Pierce et al., 2006) and may be applied to a
number of different numerical modelling applications (i.e. cave analysis, slope
stability).
Commensurate with the development of the SRM standard suite of laboratory
tests, a testing environment used to calibrate the response of a subiquitous sample(direct tensile test, uniaxial compressive strength test and triaxial test) has also
been developed.
5.2.1.1 Int act Calibr ation
The standard suite of laboratory tests, as discussed in Section 2.2.3 have been
carried out on four rock mass domains at the Palabora Mine in South Africa. A
detailed description on the testing program and results can be found in Mas Ivars
et al. (2008). The measured rock mass UCS strength used for the intact calibration
is provided in Table 4.
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Figure 62. Joint orientations considered in the development of the DFN for (a)carbonatite (b) micaceous pyroxenite (c) dolerite (d) foskorite (afterSainsbury et al., 2008).
Fractures are represented within the sample as ubiquitous joints. The assignment
of the joint dip, dip direction and radius is achieved via a random sampling
procedure from the DFN developed for the rock. The persistence of joints can be
honoured throughout the grid via extrapolating the joint dip and dip direction to
adjoining zones, which honours the fracture radius. To ensure complete
randomness in the model, a random list of all the zones is generated for the
importation of the fracture network and the presence of existing joints is honoured
(i.e., not overwritten) when importing the DFN.
An example of the ubiquitous joint orientations represented by this sampling
procedure is provided in Figure 63b. The actual joint orientation data is provided
in Figure 63a.
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Summary of laboratory test results for three rock mass domains.Table 9.
The intact rock calibrations have been completed on samples sizes of 2 m, 5.2 m
and 2 m height (2:1 height: width ratio) for the Domain 1, 2 and 3 rock massesrespectively. Figure 67 illustrates the calibrated UCS response for each of the rock
mass domains.
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yielding was confined to the surface of the material since dilation causes build-up
of isotropic stress in the interior elements, thus causing failure.
Results of SRM testing conducted by Pierce et al. (2006) indicate that alternativeand/or additional fracture modes are likely within the cave back. As a result,
Pierce et al. (2006), simulated dilation as a constant value that was reduced to zero
when the maximum bulking potential was reached.
Based on the published information it appears that the constant dilation angle
assumed by most models is not realistic but should vary with rock mass damage
(decreasing GSI values) and confinement. This is confirmed by triaxial testing of
intact samples undertaken by Medhurst (1996) and Ribacchi (2000) and Zhao and
Cai (2010).
Table 14 presents a summary of the dilation angles calculated from large-scale
triaxial tests conducted on granular material by Marachi et al. (1972).
Dilation angle in large-scale triaxial tests on rock fill material (after MarachiTable 14.et al., 1972)
Vermeer and de Borst (1984) conclude that the dilation angle is at least 20o less
than the friction angle.
Other researchers have provided guidelines for the selection of a dilation angle.
Hoek and Brown (1997) suggest that dilation is greatest in competent rock masses,
and tends to zero as damage accumulated:
Maximum
Particle
Size
Confining
Stress
Dilation
Angle
Source [mm] [MPa] [Degrees]
Oroville Dam 50 1 6.5
Oroville Dam 150 1 4
Oroville Dam 50 0.2 13
Oroville Dam 150 0.2 11
Crushed basalt 50 0.2 7.5
Crushed basalt 150 0.2 9
Pyramid Dam 50 0.2 7.5Pyramid Dam 150 0.2 6.5
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GSI = 75 dilation angle is 25% of the friction angle of the rock mass ; 11o –
16o
GSI = 50 dilation angle is 12.5% of friction angle of the rock mass; 6o – 8o
GSI ≤ 30 dilation angle is zero.
Based on laboratory test results of Duncan-Farmer, (1993) Medhurst (1996) and
Ribacchi (2000); Alejano and Alonso (2005) developed a relationship for the
estimation of peak dilation angle based on confinement, friction angle and UCS. It
is presented in Equation [14].
[14]
Where is the peak dilation angle (o), ø is the angle of friction (degrees), isthe Intact Unconfined Compressive Strength (MPa) and is the inor Principal
Stress magnitude (MPa).
It is also assumed, that dilation must tend to zero at zero confinement (after
Barton and Bandis, 1982) and once the maximum volumetric strain has been
reached (estimated by Equation [11]).
The implementation of the Alejano and Alonso (2005) relation is considered the
most appropriate for cave propagation and subsidence analysis since it is based on
the reinterpretation of previously published compressive test results for a range of
rocks. The relationship reflects dependencies on confining stress, plasticity and
indirectly on scale through UCS estimates.
The relation does not increase the number of parameters needed to model the
strain-softening rock mass and can be easily implemented with the existing
information in the subiquitous constitutive model.
The implementation of this equation on a conceptual rock mass with a UCS of 100
MPa and friction angle of 45 degrees is provided in Figure 79.
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A value of 250 MPa has previously been determined for a fully bulked deformation
modulus (Pierce et al., 2006). A schematic representation of the linear softening
relation (defined in Equation [15]) is provided in Figure 81.
Figure 81. Schematic linear relationship for rock mass deformation modulus reductionbased on Pierce et al. (2006) relation.
However, Hoek and Diederichs (2006) report that the deformation modulus isnon-linear in nature and can be related to GSI of the rock mass as shown in Figure
82.
Figure 82. In situ rock mass deformation modulus versus GSI for Disturbance Factorsof 0, 0.5 and 1.0 (after Hoek and Diederichs, 2006).
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Figure 87. Simulated evolution of the bulk modulus in the back of demonstrationmodel undercut; the linear and non-linear relations compared in the cave
demonstration model.
Significant variations in the simulated modulus values within each of the linear and
non-linear model relations are presented. The non-linear relation provides results
that soften the rock mass at a greater rate than the linear model. These simulated
differences between the two relations will affect the capacity of the caved rock
mass to carry stress/load and impact propagation rates.
This relation will provide a more rigorous estimate of the cave propagation rates
and allow more realistic bulking factors to develop within the cave.
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Figure 88. Conceptual models of subsidence a) continuous subsidence (after Kratzsch,1983) b) discontinuous subsidence (after Whittaker and Reddish, 1989).
Subsidence associated with the extraction of coal seams has been studied in detailsince the late 19th Century. The mechanisms and associated terminologies used in
the analyses are now well understood and largely standardised. However, in
metalliferous mining and especially in massive orebodies, the mechanisms are not
as well established and the terminology used is not standardised. Consequently
there is still some debate over the terminology used and the key parameters used
to analyse or predict discontinuous subsidence. Numerous researchers have
proposed conceptual models of subsidence which have used diverse terminologyas presented in Table 15.
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Figure 91. Conceptual model of chimney cave development (Betourney et al., 1994), b)surface expression of a chimney pipe in a kimberlite caving operation (aftervan As et al., 2003).
van As et al. (2003) suggest that chimney caves are usually the result of poor cave
management, in that, excessive draw from an isolated drawpoint is allowed to
occur that causes these features.
Plug Caving7.3.3
Plug caving (or plug subsidence) is a form of chimney caving that occurs suddenly
rather than progressively and is controlled by one or more major structural
features which provide low strength surfaces on which the plug of undercut rock
may slide under the influence of gravity. In this case, the rock will undergoessentially rigid body displacement without breaking up or dilating if the vertical
distance through which it falls is restricted (Brown, 2003). Figure 92 illustrates the
observed plug subsidence controlled by intrusive dykes at the Athens Mine, in
Michigan, USA.
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Figure 94. Photo showing crater and caved rock zone at Henderson Mine (after Lupo,1998).
7.4.1.2 Zone of Large-Scale Fr actur in g
The zone of large-scale fracturing consists of an area in which the ground surface is
broken and has large open tension cracks, benches, and rotational blocks. The
primary failure mechanism of surface cracks associated with cave mines is shear
and tensile failure of the side rock, which results in stepped benches and scarps.
Other types of failure mechanisms, such as toppling and block rotation, are also
present, but they appear to be secondary mechanisms that form after the primaryshear failure develops. Figure 95 illustrates the typical scarp and cracking features
observed at Northparkes E26 Lift 1 Mine, in NSW, Australia.
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Figure 95. Photo showing large-scale surface cracking at Northparkes E26 Lift 1 Mine (after van As et al, 2003).
Sainsbury et al. (2010) report that a total strain criterion of 0.005 (0.5%) can be
used to assess the limits of the large-scale fracturing at the Grace Mine. This totalstrain criterion has also been used to calibrate the limit of large-scale fracturing at
the El Teniente block cave mine in Chile (Cavieres et al., 2003).
7.4.1.3 Smal l-Scale Displacement Zone (Cont inuous Zone of Subsidence)
Continuous surface subsidence, as defined by Brauner (1973), is the response of
the rock mass to a mined void, which results in the formation of a gentle surface
depression. Generally, the continuous subsidence zone forms between the large-
scale fractured zone and the undisturbed surface.
Surface buildings, roads, underground power lines, railroads and other structures
can be impacted by continuous surface subsidence. Lupo (1998) reports measured
subsidence up to 200 mm in a continuous subsidence zone at a distance of 250 m
from a large-scale fractured zone that caused heavy damage to nearby surface
structures.
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7 – Impact of Large-Scale Discontinuities on Cave Propagation Behavioiur
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Fault Impacted Caving7.5.1
The following section provides documented case histories of when large-scale
discontinuities have impacted cave growth. These documented case studiesprovide the basis for validating an appropriate numerical modelling technique for
representing cave propagation behaviour in the numerical model of cave
propagation and subsidence assessment.
7.5.1.1 San Manuel Mine
Faults at the San Manuel Mine are important factors in causing and forming
boundaries to surface subsidence (Blodgett, 2002). Hatheway (1966) reported that
vertical cave propagation was halted and then deflected by the shallow dipping San
Manuel fault, as illustrated in Figure 101.
Figure 101. Conceptual development of surface subsidence at the San Manuel Mine(after Hatheway, 1966).
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7.6 Fault Properties
One of the first problems associated with analysing the effects of geologic structure
on ground movements is characterising the properties of the discontinuities. These
properties are highly variable and include: orientation, infill, previous
displacement, planarity and shear strength.
There is limited information available regarding the large-scale shear strength of
fault structures. Figure 108 illustrates the results of direct shear tests carried out
to determine the peak friction angle and cohesion of filled discontinuities as
reported by Wyllie and Mah (2007).
Figure 108. Estimated shear strength of filled discontinuities (after Wyllie and Mah,2007).
It can be seen that the range of fault properties derived from numerical backanalyses is highly variable, and, at the current time, there is no real way to
determine these properties from large-scale in situ testing. As a result of this,
sensitivity studies are required to determine the range of caving and subsidence
behaviour expected when large-scale discontinuities are present within and
around a propagating cave.
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Figure 110. Conceptual geological structures simulated in numerical demonstrationmodel.
As discussed, whether or not a discontinuity affects cave propagation andsubsidence depends primarily on its shear strength. Based upon the range of shear
strength parameters, provided in Figure 108, three property sets have been
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Figure 113. Cross-section of mobilised zone (2m displacement) – implicit, ubiquitous joint approach used to simulate conceptual discontinuity surfaces.
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9 – Development of an Algorithm to Consider Evolving Ground Surface Profile
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Figure 132. Subsidence limits predicted with/without surface update algorithm. The
darker (more bold) lines represent the subsidence limits predicted with thesurface update algorithm switched on, and the lighter (fainter) lines representthe predicted subsidence without using the surface update algorithm.
The implementation of the algorithm shows that the subsidence limits are
increased when a toppling failure mechanism is allowed to develop at the crater
edges. Additional model results are provided in Figure 133 that shows the
updated surface elevation within the model as a result of the algorithm. Any
changes to the topography shown in the figure are due to the implementation of
the algorithm since the small-strain calculation mode has been used. The
development of a crater (depicted by the blue coloured zones) is clearly seen after
the simulation of mining.
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DEVELOPMENT OF A SUB-LEVEL CAVING10
ALGORITHM
10.1 Sub-Level Caving Mining Method
In block and panel caving, mobilisation of the ore is achieved without drilling and
blasting. The disintegration is brought about by natural processes that include the
in situ fracturing of the rock mass, stress redistribution, the limited strength of the
rock mass and gravitational forces. Sub-level Caving (SLC) requires the
transformation of in situ ore into a mobile state by conventional drilling and
blasting. This may be a result of a high rock mass strength or strategy to reduce
dilution.
The sub-level caving method is thought to have evolved as an up-scaling technique
to the top slicing mining method (Peele, 1918). Block caving, in turn, was the
logical scale-up from sub-level caving. In the first application of sub-level caving,
the ore was not drilled and blasted completely between two sub-levels, but only
parts were broken by induced caving; hence the name sub-level caving (Janelid,1972). At current day SLC operations, the ore mass between the sub-levels is
blasted. As a result of this, the primary concern with SLC mining methods is not
the strength of the orebody itself but the competency of the hangingwall material
(for subsidence and dilution predictions) and prediction of fragmentation and
gravity flow of the blasted ore material through the SLC rings.
Existing caving algorithms described by Pierce et al. (2006) have been developed
based on a block and panel caving scenarios only. In order to simulate sub-level
caving, some modifications are required.
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During the simulated production draw, each of the cave behavioural regions were
tracked and compared to physical observations made at the Palabora mine during
that time period.
11.5 Simulation Results
Cave Initiation11.5.1
The location and magnitude of seismic events recorded during the early stages of
production at the Palabora mine are illustrated in Figure 142(a). Based on this
data, the location of the yield zone (or aseismic zone) has been inferred to extend
approximately 55–83 m beyond the mobilised zone. As illustrated in Figure
139(b), the predicted yield zone within the numerical model extends
approximately 50–80 m above the cave zone, providing a good correlation with the
monitoring data.
Figure 142. Observed seismicity at the Palabora Mine during cave initiation and propagation (a) observed mobilised, yield and seismogenic zones during production (after Glazer and Hepworth, 2004); (b) numerical prediction ofmobilised and yield zones during production simulation at the Palaboramine.
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Yielding of the Crown Pillar – Q4 200211.5.2
During the fourth quarter of 2002, the yielded rock mass (aseismic) zone connects
through to the open pit. Prior to this time, an un-yielded crown pillar remains.The yielding of the crown pillar drives seismicity (high induced stresses) beneath
the extraction level. The results of the numerical simulation for this period in time
are provided in Figure 144.
Figure 144. Numerical simulation - yielding of the crown pillar during Q4 2002.
The simulated yielded rock mass zone within the numerical model breaks through
to the open pit at the same time as the aseismic zone on site that was interpreted
by Glazer (2006).
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Cave Break-Through – Q1 200411.5.3
During the first quarter of 2004, the mobilised zone connects through to the pit
floor. Immediately after this first instance of mobilisation, a crater emerges.Mobilisation within the numerical model occurs initially along pre-existing fault
traces in the base of the open pit as presented in Figure 145.
Figure 145. Numerical simulation – cave breakthrough during Q1 2004.
The simulation results show that the mobilised zone intersects the pit floor during
Q1 -2004. This is consistent with the interpretations made by Glazer (2006). In
addition, immediately prior to the development of the crater within the pit, the
shape of the cave back in the numerical model (Figure 146b) is consistent with the
shape of the cave back interpreted by Glazer (2006) that is provided in Figure
146a.
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North Wall Failure – Q4 200411.5.4
During the fourth quarter of 2004, mining on the extraction level extends further
west. As material is withdrawn from these drawbells the mobilised zone intersectsa number of faults that act, along with localised jointing, as a failure surface.
During this increment, the mobilisation and fracturing of the ground surface up to
the top of the pit in the area of the north wall failure occurs in the model. The
simulated model state at the end of 2004 is provided in Figure 147.
Figure 147. Numerical simulation – north wall failure during Q4 2004.
The timing of this event in the numerical model is consistent with the observations
made on site.
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initiation (Figure 152a). Past experience at the Henderson Mine has shown that
intrusive contacts are weak zones that fail quickly.
During early August 2006, migration of the propagating cave beyond the undercutfootprint on the north and west sides was observed along the weak intrusive
contact. Figure 152b illustrates the shape of the 7210 Level yield zone during
December 2007.
Figure 152. Geological domains at the Henderson Mine a) plan view of weak contact;b) 7210 Level yield zone during December 2007.
12.2 Model Geometry and Production Schedule
A large-scale FLAC 3D model was constructed to simulate the regional extents of the
Henderson Mine, as illustrated in Figure 153a. The existing cave volumes (8100
and 7700), developed prior to the 7210 Level were initialised within the model
based upon historical mining records, as illustrated in Figure 153b.
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Figure 155. Simulated production schedule (cumulative solid rock height of draw) basedon actual draw heights.
12.3 Material Properties and Pre-Mining Stresses
Multiple geotechnical domains have been mapped throughout the 7210 Level. Thegeomechanical properties used to simulate the main caving domain, the Urad
Porphyry, are presented in Table 20.
Rock mass geomechanical properties of the porphyry at the Henderson Mine.Table 20.
Seg.1 Seg.2
ci Erm Tens. Coh Coh.
(MPa) GSI mi (GPa) v (MPa) (MPa) (Deg.) (MPa)
(Deg.)
Porphyry 118 55 10 11 0.2 0.4 2.3 48 6.3 35
Table 21 presents the interface material properties used to simulate the weak
geological contact.
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Due to the significant topographic relief and complex previous mining history at
Henderson, it is difficult to estimate the pre-mining stress regime. A stress
calibration exercise has previously been conducted at Henderson whereby nine
stress measurements taken from 1970 to 1989 were calibrated determining the in
situ tectonic stresses that result in a best-fit of model predicted stress to thosemeasured by over coring. The results of the stress calibration exercise, which
indicated a major principal stress oriented at 155 degrees, were directly applied to
the back-analysis model.
12.4 Simulation Results
The evolution of the model-predicted yield zone is illustrated in Figure 156. The
modelled yield zone is observed to provide a close match to the TDR breakages
(blue spheres) monitored during cave propagation. Shear failure along the weak
contact can be observed to develop along the interface - coincident with vertical
propagation of the yield zone. After initial breakthrough of the yield zone to the
overlying 7700 Level in January 2006, the yield zone is observed to follow the
weak contact outside the northern and western limits of the undercut footprint.
The modelled cave breakthrough timing and dimensions match closely the
observed 7700 level breakthroughs as shown Figure 156.
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Figure 159. Geometry of the Grace Mine a) extent of underground production drives(plan view) b) two-dimensional schematic of panel caving at Grace Mine(after Stafford, 2002).
At the completion of mining, mining induced subsidence had significantly altered
the topography above the mine workings. Mine dewatering continued until 1981-
2. Upon recovery of the water table, a lake formed over the subsided area, as
illustrated in Figure 160.
Figure 160. Photo showing present day subsidence lake at the Grace Mine.
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13.2 Geomechanical Properties
Currently, the only core information available from the Grace Mine site is drilling
logs from a diamond drilling programme conducted in 1998 to investigate the near
surface conditions for construction of a large scale industrial facility near the
western edge of the subsidence lake. Owing to the location of the drill holes above
the mining horizon, the intersected rock mass has been disturbed by the caving
process and does not represent the in situ (pre-mining) rock mass condition.
The following descriptions of the rock units at the Grace Mine have been compiled
from the aforementioned drilling logs, mapping of surface outcrops and other
available literature.
13.3 Local Geology
Three rock types are associated with the Grace Mine: diabase footwall, replaced
limestone and Triassic sediments. Sims (1968) suggested that the magnetite
deposit occurs in a lens of Cambrian limestone that is overlain unconformably by
Triassic sedimentary rocks. The magnetite deposit was formed by replacement ofcontact metamorphic minerals in the limestone lens, caused by the intrusion of an
underlying diabase sheet. The orebody is roughly tabular in shape, strikes
approximately 60o and dips 20–30o to the northeast. It is approximately 1067 m
long and 213–457 m wide, and ranges from less than 15 m to more than 121 m in
thickness. Figure 161a illustrates an isometric view of the original ground surface
and orebody shape. The surfaces were reconstructed from the original mine
geological cross-sections.
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18 February 1963: cracks on the surface were noted, and a slumped zone
widened and steadily descended
16 December 1963: the underground caved to the surface
17 April 1964: cracks extended to circle the crater and extended in a
concentric pattern
8 June 1965: the subsidence trough was observed to progress to the
northeast
3 June 1969: the subsidence trough moves to the northeast following the
development and extraction pattern.
Figure 162 illustrates different aerial views of the subsidence trough. The initial
cave breakthrough appears to have been facilitated by the presence of a steeply
dipping joint/fault structure oriented at approximately 60o. As the subsidence
trough progressed to the northeast, the actual cave did not break through to the
surface. In the south-western section of the subsidence trough, large concentric
surface cracks can be observed, while two sets of cracks oriented at approximately60o and 110o are observed in the north-eastern section. The ground within the
approximate extent of surface cracking can be clearly observed to be highly
fractured and disturbed.
Approximately 30 monuments were installed on the surface above the mining
horizon and monitored by the USBM between 1962 and 1969. Surveying
techniques used over the monitoring period included chaining, levelling and
triangulation. The maximum elevation change as of 1969 was reported to be 35 m.
Goodman (1970) noted that uplift generally occurred in pins around the periphery
of the orebody outline, while acceleration of subsidence was greatest directly over
recently developed panels. Surface uplift outside the undercut footprint was also
monitored at the Lakeshore Mine, in Arizona (Panek, 1984).
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Model Validation13.5.6
The predicted vertical displacement was monitored within the model at the same
locations as the USBM subsidence monitoring monuments that were documentedby Goodman (1970). The measured versus predicted vertical displacement at three
survey monuments surrounding the subsidence trough are illustrated in Figure
167. The predicted surface displacements provide a close match to the monitoring
results and provide good confidence in the predicted surface displacements
beyond 1969.
Figure 167. Measured verses predicted vertical displacements from numerical model ofGrace Mine.
The introduction of the tonnes-based production schedule (rather than traditional
height of draw) has highlighted the mechanism for the glory hole at the surface
that was created during 1963. A typical PCBC HOD schedule usually under-
estimates the tonnes withdrawn as a result of the uniform bulking factor applied.
The result of assuming a HOD production schedule with a typical Bulking Factor of
0.2 is provided in Figure 168.
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production from the Lake Orebody was the 792 Level, and the 935 m Level (693 m
below ground surface) in the Main Orebody (Figure 169).
14.3 Evolution of Surface Subsidence
Since sub-level caving commenced at the Kiirunavaara Mine, the hangingwall has
experienced surface displacements ranging from millimetres up to several metres
in magnitude. The development of caving induced subsidence around the Lake
Orebody has been monitored through routine ground surveys since production
commenced in 2003. The following section provides a summary of the
observations and measurements. The observations are made in reference to cave
subsidence zones that are described in Section 1.4. A view of the existing surface
conditions are presented in Figure 170.
Figure 170. Subsidence regions at Kiirunavaara.
Approximately three years after mining commenced in the Lake Orebody, a crater
developed on the northern extents of the existing open pit - as illustrated in Figure
171. Initially developed as an isolated subsidence feature during 2006, additionalproduction during 2007 and 2008 caused the enlargement of the crater towards
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the south. The development of this isolated crater can best be described as a
chimney or plug cave. Lupo (1997) completed a detailed review of the chimney
subsidence features that occur east of the Main Orebody, and suggested that they
are formed when the flow channel of a sub-level ring reaches the ground surface.
Figure 171. Photos showing the development of a crater at northern extent of LakeOrebody during 2006 and its subsequent enlargement.
Limits of Large-Scale Fracturing / Yield Zone14.3.1
The progression of the large-scale fracture limits at the ground surface between1997 and 2006 is presented in Figure 172. An angle of break for the fractured
zone of approximately 60o has been reported by Villegas et al. (2011), Lupo (1996)
and Stephansson et al. (1978). Surface disturbances in this zone have previously
been documented by Lupo (1997) and consist largely of surface cracks, and shear
displacements.
Figure 172. Fracture mapping at Kiirunavaara (a) plan above Lake Orebody (b)section through Main Orebody (modified after Villegas et al., 2011).
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Limits of Continuous Deformation14.3.2
GPS data shows that an area of continuous deformation extends approximately
150-200 m beyond the limits of large-scale fracturing (Villegas et al., 2011). Themeasured surface displacements from 2002 – 2010 above the Lake Orebody are
provided in Figure 173. Surface displacements in the order of 0-250 mm were
measured prior to the commencement of mining of the Lake Orebody in 2003.
Figure 173. Evolution of measured surface total displacement profile around the LakeOrebody.
14.4 Numerical Simulation of Caving Induced Subsidence
A three-dimensional model of the Kiirunavaara Mine and its surroundings has
been developed to assess the impact of the production schedule on the
development of the surface displacement profile that is evident today. The model
extents are provided in Figure 174.
Figure 174. Regional extents of Kiirunavaara numerical mesh.
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In situ Stress14.4.1
The pre-mining in situ stresses at the Kiirunavaara Mine have previously
documented by Sandström (2003). The major principal stress is estimated to bealigned perpendicular to the orebody and is approximately 1.28 times the vertical
stress. Equations for deriving the principal stress components in MPa are
provided below.
0.37 3.7 ymW
0.28 2.8 ym NS h 0.029 2.9v ym Where y m represents the depth below -100m RL and the stresses are expressed in
terms of MPa.
Rock Mass Properties14.4.2
Historically, material properties for the Lake Orebody have been developed based
on a calibrated response of drive scale displacements and failure mechanisms in
the Main Orebody. Previous analyses conducted by Perman et al., (2011) have
derived a lower bound property set for the hangingwall domain in the Main
Orebody that is defined by a UCS 130 MPa, GSI 58, mi 16 and Erm 15.8 GPa. This
GSI value has been confirmed for the Lake Orebody by scanline mapping
conducted during 2010.
A bi-linear, Mohr-Coulomb, strain-softening constitutive model has been used to
simulate the complex process of the progressive failure and disintegration of the
rock mass from an intact, jointed material to a bulked state during the caving
process in the numerical model. The low magnitude in situ stresses in relation to
the strength estimates suggest a gravity driven caving mechanism is dominant at
Kiirunavaara.
Production Schedule14.4.3
In order to ensure an accurate induced stress state in the model prior to the
simulation of mining from the Lake Orebody, simulation of the extents of open-cut
mining was conducted during the development of the initial model state.
Production from the Main Orebody has been simulated based on an elevation and
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Figure 177. Simulated evolution of total surface displacements within the numericalmodel of Kiirunavaara compared to observations onsite.
The 1 m displacement contour has been used to define the crater limits within the
numerical model at the end of 2010 (Figure 178). The simulated limits compare
well with the in situ observations based on their comparison to the visual
observations presented in Figure 171.
Figure 178. Plan view of simulated displacement and strain-based subsidence criteriaand subsidence zone of influence at the end of 2010 as simulated in thenumerical model of Kiirunavaara.
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15.1 Summary of Original Contributions
A model for cave propagation and subsidence assessment in jointed rock masses
has been developed that relies on the fundamental behaviour of rock masses for
caving analyses. In the process, original contributions were made to the numerical
simulation of rock mass behaviour and numerical methods for cave propagation
and subsidence assessment. A summary of the contributions are provided below.
Rock Mass Behaviour15.1.1
15.1.1.1 Development of t he Ubiqu it ous Join t Rock Mass (UJRM) Model
Synthetic Rock Mass Modelling (SRM) is generally accepted as the existing state-of-
the-art in anisotropic rock mass behaviour analysis. A methodology has been
developed that can be used to derive material input properties for the FLAC 3D
Subiquitous (Strain-Softening Ubiquitous Joint) constitutive model so that it
exhibits strength and deformation behaviours similar to what may be derived from
SRM testing. The successful implementation of these strengths in a large-scale
caving back-analysis at the Palabora Mine provides validation for the technique.
15.1.1.2 Considerat ion of the Volumetr ic Changes th at Accompany Cave
Propagation
Due to computational constraints at the present time, the numerical model of cave
propagation must be implemented using a small-strain calculation mode. As a
result of this, the manual modification of the density and bulking/dilational
behaviour of the rock mass during volumetric expansion is required. A non-linear
deformation modulus softening and dilation relation has been implemented withinthe numerical model of cave propagation to provide a more rigorous assessment of
rock mass bulking. The methodology has been validated based on four large-scale
back-analyses of cave propagation behaviour detailed herein.
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