Numerical analysis of the influence of geological structures on the development of surface subsidence associated with block caving mining

A. Vyazmensky Simon Fraser University, Canada http://alex.vyazmensky.googlepages.com/ D. Elmo Simon Fraser University, Canada

D. Stead Simon Fraser University, Canada

J. Rance Rockfield Technology Ltd, UK

Abstract Extraction of a massive volume of ore during block caving can lead to formation of significant surface subsidence. Current knowledge of subsidence development mechanisms is limited as are our subsidence prediction capabilities. Mining experience suggests that among other contributing factors geological structures play a particular important role in subsidence development. As part of the current research a conceptual modelling study is being undertaken to evaluate the significance of geological structure on surface subsidence development. A novel finite/discrete element technique incorporating a coupled elasto-plastic fracture mechanics constitutive criterion is adopted; this allows physically realistic modelling of block caving through simulation of the transition from a continuum to a discontinuum. Numerical experiments presented highlight the importance of joints orientation, fault location, and inclination, on subsidence development mechanisms and the governing role of geological structure in defining the degree of surface subsidence asymmetry.

1 Introduction Block caving mining is characterized by extraction of a massive volume of rock usually accompanied by the formation of a significant surface depression above and in the vicinity of the mining operation. The ability to predict surface subsidence associated with block caving mining is important for mine planning, operational hazard assessment and evaluation of environmental and socio-economic impacts.

Owing to problems of scale and lack of access, the fundamental understanding of the complex rock mass response leading to subsidence development is limited as are current subsidence prediction capabilities. Current knowledge of subsidence phenomena can be improved by employing numerical modelling techniques in order to enhance our understanding of the basic factors governing subsidence development; essential if the required advances in subsidence prediction capability are to be achieved.

A comprehensive numerical modelling study focused on block caving related surface subsidence is being carried out at the Simon Fraser University in collaboration with the University of British Columbia. As part of this research conceptual modelling is being undertaken to evaluate the relative significance of the factors governing subsidence development.

This paper investigates the role of geological structures in surface subsidence development through a series of numerical experiments employing state of the art finite element /discrete element modelling techniques.

2 Geological structures and block caving induced surface subsidence Mining experience suggests a range of factors influencing the block caving surface subsidence footprint including geological structures (jointing and faults), rock mass strength, in-situ stress level, mining depth, varying geological domains and surface topography. Among other contributing factors many authors emphasize the particular importance of the geological structures on surface subsidence development.

A literature survey has shown that published accounts provide a general, qualitative rather than quantitative, description of the influence of geological structures on the observed subsidence, as summarized in Table 1. Such qualitative observations are useful for initial subsidence analysis, however they require further

validation. More research is needed to address the deficiency in quantitative data. Modelling presented in this paper represents an initial attempt to address these issues.

Table 1 Influence of geological structure on block caving surface subsidence development

Geological structure

Influence on block caving subsidence Reference

Joints In the absence of faults and dykes, joint dip governs the angle of break. Angle of break for a mine should be equal to the dip of the most prominent joint.

Crane (1929), Wilson (1958)

Faults

When a mining face encounters a significant discontinuity, such as a fault, with moderate to steep dip, movement will occur on the fault regardless of the cave angle through intact rock. A stepped crack will result where the fault daylights at surface. If mining is only on the hanging wall side of the fault there will only be surface movements on the one side. If the fault dip is steeper than the cave angle the extent of surface subsidence will be reduced, conversely, if the fault dip is less than the cave angle the extent of surface subsidence will be increased.

Abel & Lee (1980), Stacey & Swart (2001), van As (2003)

3 New approach to numerical analysis of caving induced surface subsidence Conventional numerical modelling techniques applied to the analysis of rock engineering problems treat the rock mass either as a continuum or as a discontinuum. The use of finite element, finite difference methods is based on the assumption that the rock mass behaves as a continuum medium. In contrast, distinct element methods (DEM) methods are based on the assumption of the rock mass as a discontinuum, consisting of an assembly or finite number of interacting singularities. Both continuum and discontinuum techniques provide a convenient framework for the analysis of many complex engineering problems.

One important limitation of continuum techniques is their inability to simulate the kinematic aspects of rock mass failure. The solutions based on discontinuum modelling are strongly dependant on the contact properties of the discrete elements, which govern their interaction. Scalable and robust methods for obtaining these properties are yet to be developed. Moreover, as indicated by Stead et al (2004), neither technique can capture the interaction of existing discontinuities and the creation of new fractures through fracturing of the intact rock material. A key failure mechanism, rock brittle fracturing, can only be simulated indirectly.

Block caving subsidence is a product of a complex rock mass response to caving. This response comprises massive failure of rock mass in tension and compression, along both existing discontinuities and through intact rock bridges, and involving complex kinematic mechanisms. Clearly, the analysis of this phenomenon assuming a pure continuum or discontinuum model may not be adequate. It is evident that the numerical treatment of such a complex problem necessitates consideration of a blend of continuous and discrete computational processes to provide an adequate solution.

In the current study a state-of-the-art hybrid continuum-discontinuum technique based on finite/discrete element method (Munjiza et al, 1995) and fracture mechanics principles is adopted. An implementation of this approach using the numerical code ELFEN (Rockfield Software Ltd., 2007) is employed. The ELFEN code is a multipurpose FE/DE software package that utilizes a variety of constitutive criteria and is capable of undertaking both implicit and explicit analyses in 2-D and 3-D space. Capability exists to simulate continuum materials, jointed media and particle flow behaviour.

In the combined finite-discrete element method the finite element-based analysis of continua is merged with discrete element-based transient dynamics, contact detection and contact interaction solutions (Munjiza, 2004). Use of fracture mechanics principles in a context of finite-discrete element method allows the caving process to be simulated in a physically realistic manner. Rock mass failure is simulated through a brittle fracture driven continuum to discontinuum transition with the development of new fractures and discrete blocks, and a full consideration of the failure kinematics. Table 2 compares continuum, discontinuum and hybrid continuum-discontinuum modelling techniques.

Table 2 Comparison of continuum, discontinuum and hybrid continuum-discontinuum modelling techniques

Modelling technique

Numerical method

Rock mass representation

Rock mass failure realization

Continuum FDM, FEM Continuous medium Flexural deformation, plastic yield

Discontinuum

DEM Assembly of deformable or rigid blocks

Block movement and/or block deformation

Assembly of rigid bonded particles

Bond breakage, particle movements

Hybrid continuum -discontinuum + fracture

FEM/DEM Continuous medium Degradation of continuum into discrete deformable blocks through fracturing and fragmentation

The simulation of fracturing, damage and associated softening in ELFEN is achieved by employing a fracture energy approach controlled by a designated constitutive fracture criterion. The current study employed a Mohr-Coulomb model with a Rankine cut-off. A detailed description of this constitutive model can be found in Klerck (2000) and a summary of the ELFEN solution procedure is given by Owen et al (2004).

It should be noted that the ELFEN computational methodology has been extensively tested and fully validated against controlled laboratory tests by Yu (1999) and Klerck (2000). Among others, research by Coggan et al (2003), Cai & Kaiser (2004), Stead et al (2004) and Elmo (2006) has demonstrated the capabilities of the code in the analysis of various rock mechanics problems involving brittle failure, including analysis of Brazilian, UCS and direct shear laboratory tests, analysis of slope failures and underground pillar stability. Initial applications of the code to the analysis of block caving by Pine et al (2006), Vyazmensky et al (2007), Elmo et al (2007) and Rance at al (2007) showed encouraging results.

According to Vyazmensky et al (2007) in the context of finite-discrete element method there are three possible approaches to the representation of the jointed rock mass systems:

• Equivalent Continuum • Discrete Network • Mixed discrete/equivalent continuum approach

In the Equivalent Continuum approach, similar to analysis employing continuum techniques, the jointed intact rock mass system is represented as a continuum with assumed reduced intact rock properties to account for the presence of discontinuities. Clearly such an approach is not entirely acceptable, as the mechanical behaviour of a jointed rock mass is strongly influenced by the presence of discontinuities which provide kinematic control and in many cases govern the operative failure mechanisms. In this sense, the Discrete Network approach is a more physically realistic option where the jointed rock mass is represented as an assembly of a maximum number of discontinuities and intact rock regions. It should be emphasized that such a detailed representation of discontinuities for highly jointed rock masses requires a very fine mesh discretization; hence the computational efficiency of this approach is limited to the analysis of relatively small scale problems. For the analysis of practical engineering problems it is neither feasible nor necessary to consider every single discontinuity in the jointed rock mass; the resolution of fracture representation should however be sufficient to capture the salient features of the simulated behaviour. In the Mixed approach key discontinuities defining the behaviour of the jointed rock mass are represented explicitly and presence of other discontinuities in inter-fracture regions is accounted for implicitly through reduced intact rock properties. This approach was adopted for the current study.

Geologically sound representation of key natural discontinuities can be achieved through use of Discrete Fracture Network (DFN) models. In the current study the DFN code FracMan (Golder, 2007) was utilized. FracMan is a convenient tool to generate 3D stochastical models of fracture networks based on collected discontinuities data; it allows export of 2D and 3D fracture sets into ELFEN. Integrated use of ELFEN and FracMan has previously been presented by Elmo et al (2006), Pine et al (2006), Rance at al (2007), Elmo et al (2007), and Vyazmensky et al (2007).

4 Modelling Methodology Although full 3D mine scale analysis of block caving subsidence is undoubtedly desirable, available modelling tools are yet to reach the computational efficiency to allow a detailed and realistic 3D analysis. In the current 2D modeling study emphasize is given to the representation of a maximum level of detail allowable with the computational efficiency available. Modelling results presented herein are conceptual and as such not related to any particular site. However, model geometry and geomechanical characteristics are generally representative of the conditions in actual block caving settings.

Flores & Karzulovic (2002) studied a number of block caving mines and reported typical caved ore block heights of around 200m. For the current study a square ore block 100x100m, located at 200m meter depth is considered. Block caving mining is simulated by undercutting the block and subsequent extraction of the caved ore. The undercut (100m x 4 m) is developed in five stages - 20m at each stage. A uniform draw of caved material was implemented. It should be noted that uniform material properties were assumed throughout the model and the draw was continued until the volume of rock corresponding to the volume of the ore block is extracted.

Mahtab et al (1973) noted that the fracture system most favourable for caving includes a low dipping and two nearly orthogonal steeply dipping joint sets. The 3D FracMan DFN model adopted in the current analysis incorporated one horizontal and two orthogonal vertical sets with sparsely spaced and moderately persistent joints. The fracture pattern for the 2D model was derived by assuming a plane parallel to one of the vertical sets within the 3D DFN model. Fracture traces intersecting this plane were delineated and exported into ELFEN.

One of the main challenges in rock mechanics modelling is establishing representative rock mass properties. Rock mass classification systems such as RMR, Q or GSI are traditionally used to derive properties for the equivalent continuum rock mass. Vyazmensky et al (2007) indicated that use of equivalent continuum properties in combination with pre-inserted discontinuities may result in a softer response. Therefore model calibration is required to ensure that a combined system of pre-inserted fractures and equivalent continuum rock mass is able to simulate caving behaviour in a close agreement with the observed in-situ mine experience.

The model setup and proposed response calibration procedure for the block caving analysis are shown in Figure 1.

100m

oreblock

100m

100m

FracMan DFN model

3D model 2D trace plane

2D ELFEN model

Properties calibration criteria:

Constraint:

Caveability Laubscher’s caveability chart

Cave development progression

Conceptual model of caving by Duplancic & Brady (1999)

Subsidence limits Mining experience:Rules of thumb byMcIntosh Engineering Ltd. (2003)

Constraint

fracturesexported into ELFEN

calibrated rock mass properties

Figure 1 ELFEN model setup and response calibration procedure

For the analysis presented in this paper Barton’s Q rock mass classification system (Barton et al, 1974) was used as a source of initial equivalent continuum rock mass properties. These properties were calibrated (primarily through adjustment of tensile strength) so that the model response correlates well with the constraining criteria and is representative of the caving behaviour of a rock mass with MRMR ~ 55-60, (within a typical block caving range of MRMR 30 to 70). ELFEN input parameters are given in Table 3. Figures 2 and 3 illustrate examples of caving simulations of and subsequent subsidence development using the adopted methodology.

A series of parametric numerical experiments were carried out to evaluate the relative significance of joint inclination, faults location and inclination. The list of modelling scenarios assumed is shown in Table 4.

Table 3 Input parameters for ELFEN modelling

Parameter Unit Value Parameter Unit Value Rock mass Preinserted or newly generated fract. Young’s Modulus, E GPa 18 Fracture cohesion, cf MPa 0 Poisson’s ratio, ν 0.25 Fracture friction, φf degree 35 Density, ρ kgm-3 2600 Normal penalty, Pn GPa/m 2 Tensile strength, σt MPa 1 Tangential penalty, Pt GPa/m 0.2 Fracture energy, Gf Jm-2 60 Internal cohesion, ci MPa 5.5 Stress level Internal friction, φi

degree 45 In-situ stress ratio, K 1 Dilation, ψ degree 5

end of block undercutting 5% ore extraction 10% ore extraction

Figure 2 Gradual cave front propagation at early stages of ore extraction

20% ore extraction 40%

60% 80%

surface subsidence, m

Figure 3 Surface depression and crater development with continuous ore extraction

Table 4 Modelling scenarios

Scenario Description Base case Vertical and horizontal joint sets J1 Sub-vertical set dipping at 80° with orthogonal sub-horizontal set J2 Sub-vertical set dipping at 70° with orthogonal sub-horizontal set F1 Vertical and horizontal joint sets, 60° dipping fault located 50m west of the model centre F2 Vertical and horizontal joint sets, 60° dipping fault located 100m west of the model F3 Vertical and horizontal joint sets, 60° dipping fault located 150m west of the model F4 Vertical and horizontal joint sets, 45° dipping fault located 100m west of the model F5 Vertical and horizontal joint sets, 75° dipping fault located 100m west of the model

5 Modelling Results Modelling results are presented in Figures 4 - 7. Figure 4 illustrates final subsidence profiles at full ore extraction. Figure 5 compares the extent of surface deformation, subsidence angles and subsidence zone asymmetry in relation to the block centre. Figure 6 evaluates the violation of an assumed critical deformation threshold of 3cm with percentage ore extraction for vertical and horizontal deformation at different distances from the block centre. It should be noted that only deformations west of the block centre (see Figure 4a), where the major asymmetry was anticipated, were analysed. A critical deformation threshold value was chosen based on the assumption that most engineering structures can sustain displacements of up to 3cm without major damage. Figure 7 compares movements along fault surfaces. The following sections summarize the key modelling results and interpretation.

5.1 Effect of joint orientation The effect of joint orientation was evaluated through comparison of scenarios with three different orientations - Base case (vertical/horizontal sets), J1 (80°/orthogonal) and J2 (70°/orthogonal). The joint pattern was limited to a single FracMan realization with the desired dip achieved by rotating the joints with respect to the model centre.

As illustrated in Figures 4a and 4b, orientation of the vertical joint set affects the cave propagation, which tends to follow the dip of the sub-vertical joint set.

According to Figures 4a, 4b and 5 for the case with vertical and horizontal joints (Base case) the extent of failure zone at full ore extraction is nearly symmetrical. Rotating the joint pattern results in failure zone asymmetry, with a rotation of the joint pattern of 10° causing an increase in the extent of the failure zone by about 25%. The principal surface subsidence asymmetry is observed in the dip direction of the sub-vertical joint set, west of the block centre. It appears that in this region a combination of sub-vertical and low dipping joint sets creates favourable conditions for gradual flexural and block toppling, triggered by unloading due to continuous ore extraction. At later stages of ore extraction large scale rock segments may form and fail along the low dipping joint set. The lower the dip of the sub-vertical joint set and steeper the dip of the sub-horizontal set the larger area of the rock mass mobilized. To the east of the block centre, the rock mass fails primarily through sliding along the sub-vertical set. This effect becomes more pronounced as the dip of the sub-vertical set is reduced. As illustrated in Figure 6, the 3cm deformation threshold was reached at later stages of ore extraction for the Base case scenario than for scenarios with inclined joints. This reflects the more gradual character of the surface deformation development. Vertical and horizontal deformations for the Base case and scenario J1 exceed the assumed 3cm threshold at a distance of 100m from the block centre, whereas for scenario J2 the threshold was exceeded at a distances of up to 150m from the centre . Interestingly for scenario J2 critical deformations were attained almost simultaneously at 100 and 150m locations implying failure of a major rock mass segment.

Overall, modelling results suggest the following effects of joint orientation on subsidence development: • Steeply dipping joint sets tends to govern the direction of cave propagation. • A combination of vertical and horizontal joint sets results in a nearly symmetrical subsidence profile. • Subsidence asymmetry is strongly controlled by the inclination of sub-vertical and sub-horizontal sets. • Major subsidence asymmetry is observed in the dip direction of the sub-vertical set, where the rock

mass fails through flexural and block toppling and detachment and sliding of major rock segments. • Surface deformations in the reversed direction are controlled by the dip of sub-vertical set. In this case

the rock mass fails predominantly through rock bridge breakage and sliding along the sub-vertical joints.

The modelling results provided some interesting insights into the effect of sub-vertical joint set which go beyond reported field observations. Further research is being conducted to investigate the significance of the dip of sub-horizontal joint set in instigating large scale failures.

5.2 Influence of fault location and inclination Three scenarios were considered to evaluate the effect of fault location on surface subsidence development. Model geometry was assumed to be the same as in the Base case. As shown in Figure 4c, in scenario F1 the fault was located 50m from the model centre, in scenario F2 at 100m and in scenario F3 at 150m, Figure 4c. In all the scenarios a fault dip of 60° was assumed, with the vertical and horizontals joint sets as used in the Base case.

According to Figures 4c and 5 faults located at 100m and 150m resulted in asymmetry of the surface deformations and increased the extent of the deformation by 19% and 41% respectively. The fault plane acted as a boundary defining major surface deformation. The fault located in close proximity to the block was fully consumed by the caving and played practically no role in formation of the final subsidence footprint. The fault located 100m from the block centre was partially caved, although its remnant portion near the surface acted as a sliding plane for hanging wall failure. Movement of the hanging wall created a topographical step of about 2m in the surface profile (see Figure 7). Only limited movements of the hanging wall were observed for the fault located at 150m from the block centre, with only a minor step in the surface profile being created.

Two additional scenarios were considered in order to evaluate the effect of fault inclination. The assumed model geometry was the same as in scenario F2, with fault dips of 45° (scenario F4) and 75° (scenario F5), Figure 4c.

As illustrated in Figure 4c the fault inclination played a major role in defining the extent of surface deformations. A low dipping fault created favourable conditions for planar failure of the hanging wall as it was unloaded by ore extraction. Based on Figure 6 the entire hanging wall was failing nearly simultaneously, so that critical 3cm deformation threshold was violated as far as 200m from the block centre. For the case with a steeply dipping fault the zone of surface subsidence deformation was significantly smaller. Although eventually consumed by caving, during earlier stages of ore extraction the fault acted as a barrier limiting mobilization of the rock mass in the footwall. Preliminary results shows that a change of fault dip by 15° resulted in a change in the extent of surface subsidence of about 30% (Figure 5a).

Overall, the following can be inferred with respect to the effect of fault location and inclination on block caving induced surface subsidence:

• Under certain circumstances the fault’s position may play an important role in defining the extent of surface subsidence deformation. It appears that faults located within an area of imminent caving are likely to be caved and are unlikely to play any major role in the resultant subsidence. Faults partially intersecting the caving area may create favourable conditions for failure of the entire hanging wall. Faults located in close vicinity of the caving zone extend the area of subsidence deformations, although in this case, hanging wall failure is unlikely. In the latter two cases a topographical step in the surface profile is formed where the fault daylights at the surface.

• Unequivocally, inclination of the fault intersecting the caving area controls the extent of surface subsidence deformations. Low dipping faults will extend and steeply dipping fault will decrease the area of surface subsidence deformation.

The modelling results are in a good agreement with field observations reported in the literature (Table 1). In the current modelling only vertical and horizontal joint sets were considered. Further studies should investigate how observed behaviour changes with variation in the dip of the joint sets.

6 Discussion and Conclusions In a complex block caving mining environment subsidence development is a result of a complex interplay of several governing factors; in such circumstances discerning the effect of a particular factor can be challenging.

The modelling methodology for subsidence analysis, outlined in this paper, employs an integrated state-of-the-art hybrid continuum-discontinuum modelling - DFN approach to rock discontinuity representation. A novel model calibration procedure was developed to ensure that the simulated behaviour is well constrained against observed trends in real block caving settings. This allows realistic modelling of rock mass caving and subsidence development. The proposed methodology offers an excellent platform for parametric numerical experiments intended to enhance understanding of the factors governing subsidence development.

Numerical analyses presented in this paper were focused on the effect one of the most prominent factors - geological structures. A series of initial numerical experiments highlighted the importance of joint set orientation, fault location and inclination, in determining the subsidence development mechanisms and their governing role in defining the degree of surface subsidence asymmetry. The modelling findings correlated reasonably well with published field observations and offered some new and interesting insight into block cave related subsidence.

(a) (b)

(c)

240

310

380

252287

340

404

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100% 12

9% 158%

105%

119% 14

1% 168%

92%

0

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100150200250300350400450

Tota

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Ang

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BC J1 J2 F1 F2 F3 F4 F5

Angle of Fracture InitiationAngle of Break

-120

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-190

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-132

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-160

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-102

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-300 -200 -100 0 100 200

Extent of Major Surface Deformations in Relation to Central Axis of Block, m

BCJ1J2F1F2F3F4

100

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158

100

208

108

110

100

133

106

175

108

204

133

85

100

0 50 100 150 200 250

Extent of Major Surface Deformations in Relation to Central Axis of Block, Normalized by Base Case, %

BCJ1J2F1F2F3F4F5

Figure 5 Subsidence characterization: (a) total extent of major surface deformations in m and in %; (b) angles of break and fracture initiation; (c) extent of major surface deformations in relation to central axis of the block, in m and in %

J2

F2 F2

F4F4

05

101520253035404550

50 100 150 200

Ore

Ext

ract

ion,

%

Distance from Block Centre, mBC J1 J2 F1 F2 F3 F4 F5

(a) (b)

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F2

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05

101520253035404550

50 100 150 200

Ore

Ext

ract

ion,

%

Distance from Block Centre, mBC J1 J2 F1 F2 F3 F4 F5

horizontal deformationsvertical deformations

Figure 6 Violation of 3cm critical deformation threshold at different distances from the block central axis with continuing ore extraction: (a) vertical displacements, (b) horizontal displacements

footwall

hanging wall

differentialXY displacement

-4.31m

-2.37m

-0.02m

-1.36m -1.16m

-5-4.5

-4-3.5

-3-2.5

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-1-0.5

0

0 10 20 30 40 50 60 70 80 90 100

Diff

eren

tial X

Y D

ispl

acem

ents

, m

Extracted Ore, %

F1 F2 F3 F5 F4

hangingwall failed

Figure 7 Differential XY displacements for surface points on the fault hanging and foot walls for scenarios F1 to F5.

In summary, the conducted analysis illustrate the significant potential of the proposed modelling methodology. More work is ongoing to evaluate the relative significance of other factors controlling subsidence development, such as rock mass strength, in-situ stress level, mining depth, varying geological domains and surface topography. Furthermore, it is planned to adopt this modelling methodology in the analysis of the factors controlling block caving mining induced instability in natural and man-made slopes and subsequently evaluate subsidence amelioration strategies.

Acknowledgements The authors would like to acknowledge research funding provided by Rio Tinto. We would also like to acknowledge research collaboration with Dr. Erik Eberhardt, Dr. Scott Dunbar and Dr. Malcolm Scoble (University of British Columbia) and Dr. Steve Rogers (Golder Associates).

References Abel, J. F.& Lee, T.F. (1980) Subsidence Potential in Shale and Crystalline Rocks. U.S. Geological Survey Open File

Report 80-1072. 49pp. Barton, N., Lien, R. & Lunde, J. (1974) Engineering classification of rock masses for design of tunnel support. Rock

Mech. 6(4): 189–236. Cai, M. & Kaiser, P. K. (2004) Numerical simulation of the Brazilian test and the tensile strength of anisotropic rocks and

rocks with pre-existing cracks. Int J Rock Mech Min Sci, 41(1): 478-483. Coggan, J. S., Pine, R. J., Stead, D. & Rance, J. (2003) Numerical modelling of brittle rock failure using a combined finite-

discrete element approach: Implications for rock engineering design. In: Proc. ISRM 2003 Series S33: 211-218. Crane, W.R. 1929. Subsidence and Ground Movement the Copper and Iron Mines of the Upper Peninsula, Michigan.

USBM Bulletin 285. 66pp. Duplancic, P. & Brady, B.H. (1999). “Characterisation of caving mechanisms by analysis of seismicity and rock stress.”

Proceeding 9th International Congress on Rock Mechanics, Paris, A.A. Balkema, Vol. 2, pp. 1049-1054. Elmo, D. (2006) Evaluation of a hybrid FEM/DEM approach for determination of rock mass strength using a combination

of discontinuity mapping and fracture mechanics modelling, with particular emphasis on modelling of jointed pillars. PhD Thesis. Camborne School of Mines, University of Exeter U.K.

Elmo, D., Vyazmensky, A., Stead, D. & Rance, J.R. (2007) A hybrid FEM/DEM approach to model the interaction between open pit and underground block caving mining. Proc. 1st Canada-U.S. Rock Mechanics Symposium., Vol 2, 1287-94pp.

Flores, G. & Karzulovic A. (2002) “Geotechnical Guidelines for a Transition from Open Pit to Undeground Mining”. Benchmarking Report for ICSII, Task 4. 392pp.

Golder Associates. (2007) FracMan Technology Group. http://www.fracman.golder.com Klerck, P. A. 2000. The finite element modelling of discrete fracture in quasi-brittle materials. Ph.D. thesis, University of

Wales, Swansea. Mahtab, M.A., Bolstad, D.D. & Kendorski, F.S. (1973) Analysis of the geometry of fractures in San Manuel Copper Mine,

Arizona. US Bur Mines Rept Invns 7715. McIntosh Engineering Ltd. 2003. “Hard Rock Miners Handbook. Rules of thumb”. On-line publication. 3rd edition.

http://www.mcintoshengineering.com Munjiza, A., Owen, D.R.J. & Bicanic, N. (1995). A combined finite/discrete element method in transient dynamics of

fracturing solids. Int. J. Engng Comput. 12(2): 145–174. Munjiza, A. (2004). The combined finite-discrete element method. Chichester: J. Wiley & Sons. 348pp. Owen, D. R. J., Feng, Y. T., de Souza Neto, E. A., Cottrell, M. G.,Wang, F., Andrade Pires, F. M. & Yu, J. (2004) The

modelling of multi-fracturing solids and particulate media. Int. J. Num. Meth. Eng. 60(1): 317-339. Pine, R.J., Coggan, J.S., Flynn, Z.N. & Elmo, D. (2006) The development of a new numerical modelling approach for

naturally fractured rock masses. Rock Mech. Rock Engng. 39(5): 395-419. Rance, J.M., van As, A., Owen D.R.J., Feng Y.T & Pine R.J. 2007. Computational modelling of multiple fragmentation in rock

masses with application to block caving. Proc. 1st Canada-U.S. Rock Mechanics Symposium. Vancouver Vol 1: 477-484pp. Rockfield Software Ltd (2007) ELFEN user manual, Swansea, UK, http://www.rockfield.co.uk Stacey, T.R. & Swart, A.H. 2001. Practical rock engineering practice for practice for shallow and opencast mines.

SIMRAC The safety of mines research advisory committee, 66pp. Stead, D., Coggan, J.S. & Eberhardt, E. 2004. Realistic simulation of rock slope failure mechanisms: The need to incorporate

principles of fracture mechanics. SINOROCK 2004: Special Issue of Int. Journal of Rock Mechanics. 41(3). 6pp. van As, A. (2003) Subsidence Definitions for Block Caving Mines. Technical report. 59pp. Vyazmensky, A., Elmo, D., Stead, D. & Rance, J.R. (2007) Combined finite-discrete element modelling of surface subsidence

associated with block caving mining. In Proc. 1st Canada-U.S. Rock Mechanics Symposium. Vancouver Vol 1: 467-475. Wilson, E.D. (1958) Geologic Factors Related to Block Caving at San Manuel Copper Mine, Pinal County, Arizona.

Progress Report, April 1956-1958. Bureau of Mines Rept. of Inv. 5336. 40pp. Yu, J. (1999) A contact interaction framework for numerical simulation of multi-body problems and aspects of damage

and fracture for brittle materials. PhD dissertation, University of Wales Swansea.