Role of rock mass fabric and faulting in the development of block caving induced surface subsidence

Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533
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Role of Rock Mass Fabric and Faulting in the
Development of Block Caving Induced Surface
Subsidence
Vyazmensky A. 1
, Elmo D. 2
, Stead D. 3
(1) Senior Geotechnical Engineer, Copper Projects Group, Rio Tinto Ltd., Vancouver,
Canada
Mailing address: Dr. Alexander Vyazmensky. Rio Tinto Ltd. Copper Projects. 354-200 Granville St.,
Vancouver, BC, Canada, V6C 1S4
E-mail: alex.vyazmensky@riotinto.com (alt. alex.vyazmensky@gmail.com)
(2) Rock Mechanics Specialist, Golder Associates Ltd., Mining Division, Vancouver,
Canada
(3) Professor, Department of Earth Science, Simon Fraser University, Vancouver,
Canada
Abstract:
Extraction of a large volume of ore during block caving can lead to the formation of
significant surface subsidence. Current knowledge of the mechanisms that control
subsidence development is limited as are our subsidence prediction capabilities. Mining
experience suggests that, among other contributing factors, geological structures play a
particularly important role in subsidence development. A conceptual modeling study has
been undertaken to evaluate the significance of geological structure on surface subsidence.
A hybrid finite/discrete element technique incorporating a coupled elasto-plastic fracture
mechanics constitutive criterion is adopted; this allows physically realistic modeling of
block caving through simulation of the transition from a continuum to a discontinuum.
Numerical experiments presented emphasize the importance of joint orientation and fault
location on mechanisms of subsidence development and the governing role of geological
structure in defining the degree of surface subsidence asymmetry.
Keywords:
surface subsidence; rock mass fabric; faulting; block caving; numerical modeling;
FEM/DEM-DFN

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1 Introduction
Block caving mining is one of the most cost effective underground mining
techniques. High efficiency and low production costs coupled with a growing
demand on natural resources have led to the increasing importance of this mining
method.
A typical block caving mine layout consists of two mining levels (a production level
and an undercut level) placed within the ore column. Ore is mined sequentially in
large sections over areas of several thousands of square metres. Caving is initiated
by blasting an extensive horizontal panel (undercut) beneath the mined block. Stress
redistribution and gravity combine to trigger progressive fracturing and caving of the
ore into the undercut. As caving of the ore is initiated, the undercut is connected with
the production level by blasting bell-shaped ore passages, called drawbells, each
consisting of at least two drawpoints. Broken ore falls through the drawpoints to the
production level where it is collected and transported to the crusher and
subsequently brought to the surface. As broken ore is removed from the drawpoints,
the ore above continues to break and cave by gravity, as illustrated in Fig. 1. Caving
extends progressively upwards as the ore is extracted, causing significant surface
depression, or subsidence, above the undercut and in the adjacent areas.
The ability to predict surface subsidence associated with block cave mining is
increasingly important for mine planning, operational hazard assessment and the
evaluation of environmental and socio-economic impact. Owing to problems of
scale and lack of access, our fundamental understanding of the complex rock
mass responses leading to subsidence development remains limited as are
available subsidence prediction capabilities. Current knowledge of subsidence
phenomena can be improved by employing numerical modelling techniques in
order to enhance our understanding of the primary factors governing subsidence
development; an essential prerequisite if the required advances in subsidence
prediction capability are to be achieved.

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This paper employs an integrated Finite Element Method / Discrete Element
Method - Discrete Fracture Network (FEM/DEM-DFN) numerical modelling
methodology and investigates the role of rock mass fabric and faults on surface
subsidence development. Presented models constitute part of a comprehensive
FEM/DEM-DFN parametric modelling study of surface subsidence associated
with block cave mining (Vyazmensky, 2008), which comprised more than 30
modelling scenarios with a total computational time equivalent to more than 500
days of continuous run-time on multiple Pentium 4 single processor (32bit)
personal computers.
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 structure (jointing and faults),
rock mass strength, in-situ stress level, mining depth and surface topography.
Among other contributing factors many authors emphasize the particular
importance of discrete geological structures on surface subsidence development.
A survey of the literature shows that published material provides in general a
qualitative rather than quantitative description of the influence of geological
structures on the observed subsidence; important observations from selected
references are summarized in Table 1. Although such qualitative observations
are useful in initial subsidence analysis they require further validation with
additional research in order to address a deficiency in quantitative data. To the
authors knowledge, modelling presented in this paper represents the first
comprehensive attempt to address this issue.
3 An Integrated FEM/DEM-DFN Approach to the Numerical Analysis of
Caving Induced Surface Subsidence
Conventional numerical modeling techniques applied to the analysis of rock
engineering problems treat the rock mass either as a continuum or as a
discontinuum. Finite element and finite difference methods model the rock mass

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as a continuum medium. In contrast, distinct/discrete element methods model the
rock mass as a discontinuum, consisting of an assembly or finite number of
interacting singularities. Both continuum and discontinuum modeling techniques
provide a convenient framework for the analysis of many complex engineering
problems.
Block caving subsidence is the product of a complex rock mass response to
caving. This response involves complex kinematic mechanisms and comprises
widespread failure of the rock mass in tension, and shear, along both existing
discontinuities and through intact rock bridges. Clearly, an analysis of this
phenomenon assuming either a pure continuum or discontinuum model may not
be realistic or adequate. The authors believe 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 and fracture mechanics principles is
adopted (Munjiza et al. 1995). An implementation of this approach using the
numerical code ELFEN (Rockfield Software Ltd. 2006) is employed. The ELFEN
code is a multipurpose finite element / discrete element software package that
utilizes a variety of constitutive criteria and is capable of undertaking both implicit
and explicit analyses in 2D and 3D space. Facility exists to simulate continuum
materials, jointed media and particle flow behavior.
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 integrated within the 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.

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In modelling quasi-brittle materials, ELFEN provides a variety of constitutive
models including the Rotating Crack and Rankine tensile smeared crack criteria,
in which material strain softening is fully governed by the tensile strength and
specific fracture energy parameters. Both of these models can be applied within
a standard continuum finite element framework whereby material failure is
confined to the concept of material strain softening, or they can be explicitly
coupled to the fracture insertion algorithm within ELFEN to introduce physical
cracking of material. For tension/compression stress states, the Rankine model is
complemented with a capped Mohr-Coulomb criterion in which the softening
response is coupled to the tensile model. A detailed description of this
constitutive model and a summary of the ELFEN solution procedure can be
found in Pine et al. (2007).
Geologically realistic representation of key natural discontinuities can be
achieved through use of DFN models. In the current study the DFN code
FracMan (Golder 2007) was utilized. FracMan is a convenient tool for generating
3D stochastical models of fracture networks based on collected discontinuity data
and allows the export of 2D fracture traces and complete 3D fracture sets into
geomechanical codes, including ELFEN. Examples of the integrated use of
ELFEN and FracMan have been presented by Pine et al. (2006), Rance at al.
(2007), Elmo et al. (2007), Vyazmensky et al. (2007), Elmo and Stead (2009),
and Vyazmensky et al. (2009).
4 Modelling Methodology
Although full 3D mine scale analysis of block caving subsidence is undoubtedly
desirable, available modeling tools are yet to reach the computational efficiency
required to allow detailed and realistic 3D analysis. ELFEN allows simulation of
brittle fracturing in 3D, although given long run-times, practical applications at
present are limited to pillar scale synthetic rock mass testing (Rockfield Software
Ltd 2009).

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In the current 2D modeling study emphasis is given to the representation of the
maximum level of detail allowable with the available computational efficiency.
Modeling results presented herein are conceptual and as such not related to any
particular case study. However, model geometry and geomechanical
characteristics are generally representative of the conditions in actual block
caving settings.
The ELFEN model, with dimensions 4000m by 600m, sub-divided into non-
fracturing and fracturing regions is shown in Fig. 2. The fracturing region spans
up to 1000m and encompasses the principal area where fractures may
potentially develop and consequently has a higher mesh resolution (2m sized
elements). The non-fracturing region has a lower discretization density (up to
50m elements) and extends to the model boundaries in order to minimize
potential boundary effects on simulation results.
Mahtab et al. (1973) noted that the fracture system most favorable 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 widely spaced and moderately
persistent joints. The joint pattern for the 2D model was derived by assuming a
plane parallel to one of the vertical sets within the 3D DFN model. Joint traces
intersecting this plane were delineated and exported into ELFEN. Imported joint
sets were rotated with respect to the model centre to achieve the desired dip.
The authors recognize the idealised nature of the embedded DFN traces, which
although not fully maximizing the statistical distributions available in FracMan,
were purposely chosen as a practical preliminary analysis stage prior to later
more rigorous site-specific models.
Flores and Karzulovic (2002) studied a number of block caving mines and
reported average caved ore block heights of around 200m. In this preliminary
study block caving mining is simulated by the undercutting and full extraction of a
block of ore (100m x 100m) located at 200m depth. The undercut (100m x 4m) is
developed in stages in 20m increments. A uniform draw of ore is assumed.

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Material extraction is simulated by gradual lowering of the undercut floor (see
Fig. 2).
One of the main challenges in rock mechanics modeling is establishing
representative rock mass properties. Rock mass classification systems such as
the rock mass rating system (RMR; Bieniawski 1989), Q-index (Barton et al.
1974) and the Geological Strength Index (GSI; Hoek et al. 1995) are traditionally
used to derive properties for the equivalent continuum rock mass. An equivalent
continuum approach accounts for the occurrence of all discontinuities in an
implicit sense. In the models presented in this paper the effects of discontinuities
in terms of rock mass strength are directly represented by the shear strength
properties of the discretised fracture elements. It is however clearly not possible
to represent all fractures present in a rock mass, consequently equivalent rock
mass properties are used to represent the strength and deformation properties of
the rock in which the discontinuities are inserted. Model calibration is required to
ensure that the combined system of pre-inserted fractures and selected
equivalent continuum rock mass properties is able to simulate caving behavior in
a close agreement with observed in-situ mine experience.
In this study the Barton’s Q-index is used to define the initial equivalent
continuum rock mass properties. These properties are further calibrated
(primarily through adjustment of tensile strength) so that the model response is
representative of the caving behavior of a rock mass with MRMR 55 to 60 for an
assumed hydraulic radius of 50. The MRMR is the mining rock mass rating
(Laubscher 1980) and typical MRMR values for block cave mines are in the
range of MRMR 30 to 70 (Flores and Karzulovic 2002). The input parameters for
the ELFEN modeling are given in Table 2.
A series of parametric numerical experiments were carried out to evaluate the
relative significance of joint orientation, fault location and inclination as outlined in
the following sections.

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5 Influence of Jointing
Vyazmensky (2008) presents a comprehensive analysis of the influence of rock
mass fabric on surface subsidence development, including the effect of varying
joint set orientation, persistence and joint condition. Here five modeling scenarios
(Table 3) focussing on the influence of joint orientation are presented and
discussed.
The Base Case, J1 and J2 models are intended to illustrate how varying the
orientation of a joint pattern affects subsidence development mechanisms and
the final subsidence footprint. Models J3 and J4 are based on the J2 model and
are used to evaluate the significance of the change in orientation of the sub-
vertical set and the presence of an additional vertical set, respectively. The Base
Case model was selected as a reference, a combination of vertical and horizontal
joints representing conditions “ideal” for caving.
5.1 Subsidence Mechanisms
Fig. 3 presents the mechanism of surface deformation development for the Base
Case, J1, J2, J3 and J4 models at 35, 50 and 60% caved ore extraction. All
models show a common subsidence crater formation mechanism which can be
summarized as:
 caving/unloading induced fracturing coupled with continuous ore extraction
creates favourable kinematic conditions for the detachment of major near
surface rock mass segments adjacent to the caving front;
 the detached rock mass segments collapse into the cave through
rotational and/or translation failure; surface expressions of such failure
involve formation and growth of multiple tensile cracks which eventually
disappear as the rock mass disintegrates;
 the extreme limits of these detaching segments are manifested at the
surface by the initial subsidence crater walls;

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 continuous removal of the ore leads to lowering of the fragmented rock
within the crater reducing lateral support to the crater walls. This promotes
further lateral growth of the subsidence crater through rotational and/or
translational failures of the crater wall segments into the cave.
The described mechanism of subsidence deformation development is in general
agreement with that suggested by Abel and Lee (1980) based on subsidence
observations.
It can be inferred from Fig. 3 that the direction of cave propagation toward the
surface, the location of the cave breakthrough and the mechanisms of near
surface rock mass failure are all strongly controlled by joint orientation. Fig. 4
illustrates the variation of the vertical stress contours at an early stage of ore
extraction for the Base Case and J2 models. This figure shows that the
orientation of the sub-vertical/steeply dipping joint set predetermines the direction
of caving induced rock mass unloading and thus the direction of cave
propagation. Comparing the centre of the surface depression at 35% ore
extraction for the Base Case (Fig. 3a), J1 (Fig. 3b) and J2 (Fig. 3c) models, it is
clear that a rotation of the joint pattern skews the direction of cave propagation
away from the block centre vertical axis, cave propagation being largely
controlled by the steeply inclined joint set. Rotation of the joint pattern by 10°
moves the centre of surface depression by about 4°, reaching 9° for the J2
model. This trend however may be altered depending on the orientation of the
gently dipping set. Comparing models J2 (Fig. 3b) and J3 (Fig. 3c) a change of
inclination of the sub-horizontal set from 20° dip to horizontal shifts the centre of
surface depression closer to the block centre vertical axis by 5°, i.e. more than
50%. Moreover, comparing models J2 (Fig. 3c) and J4 (Fig. 3e) it is evident that
the presence of an additional well defined vertical joint set reduces the
significance of the steeply dipping set, so that the centre of initial surface
depression is nearly aligned with the block centre vertical axis.
Joint orientation controls not only the cave propagation direction but also plays a
significant role in the manner in which the rock mass is mobilized by caving. In

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order to characterize the development of rock mass mobilization Fig. 3 delineates
zones of active rock mass movement and developing rock mass failure. Within
the former the rock mass is fully disintegrated whereas the latter zone indicates
the damaged and potentially unstable rock mass. Figs. 3(a) and (e) show that the
effect of the vertical joint set is relatively limited and that the extent of the rock
mass mobilized during initial stages of caving and ore extraction is largely
symmetrical (with respect to the ore block centre axis). As observed in Figs.
3(b,c,d) simulations assuming sub-vertical and steeply dipping joint sets result in
a larger extent of the mobilized rock mass. The overall failure response is
asymmetrical and more pronounced within the zone where sub-vertical/steeply
dipping joints are inclined towards the cave (west of the block centre vertical
axis). Conversely, a more limited failure zone is observed in models where the
joints dip towards the cave (east of the block centre vertical axis). This
asymmetry can be attributed to the varying mechanisms in failure of the rock
mass as governed by the inclination of the vertical/steeply dipping joints. West of
the block centre vertical axis, inclination of the joint sets favours rock mass failure
through flexural and block-flexural toppling, coupled with inclined cave
propagation this creates suitable kinematic conditions for toppling of massive
rock mass segments. In an eastwards direction, a sub-vertical/steeply dipping
joint set creates favourable conditions for sliding and, in combination with an
orthogonal joint set promotes slide toe toppling. Such a failure does not appear to
exceed the dip angle of the sub-vertical joint set, hence limiting the extent of the
mobilized rock mass.
5.2 Subsidence Topography
Final subsidence deformation and the resultant surface profiles at 100% ore
extraction for the Base Case, J1, J2, J3 and J4 models are shown in Figs. 5 and
6 respectively. It is clear from these figures that the rock mass deformation and
the surface depression formed due to caving can vary significantly depending on
the assumed joint set orientation. Rotation of the joint pattern shifts the centre of
the surface depression, positioned at the block centre vertical axis for Base Case

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model, in a direction opposite to that of surface asymmetry (i.e. eastwards) and
also results in a shallower subsidence crater. Rotation of the jointing pattern by
only 10° results in a decrease of the maximum depth of the crater by about 10%.
The maximum crater depth was observed for the model with vertical/horizontal
joint sets (Base Case) and the minimum for the simulation assuming steeply
dipping/horizontal joint sets (J3).
Models with different joint orientation are noted to exhibit varying subsidence
crater topography. For the Base Case model a distinct, nearly symmetrical and
stepped V-shaped crater is formed. In contrast, for simulations with inclined joints
(J1 to J3) the subsidence crater is asymmetrical. In the direction of maximum
asymmetry (i.e. westwards) the surface subsides without forming major steps,
with the exception the crater wall. It is interesting to note that the addition of the
vertical joint set in model J4 reduced crater asymmetry and resulted in a stepped
crater topography.
5.3 Characterization of Major Surface Displacements
In order to quantify the extent of major surface subsidence deformation a 10cm
displacement threshold is adopted. It is assumed that this threshold limits the
zone of major surface disturbance. The contours of 10cm vertical and horizontal
displacements at 100% ore extraction for Base Case, J1, J2, J3 and J4 models
are used to define the Mobilized Rock mass Volume (MRV), as indicated in Fig.
5. The maximum span of the major surface displacement induced by the caving
is delineated using angular limits. Comparing angles limiting major surface
deformations, for the models presented, it can be seen that in an eastward
direction from the block centre vertical axis all models show consistently steep
limiting angles ranging from 72° to 76°. In a westward direction, the dissimilarity
in the limiting angles between the different models is apparent. The lowest
minimum angle of fracture initiation, 53°, is observed for model J2 (Fig. 5c) and
the highest angle, 71°, for the Base Case model (Fig. 5a), i.e. rotation of the joint
pattern by 20° results in an increase in the extent of subsidence in the direction

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of the sub-vertical joint set by about 20%. Interestingly, the initially asymmetrical
subsidence development for model J1 with a 10° joint pattern rotation eventually
becomes more symmetrical, and only a minor increase in the limiting angle is
observed (see Figs. 3b and 5b). It appears that the 80° dip of the sub-vertical set
is insufficient to cause extensive flexural toppling. Model J4 (Fig. 5e) yields the
second lowest limiting angle, 61°, which is about 10% lower than for the J2
model. This indicates that the inclusion of the vertical joint set provides additional
planes of weakness in the model and thereby limits the simulated extent of the
rock mass mobilized by the caving. The initial subsidence development for the
J4 model is nearly symmetrical, as shown in Fig. 3(e). Subsidence asymmetry in
a westerly direction begins to develop as the constraining effect of the
fragmented rock diminishes due to continuous ore extraction; block toppling and
sliding of the crater wall segments are then possible along the gently dipping joint
set. Comparing models J2 and J3, it can be concluded that decreasing the dip of
the gently dipping set by 20° increases the limiting angle by 10° or about 20%.
Such an influence can tentatively be explained by reduction of the potential for
rotation and sliding towards the cave along the gently dipping joint set.
To characterize subsidence asymmetry a block cave subsidence parameter, the
Asymmetry Index (AI) is introduced. This index is defined as the ratio of the
minimum to maximum angles delineating the extent of major (≥10cm) surface
displacements, as shown in Fig. 5. Perfect symmetry corresponds to an AI of 1.
In addition to using the limiting angles, the zone of major surface deformation can
be further characterized by its total extent and relative significance with respect
to the vertical axis at the block centre, Fig. 7. Changes in the joint set orientation
cause an increase in the extent of the total major surface deformations by up to
30% and 41% for major vertical and horizontal surface displacement,
respectively. For all models the total extent of the major surface horizontal
deformation is consistently larger than or equal to the extent of vertical
displacements. Examining Fig. 7(c) and (d) shows that depending on the
assumed joint set orientations:

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 west of the block centre vertical axis the extent of major surface
deformations increases up to a maximum of about 40% and 80% for
vertical and horizontal displacements;
 east of the block centre vertical axis a moderate increase only of up to
20% for both vertical and horizontal displacements is observed.
Evolution of the zone of major (≥10cm) surface deformation with continuous ore
extraction and the rate of growth west of the block centre vertical axis for Base
Case, J1, J2, J3 and J4 models is shown in Figs. 8 and 9, respectively. It can be
inferred that major subsidence deformation develops in a relatively rapid manner
suggesting a quick mobilization of the massive rock mass segments. Fig. 9a
shows that for the majority of the models, with the exception of model J4, about
90% of the maximum vertical deformations is achieved by 50% ore extraction.
Model J4 exhibits a more subtle trend in vertical deformation which can be
attributed to the previously discussed gradual block toppling failure mechanism.
Horizontal deformation trends are presented in Fig. 9b, which indicates that for
simulations which involve flexural toppling failure (models J1, J2, and J3)
horizontal displacements generally increase at a rate of up to 80% greater than
the vertical displacements.
5.4 Characterization of Far-Field Displacements
When considering the location of mine infrastructure it is important to appreciate
the magnitude of surface displacements at specific distances from the area of
imminent failure (caving boundary and its immediate vicinity). Fig. 10 shows total
vertical and horizontal displacements at the end of ore extraction and at
distances of 300, 250, 200 and 150m from the block centre for the Base Case,
J1, J2, J3 and J4 models.
According to this figure the minimum amount of surface displacement is exhibited
by the Base Case model (90°/0°), in which only minor horizontal displacements
of about 1cm are observed 100m from the caving boundaries (150m from the
block centre vertical axis). The maximum magnitude of displacement is observed

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for the J2 (70°/20°) and J3 (70°/0°) models, where 1cm horizontal displacements
are noted as far as 200m west of the caving boundaries. Far-field surface
displacements generally mirror the trends observed for the major surface
deformations, showing strong asymmetry in the dip direction of the sub-
vertical/gently dipping joint sets. Apparently, the magnitude of accumulated
surface displacement as well as its extent will depend on the mechanism of the
rock mass failure induced by caving, which, as discussed earlier is strongly
controlled by the joint orientation. Comparing vertical (Fig. 10a) and horizontal
(Fig. 10b) far-field displacements in the simulations undertaken in this paper,
there is a clear trend of higher far-field horizontal displacements which is in
agreement with the measurements of caving induced surface displacements at
the Lakeshore mine, Panek (1984).
6 Influence of Faulting
The influence of faults on surface subsidence development was evaluated
through a series of models assuming a fault that dips toward the cave,
considering different fault locations with respect to the block centre vertical axis
and varying the fault inclination. Model geometries are shown in Fig. 11. Two
different jointing conditions, 90°/ 0° and 70°/ 20°, based on the Base Case (Fig.
5a) and J2 (Fig. 5c) scenarios, were employed. The contact properties on the
fault interfaces were assumed to be identical to the contact characteristics of pre-
inserted discontinuities (shown in Table 2).
6.1 Effect of Fault Location
The effect of fault location on surface subsidence development was evaluated
using five scenarios, Table 4.
Figs. 12(a,b,c) illustrate the mechanisms of surface subsidence at 35, 50 and
60% ore extraction and Fig. 13(a,b,c) show the resultant subsidence
deformations at 100% ore extraction for the models employing vertical/horizontal
joints (F1, F2, F3). Comparing these models it is clear that the degree of

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influence of the fault on caving induced surface subsidence varies with its
location. For the model with a fault located at 50m from the block centre vertical
axis (F1, Figs. 12a and 13a), caving induced unloading quickly triggers
translational failure and full disintegration of the fault hanging wall and a gradual
failure of the fault footwall. By the end of ore extraction the fault is almost fully
consumed by the caving. Observed surface subsidence deformations are largely
symmetrical with respect to the block centre vertical axis. The minimum angle
delineating the extent of major (10cm) surface displacements is 73°, which is
only 2° higher than for the same model but without a fault (Base Case, Fig. 5a).
For the model with a fault located 100m from the block centre vertical axis (F2,
Figs. 12b and 13b) a notably different subsidence development mechanism is
observed. Only a minor undercuting of the fault coupled with caving induced
unloading triggers translational failure of major hanging wall segments along the
fault interface, eventually resulting in the hanging wall “sagging” into the cave.
The fault footwall withstood the caving sustaining only minor damage. Surface
subsidence is clearly asymmetrical in a direction towards the fault. The minimum
angle delineating the extent of major surface displacement is 61°, which is 10°
less than for the Base Case model (Fig. 5a). A fault positioned outside the caving
boundaries, at 150m from the block centre vertical axis (F3, Figs. 12c and 13c),
has no significant influence on the simulated surface subsidence. As seen in Fig.
14, the presence of a steeply dipping fault in a vertical/horizontal jointed rock
mass, located at 50m (F1) and 150m (F3) from the block centre vertical axis has
negligible effect on the extent of the zone of major surface displacements. In
contrast, a fault located at 100m (F2) has been shown to increase the extent of
major vertical and horizontal displacements zone by approximately 20%,
primarily in a direction towards the fault.
Subsidence development mechanisms for the F4 and F5 models, which assume
steeply/gently dipping (70°/20°) joints, are illustrated in Figs. 12(d,e) and show
similar observed trends as previously discussed for the F2 and F3 models. Final
surface subsidence deformation at 100% ore extraction for models F4 and F5 is

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given in Fig. 13(d,e). Comparing the models where a fault is intersecting the
block (F2, F4), it can be noted that the change of joint orientation does not affect
the extent of major surface deformation, which is limited by the fault. For models,
where the fault does not intersect the block (F3, F5), subsidence is primarily
governed by jointing. Comparing the F3 (Fig. 13c) and Base Case (Fig. 5a)
models, increased tensile fracturing can be noted in the hanging wall in the
vicinity of the caving boundary indicating the weakening effect of the fault on the
hanging wall rock mass. The J2 (Fig. 5c) and F5 (Fig. 13e) models illustrate the
limiting effect of the fault on rock mass mobilization, clearly indicating that the
fault prevents mobilization of the rock mass in the footwall, increasing the limiting
angle from 53° to 59°. According to Fig. 15, the presence of a fault in
steeply/gently dipping (70°/20°) joint settings located at 100m and 150m from the
block centre vertical axis decreased the zone of major surface horizontal
displacements by 13% and 9%, respectively, in the direction towards the fault.
Figs. 16 and 17 illustrate far-field displacements for models based on
vertical/horizontal and inclined joint sets, respectively. For models with
vertical/horizontal joints, faults generally increased the magnitude and extent of
the far-field displacement. The largest increase is observed for the model with a
fault located 150m from the block centre vertical axis (F3), where horizontal
displacements in excess of 1cm are observed as far as 200m from the caving
boundary, which is twice the extent simulated in the model without a fault (Base
case). For models with inclined joints the opposite trend is observed, the
presence of a fault limiting both the magnitude and extent of far-field
displacement. Irrespective of joint set orientation horizontal displacements are
predominant.
Caving induced unloading of the hanging wall results in the formation of a
topographical step where the fault daylights. Fig. 18 compares differential XY
displacements along fault surfaces with continuous ore extraction for all
simulations. Depending on the fault location with respect to the block centre,
movements at the fault surface may vary significantly. For the models F1, F2 and

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F4, where a fault intersects the block, movements in the order of metres are
observed, whereas for models F3 and F5, where a fault does not intersect the
block, movements limited to several centimetres are noted. Inclination of the joint
sets affects these movements, such that larger XY displacements, which develop
more rapidly, are observed for models with inclined joints.
6.2 Effect of Fault Inclination
The effect of fault inclination on the development of surface subsidence was
evaluated based on six modelling scenarios, for a fault partially intersecting the
block. Three different fault inclinations and two different joint set conditions were
considered, as summarized in Table 5.
Figs. 12b, 19a and 19b illustrate the development of surface subsidence at 35,
50 and 60% ore extraction, and, Figs. 13b and 20(a,b) show resultant
subsidence deformations at 100% ore extraction for models F2, F6 and F7,
assuming vertical/horizontal joints. Figs. 12d, 19c and 19d present surface
subsidence development at 35, 50 and 60% ore extraction and Figs. 13d and
20(c,d) show the resultant subsidence deformation at 100% ore extraction for
models F4, F8 and F9, assuming steeply/gently dipping joints. Comparing
subsidence deformation development for varying fault inclinations and varying
joint set orientations it should be noted that, for all assumed inclinations, faults
affect the development of subsidence deformation. Irrespective of jointing
orientation caving induced failure is predominantly controlled by the plane of
weakness provided by the fault. Continuous ore extraction leads to full
mobilization of the entire hanging wall and its disintegration into segments. The
mode of hanging wall segmentation appears to be controlled by joint orientation.
Failure of the hanging wall leads to formation of a crater wall along the footwall of
the exposed fault; particularly pronounced for the 75° and 60° faults. For the 75°
fault models (F7, F9, Fig. 20(b,d)) exposure of a steep footwall by the caving
causes its partial failure, the magnitude of this failure is strongly controlled by the
jointing.

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18
Vertical/horizontal jointing contributes to formation of a nearly vertical wall,
whereas inclined joint sets favour kinematic instability of major near surface rock
mass blocks. For the 60° faults (F2, F4, Fig. 13(b,d)), the moderately inclined
footwall was more limited in exposure and the passive support provided by the
muck pile prevented development of major internal instability. Here it should be
noted that removal of this support will likely trigger further footwall damage,
particularly for the case with inclined joints. For the 45° faults (F6, F8, Fig.
20(a,c)), the footwall sustained only minor damage. It appears that for the
simulated jointing conditions development of major instability in a 45° footwall
slope even with continuous ore extraction is highly unlikely.
Inclination of the fault significantly alters the extent of the caving influence. For
the 45° and 60° faults, irrespective of the assumed joint set conditions, the extent
of major surface deformation toward the fault was determined by the fault
inclination, so that the angular limits of major (10cm) surface displacements are
equal or nearly equal to the fault inclination. For the 75° faults the extent of major
surface deformation is a function of the stability of the exposed footwall. For the
model with vertical/horizontal joints the limiting angle is 75, whereas for the
model with inclined joints it is 59.
Comparison of the extent of major surface displacements for the models with
vertical/horizontal joints without a fault (Base Case) and with fault dips of 75
(F6), 60 (F2) and 45 (F7) is presented in Fig. 21. This figure shows that faults
with inclinations of 60 and 45 extended the total zones of major displacement
by about 20 and 60%, respectively. In the direction towards the fault, for 60 and
45 dipping faults, the zone of influence was increased by 40 and 120%,
respectively, i.e. a decrease in fault inclination by 15 extended the zone of major
surface displacements by 80%. The fault with 75 inclination had only a minor
influence on the observed extent of major surface displacements. Comparison of
the extent of major surface displacements for the models with inclined joints
without a fault (J2) and with a fault of 75 (F9), 60 (F4) and 45 (F8) inclination is

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19
given in Fig. 22. As can be inferred from this figure for faults with inclinations of
60 and 75 the extent of the zone of major surface displacement towards the
fault was reduced by as much as 50%. The surface outcrop location of the 45
fault coincided approximately with the extent of major displacements for the
model without a fault (see Figs. 5c and 20d), hence no major influence was
observed. Interestingly models with 45 and 75 dipping faults exhibit increased
zones of influence in an eastward direction from the block centre vertical axis.
Far-field displacements for models with vertical/horizontal and inclined joints are
presented in Figs. 23 and 24, respectively. It can be inferred from these figures
that, in the direction towards the fault, the extent of the far-field displacements is
a function of fault inclination. A shallower fault inclination resulted in a larger area
mobilized by the caving. Conversely, steeper faults limit such an area. Within the
failing hanging wall higher deformation magnitudes were observed for models
with vertical/horizontal joints. Depending on the fault inclination the amount of
differential displacement at the surface outcrop of the fault varies, higher
displacements being observed for models with steeper faults (see Fig. 25).
7. Results Synthesis and Conclusions
The adopted modelling methodology has allowed physically realistic simulation of
subsidence deformation mechanisms, from caving initiation to the final
subsidence topography. It thereby has provided quantitative support for the
observational-based conceptual model of subsidence development proposed by
Abel and Lee (1980). The 2D FEM/DEM-DFN modelling offers a convenient
framework for future quantitative analysis of block caving induced surface
subsidence and has significant potential for improving subsidence prediction
capabilities. Vyazmensky et al. (2009) have applied this approach to the analysis
of a block caving induced large open pit slope failure at the Palabora mine and
illustrated that the 2D FEM/DEM-DFN modelling methodology can be
successfully applied to the analysis of complex industrial scale problems.

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20
The program of 2D FEM/DEM with fracture simulations presented in this paper is
the most comprehensive of its kind to date constituting a significant advance in
the 2D simulation of fracture and subsidence associated with block caving. New
and valuable insights were gained into the complex mechanisms governing
caving induced rock mass deformations and associated subsidence
development. The numerical experiments presented in this paper have
highlighted the importance of both joint set orientation and fault location and
inclination, in determining the mechanisms of subsidence development; in
addition their governing role in defining the degree of surface subsidence
asymmetry has been demonstrated. Key model observations are summarized in
Table 6. Based on the modelling analyses a preliminary classification of the
influence of major geological discontinuities on surface subsidence is proposed,
Table 7. Further analysis should consider a range of stochastically generated
DFN realisations. It should be noted that presented modelling results represent
only a small part of a larger study investigating factors governing block cave
subsidence development (Vyazmensky, 2009).
While 3D analysis of geomechanical problems is preferred, the simulation of
block caving related subsidence in 3D has to date almost exclusively involved
continuum modelling. This choice is primarily driven by the higher computational
efficiency of continuum codes for large scale modelling. It should be recognized
that these continuum codes are unable to simulate explicitly important
mechanisms for block caving subsidence development such as brittle fracture
and failure kinematics and therefore may not be applicable in all cases. As
illustrated by Stead et al. (2007) applications of discontinuum codes for detailed
block caving analysis face extreme computational challenges. Detailed and
realistic mine scale block caving modelling in 3D has yet to be achieved.
In the authors' opinion FEM/DEM-DFN modeling provides an important
alternative to traditional modelling approaches and represents a new and
valuable tool in the rock engineer’s geotechnical modelling toolbox. The initial
applications of this technique are very encouraging. As the requisite computing

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21
power becomes available and the existing FEM/DEM codes are adapted to
maximize the use of 64 bit architectures and parallel processing facilities
FEM/DEM-DFN technique will be adopted to mine scale 3D modelling, allowing
physically realistic simulation of the block caving process, including caving
initiation, fragmentation, mass flow and resultant surface subsidence.
Acknowledgements
The authors would like to acknowledge research funding provided by Rio Tinto and
Natural Sciences and Engineering Research Council of Canada. We would also like to
acknowledge research collaboration with Allan Moss and Andre van As (Rio Tinto), Erik
Eberhardt, Scott Dunbar and Malcolm Scoble (University of British Columbia). Technical
support of Rockfield Technology Ltd. (UK) is gratefully appreciated.

- 556.
22
References
Abel JF, Lee TF (1980) Subsidence Potential in Shale and Crystalline Rocks. U.S.
Geological Survey Open File Report 80-1072. 49pp.
Barton N, Lien R, Lunde J (1974) Engineering classification of rock masses for design of
tunnel support. Rock Mech. 6(4): 189–236.
Bieniawski ZT (1989) Engineering Rock Mass Classifications. Wiley. 272 pp.
Crane WR (1929) Subsidence and Ground Movement in the Copper and Iron Mines of
the Upper Peninsula, Michigan. USBM Bulletin 285. 66pp.
Elmo D (2006) Evaluation of a hybrid FEM/DEM approach for determination of rock
mass strength using a combination of discontinuity mapping and fracture
mechanics modelling, with particular emphasis on modelling of jointed pillars.
PhD Thesis. Camborne School of Mines, University of Exeter, UK.
Elmo D, Vyazmensky A, Stead D, Rance JR (2008) A hybrid FEM/DEM approach to
model the interaction between open pit and underground block caving mining.
Proc. 1st Canada-U.S. Rock Mechanics Symposium, Vol 2, 1287-94pp.
Elmo D, Stead D (2009) An integrated numerical modelling - discrete fracture network
approach applied to the characterisation of rock mass strength of naturally
fractured pillars. Rock Mechanics and Rock Engineering, DOI 10.1007/s00603-
009-0027-3.
Flores G, Karzulovic A (2002) Geotechnical guidelines for a transition from open pit to
undeground mining. Benchmarking Report for ICSII. Task 4. 91 pp.
Golder Associates (2007) FracMan Technology Group. Home page at:
http://www.fracman.golder.com
Hoek ET, Kaiser PK, Bawden WF (1995) Support of underground excavations in hard
rock. A.A. Balkena. Rotterdam. 300pp.
Klerck PA (2000) The finite element modelling of discrete fracture in quasi-brittle
materials. Ph.D. thesis, University of Wales, Swansea.
Laubscher DH (1990) A geomechanics classification system for the rating of rock mass
in mine design. J. S. Atr. Inst. Min. Metall. 90(1): 257-293.
Mahtab MA, Bolstad DD, Kendorski FS (1973) Analysis of the geometry of fractures in
San Manuel copper mine, Arizona. Bureau of Mines. Technical report RI 7715.
Munjiza A, Owen DRJ, Bicanic N (1995). A combined finite/discrete element method in
transient dynamics of fracturing solids. Int. J. Engng Comput. 12(2): 145–174.
Munjiza A (2004) The combined finite-discrete element method. Chichester: J. Wiley &
Sons. 348pp.
Owen DRJ, Feng YT, de Souza Neto EA, Cottrell M G,Wang F, Andrade Pires FM, Yu J.
(2004) The modelling of multi-fracturing solids and particulate media. Int. J. Num.
Meth. Eng. 60(1): 317-339.

- 556.
23
Panek LA (1984) Subsidence in undercut - cave operations, subsidence resulting from
limited extraction of two neighboring cave operations. In: Geomechanical
Applications in Hard Rock Mining. (ed. Pariseau, W.G.) pp 225-240.
Pine RJ, Owen DRJ, Coggan JS, Rance JM (2007) A new discrete modelling approach
for rock masses. Geotechnique. 57(9): 757-766.
Pine RJ, Coggan JS, Flynn ZN, Elmo D (2006) The development of a new numerical
modelling approach for naturally fractured rock masses. Rock Mech. Rock
Engng. 39(5): 395-419.
Rance JM, van As A, Owen DRJ, Feng YT, Pine RJ (2007) Computational modelling of
multiple fragmentation in rock masses with application to block caving. Proc. 1st
Canada-U.S. Rock Mechanics Symposium. Vancouver Vol 1: 477-484pp
Rockfield Software Ltd (2007) ELFEN user manual, Swansea, UK. Home page at:
http://www.rockfield.co.uk
Rockfield Software Ltd (2009) Primary fragmentation at Northparkes E26 Lift 2 block
cave. Technical report PRF1884. 271pp.
Sandvik Group (2004) Block caving animation.
Stacey TR, Swart AH (2001) Practical rock engineering practice for practice for shallow
and opencast mines. SIMRAC The safety of mines research advisory committee,
66pp.
Stead D, Coggan JS, Eberhardt E (2004) Realistic simulation of rock slope failure
mechanisms: The need to incorporate principles of fracture mechanics.
SINOROCK 2004: Special Issue of Int. Journal of Rock Mechanics. 41(3). 6pp.
Stead D, Coggan JS, Elmo D, Yan M (2007) Modelling brittle fracture in rock slopes:
experience gained and lessons learned. In Proc. Int. Symp. on Rock Slope
Stability in Open Pit Mining and Civil Engineering. Perth. pp. 239-252.
van As A, Davison J, Moss A (2003) Subsidence Definitions for Block Caving Mines.
Technical report. 59pp.
Vyazmensky A, Elmo D, Stead D, Rance JR (2007) Combined finite-discrete element
modelling of surface subsidence associated with block caving mining. In Proc.
1st Canada-U.S. Rock Mechanics Symposium. Vancouver Vol 1: 467-475.
Vyazmensky A (2008) Numerical modelling of surface subsidence associated with block
cave mining using a finite element / discrete element approach. PhD thesis.
Simon Fraser University, Canada.
Vyazmensky A, Stead D, Elmo D, Moss A (2009) Numerical Analysis of Block Caving-
Induced Instability in Large Open Pit Slopes: A Finite Element/Discrete Element
Approach. Rock Mechanics and Rock Engineering, DOI 10.1007/s00603-009-
0035-3
Wilson ED (1958) Geologic Factors Related to Block Caving at San Manuel Copper
Mine, Pinal County, Arizona. Progress Report, April 1956-1958. Bureau of Mines
Rept. of Inv. 5336. 40pp.

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Table 1 Influence of geological structure on block caving surface subsidence
development
Geological
structure
Influence on block caving subsidence Reference
Joints
In the absence of faults and dykes, joint dip governs the
angle of break. Angle of break for a mine should be equal
to the dip of the most prominent joint set.
Crane (1929),
Wilson (1958)
Faults
When a mining face encounters a significant
discontinuity, such as a fault, with moderate to steep
dip, movement will occur on the fault regardless of the
cave angle through intact rock. A stepped crack will
result where the fault daylights at surface. If mining is
only on the hanging wall side of the fault there will only
be surface movements on the one side. If the fault dip
is steeper than the cave angle the extent of surface
subsidence will be reduced, conversely, if the fault dip
is less than the cave angle the extent of surface
subsidence will be increased.
Abel and Lee
(1980),
Stacey and
Swart (2001),
van As et al.
(2003)
Table 2 Modelling input parameters
Parameter Unit Value Parameter Unit Value
Rock mass Discontinuities
Young’s Modulus, E GPa 18 Fracture cohesion, cf MPa 0
Poisson’s ratio,  0.25 Fracture friction, f degrees 35
Density, ρ kgm-3
2600 Normal stiffness GPa/m 2
Tensile strength, t MPa 1 Shear stiffness GPa/m 0.2
Fracture energy, Gf Jm-2
60
Cohesion, ci MPa 4.7 Stress level
Friction, i degrees 45 In-situ stress ratio, K 1
Dilation, ψ degrees 5

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25
Table 3 Modelling scenarios for analysis of the effect of joint orientation
Scenario Number
of sets
Joint sets
dips, °
Description
Base
Case (BC)
Two sets 90/0 Orthogonal sets, vertical/horizontal
J1 Two sets 80/10 Orthogonal sets, sub-vertical/sub-horizontal
J2 Two sets 70/20 Orthogonal sets, steeply dipping/gently dipping
J3 Two sets 70/0 Orthogonal sets, steeply dipping/horizontal
J4 Three sets 70/20/90
Orthogonal sets, steeply dipping/gently
dipping/vertical
Table 4 Modelling scenarios for analysis of the effect of fault location
Scenario Joint set dips, ° Fault dip, ° Fault location
with respect to
block centre
axis, m
Figure
F1
90/0
60
50 10(a)
F2 100 10(b)
F3 150 10(c)
F4
70/20
100 10(d)
F5 150 10(e)
Table 5 Modelling scenarios for analysis of the effect of fault inclination
Scenario Joint set dips, ° Fault dip, ° Figure
F6
90/0
45 10(f)
F2 60 10(b)
F7 75 10(h)
F8
70/20
45 10(g)
F4 60 10(c)
F9 75 10(i)
Table 6 Summary of modelling findings

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26
Influence on block caving subsidence
Jointorientation
 Well defined, vertical to steeply dipping joints govern the direction of cave
propagation and the mechanism of near surface rock mass mobilization. The
shallower the dip of these joints the more inclined from vertical the cave
propagation direction is and the more asymmetrical the surface deformation
with respect to the block centre vertical axis. In cases where multiple well
defined and persistent steeply dipping joint sets are present, the steepest set
will generally have the predominant influence.
 Significant subsidence asymmetry is observed in the dip direction of the sub-
vertical/steeply dipping set. Where joints are inclined towards the cave, the
rock mass fails through a combination of block-flexural and block toppling
and the detachment and sliding of major rock segments. Where a sub-
vertical joint set is dipping into the cave, the surface deformation direction is
controlled by the dip of the sub-vertical joint set. In this case the rock mass
fails predominantly through block toppling and sliding along the sub-vertical
joints.
 The orientation of well defined, gently dipping joints influences the extent of
the rock mass mobilized by the failure and the degree of subsidence
asymmetry.
Faultsinclinationandlocation
 Unequivocally, the inclination of the fault partially intersecting the caving
area controls the extent of surface subsidence deformations. Low dipping
faults will extend and steeply dipping faults will decrease the area of surface
subsidence.
 For faults daylighting into the cave, failure of the hanging wall is likely
inevitable. For the assumed hard rock mass conditions in the current
modelling, the stability of the exposed footwall is dependent on its slope, the
amount of passive support provided by the muck pile and the orientation and
persistence of jointing within the footwall. The presence of well defined
steeply/gently dipping joint set approaching perpendicular orientation with
relation to the fault will increase the kinematic potential for failure of major
near surface footwall segments. In such circumstances a model combining
the fault/jointing system is extremely important.
 Steeply dipping faults, daylighting into the cave and located within an area of
imminent caving are likely to be caved and therefore are unlikely to play any
major role in the resultant subsidence.
 Faults partially intersecting the caving area may create unfavourable
conditions with potential for failure of the entire hanging wall.
 Depending on rock mass fabric, faults located in the vicinity of the caving
zone may have a minimal influence or decrease the extent of the area of
subsidence deformation. The former behaviour was observed in models with
horizontal/vertical joint sets and the latter for orthogonal steeply/gently
dipping joints.
 A topographical step in the surface profile is formed where the fault daylights
at the surface. Significant movements should be anticipated if the fault
daylights into the cave.

Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556.
27
Table 7 Preliminary classification of the influence of major geological discontinuities on caving induced surface subsidence
Degree of influence Typical subsidence deformations Description
I. Low to Moderate
I(a)
fault
highly
disturbed to
rubblized
rock mass
intact
rock mass
disturbed
rock mass
2H
W=H
I(b)
fault
I(a) fault located at distances exceeding 0.5H from
the caving boundary
fault may act as a displacement barrier limiting rock
mass movements in the far-field
I(b) more than 2/3 of the fault near surface segment
is located within the caving zone
fault may affect caving mechanism
II. Significant to Extensive
II(a)
fault
II(b)
fault
major
block
II(a) steeply inclined (80 - 60) faults intersecting
caving boundary
II(b) moderately inclined (60 - 30) faults intersecting
caving boundary
in both cases the extent of surface subsidence and
subsidence asymmetry will be governed by fault
inclination
Note: this classification is based on the modelling that assumed rock mass corresponding to ~ MRMR 55-60, uniform ore extraction and block
depth 2H (where H is block height).

- 556.
28
Fig. 1 Schematic illustration of block cave mining and associated surface subsidence
(modified after block caving animation (Sandvik Group 2004)).

Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556.
29
Model geometry
Non-fracturing zone
Fracturing zone
100m
ore
block
100m
100m
70o
20o
4m
FracMan 3D model 2D trace plane
fractures
exported
into ELFEN
4000m
600m
Model setup
140m
undercut
moving platform
Caveability Laubscher’s caveability chart
Cave development
progression
Conceptual model of caving
by Duplancic & Brady (1999)
Subsidence limits Mining experience
Caveability Laubscher’s caveability chart
Cave development
progression
Conceptual model of caving
by Duplancic & Brady (1999)
Subsidence limits Mining experience
Model geometry
Non-fracturing zone
Fracturing zone
100m
ore
block
100m
100m
70o
20o
4m
FracMan 3D model 2D trace plane
fractures
exported
into ELFEN
Constraints
model response
evaluation
4000m
600m
Model setup
140m
undercut
moving platform
Fig. 2 ELFEN model setup

30
35% ore extraction 50% ore extraction 60% ore extraction
(a)BC(b)J1(c)J2(d)J3(e)J4
Legend: rotational failure; translational failure; active rock mass movement;
developing rock mass failure; centre of surface depression
Fig. 3 Subsidence crater formation for BC (a), J1 (b), J2 (c), J3 (d) & J4 (e) models

31
Fig. 4 Variation of vertical stress (Pa) contours with caving at 5% ore extraction for Base
Case and J2 models

32
0-100 -50-150-200-250 10050 150 200 250 300-300
(a)
BC
(b)
J1
(c)
J2
(d)
J3
(e)
J4
Fig. 5 Subsidence at 100% ore extraction for BC (a), J1 (b), J2 (c), J3 (d) & J4 (e) models
90°
0°
80°
10°
70°
20°
70°
0°
0°
70°
20°
10cm displ. contours
vertical
horizontal
Legend:
angle
of fracture
initiation
71°
70°
53°
61°
59°
71°
76°
73°
74°
74°
72°
MRV = 28114m3
AI = 0.93
MRV = 30762m3
AI = 0.96
MRV = 34990m3
AI = 0.72
MRV = 35250m3
AI = 0.82
MRV = 30836m3
AI = 0.82

33
-80
-70
-60
-50
-40
-30
-20
-10
0
-350 -250 -150 -50 50 150 250 350
Verticaldisplacements,m
Distance from block centre, m
Base case
J1
J2
J3
J4
0, -55
9.4, -49.6
28.6, -41
9.4, -44.5
10, -50
Lowest point
coordinates, m
Fig. 5 Surface profiles at the end of ore extraction for BC, J1, J2, J3 and J4 models
207
234
268 269
245
100%
113%
129%
130%
118%
0
50
100
150
200
250
300
350
0
50
100
150
200
250
300
350
Totalextentof10cmvertical
surfacedisplacements
normalizedbyBaseCase,%
surfacedisplacements,m
BC J1 J2 J3 J4
218
235
308
269
290
100%
108%
141%
123%
133%
0
50
100
150
200
250
300
350
0
50
100
150
200
250
300
350
Totalextentof10cmhoriz.
BC J1 J2 J3 J4
-112
95
-123
111
-161
107
-161
108
-132
113119%
132%
114%
144%
113%
144%
117%
110%
100%
100%
-300 -200 -100 0 100 200 300
-250 -200 -150 -100 -50 0 50 100 150 200 250
Extent of 10cm surface vertical displacements in
relation to block centre, normalized by Base Case, %
Extent of 10cm surface vertical dispacements in
relation to block centre, m
BC
J1
J2
J3
J4
BC
J1
J2
J3
J4
-118
100
-123
112
-201
107
-161
108
-173
117117%
147%
108%
136%
107%
170%
116%
104%
100%
100%
-300 -200 -100 0 100 200 300
-250 -200 -150 -100 -50 0 50 100 150 200 250
Extent of 10cm surface horizontal displacements in
BC
J1
J2
J3
J4
BC
J1
J2
J3
J4
Fig. 7 Subsidence characterization for Base Case, J1, J2, J3 and J4 models
Total extent of 10cm vertical (a) and horiz. (b) surface displacement; extent of 10cm
surface vertical (c) and horiz. (d) displacement in relation to centre axis of the block, in m
(c) (d)
(a) (b)

34
0
10
20
30
40
50
60
70
80
90
100
-250 -200 -150 -100 -50 0 50 100 150 200 250
Oreextraction,%
Extent of 10cm surface deformations, m
YY
XX
0
10
20
30
40
50
60
70
80
90
100
-250 -200 -150 -100 -50 0 50 100 150 200 250
Oreextraction,%
YY
XX
Fig. 8 Evolution of zone of major (≥10cm) vertical (YY) and horizontal (XX) surface
deformation with continuous ore extraction for Base Case (a), J1 (b), J2 (c), J3 (d) and
J4 (e) models
Fig. 9 Rate of growth of 10cm surface displacement zone west of the block centre
vertical axis with continuous ore extraction for Base Case, J1, J2, J3 and J4 models
(a) vertical displacement, (b) horizontal displacement
0
10
20
30
40
50
60
70
80
90
100
-250 -200 -150 -100 -50 0 50 100 150 200 250
Oreextraction,%
YY
XX
0
10
20
30
40
50
60
70
80
90
100
-250 -200 -150 -100 -50 0 50 100 150 200 250
Oreextraction,%
YY
XX
0
10
20
30
40
50
60
70
80
90
100
-250 -200 -150 -100 -50 0 50 100 150 200 250
Oreextraction,%
YY
XX
0
20
40
60
80
100
120
0 20 40 60 80 100 120
extentofvertical10cmsurface
displacements,%
Ore extraction, %
BC_YY
J1_YY
J2_YY
J3_YY
J4_YY
0
20
40
60
80
100
120
0 20 40 60 80 100 120
extentofhorizontal10cmsurface
displacements,%
Ore extraction, %
BC_XX
J1_XX
J2_XX
J3_XX
J4_XX
(d) J3
(e) J4
(b) J1(a) BC
(c) J2
(a) (b)

35
J2
J3
J4
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
-300 -250 -200 -150 150 200 250 300
-0.38 -2.1
J2
J3
BC
BC
BC
J1
J1
J1
J2
J2
J2
J2
J3
J3
J3
J3
J4
J4
J4
0
0.05
0.1
0.15
0.2
0.25
0.3
-300 -250 -200 -150 150 200 250 300
Horizontaldisplacements,m
0.9 3.8
Fig. 10 Total vertical (a) and horizontal (b) surface displacement at the end of ore
extraction at different distances from block centre for Base Case, J1, J2, J3 and J4 models
(a)
(b)

36
0-100 -50-150-200-250 10050 150 200 250 300-300
(a) F1
(b) F2
(c) F4
(d) F3
(e) F5
(f) F6
(g) F8
(h) F7
(i) F9
Fig. 11 Assumed fracture orientations and fault positions for F1 to F9 models
90°
0°
70°
20°
90°
0°
70°
20°
90°
0°
90°
0°
70°
20°
90°
0°
70°
20°
fault
60°
50m
60°
100m
60°
150m
45°
75°

37
(a) (b) (c) (d) (e)
Legend: rotational failure; translational failure; fault location prior to failure
active rock mass movement; developing rock mass failure
Fig. 12 Subsidence crater formation for F1 (a), F2 (b), F3 (c), F4 (d) and F5 (e) models
fault fault fault fault fault

38
0-100 -50-150-200-250 10050 150 200 250 300-300
(a)
F1
(b)
F2
(c)
F3
(d)
F4
(e)
F5
Fig. 13 Subsidence at 100% ore extraction for F1, F2, F3, F4 and F5 model
fault location prior
to caving
90°
0°
73°
vertical
horizontal
Legend:
angle
of fracture
initiation
73°
73°
MRV = 30154m3
AI = 1.0
90°
0°
61° 76°
MRV = 32207m3
AI = 0.80
90°
0°
73° 74°
MRV = 27519m3
AI = 0.99
70°
20°
61° 74°
MRV = 34630m3
AI = 0.82
70°
20°
59° 74°
MRV = 35602m3
AI = 0.80

39
207 202
255
212
100%
98%
123%
102%
0
50
100
150
200
250
300
350
0
50
100
150
200
250
300
350
BC F1 F2 F3
218 220
258
220
100%
101%
118%
101%
0
50
100
150
200
250
300
350
0
50
100
150
200
250
300
350
BC F1 F2 F3
-112
95
-110
92
-160
95
-112
100105%
100%
100%
143%
97%
98%
100%
100%
-300 -200 -100 0 100 200 300
-250 -200 -150 -100 -50 0 50 100 150 200 250
BC
F1
F2
F3
BC
F1
F2
F3
-118
100
-110
110
-160
98
-112
108108%
95%
98%
136%
110%
93%
100%
100%
-300 -200 -100 0 100 200 300
-250 -200 -150 -100 -50 0 50 100 150 200 250
BC
F1
F2
F3
BC
F1
F2
F3
Fig. 14 Subsidence characterization for Base case, F1, F2 and F3
Total extent of major (≥10cm) vertical (a) and horizontal (b) surface displacement in m
and in % of Base case value; extent of 10cm surface vertical (c) and horizontal (d)
displacement in relation to centre axis of the block, in m
(a) (b)
(c) (d)

40
268 269 275
100%
100%
103%
0
50
100
150
200
250
300
350
0
50
100
150
200
250
300
350
normalizedbyJ2,%
J2 F4 F5
308
268
279
100%
87%
91%
0
50
100
150
200
250
300
350
240
250
260
270
280
290
300
310
320
normalizedbyJ2,%
J2 F4 F5
-161
107
-161
108
-167
108101%
104%
101%
100%
100%
100%
-300 -200 -100 0 100 200 300
-250 -200 -150 -100 -50 0 50 100 150 200 250
relation to block centre, normalized by J2, %
J2
F4
F5
J2
F4
F5
-201
107
-160
108
-171
108101%
85%
101%
80%
100%
100%
-300 -200 -100 0 100 200 300
-250 -200 -150 -100 -50 0 50 100 150 200 250
J2
F4
F5
J2
F4
F5
Fig. 15 Subsidence characterization for J2, F4 and F5
Total extent of major (≥10cm) vertical (a) and horizontal (b) surface displacement in m
and in % of J2 value; extent of 10cm surface vertical (c) and horizontal (d) displacement
in relation to central axis of the block, in m
(a) (b)
(c) (d)

41
F3
F3
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
-300 -250 -200 -150 150 200 250 300
-2
F2
BC
BC
F1
F1
F1
F2
F2
F3
F3
F3
F3
0
0.05
0.1
0.15
0.2
0.25
0.3
-300 -250 -200 -150 150 200 250 300
1.2
Fig. 16 Total vertical (a) and horizontal (b) surface displacement at the end of ore extraction
at different distances from block centre for Base Case, F1, F2 and F3 models
J2
J2
F4
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
-300 -250 -200 -150 150 200 250 300
-0.4
F5
-3.2
J2
J2
J2
J2
F4
F4
F4
F5
F5
F5
0
0.05
0.1
0.15
0.2
0.25
0.3
-300 -250 -200 -150 150 200 250 300
1.20.8
Fig. 17 Total vertical (a) and horizontal (b) surface displacement at the end of ore extraction
at different distances from block centre for J2, F4 and F5 models
(a)
(b)
(a)
(b)

42
Fig. 18 Differential XY displacement for surface points on the fault hanging and footwalls:
(a) F1, F2 and F3; (b) F4 and F5 models
footwall
hanging
wall
differential
XYdisplacement -4.31m
-2.37m
-0.02m
-5
-4
-3
-2
-1
0
0 10 20 30 40 50 60 70 80 90 100
DifferentialXY
displacements,m
Ore extraction, %
F1
F2
F3
-3.73m
-5
-4
-3
-2
-1
0
0 10 20 30 40 50 60 70 80 90 100
DifferentialXY
displacements,m
Ore extraction, %
F4
F5
-0.07m
hangingwall
disintegrated
(b)
(a)
90°
0°
70°
20°

43
(a) (b) (c) (d)
Legend: rotational failure; translational failure; fault location prior to failure
active rock mass movement; developing rock mass failure
Fig. 19 Subsidence crater formation for F6 (a), F7 (b), F8 (c) and F9 (d) models
fault fault fault fault

44
0-100 -50-150-200-250 10050 150 200 250 300-300
(a)
F6
(b)
F7
(c)
F8
(d)
F9
Fig. 20 Subsidence at 100% ore extraction for F6, F7, F8 and F9 models
90°
0°
70°
20°
fault location prior
to caving
70°
20°
46°
71°
46°
59°
vertical
horizontal
Legend:
angle
of fracture
initiation
46°
75°
75°
66°
67°
90°
0°
MRV = 40798m3
AI = 0.61
MRV = 29594m3
AI = 0.95
MRV = 43319m3
AI = 0.70
MRV = 33922m3
AI = 0.88

45
207 204
255
331
100%
102%
125%
161%
0
50
100
150
200
250
300
350
0
50
100
150
200
250
300
350
BC F7 F2 F6
218 222
258
350
100%
102%
118%
161%
0
50
100
150
200
250
300
350
0
50
100
150
200
250
300
350
BC F7 F2 F6
-112
95
-102
102
-160
95
-245
8691%
219%
100%
143%
107%
91%
100%
100%
-300 -200 -100 0 100 200 300
-250 -200 -150 -100 -50 0 50 100 150 200 250
BC
F7
F2
F6
BC
F7
F2
F6
-118
100
-102
120
-160
98
-245
105105%
208%
98%
136%
120%
86%
100%
100%
-300 -200 -100 0 100 200 300
-250 -200 -150 -100 -50 0 50 100 150 200 250
BC
F7
F2
F6
BC
F7
F2
F6
Fig. 21 Subsidence characterization for BC, F2, F6 and F7 models
Total extent of major (≥10cm) vertical (a) and horizontal (b) surface displacement in
m and in % of Base Case value; extent of 10cm surface vertical (c) and horizontal (d)
(a) (b)
(c) (d)

46
268
254
269
100%
95%
100%
140%
0
50
100
150
200
250
300
350
0
50
100
150
200
250
300
350
normalizedbyJ2,%
375
J2 F9 F4 F8
308 305
268
100%
99%
87%
125%
0
50
100
150
200
250
300
350
0
50
100
150
200
250
300
350
normalizedbyJ2,%
J2 F9 F4 F8
384
-161
107
-126
128
-161
108
-245
130151%
100%
126%
66%
149%
51%
100%
100%
-350 -250 -150 -50 50 150 250 350
-250 -200 -150 -100 -50 0 50 100 150 200 250
J2
F9
F4
F8
J2
F9
F4
F8
-245
105
-169
136
-160
108
-245
139132%
100%
103%
65%
130%
69%
100%
100%
-300 -200 -100 0 100 200 300
-250 -200 -150 -100 -50 0 50 100 150 200 250
J2
F9
F4
F8
J2
F9
F4
F8
Fig. 22 Subsidence characterization for J2, F4, F8 and F9 models
Total extent of major (≥10cm) vertical (a) and horizontal (b) surface displacement in
m and in % of J2 value; extent of 10cm surface vertical (c) and horizontal (d)
(a) (b)
(c) (d)

47
F6
F6
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
-300 -250 -200 -150 150 200 250 300
-2
F2
-0.8-0.8
BC
BC
F7
F7
F2
F2
F6
F6
F6
0
0.05
0.1
0.15
0.2
0.25
0.3
-300 -250 -200 -150 150 200 250 300
1.20.8 0.8
extraction at different distances from block centre for Base Case, F2, F6 and F7 models
J2
J2
F9
F4
F8
F8
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
-300 -250 -200 -150 150 200 250 300
-0.4
J2
J2
J2
J2
F9
F9
F9
F4
F4
F4
F8
F8
F8
F8
0
0.05
0.1
0.15
0.2
0.25
0.3
-300 -250 -200 -150 150 200 250 300
0.450.8
extraction at different distances from block centre for J2, F4, F8 and F9 models
(a)
(b)
(a)
(b)

48
Fig. 25 Differential XY displacement for surface points on the fault hanging and foot
walls for F2, F6 and F7 models
footwall
hanging
wall
differential
XYdisplacement
-4.31m
-2.37m
-0.02m
-5
-4
-3
-2
-1
0
0 10 20 30 40 50 60 70 80 90 100
DifferentialXY
displacements,m
Ore extraction, %
F1
F2
F3
hangingwall
desintegrated
-1.16m
-2.37m
-5
-4
-3
-2
-1
0
0 10 20 30 40 50 60 70 80 90 100DifferentialXY
displacements,m Ore extraction, %
F7
F2
F6
hangingwall
desintegrated
-1.36m
90°
0°
70°
20°

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