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 - 556.

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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.

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(1) Senior Geotechnical Engineer, Copper Projects Group, Rio Tinto Ltd., Vancouver,

Canada

Mailing address: Dr. Alexander Vyazmensky. Rio Tinto Ltd. Copper Projects. 354-200 Granville St.,

Vancouver, BC, Canada, V6C 1S4

E-mail: [email protected] (alt. [email protected])

(2) Rock Mechanics Specialist, Golder Associates Ltd., Mining Division, Vancouver,

Canada

(3) Professor, Department of Earth Science, Simon Fraser University, Vancouver,

Canada

Abstract:

Extraction of a large volume of ore during block caving can lead to the formation of

significant surface subsidence. Current knowledge of the mechanisms that control

subsidence development is limited as are our subsidence prediction capabilities. Mining

experience suggests that, among other contributing factors, geological structures play a

particularly important role in subsidence development. A conceptual modeling study has

been undertaken to evaluate the significance of geological structure on surface subsidence.

A hybrid finite/discrete element technique incorporating a coupled elasto-plastic fracture

mechanics constitutive criterion is adopted; this allows physically realistic modeling of

block caving through simulation of the transition from a continuum to a discontinuum.

Numerical experiments presented emphasize the importance of joint orientation and fault

location on mechanisms of subsidence development and the governing role of geological

structure in defining the degree of surface subsidence asymmetry.

Keywords:

surface subsidence; rock mass fabric; faulting; block caving; numerical modeling;

FEM/DEM-DFN

mailto:[email protected]

mailto:[email protected]


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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.


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


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.


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


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.


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.

http://www.fracman.golder.com/


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.

http://www.rockfield.co.uk/


24

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


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


26

Influence on block caving subsidence

Jo

int

orienta

tion

Well defined, vertical to steeply dipping joints govern the direction of cave propagation and the mechanism of near surface rock mass mobilization. The shallower the dip of these joints the more inclined from vertical the cave propagation direction is and the more asymmetrical the surface deformation with respect to the block centre vertical axis. In cases where multiple well defined and persistent steeply dipping joint sets are present, the steepest set will generally have the predominant influence.

Significant subsidence asymmetry is observed in the dip direction of the sub-vertical/steeply dipping set. Where joints are inclined towards the cave, the rock mass fails through a combination of block-flexural and block toppling and the detachment and sliding of major rock segments. Where a sub-vertical joint set is dipping into the cave, the surface deformation direction is controlled by the dip of the sub-vertical joint set. In this case the rock mass fails predominantly through block toppling and sliding along the sub-vertical joints.

The orientation of well defined, gently dipping joints influences the extent of the rock mass mobilized by the failure and the degree of subsidence asymmetry.

Fau

lts in

clin

atio

n a

nd

loca

tion

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

For faults daylighting into the cave, failure of the hanging wall is likely inevitable. For the assumed hard rock mass conditions in the current modelling, the stability of the exposed footwall is dependent on its slope, the amount of passive support provided by the muck pile and the orientation and persistence of jointing within the footwall. The presence of well defined steeply/gently dipping joint set approaching perpendicular orientation with relation to the fault will increase the kinematic potential for failure of major near surface footwall segments. In such circumstances a model combining the fault/jointing system is extremely important.

Steeply dipping faults, daylighting into the cave and located within an area of imminent caving are likely to be caved and therefore are unlikely to play any major role in the resultant subsidence.

Faults partially intersecting the caving area may create unfavourable conditions with potential for failure of the entire hanging wall.

Depending on rock mass fabric, faults located in the vicinity of the caving zone may have a minimal influence or decrease the extent of the area of subsidence deformation. The former behaviour was observed in models with horizontal/vertical joint sets and the latter for orthogonal steeply/gently dipping joints.

A topographical step in the surface profile is formed where the fault daylights at the surface. Significant movements should be anticipated if the fault daylights into the cave.


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 torubblizedrock mass

intact

rock mass

disturbed

rock mass

2H

W=H

I(b)

fault

I(a) fault located at distances exceeding 0.5H from the caving boundary

fault may act as a displacement barrier limiting rock mass movements in the far-field

I(b) more than 2/3 of the fault near surface segment is located within the caving zone

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).


28

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


29

Model geometry

Non-fracturing zone

Fracturing zone

100m

ore

block

100m

100m

70o

20o4m

FracMan 3D model 2D trace planefractures

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

20o4m

FracMan 3D model 2D trace planefractures

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

Vert

ical d

isp

lacem

en

ts,

m

Distance from block centre, m

Base case

J1

J2

J3

J4

0, -55

9.4, -49.6

28.6, -41

9.4, -44.5

10, -50

Lowest point coordinates, m

Fig. 5 Surface profiles at the end of ore extraction for BC, J1, J2, J3 and J4 models

207234

268 269245

100%

113%

129%

130%

118%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal exte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts

no

rmalized

b

y B

ase C

ase, %

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts,

m

BC J1 J2 J3 J4

218235

308

269290

100%

108% 141%

123%

133%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal exte

nt o

f 10cm

ho

riz.

su

rface d

isp

lacem

en

ts

no

rmalized

b

y B

ase C

ase, %

To

tal e

xte

nt o

f 10cm

ho

riz.

su

rface d

isp

lacem

en

ts,

m

BC J1 J2 J3 J4

-112

95

-123

111

-161

107

-161

108

-132

113119%

132%

114%

144%

113%

144%

117%

110%

100%

100%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250

Extent of 10cm surface vertical displacements in relation to block centre, normalized by Base Case, %

Extent of 10cm surface vertical dispacements in relation to block centre, m

BCJ1J2J3J4

BCJ1J2J3J4

-118

100

-123

112

-201

107

-161

108

-173

117117%

147%

108%

136%

107%

170%

116%

104%

100%

100%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250

Extent of 10cm surface horizontal displacements in relation to block centre, normalized by Base Case, %

Extent of 10cm surface horizontal displacements in relation to block centre, m

BCJ1J2J3J4

BCJ1J2J3J4

Fig. 7 Subsidence characterization for Base Case, J1, J2, J3 and J4 models Total extent of 10cm vertical (a) and horiz. (b) surface displacement; extent of 10cm surface vertical (c) and horiz. (d) displacement in relation to centre axis of the block, in m

(c) (d)

(a) (b)

34

0

10

20

30

40

50

60

70

80

90

100

-250 -200 -150 -100 -50 0 50 100 150 200 250

Ore

extr

acti

on

, %

Extent of 10cm surface deformations, m

YY

XX

0

10

20

30

40

50

60

70

80

90

100

-250 -200 -150 -100 -50 0 50 100 150 200 250

Ore

extr

acti

on

, %


YY

XX

Fig. 8 Evolution of zone of major (≥10cm) vertical (YY) and horizontal (XX) surface deformation with continuous ore extraction for Base Case (a), J1 (b), J2 (c), J3 (d) and J4 (e) models

Fig. 9 Rate of growth of 10cm surface displacement zone west of the block centre vertical axis with continuous ore extraction for Base Case, J1, J2, J3 and J4 models (a) vertical displacement, (b) horizontal displacement

0

10

20

30

40

50

60

70

80

90

100

-250 -200 -150 -100 -50 0 50 100 150 200 250

Ore

extr

acti

on

, %


YY

XX

0

10

20

30

40

50

60

70

80

90

100

-250 -200 -150 -100 -50 0 50 100 150 200 250

Ore

extr

acti

on

, %


YY

XX

0

10

20

30

40

50

60

70

80

90

100

-250 -200 -150 -100 -50 0 50 100 150 200 250

Ore

extr

acti

on

, %


YY

XX

0

20

40

60

80

100

120

0 20 40 60 80 100 120

exte

nt

of

vert

ical

10cm

su

rface

dis

pla

cem

en

ts,

%

Ore extraction, %

BC_YY

J1_YY

J2_YY

J3_YY

J4_YY

0

20

40

60

80

100

120

0 20 40 60 80 100 120

exte

nt

of

ho

rizo

nta

l 10cm

su

rface

dis

pla

cem

en

ts,

%

Ore extraction, %

BC_XX

J1_XX

J2_XX

J3_XX

J4_XX

(d) J3

(e) J4

(b) J1 (a) BC

(c) J2

(a) (b)

35

J2 J3

J4

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

-300 -250 -200 -150 150 200 250 300

Vert

ical d

isp

lacem

en

ts,

m


-0.38 -2.1

J2

J3

BC

BC BC

J1

J1

J1J2

J2

J2

J2

J3

J3

J3

J3

J4

J4

J4

0

0.05

0.1

0.15

0.2

0.25

0.3

-300 -250 -200 -150 150 200 250 300

Ho

rizo

nta

l dis

pla

cem

en

ts, m


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

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts

no

rmalized

by B

ase C

ase, %

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts,

m

BC F1 F2 F3

218 220

258

220

100%

101%

118%

101%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts

no

rmalized

by B

ase C

ase, %

To

tal e

xte

nt o

f 10cm

ho

riz.

su

rface d

isp

lacem

en

ts,

m

BC F1 F2 F3

-112

95

-110

92

-160

95

-112

100105%

100%

100%

143%

97%

98%

100%

100%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250



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

To

tal exte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts

no

rmalized

b

y J

2, %

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts,

m

J2 F4 F5

308

268

279

100%

87%

91%

0

50

100

150

200

250

300

350

240

250

260

270

280

290

300

310

320

To

tal exte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts

no

rmalized

b

y J

2, %

To

tal e

xte

nt o

f 10cm

ho

riz.

su

rface d

isp

lacem

en

ts,

m

J2 F4 F5

-161

107

-161

108

-167

108101%

104%

101%

100%

100%

100%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250

Extent of 10cm surface vertical displacements in relation to block centre, normalized by J2, %


J2

F4

F5

J2

F4

F5

-201

107

-160

108

-171

108101%

85%

101%

80%

100%

100%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250

Extent of 10cm surface horizontal displacements in relation to block centre, normalized by J2, %


J2

F4

F5

J2

F4

F5

Fig. 15 Subsidence characterization for J2, F4 and F5 Total extent of major (≥10cm) vertical (a) and horizontal (b) surface displacement in m and in % of J2 value; extent of 10cm surface vertical (c) and horizontal (d) displacement in relation to central axis of the block, in m

(a) (b)

(c) (d)

41

F3

F3

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

-300 -250 -200 -150 150 200 250 300

Vert

ical d

isp

lacem

en

ts,

m


-2

F2

B

C BCF

1

F1

F1

F2

F2

F3 F3

F3

F3

0

0.05

0.1

0.15

0.2

0.25

0.3

-300 -250 -200 -150 150 200 250 300

Ho

rizo

nta

l dis

pla

cem

en

ts, m


1.2

Fig. 16 Total vertical (a) and horizontal (b) surface displacement at the end of ore extraction at different distances from block centre for Base Case, F1, F2 and F3 models

J2

J2

F4

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

-300 -250 -200 -150 150 200 250 300

Vert

ical d

isp

lacem

en

ts,

m


-0.4

F5

-3.2

J2

J2

J2

J2F4

F4

F4F5

F5

F5

0

0.05

0.1

0.15

0.2

0.25

0.3

-300 -250 -200 -150 150 200 250 300

Ho

rizo

nta

l d

isp

lacem

en

ts, m


1.20.8

Fig. 17 Total vertical (a) and horizontal (b) surface displacement at the end of ore extraction at different distances from block centre for J2, F4 and F5 models

(a)

(b)

(a)

(b)

42

Fig. 18 Differential XY displacement for surface points on the fault hanging and footwalls: (a) F1, F2 and F3; (b) F4 and F5 models

footwall

hanging

wall

differential

XY displacement

-4.31m

-2.37m

-0.02m

-5

-4

-3

-2

-1

0

0 10 20 30 40 50 60 70 80 90 100

Dif

fere

nti

al

XY

d

isp

lac

em

en

ts, m

Ore extraction, %

F1

F2

F3

-3.73m

-5

-4

-3

-2

-1

0

0 10 20 30 40 50 60 70 80 90 100

Dif

fere

nti

al

XY

d

isp

lac

em

en

ts, m

Ore extraction, %

F4

F5

-0.07m

hangingwall disintegrated

(b)

(a)

90°

0°

70°

20°

43

(a) (b) (c) (d)

Legend: rotational failure; translational failure; fault location prior to failure

active rock mass movement; developing rock mass failure

Fig. 19 Subsidence crater formation for F6 (a), F7 (b), F8 (c) and F9 (d) models

fault fault fault fault

44

0-100 -50-150-200-250 10050 150 200 250 300-300

(a)

F6

(b)

F7

(c)

F8

(d)

F9

Fig. 20 Subsidence at 100% ore extraction for F6, F7, F8 and F9 models

90°

0°

70°

20°

fault location prior

to caving

70°

20°

46°

71°

46°

59°


vertical

horizontal

Legend:

angle

of fracture

initiation

46°

75°

75°

66°

67°

90°

0°

MRV = 40798m3

AI = 0.61

MRV = 29594m3

AI = 0.95

MRV = 43319m3

AI = 0.70

MRV = 33922m3

AI = 0.88

45

207 204

255

331

100%

102% 125% 161%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal exte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts

no

rmalized

b

y B

ase C

ase, %

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts,

m

BC F7 F2 F6

218 222

258

350

100%

102%

118% 161%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal exte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts

no

rmalized

b

y B

ase C

ase, %

To

tal e

xte

nt o

f 10cm

ho

riz.

su

rface d

isp

lacem

en

ts,

m

BC F7 F2 F6

-112

95

-102

102

-160

95

-245

8691%

219%

100%

143%

107%

91%

100%

100%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250



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) displacement in relation to centre axis of the block, in m

(a) (b)

(c) (d)

46

268254

269

100%

95%

100% 1

40%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts

no

rmalized

by J

2, %

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts,

m

375

J2 F9 F4 F8

308 305

268

100%

99%

87% 125%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts

no

rmalized

by J

2, %

To

tal e

xte

nt o

f 10cm

ho

riz.

su

rface d

isp

lacem

en

ts,

m

J2 F9 F4 F8

384

-161

107

-126

128

-161

108

-245

130151%

100%

126%

66%

149%

51%

100%

100%

-350 -250 -150 -50 50 150 250 350

-250 -200 -150 -100 -50 0 50 100 150 200 250

Extent of 10cm surface vertical displacements in relation to block centre, normalized by J2, %


J2

F9

F4

F8

J2

F9

F4

F8

-245

105

-169

136

-160

108

-245

139132%

100%

103%

65%

130%

69%

100%

100%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250

Extent of 10cm surface horizontal displacements in relation to block centre, normalized by J2, %


J2

F9

F4

F8

J2

F9

F4

F8

Fig. 22 Subsidence characterization for J2, F4, F8 and F9 models Total extent of major (≥10cm) vertical (a) and horizontal (b) surface displacement in m and in % of J2 value; extent of 10cm surface vertical (c) and horizontal (d) displacement in relation to centre axis of the block, in m

(a) (b)

(c) (d)

47

F6

F6

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

-300 -250 -200 -150 150 200 250 300

Vert

ical d

isp

lacem

en

ts,

m


-2

F2

-0.8-0.8

BC BC

F7 F7

F2

F2

F6 F6

F6

0

0.05

0.1

0.15

0.2

0.25

0.3

-300 -250 -200 -150 150 200 250 300

Ho

rizo

nta

l d

isp

lacem

en

ts, m


1.20.8 0.8

Fig. 23 Total vertical (a) and horizontal (b) surface displacement at the end of ore extraction at different distances from block centre for Base Case, F2, F6 and F7 models

J2

J2

F9 F4

F8

F8

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

-300 -250 -200 -150 150 200 250 300

Vert

ical d

isp

lacem

en

ts,

m


-0.4

J2

J2

J2

J2F9

F9

F9

F4

F4

F4F8

F8

F8

F8

0

0.05

0.1

0.15

0.2

0.25

0.3

-300 -250 -200 -150 150 200 250 300

Ho

rizo

nta

l d

isp

lacem

en

ts, m


0.450.8

Fig. 24 Total vertical (a) and horizontal (b) surface displacement at the end of ore extraction at different distances from block centre for J2, F4, F8 and F9 models

(a)

(b)

(a)

(b)

48

Fig. 25 Differential XY displacement for surface points on the fault hanging and foot walls for F2, F6 and F7 models

footwall

hanging

wall

differential

XY displacement

-4.31m

-2.37m

-0.02m

-5

-4

-3

-2

-1

0

0 10 20 30 40 50 60 70 80 90 100

Dif

fere

nti

al

XY

d

isp

lac

em

en

ts, m

Ore extraction, %

F1

F2

F3hangingwall desintegrated

-1.16m

-2.37m

-5

-4

-3

-2

-1

0

0 10 20 30 40 50 60 70 80 90 100D

iffe

ren

tia

l X

Y

dis

pla

ce

me

nts

, m

Ore extraction, %

F7

F2

F6

hangingwall desintegrated

-1.36m

90°

0°

70°

20°

Date post:	16-May-2015
Category:	Science
Upload:	alexander-vyazmensky
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