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

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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 …

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

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  • 1. Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556. 1 Role of Rock Mass Fabric and Faulting in the Development of Block Caving Induced Surface Subsidence Vyazmensky A. 1 , Elmo D. 2 , Stead D. 3 (1) Senior Geotechnical Engineer, Copper Projects Group, Rio Tinto Ltd., Vancouver, Canada Mailing address: Dr. Alexander Vyazmensky. Rio Tinto Ltd. Copper Projects. 354-200 Granville St., Vancouver, BC, Canada, V6C 1S4 E-mail: 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
  • 2. Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556. 2 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.
  • 3. Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556. 3 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
  • 4. Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556. 4 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.
  • 5. Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556. 5 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).
  • 6. Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556. 6 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.
  • 7. Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556. 7 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.
  • 8. Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556. 8 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;
  • 9. Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556. 9  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
  • 10. Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556. 10 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
  • 11. Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556. 11 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
  • 12. Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556. 12 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:
  • 13. Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556. 13  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
  • 14. Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556. 14 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
  • 15. Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556. 15 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
  • 16. Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556. 16 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
  • 17. Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556. 17 F4, where a fault intersects the block, movements in the order of metres are observed, whereas for models F3 and F5, where a fault does not intersect the block, movements limited to several centimetres are noted. Inclination of the joint sets affects these movements, such that larger XY displacements, which develop more rapidly, are observed for models with inclined joints. 6.2 Effect of Fault Inclination The effect of fault inclination on the development of surface subsidence was evaluated based on six modelling scenarios, for a fault partially intersecting the block. Three different fault inclinations and two different joint set conditions were considered, as summarized in Table 5. Figs. 12b, 19a and 19b illustrate the development of surface subsidence at 35, 50 and 60% ore extraction, and, Figs. 13b and 20(a,b) show resultant subsidence deformations at 100% ore extraction for models F2, F6 and F7, assuming vertical/horizontal joints. Figs. 12d, 19c and 19d present surface subsidence development at 35, 50 and 60% ore extraction and Figs. 13d and 20(c,d) show the resultant subsidence deformation at 100% ore extraction for models F4, F8 and F9, assuming steeply/gently dipping joints. Comparing subsidence deformation development for varying fault inclinations and varying joint set orientations it should be noted that, for all assumed inclinations, faults affect the development of subsidence deformation. Irrespective of jointing orientation caving induced failure is predominantly controlled by the plane of weakness provided by the fault. Continuous ore extraction leads to full mobilization of the entire hanging wall and its disintegration into segments. The mode of hanging wall segmentation appears to be controlled by joint orientation. Failure of the hanging wall leads to formation of a crater wall along the footwall of the exposed fault; particularly pronounced for the 75° and 60° faults. For the 75° fault models (F7, F9, Fig. 20(b,d)) exposure of a steep footwall by the caving causes its partial failure, the magnitude of this failure is strongly controlled by the jointing.
  • 18. Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556. 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. Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556. 19 given in Fig. 22. As can be inferred from this figure for faults with inclinations of 60 and 75 the extent of the zone of major surface displacement towards the fault was reduced by as much as 50%. The surface outcrop location of the 45 fault coincided approximately with the extent of major displacements for the model without a fault (see Figs. 5c and 20d), hence no major influence was observed. Interestingly models with 45 and 75 dipping faults exhibit increased zones of influence in an eastward direction from the block centre vertical axis. Far-field displacements for models with vertical/horizontal and inclined joints are presented in Figs. 23 and 24, respectively. It can be inferred from these figures that, in the direction towards the fault, the extent of the far-field displacements is a function of fault inclination. A shallower fault inclination resulted in a larger area mobilized by the caving. Conversely, steeper faults limit such an area. Within the failing hanging wall higher deformation magnitudes were observed for models with vertical/horizontal joints. Depending on the fault inclination the amount of differential displacement at the surface outcrop of the fault varies, higher displacements being observed for models with steeper faults (see Fig. 25). 7. Results Synthesis and Conclusions The adopted modelling methodology has allowed physically realistic simulation of subsidence deformation mechanisms, from caving initiation to the final subsidence topography. It thereby has provided quantitative support for the observational-based conceptual model of subsidence development proposed by Abel and Lee (1980). The 2D FEM/DEM-DFN modelling offers a convenient framework for future quantitative analysis of block caving induced surface subsidence and has significant potential for improving subsidence prediction capabilities. Vyazmensky et al. (2009) have applied this approach to the analysis of a block caving induced large open pit slope failure at the Palabora mine and illustrated that the 2D FEM/DEM-DFN modelling methodology can be successfully applied to the analysis of complex industrial scale problems.
  • 20. Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556. 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. Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556. 21 power becomes available and the existing FEM/DEM codes are adapted to maximize the use of 64 bit architectures and parallel processing facilities FEM/DEM-DFN technique will be adopted to mine scale 3D modelling, allowing physically realistic simulation of the block caving process, including caving initiation, fragmentation, mass flow and resultant surface subsidence. Acknowledgements The authors would like to acknowledge research funding provided by Rio Tinto and Natural Sciences and Engineering Research Council of Canada. We would also like to acknowledge research collaboration with Allan Moss and Andre van As (Rio Tinto), Erik Eberhardt, Scott Dunbar and Malcolm Scoble (University of British Columbia). Technical support of Rockfield Technology Ltd. (UK) is gratefully appreciated.
  • 22. Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 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.
  • 23. Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556. 23 Panek LA (1984) Subsidence in undercut - cave operations, subsidence resulting from limited extraction of two neighboring cave operations. In: Geomechanical Applications in Hard Rock Mining. (ed. Pariseau, W.G.) pp 225-240. Pine RJ, Owen DRJ, Coggan JS, Rance JM (2007) A new discrete modelling approach for rock masses. Geotechnique. 57(9): 757-766. Pine RJ, Coggan JS, Flynn ZN, Elmo D (2006) The development of a new numerical modelling approach for naturally fractured rock masses. Rock Mech. Rock Engng. 39(5): 395-419. Rance JM, van As A, Owen DRJ, Feng YT, Pine RJ (2007) Computational modelling of multiple fragmentation in rock masses with application to block caving. Proc. 1st Canada-U.S. Rock Mechanics Symposium. Vancouver Vol 1: 477-484pp Rockfield Software Ltd (2007) ELFEN user manual, Swansea, UK. Home page at: http://www.rockfield.co.uk 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.
  • 24. Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556. 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. Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556. 25 Table 3 Modelling scenarios for analysis of the effect of joint orientation Scenario Number of sets Joint sets dips, ° Description Base Case (BC) Two sets 90/0 Orthogonal sets, vertical/horizontal J1 Two sets 80/10 Orthogonal sets, sub-vertical/sub-horizontal J2 Two sets 70/20 Orthogonal sets, steeply dipping/gently dipping J3 Two sets 70/0 Orthogonal sets, steeply dipping/horizontal J4 Three sets 70/20/90 Orthogonal sets, steeply dipping/gently dipping/vertical Table 4 Modelling scenarios for analysis of the effect of fault location Scenario Joint set dips, ° Fault dip, ° Fault location with respect to block centre axis, m Figure F1 90/0 60 50 10(a) F2 100 10(b) F3 150 10(c) F4 70/20 100 10(d) F5 150 10(e) Table 5 Modelling scenarios for analysis of the effect of fault inclination Scenario Joint set dips, ° Fault dip, ° Figure F6 90/0 45 10(f) F2 60 10(b) F7 75 10(h) F8 70/20 45 10(g) F4 60 10(c) F9 75 10(i) Table 6 Summary of modelling findings
  • 26. Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556. 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.
  • 27. 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).
  • 28. Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556. 28 Fig. 1 Schematic illustration of block cave mining and associated surface subsidence (modified after block caving animation (Sandvik Group 2004)).
  • 29. 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. 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. 31 Fig. 4 Variation of vertical stress (Pa) contours with caving at 5% ore extraction for Base Case and J2 models
  • 32. 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. 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,% Totalextentof10cmvertical 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. surfacedisplacements normalizedbyBaseCase,% Totalextentof10cmhoriz. surfacedisplacements,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 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 relation to block centre, normalized by Base Case, % Extent of 10cm surface horizontal displacements in relation to block centre, m 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. 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,% Extent of 10cm surface deformations, m YY XX Fig. 8 Evolution of zone of major (≥10cm) vertical (YY) and horizontal (XX) surface deformation with continuous ore extraction for Base Case (a), J1 (b), J2 (c), J3 (d) and J4 (e) models Fig. 9 Rate of growth of 10cm surface displacement zone west of the block centre vertical axis with continuous ore extraction for Base Case, J1, J2, J3 and J4 models (a) vertical displacement, (b) horizontal displacement 0 10 20 30 40 50 60 70 80 90 100 -250 -200 -150 -100 -50 0 50 100 150 200 250 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,% 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,% Extent of 10cm surface deformations, m 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. 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 Verticaldisplacements,m Distance from block centre, m -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 Distance from block centre, m 0.9 3.8 Fig. 10 Total vertical (a) and horizontal (b) surface displacement at the end of ore extraction at different distances from block centre for Base Case, J1, J2, J3 and J4 models (a) (b)
  • 36. 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. 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. 38 0-100 -50-150-200-250 10050 150 200 250 300-300 (a) F1 (b) F2 (c) F3 (d) F4 (e) F5 Fig. 13 Subsidence at 100% ore extraction for F1, F2, F3, F4 and F5 model fault location prior to caving 90° 0° 73° 10cm displ. contours vertical horizontal Legend: angle of fracture initiation 73° 73° MRV = 30154m3 AI = 1.0 90° 0° 61° 76° MRV = 32207m3 AI = 0.80 90° 0° 73° 74° MRV = 27519m3 AI = 0.99 70° 20° 61° 74° MRV = 34630m3 AI = 0.82 70° 20° 59° 74° MRV = 35602m3 AI = 0.80
  • 39. 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 Totalextentof10cmvertical surfacedisplacements normalizedbyBaseCase,% Totalextentof10cmvertical surfacedisplacements,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 Totalextentof10cmvertical surfacedisplacements normalizedbyBaseCase,% Totalextentof10cmhoriz. surfacedisplacements,m BC F1 F2 F3 -112 95 -110 92 -160 95 -112 100105% 100% 100% 143% 97% 98% 100% 100% -300 -200 -100 0 100 200 300 -250 -200 -150 -100 -50 0 50 100 150 200 250 Extent of 10cm surface vertical displacements in relation to block centre, normalized by Base Case, % Extent of 10cm surface vertical dispacements in relation to block centre, m BC F1 F2 F3 BC F1 F2 F3 -118 100 -110 110 -160 98 -112 108108% 95% 98% 136% 110% 93% 100% 100% -300 -200 -100 0 100 200 300 -250 -200 -150 -100 -50 0 50 100 150 200 250 Extent of 10cm surface horizontal displacements in relation to block centre, normalized by Base Case, % Extent of 10cm surface horizontal displacements in relation to block centre, m BC F1 F2 F3 BC F1 F2 F3 Fig. 14 Subsidence characterization for Base case, F1, F2 and F3 Total extent of major (≥10cm) vertical (a) and horizontal (b) surface displacement in m and in % of Base case value; extent of 10cm surface vertical (c) and horizontal (d) displacement in relation to centre axis of the block, in m (a) (b) (c) (d)
  • 40. 40 268 269 275 100% 100% 103% 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Totalextentof10cmvertical surfacedisplacements normalizedbyJ2,% Totalextentof10cmvertical surfacedisplacements,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 Totalextentof10cmvertical surfacedisplacements normalizedbyJ2,% Totalextentof10cmhoriz. surfacedisplacements,m J2 F4 F5 -161 107 -161 108 -167 108101% 104% 101% 100% 100% 100% -300 -200 -100 0 100 200 300 -250 -200 -150 -100 -50 0 50 100 150 200 250 Extent of 10cm surface vertical displacements in relation to block centre, normalized by J2, % Extent of 10cm surface vertical dispacements in relation to block centre, m J2 F4 F5 J2 F4 F5 -201 107 -160 108 -171 108101% 85% 101% 80% 100% 100% -300 -200 -100 0 100 200 300 -250 -200 -150 -100 -50 0 50 100 150 200 250 Extent of 10cm surface horizontal displacements in relation to block centre, normalized by J2, % Extent of 10cm surface horizontal displacements in relation to block centre, m J2 F4 F5 J2 F4 F5 Fig. 15 Subsidence characterization for J2, F4 and F5 Total extent of major (≥10cm) vertical (a) and horizontal (b) surface displacement in m and in % of J2 value; extent of 10cm surface vertical (c) and horizontal (d) displacement in relation to central axis of the block, in m (a) (b) (c) (d)
  • 41. 41 F3 F3 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 -300 -250 -200 -150 150 200 250 300 Verticaldisplacements,m Distance from block centre, m -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 Horizontaldisplacements,m Distance from block centre, m 1.2 Fig. 16 Total vertical (a) and horizontal (b) surface displacement at the end of ore extraction at different distances from block centre for Base Case, F1, F2 and F3 models J2 J2 F4 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 -300 -250 -200 -150 150 200 250 300 Verticaldisplacements,m Distance from block centre, m -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 Horizontaldisplacements,m Distance from block centre, m 1.20.8 Fig. 17 Total vertical (a) and horizontal (b) surface displacement at the end of ore extraction at different distances from block centre for J2, F4 and F5 models (a) (b) (a) (b)
  • 42. 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. 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. 44 0-100 -50-150-200-250 10050 150 200 250 300-300 (a) F6 (b) F7 (c) F8 (d) F9 Fig. 20 Subsidence at 100% ore extraction for F6, F7, F8 and F9 models 90° 0° 70° 20° fault location prior to caving 70° 20° 46° 71° 46° 59° 10cm displ. contours vertical horizontal Legend: angle of fracture initiation 46° 75° 75° 66° 67° 90° 0° MRV = 40798m3 AI = 0.61 MRV = 29594m3 AI = 0.95 MRV = 43319m3 AI = 0.70 MRV = 33922m3 AI = 0.88
  • 45. 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 Totalextentof10cmvertical surfacedisplacements normalizedbyBaseCase,% Totalextentof10cmvertical surfacedisplacements,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 Totalextentof10cmvertical surfacedisplacements normalizedbyBaseCase,% Totalextentof10cmhoriz. surfacedisplacements,m BC F7 F2 F6 -112 95 -102 102 -160 95 -245 8691% 219% 100% 143% 107% 91% 100% 100% -300 -200 -100 0 100 200 300 -250 -200 -150 -100 -50 0 50 100 150 200 250 Extent of 10cm surface vertical displacements in relation to block centre, normalized by Base Case, % Extent of 10cm surface vertical dispacements in relation to block centre, m BC F7 F2 F6 BC F7 F2 F6 -118 100 -102 120 -160 98 -245 105105% 208% 98% 136% 120% 86% 100% 100% -300 -200 -100 0 100 200 300 -250 -200 -150 -100 -50 0 50 100 150 200 250 Extent of 10cm surface horizontal displacements in relation to block centre, normalized by Base Case, % Extent of 10cm surface horizontal displacements in relation to block centre, m BC F7 F2 F6 BC F7 F2 F6 Fig. 21 Subsidence characterization for BC, F2, F6 and F7 models Total extent of major (≥10cm) vertical (a) and horizontal (b) surface displacement in m and in % of Base Case value; extent of 10cm surface vertical (c) and horizontal (d) displacement in relation to centre axis of the block, in m (a) (b) (c) (d)
  • 46. 46 268 254 269 100% 95% 100% 140% 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Totalextentof10cmvertical surfacedisplacements normalizedbyJ2,% Totalextentof10cmvertical surfacedisplacements,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 Totalextentof10cmvertical surfacedisplacements normalizedbyJ2,% Totalextentof10cmhoriz. surfacedisplacements,m J2 F9 F4 F8 384 -161 107 -126 128 -161 108 -245 130151% 100% 126% 66% 149% 51% 100% 100% -350 -250 -150 -50 50 150 250 350 -250 -200 -150 -100 -50 0 50 100 150 200 250 Extent of 10cm surface vertical displacements in relation to block centre, normalized by J2, % Extent of 10cm surface vertical dispacements in relation to block centre, m J2 F9 F4 F8 J2 F9 F4 F8 -245 105 -169 136 -160 108 -245 139132% 100% 103% 65% 130% 69% 100% 100% -300 -200 -100 0 100 200 300 -250 -200 -150 -100 -50 0 50 100 150 200 250 Extent of 10cm surface horizontal displacements in relation to block centre, normalized by J2, % Extent of 10cm surface horizontal displacements in relation to block centre, m J2 F9 F4 F8 J2 F9 F4 F8 Fig. 22 Subsidence characterization for J2, F4, F8 and F9 models Total extent of major (≥10cm) vertical (a) and horizontal (b) surface displacement in m and in % of J2 value; extent of 10cm surface vertical (c) and horizontal (d) displacement in relation to centre axis of the block, in m (a) (b) (c) (d)
  • 47. 47 F6 F6 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 -300 -250 -200 -150 150 200 250 300 Verticaldisplacements,m Distance from block centre, m -2 F2 -0.8-0.8 BC BC F7 F7 F2 F2 F6 F6 F6 0 0.05 0.1 0.15 0.2 0.25 0.3 -300 -250 -200 -150 150 200 250 300 Horizontaldisplacements,m Distance from block centre, m 1.20.8 0.8 Fig. 23 Total vertical (a) and horizontal (b) surface displacement at the end of ore extraction at different distances from block centre for Base Case, F2, F6 and F7 models J2 J2 F9 F4 F8 F8 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 -300 -250 -200 -150 150 200 250 300 Verticaldisplacements,m Distance from block centre, m -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 Horizontaldisplacements,m Distance from block centre, m 0.450.8 Fig. 24 Total vertical (a) and horizontal (b) surface displacement at the end of ore extraction at different distances from block centre for J2, F4, F8 and F9 models (a) (b) (a) (b)
  • 48. 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°