D. Elmo

Applications of Finite/Discrete Element Modeling to Rock Engineering Problems

AbstractIn this paper, the authors review recent applications of an integrated numerical modeling approach based on the analysis of the mechanical behavior of discrete systems. The numerical analysis includes both a more realistic representation of fracture networks and the simulation of rock mass behavior as a combination of failure through intact rock and displacement/rotation along predefined discontinuities. Selected examples are presented with respect to a variety of engineering problems, including shear testing, failure of hard-rock pillars, slope stability, and block/panel cave mining. The results clearly illustrate the importance of including natural jointing to better capture rock mass behavior in response to loading and unloading. Particular emphasis is given to modeling cave development and surface subsidence, and the proposed numerical method is shown to capture fully the complex rock mass response to caving associated with multi lift extraction. Whereas the use of relatively complex numerical...

Volumetric Fracture Intensity Measurement for Improved Rock Mass Characterisation and Fragmentation Assessment in Block Caving Operations

Recent discrete fracture network (DFN) related analysis of a number of block caving projects has demonstrated the role that the 3D volumetric fracture intensity measure (P32) plays on controlling a number of rock mass properties critical to caving operations. P32 represents the fracture area per unit volume and as such represents a non-directional intrinsic measure of the degree of rock mass fracturing, incorporating both a frequency measure and a fracture size component. Preliminary results suggest that the P32 intensity of a DFN model would strongly control the overall fragmentation of the rock mass. The implication would be that by taking the overall distribution of P32, the in situ fragmentation of a large rock mass volume could be determined in a computationally efficient way. With P32 also being shown to be one of the dominant controls on DFN derived directional stiffness measures, increasingly these DFN related work flows are being shown to be central to an improved rock mass characterisation process and ultimately the more accurate capturing of the caving process.

Discrete Fracture Network approach to characterise rock mass fragmentation and implications for geomechanical upscaling

Abstract Natural fragmentation is a function of the fracture length and connectivity of naturally occurring rock discontinuities. This study reviews the use of a Discrete Fracture Network (DFN) method as an effective tool to assist with fragmentation assessment, primarily by providing a better description of the natural fragmentation distribution. This approach has at its core the development of a full-scale DFN model description of fracture orientation, size and intensity built up from all available geotechnical data. The model fully accounts for a spatially variable description of the fracture intensity distribution. The results suggest that DFN models could effectively be used to define equivalent rock mass parameters to improve the predictability achieved by current geomechanical simulations and empirical rock mass classification schemes. As shown in this study, a mine-scale DFN model could be converted to equivalent directional rock mass properties using a rapid analytical approach, allowing the creation of a rock mass model that incorporates the influence of a local variable structure with continuous spatial variability. When coupled with more detailed numerical synthetic rock mass simulations for calibration and validation, a balanced and representative approach could be established that puts more equal emphasis on data collection, local- and large-scale characterisation, conceptualisation and geomechanical simulation.

A Combined Remote Sensing–Numerical Modelling Approach to the Stability Analysis of Delabole Slate Quarry, Cornwall, UK

Rock slope geometry and discontinuity properties are among the most important factors in realistic rock slope analysis yet they are often oversimplified in numerical simulations. This is primarily due to the difficulties in obtaining accurate structural and geometrical data as well as the stochastic representation of discontinuities. Recent improvements in both digital data acquisition and incorporation of discrete fracture network data into numerical modelling software have provided better tools to capture rock mass characteristics, slope geometries and digital terrain models allowing more effective modelling of rock slopes. Advantages of using improved data acquisition technology include safer and faster data collection, greater areal coverage, and accurate data geo-referencing far exceed limitations due to orientation bias and occlusion. A key benefit of a detailed point cloud dataset is the ability to measure and evaluate discontinuity characteristics such as orientation, spacing/intensity and persistence. This data can be used to develop a discrete fracture network which can be imported into the numerical simulations to study the influence of the stochastic nature of the discontinuities on the failure mechanism. We demonstrate the application of digital terrestrial photogrammetry in discontinuity characterization and distinct element simulations within a slate quarry. An accurately geo-referenced photogrammetry model is used to derive the slope geometry and to characterize geological structures. We first show how a discontinuity dataset, obtained from a photogrammetry model can be used to characterize discontinuities and to develop discrete fracture networks. A deterministic three-dimensional distinct element model is then used to investigate the effect of some key input parameters (friction angle, spacing and persistence) on the stability of the quarry slope model. Finally, adopting a stochastic approach, discrete fracture networks are used as input for 3D distinct element simulations to better understand the stochastic nature of the geological structure and its effect on the quarry slope failure mechanism. The numerical modelling results highlight the influence of discontinuity characteristics and kinematics on the slope failure mechanism and the variability in the size and shape of the failed blocks.

Cave fragmentation in a cave-to-mill context at the New Afton Mine part I: fragmentation and hang-up frequency prediction

Abstract Block and panel caving methods are increasingly being proposed as an economical means for the excavation of ore deposits. The development of methods for predicting cave fragment size holds significant potential for reducing risk associated with cave mining projects. A fragmentation study was carried out for the New Afton B1 and B2 caves to generate fragmentation models that could be applied to future lifts. In part 1 of this paper, implications of fragmentation size for the mine are considered, whereas the effects on mill performance are addressed in part 2. Fragmentation measurements, from sieving and image-based methods, as well as historical logs of hang-up events are presented. Measurements showed that for the B1 and B2 caves, secondary fragmentation size, representing the size of material at drawpoints, is strongly related to faulting, height of draw and effects of the cave boundary.

Cave-to-Mill: a Mine-to-Mill approach for block cave mines

Abstract A refinement of the traditional Mine-to-Mill integration opportunity for copper block cave mines is introduced here as a Cave-to-Mill production management concept. This is essentially the integration of underground mine production scheduling and monitoring with surface mineral processing management based upon fragment size and geometallurgical ore characteristics. Cave-to-Mill defines ore block models with respect to both mine and mill performance. Linkages between key cave and mill parameters have been established so that coordinated efforts towards maximizing net present value (NPV) can be made. Discrete fracture network (DFN) based methods were found to hold significant value within the Cave-to-Mill approach. The variable and relatively uncontrollable nature of cave fragmentation is considered to be a key distinguishing feature of Cave-to-Mill when compared with typical Mine-to-Mill strategies established for open-pit mines. It is envisioned that Cave-to-Mill will be an important design and operational strategy for block cave mines.

Benchmark testing of numerical approaches for modelling the influence of undercut depth on caving, fracture initiation and subsidence angles associated with block cave mining

Abstract This paper reports the findings from a benchmark study testing several numerical methods, with a focus on the influence of undercut depth on block caving-induced surface deformation. A comparison is drawn between continuum v. discontinuum treatments of the modelled geology. Results were evaluated with respect to different simulated levels of ground disturbance, from complete collapse to small-strain subsidence. The results show that for a given extraction volume, the extent of ground collapse at surface decreases as undercut depth increases. The presence of sub-vertical faults was seen to limit the extent of the modelled caving zones. In contrast, the extent of small-strain surface subsidence was seen to increase with increasing undercut depth. The faults in this case did not have the same limiting effect. Overall, the findings emphasise the importance of balancing model simplification against the need to incorporate more complex and computationally demanding representations of the rock mass structure.

A Study of Gravity Flow Based on the Upside-Down Drop Shape Theory and Considering Rock Shape and Breakage

The cave mining method relies on gravity to fragment the rock mass into blocks that can be extracted out of drawpoints. Several discrete element method (DEM) models on gravity flow are presented in the literature; however, only a few of those consider rock shape and secondary fragmentation. In this paper, the reliability of the particle flow code (PFC) to model gravity flow of fragmented rock is validated against known experimental results. A new method to create complex shape clusters is proposed and then used to investigate the mechanisms of gravity flow and the influence of particle bond strength on the secondary fragmentation, and the evolutions of the movement zone and extraction zone. The model results are validated against the upside-down drop shape theory for two cases: (1) constant size of fragmented rock blocks and (2) changing size due to breakage of the fragmented rock blocks. For the latter case, the results show that secondary fragmentation of weaker rocks would result in a wider movement zone and extraction zone than that of stronger rocks.

Cave fragmentation in a cave-to-mill context at the New Afton mine Part II: implications to mill performance

Abstract The productivity of milling circuits is sensitive to the size of mill feed. Uncertainty about the size of caved ore presents unique challenges to forecasting and controlling mill throughput rates. Part I of this paper showed how fragmentation size and hang-up frequency relate to geology, proximity of drawpoints to the cave boundary and the height of draw at the New Afton mine. The second part, presented here, investigates the impact of varying caved fragment size on mill performance. Analysis of historical mine and mill data showed that mill feed size and subsequently mill throughput are sensitive to the areas being mucked within the cave. Fragmentation measurements of drawpoint muck, comminution tests and calibrated mill models were used to assess the impact of variations in feed size and hardness on New Afton mill performance. Image-based size analyses of drawpoint muck and comminution tests showed that coarser material generally contained harder rock.

A discrete fracture network approach for the design of rock foundation anchorage

A major consideration in the design of high-capacity tiedown anchors for dams, bridges and tower foundations includes the tensile resistance of the rock mass to pullout typically as a result of overturning moments or hydrostatic uplift. Rock mass pullout capacity for installed anchors is developed from the tensile strength and fracture propagation properties of intact rock, the orientation and physical properties of the discontinuities and anchor confinement at depth. The typically assumed but conservative design approach is to assume that only the dead weight of a uniformly shaped inverted ‘rock pull out cone’ provides resistance to anchor pullout with an assumed initiation point and breakout angle. It is appreciated that the ‘dead weight’ cone assumption may be valid if the discontinuities are continuous and the geometry allows for a discrete block to form in the area of anchorage. However, if these persistent joints are not ubiquitously developed this failure mechanism may not represent the conditions across a foundation and can lead to a very conservative anchor designs. A less conservative approach is to consider the deadweight and the tensile strength across the surface area of the assumed pullout cones. Strength estimates are often estimated by a designer using correlations based on the Hoek–Brown failure criteria or the Barton Q-system. However, fundamental assumption of these empirical methods is that the discontinuities are sufficiently closely spaced such that the rock mass can be considered homogenous and isotropic – and this often not the case (Hoek, Carter and Diederichs 2013). In reality, at the scale of many rock anchor pullout problems, the strength and deformation properties of the rock mass are anisotropic, controlled by a few persistent discontinuities and small ‘rock bridges’ that exist between naturally occurring joints. To accommodate scale effects and the variability of jointing, this paper introduces a reliability-based design (RBD) approach for anchors that uses discrete fracture networks (DFNs) combined with numerical models. With this approach, limitations of the current practice for anchor design are addressed and opportunities are identified to optimise rock anchor designs provided that sufficient information is available to produce a representative DFN. Typically, this requires geological mapping to characterise the rock mass and verify the conditions at discrete anchor locations and in situ anchor testing can be carried out during construction.