Numerical Analysis of Block Caving-Induced Instability in Large Open Pit Slopes: A Finite Element/Discrete Element Approach

This paper addresses one of the most challenging problems in mining rock engineering—the interaction between block cave mining and a large overlying open pit. The finite element modeling/discrete element modeling (FEM/DEM) approach was utilized in the analysis of block caving-induced step-path failure development in a large open pit slope. The analysis indicated that there is a threshold percentage of critical intact rock bridges along a step-path failure plane that may ensure the stability of an open pit throughout caving operations. Transition from open pit to underground mining at Palabora mine presents an important example of a pit wall instability triggered by caving. Using combined FEM/DEM-DFN (discrete fracture network) modeling, it was possible to investigate the formation of a basal failure surface within an open pit slope as a direct result of cave mining. The modeling of Palabora highlighted the importance of rock mass tensile strength and its influence on caving-induced slope response.     

An Integrated Numerical Modelling–Discrete Fracture Network Approach Applied to the Characterisation of Rock Mass Strength of Naturally Fractured Pillars

Naturally fractured mine pillars provide an excellent example of the importance of accurately determining rock mass strength. Failure in slender pillars is predominantly controlled by naturally occurring discontinuities, their influence diminishing with increasing pillar width, with wider pillars failing through a combination of brittle and shearing processes. To accurately simulate this behaviour by numerical modelling, the current analysis incorporates a more realistic representation of the mechanical behaviour of discrete fracture systems. This involves realistic simulation and representation of fracture networks, either as individual entities or as a collective system of fracture sets, or a combination of both. By using an integrated finite element/discrete element–discrete fracture network approach it is possible to study the failure of rock masses in tension and compression, along both existing pre-existing fractures and through intact rock bridges, and incorporating complex kinematic mechanisms. The proposed modelling approach fully captures the anisotropic and inhomogeneous effects of natural jointing and is considered to be more realistic than methods relying solely on continuum or discontinuum representation. The paper concludes with a discussion on the development of synthetic rock mass properties, with the intention of providing a more robust link between rock mass strength and rock mass classification systems.     

The Development of a new Numerical Modelling Approach for Naturally Fractured Rock Masses

Summary. An approach for modelling fractured rock masses has been developed which has two main objectives: to maximise the quality of representation of the geometry of existing rock jointing and to use this within a loading model which takes full account of this style of jointing. Initially the work has been applied to the modelling of mine pillars and data from the Middleton Mine in the UK has been used as a case example. However, the general approach is applicable to all aspects of rock mass behaviour including the stress conditions found in hangingwalls, tunnels, block caving, and slopes. The rock mass fracture representation was based on a combination of explicit mapping of rock faces and the synthesis of this data into a three-dimensional model, based on the use of the FracMan computer model suite. Two-dimensional cross sections from this model were imported into the finite element computer model, ELFEN, for loading simulation. The ELFEN constitutive model for fracture simulation includes the Rotating Crack, and Rankine material models, in which fracturing is controlled by tensile strength and fracture energy parameters. For tension/compression stress states, the model is complemented with a capped Mohr-Coulomb criterion in which the softening response is coupled to the tensile model. Fracturing due to dilation is accommodated by introducing an explicit coupling between the inelastic strain accrued by the Mohr-Coulomb yield surface and the anisotropic degradation of the mutually orthogonal tensile yield surfaces of the rotating crack model. Pillars have been simulated with widths of 2.8, 7 and 14 m and a height of 7 m (the Middleton Mine pillars are typically 14 m wide and 7 m high). The evolution of the pillar failure under progressive loading through fracture extension and creation of new fractures is presented, and pillar capacities and stiffnesses are compared with empirical models. The agreement between the models is promising and the new model provides useful insights into the influence of pre-existing fractures. Further work is needed to consider the effects of three-dimensional loading and other boundary condition problems.     

Factors that contribute to the elongation of drumlins beneath the Green Bay Lobe,Laurentide Ice Sheet

Drumlin shape has been hypothesized to correlate with ice-flow duration and slip speed, but modern-day analogues and the Coulomb nature of till render the basis of these correlations in question. The evolution of flow-parallel subglacial landforms is of importance for ice flow because the form drag they provide may be a dominant factor in regulating glacier slip speeds. Here we examine the relationship between drumlin shape and cumulative slip displacement (i.e. time-integrated slip speed) as a dominant glaciological control on drumlin shape. First, a new method is developed that allows slip speed to be estimated for deformable bedded glaciers along a flow line from an ice surface profile. Then, reconstructed surface profiles for ice margin chronologies of the Green Bay Lobe (GBL) are used to construct and estimate the spatially varying cumulative slip displacement for use in comparison with drumlin elongation ratios. We focus on a sector of the GBL near the central flow line where the geology is simple and glaciological controls are likely to dominate bedform development. Using Bayesian statistical analysis, a positive and statistically robust relationship between cumulative slip displacement and drumlin elongation ratio is found. Our analysis indicates that drumlin shape could be used to infer palaeo glacier slip speeds if time under the ice can be well constrained and geologic influences are minimal. These findings also suggest that drumlin-supplied drag could decrease with increased cumulative slip displacement in the absence of rigid geologic features that fix drumlin positions.     

Modeling the Newtonian dynamics for rotation curve analysis of thin-disk galaxies

We present an efficient,robust computational method for modeling the Newtonian dynamics for rotation curve analysis of thin-disk galaxies.With appropriate mathematical treatments,the apparent numerical difficulties associated with singularities in computing elliptic integrals are completely removed.Using a boundary element discretization procedure,the governing equations are transformed into a linear algebra matrix equation that can be solved by straightforward Gauss elimination in one step without further ...     

Role of Rock Mass Fabric and Faulting in the Development of Block Caving Induced Surface Subsidence

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.