A Limit Equilibrium Model of Tabular Mine Pillar Failure
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ORIGINAL PAPER
A Limit Equilibrium Model of Tabular Mine Pillar Failure J. A. L. Napier1 · D. F. Malan1 Received: 28 April 2020 / Accepted: 29 September 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract An improved understanding of pillar strength and pillar failure mechanisms is required to optimize tabular mine layout designs. The paper describes the application of a limit equilibrium model for pillar failure analysis. It is shown that the model is capable of reproducing a hardening or softening response for uniformly compressed strip or square pillars. The stress–strain behavior depends on three non-dimensional parameters Q, M and β. Q represents the ratio of the limit failed uniaxial strength to the intact material strength, M is the ratio of the failed limit strength envelope slope to the intact strength envelope slope and β is proportional to the pillar width to height ratio. The model is implemented in a displacement discontinuity solution scheme using unstructured triangular elements to allow irregular plan-view pillar shapes and mining step increments to be represented. The seam-parallel confining stress distribution in the fracture zone is determined using a fast marching solution algorithm. A case study of an experimental pillar extraction site in a platinum mine is presented to illustrate the capability of the model to simulate the evolution of pillar failure as pillar extraction proceeds. Good qualitative agreement to observed failure trends are obtained but the detailed calibration of the model parameters remains a challenge. Further work is required to enhance the representation of pillar edge spalling processes. Keywords Pillar failure · Limit equilibrium model · Fast marching method · Tabular mine layout · Triangular elements
1 Introduction A number of shallow coal or hard rock mines employ pillar mining systems as a strategy for roof failure control (Van der Merwe and Madden 2010; Ryder and Jager 2002). In certain platinum mine layouts, pillars are designed to "crush" in a stable manner as they become loaded in the panel back area (Du Plessis and Malan 2015). The correct sizing of pillars demands some knowledge of the pillar strength and the overall layout stress distribution. It is particularly important to understand the impact of the layout extraction pattern on the effective regional “stiffness” of the rock mass around each pillar and to assess the macroscopic response of the overburden region as mining progresses. Two broad strategies may be followed to achieve a satisfactory pillar layout design. The traditional approach is to employ empirically determined pillar strength formulas to select the pillar dimensions (see, e.g., Lunder and Pakalnis * D. F. Malan [email protected] 1
Department of Mining Engineering, University of Pretoria, Pretoria, South Africa
1997; Martin and Maybee 2000; Gonzalez-Nicieza et al. 2006; Watson et al. 2008; Esterhuizen et al. 2011). This approach can lead to conservative designs in which pillars are over-sized with a corres
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