Back analysis of LG6/LG6A chromitite pillar strength using displacement discontinuity modelling

Almost no work has been published on the strength of pillars in mines exploiting the LG6/LG6A chromitite bands in the Western Bushveld Complex. The strength of these pillars is unknown, and the hard rock industry still uses the Hedley and Grant formula. Numerical modelling, using inelastic constitutive models, may be of some value in estimating the pillar strength, but this approach is difficult and prone to errors as many assumptions are made. This paper explores the alternative approach of the back-analysis of actual LG6/LG6A mining layouts, using displacement discontinuity codes to simulate the average pillar stresses on a mine-wide scale. From this, and underground observations, a 'minimum' pillar strength (K-value in the pillar strength formula) can be estimated. The codes TEXAN and Map3D are both used in the paper to simulate the actual pillar shapes and sizes in an LG6/LG6A mine. The results are encouraging as the two codes produced similar APS values for a complex pillar geometry. An estimated K-value of 77 MPa was determined for the LG6/LG6A pillars in this particular area. This is more or less similar to earlier work done for the UG2 chromitite seam, but higher than the K-value of 39 MPa for a linear formula obtained by other workers for LG6/LG6A pillars. Caution should therefore be exercised before using this higher value for all areas. The effect of element sizes and explicitly simulating the effect of the surface for shallow pillars is illustrated in the manuscript using both codes. The need for actual pillar observations and an iterative design process, which cycles between modelling and observations, is also emphasized.