| Abstract: | A simple algorithm (PILLR) for obtaining by two-dimensional analysis thee essential results that would be obtained in an actual three-dimensional finite element analysis of stress about mine pillars in flat-laying stratified rock is presented. A series of comparisons between the distributions of the local factor of safety calculated from the results of three-dimensional analysis and that obtained in the PILLR two-dimensional analyses for pillars of length/width ratio ranging from 0.33 to 8.0 shows the algorithm to be quite effective. The average vertical stress over the horizontal mid-plane of the pillar in the PILLR two-dimensional analyses is always within 0.5 per cent of the exact average; the local safety factor distribution is always within 10 per cent of the three-dimensional result. The ratio of the computer core x time product for the 2D' to 3D analyses is approimately 1/150. Additional improvements ard possible, although with the current PILLR algorithm 3D analyses require less than 1 minute for execution. This fact makes technically sound 3D mine pillar design analyses economically feasible on a routine basis. |
