Numerical Analysis of Hard Rock Pillars using the Cohesion Weakening Friction Strengthening Model

"The Cohesion Weakening Friction Strengthening (CWFS) is adopted in numerical analysis to capture the observed progressive failure of hard rock pillars. As a case study, pillars at the Elliot Lake mines with width to height ratios of 0.5 to 3 were analyzed in FLAC3D. Pillars with width to height ratios of 0.5 and 1 show a very similar strain softening behavior while with width to height ratios of 2 and especially 3 indicated prolonged strain hardening. The CWFS model successfully captured the mechanism of progressive failure observed in hard rock pillars including initiation of spalling at the corners, progress of spalling towards the centre and formation of hour-glass shaped pillar, and eventually shearing through the width of pillar. Both the CWFS model and site specific empirical formula successfully separated the stable and failed cases in the Elliot Lake mines. While both models are in reasonable agreement for width to height ratios of less than 2, the empirical formula gives increasingly lower strength values for wider pillars which may result in excessively conservative and uneconomical design.INTRODUCTIONPillars are the portion of in situ rock left between the adjacent openings to maintain the stability of excavations. Conditions of equilibrium require that the loads previously carried by the excavated rocks be transferred to the pillars resulting in elevated stresses within the pillar. Hence, prediction of the behavior of pillars under these loads is important for underground design. Determination of the strength of pillars is a classic subject in underground mining. In conventional mining methods such as room and pillar operations, economic incentives point towards higher excavation ratios i.e., leaving smaller pillars between the mined excavations, while safety and stability requirements favor wider stronger pillars. In some mining methods such as caving operations, the problem is even more challenging. On one hand, the whole operation is directly dependent on the proper continuous flow of caved ore between the drawpoints which requires optimizing the spacing between drawpoints and thereby often leaving narrower pillars. On the other hand, the pillars should be wide enough to ensure the safety of mining operation. Both the blockage of drawpoints as a result of wide pillars and uncontrolled failure of narrow pillars can jeopardize the investments and mining operation.Therefore, design of pillar poses a somewhat unique challenge to rock engineers where simple conservative approaches frequently used in other design methods are no longer acceptable. The behavior of pillar under elevated loads should be predicted accurately."