Assessment of the strength deterioration of a coal pillar using a strain-softening time-dependent constitutive model

In this study, a time-dependent constitutive model of a coal pillar was developed using the Hoek–Brown strain-softening model, which is useful for studying the strength deterioration of a coal pillar over time. A database of 32 failed cases of coal pillars of different ages from the Witbank Coalfield has been utilized to deduce the strength parameters of the coal seam through back analysis. A three-dimensional finite-difference method (FDM) has been chosen to simulate the failed cases. The simulation results have been obtained in terms of pillar strength and FOS of the pillar concerning time. Based on the simulation results the life of the pillar is considered when FOS is nearly equal to 1. The appropriate strength parameters have been derived as peak strength parameters: $m_i=1.47$ $m_{i} = 1.47$ and $s_i=0.01$ $s_{i} = 0.01$ ; residual parameters: $m_r=0.125$ $m_{r} = 0.125$ and $s_r=0.00001$ $s_{r} = 0.00001$ ; strength-reduction parameters: $\alpha =0.04$ $\alpha = 0.04$ , $\beta =200$ $\beta = 200$ for a coal mass. 39 stable cases from the same coalfields (Witbank) have been considered to validate the strength parameters. The simulation results of all the stable cases were showing FOS > 1. The proposed constitutive model is suitable for assessing a pillar’s time-dependent strength deterioration and creep behavior. The deterioration/yielding of the pillar is observed to be initiated from the skin/side, extending deeper into the pillar’s core with time and ultimately forming an hourglass shape. It is also observed that the FOS of the pillar decreases with time.