Probabilistic stability analysis of failed and stable cases of coal pillars

Abstract

The conventional design criterion of the safety factor for pillar stability is a deterministic approach characterised by non-random and exact values of its input parameters i.e. strength and stress. The integrity of pillars often jeopardized when some fluctuations or deviations occur in their strength and stress due to uncertainties in field conditions. To counter these unknown fluctuations or deviations, the coal pillars are designed with safety factors greater than unity and their exact values are selected based on local geomining factors. This practice does not guarantee stability against the geomining uncertainties and consequently lock-up the coal in the bigger size of the pillars. Therefore, to assess the variability in the input parameters in pillar design, this paper presents a probabilistic approach to analyse the stability of coal pillars considering the cases of stable and failed pillars in Indian coalfields. The databases of input design parameters are collected for stable and failed coal pillars from different Indian coal mines. The probabilistic distribution fittings of strengths, stresses and safety factors of stable flat, stable inclined, failed flat and failed inclined pillar cases are derived to know their means and standard deviations. The Monte Carlo Simulation and the First Order Reliability Method have been implemented to solve the limit state functions. The failure probabilities estimated for stable flat, stable inclined, failed flat and failed inclined cases are 0.29, 0.28, 0.56, and 0.99 respectively. The analysis recommends the safety factors of corresponding threshold failure probabilities of stable flat pillars as 1.61 and for stable inclined pillars as 1.41 in Indian mines with the ranges of design parameters considered in their databases. Therefore, the probabilistic stability analysis can provide an additional design criterion to select the optimum safety factor of pillars for improved recovery rates in coal mines.