Generalised Analytical Models for the Strength of the Inclined as well as the Flat Coal Pillars using Rock Mass Failure Criterion

The assessment of the strength of the coal pillars is essential for the safe extraction of the coal seam. All the pillar strength formulae used worldwide are developed for the flat coal pillars. Therefore, their adoption in evaluating the strength of the inclined coal pillars may endanger the workings of the inclined coal seams. The strength of an inclined coal pillar should be estimated by considering the inclination of the coal seam and its associated behaviour, because the shearing effect along the true dip aggravates the instability of the inclined coal pillars. In this paper, generalised analytical solutions have been developed to estimate the strength of the coal pillars which can be applied for both the inclined and flat coal pillars. The mathematical models are derived to obtain the confining stress in the coal pillar and the corresponding peak stress at the time of its failure using a rock mass failure criterion. The mathematical expressions are also developed for the stress distribution over the pillar considering the increase of the shearing effect with the dip of the coal seam. The Mohr-Coulomb criterion is considered for the shear characteristics at the interfaces of pillar-floor and pillar-roof. The asymmetrical stress distribution and failure along the dip-rise and the strike directions of the inclined coal pillars are addressed in this study. The concept of the confined core and three-dimensional stress distribution over the coal pillar are used to derive the strength formulae for the square, rectangular, and very long pillars. The performance of the derived strength formulae is assessed by the stable and failed cases of the flat and the inclined coal pillars. It is observed that all the inclined and flat coal pillars cases are correctly predicted by the derived generalised strength formulae. According to the derived strength formulae, the strength of the inclined coal pillar decreases with the increase of the inclination of the coal pillar. This paper also describes the variation of the strength of the inclined coal pillars with respect to the coal seam inclinations and the frictional properties of the contact planes for the different width-to-height ratios.