Average vertical stress on irregular elastic pillars estimated by a function of the relative extraction ratio

•The concept of relative extraction ratio is introduced in this article as an explanatory variable of the average vertical stress acting on mine pillars.•A quadratic function of the relative extraction ratio, the coefficients of which are derived from numerical modeling, is proposed.•A numerical comparison of the proposed function with two existing methods is conducted (2D and 3D elastic conditions).•The quadratic function offers the best approximation of the pillar load in elastic conditions when the pillars are of irregular size.•The quadratic function is shown to be applicable to various mining geometries.

Two principal existing analytical methods, which are presented in this paper, can be used to estimate the vertical stress acting on pillars in room-and-pillar mines, based on the concept of extraction ratio. These two methods can adequately predict the pillar load in specific geometrical and mechanical conditions. However, they are not always suitable in the case of irregular geometries with important local variations of the extraction ratio. In fact, one of these methods tends to underestimate the average vertical stresses while the other significantly overestimates the highest values. Therefore, the work undertaken here is focused on the development of a more accurate analytical method for calculating the vertical stress on pillars of irregular size. By using a finite difference code, several hundreds of room-and-pillar mines with random geometries have been simulated in order to obtain numerical estimations of the average vertical stress on pillars under different configurations. A quadratic function of the relative extraction ratio is shown to provide a good fit to the numerical results. It is proposed as a new method for calculating the vertical load on elastic pillars, which offers a better approximation than the existing methods. This is verified for typical ranges of depths and extraction ratios observed in room-and-pillar mines.