Modified Tributary Area and Pressure Arch Theories for Mine Pillar Stress Estimation in Mountainous Areas

This paper describes a parametric study using discrete element modeling (DEM) of partial mining in a mountain terrain with in situ pillars for overburden support. For room and pillar mining or strip pillar mining, the accurate estimation of pillar stress is essential to ensure pillar stability and mine safety. Classical mine design methods such as the tributary area theory (TAT) and the pressure arch theory (PAT) are commonly used to calculate the pillar stress for mines under a relatively flat terrain. However, mine sites with uneven terrains can result in nonuniform stress distributions in the mine system and the classical methods may underestimate the pillar stresses by several times. In this paper, 1200 DEM mine models with terrains that include either a single slope or a valley, have been constructed. Through rigorous numerical modeling, the effects of several design parameters are identified: The influence factors, influence range, and mechanism of the concentrated pillar stresses computed from the models indicate that the shape of an extended pressure arch (EPA) can dictate the accuracy of the TAT and PAT methods. Based on the EPA estimation, a pillar stress estimation method is proposed for the design of mines in mountainous terrains. This paper updated the method of terrain-induced pillar stress concentrations with an improved EPA theory, and the gap between PAT and TAT theories is addressed by further discussion on their relationship and applicability.