Analytical Solution for Estimating the Stress State in Backfill Considering Patterns of Stress Distribution

Abstract

Large underground voids created by removal of ore are usually backfilled with mill tailings. The stress state in the backfill must be estimated to ensure safety. Most of the existing analytical solutions for estimating stress at any depth within mine fills had adopted the assumption of uniform vertical stress. However, this assumption does not make for a valid hypothesis. This paper presents an analytical solution to estimate the stress state in vertical backfilled stopes with stress patterns of distribution in the fill considered. The trajectory of minor principal stress in the fill from the centerline to the wall was assumed to be either a circular-arc, parabola, or catenary. The direction of the minor principal stress at the centerline was vertical to the centerline, and the direction along the rock mass was determined using the geometrical relationship of Mohr’s stress circle. The stress states of the differential flat elements in the backfill were analyzed through equilibrium considerations. Then, the analytical solution for estimating the stress state in the backfill was obtained. A series of examples are presented and compared with existing analytical solutions and numerical results carried out in ABAQUS (version 6.13). A nonuniform stress distribution across the backfill width is also presented. The vertical normal stress component at the centerline was greater than that along the wall. The stress state in the backfill was affected by the friction angle and cohesive strength of the backfill soils, friction angle at the wall interface, and trajectory of the minor principal stress. A discussion is presented after the comparison of numerical and analytical results and addresses the limitations of the proposed analytical solutions.