Three-dimensional stress state in inclined backfilled stopes obtained from numerical simulations and new closed-form solution

Backfill is commonly used world-wide in underground mines to improve ground stability and reduce solid waste disposal on the surface. Practical solutions are required to assess the stress state in the backfilled stopes, as the stress state is influenced by the fill settlement that produces a stress transfer to the adjacent rock walls. The majority of existing analytical and numerical solutions for the stresses in backfilled openings were developed for two-dimensional (plane strain) conditions. In reality, mine stopes have a limited extension in the horizontal plane so the stresses are influenced by the four walls. This paper presents recent three-dimensional (3D) simulations results and a new 3D closed-form solution for the vertical and horizontal stresses in inclined backfilled stopes with parallel walls. This solution takes into account the variation of the stresses along the opening width and height, for various inclination angles and fills properties. The numerical results are used to validate the analytical solution and illustrate how the stress state varies along the opening height, length, and width, for different opening sizes and inclination angles of the footwall and hanging wall. Experimental results are also used to assess the validity of the proposed solution.