An analytical solution for the nonlinear distribution of effective and total stresses in vertical backfilled stopes

The increasing use of backfill in underground mines requires a proper evaluation of the stress state in and around the filled openings. This is, however, a relatively complex issue due, in part, to the large contrast in strength and stiffness between the backfill material and surrounding rock mass. In recent years, it has been shown that arching theory, based on limit equilibrium analysis, can be used to estimate the stress distribution in backfilled stopes. Nonetheless, many simplifications are involved in such analytical solutions and this affects the precision and significance of the calculated results. In this paper, a previously developed solution is enhanced by introducing the combined effects of non-uniform vertical stress distribution and positive pore water pressure. This leads to a more representative analytical solution, as demonstrated by successful comparisons with numerical simulations. The results indicate that the proposed solution can be used to estimate the effective and total stress state in submerged or partially submerged backfilled stopes with a simple geometry.