Analytical solution for determining wall closure associated with stope excavation underneath sill mat constructed by cemented backfill

In the underhand cut-and-fill mining method, a sill mat (i.e. an artificial horizontal pillar) constructed by cemented backfill is essential to prevent mine workers from being directly exposed under problematic rock roofs. A critical issue is to determine the minimum required strength of the sill mat to ensure a safe and cost-effective design. Until now, Mitchell's analytical solution is the only available option, considering two stiff and immobile rock walls. Unavoidable rock wall closure associated with stope excavation below the sill mat was neglected. This, along with other undefined parameters, explains why Mitchell's solution is rarely used in sill mat design. A new analytical solution for determining the minimum required strength of the sill mat accounting for wall closure is necessary. In this study, a closed-form analytical solution for estimating rock wall closure generated by stope excavation below a sill mat is developed by using Salamon's and Flamant's models. The proposed analytical solution does not contain any coefficients of correction or calibration. Despite several assumptions (or somewhat of oversimplifications) necessary to render a simple analytical solution possible, good agreements are obtained between the rock wall closures predicted by applying the proposed analytical solution and those obtained numerically with FLAC3D for many cases with arbitrarily chosen geometrical and material parameters. The proposed analytical solution is therefore validated and can be used to evaluate the rock wall closure generated by stope excavation below a sill mat.