Numerical-analytical method for slope stability assessment using circular slip surfaces in homogeneous massifs: Refined

Abstract

Slope stability determination within homogeneous rock masses was examined using analytical-numerical calculations tailored for circular cylindrical slip surfaces. Traditional pit wall and waste dump stability calculations faced delays due to time-consuming iterative approximations, which limited automated monitoring software and elevated human error risks during critical infrastructure design. To resolve this problem, the limit equilibrium method was modified by deploying a non-iterative direct algorithm. The sliding wedge was discretized into separate blocks bounded by specific vertical axes ( Bx , C x , A x , and M x ), which allowed for the optimization of partition density based on the weight of each segment within the total force balance. This approach provided an exact analytical-numerical solution, determining the minimum safety factor without relying on traditional iterations. Computational testing demonstrated that result convergence depended on blocks density between specific axes. While a single block was sufficient for the linear B x – C x segment, the curvilinear sections C x – A x and A x – M x required finer discretization. Specifically, partitioning the A x – M x zone into at least five blocks decreased the relative calculation error below the 2% threshold. The derived mathematical dependencies were adapted for software integration, laying the groundwork for automated geometric monitoring systems to provide instant geomechanics risk verification.