Numerical Instability in Slope Stability Analysis: A Finite Difference Approach

ABSTRACT In geotechnical engineering, slice methods are the most widely used computational techniques for analyzing slope stability. Notably, the Morgenstern‐Price and Janbu approaches rigorously enforce the equilibrium of forces and moments within these slice methods. However, these rigorous methods often encounter challenges with numerical convergence, particularly when using very thin slices. This study addresses these issues by building on previous research that examined the indeterminacy and numerical instability of the differential equations governing slope stability. It extends these differential models into discrete finite difference models, similar to those utilized in slice methods. Finite difference (FD) schemes are employed to construct three FD models (namely, dM, dJ, and dB models), which inherit their differential counterparts' local indeterminacy and numerical instability. Inspired by the Morgenstern‐Price method, the dM‐model and the proposed dB‐model demonstrate greater stability than the dJ‐model deriving from the Janbu method. The findings offer valuable insights into the impact of thin slices on numerical stability and enhance our understanding of the limitations inherent in slope stability analyses.