Automatic Differentiation-Aided Regional-Scale 3D Limit Equilibrium Slope Stability Analysis
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Three-dimensional limit equilibrium methods (3D LEM) are widely used for slope stability analysis due to their mechanical clarity and practical relevance. However, for the simplified Bishop’s method, the simplified Janbu’s method, and Spencer's method, regional-scale analyses are computationally demanding because the governing equilibrium system involves at least two coupled nonlinear unknowns: the factor of safety (FoS) and the interslice force inclinations in the horizontal and vertical directions, which must be solved by iterative convergence calculations. Conventional solvers typically rely on finite difference (FD) Jacobians, which increase computational cost and are sensitive to step size, limiting numerical robustness. This study introduces an automatic differentiation (AD)-computed Jacobian within a Newton-Raphson framework in the simplified Bishop’s method. By computing Jacobian via AD, the proposed method eliminates step-size dependence and improves convergence behaviour relative to FD-based approaches. The framework is implemented within a 3D LEM program code and verified on a simple benchmark slope. The obtained results show that the AD-computed Jacobians reduce iteration counts and overall computational effort relative to the FD-based solvers, while maintaining consistent FoS predictions. Additional experiments assess the potential benefits of GPU acceleration. Following the solver verification, the framework is applied to a regional-scale slope stability analysis considering a heavy-rainfall event that occurred in Japan, represented under a fully saturated assumption. Predictive consistency is assessed using receiver operating characteristic (ROC) analysis against observed failure occurrences. The results demonstrate the potential of combining automatic differentiation with high-performance computing to improve numerical efficiency and reliability in regional-scale 3D limit equilibrium slope stability analysis.
