A two-grid search scheme for large-scale 3-D finite element analyses of slope stability

It is well known that the trial process for seeking the safety factor in the shear strength reduction finite element method (SSRFEM) is quite expensive, particularly for large 3-D slope stability analyses. The search algorithm for the safety factor is crucial to the entire solution process for the shear strength reduction finite element method, but few studies have attempted to exploit it. Among search algorithms, the commonly used bracketing and bisection search has not been fully optimised. Consequently, to improve the search scheme for the safety factor associated with the shear strength reduction finite element method, two strategies are suggested. First, a generalised bisection search algorithm is proposed to reduce the possibility of encountering non-convergence from a statistical point of view. To further improve the efficiency, a new two-grid scheme, characterised by a coarse mesh search and followed by a fine mesh search, is developed. Based on the drained or undrained analyses of the 3-D slope examples, the new search algorithm can markedly outperform the commonly used bisection search algorithms based on a single finite element mesh.