Strength reduction search algorithms for slope stability analysis using spectral finite element method: From ‘brittle’ to ‘ductile’ failure

Three-dimensional slope stability analysis has been a grand change in geotechnical engineering. In this work, the spectral finite element method (SpecFEM), which effectively combines the geometric flexibility of FEM with the high accuracy of spectral methods, is adopted in combination with the strength reduction technique (named SRSpecFEM) for slope stability analyses. Nine classical slope cases are analyzed using SRSpecFEM, and two ‘ductility’ indexes, I d DISP and I d ITS , are defined based on the u max - SRF and ITS - SRF curves, allowing the nine slope cases to be classified readily into ‘brittle’ and ‘ductile’ groups using either a threshold method or the K-Means method. For the u max - SRF curves obtained from the nine slopes, four inflection-point detection methods are used to identify the factor of safety (FoS). It is observed that the maximum curvature method consistently identifies the correct FoS. Six search algorithms, namely IncRef, StdBis, GenBis, StdBis(L2), HybFalPos and adaptive, are investigated and compared across the nine cases. Numerical experiments reveal that IncRef, GenBis, StdBis(L2), and HybFalPos perform less effectively for ‘ductile’ slopes than for ‘brittle’ ones, whereas the adaptive search algorithm remains suitable for both failure types. Computational cost for the nine slope cases is reduced by approximately 28%-57% using the adaptive algorithm compared to StdBis. However, when a large maxITS (e.g., 500) is set, StdBis(L2) becomes competitive with the adaptive algorithm for ‘brittle’ slope failure.