Integrated reliability analysis procedure for spatially variable soil slopes using recursive FORM algorithm enhanced by importance sampling: Abaqus via Python implementations

This paper proposes an efficient geotechnical reliability analysis framework that integrates the advantages of the first-order reliability method (FORM) and the Karhunen-Loeve expansion (KL) to evaluate the reliability of spatially variable soil slopes. The improved Hasofer-Lind-Rackwitz-Fiessler (iHLRF) recursive algorithm is adopted to implement the FORM procedure when coupled with finite element codes for slope stability analysis, and the KL is used to reduce the dimension of random variables representing the soil random fields. To enhance the accuracy of the failure probability estimated by KL-iHLRF, the importance sampling (IS) is also conducted in this study, resulting in an innovative slope reliability analysis framework, KL-iHLRF-IS. It is found that although the FORM analysis by itself may not be able to confidently estimate the failure probability of spatially variable soil slopes because of the very high dimension of random variables and the strong nonlinearity of the limit state function, it provides useful information on the design point values for KL-iHLRF-IS to rapidly compute the failure probability. The efficiency of KL-iHLRF-IS for slope reliability analysis is illustrated by three example slope case studies. The proposed framework is particularly useful when fast yet accurate slope reliability analysis using the finite element method is needed.

Automated summary

This paper proposes an efficient geotechnical reliability analysis framework that integrates the advantages of FORM and KL to evaluate the reliability of spatially variable soil slopes. The improved iHLRF algorithm is used to implement the FORM procedure, and KL is used to reduce the dimension of random variables. The proposed framework is particularly useful for fast and accurate slope reliability analysis using the finite element method.