Reliability back analysis of shear strength parameters of landslide with three-dimensional upper bound limit analysis theory

It is essential to determine the shear strength parameters c and phi on the sliding surface for stability evaluation and engineering design of a landslide. In this study, a new parameter back analysis method is proposed by combining the 2D/3D upper bound method of limit analysis and reliability theory to accurately determine the shear strength parameters for a 3D slope with a single failure surface. The proposed reliability back analysis method overcomes the shortcomings of the traditional deterministic analysis method of slope stability that cannot take into account the randomness and uncertainty of geotechnical parameters. Based on the reliability theory, two methods were studied: first-order reliability method (implemented by spreadsheet and Matlab, called spreadsheet method and constrained optimization method, respectively, in this paper) and Monte Carlo simulation. The optimized values of c and phi were obtained by establishing only one balance equation with the consideration of the pore water pressure or other complex conditions, which can solve the problem of the back analysis of strength parameters for a single 3D sliding surface condition. The correlation research showed that the negative correlation between c and phi greatly affected the back analysis results, and the reliability index values were conservative without considering such a negative correlation. A case study for the back analysis of shear strength parameters is conducted based on a practical landslide model with a broken line slip surface slope in Zhuquedong village, Luxi town, Xiangxi County, Hunan Province, China, and a suggestion for the selection of landslide cross section is presented. The results show that the back analysis results determined by the reliability theory coincide well with the survey and experimental results. The proposed method is found to be more accurate and effective in determining the values of shear parameters than that of the traditional deterministic inversion method.