First- and Second-Order Reliability Analysis of Rainfall-Induced Kotropi Slope Failure

First- and second-order reliability-based optimization of rainfall-triggered slope failures has not received significant attention in the past few decades. The application of first-order reliability method (FORM) and second-order reliability method (SORM) to analyze the slopes under rainfall conditions is presented in this paper. Moreover, the most appropriate continuous probability density functions (PDFs) for fitting parameters of soil water characteristic curve (SWCC) and saturated hydraulic conductivity are proposed based on minimum quantile, percentile, and cumulative distribution function (CDF) errors. The study recommends the use of the best-fit PDFs for the representation of fitting parameters alpha, n, and k(s) as Gamma, Weibull, and inverse Gaussian distributions, respectively. Furthermore, the probability of failures estimated using FORM and SORM is compared. The probability of failure estimated using FORM overestimates when compared to SORM. Moreover, the mean and coefficient of variation (COV) of the fitting parameters of SWCC and rainfall intensity have a considerable influence on the reliability index. Furthermore, the effect of rainfall intensity on the critical slip centers and critical slip surfaces is presented. The results demonstrated that there is a significant change in the critical slip surface and critical centers due to the change in rainfall intensity. In order to demonstrate the application of FORM and SORM, the rainfall-induced Kotropi slope failure in Himachal Pradesh is presented as a case study. The proposed SORM approach signifies that the Kotropi slope failure is highly likely for the normalized rainfall intensity of 0.45. Overall, the developed rigorous second-order reliability-based design optimization framework enables the assessment of the critical failure surface, critical centers, and stability of slopes under rainfall conditions considering the variability of shear strength parameters, SWCC fitting parameters, and rainfall intensity.