Reliability Analysis of Unsaturated Soil Slopes Using Advanced Surrogate Models: A Comparative Study of PCE-MCS, K-MCS, and Gradient-Based Methods

Abstract Probabilistic stability analysis of soil slopes is essential for reliable geotechnical design due to pronounced uncertainties in soil strength and hydraulic parameters. Although crude Monte Carlo simulation (MCS) provides a robust benchmark, its prohibitive computational cost and the limitations of gradient-based methods such as FORM and SORM in handling nonlinear and non-Gaussian performance functions restrict their practical applicability. To address these challenges, this study conducts a comparative analysis of advanced surrogate-based reliability methods, specifically polynomial chaos expansion–enhanced Monte Carlo simulation (PCE-MCS) and kriging-enhanced Monte Carlo simulation (K-MCS), against traditional gradient-based methods such as the first-order reliability method (FORM) and second-order reliability method (SORM) for evaluating the stability of unsaturated finite soil slopes. The crude MCS serves as the benchmark. The work examines the predictive accuracy and computational efficiency of these methods in estimating the probability of failure ( p f ). Parametric studies demonstrate nonlinear variations in p f with mean and coefficient of variation of stability number ( c / γ H ), internal friction angle ( ϕ ), and fitting parameters of soil-water characteristic curve (SWCC) ( a f / γ H , n f , and m f ). In terms of computational efficiency, surrogate-assisted approaches provide orders-of-magnitude reductions in wall-clock time compared to crude MCS. When normalized with respect to PCE-MCS (unity), K-MCS requires only 1.85 times the computational cost, whereas FORM/SORM requires approximately 28 times. In contrast, crude MCS incurs computational costs exceeding four orders of magnitude for large sample sizes. Statistical testing confirms that stochastic methods (K-MCS, PCE-MCS) significantly outperformed gradient-based methods (FORM, SORM). Although no statistically significant difference is observed between K-MCS and PCE-MCS ( p -value = 0.83), K-MCS exhibited slightly narrower confidence intervals and lower mean error (0.0116 versus 0.0153), indicating marginally greater robustness. Moreover, K-MCS maintains point-estimate error percentages below 8% across most scenarios, with PCE-MCS below 11%. In contrast, FORM showed maximum errors of up to 50.67%, followed by SORM with errors as high as 31.97%. The study also includes Sobol’ sensitivity analysis to identify the influence of each input parameter on the factor of safety. Comparisons of Sobol’ indices derived using post-processed PCE, PCE-MCS, and K-MCS reveal consistent results, with friction angle ( ϕ ) identified as the most influential parameter (total-order Sobol’ index = 0.66). To facilitate practical application, the study concludes with developing design charts using kriging for target reliability indices of 3.0. These charts provide an important tool for slope stability assessment, enabling precise and efficient evaluations under unsaturated soil conditions. The findings emphasize the efficacy of PCE-MCS and K-MCS as robust and computationally efficient surrogate modeling techniques for quantifying the probability of failure of unsaturated soil slopes and facilitating reliability-based design optimization of finite slopes.