Probabilistic slope stability assessment framework using Box–Behnken Design based response surface method

Slope failures are major geohazards that often cause severe damage in hilly terrains. Therefore, slope stability assessment is imperative for effective geohazard risk reduction. However, such analyses involve uncertainties related to material properties and loading conditions. Probabilistic methods address these uncertainties more reliably than deterministic approaches. This study proposes a Box–Behnken Design (BBD) based response surface method for probabilistic slope stability analysis. Six input parameters, including cohesion, internal friction angle, surcharge load, nail spacing, nail length and pseudo-static coefficient are considered as random variables in the probabilistic analysis. Using BBD, 54 design points are generated and analysed with the Finite Difference Method (FDM) to determine the corresponding Factors of Safety (FOS) values. These FOS values are then used to develop a second-order polynomial equation that serves as a response surface to estimate FOS for any new combination of input variables. Validation using 50 additional random parameter sets shows strong agreement with the numerical results. The probability of failure ( \:Pf ) result based on 50,000 generated samples revealed relatively high value, primarily due to the reduction in factor of safety (FOS) caused by pseudo-static force effects. Sensitivity analysis identifies cohesion as the most influential factor, followed by internal friction angle and pseudo-static coefficient. Therefore, the presented methodology is envisaged to enable efficient probabilistic slope stability assessment and support data-informed geohazard risk reduction for similar efforts.