Probabilistic Rock Slope Stability Assessment of Heterogeneous Pyroclastic Slopes Considering Collapse Using Monte Carlo Methodology

Volcanic terrains exhibit a complex structure of pyroclastic deposits interspersed with sedimentary processes, resulting in irregular lithological sequences that lack lateral continuity and distinct stratigraphic patterns. This complexity poses significant challenges for slope stability analysis, requiring the development of specialized techniques to address these issues. This research presents a numerical methodology that incorporates spatial variability, nonlinear material characterization, and probabilistic analysis using a Monte Carlo framework to address this issue. The heterogeneous structure is represented by randomly assigning different lithotypes across the slope, while maintaining predefined global proportions. This contrasts with the more common approach of applying probabilistic variability to mechanical parameters within a homogeneous slope model. The material behavior is defined using complex nonlinear failure criteria, such as the Hoek–Brown model and a parabolic model with collapse, both implemented through linearization techniques. The Discontinuity Layout Optimization (DLO) method, a novel numerical approach based on limit analysis, is employed to efficiently incorporate these advances and compute the factor of safety of the slope. Within this framework, the Monte Carlo procedure is used to assess slope stability by conducting a large number of simulations, each with a different lithotype distribution. Based on the results, a hybrid method is proposed that combines probabilistic modeling with deterministic design principles for the slope stability assessment. As a case study, the methodology is applied to a 20-m-high vertical slope composed of three lithotypes (altered scoria, welded scoria, and basalt) randomly distributed in proportions of 15%, 60%, and 25%, respectively. The results show convergence of mean values after approximately 400 simulations and highlight the significant influence of spatial heterogeneity, with variations of the factor of safety between 5 and 12 in 85% of cases. They also reveal non-circular and mid-slope failure wedges not captured by traditional stability methods. Finally, an equivalent normal probability distribution is proposed as a reliable approximation of the factor of safety for use in risk analysis and engineering decision-making.