Probabilistic failure assessment of bolt-stabilized pro-dip slopes considering shear effect

This study presents a probabilistic failure assessment model for bolt-stabilized pro-dip slopes, explicitly addressing the critical yet overlooked shear effect in conventional stability analyses. Conventional analytical approaches oversimplify the mechanical interactions between sliding slope masses and stabilizing bolts through the assumption of uniaxial tensile loading, thereby neglecting the combined tensile-shear stress states observed in real-world scenarios. To bridge this gap, the proposed model integrates force and moment equilibrium analyses, adopts the von Mises strength criterion for bolt rupture assessment, and systematically incorporates bedrock stratigraphy through differentiated parameter assignments. A comprehensive Monte Carlo simulation framework quantifies failure probabilities across three dominant modes: tensile-shear failure of bolts, rock-grout bond failure, and grout-bolt bond failure. Validation through the Freeway No.3 landslide case study demonstrates that shear-inclusive calculations yield significantly higher failure probabilities (exceeding 80% underestimation in shear-neglected models under high groundwater conditions). Parametric analyses reveal distinct behavioral regimes governed by bolt inclination, fixed length, and hydrological factors. The results emphasize that shear effect fundamentally alters failure mode dominance, with bolt failure becoming predominant under realistic stress conditions. This work provides a critical advancement in reliability-based design for pro-dip slopes, offering engineers a tool to mitigate catastrophic risks through physics-informed probabilistic assessments.