A method for calculating the downslope sliding force of gently dipping bedding rock slopes while accounting for the uncertainty of rear-edge vertical fissures

Abstract

The position of rear-edge vertical fissures in gently dipping bedding rock slopes is a critical factor in controlling their stability. However, the exact location of these fissures is often uncertain, which presents challenges for stability assessment and hazard prediction. Therefore, it is essential to develop a theoretical method capable of identifying the most unfavorable fissure position. Based on the geometric relationships and static equilibrium conditions of the unstable slope mass, this study systematically analyzes the water pressure distribution characteristics of rear-edge fissures under various water filling and outflow conditions. Four typical mechanical calculation models are constructed: (a) fissure filled with water and blocked outflow fissures, (b) fissure filled with water and unblocked outflow fissures, (c) considering only hydrostatic pressure, and (d) no water pressure scenario. By deriving the sliding force calculation formula and introducing an extremum criterion, the most critical fissure position and its corresponding maximum residual sliding force are determined. The results indicate that: (1) the width of the potential slip surface increases with the slope crest inclination ( α ) and slope height ( H ), but decreases as the bedding dip angle ( θ ) increases, (2) the geometric parameters ( H , α , θ ) have a significantly greater impact on the slip surface width than the shear strength parameters ( c , φ ) of the rock mass and (3) water pressure plays a significant role in altering the most unfavorable fissure position and serves as a critical hazard-inducing factor. Compared to traditional methods, which fix the fissure position at 1.5 times the slope height behind the slope face, the proposed method accurately identifies the most critical fissure location, effectively minimizing calculation errors. This study provides a more reliable mechanical model and computational foundation for stability analysis of gently inclined bedding rock slopes, offering direct guidance for disaster prevention design, risk management, and reinforcement strategies in similar slope engineering projects.