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

Unlike previous studies, this work specifically focuses on the positional uncertainty of rear-edge vertical fissures. Because water-filling and drainage conditions (blocked or unblocked) strongly affect hydro-mechanical behavior, four representative scenarios are defined: (I) water-filled fissure with blocked drainage, (II) water-filled fissure with unblocked drainage, (III) water-filled fissure without drainage effects, and (IV) dry fissure without water pressure. An extremum-based criterion was employed to identify the maximum residual sliding force and the corresponding critical fissure position. The effects of key parameters—including crest inclination, bedding dip, internal friction angle, cohesion, and slope height—on the critical fissure location were systematically investigated. Validation through real engineering cases confirmed the accuracy and applicability of the proposed formulation. The findings provide a solid theoretical foundation for hazard prevention, risk management, and reinforcement design of gently inclined layered rock slopes.