Cantilever beam limit equilibrium model of anti-dip rock slopes considering tensile-shear strength characteristics

Stability analysis of anti-dip rock slopes is a critical concern in rock mechanics and engineering. The classical cantilever beam limit equilibrium model often simplifies the interlayer interaction forces as concentrated forces, potentially overlooking the impact of reduced rock tensile strength due to shear stress on stability. This study employs a simplified distributed load model to analyze the stress state of rock layers, confirming the existence of shear stress at the most critical point during flexural toppling. Subsequently, based on the bi-linear and tensile cut-off types of the Mohr-Coulomb criterion, two improved cantilever beam limit equilibrium models are established, which consider the tensile-shear strength characteristics of rocks. The effectiveness of the improved models is validated through a case study, and the factors influencing the differences in safety factors between the improved models and the classical model are analyzed. The results indicate that, compared to the traditional model, the safety factors of the improved models decrease, with the bilinear improved model showing a reduction of 12% to 16% and the tensile cut-off improved model showing a reduction of 5% to 8%. The reduction in the safety factor is influenced by factors such as the ratio η of the tensile strength σ_t to the cohesion C, as well as the distribution form of the interlayer interaction forces. As the ratio η increases, the difference in safety factors between the tensile cut-off improved model and the classical model increases, while the difference with the bilinear improved model decreases. Compared to the uniformly distributed load form, when the interlayer interaction forces adopt a triangular distribution form, the reduction in the safety factor of the improved models compared to the traditional model is more pronounced.