Stability Analysis of Anti-dip Rock Slopes with Flexural Toppling Failure Based on Deformation Compatibility

Flexural toppling often occurs in layered rock slopes, and rock columns behave like inclined superimposed cantilever beams that bend under their own weight. However, anti-dip rock slopes always have nonuniform joint spacing, and rock columns do not have the same ability of deformation due to different stiffness. To have the same deflection, based on the mechanics of materials, the moment and shear force at the failure surface should satisfy a certain proportional relationship. An analytical model based on deformation compatibility against the flexural toppling failure has been established. In the proposed model, the slope is divided into free deflection zones and compatible deflection zones by shear forces on the failure surface. The safety factor of each block can be calculated by the bending moment, and the least factor is used to represent the safety of the slope. In addition, for an equal thickness model, the average stiffness method is suggested to determine the calculated thickness for foliated rock slopes with nonuniform joint spacing. Finally, a case study is used for practical verification of the proposed method.