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According to the results of the physical model tests, the failure plane of an anaclinal layered rock slope was a linear-type plane at an angle above the plane normal to the discontinuities, and the failure mode of rock strata was bending tension. However, the shear failure occurred near the slope toe, the effects of the cohesion of the discontinuities on the stability of the slope, and the contribution of tangential force to cross-section axial force were neglected in such studies. Moreover, none of the experts had developed a rigorously theoretical method for determining the angle between the failure plane and the plane normal to the discontinuities. This paper was initiated for the purpose of solving the problems described above. With the cantilever beam model and a step-by-step analytical method, an optimization of the analytical method for determining the flexural toppling failure plane based on the limit equilibrium theory was developed and the corresponding formulations were derived. Based on the present computational framework, comparisons with other studies were carried out by taking a slate slope in South Anhui in China and a rock slope facing the Tehran-Chalus Road near the Amir-Kabir Dam Lake in Iran. Furthermore, the sensitivity analyses of the parameters used in the calculation process of the failure angle of the slate slope in South Anhui in China were performed. The results demonstrated that the failure plane and the safety factor of the stability obtained with the presented method were credible, which verified the proposed method. The dip angle of the slope, the dip angle of the rock stratum, and the friction angle of the discontinuities were the controlling factors for the overall failure of the slate slope in South Anhui in China.

An Optimization of the Analytical Method for Determining the Flexural Toppling Failure Plane