Analysis of Flexural Toppling Failure in Rock Slopes Using Discrete Element Method

Flexural toppling failure is a common failure mode of natural and artificial rock slopes, which has caused serious damage to human life and property. In this work, an advanced numerical method called the Universal Distinct Element Code (UDEC) was used to study the mechanism of flexural toppling failure. In total, more than twenty slope models were built and analyzed. Two new parameters (displacement discontinuity and transition coefficient of failure surface) were introduced to present a further understanding of flexural toppling. The results show the failure zone of rock slopes subjected to flexural toppling includes two parts: the first-order instability part (FOIP) and the independent toppling zone (ITZ). The FOIP can be further divided into two subzones: the sliding zone (SZ) and the superimposed toppling zone (STZ). The occurrence of surface deformation discontinuities is the precursor to flexural toppling failure. The first displacement discontinuity occurs on the boundary between the FOIP and the ITZ. The angle, spacing, and angle of the joints, the angle of the slope has a significant influence on the stability of anti-dip bedding rock slopes. However, they do not affect the deformation and failure pattern of the slope.

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

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.