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

Xin Qu,Fangfang Diao

doi:10.1155/2020/5732596

Abstract

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.

Highlights

Toppling failure, being a kind of typical instability mode for rock slopes, widely exists in domestic and foreign water conservancy, hydropower, highways, and open-pit mine slope engineering. e toppling instability of slopes has caused great harm to people’s lives, property safety, and engineering construction [1,2,3,4]
In order to solve the above problems, an optimization of the analytical method for determining the flexural toppling failure plane based on the limit equilibrium theory [27,28,29] was developed in this study. e basal failure plane was considered as a plane at which the stress of the slope arrived at the state of limit equilibrium, i.e., the plane, at which the residual sliding force at the toe of the slope was equal to zero, was the basal failure plane
Toppling failure occurred in the slate slope in South Anhui in China, which was consistent with field observations and the results reported in [30, 31]. e angle between the failure plane and plane normal to discontinuities, θr, was 7.9766°, and the amount of total failed strata was 38

Summary

Introduction

Toppling failure, being a kind of typical instability mode for rock slopes, widely exists in domestic and foreign water conservancy, hydropower, highways, and open-pit mine slope engineering. e toppling instability of slopes has caused great harm to people’s lives, property safety, and engineering construction [1,2,3,4]. By using the principles of compatibility and the equations of equilibrium along with the governing equations of elastic deformation for the beams, the authors of [25, 26] derived equations for determining the intercolumn forces in rock masses with the potential for flexural toppling failure Since this model did not allow for slippage between layers, this method might yield very low safety factors for short layers near the slope toe, which might only be true for small deflections. E significant achievements can be summarized as two viewpoints, i.e., 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 These studies still have some issues needed to be resolved.

Searching Failure Plane

Numerical Example

Discussion

Conclusions