Rigorous Limit-Equilibrium Solution for Three-Dimensional Slope Stability with an Asymmetric Slip Surface

Abstract

In practice, slope instability failure often occurs in the form of an asymmetric three-dimensional (3D) slip surface. The movement trend of the asymmetric sliding body is in the form of simultaneous translation and rotation around the vertical axis; thus, the route of the main sliding (RMS) exhibits non-linear characteristics. Therefore, the purpose of this study was to propose a rigorous 3D limit equilibrium method for slope stability with the asymmetric 3D slip surface. The function of normal stress over the slip surface was assumed, and all the equilibrium conditions of the entire sliding body (i.e., three forces and three moments) were considered. The mapping function relationship between curvilinear coordinates and Cartesian coordinates was established, and the expressions of basic physical quantities in the equilibrium equations were derived. Through optimizing the RMS, a rigorous solution of the factor of safety was obtained for an asymmetric slip surface. The research results indicated that the present method well reflected the influence of the RMS, which was applicable to analyzing 3D slope stability with an asymmetric slip surface. We found that if the RMS is ignored, the factor of safety will be overestimated. The more significant the asymmetry of the 3D slip surface, the greater the proportion of rotation for the sliding body, and the more significant the bending degree of the RMS. The study results suggested that a rotation hardly existed, and the RMS tended to be a linear route in a symmetrical sliding body. The research results can provide a theoretical reference for 3D slope stability evaluation.