Method of Generation and Model of Calculation of Arbitrary Curved Slip Surfaces for Three-Dimensional Convex and Concave Slopes

Abstract

Compared with the three-dimensional (3D) simple slope, actual slopes often have irregular slope topography. The 3D convex and concave slopes are two important types of actual slopes. To analyze the stability of 3D convex and concave slopes, it is very important to construct reasonable 3D slip surfaces. Usually, spheres and ellipsoids are used; however, engineering examples show that these specific types of surfaces may be quite different from an actual slip surface. Therefore, based on the study of 3D convex and concave slope models, this work first establishes a new method to generate an arbitrary 3D curved slip surface. According to the generation characteristics of an arbitrary 3D curved slip surface, the 3D sliding body can be divided into several columns during the forming process of the slip surface. Therefore, the generated 3D slip surface is easily combined with the limit equilibrium (LE) column method for calculating the slope factor of safety (FOS) to achieve the purpose of analyzing slope stability. By simulating approximately a number of regular surfaces, such as the sphere, ellipsoid, and so on, the proposed method’s rationality is verified. Additionally, the results of some examples of 3D convex and concave slopes show that compared with a 3D simple slope, the 3D convex slope has poorer stability, whereas the 3D concave slope has better stability.