A three-dimensional slope stability analysis method using the upper bound theorem. Part II: numerical approaches, applications and extensions

The second part of this paper provides the numerical procedures that implement the three-dimensional upper-bound slope stability analysis method described in Part I. A three-dimensional failure surface is generated by elliptical lines based on the slip surface in the neutral plane and extended in the z direction. This failure surface is mathematically represented by a series of variables including the co-ordinates of the nodal points that define the slip surface at the neutral plane, the inclinations of the row-to-row interfaces and the coefficients that define the ratio of the long axis over the low one of the elliptic. A method of optimisation is followed in order to find a set of these variables that offers the minimum factor of safety. A computer program EMU-3D is coded to perform the calculation for practical problems. Applications and extensions of the method presented in this paper include a case study of the Tianshenqiao Landslide, the stability analysis of the right abutment of the Xiaowan arch dam, and the portal of the Hongjiadu hydropower project.