This paper presents a numerical method based on the upper bound theory of Plasticity. The method is an extension of the two-dimensional approach developed by Donald and Chen (1998). The failure mass is divided into a number of prisms with inclined interfaces. It has been found that the velocities of the prisms can be determined by the Mohr-Coulombs associative flow law that enforces velocities to be inclined at angles of f to their respective shear surfaces. The factor of safety is obtained by the energy and work balance equation. It uses optimization methods to find the minimum factor of safety associated with the critical slip surface and the inclinations of the interfaces. A test problem is analyzed to show that this method can produce results consistent with the closed-form solution and other published solutions.
Most landslides do not exhibit plain-strain characteristics, although this assumption is made whenever conventional two-dimensional slope stability analyses are performed. It is well recognised that there is a need for continuing development of three-dimensional slope stability analysis methods (Stark and Eid, 1998). There are a large number of publications in the literature that deal with three-dimensional slope stability analysis. Duncan (1996) reviews the main aspects of 24 of these papers. In general, these methods can be classified into two categories. The failure mass is divided into a number of columns with vertical interfaces. Hungr (1987, 1989), Chen and Chameau (1983) and Lam and Fredlund (1993) extended Bishop's simplified method, Spencer's method, and Morgenstern and Price method respectively. These methods have suffered from a large number of assumptions that must be introduced to render the problem statically determinate. Lam and Fredlund (1993) balanced the number of equations that can be established from physical and mechanical requirements to the number of unknowns involved in these equations.