Abstract
The Limit Equilibrium Method (LEM) is an empirical technique, and the characteristic of its solution has not been clarified yet. The authors have been studying LEM in which slices or blocks are used to represent the sliding mass, and they suggested that LEM is a method which satisfies the necessary condition of Slip Line Method (SLM), because a block cut out from the stress field obtained by SLM always satisfies the limit equilibrium condition for LEM. Then, the authors have proposed Generalized LEM (GLEM), in which triangle or quadrangle blocks can be treated and safety factors are defined both on the base planes of blocks and on interblock planes. In this paper, the validity of the assumption on interblock forces is investigated, and a new formulation of GLEM using the displacement rate field and the principle of virtual work is introduced. Then, it is shown that the solution by LEM may sometime equal to one of LBM (Lower Bound Method) and sometime one of UBM (Upper Bound Method), depending on the assumption of interblock forces or interblock safety factors. To show the evidences, two GLEM solutions of a bearing capacity problem are demonstrated each of which completely agrees with either lower or upper bound solution. To obtain an upper bound solution closer to the actual one, the adjustments of block geometry during the minimization of bearing capacity are required in GLEM.
