Fundamentals of the Block Element Analysis

Abstract

In this chapter, the principles and basic algorithms of the block element analysis (BEA) are presented, to show how a practical method in computational geomechanics may be inspired and established through a simple engineering problem. An attempt to improve the limit equilibrium method (LEM) for a more rational solution of rock wedge stability in slope gives rise to the consideration of the deformation characteristics of slip planes. The governing equations for the block system are formulated by taking into account of the force and moment equilibrium condition for rigid blocks, the deformation compatibility condition between blocks, and the elasto-viscoplastic constitutive relation of discontinuities. Since the seepage flow imposes a remarkable influence on the stability of rock masses, the interest is further directed to establishing a seepage analysis algorithm competent to the BEA. With the basic assumption that the seepage is merely permitted in discontinuities whereas the rock blocks are impervious, and use is made of the messages provided by the block system identification, the variational function of the seepage flow in discontinuity network can be automatically discretized and solved. Two engineering application cases related to the natural and cut slopes demonstrate unique merit of the BEA, namely, it possesses both the reliability of the FEM and the simplicity of the LEM.