Explicit Discontinuous Deformation Analysis Method with Lumped Mass Matrix for Highly Discrete Block System

Abstract

In the traditional discontinuous deformation analysis (DDA) method, the implicit time integration scheme is used to integrate equations of motion for modeling the mechanical behavior of a highly discrete rock block system. This requires that global equations be constantly solved. Hence, the computational efficiency of the traditional DDA method will decrease, especially when large-scale discontinuous problems are involved. Based on the explicit time integration scheme, an explicit version of the DDA (EDDA) method is proposed to improve computational efficiency of the traditional DDA method. Since a lumped mass matrix is used, there is no need to assemble global mass and stiffness matrices. More importantly, solving large-scale simultaneous algebraic equations can be avoided. The open–close iteration, which can assure the correct arrangement of constraints, is kept in the EDDA method. In addition, the simplex integration method, which is capable of conducting exact integration over an arbitrarily shaped block, is employed. Two numerical examples, including a sliding problem with an analytical solution and an underground cavern, are solved. The numerical results indicate the accuracy and robustness of the proposed EDDA method.