Abstract: Discontinuous deformation analysis (DDA) is a new numerical method parallel to the finite element method. Based on the principle of minimum potential energy, the method unifies the deformation, motion and contact of each discrete block into the equilibrium equation for implicit solution. However, the traditional DDA method requires assembling the whole stiffness matrix to solve the equations in parallel, which occupies a large amount of memory, takes a long time and has a very low computational efficiency in the three-dimensional numerical simulation of large geotechnical engineering problems. Therefore, a three-dimensional spherical DDA method based on explicit time integration is proposed. This method does not require assembling the whole stiffness matrix. Because of the mass matrix is diagonal matrix, it can be stored as a one-dimensional vector with less memory, and can be solved block by block with higher efficiency in the acceleration solving process. The maximum displacement criterion is used to simplify the contact algorithm in the contact judgment, and the smaller time step ensures the accuracy of calculation. Finally, the accuracy and efficiency of the method are verified by several classical examples.

Key words: discontinuous deformation, explicit time integration, mass matrix, maximum displacement criterion, geotechnical engineering