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.