Parametric research on the time step and spring stiffness in three-dimensional discontinuous deformation analysis method

Three-dimensional discontinuous deformation analysis method (3D.DDA) is a dynamic calculation method based on the implicit solution. Inertial force is introduced in the solution process to ensure that the time variable is the real time variable, and springs are applied at the block boundary to avoid mutual intrusion between blocks. Therefore, the value of time step and contact spring stiffness directly affect the accuracy of 3D.DDA calculation results. Firstly, we analyzed the effects of the time step and contact spring stiffness on the numerical calculation results of the 3D.DDA method based on the theoretical formula derivation. Secondly, we studied the influence mechanism of time step on the simulation results of the 3D.DDA method individually based on the double block free falling model. And we determined the reasonable value area of time step. Then, considering the contacts between blocks, we studied the joint influence mechanism of time step and contact spring stiffness on the 3D.DDA simulation results based on the double block sliding model. And we analyzed the error between the 3D.DDA simulation value and the theoretical value under the conditions of different time step and contact spring stiffness. Based on that, we divided the combined value area of time step and contact spring stiffness into four regions (Q1, Q2, Q3, and Q4) and determined the optimal value area of time step and contact spring stiffness. At last, we carried out the slope rockfall model experiment and numerical simulation, and the trajectory of the falling rock in the numerical simulation was basically consistent with the experiment results, which verified the effectiveness of the optimal value area of time step and contact spring stiffness. The research results can provide a reference for the choice of the value of time step and contact spring stiffness in the numerical simulation based on the 3D.DDA method.

Automated summary

This study investigates the effects of time step and contact spring stiffness on the results of 3D.DDA method through theoretical analysis and numerical simulations. The reasonable value range and optimal value range of time step and contact spring stiffness are determined, and their effectiveness is verified through experiments.