Application of the discontinuous deformation analysis method to stress wave propagation through a one-dimensional rock mass

• The seismic DDA method is employed based on the Newmark integration method.
• Computing methods of damping ratio for viscous and numerical damping are presented.
• Suggested block size is obtained considering homogeneous rock and joint rock mass.
• Abilities of DDA to simulate the no tension and slip of the joint are validated.

The analysis of stress wave propagation through a rock mass is an important issue in rock engineering, and the discontinuous deformation analysis (DDA) method provides an effective tool to solve this problem. In this paper, based on the motion equations of block system with the Newmark integration method, the DDA method improved by the viscous boundary and the force input method is employed, and some investigations are made to extend the capability of the DDA method to address the wave propagation problem. First, for providing a quantitative method to control the damping of the DDA method, the computing methods of the damping ratio for both viscous damping and numerical damping are presented, which can effectively simulate the energy dissipation of stress wave propagation. Second, based on the one-dimensional DDA model, a further study on the size choice of a sub block for stress wave propagation is developed, which considers the homogeneous rock and the joint rock mass, and suggested values of block element ratio for both P-wave incidence and S-wave incidence are obtained by comparing with the theoretical solutions. Last, abilities of the DDA method to simulate both the no tension and slipping characteristics of a joint are validated, and the effects of the joint on wave propagation are also investigated.