Numerical simulation of dynamic process of the Tangshan earthquake by a new method - LDDA

LDDA (Lagrangian Discontinuous Deformation Analysis) is a new numerical ana lysis method to deal with the problems of discontinuous deformation in elas tic block systems. The method is based on DDA (Discontinuous Deformation An alysis) and the domain decomposition algorithm. Due to the use of the conta ct criteria of the DDA, it is not necessary to define a slide line in advan ce for contact problems, which is needed in the classical FEM. The method p revails over the penalty method in the satisfaction of constrain conditions . By using the domain decomposition algorithm, the efficiency in solving eq uations is improved greatly. The process of solving a multi-elastic body system by LDDA is as follows: 1 ) to find total contact points (Lagrange multiplier points) among the elast ic bodies according to the contact criteria of the DDA; 2) to solve the con tact forces (Lagrange multipliers) by domain decomposition method; and 3) t o calculate the displacement and stress caused by the contact forces and ot her loads by the FEM for each elastic body. In this paper, the method is used to model the dynamic process of the Tangs han earthquake (M-s = 7.8) of 28 July, 1976 and to directly obtain the quas i-static and dynamic dislocations. shear stress drop, and rupture velocity of the earthquake fault. The simulation shows that the method can be used to efficiently solve the d ynamic problems of earthquakes. It is also applicable for solving rock-engi neering problems as a multi-elastic body system.