Numerical Simulation of Dynamic Process of the Tangshan Earthquake by a New Method—LDDA

Abstract

—LDDA (Lagrangian Discontinuous Deformation Analysis) is a new numerical analysis method to deal with the problems of discontinuous deformation in elastic block systems. The method is based on DDA (Discontinuous Deformation Analysis) and the domain decomposition algorithm. Due to the use of the contact criteria of the DDA, it is not necessary to define a slide line in advance for contact problems, which is needed in the classical FEM. The method prevails over the penalty method in the satisfaction of constrain conditions. By using the domain decomposition algorithm, the efficiency in solving equations 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 elastic bodies according to the contact criteria of the DDA; 2) to solve the contact forces (Lagrange multipliers) by domain decomposition method; and 3) to calculate the displacement and stress caused by the contact forces and other loads by the FEM for each elastic body.¶In this paper, the method is used to model the dynamic process of the Tangshan earthquake (M _s = 7.8) of 28 July, 1976 and to directly obtain the quasi-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 dynamic problems of earthquakes. It is also applicable for solving rock-engineering problems as a multi-elastic body system.