Finite element analyses of wave propagations due to a high-speed train across bridges

The nite element mesh of the unbounded wave problem often contains a large number of degrees of freedom. Moreover, the wave re ection along the mesh boundary cannot be avoided if only the traditional time-domain nite element method (FEM) is used. Thus, the main purpose of this study is to overcome those drawbacks and discuss how to use the three-dimensional FEM to simulate the soil vibration due to a moving high-speed train across bridges. A number of nite element analyses (FEA) including the isolation schemes of in- lled and open trenches were performed. The appropriate mesh dimension in the direction of the railroad is suggested and validated. Moreover, the 3-node wheel element for simulating the moving train and the least-squares method for nding foundation properties are proposed. Since the nite element mesh contains a large number of degrees of freedom, the conjugated gradient method with the SSOR preconditioning scheme is recommended. In conclusion, this study indicates that the di culty of the FEA for unbounded problems can be overcome e ciently even by using a personal computer