The precise computation for wave propagation in stratified materials

The problem of random wave travelling along stratified materials is important for earthquake engineering. The soil is considered multi-layered and located above the base-rock, whose material property is assumed to be much stiffer than the soil, and the power spectrum density of the random excitation is given at the base rock. The soils can be arbitrarily anisotropic for each layer. The governing differential equations are derived in frequency and wavenumber domain and only a set of ordinary differential equations must then be solved. The eigensolution expansion method is used to solve for the responses of the layers. The precise integration algorithm in combination with the extended W–W algorithm is applied to obtain all the eigensolutions of the ODE (ordinary differential equation). Thereafter, the recently developed pseudo-excitation method for structural random vibration is transplanted to the solution of the layered soil responses. Numerical results are given and compared with some classical results. This shows the relevance of the presented method