Transient wave propagation in a multi-layered soil with a fluid surface layer: 1D analytical/semi-analytical solutions

This paper studies one-dimensional transient wave propagation in a saturated multi-layered soil with a fluid surface layer. Based on Biot theory, the eigenfunction expansion method, the transfer matrix method, the state-space method, and the precise time step integration method are employed to develop analytical/semi-analytical solutions. For a special case (large dynamic permeability coefficient), we obtain an analytical solution. For a general case (arbitrary dynamic permeability coefficient), due to the influence of the damping term, we develop a semi-analytical solution that can be used to evaluate sediment with small dynamic permeability coefficients. The newly derived solutions are verified with solutions obtained by the Laplace transformation and numerical inverse Laplace transformation, which are also presented here. The newly derived solutions are presented in series form in the time domain and are straightforward and explicit so that the solutions are easy to implement. Through numerical examples, we analyse the influences of the dynamic fluid permeability coefficients on the transient response of the model, which is important in marine seismic and ocean acoustics applications.