Reflection of P1-wave incident obliquely at the free surface of a fluid-saturated half-space: a comprehensive study via the model of soil mechanics

Introduction Elastic wave propagation in fluid-saturated porous media is of great significance in various fields. Based on the soil mechanics model of a two-phase medium, the reflection problem of an obliquely incident plane P 1 -wave at the free surface is systematically explored, which aims to reveal the physical mechanism of wave propagation in saturated semi-infinite space. Methods The dispersion characteristic equations of body waves are obtained by using the Helmholtz decomposition method. The theoretical formulas of reflection coefficients and surface displacements are derived and verified for correctness by simplifying. Finally, numerical investigations are carried out on the variations of the displacement reflection coefficients and surface displacements with the incident angle for different boundary conditions, wave frequencies f , porosities n , Poisson’s ratios ν , and modulus ratios E w /μ . Results It is shown that the surface response of half-space is somewhat affected by the boundary conditions while little influenced by the wave frequency. It is also found that the effects of material properties on the surface response cannot be ignored. Discussion These conclusions provide a theoretical basis for wave survey technology of seismic engineering and site seismic response analysis.