Theoretical solutions of transmission and reflection of seismic waves propagation in three-phase unsaturated soil-seawater interface and research implications

In offshore anti-seismic engineering, partially saturated soil is usually regarded as fully saturated one for engineering purpose, which inevitably causes some error. This study is conducted to investigate the action mechanism of seismic waves propagation at the three-phase unsaturated soil-water interface, revealing significant discrepancies arising from the widely-held approximation. Firstly, the wave equations of the unsaturated soil-water with the interaction of solid, liquid, gas and seawater are specially constructed and solved successfully, and the theoretical solutions are obtained. These solutions have wider applicability because it can be directly reduced to that of saturated soil site. Secondly, the formulation of energy coefficients is derived and obtained, then energy distribution and conservation are further elucidated, thereby verifying the accuracy of theoretical results. Subsequently, the results of the three-phase unsaturated soil and two-phase saturated one are compared, fully demonstrating the significant influence due to the existence of gas, and we find that a pronounced shift of coefficients can be observed even with a slight change in saturation. Finally, numerical investigations indicate that the coefficients obtained from the unsaturated soil model differ significantly from those of the fully saturated one, and vary as a function of the incident angle, saturation and porosity.