Analytic solution for wave propagations in layered unsaturated soil and its application

In most of the current analyses of free field seismic response, the unsaturated soils are usually regarded as the quasi-saturated or single-phase media. It is difficult to describe the characteristics of unsaturated soils. A free field model for rock-layered unsaturated soil system is established. Based on the theory of wave motion in poroelastic medium, the elastic wave propagation under plane P-wave and SV-wave incidence in the rock-layered unsaturated soil system is solved using the transfer matrix method. By comparison with the existing solutions for an overlying unsaturated soil layer on the bedrock half-space, the solution given here is verified. Assuming the saturation of the soils above the groundwater layer has a gradient variation along the depth, the effects of variation of groundwater level on earthquake ground motions are analyzed using this solution. It is shown that the effects of variation of groundwater level on ground motions are related with the wave frequency and incident angle. At the same frequency, the variation of groundwater level has a great effect on the vertical displacement at ground surface when the incident angle is small. The effect of the groundwater level on the horizontal displacement first increases and then decreases with the incident angle increasing from 0° to 90°. At the same incident angle, the response peaks of the vertical displacement at ground surface decrease, and the frequencies of the resonance peaks increase with the increase of the groundwater level. But the variation of groundwater level has little effects on the horizontal displacement at ground surface.