Dynamic responses of an underwater site subjected to plane P- or SV-wave incidence

The displacement responses of an underwater site due to plane P- or SV-wave incidence are studied. The site consists of a water layer and a saturated soil deposit overlying bedrock. Based on the wave propagation theory in single-phase elastic medium, fluid saturated porous medium and ideal fluid, the displacement formula at the interface between water and soil is developed. The effect of water depth on the displacement response is explored by a numerical example in the case of different stiffnesses and saturation degrees of the soil deposit and incident angle of plane waves. The results show that the peak value of horizontal displacement has little change with water depth. However, the resonance frequency increases with water depth. The peak value and resonance frequency of vertical displacement do not increase with water depth monotonically. For the horizontal and vertical displacements, the peak value increases and the resonance frequency decreases with the soil stiffness at the same water depth. Compared with the full saturation, a slight decrease in the saturation can obviously amplify the peak value and decrease the resonant frequency of vertical displacement. The peak value and resonance frequency of horizontal displacement are hardly affected by soil saturation. At the fundamental frequency of the site, under incident plane P-waves, the horizontal displacement increases firstly and then decreases with the increase of incident angle in the presence of water layer, and the water depth has little effect on the vertical displacement with different incident angles. In the presence of SV-wave incidence and water layer, the horizontal displacement decreases with the increase of water depth with different incident angles, and the vertical displacement decreases with the increase of water depth within the range of the incident angle of 35°to 45°, however, the water depth has little effect on the vertical displacement beyond the range.