Theoretical study of P1 wave passing through a double-layer wave impeding block in the unsaturated soil

Abstract

Based on the propagation theory of elastic waves in unsaturated porous medium and single-phase elastic medium, the calculation model of a double-layer wave impeding block (WIB) as vibration isolation barrier in unsaturated soil foundation is established. The analytical solution of the transmission/reflection amplitude ratio of P1 wave passing through a double-layer WIB in unsaturated soil foundation are derived by Helmholtz vector decomposition theorem. The influences of physical and mechanical parameters such as saturation, wave impedance ratio, density, and shear modulus on the vibration isolation effect of the double-layer WIB when P1 wave passing through the double-layer WIB in the unsaturated soil foundation are analyzed by parametric studies. The results show that the saturation has a small effect on the transmission/reflection coefficients of P1 and S waves and a significant effect on the transmission/reflection coefficients of P2 and P3 waves. The wave impedance ratio and the shear modulus and density of the double-layer WIB have a significant effect on the transmission/reflection coefficients. The optimal shear modulus and wave impedance ratio of the double-layer WIB can be selected to obtain the best vibration isolation effect, which provides theoretical guidance for the application of the double-layer WIB in the field of unsaturated ground vibration control.