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

In foundation vibration control, the multi-layer isolation barrier has a good vibration isolation effect due to its ability to block the propagation of elastic waves multiple times. In this paper, using the double-layer wave impeding block(WIB) as an example, the calculation model of a double-layer WIB as a vibration isolation barrier in the unsaturated soil foundation is established. The analytical solution of the transmission/reflection amplitude ratio when the S wave passes through the double-layer WIB in the unsaturated soil foundation is calculated by using the Helmholtz vector decomposition theorem. In addition, the influence of parameters such as the wave impedance ratio, saturation, shear modulus and density on the vibration isolation performance of the WIB are analyzed by numerical examples. The results show that the wave impedance ratio, shear modulus and density of the WIB material have a significant influence on the transmission/reflection amplitude ratio. Saturation has little effect on the transmission/reflection amplitude ratio of P1 and S waves but has a great effect on the amplitude ratio of P2 and P3 waves. The best vibration isolation effect can be obtained by selecting the optimal wave impedance ratio and shear modulus of the double-layer WIB material.