Reflection and refraction of elastic waves at the interface of an elastic solid and partially saturated soils

Abstract

The present problem deals with the reflection and refraction of plane waves at the interface of an elastic solid and partially saturated soils. A mathematical model of partially saturated soils developed by Ghasemzadeh and Abounouri (Soil Dyn Earthq Eng 51:1–8, 2013) is employed. The incidence of two main waves (P and SV) is considered. As a result of the incident wave, two reflected waves (in an elastic solid) and four refracted waves (in partially saturated soils) are generated. The elastic solid behaves non-dissipative, while partially saturated soils behave dissipative due to the presence of viscous pore fluids, as a result of which the incident and reflected waves are homogeneous and all the refracted waves are inhomogeneous. The coefficients of reflection and refraction for a given incident wave result in a non-singular system of linear equations. Further, these reflection and refraction coefficients are used to obtain the energy shares of various reflected and refracted waves. This study has been numerically tested to determine the effects of various properties of partially saturated soils on the various energy shares. The numerical example confirms that during the reflection or refraction process conservation of incident energy is obtained at each angle of incidence.