Effect of various physical properties on the reflection coefficients of inhomogeneous waves at the stress-free surface of partially saturated soils induced by obliquely incident fast P-wave

Ghasemzadeh and Abounouri[1]developed a mathematical model of partially saturated soils that is solved using the potential method,which decomposes elastodynamics equations into two standard wave equations,a scalar wave equation for scalar potential and a vector wave equation for vector potential.In such a medium,four waves exist three longitudinal and one shear.Each fluid phase tortuous path is taken into account in this model.The inertial coupling between solid and fluid particles is consid-ered.Furthermore,both open-pore and sealed-pore boundaries are explored to investigate the reflection phenomenon at the surface of partially saturated soils.For both boundaries,the reflection coefficients of inhomogeneous waves at a partially saturated soil surface are found as a non-singular set of linear equations.All waves(both reflected and incident)in partially saturated soils are pronounced as inhomogeneous due to viscosity in pore fluids(i.e.,distinct directions of attenuation and propagation).The energy shares of reflected waves are determined using an energy matrix.A numerical example is used to determine the reflection coefficients and the distribution of incident energy among the various reflected waves.The effect of different physical features on reflection coefficients and incident energy partitioning is illustrated graphically.The conservation of incident energy at the surface of partially saturated soils is mathematically confirmed at all angles of incidence.