Reflection of elastic waves under initial stress at a free surface: P and SV motion

The phenomenon of reflection of elastic waves at a free surface of an initially stressed sandy medium has been studied here. The reflection coefficients have been computed numerically for both P and SV motion. The variations of reflection coefficients for different values of η, initial stress parameter, and angle of incidence have been represented graphically. The effects of initial stress and sandiness of the layer on surface waves have also been studied. To the best of our knowledge the idea of a sandy medium under initial stress is a new one which is physically possible. Taking into consideration of the theories given by Weiskopf [J. Franklin Inst. 239, 445 (1945)] and Biot [Mechanics of Incremental Deformations (Wiley, New York, 1965)] the equations of motion have been deduced here.