Elastic wave theory for propagation of Rayleigh waves at surface of unsaturated semi-infinite media

Abstract

Seismic energy is scattered in the form of seismic waves from the underground source to the surficial structures. These waves are known as body waves and will generate volumetric deformations by compressional waves or distortional deformations generated by rotational or shear wave. However, the body waves will generate other deformations at the interface of layers or the ground surface due to specific boundary conditions. Boundary conditions corresponding to the free surface allows additional answers to the equations of motion obtained. Since the earthquake engineering examines effects of seismic waves on the structures which are in or near ground surface and because surface waves are attenuated slower than body waves with distance, the surface waves are more important. Problem of wave propagation in saturated porous media was discussed first by Biot in the mid-twentieth century, after the formulation of the theory of saturated porous medium. Extension of the theory of elastic wave propagation in unsaturated soils which are made of a solid porous skeleton that the empty space is filled with water and air, founded the basis for solving the most complex problems of waves propagation in unsaturated soils. It was found that three compression waves (P1, P2 and P3) and a shear wave propagate in unsaturated porous media. Furthermore, Rayleigh wave are identified as the superposition of P and S-waves at the free surface. This results in propagation of three Rayleigh waves (R1, R2 and R3) at the free surface. The purpose of this research is to obtain the Rayleigh wave characteristics and the governing equations, according to the compression and shear waves. The theoretical results are demonstrated through examples at the end.