Dynamic responses of a sediment-filled valley with a fluid layer subject to incident waves

The diffraction of elastic waves by a sedimentary valley in a homogeneous elastic half-space is studied in this paper. The sediment-filled valley is composed of a fluid layer over a soft soil deposit whose characteristics may be significant and should be carefully considered when designing long span bridges with high piers. The method of analysis adopted in the paper is to decompose the problem into an interior region and an exterior region. In the exterior region, the scattered wave fields are constructed with the linear combinations of two independent sets of Lamb's singular solutions, i. e., the integral solutions for two concentrated surface loads in two directions; and their derivatives are used to represent the scattered wave fields. A technique is proposed to calculate the integrals in the wave-number domain based on the method of steepest descent. For the interior region, the wave fields for the fluid layer and soft soil deposit are expressed in terms of wave functions which satisfy the equation of motion. The continuity condition at the interface of the media is satisfied in the least square sense. The effects of geometric topography, soil amplification and fluid layer subject to different types of incident harmonic plane waves are analyzed and discussed.