Dynamic Soil-Structure Interaction for a SDOF with Rigid Foundation Embedded in a Radially Inhomogeneous Bearing Stratum Under SH Waves

Dynamic soil-structure interaction will occur when the seismic wave passes through a soil-structure system. It involves the scattering of incident wave by the foundation of superstructure, the transfer of incident wave energy to the superstructure and the radiation of structural vibration energy back into the soil. In this kind of wave process, the local soil stratum condition of the bearing stratum has an important role, especially for those engineering sites with either sedimentation- or load-induced inhomogeneous shear modulus profile. In this study, an analytical model of dynamic interaction between inhomogeneous bearing stratum and superstructure in bedrock half space under plane SH wave is established. The shear modulus of the inhomogeneous bearing stratum is assumed to vary with radius in a power-law manner, and the superstructure adopts the classical single degree of freedom (SDOF) oscillator model. By using a wave function expansion method, an analytical series solution for the foundation displacement and relative displacement of superstructure is derived. The influence of the inhomogeneous bearing stratum on the system response is studied. When the inhomogeneous bearing stratum is more flexible than the bedrock half space, the peak value of foundation displacement is obviously larger than that without considering the inhomogeneous bearing stratum. With the decrease of the stiffness of the superstructure, the peak frequency of the system response shifts to the low frequency.