To elucidate whether an irregular topography affects the seismic response of nearby structures, an analytical solution to the dynamic interaction between a symmetric V-shaped canyon and an adjacent building under the incidence of SH waves is proposed by using the wave function expansion method. The dynamic canyon-soil-structure interaction is decomposed into two problems of scattering and radiation. The building is idealized as a shear wall supported by a semicircular rigid foundation. The analytical solution can be degenerated theoretically to the canonical model of a shear wall embedded in a half-space for either a zero depth-to-width ratio of the canyon or an infinite canyon-building distance. Through a numerical comparison with two past exact solutions to the sole shear wall model as well as the sole V-shaped canyon model, the correctness of the method in this paper is verified. A systematic parametrical analysis in both frequency and time domains is performed. It is found that the seismic response of the building may be amplified when it is on the wave-facing side of the canyon. The degree of amplification is closely related to the size and depth-to-width ratio of canyon, the wave velocity of half-space, and the incident angle and frequency content of seismic waves. The potential adverse effects of the V-shaped canyon on the ground motion input of adjacent buildings should be considered in the seismic design.

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.