In this study, the anisotropic nature of the medium is used to simulate the stratigraphic conditions. Taking the embankment of a high-speed railway as the object of study, the wave function expansion method is used to obtain the level solution for inverse plane shear wave scattering of the anisotropic half-space medium-waisted ladder form of the embankment. Then, by changing the anisotropy parameter of the soil medium, the effects of different incidence angles, dimensionless frequencies, embankment slopes, and anisotropic parameters on the isosceles trapezoidal form of the embankment structure are investigated. The results show that the anisotropy of the medium not only has a significant effect on the surface displacement of the embankment site but also makes other parameters more sensitive to the site effect, as manifested by the larger amplitude of the surface displacement caused by the incident wave along a certain angle at a certain dimensionless frequency compared to that of the isotropic medium. The embankment structure plays an important role in vibration damping and isolation during the propagation of vibration waves in the horizontal direction, and this phenomenon becomes less obvious with larger dimensionless frequency.

In this study, the segment joint and ring joint of the lining of the straight-jointed tunnel are simplified as an equivalent open cylindrical shell with a small central angle and an equivalent closed cylindrical shell with a small width, and the lining of the straight-jointed tunnel is thus simplified as an equivalent continuous periodic shell (ECPS) described by the cylindrical shell theory. Since the ECPS lining is periodic along the longitudinal direction, the tunnel-soil system can thus be treated as a periodic system, which is referred to as the periodic tunnel-soil system (PTSS) in this study. Based on the proposed ECPS lining model, an analytical method for the tunnel with the ECPS lining (ECPS tunnel) under seismic waves is established in this study. By employing the periodicity condition for the PTSS as well as the wave function expansion method, the representation for the wave field in the soil is established. With the aforementioned cylindrical shell theory and Fourier series expansion method, the convolution type constitutive relation for the ECPS lining and the Fourier space equations of motion are derived. By using the soil-lining continuity condition and aforementioned formulations for the ECPS lining and soil, the coupled Fourier space equations of motion for the PTSS are established, with which the response of the ECPS lining and scattered waves in the soil can be determined.

To elucidate the effect of canyon topography on dynamic response of a bridge, an analytical model for a simply supported bridge crossing a symmetric or non-symmetric V-shaped canyon in an elastic half-space under SH waves is proposed. An exact solution to the dynamic canyon-bridge interaction problem is derived using wave function expansion and verified by its comparison with past exact solution for a sole bridge model without a canyon. The wave propagation in the half-space, wave scattering by the canyon and wave radiation from the bridge are all taken into account rigorously. Through a systematical parametrical study, it is found that the seismic response of the bridge beam and the wave-facing side foundation will be significantly amplified. The degree of the topographic amplification is closely related to the geometry of the canyon, the mass and the stiffness of the bridge beam, and the frequency content and angle of the incident wave. The potential adverse effects of a V-shaped canyon on a bridge should be considered in its seismic design.