Under most engineering conditions, soil disturbance due to pile installation may cause soil properties to vary within the region adjacent to the pile in the radial direction. This paper derives a rigorous solution to investigate the kinematic response of end-bearing piles under the excitation of vertical P-waves considering the construction effect. The displacement responses of piles and soil, governed by the dynamic equilibrium equation, are theoretically derived with the separation of variables method. The scattered waves induced by the pile–soil system, which is the key factor of the problem, are decoupled from the total wavefields. Moreover, the friction occurring at the interface of the soil and pile shaft are directly obtained. Thus, the present solution can accurately account for the pile–soil interaction. Comparisons between the numerical results of the present method and the available results are performed. A detailed discussion on the kinematic response coefficient, amplification factor, and soil motion is provided.

An analytical solution is presented for scattering nonplanar SH waves emanating from a fault source using a lined tunnel. The lined tunnel is assumed to be an annular elastic solid in half-space. A simplified circular arc fault model is employed to represent the wave source. By means of the separation of variables method, all wave fields are given in terms of the wave function series with unknown coefficients. Taking advantage of the method of images, the zero-stress boundary condition on the horizontal ground surface is satisfied automatically. By applying Graf’s addition formula, a system of equations for seeking the unknowns is derived by taking advantage of the boundary conditions. The problem of wave scattering is finally solved after seeking solutions for the system of equations through standard matrix techniques. The effects of fault distance, fault curvature, and fault orientation are revealed with numerical results. It is found that the plane waves provide a good approximation to the fault-induced cylindrical waves when the source-receiver distance or fault radius of curvature is larger enough. Fault-induced topographic effects are strongly affected by source orientation.