Vertical and torsional vibrations of a rigid circular disc on a transversely isotropic and layered half-space with imperfect interfaces

Rigid disc vibration over a layered half-space is essential to understand soil-structure interaction (SSI) between a foundation and the structure over it. In this article, we present a novel semi-analytical and very efficient method to calculate the SSI coefficients on the layered foundation due to both vertical and torsional vibrations. The material properties in each layer are transversely isotropic to take care of the possible different Young's moduli in different directions (vertical vs. horizontal). Furthermore, the interface between the layers is assumed to be general so that possible loose bonding between the layers (where the displacements and/or tractions are discontinuous across the interface) can be considered. The semi-analytical solution is based on the recently developed forward solution of the layered structure with imperfect interface under time-harmonic loadings within the circle on the surface. Since the present SSI problem is a mixed boundary-value problem, the method of superposition in terms of the powerful cylindrical system of vector functions combining with the integral least-square approach is proposed. To take care of multiple layers, the dual variable and position (DVP) is further introduced. The cylindrical system of vector functions has the advantage of separating the torsional vibration from the vertical vibration and yet expressing the two types of solutions uniformly. After validating the proposed semi-analytical method, numerical examples are presented to demonstrate the effect of material layering, interface imperfection, elastic anisotropy, and input frequency on the SSI coefficients, and on the surface displacement and stress variation. These new results should be also good benchmarks for future numerical methods.