Vertical Vibration of a Rigid Cylindrical Foundation Embedded in a Half-Space of Unsaturated Poroelastic Soil

This work presents an analytical method for determining vertical dynamic impedance and displacement response factor of a rigid cylindrical foundation embedded in unsaturated poroelastic soils. The foundation is assumed to be perfectly boned to its surrounding soil and its overlying half-space of unsaturated poroelastic soil, subjected to harmonic vertical loadings. The soil surrounding the circumference of the cylinder is modeled as a number of infinitely thin horizontal soil layers. Based on the Biot-type soil constitutive model, the equations governing the interaction of unsaturated soils with the cylindrical foundation are derived. Solutions are obtained by solving ordinary differential equations transformed from partial differential governing equations using the Hankel transform. The proposed solutions are verified against existing solutions of benchmark elastodynamic problems for embedded cylindrical foundations in dry and saturated soils. Using the derived solutions, several influencing parameters defining the stiffness and mass of the foundation system are examined to investigate the dynamics of the foundation interacting with it adjacent soils. It is concluded that the dynamic displacement response factor is sensitive to soil saturation. It is believed that the proposed solution should be beneficial to dynamic design with cylindrical foundations embedded in unsaturated soils.