Rocking vibrations of rigid cylindrical foundations embedded in saturated soil

Based on the Biot’s poroelastodynamic theory, rocking vibrations of rigid cylindrical foundations embedded in saturated soil subjected to time-harmonic excitation are studied by analytical methods. The soil underlying the foundation base is represented by a saturated half-space while the soil along the side of the foundation is modeled as an independent stratum composed of a series of infinitesimally thin poroelastic layers. The contact surface between the foundation and the soil is assumed to be perfect and fully permeable. General solutions of governing equations for saturated soils are obtained by using the Hankel transform. Based on the mixed boundary value conditions at the contact surface, the rocking integral equations are established by which the dynamic interaction problem is solved. Analytical solutions for the equivalent dynamic impedance of the rigid cylindrical foundation embedded in saturated soil are presented. The accuracy of the present solution is verified by comparisons with exciting solutions of dynamic compliance coefficients for surface foundations. Numerical results indicate that the dynamic response of foundations in a saturated medium is substantially different from that in an ideal elastic medium. The dimensionless frequency of the excitation, the depth ratio of foundation, the permeability coefficient and the Possion’s ratio have significant effects on the rocking dynamic impedance in saturated soil.