Dynamical response of vertically loaded pile in half-space of unsaturated porous media

By virtue of the 3D axisymmetric three-phase elastodynamic theory and considering the effect of matric suction on the dynamic shear modulus, the harmonic dynamic response of end-bearing piles embedded in unsaturated poroelastic medium subjected to vertical loading is investigated. The resistance factor and vibration modes of the soil layer are obtained from the direct decoupling of the governing equations by employing the differential operator splitting and variable separation method. On the basis of the assumptions of perfect contact along the pile-soil and the rigid supported type at the pile tip, the wave equation for the pile treated as a bar and described by the conventional 1-D structure vibration theory is then solved. Ultimately, the functions of complex stiffness at the top of the pile together with the soil impedances in the frequency domain are derived, and the selected numerical solutions are presented to portray the influences of principal parameters on the dynamic behaviors of pile. The results show that as the saturation decreases, the dynamic stiffness factor and the equivalent damping both decrease, while the resonance frequencies of the pile-soil system are almost not affected. It is necessary to differentiate the various responses evoked by the moduli of soil and pile during the analysis of pile-soil modulus ratio. The proposed model reveals an entire evolutional process of dynamic response of soil from single-phase media to two phase saturated media, and provides a comprehensive theoretical framework to describe the dynamic behavior of pile under actual soil environment.