Vertical vibration of an end bearing pile embedded in saturated soil

Dynamic interaction of pile and soil plays an importantrole in structure design. Although many researches have been carried out onthe field in past two decades, the emphasis is mainly focused on pilevibration in single phase medium. Such a fact has been neglected that soilis multi-phase medium. The effects of ground water on the interaction areseldom discussed.In this paper, vertical vibration of an end bearing pile embedded in asaturated soil layer is theoretically investigated. The pile is assumed tobe vertical and can be dealt with one dimensional elastic theory. The soilis considered as a linear saturated isotropic poroelastic medium andsatisfies rigorous three dimensional poroelasticity. Potential functions areapplied to decouple governing differential equations of the soil layeroriginally presented by Biot. By virtue of differential operator splittingand variable separation method, soil vibration displacement solutions withan undetermined constant are obtained at first. Under the assumption ofperfect contact between the pile and the soil, the pile response to anarbitrary vertical load is analytically derived in a closed form. Thenharmonic complex stiffness and admittance at the pile head are defined infrequency domain. And velocity response in time domain is gained by means ofFourier inverse transform. Based on the solutions, a parametric study isconducted to determine the main features of the soil-pile interaction invertical vibration. As a result, the pile slenderness and the pile-soilmodulus ratio are major on the pile dynamic response, while the seepageforce has minor influence on the response. Finally, it is shown that thetheoretical curves are in good agreement with those obtained from fieldtest.