SIMPLIFIED SOLUTION FOR VERTICAL VIBRATION OF AN END BEARING PILE EMBEDDED IN UNSATURATED SOIL

Based on one-phase flow consolidation theory and Bishop’s effective stress principle, the dynamic response of an end bearing pile embedded in unsaturated soil and subjected to a vertical load is theoretically investigated. The simplified dynamic equilibrium equation of the unsaturated soil is established at first. Then, Laplace transform and potential functions are introduced to decouple the governing equation of the unsaturated soil. By virtue of the differential operator splitting and variable separation methods, the soil vibration displacement solution with an undetermined constant is obtained. Combined with the boundary and continuity conditions of the pile-soil system, the dynamic response at the pile top is derived in a closed form. Finally, the influences of major parameters on velocity admittance at the pile top and the velocity response in time domain are analyzed. It is shown that the influences of slenderness ratio of the pile and the pile-soil modulus ratio are remarkable but that the influence of reduction coefficient of the suction is negligible.