饱和土中考虑竖向荷载的端承桩水平振动响应解析解

Analytical solution for horizontal dynamic response of an end-bearing pile considering axial loads in saturated soil

考虑桩周土三维波动效应变化,将桩基等效为Euler模型,考虑竖向荷载的影响,对饱和地基中端承桩水平振动问题进行了理论研究。引入势函数解耦Biot动力固结方程,通过Laplace变换和分离变量法得到土体应力和位移解析表达式,结合桩土相互作用连续性条件得到桩基位移、内力和桩顶水平动力复阻抗解析表达式。通过算例分析,研究径向孔压分布规律、竖向荷载和长径比对桩基位移和内力的影响,研究结果表明：桩土接触面附近孔压达到峰值;竖向荷载和长径比均会导致桩身位移和内力发生重分布。

The lateral dynamic response of an end axial loaded pile in saturated soil is investigated in this paper. The pile is considered as an Euler Model. Potential functions are introduced to decouple the wave equation of the soil by considering variations of soil stress and strain along depth based on Biot dynamic consolidation theory. Expressions of soil stress and displacement are obtained by Laplace transformation and variable separation method. The lateral displacement and complex impedances of the pile under horizontal vibration are derived based on the continuous conditions between the pile and soil. Numerical analysis studies the distribution law of pore pressures and influences of axial loads and slenderness ratio on displacements and internal forces of pile. The study shows that the soil pore pressure reaches a maximum value near the pile-soil interface; redistributions of pile displacements and internal forces are caused by axial loads and slenderness ratio.