考虑竖向荷载的桩基水平振动响应解析解*
- 摘 要
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(1 河海大学土木与交通学院， 南京 210098； 2 重庆大学土木工程学院， 重庆 400045)
［摘要］针对粘弹性土中桩土水平耦合振动问题，考虑土体竖向应力梯度变化以及竖向荷载二阶效应的影响，通过微分变换及分离变量法解耦土体波动方程，求得桩周土体位移和应力解析表达式，结合桩土耦合连续性条件，推导出桩身位移、内力解析表达式，讨论了竖向荷载及桩土模量比对桩身位移、内力的影响。研究结果表明，竖向荷载超过某一临界值时，会使桩基位移和内力发生重分布，桩身最大位移和剪力由桩顶向桩底转移；桩土模量比对桩身位移和内力具有明显影响，位移和内力随桩土模量比的变化而变化，具体变化趋势与深度有关。［关键词］竖向荷载; 水平振动; 三维波动效应; 解析解; 粘弹性地基中图分类号：TU473.1 文献标识码：A 文章编号：1002-848X(2015)19-0080-07
Analytical solution of lateral vibration response of an axial loaded pileLuan Lubao 1, Ding Xuanming2, Zhou Shili 1, Zhu Zhensheng 1(1 College of Civil and Transportation Engineering, Hohai University, Nanjing 210098, China; 2 College of Civil Engineering, Chongqing University, Chongqing 400045, China)Abstract: In view of the lateral coupled vibration problem of the pile and soil in visco-elastic soil, considering the influences of vertical stress gradient changeand second-order effect of axial load, the analytic expressions of displacement and stress of the soil around the pile were obtained by differential transformation and using separation of variable method to solve soil wave equation. Combined with the coupling continuous conditions of the pile and soil, the analytic expressions of displacement and internal force of the piles were derived, and the influences of the vertical load and the pile-soil modulus ratio on the pile displacement and the internal force were discussed. The research results show that when the axial load exceeds a critical value, displacement and the internal force of the pile foundation redistribute, and the maximum pile displacement and shear force transfer from the pile top to the pile bottom. Pile-soil modulus ratio has obvious effect on pile displacement and internal force, while displacement and internal force change with pile-soil modulus ratio and specific change trend relates to depth.Keywords: axial load; lateral vibration; 3D wave effect; analytical solution; visco-elastic foundation
* 国家自然科学基金项目(No.51378177，No.51420105013)。作者简介：栾鲁宝，研究生，Email：luanlub@163.com。
