基于能量法的轴横向荷载作用下单桩受力变形分析

轴向和横向荷载作用下单桩的受力变形分析是桩基研究的重点内容之一。单桩在水平荷载作用下会产生一定的水平位移与弯矩，而此时作用轴向荷载会使得桩体出现一定的压曲与附加弯矩，以致轴横向荷载作用下的单桩受力变形与单独作用水平荷载或轴向荷载的单桩存在较大的区别。故本文基于能量法，首先分别建立轴横向荷载作用下单桩的受力变形能量方程以及桩周土体能量方程，然后考虑桩土变形协调与一定的桩土相互作用，基于最小势能原理得到单桩变形控制微分方程，并采用幂级数法进行求解，最终得到轴横向荷载作用下单桩受力变形分析的幂级数解答。通过编程计算，将本文方法计算结果与试验结果、数值分析结果、规范法计算结果进行对比分析，验证了本文方法的合理性和可行性。在此基础上，基于本文解答进行了影响参数分析，结果表明:桩体长径比、桩土弹性模量比、桩周土模量深度变化系数均对轴横向受荷单桩的桩身水平位移与最大弯矩值有一定的影响，其中桩周土模量深度变化系数以不小于0.6为宜。

Deformation analysis of pile under combined axial and lateral loads by using the energy method

An analysis of deformation and inner force of pile under combined axial and lateral loads is one of the most important aspects for pile foundation. Under the action of lateral load, the single pile will produce certain lateral displacement and bending moment, at this time, the axial load will make the pile appear certain buckling and additional bending moment. The deformation of a single pile under the action of combined axial and lateral loads is different from that under the action of the lateral load or axial load. By using the energy method, this study firstly deduces the energy equations for the pile under combined axial and lateral loads and the surrounding soils, respectively. Combining with deformation compatibility and certain interaction for the pile-soil, the governing differential equation of pile deformation is obtained based on the principle of the minimum potential energy. A power series method is employed to solve the equation, and the power series solutions for the deformation and inner force of pile under the axial and lateral loads is finally obtained. To validate the presented solutions in this study, the results from current solutions are compared with the test results, numerical results, and the calculation results from the code method, showing a good agreement with the existed methods. The influence parameters are discussed. The results indicate that the ratio of length to pile diameter, the ratio of elastic modulus of pile to soil and the coefficient of modulus of soil around pile all have certain influence on the lateral displacement and the maximum bending moment of pile under the axial and lateral loads. It is found that the coefficient of modulus of soil around pile should be no less than 0.6.