Canadian Geotechnical Journal, Ahead of Print.
The traditional method for analysis and design of laterally loaded piles with non-circular cross-sections such as rectangular, H-shaped, and X-shaped piles involves the simplification of converting the non-circular pile to a circular pile with equivalent second moment of inertia. A rigorous semi-analytical method is developed for calculating the response for laterally loaded piles with arbitrary non-circular cross-sections in multi-layered elastic soil without using any simplification regarding the shape of the pile cross-section. The governing differential equations for the pile–soil system are obtained using the principle of virtual work. The soil displacements around the pile are described as products of separable functions that are compatible with horizontal pile movement. As a result, the three-dimensional (3 D) boundary value problem (BVP) is described by a fourth-order linear ordinary differential equation (ODE) governing horizontal pile displacement and second-order partial differential equations (PDEs) governing soil displacements. New solution techniques for the ODE and PDEs are proposed, and the accuracy of the present method is verified by comparing the predicted pile and soil responses with the corresponding results of equivalent 3 D finite element method. The effects of pile cross-section shape and lateral loading direction on the pile and soil responses are highlighted through a series of parametric analyses.

中文翻译：

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弹性土中横向受力非圆形桩的半解析解

加拿大岩土工程杂志，印刷前。
传统的矩形、H形、X形等非圆形截面水平荷载桩的分析和设计方法是将非圆形桩简化为等效二阶矩为的圆形桩。惯性。开发了一种严格的半解析方法，用于计算多层弹性土中任意非圆形横截面的侧向加载桩的响应，而不使用有关桩横截面形状的任何简化。利用虚功原理得到了桩-土系统的控制微分方程。桩周围的土壤位移被描述为与水平桩运动兼容的可分离函数的产物。因此，三维 (3 D) 边值问题 (BVP) 通过控制水平桩位移的四阶线性常微分方程 (ODE) 和控制土体位移的二阶偏微分方程 (PDE) 来描述。提出了 ODE 和 PDE 的新求解技术，并通过将预测的桩和土响应与等效 3D 有限元方法的相应结果进行比较来验证本方法的准确性。通过一系列参数分析，强调了桩截面形状和横向荷载方向对桩和土响应的影响。