To investigate the settlement response, load transfer behavior, and geometric effect of noncircular piles, a general three-dimensional (3D) analytical continuum model for axially loaded noncircular pile-multilayered homogeneous soil systems is presented. In the analysis, both the vertical and horizontal soil displacement fields are considered, and the variations of the soil displacement components are described by the three displacement transfer functions along the x, y, and z directions. The governing differential equations of noncircular piles and soil are derived by applying the principle minimum potential energy and variational method to the pile-soil system. A complex variable function conformal mapping technique is introduced to overcome the complex boundary conditions of the transfer functions. Then, the numerical solutions of all the governing differential equations are simultaneously solved following an iterative algorithm. The reliability of this approach is validated by comparing some pile and soil responses with the results from existing analytical solutions or a rigorous finite element analysis. Differences in the settlement response and the axial force distribution between noncircular and circular piles are observed. In addition, the pile shaft resistance along the perimeter of the cross-sections shows that a greater load is required in order to fully mobilize the ultimate resistance of the noncircular piles. We also compare the stress (${\sigma }_1-{\sigma }_3$) contours of some typical noncircular piles with a circular pile, which provides useful insights into the geometric effect.

中文翻译：

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多层弹性土中轴向受力非圆形桩的三维解析连续介质模型

为了研究非圆形桩的沉降响应、荷载传递行为和几何效应，提出了轴向加载非圆形桩-多层均质土系统的一般三维 (3D) 连续分析模型。分析中同时考虑了垂直和水平土壤位移场，土壤位移分量的变化由沿x、y和z的三个位移传递函数来描述方向。将最小势能原理和变分法应用于桩土系统，推导出非圆桩土的控制微分方程。引入了复杂的变量函数保角映射技术来克服传递函数的复杂边界条件。然后，按照迭代算法同时求解所有控制微分方程的数值解。通过将一些桩和土壤响应与现有分析解决方案或严格的有限元分析的结果进行比较，验证了该方法的可靠性。观察到非圆形和圆形桩之间沉降响应和轴力分布的差异。此外，沿横截面周边的桩轴阻力表明，需要更大的载荷才能充分调动非圆形桩的极限阻力。我们还比较了压力（${\sigma }_1-{\sigma }_3$) 一些带有圆形桩的典型非圆形桩的轮廓，这提供了对几何效果的有用见解。