In this paper, numerical limit analysis is applied to evaluate the bearing capacity of a single rigid pile embedded in a ponderable homogeneous cohesive‐frictionless soil subjected to vertical, horizontal, and moment (VHM) loading combinations. All loads act in the same plane. Accurate lower and upper bounds are calculated using finite element limit analysis code ${\text{OPTUM}}^{\text{G3}}$. As the gap between the bounds hardly exceeds $5\%$, the average limit load provides a good estimate of the exact ultimate load and can be used with confidence for design purposes. By adopting typical values for the dimensionless pile length‐to‐diameter ratio, most cases of practical interest are treated. The numerical results are compared against failure surfaces predicted by theories from the literature. Comparison shows that previously developed methods can be conservative or slightly overestimates the limit loads. New design charts are provided. The safe loads domain is constructed in the VHM space using the average limit load. Closed‐form expressions are proposed to describe the native and the normalized VMH failure envelope as a function of the pile length‐to‐diameter ratio. In the VH plane, the failure surface is described by an eccentric superellipse, whereas in the MH plane, the limit curve is an inclined ellipse.

中文翻译：

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基于有限元极限分析的黏土中刚性桩的3D破坏包络

在本文中，数值极限分析被用于评估单个刚性桩在垂直，水平和弯矩（VHM）荷载组合下埋入可沉陷的均质粘性无摩擦土中的承载力。所有负载都在同一平面上作用。使用有限元限制分析代码计算出准确的上下限${\text{OPTUM}}^{\text{G3}}$。由于界限之间的距离几乎不会超过$5％$，平均极限载荷可以准确估算出最终极限载荷，并且可以放心地用于设计目的。通过采用无因次桩长与直径之比的典型值，可以处理大多数有实际意义的情况。将数值结果与文献中理论预测的破坏面进行比较。比较表明，以前开发的方法可能比较保守，也可能高估了极限载荷。提供了新的设计图。使用平均极限载荷在VHM空间中构造安全载荷域。提出了封闭形式的表达式来描述固有的和规范化的VMH破坏包络随桩长与直径之比的函数。在VH中在平面上，破坏面用偏心超椭圆形表示，而在MH平面上，极限曲线是倾斜的椭圆形。