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Upper bound analysis of ultimate pullout capacity of shallow 3-D circular plate anchors based on nonlinear Mohr-Coulomb failure criterion

非线性Mohr-Coulomb 破坏准则下浅埋三维圆形锚板极限抗拔力上限分析

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Abstract

Based on the nonlinear Mohr-Coulomb failure criterion and the associated flow rules, the three-dimensional (3-D) axisymmetric failure mechanism of shallow horizontal circular plate anchors that are subjected to the ultimate pullout capacity (UPC) is determined. A derivative function of the projection function for projecting the 3-D axisymmetric failure surface on plane is deduced using the variation theory. By using difference principle, the primitive function of failure surface satisfying boundary condition and numerical solution to its corresponding ultimate pullout capacity function are obtained. The influences of nonlinear Mohr-Coulomb parameters on UPC and failure mechanism are studied. The result shows that UPC decreases with dimensionless parameter m and uniaxial tensile strength increases but increases when depth and radius of plate anchor, surface overload, initial cohesion, geomaterial density and friction angle increase. The failure surface is similar to a symmetrical spatial funnel, and its shape is mainly determined by dimensionless parameter m; the surface damage range expands with the increase of radius and depth of the plate anchor as well as initial cohesion but decreases with the increase of dimensionless parameter m and uniaxial tensile strength as well as geomaterial density. As the dimensionless parameter m=2.0, the numerical solution of UPC based on the difference principle is proved to be feasible and effective through the comparison with the exact solution. In addition, the comparison between solutions of UPC computed by variation method and those computed by upper bound method indicate that variation method outperforms upper bound method.

摘要

基于非线性 Mohr-Coulomb 强度准则及相关流动法则, 构建了浅埋水平圆形锚板承受极限抗拔力时上方土体的三维轴对称破坏机制; 利用变分原理, 推导出三维轴对称破坏曲面在平面上投影函数的导函数。 利用差分原理迭代获得了满足边界条件的破坏面原函数及其与之对应的极限抗拔力函数数值解答; 进一步分析了非线性 MC 参数变化对圆形浅埋锚板极限抗拔力和破坏模式的影响规律。 结果表明: 圆形锚板极限抗拔力随无量纲参数m 的增大而减小, 锚板埋深、 锚板半径、 地表超载、 初始粘聚力、 土体重度以及土体摩擦角的增大而增大, 随土体单轴抗拉强度的增大而减小; 圆形锚板上方土体破坏面呈对称的空间漏斗形态, 且其形状主要取决于无量纲参数 m; 地表破坏范围随锚板半径、 锚板埋深、 初始粘聚力的增大而增大, 随土体单轴抗拉强度、 土体重度的增大而减小。 在无量纲参数 m=2.0 时的特殊条件下, 极限抗拔力精确解与数值解对比分析证明了本文基于差分法原理数值解答的可行性和有效性。 同时, 对比分析了变分法与上限法的极限抗拔力计算结果, 表明在极限分析上限法理论框架内, 变分分析方法结果优于上限法结果。

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Authors and Affiliations

  1. School of Civil Engineering, Central South University, Changsha, 410075, China

    Lian-heng Zhao  (赵炼恒), Yi-gao Tan  (谭亦高), Shi-hong Hu  (胡世红), Dong-ping Deng  (邓东平) & Xin-ping Yang  (杨新平)

  2. Key Laboratory of Heavy-haul Railway Engineering Structure of Ministry of Education, Central South University, Changsha, 410075, China

    Lian-heng Zhao  (赵炼恒)

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  1. Lian-heng Zhao  (赵炼恒)
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  2. Yi-gao Tan  (谭亦高)
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Correspondence to Lian-heng Zhao  (赵炼恒) or Dong-ping Deng  (邓东平).

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Foundation item: Project(51478477) supported by the National Natural Science Foundation of China; Project(2016CX012) supported by the Innovation-driven Project of Central South University, China; Project(2014122006) supported by the Guizhou Provincial Department of Transportation Foundation, China

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Zhao, Lh., Tan, Yg., Hu, Sh. et al. Upper bound analysis of ultimate pullout capacity of shallow 3-D circular plate anchors based on nonlinear Mohr-Coulomb failure criterion. J. Cent. South Univ. 25, 2272–2288 (2018). https://doi.org/10.1007/s11771-018-3912-7

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