| 边坡稳定分析刚体有限元上限法的锥规划模型 |
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| 引用本文： | 刘锋涛,张绍发,戴北冰,张澄博,林凯荣.边坡稳定分析刚体有限元上限法的锥规划模型[J].岩土力学,2019,40(10):4084-4091. |
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| 作者姓名： | 刘锋涛 张绍发 戴北冰 张澄博 林凯荣 |
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| 作者单位： | 1. 中山大学 地球科学与工程学院 广东省地球动力作用与地质灾害重点实验室，广东 广州 510275；
2. 中山大学 土木工程学院，广东 广州 510275 |
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| 基金项目： | 国家自然科学基金(No. 51209237，No.51779279)；广州市科技计划项目(No. 201707010082)；中央高校基本科研业务费(No. 18lgp16)。 |
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| 摘 要： | 极限分析方法是土边坡稳定性分析的重要方法之一。刚体有限元上限法是其中的一类，此类方法仍旧存在一些关键问题需要完善。由于单元的刚性假设，系统的塑性变形内能耗散仅发生在单元间的界面上，故此类方法的性能主要取决于界面的布局，即采用非结构化三角形单元计算往往精度较差。为此，提出了基于滑动面摄动的刚体有限元上限法及临界滑动面的搜索方法。首先，在考虑刚体转动的基础上构造刚体有限元上限法的二阶锥规划模型，用于确定在给定试滑动面条件下的运动许可速度场。其次，将试滑动面的控制参数视为决策变量，建立搜索临界滑动面的非线性非凸优化问题模型，并采用非线性单纯形方法和粒子群方法求解此优化问题找出临界滑动面。通过经典边坡稳定问题的分析求解，验证了所提出的新方法，进一步证实了网格类型（即界面的布局）是影响刚体有限元上限法计算精度的主要因素。经过计算结果的对比发现，在刚体有限元上限法中考虑刚体转动是非常必要的，不仅可以提高刚体有限元上限法的计算精度，还可以克服此方法对界面布局的依赖性。
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| 关 键 词： | 边坡稳定 刚体有限元上限法 二阶锥规划 临界滑动面 |
| 收稿时间： | 2019-01-28 |
Upper bound limit analysis of soil slopes based on rigid finite element method and second-order cone programming |
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| LIU Feng-tao,ZHANG Shao-fa,DAI Bei-bing,ZHANG Cheng-bo,LIN Kai-rong.Upper bound limit analysis of soil slopes based on rigid finite element method and second-order cone programming[J].Rock and Soil Mechanics,2019,40(10):4084-4091. |
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| Authors: | LIU Feng-tao ZHANG Shao-fa DAI Bei-bing ZHANG Cheng-bo LIN Kai-rong |
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| Institution: | 1. Guangdong Provincial Key Lab of Geodynamics and Geohazards, School of Geoscience and Engineering, Sun Yat-Sen University, Guangzhou, Guangdong 510275, China; 2. School of Civil Engineering, Sun Yat-Sen University, Guangzhou, Guangdong 510275, China |
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| Abstract: | The upper bound approach based on rigid finite element method (RFEM) is one of the limit analysis methods, and it is an important method for stability analysis of soil slopes. However, there are still some key problems to be overcome in this method. Due to the assumption of rigidity, the plastic deformation energy of the system is stored only at the interfaces of all elements. Therefore, the accuracy of the approach is highly dependent on the alignment of the interfaces, which indicates that the accuracy is poor if an unstructured mesh is employed. To overcome this limitation, we propose a novel RFEM-based upper bound approach using perturbation method, according to the sequential limit analysis. Firstly, considering the rotation of elements, a novel second-order cone programming (SOCP) is put forward to construct the kinematically admissible velocity field based on RFEM. Secondly, a model for searching the critical slip surface is built by using sequential SOCP of RFEM-based upper bound approach and then solved by the nonlinear simplex and particle swarm optimization algorithm. From the analysis on stability problems of two benchmark soil slopes, the proposed method is verified. The main influence factors on computational efficiency and accuracy are also investigated in this paper. We have found that the type of mesh is a significant factor affecting the accuracy of the proposed method. It is necessary to consider the rotation of element in RFEM-based upper bound approach, which can not only improve the accuracy of the approach but also overcome the dependence of RFEM-based upper bound limit analysis on the alignment of interfaces. |
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| Keywords: | slope stability RFEM-based upper bound limit analysis second-order cone programming critical slip surface |
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