Analysis of stability of three-dimensional slopes using the rigorous limit equilibrium method
Analysis of stability of three-dimensional slopes using the rigorous limit equilibrium method
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DOI：
10.1016/j.enggeo.2013.03.027
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发表时间：
2013-06
影响因子：
7.4
通讯作者：
Xiaoping Zhou;H. Cheng
中科院分区：
文献类型：
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作者：
Xiaoping Zhou;H. Cheng
此前，三维边坡或滑坡的稳定性分析采用准严格极限平衡方法，仅满足三向力平衡和一向或二向力矩平衡。本文基于六个平衡条件建立了考虑柱间力的严格极限平衡柱法，包括沿坐标轴的三个方向力平衡条件和绕三个坐标轴的三个方向力矩平衡条件。利用信赖域反射迭代算法确定滑动体宽度与安全系数之间的关系。安全系数的值是使用 Levenberg-Marquardt 最小二乘法获得的。此外，该方法还可用于三维滑坡滑移面的自动搜索，并可利用已知的任意滑移面确定三维滑坡的安全系数。讨论了三个例子来详细验证本方法的鲁棒性和精度。与仅考虑四五个平衡条件的准严格极限平衡方法相比，该方法更加准确和严谨。
Previously, quasi-rigorous limit equilibrium methods were applied to analyze the stability of three-dimensional slopes or landslides, which only satisfy three direction force equilibrium, and one or two direction moment equilibrium. In this paper, the rigorous limit equilibrium column method, in which inter-column forces are taken into account, is established based on six equilibrium conditions which include three direction force equilibrium conditions along coordinate axes and three direction moment equilibrium conditions around three coordinate axes. The relationship between the width of sliding body and factor of safety is determined using trust-region-reflective iterative algorithm. The value of the factor of safety is obtained using Levenberg–Marquardt least square method. Moreover, the present method can be applied to automatically search slip surface of three-dimensional landslides and to determine the factor of safety of three-dimensional landslides with the known arbitrary slip surface. Three examples are discussed to verify the robustness and precision of the present method in detail. Comparing with quasi-rigorous limit equilibrium methods which only considered four or five equilibrium conditions, the present method is more accurate and rigorous.