应力场柱网离散法三维边坡稳定性控制分析研究

doi:10.13722/j.cnki.jrme.2021.0183

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摘要为更好地将数值方法应用于边坡稳定性计算，提出一种基于应力场柱网离散式三维边坡稳定性控制分析方法。在完成三维边坡数值计算的基础上，将三维边坡的长、宽和高所围成的最小立方体划分为m×n×k个立方体网格，并使平面位置相同的方格沿高度方向串联成m×n个条柱，构建出三维边坡条柱网格和数值计算单元网格并存的空间坐标体系。首先，通过搜索任意第i个立方网格中心点对应的数值计算单元，实现了数值应力场网格化离散；其次，提出了基于滑面上下滑方向剪应力的安全系数表达式，推导了柱网内任意滑移面上下滑方向矢量的求解方法，并建立方格网内最小安全系数的计算模型；再次，提出了基于安全系数与变形组合控制的滑移面搜索条件和搜索模式，通过搜索最符合控制条件的潜在滑移网格，得到了三维边坡空间滑移面；最后，通过典型算例，验证了该方法的可行性、合理性及优越性，并分析了空间效应对三维边坡安全系数和变形的影响，得到了可控条件下安全系数与位移相关曲线。研究结论对复杂工况下三维边坡稳定性及安全控制的数值计算研究具有重要的科学意义和应用价值。

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	李忠1
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	倪嘉卿1
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关键词 ：边坡工程, 三维边坡, 应力场, 空间滑移面, 下滑矢量, 安全系数, 稳定性控制

Abstract：In order to better apply the numerical methods to the slope stability calculation，a 3D slope stability control analysis method based on the column grid discretization of stress fields is proposed. After the numerical calculation of a three-dimensional slope is completed，the minimum cube surrounded by the length，width and height of the three-dimensional slope is divided into m×n×k cube grids，then those cube grids at the same plane position are connected in series along the height direction to form m×n column grids. In this way，a three-dimensional coordinate system is constructed，which includes both the three-dimensional grid of slope columns and the grid of numerical calculation units. Firstly，by searching the numerical element corresponding to the center point of any i cubic grid，the numerical stress field is discretized into grids. Secondly，the expression of the safety factor based on the shear stress in the sliding direction of the sliding surface is proposed，the solution method of the vector of the sliding direction of any sliding surface in the column grid is derived，and the calculation model of the minimum safety factor in the grid is established. Thirdly，the search condition and search mode of the slip surface based on the combined control of the safety factor and the deformation are proposed，and the 3D slope spatial slip surface is obtained by searching the potential slip grid that best meets the control condition. Finally，the feasibility，rationality and superiority of this method are verified by typical examples，the influence of the spatial effect on the safety factor and the deformation of a three-dimensional slope is analyzed，and a correlation curve between the safety factor and the displacement under controllable conditions is proposed. The research results have important scientific significance and application value for the numerical calculation of 3D slope stability and safety control under complex conditions.

Key words： slope engineering 3D slope stress state spatial slip surface slip direction vector safety factor stability control

引用本文:

李忠1，2，倪嘉卿1，孟唱1. 应力场柱网离散法三维边坡稳定性控制分析研究[J]. 岩石力学与工程学报, 2021, 40(10): 2062-2082.
LI Zhong1，2，NI Jiaqing1，MENG Chang1. Research on stability control of 3D slopes based on column grid discretization of stress fields. , 2021, 40(10): 2062-2082.

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http://rockmech.whrsm.ac.cn/CN/10.13722/j.cnki.jrme.2021.0183 或 http://rockmech.whrsm.ac.cn/CN/Y2021/V40/I10/2062

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