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基于构造滑面正应力分布的岩质边坡三维极限平衡法与应用

卢坤林, 梅一帆, 王林飞, 贾森林, 秦涛, 朱大勇

卢坤林, 梅一帆, 王林飞, 贾森林, 秦涛, 朱大勇. 基于构造滑面正应力分布的岩质边坡三维极限平衡法与应用[J]. 岩土工程学报, 2024, 46(11): 2265-2274. DOI: 10.11779/CJGE20230753
引用本文: 卢坤林, 梅一帆, 王林飞, 贾森林, 秦涛, 朱大勇. 基于构造滑面正应力分布的岩质边坡三维极限平衡法与应用[J]. 岩土工程学报, 2024, 46(11): 2265-2274. DOI: 10.11779/CJGE20230753
LU Kunlin, MEI Yifan, WANG Linfei, JIA Senlin, QIN Tao, ZHU Dayong. Three-dimensional limit equilibrium method for rock slopes by constructing normal stress distribution over sliding surface and its application[J]. Chinese Journal of Geotechnical Engineering, 2024, 46(11): 2265-2274. DOI: 10.11779/CJGE20230753
Citation: LU Kunlin, MEI Yifan, WANG Linfei, JIA Senlin, QIN Tao, ZHU Dayong. Three-dimensional limit equilibrium method for rock slopes by constructing normal stress distribution over sliding surface and its application[J]. Chinese Journal of Geotechnical Engineering, 2024, 46(11): 2265-2274. DOI: 10.11779/CJGE20230753

基于构造滑面正应力分布的岩质边坡三维极限平衡法与应用  English Version

基金项目: 

国家自然科学基金项目 52079121

安徽省自然科学基金项目 2208085ME149

详细信息
    作者简介:

    卢坤林(1980—),男,安徽庐江人,副教授,主要从事岩土工程方面的研究工作。E-mail: lukunlin@hfut.edu.cn

  • 中图分类号: TU457

Three-dimensional limit equilibrium method for rock slopes by constructing normal stress distribution over sliding surface and its application

  • 摘要: 开展岩质边坡三维稳定性分析方法研究具有重要的理论意义和工程应用前景。常规的等效Mohr-Coulomb强度参数来分析岩质边坡的稳定性,不能准确反映岩体材料强度包线呈非线性分布的特征,计算结果偏于保守。建议了一种逐点等效Mohr-Coulomb强度参数替代常规的等效Mohr-Coulomb强度参数,通过构造滑面上的正应力分布,滑面上各点的等效黏聚力和等效内摩擦角则随着滑面正应力分布而逐点变化。在此基础上,将逐点等效Mohr-Coulomb强度参数方法和基于滑面正应力修正的极限平衡法相结合,提出了一种基于构造滑面正应力分布的岩质边坡三维稳定性分析方法。算例表明该方法计算结果与已有方法相印证,适用于任意空间滑面形态。与常规等效Mohr-Coulomb强度参数相比,该方法得到稳定性系数显著偏低。进一步将该方法应用于某露天矿边坡的整体稳定性评价,效果理想,并被工程单位所采纳。该方法结果可靠,计算过程简单且易于编程,可为岩质边坡工程稳定性评价提供理论参考。
    Abstract: The researches on the three-dimensional stability of rock slopes are of important theoretical significance and engineering application prospect. The conventional equivalent Mohr-Coulomb strength parameters used to analyze the stability of rock slopes cannot accurately reflect the nonlinear distribution of strength envelope of rock mass, resulting in conservative results. A point-by-point equivalent Mohr-Coulomb strength parameter is proposed to replace the conventional equivalent Mohr-Coulomb strength parameters. By constructing the normal stress distribution over the sliding surface, the equivalent cohesion and internal friction angle of the sliding surface change point-by-point with the normal stress distribution over the sliding surface. On this basis, a three-dimensional stability analysis method for rock slopes is proposed by combining the point-by-point equivalent Mohr-Coulomb strength parameter and the limit equilibrium method based on constructing the normal stress distribution over the sliding surface. Some examples show that the proposed method is correct and suitable for any spatial sliding surface shape. Compared with the conventional equivalent Mohr-Coulomb strength parameters, the stability coefficient obtained by the proposed method is lower. The method has successfully applied to a practical project and achieved good results. The results are reliable, and the calculation process is simple and easy to program, which can provide a theoretical reference for the stability evaluation of rock slope engineering.
  • 图  1   H-B逐点等效M-C等效方式示意

    Figure  1.   Schematic of H-B strength parameters by point-by-point equivalent M-C strength parameter

    图  2   3D滑面及条柱受力

    Figure  2.   3D slip surface and forces acting on a column

    图  3   稳定性系数计算流程图

    Figure  3.   Flow chart of calculation of stability coefficient

    图  4   算例1计算模型

    Figure  4.   Computational model for example 1

    图  5   算例2计算模型

    Figure  5.   Computational model for example 2

    图  6   迭代过程图

    Figure  6.   Diagram of iterative process

    图  7   构造滑面正应力分布

    Figure  7.   Distribution of constructed normal stress of sliding surface

    图  8   逐点等效黏聚力分布

    Figure  8.   Distribution of point-by-point equivalent cohesion

    图  9   逐点等效内摩擦角分布

    Figure  9.   Distribution of point-by-point equivalent internal friction angle

    图  10   算例3计算模型

    Figure  10.   Computational model for example 3

    图  11   算例4计算模型(n=5)

    Figure  11.   Computational model for example 4(n=5)

    图  12   不同正应力分布对应的稳定性系数

    Figure  12.   Stability coefficient corresponding to different normal stress distributions

    图  13   不稳定坡体区域全貌

    Figure  13.   Overall view of slope

    图  14   三维边坡计算模型

    Figure  14.   Computational model for three-dimensional slope

    图  15   迭代过程图

    Figure  15.   Diagram of iterative process

    图  16   滑面正应力分布

    Figure  16.   Distribution of normal stress of sliding surface

    图  17   逐点等效黏聚力分布

    Figure  17.   Distribution of point-by-point equivalent cohesion

    图  18   逐点等效内摩擦角分布

    Figure  18.   Distribution of point-by-point equivalent internal friction angel

    表  1   符号对应具体表达式

    Table  1   Symbols corresponding to specific expressions

    简写符号 表达式 简写符号 表达式 简写符号 表达式
    D1 Syσ0dxdy A14 Sxσ0dxdy A31 σ0(x+SSx)dxdy
    D2 Syσ0xdxdy A14 (c+σ0tanφ)ΔΔdxdy A31 (xSxS)ΔΔtanφσ0dxdy
    D3 Syσ0ydxdy A21 σ0dxdy A32 σ0(x+SSx)xdxdy
    D4 Syσ0dxdy A21 SxΔΔtanφσ0dxdy A32 (xSxS)ΔΔtanφσ0xdxdy
    A11 Sxσ0dxdy A22 σ0xdxdy A33 σ0(x+SSx)ydxdy
    A11 ΔΔtanφσ0dxdy A22 SxΔΔtanφσ0xdxdy A33 (xSxS)ΔΔtanφσ0ydxdy
    A12 Sxσ0xdxdy A23 σ0ydxdy A34 Mσ0(x+SSx)dxdy
    A12 ΔΔtanφσ0xdxdy A23 SxΔΔtanφσ0ydxdy A34 (c+σ0tanφ)(xSxS)ΔΔdxdy
    A13 Sxσ0ydxdy A24 Wσ0dxdy
    A13 ΔΔtanφσ0ydxdy A24 (c+σ0tanφ)SxΔΔdxdy
    下载: 导出CSV

    表  2   岩体参数

    Table  2   Material parameters of rock mass

    参数 滑面ABC 滑面ABD
    重度γ/(kN·m-3) 25.0 25.0
    单轴抗压强度σci/MPa 0.818 0.682
    完整岩石材料参数mi 20 15
    地质强度指标GSI 100 75
    扰动因子D 0 0
    mb 20 6.142
    s 1 6.22×10-2
    a 0.5 0.501
    下载: 导出CSV

    表  3   算例1稳定性系数计算结果

    Table  3   Calculated results of stability coefficient of example 1

    计算方法 计算结果 误差/%
    逐点等效M-C(本文方法) 3.562
    广义H-B(Deng[20] 3.593 0.86
    等效M-C(Deng[20] 4.657 23.51
    下载: 导出CSV

    表  4   岩体参数及H-B计算参数

    Table  4   Parameters of rock mass and Hoek-Brown criterion

    参数 取值
    重度γ/(kN·m-3) 25.0
    单轴抗压强度σci/MPa 0.4
    完整岩石材料参数mi 8
    地质强度指标GSI 60
    扰动因子D 0
    mb 1.917
    s 1.17×10-2
    a 0.503
    σtm/kPa 2.44
    A 0.5630
    B 0.6933
    下载: 导出CSV

    表  5   算例2稳定性系数计算结果

    Table  5   Calculated results of stability coefficient of example 2

    计算方法 计算结果 误差/%
    逐点等效M-C(本文方法) 1.614
    常规等效M-C(卢坤林等[8]) 1.913 15.63
    常规等效M-C(三维楔形体法) 1.921 15.98
    下载: 导出CSV

    表  6   算例3稳定性系数计算结果

    Table  6   Calculated results of stability coefficient of example 3

    计算方法 计算结果 误差/%
    逐点等效M-C(本文方法) 2.547
    常规等效M-C(朱大勇等[3] 2.922 12.83
    下载: 导出CSV

    表  7   岩体参数

    Table  7   Material parameters of rock mass

    参数 取值
    重度γ/(kN·m-3) 23.0
    单轴抗压强度σci/MPa 0.081
    完整岩石材料参数mi 15
    地质强度指标GSI 70
    扰动因子D 0
    mb 5.138
    s 3.57×10-2
    a 0.501
    σtm/kPa 0.842
    A 0.7771
    B 0.7101
    下载: 导出CSV

    表  8   算例4稳定性系数计算结果

    Table  8   Calculated results of stability coefficient of example 4

    n 逐点等效M-C(本文) 常规等效M-C(朱大勇等[3] 二维(Li等[21] 误差/%
    1 1.100 1.210 9.15
    2 1.079 1.179 8.46
    5 1.073 1.170 8.27
    10 1.072 1.168 8.23
    20 1.072 1.168 8.22
    1.002
    下载: 导出CSV

    表  9   岩体参数

    Table  9   Material parameters of rock mass

    参数 取值
    重度γ/(kN·m-3) 28.0
    单轴抗压强度σci /MPa 10
    完整岩石材料参数mi 6
    地质强度指标GSI 26
    扰动因子D 0.8
    mb 0.0733
    s 1.4×10-5
    a 0.529
    下载: 导出CSV

    表  10   不稳定坡体稳定性系数计算结果

    Table  10   Calculated results of stability coefficient of landslide area

    计算方法 计算结果 误差/%
    逐点等效M-C(本文方法) 0.942
    常规等效M-C(朱大勇等[3] 1.154 18.37
    下载: 导出CSV
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出版历程
  • 收稿日期:  2023-08-06
  • 网络出版日期:  2024-03-24
  • 刊出日期:  2024-10-31

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