Three-dimensional limit equilibrium method for rock slopes by constructing normal stress distribution over sliding surface and its application
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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。
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关键词:
- 岩质边坡 /
- 三维稳定性 /
- 极限平衡 /
- 稳定性系数 /
- Hoek-Brown强度准则 /
- 逐点等效Mohr-Coulomb强度
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. -
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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+S⋅Sx)dxdy D2 ∬−Syσ0xdxdy A′14 ∬−(c+σ0tanφ)ΔΔ′dxdy A′31 ∬(xSx−S)ΔΔ′tanφσ0dxdy D3 ∬−Syσ0ydxdy A21 ∬σ0dxdy A32 ∬σ0(x+S⋅Sx)xdxdy D4 ∬Syσ0dxdy A′21 ∬SxΔΔ′tanφσ0dxdy A′32 ∬(xSx−S)ΔΔ′tanφσ0xdxdy A11 ∬−Sxσ0dxdy A22 ∬σ0xdxdy A33 ∬σ0(x+S⋅Sx)ydxdy A′11 ∬ΔΔ′tanφσ0dxdy A′22 ∬SxΔΔ′tanφσ0xdxdy A′33 ∬(xSx−S)ΔΔ′tanφσ0ydxdy A12 ∬−Sxσ0xdxdy A23 ∬σ0ydxdy A34 M−∬σ0(x+S⋅Sx)dxdy A′12 ∬ΔΔ′tanφσ0xdxdy A′23 ∬SxΔΔ′tanφσ0ydxdy A′34 ∬−(c+σ0tanφ)(xSx−S)ΔΔ′dxdy A13 ∬−Sxσ0ydxdy A24 W−∬σ0dxdy A′13 ∬ΔΔ′tanφσ0ydxdy A′24 ∬−(c+σ0tanφ)SxΔΔ′dxdy 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 表 3 算例1稳定性系数计算结果
Table 3 Calculated results of stability coefficient of example 1
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 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 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 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 表 8 算例4稳定性系数计算结果
Table 8 Calculated results of stability coefficient of example 4
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 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 -
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