Peak Shear Strength Criterion for Discontinuities with Different Rock Types Based on Revisiting Frictional Angle
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摘要: 异性岩石结构面在三峡库区广泛发育，准确评估其峰值剪切强度对库区岩体稳定性评价至关重要. 采用类岩石材料浇筑若干具有相同形貌、不同壁岩强度组合的异性结构面试块，在0.3~3.0 MPa常法向应力下开展直剪试验，并引入“壁岩强度组合系数λ”来表征岩石抗压强度和基本摩擦角对异性结构面峰值剪切强度的综合影响. 结果表明，异性结构面的峰值剪切强度随λ的增加而呈非线性降低，降低程度主要受粗糙度控制，而与法向应力关系不明显. 采用简单幂函数分析了峰值摩擦角与λ之间的关系，并在此基础上建立含三维形貌参数的异性岩石结构面抗剪强度经验准则. 最后，利用在三峡库区采集的天然样品进一步验证了新准则对天然异性岩石结构面峰值剪切强度评估的可靠性. 新准则可在一定程度上为三峡库区含异性结构面的岩体稳定性评价提供理论依据.Abstract: Discontinuities with different rock types are widely distributed in the Three Gorges reservoir area, and accurately evaluating the peak shear strengths of them is vital for rock mass stability analysis in this reservoir area. A batch of rock-like joint replicas with the same natural morphology but different joint wall strength combinations is prepared, and direct shear tests are conducted on them under constant normal stresses ranging from 0.3 to 3.0 MPa. Further, the joint wall strength combination coefficient (λ) is introduced to capture the combined effect of rock compressive strength and basic angle on the peak shear strength of discontinuities with different rock types. Testing results illustrate that the peak shear strengths of discontinuities with different rock types decrease non⁃linearly with increasing λ, and the decrease degree is mainly controlled by roughness while showing no obvious relationship with normal stress. A simple power law function is selected to analyze the correlation between the peak friction angles and λ, and an empirical strength criterion with the inclusion of three⁃dimensional morphology parameters is developed to predict the peak shear strengths of discontinuities with different rock types. Finally, natural samples collected from the Three Gorges reservoir area are used to further validate the reliability of the new criterion for evaluating the peak shear strength of natural discontinuities with different rock types. To some extent, the new criterion can provide a theoretical basis for the stability evaluation of rock masses containing discontinuities with different rock types in the Three Gorges reservoir area.
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图 1 三峡库区典型异性岩石结构面(亢金涛等, 2019)
Fig. 1. Typical rock discontinuities with different rock types in the Three Gorges reservoir area (Kang et al., 2019)
图 3 典型剪切应力-剪切位移曲线(以B组J⁃Ⅰ/J⁃Ⅴ组合为例)
Fig. 3. Typical shear stress versus shear displacement curves (taking J⁃Ⅰ/J⁃Ⅴ combination in Group B as examples)
图 4 异性结构面峰值剪切强度随λ的变化
a. A组；b. B组；c. C组
Fig. 4. Variation of the peak shear strength of discontinuities with different rock types versus λ
图 5 同性结构面试验剪切强度与Yang公式预测包络线比较
Fig. 5. Comparison between experimental shear strengths and predicted envelopes by Yang's criterion for discontinuities with identical rock type
图 6 异性结构面峰值剪切强度试验值与Yang公式预测值的相关性
Fig. 6. Correlation between experimental peak shear strengths and predicted results by Yang's criterion for discontinuities with different rock types
图 7 异性结构面峰值摩擦角变化
a. A组；b. B组；c. C组
Fig. 7. Variation of peak friction angles of discontinuities with different rock types
图 8 不同法向应力下ξ值随粗糙度参数的变化
Fig. 8. Variation of ξ versus roughness parameters under different normal stresses
图 10 3组试块峰值剪切强度试验值与新公式预测值的对比
a. A组；b. B组；c. C组
Fig. 10. Comparison between experimental peak shear strengths and predicted values by the new criterion for the three groups specimens
图 11 三组试块峰值剪切强度试验值与新公式预测值的相关性
Fig. 11. Correlation between experimental peak shear strengths and predicted values by the new criterion for the three groups of specimens
图 12 天然样品试验剪切强度与新公式预测值的对比
Fig. 12. Comparison between experimental shear strengths of natural samples and predicted values by the new criterion
图 13 天然样品试验剪切强度与新公式预测值的相关性
Fig. 13. Correlation between experimental shear strengths of natural samples and predicted values by the new criterion
图 14 JRC与$ {\theta }_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{*}}/\left(C+1\right) $间的关系
Fig. 14. Correlation between JRC and $ {\theta }_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{*}}/\left(C+1\right) $
图 15 Wu et al. (2018)的试验剪切强度与新公式预测值的对比
Fig. 15. Comparison between experimental shear strengths of Wu et al. (2018) and predicted values by the new criterion
图 16 Wu et al.(2018)的试验剪切强度与新公式预测值的相关性
Fig. 16. Correlation between experimental shear strengths of Wu et al. (2018) and predicted values by the new criterion
表 1 类岩石材料的主要力学参数
Table 1. Main mechanical parameters of rock⁃like materials
材料 水/石膏(质量比) 抗拉强度$ {\sigma }_{\mathrm{t}} $(MPa) 单轴压缩强度$ {\sigma }_{\mathrm{c}} $(MPa) 基本摩擦角$ {\varphi }_{\mathrm{b}} $(°) J-Ⅰ 0.70 0.82 10.3 35.3 J-Ⅱ 0.57 1.49 16.8 35.8 J-Ⅲ 0.45 2.01 27.4 36.5 J-Ⅳ 0.35 2.74 33.9 37.6 J-Ⅴ 0.30 4.33 45.3 38.1 
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表 2 结构面粗糙参数
Table 2. Roughness parameters of discontinuities
组别 $ {A}_{0} $ $ {\theta }_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{*}} $ C $ {\theta }_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{*}}/\left(C+1\right) $ JRC A 0.486 55.4 13.6 3.795 7.2 B 0.502 64.3 9.4 6.183 14.8 C 0.491 75.8 7.3 9.133 18.7
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表 4 天然异性结构面的试验数据
Table 4. Experimental data of natural discontinuities with different rock types
试件编号 岩石类型 三维形貌参数 $ {\sigma }_{\mathrm{n}} $(MPa) 岩石力学参数 剪切强度(MPa) 相对误差 $ {A}_{0} $ $ {\theta }_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{*}} $ C $ {\sigma }_{\mathrm{c}} $(MPa) $ {\varphi }_{\mathrm{b}} $(°) 试验值 预测值 1# 粉砂质泥岩/长石石英砂岩 0.501 48.1 12.3 0.5 34.7/80.6 32.7/36.5 0.452 0.545 20.58% 2# 粉砂质泥岩/长石石英砂岩 0.488 50.8 11.9 0.7 34.7/80.6 32.7/36.5 0.801 0.791 1.20% 3# 粉砂质泥岩/长石石英砂岩 0.492 51.4 11.7 1.3 34.7/80.6 32.7/36.5 1.325 1.454 9.75% 4# 泥岩/泥质灰岩 0.500 55.4 10.1 1.1 26.4/126.5 25.7/38.1 1.207 1.322 9.50% 5# 泥岩/泥质灰岩 0.489 45.7 11.2 1.8 26.4/126.5 25.7/38.1 2.030 1.768 12.89% 6# 泥岩/泥质灰岩 0.507 45.6 10.3 2.5 26.4/126.5 25.7/38.1 2.975 2.504 15.83% 7# 泥质粉砂岩/泥质灰岩 0.490 55.4 10.5 0.6 58.2/126.5 25.7/38.1 0.652 0.787 20.70% 8# 泥质粉砂岩/泥质灰岩 0.493 57.2 9.8 0.9 58.2/126.5 25.7/38.1 1.324 1.239 6.45% 9# 泥质粉砂岩/泥质灰岩 0.510 60.1 8.6 1.0 58.2/126.5 25.7/38.1 1.627 1.530 5.97% 10# 粉砂质泥岩/泥质粉砂岩 0.504 58.3 10.2 0.7 40.6/58.2 34.1/35.0 0.803 0.926 15.34% 11# 粉砂质泥岩/泥质粉砂岩 0.495 52.1 9.9 1.4 40.6/58.2 34.1/35.0 1.508 1.666 10.51%
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