Conversion relationship between uniaxial compressive strength and point load strength of sandy slate
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摘要: 以甘肃渭源—武都高速公路木寨岭隧道开挖揭露的砂质板岩为对象，开展了砂质板岩单轴抗压强度试验和点荷载强度试验；通过对试验数据进行正态分布检验、高度异常数据剔除和置信区间强度统计，获得了砂质板岩单轴抗压强度、点荷载强度以及两者之间的换算关系，并与岩石试验相关规范和国际岩石力学学会(ISRM)推荐换算公式进行了对比。研究结果表明：饱和砂质板岩单轴抗压强度服从正态分布，平均值为56.3 MPa，95%置信度下的置信区间为49.20~63.50 MPa；饱和砂质板岩点荷载强度与正态分布不完全一致，平均值为7.36 MPa，95%置信度下的置信区间为6.50~8.22 MPa；饱和砂质板岩点荷载强度与单轴抗压强度之间具有显著的线性正相关性；岩石强度受各试件内部节理裂隙的方向、填充物、宽度和长度等的影响，强度数据总体离散性较大；饱和、烘干状态下砂质板岩单轴抗压强度与点荷载强度的换算系数分别为7.72和8.72，均明显小于大多数研究中15~30的换算系数，原因在于砂质板岩内部赋存有层理或不同角度的节理裂隙等缺陷，单轴抗压强度受试件内部节理裂隙的影响较大，导致其强度平均值偏低，而点荷载强度受试件内部节理裂隙的影响较小；采用规范和ISRM推荐公式所得砂质板岩单轴抗压强度为实测值的2~4倍，用于隧道设计难免会产生较大偏差；相比规范和ISRM推荐公式，研究所得砂质板岩单轴抗压强度与点荷载强度换算关系的相对误差未超过15%，可作为规范中公式的有益补充。Abstract: The sandy slate exposed in the excavation of the Muzhailing Tunnel of Weiyuan-Wudu Expressway in Gansu Province was taken as the object, and the uniaxial compressive strength test and point load strength test of sandy slate were carried out. The uniaxial compressive strength and point load strength of sandy slate as well as their conversion relationship were obtained through a normal distribution test, highly abnormal data elimination, and confidence interval strength statistic analysis of the test data. In addition, the conversion formulas were compared with those recommended by relevant codes for rock tests and the International Society for Rock Mechanics (ISRM). Research results show that the uniaxial compressive strength of saturated sandy slate obeys the normal distribution, with an average value of 56.3 MPa and a confidence interval of 49.2-63.5 MPa under a confidence level of 95%. The point load strength of saturated sandy slates is not completely consistent with the normal distribution, with an average value of 7.36 MPa and a confidence interval of 6.50-8.22 MPa under a confidence level of 95%. There is a significant linear positive correlation between the point load strength and uniaxial compressive strength of the saturated sandy slate. The rock strength is affected by the direction, filler, width, and length of internal joints and fissures of each specimen, and the overall discreteness of the strength data is high. The conversion coefficients between the uniaxial compressive strength and point load strength of sandy slate in saturated and dryed states are 7.72 and 8.72, respectively. They are obviously smaller than the conversion coefficient ranging from 15 to 30 in most studies. The reason is that there are bedding or joints and fissures with different angles in the sandy slate, and the uniaxial compressive strength is greatly affected by the internal joints and fissures of the specimen, resulting in a low average strength, while the point load strength is less affected by the internal joints and fissures of the specimen. The uniaxial compressive strength of sandy slate predicted by the formulas recommended by codes and ISRM is 2-4 times the measured value and will inevitably lead to large deviations in tunnel designs. In comparison with the formulas recommended by codes and ISRM, the obtained relative error of the conversion relationship between the uniaxial compressive strength and point load strength is not more than 15%. It can be used as a useful supplement to the formulas in codes.
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图 5 饱和砂质板岩Rc正态分布Q-Q图
Figure 5. Q-Q diagram of normal distribution of Rc for saturated sandy slate
图 6 饱和砂质板岩Is(50)正态分布Q-Q图
Figure 6. Q-Q diagram of normal distribution of Is(50)for saturated sandy slate
图 8 饱和砂质板岩Is(50)频数分布
Figure 8. Frequency distribution of Is(50)for saturated sandy slate
图 9 饱和砂质板岩Rc与Is(50)的关系
Figure 9. Relationship between Rc and Is(50)of saturated sandy slate
图 10 烘干砂质板岩Rd与Is(50)的关系
Figure 10. Relationship between Rd and Is(50) for dried sandy slate
图 11 砂质板岩R换算值与实测值比较
Figure 11. Comparison between conversion values and measured values of R for sandy slate
图 13 不同换算公式计算结果对比
Figure 13. Comparison of calculation results among different conversion formulas
表 1 饱和砂质板岩Rc与Is(50)统计
Table 1. Statistics of Rc and Is(50) for saturated sandy slate
编号 Is(50)/MPa Rc/MPa 编号 Is(50)/MPa Rc/MPa 1 1.85 11.4 30 7.28 51.8 2 2.17 17.5 31 7.42 54.1 3 2.47 19.5 32 7.91 55.2 4 2.60 23.0 33 8.01 56.9 5 2.68 23.8 34 8.10 57.5 6 2.74 23.9 35 8.27 60.8 7 2.91 25.1 36 8.34 61.9 8 3.42 28.0 37 8.90 62.6 9 3.44 28.3 38 8.99 67.2 10 3.70 30.8 39 9.29 67.6 11 3.73 32.1 40 9.31 70.4 12 3.81 32.5 41 9.32 72.1 13 3.89 32.7 42 9.39 73.4 14 4.31 33.1 43 10.01 78.8 15 4.79 35.0 44 10.61 79.0 16 4.89 35.6 45 10.77 79.0 17 5.18 36.1 46 11.12 80.2 18 5.21 36.2 47 11.47 84.6 19 5.77 36.7 48 11.49 86.3 20 5.97 41.8 49 11.53 86.8 21 6.22 41.9 50 11.66 87.5 22 6.34 44.3 51 11.71 89.0 23 6.54 45.2 52 11.72 90.2 24 6.56 46.5 53 11.73 92.8 25 6.61 48.4 54 11.90 94.1 26 6.69 49.1 55 11.94 118.7 27 6.90 50.0 56 12.41 118.7 28 7.02 50.1 57 13.60 124.2 29 7.06 50.1 
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表 2 烘干砂质板岩Rd与Is(50)统计
Table 2. Statistics of Rd and Is(50) for dried sandy slate
编号 Is(50)/MPa Rd/MPa 1 3.97 42.63 2 6.36 57.04 3 7.15 67.60 4 7.88 68.33 5 8.59 71.17 6 9.47 78.04
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表 3 饱和砂质板岩Rc单样本K-S检验
Table 3. One-sample K-S test of Rc for saturated sandy slate
个案数 57 正态参数 平均值/MPa 56.318 标准偏差/MPa 27.003 渐近显著性(双尾) 0.200
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表 4 饱和砂质板岩Is(50)单样本K-S正态性检验
Table 4. One-sample K-S test of Is(50)of saturated sandy slate
个案数 57 正态参数 平均值/MPa 7.364 标准偏差/MPa 3.253 渐近显著性(双尾) 0.200
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表 5 砂质板岩强度离群值检验结果
Table 5. Outlier test results of sandy slate strength
样本数 强度/MPa 均值/MPa 标准差/MPa 统计量G57 统计量G′57 临界值G0.975(57) 临界值G0.995(57) 57 Rc 56.30 27.00 2.514 1.664 3.180 3.539 Is(50) 7.36 3.25 2.570 1.783 3.205 3.566
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表 6 砂质板岩强度统计
Table 6. Strength statistics of sandy slate
强度 含水状态 均值/MPa 置信区间/MPa 变异系数/% 置信度/% Rc 饱和 56.30 49.20~63.50 47.90 95 烘干 64.10 51.00~77.30 19.50 Is(50) 饱和 7.36 6.50~8.22 44.20 烘干 7.24 5.21~9.27 26.70
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表 7 饱和砂质板岩Is(50)与Rc离散程度
Table 7. Dispersion degrees of Is(50)and Rc for saturated sandy slate
强度 极差系数/% 平均差系数/% 标准差系数/% Is(50) 213.2 40.7 49.0 Rc 200.4 39.4 47.9
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表 8 不同换算公式的相对误差统计
Table 8. Relative error statistics of different conversion formulas
状态 数量/个 规范中换算公式 ISRM建议公式/% 本文换算公式 均值/% 95%置信区间/% 均值/% 95%置信区间/% 饱和 57 89.67 81.83~97.50 101.18~305.70 7.74 6.28~9.20 烘干 6 55.70 50.03~61.36 86.26~203.39 6.83 0.14~13.52
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