A model for estimating hydraulic conductivity of fractured rock mass based on correlation indexes
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摘要:
掌握岩体的渗透性是精细化描述一个地区水文地质特征的重要工作。渗透系数是表征岩体渗透性的重要指标，研究渗透系数估算模型对于实际工程应用具有重要意义。在现有的渗透系数估算模型中，单因子模型忽略了其他因素对该地区渗透系数的综合影响，复合因子模型存在参数选取不够灵活、部分参数较难获取等问题。基于公开数据，分类整理和对比分析了影响裂隙岩体渗透性的正、负相关参数，提出一种拟合效果好、参数选取灵活的渗透系数估算模型——PNC（Positive and Negative Correlation）模型。研究结果表明：在研究区一，PNC模型的拟合效果（可决系数R2=0.964和R2=0.801）优于HC模型的拟合效果（R2=0.905和R2=0.563）；在研究区二，PNC模型的拟合效果（R2=0.959）优于RMP模型的拟合效果（R2=0.927）；在研究区三，PNC模型的拟合效果（R2=0.94～0.99）优于ZRF模型的拟合效果（R2=0.92～0.99）。利用纳什效率系数（Nash-Sutcliffe Coefficient，NSE）进行模型误差分析，7组数据中有5组数据的误差系数在0.95以上。这说明PNC模型具有便利性和可靠性，可以为实际工程估算和验证渗透系数提供一定的参考。
Abstract:Mastering hydraulic conductivity of rock mass is an important way to precisely describe hydrogeological characteristics of a certain region. Hydraulic conductivity is a significant indicator to reflect the rock mass’ permeability. The studies of hydraulic conductivity estimation models have important implications for the development of actual engineering. In the existing estimation models of hydraulic conductivity, the single-factor model cannot take into consideration of the comprehensive influence of various factors on hydraulic conductivity in the area, and the parameters selection of the multi-factor model lacks the flexibility and its application is limited when some parameters are difficult to be obtained, etc. The classification and comparative analyses of the positive and negative correlation parameters are conducted based on public data. We propose a set of high-fitting hydraulic conductivity estimation models, which are the PNC (Positive and negative correlation) model. The research results show that the fitting result of the PNC model (R2=0.964 and R2=0.801) is superior to that of the HC model (R2=0.905 and R2=0.563) in No. 1 study area. In No. 2 study area, the fitting result of the PNC model (R2=0.959) is superior to that of the RMP model (R2=0.927). In No. 3 study area, the fitting result of the PNC model (R2=0.94 to 0.99) is also better than that of the ZRF model (R2=0.92 to 0.99). By using Nash-Sutcliffe coefficient (NSE) to carry out the error analyses of the model, it is found that the error coefficients of 5 in 7 sets of data are above 0.95. It further illustrates the convenience and reliability of the PNC model, which can provide a certain reference for estimating and verifying hydraulic conductivity in actual engineering.
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表 1 考虑深度Z的渗透系数估算模型
Table 1. Estimation model of hydraulic conductivity considering depth Z
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表 4 HB-94-01、HB-95-01和HB-95-02相关数据的分类整理与渗透系数拟合
Table 4. Classification of relevant data of borehole HB-95-01, HB-95-01 and HB-95-02
钻孔名称 负相关指标KN 正相关指标KP 渗透系数实测值
K/（10−6cm·s−1）PNC模型的拟合值
K/（10−6cm·s−1）HC模型的拟合值
K/（10−6cm·s−1）岩石质量指标
RQD深度指标
Z/m泥质含量指标
1-GCD岩性渗透性指标
LPIHB-94-01 0.906 35.50 0.999 0.999 7.060 13.700 5.710 0.562 37.20 0.999 0.999 164.000 136.000 43.800 0.937 57.50 0.999 0.950 1.530 0.947 1.930 0.500 75.40 0.999 0.400 5.300 3.050 5.640 0.999 78.00 0.999 0.400 0.042 0.075 0.028 0.875 83.40 0.999 0.400 0.231 0.113 0.618 0.999 91.00 0.999 0.400 0.029 0.034 0.014 0.500 95.00 0.999 0.400 0.453 0.832 1.840 HB-95-01 0.655 100.45 0.200 0.400 0.980 0.832 1.020 0.310 118.65 0.999 0.850 97.600 101.000 57.700 0.276 134.65 0.286 0.999 4.680 6.140 11.400 HB-95-02 0.929 90.00 0.999 0.600 15.600 16.700 2.510 0.969 97.60 0.999 0.600 2.420 12.400 0.770 0.781 120.10 0.071 0.700 0.136 0.186 0.324 0.656 136.40 0.727 0.700 11.700 10.100 13.400 0.062 156.40 0.103 0.700 1.990 2.050 3.170 0.062 174.60 0.103 0.700 0.908 1.760 2.760 0.406 191.40 0.999 0.700 101.000 45.400 29.300 0.464 198.20 0.500 0.999 6.000 6.140 16.100 0.321 214.60 0.999 0.999 45.400 45.400 46.300 0.607 250.40 0.091 0.700 0.403 0.306 0.317 0.786 273.40 0.999 0.700 3.360 6.140 2.620
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表 5 ZK10相关数据的分类整理与渗透系数拟合
Table 5. Classification of relevant data and hydraulic conductivity fitting of borehole ZK10
钻孔名称 负相关指标KN 正相关指标KP 渗透系数实测值
K/（10−6cm·s−1）PNC模型的拟合值
K/（10−6cm·s−1）RMP模型的拟合值
K/（10−6cm·s−1）岩石质量指标
RQD岩体完整性指标
RID裂隙宽度指标
AD岩性渗透性指标
LPDZK10 0.870 0.88 1.007 0.15 0.170 0.205 0.172 0.860 0.84 1.231 0.15 0.272 0.277 0.275 0.880 0.87 1.530 0.15 0.242 0.306 0.240 0.870 0.79 0.418 0.15 0.124 0.124 0.128 0.810 0.80 4.244 0.15 1.260 1.240 1.260 0.810 0.80 0.213 0.15 0.100 0.113 0.094 0.540 0.61 3.780 0.15 4.460 6.140 4.350 0.590 0.69 3.961 0.15 4.280 4.330 4.060 0.820 0.73 3.693 0.15 1.350 1.370 1.370 0.530 0.59 3.977 0.15 9.860 1.010 6.900 0.670 0.69 3.623 0.15 3.940 2.760 3.180 0.660 0.67 3.891 0.15 4.980 5.030 3.620 0.690 0.69 3.354 0.15 2.190 2.260 2.290 0.840 0.83 3.566 0.15 0.816 0.832 0.808 0.820 0.82 3.920 0.15 1.050 1.020 1.040
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表 6 PNC模型与ZRF模型拟合结果对比
Table 6. Comparison of the fitting results between the PNC model and the ZRF model
钻孔名称 
PNC模型拟合的R2 ZRF模型拟合的R2 ZK343 2.937 −5.637 16.030 0.94 0.92 ZK204 −9.118 −0.780 −7.083 0.99 0.99 ZK223 9.857 −1.281 −4.927 0.97 0.94 ZK153 1.330 −1.921 −2.241 0.96 0.95
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表 7 纳什效率系数误差分析
Table 7. The NSE error analyses
钻孔名称 ferror HB-94-01 0.95 HB-95-01和HB-95-02 0.70 ZK10 0.96 ZK343 0.90 ZK204 0.98 ZK223 0.97 ZK153 0.96
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为系数，Z为深度
为经验参数
为经验参数
为经验参数
图(1)
表(7)
计量
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