Inverse Modeling of Parameterized Hydraulic Conductivity Field in a Fractured Medium Based on Pilot Point Method
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摘要: 在裂隙岩体地下工程中，渗透性能是工程场地水文地质条件最为关注的关键因素之一，对工程场地最终安全性能评价起着至关重要的作用.以我国沿海某核设施花岗岩场地为研究对象，采用Pilot Point调参方法、PEST并行反演程序及3D克里金插值方式，表征裂隙岩体的渗透空间结构.研究表明：该方法可较好地拟合稳定条件下钻孔水位，验证地下水位动态演化趋势；建立的参数化渗透结构模型在实测数据分布的区域反演结果更为精细，模型参数的综合灵敏度程度受观测水位的位置、数量及变程等影响.Pilot Point方法一定程度上可以识别裂隙介质渗透结构的空间差异性，有助于进一步提升裂隙介质渗流模拟预测能力.Abstract: For the underground engineering site in a fractured rock mass, the hydraulic conductivity is a critical factor influencing hydrogeological conditions and plays a pivotal role in the final assessment of site performance. This study focuses on the granite formation of nuclear facility site in the coastal area, China. It applied the Pilot Point calibration technique in conjunction with a 3D kriging interpolation method to establish a parameterized hydraulic conductivity field for the fractured medium. Besides, the inverse parameter estimation tool PEST for automated calibration and sensitivity analysis was employed. The results indicate that the simulated hydraulic heads were in a good agreement with the measured data in the steady condition, and well reproduced dynamic behavior of groundwater level with time. Notably, the hydraulic conductivity filed could be estimated more accurately around the boreholes and the parameter sensitivity was related with borehole location, borehole quantity and variogram range. Based on these findings, it could conclude that Pilot Point method could identify spatial difference of hydraulic conductivity filed in the fractured rocks. It is positive to further improve the groundwater flow prediction ability in the fracture medium.
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图 3 PEST程序参数识别流程图与相应原理方程编号
Fig. 3. Diagram of the PEST code workflow and the number points to the equation of the corresponding step
图 4 钻孔ZK11中地下水电导率与TDS的监测结果
Fig. 4. Recorded data for conductivity and TDS in borehole ZK11
图 6 研究区渗透参数垂向方向（a）和水平NE45°方向（b）实验变异函数拟合曲线
Fig. 6. Semi-variogram and correlation length of log-transformed K data along the vertical direction (a) and the NE45° direction (b) in the study area
图 7 Pilot Point调参点空间分布(a)和平面布设与参数分区(b)
Fig. 7. Pilot Point locations in the numerical model (a) and planar graphs of Pilot Point locations and parameter zones (b)
图 9 钻孔CCZK05分层监测水位埋深结果
Fig. 9. Recorded data of groundwater depth from borehole CCZK05 utilizing the multi-layer monitoring system
图 10 稳定条件下的钻孔观测水位与模拟水位对比
Fig. 10. Comparison of the numerical and recorded hydraulic head of different boreholes in the steady-state condition
图 11 研究区地下水位稳定流模拟结果
Fig. 11. Groundwater level distribution in the steady-state condition
图 13 不同钻孔模拟水位与观测水位随时间对比
Fig. 13. Comparison of the numerical and recorded hydraulic head with time in different boreholes
图 15 不同剖面图的渗透系数模拟结果
Fig. 15. Hydraulic conductivity distribution of different profiles
图 16 模型中PilotPoint参数点的反演结果
Fig. 16. Numerical results of hydraulic conductivity of Pilot Points in the model
图 17 模型中各个参数分区的综合灵敏度分析结果
Fig. 17. Comprehensive sensitivities for hydrogeological zones in the model
图 18 PilotPoint点渗透系数的综合灵敏度分析结果
Fig. 18. Comprehensive sensitivities for hydraulic conductivity of Pilot Points in the model
图 19 观测水位对微风化层渗透结构灵敏度分析结果
Fig. 19. Sensitivities of different boreholes for hydraulic conductivity field in weakly weathered granite zone
表 1 van Genuchten-Mualem模型经验参数
Table 1. Empirical parameters of van Genuchten-Mualem model
岩性 残余含水率θr 饱和含水率θs 经验参数
α（cm-1）经验参数n 砂土 0.065 0.410 0.075 000 1.89 粉质粘土 0.131 0.396 0.004 230 2.06 花岗岩 0.000 0.008 0.000 064 1.34 
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表 2 模型不同岩性净入渗量反演结果(m/d)
Table 2. Numerical results of net infiltration mass for hydrogeological zones in the model (unit: m/d)
岩性 最小值 最大值 初始值 反演结果 中细粒花岗岩 1.0×10-8 9.65×10-5 1.0×10-5 1.21×10-4 斑状花岗岩 1.0×10-8 9.65×10-5 1.0×10-5 7.69×10-4 花岗斑岩 1.0×10-8 9.65×10-5 1.0×10-5 5.67×10-4 二长花岗岩 1.0×10-8 9.65×10-5 1.0×10-5 2.87×10-7 海相砂层 1.0×10-8 9.65×10-5 1.0×10-5 4.80×10-6 人工堆积层 1.0×10-8 9.65×10-5 1.0×10-5 7.41×10-8
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表 3 模型参数分区渗透系数的反演结果(m/d)
Table 3. Numerical results of hydraulic conductivity for hydrogeological zones in the model (unit: m/d)
岩性 最小值 最大值 初始值 反演结果 全风化层 中细粒花岗岩 0.1 5.0 0.1 0.500 斑状花岗岩 0.1 5.0 0.1 0.116 花岗斑岩 0.1 5.0 0.1 0.100 二长花岗岩 0.1 5.0 0.1 0.132 强风化层 中细粒花岗岩 0.05 0.5 0.1 0.100 斑状花岗岩 0.05 0.5 0.1 0.061 花岗斑岩 0.05 0.5 0.1 0.056 二长花岗岩 0.05 0.5 0.1 0.077 中风化层 中细粒花岗岩 0.001 0.1 0.01 0.003 斑状花岗岩 0.001 0.1 0.01 0.001 花岗斑岩 0.001 0.1 0.01 0.024 二长花岗岩 0.001 0.1 0.01 0.006 第四系 海相砂层 10.0 25.0 15.0 11.170 人工堆积层 1.0 20.0 10.0 5.162
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