裂隙岩体渗流溶质运移耦合离散裂隙模型数值计算方法
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摘要
研究裂隙岩体渗流溶质运移问题对于岩土工程地下水污染物预测控制具有重要意义。基于离散裂隙网络模型,采用实体单元模拟基质岩块、无厚度单元模拟复杂裂隙网络,提出了裂隙岩体渗流溶质运移耦合的三维数值计算方法。针对无反应项和含反应项两种情况,通过算例分析了单裂隙中溶质迁移行为,并与精细模拟方法、解析方法的结果进行对比验证;进一步将该法应用于预测大规模裂隙岩体溶质浓度分布规律及发展趋势,并评价了主要影响因素。结果表明,该法可有效模拟裂隙网络、基质岩块中水分溶质传输行为;由于贯通裂隙网络的优势流影响,溶质羽主要受控于裂隙水的对流作用,出现了高度非均匀分布现象;通过参数敏感性分析发现,相较于岩块基质的扩散作用,裂隙开度产生的对流作用是影响浓度场分布的主控因素。在保证精度的前提下,该法可大幅减小计算量和计算时长,对于解决含复杂裂隙网络岩体渗流传质的三维数值模拟问题具有明显优势。
The hydraulic and solute transport in fractured rock mass is of great importance for controlling the pollutant migration in groundwater. Based on the discrete fracture network model, a 3 D computational method is proposed to investigate the coupling behavior of hydraulic and solute transport in fractured rock mass, with rock matrix modeled by solid elements and complex fracture networks represented by the zero-thickness elements. The proposed method is validated against the results from the refined modeling and analytical approach in the case of solute transport in a fracture-matrix system without and with reactions. It is further employed to simulate the mass transport process in fractured rock mass containing a large-scale fracture network, to predict the solute concentration distribution and to estimate the main influencing factors of the solute field. It is shown that the proposed numerical method is capable of capturing the water and solute movement in the fracture network and rock matrix. Due to the dominant flows in the percolated fracture network, the solute plume is greatly affected by convection of water flows in fractures, resulting in a highly heterogeneous distribution. With the aid of parametric sensitivity analysis, it is demonstrated that the convection effect attributable to fracture aperture is the main control factor affecting the solute field, compared with the diffusion effect caused by fracture matrix. On the premise of ensuring the calculation accuracy, the proposed method brings down the computational cost and also possesses an apparent advantage in settling down the three-dimensional computational solution for fractured rock mass containing a complex discrete fracture network.
The hydraulic and solute transport in fractured rock mass is of great importance for controlling the pollutant migration in groundwater. Based on the discrete fracture network model, a 3 D computational method is proposed to investigate the coupling behavior of hydraulic and solute transport in fractured rock mass, with rock matrix modeled by solid elements and complex fracture networks represented by the zero-thickness elements. The proposed method is validated against the results from the refined modeling and analytical approach in the case of solute transport in a fracture-matrix system without and with reactions. It is further employed to simulate the mass transport process in fractured rock mass containing a large-scale fracture network, to predict the solute concentration distribution and to estimate the main influencing factors of the solute field. It is shown that the proposed numerical method is capable of capturing the water and solute movement in the fracture network and rock matrix. Due to the dominant flows in the percolated fracture network, the solute plume is greatly affected by convection of water flows in fractures, resulting in a highly heterogeneous distribution. With the aid of parametric sensitivity analysis, it is demonstrated that the convection effect attributable to fracture aperture is the main control factor affecting the solute field, compared with the diffusion effect caused by fracture matrix. On the premise of ensuring the calculation accuracy, the proposed method brings down the computational cost and also possesses an apparent advantage in settling down the three-dimensional computational solution for fractured rock mass containing a complex discrete fracture network.
引文
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[17]薛娈鸾.裂隙岩体渗流-传热耦合的复合单元模型[J].岩土力学,2016,37(1):263-268.(XUE Luan-luan.Acomposite element model for coupled seepage-heat transfer of fractured rock mass[J].Rock and Soil Mechanics,2016,37(1):263-268.(in Chinese))
[18]钱鹏,徐千军.不同裂纹分布的孔隙材料渗透系数[J].工程力学,2017,34(12):39-47.(QIAN Peng,XU Qian-jun.Permeability of porous material with different crack distributions[J].Engineering Mechanics,2017,34(12):39-47.(in Chinese))
[19]陈必光,宋二祥,程晓辉.二维裂隙岩体渗流传热的离散裂隙网络模型数值计算方法[J].岩石力学与工程学报,2014,33(1):43-51.(CHEN Bi-guang,SONG Er-xiang,CHENG Xiao-hui.A numerical method for discrete fracture network model for flow and heat transfer in two-dimensional fractured rocks[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(1):43-51.(in Chinese))
[20]LI X X,CHEN S H,XU Q,et al.Modeling capillary water absorption in concrete with discrete crack network[J].Journal of Materials in Civil Engineering,2017,30(1):04017263.
[21]LI X X,XU Y,CHEN S H.Computational homogenization of effective permeability in three-phase mesoscale concrete[J].Construction and Building Materials,2016,121:100-111.
[22]梁越,王俊杰,刘明维.基于流网单元的污染物优势运移数值模型[J].岩土力学,2015,36(10):3007-3014.(LIANG Yue,WANG Jun-jie,LIU Ming-wei.Numerical model for contaminant preferential migration based on flow net element[J].Rock and Soil Mechanics,2015,36(10):3007-3014.(in Chinese))
[23]NILENIUS F,LARSSON F,LUNDGREN K,et al.Computational homogenization of diffusion in three-phase mesoscale concrete[J].Computational Mechanics,2014,54(2):461-472.
[2]ZHU Y H,ZHAN H B,JIN M G.Analytical solutions of solute transport in a fracture-matrix system with different reaction rates for fracture and matrix[J].Journal of Hydrology,2016,539:447-456.
[3]姚池,姜清辉,位伟,等.复杂裂隙岩体水-力耦合模型及溶质运移模拟[J].岩石力学与工程学报,2013,32(8):1656-1665.(YAO Chi,JIANG Qing-hui,WEI Wei,et al.Numerical simulation of hydro-mechanical coupling and solute transport in complex fractured rock masses[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(8):1656-1665.(in Chinese))
[4]王锦国,周志芳.裂隙岩体溶质运移模型研究[J].岩土力学,2005,26(2):270-276.(WANG Jin-guo,ZHOU Zhi-fang.Study on model of solute transport in fractured rock mass[J].Rock and Soil Mechanics,2005,26(2):270-276.(in Chinese))
[5]HADGU T,KARRA S,KALININA E,et al.A comparative study of discrete fracture network and equivalent continuum models for simulating flow and transport in the far field of a hypothetical nuclear waste repository in crystalline host rock[J].Journal of Hydrology,2017,553:59-70.
[6]HYMAN J D,KARRA S,MAKEDONSKA N,et al.dfnWorks:a discrete fracture network framework for modeling subsurface flow and transport[J].Computers&Geosciences,2015,84:10-19.
[7]ZHOU R J,ZHAN H B,CHEN K W.Reactive solute transport in a filled single fracture-matrix system under unilateral and radial flows[J].Advances in Water Resources,2017,104:183-194.
[8]董志高,吴继敏,黄勇.二维裂隙网络溶质运移仿真模拟[J].岩土工程学报,2008,30(8):1256-1260.(DONGZhi-gao,WU Ji-min,HUANG Yong.Simulation of solute transport in two-dimensional fracture network[J].Chinese Journal of Geotechnical Engineering,2008,30(8):1256-1260.(in Chinese))
[9]NGO T D,FOURNO A,NOETINGER B.Modeling of transport processes through large-scale discrete fracture networks using conforming meshes and open-source software[J].Journal of Hydrology,2017,554:66-79.
[10]霍吉祥,宋汉周,杜京浓,等.表面反应和扩散迁移联合控制的粗糙单裂隙渗流-溶解耦合模型[J].岩石力学与工程学报,2015,34(5):1013-1021.(HUO Ji-xiang,SONGHan-zhou,DU Jing-nong,et al.Coupled fluid flow and chemical dissolution model based on surface reaction and mass transfer control in a rough fracture[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(5):1013-1021.(in Chinese))
[11]CHEN K W,ZHAN H B.A Green's function method for two-dimensional reactive solute transport in a parallel fracture-matrix system[J].Journal of Contaminant Hydrology,2018.
[12]ZOU L,JING L,CVETKOVIC V.Assumptions of the analytical solution for solute transport in a fracture-matrix system[J].International Journal of Rock Mechanics and Mining Sciences,2016,83:211-217.
[13]TANG D H,FRIND E O,SUDICKY E A.Contaminant transport in fractured porous media:analytical solution for a single fracture[J].Water Resources Research,1981,17(3):555-564.
[14]薛强,梁冰,刘建军.裂隙岩体中污染物运移过程的数值模拟[J].岩土力学,2003(增刊2):35-38.(XUE Qiang,LIANG Bing,LIU Jian-jun.Numerical simulation of contaminant transport in jointed rock mass[J].Rock and Soil Mechanics,2003(S2):35-38.(in Chinese))
[15]THOVERT J F,MOURZENKO V V,ADLER P M.Percolation in three-dimensional fracture networks for arbitrary size and shape distributions[J].Physical Review E,2017,95(4):042112.
[16]BERRONE S,PIERACCINI S,SCIALO S.On simulations of discrete fracture network flows with an optimization-based extended finite element method[J].SIAM Journal on Scientific Computing,2013,35(2):A908-A935.
[17]薛娈鸾.裂隙岩体渗流-传热耦合的复合单元模型[J].岩土力学,2016,37(1):263-268.(XUE Luan-luan.Acomposite element model for coupled seepage-heat transfer of fractured rock mass[J].Rock and Soil Mechanics,2016,37(1):263-268.(in Chinese))
[18]钱鹏,徐千军.不同裂纹分布的孔隙材料渗透系数[J].工程力学,2017,34(12):39-47.(QIAN Peng,XU Qian-jun.Permeability of porous material with different crack distributions[J].Engineering Mechanics,2017,34(12):39-47.(in Chinese))
[19]陈必光,宋二祥,程晓辉.二维裂隙岩体渗流传热的离散裂隙网络模型数值计算方法[J].岩石力学与工程学报,2014,33(1):43-51.(CHEN Bi-guang,SONG Er-xiang,CHENG Xiao-hui.A numerical method for discrete fracture network model for flow and heat transfer in two-dimensional fractured rocks[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(1):43-51.(in Chinese))
[20]LI X X,CHEN S H,XU Q,et al.Modeling capillary water absorption in concrete with discrete crack network[J].Journal of Materials in Civil Engineering,2017,30(1):04017263.
[21]LI X X,XU Y,CHEN S H.Computational homogenization of effective permeability in three-phase mesoscale concrete[J].Construction and Building Materials,2016,121:100-111.
[22]梁越,王俊杰,刘明维.基于流网单元的污染物优势运移数值模型[J].岩土力学,2015,36(10):3007-3014.(LIANG Yue,WANG Jun-jie,LIU Ming-wei.Numerical model for contaminant preferential migration based on flow net element[J].Rock and Soil Mechanics,2015,36(10):3007-3014.(in Chinese))
[23]NILENIUS F,LARSSON F,LUNDGREN K,et al.Computational homogenization of diffusion in three-phase mesoscale concrete[J].Computational Mechanics,2014,54(2):461-472.
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