不同侧压力系数下裂隙网络岩体非线性渗流特性
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摘要
基于人工裂隙网络模型,展开一系列不同边界荷载作用下含不同交叉点个数的裂隙网络渗流试验。针对所有试验工况,模型进水口水压力范围均为0～0.6 MPa,侧压力系数均由1.0增加至5.0。试验结果表明:裂隙网络体积流速和水力梯度之间的相关性可以通过Forchheimer函数进行拟合,拟合方程中线性和非线性项系数均随着侧压力系数的增加逐渐增大,而随着裂隙网络交叉点个数的增加逐渐减小;渗流试验过程中,非线性效应系数E和水力梯度J之间的相关性可采用一个幂指数函数进行描述,随着水力梯度的增加,非线性效应系数逐渐增大;随着侧压力系数的增加,裂隙网络临界水力梯度呈现逐渐增大的趋势,对于所有裂隙网络交叉点个数(1～12),当侧压力系数由1.0增加至5.0,临界水力梯度由0.63～12.13增加至6.01～81.55;提出数学模型T/T_0=1-exp(-βJ~(-0.45))对归一化导水系数T/T_0随水力梯度的增大而减小的特征进行分析,随着侧压力系数的增加,两者之间的拟合曲线逐渐上移,拟合系数β整体呈现逐渐增大的趋势。裂隙网络的等效渗透系数随侧压力系数的增加逐渐降低。
Fluid flow tests were conducted on artificial fracture networks with different numbers of intersections and subjected to various boundary load conditions. For all cases, the inlet hydraulic pressures were ranged from 0 to 0.6 MPa, and the lateral pressure ratios were increased from 1.0 to 5.0. The test results show that the Forchheimer's law provides an excellent description of the nonlinear fluid flow in fracture networks. Both the linear and nonlinear coefficients in the Forchheimer's law generally increase as the lateral pressure ratio increases but decrease as the number of intersections increases. During the fluid flow process, relationships between nonlinear effect factor E and hydraulic gradient J can be well described using a power function. The nonlinear effect factor E shows an increase with the hydraulic gradient. As the lateral pressure ratio increases, the critical hydraulic gradient shows an increasing trend. For all numbers of intersections(1-12),in the range of lateral pressure ratio from 1.0 to 5.0, the critical hydraulic gradient shows an increase from 0.63-12.13 to 6.01-81.55. A mathematical model of T/T_0=1-exp(-βJ~(-0.45)) for decreased normalized transmissivity against the hydraulic gradient was established. An increase in the lateral pressure ratio shifts the fitted curves upward. The coefficient β generally presents an increasing trend with the lateral pressure ratio. Equivalent permeability of the fracture networks decreases with the lateral pressure ratio.
Fluid flow tests were conducted on artificial fracture networks with different numbers of intersections and subjected to various boundary load conditions. For all cases, the inlet hydraulic pressures were ranged from 0 to 0.6 MPa, and the lateral pressure ratios were increased from 1.0 to 5.0. The test results show that the Forchheimer's law provides an excellent description of the nonlinear fluid flow in fracture networks. Both the linear and nonlinear coefficients in the Forchheimer's law generally increase as the lateral pressure ratio increases but decrease as the number of intersections increases. During the fluid flow process, relationships between nonlinear effect factor E and hydraulic gradient J can be well described using a power function. The nonlinear effect factor E shows an increase with the hydraulic gradient. As the lateral pressure ratio increases, the critical hydraulic gradient shows an increasing trend. For all numbers of intersections(1-12),in the range of lateral pressure ratio from 1.0 to 5.0, the critical hydraulic gradient shows an increase from 0.63-12.13 to 6.01-81.55. A mathematical model of T/T_0=1-exp(-βJ~(-0.45)) for decreased normalized transmissivity against the hydraulic gradient was established. An increase in the lateral pressure ratio shifts the fitted curves upward. The coefficient β generally presents an increasing trend with the lateral pressure ratio. Equivalent permeability of the fracture networks decreases with the lateral pressure ratio.
引文
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[16]WANG L C,CARDENAS M B,SLOTTKE D T,et al.Modification of the local cubic law of fracture flow for weak inertia,tortuosity,and roughness[J].Water Resources Research,2015,51(4):2064-2080.
[17]ESAKI T,DU S,MITANI Y,et al.Development of a shear-flow test apparatus and determination of coupled properties for a single rock joint[J].International Journal of Rock Mechanics and Mining Sciences,1999,36(5):641-650.
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[19]RONG G,YANG J,CHENG L,et al.Laboratory investigation of nonlinear flow characteristics in rough fractures during shear process[J].Journal of Hydrology,2016,541:1385-1394.
[20]BARTON N,BANDIS S,BAKHTAR K.Strength,deformation and conductivity coupling of rock joints[J].International Journal of Rock Mechanics and Mining Sciences&Geomechanics Abstracts,1985,22(3):121-140.
[21]DURHAM W B,BONNER B P.Self-propping and fluid flow in slightly offset joints at high effective pressures[J].Journal of Geophysical Research,1994,99(B5):9391-9399.
[22]ZHANG Z Y,NEMCIK J.Fluid flow regimes and nonlinear flow characteristics in deformable rock fractures[J].Journal of Hydrology,2013,447(1):139-151.
[23]YIN Q,MA G W,JING H W,et al.Hydraulic properties of 3D rough-walled fractures during shearing:An experimental study[J].Journal of Hydrology,2017,555:169-184.
[24]TSE R,CRUDEN DM.Estimating joint roughness coefficients[J].International Journal of Rock Mechanics and Mining Sciences&Geomechanics Abstracts,1979,16(5):303-307.
[25]WANG M,CHEN Y F,MA G W,et al.Influence of surface roughness on nonlinear flow behaviors in 3Dself-affine rough fractures:Lattice Boltzmann simulations[J].Advances in Water Resources,2016,96:373-388.
[26]LIU R C,YU L Y,JIANG Y J.Quantitative estimates of normalized transmissivity and the onset of nonlinear fluid flow through rough rock fractures[J].Rock Mechanics and Rock Engineering,2016,50(4):1063-1071.
[2]倪卫达,单治钢,刘晓.基于三维节理网络模拟的坝基岩体结构分类研究[J].岩土力学,2018,39(1):287-296.NI Wei-da,SHAN Zhi-gang,LIU Xiao.Classification of rock mass structure of dam foundation based on 3D joint network simulation[J].Rock and Soil Mechanics,2018,39(1):287-296.
[3]夏才初,王伟,王筱柔.岩石节理剪切-渗流耦合试验系统的研制[J].岩石力学与工程学报,2008,27(6):1285-1291.XIA Cai-chu,WANG Wei,WANG Xiao-rou.Development of coupling shear-seepage test system for rock joints[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(6):1285-1291.
[4]刘继山.结构面力学参数与水力参数耦合关系及其应用[J].水文地质工程地质,1988,15(2):7-12.LIU Ji-shan.The coupled relationships between mechanical and hydraulic parameters of a structural surface and their applications[J].Hydrogeology&Engineering Geology,1988,15(2):7-12.
[5]俞缙,李宏,陈旭,等.渗透压-应力耦合作用下砂岩渗透率与变形关联性三轴试验研究[J].岩石力学与工程学报,2013,32(6):1203-1213.YU Jin,LI Hong,CHEN Xu,et al.Triaxial experimental study of associated permeability-deformation of sandstone under hydro-mechanical coupling[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(6):1203-1213.
[6]RUTQVIST J,STEPHANSSON O.The role of hydromechanical coupling in fractured rock engineering[J].Hydrogeology Journal,2003,11(1):7-40.
[7]李博,蒋宇静.岩石单节理面剪切与渗流特性的试验研究与数值分析[J].岩石力学与工程学报,2008,27(12):2431-2439.LI Bo,JIANG Yu-jing.Experimental study and numerical analysis of shear and flow behaviors of rock with single joint[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(12):2431-2439.
[8]ZHANG H B,LIU J S,ELSWORTH D.How sorption-induced matrix deformation affects gas flow in coal seams:A new FE model[J].International Journal of Rock Mechanics and Mining Sciences,2008,45(8):1226-1236.
[9]ZIMMERMAN R W,BODVARSSON G S.Hydraulic conductivity of rock fractures[J].Transport in Porous Media,1996,23(1):1-30.
[10]BRUSH D J,THOMSON N R.Fluid flow in synthetic rough-walled fractures:Navier-Stokes,Stokes,and local cubic law simulations[J].Water Resources Research,2003,39(4):1037-1041.
[11]WITHERSPOON P A,WANG J SY,IWAI K,et al.Validity of Cubic Law for fluid flow in a deformable rock fracture[J].Water Resources Research,1980,16(6):1016-1024.
[12]ZIMMERMAN R W,AL-YAARUBI A,PAIN C C,et al.Non-linear regimes of fluid flow in rock fractures[J].International Journal of Rock Mechanics and Mining Sciences,2004,41(3):163-169.
[13]LI B,LIU R,JIANG Y.Influences of hydraulic gradient,surface roughness,intersecting angle,and scale effect on nonlinear flow behavior at single fracture intersections[J].Journal of Hydrology,2016,538:440-453.
[14]LIU R C,LI B,JIANG Y J.Critical hydraulic gradient for nonlinear flow through rock fracture networks:The roles of aperture,surface roughness,and number of interactions[J].Advances in Water Resources,2016,88:53-65.
[15]CAI J C,YU B M,ZOU M Q,et al.Fractal analysis of surface roughness of particles in porous media[J].Chinese Physics Letters,2010,27(2):157-160.
[16]WANG L C,CARDENAS M B,SLOTTKE D T,et al.Modification of the local cubic law of fracture flow for weak inertia,tortuosity,and roughness[J].Water Resources Research,2015,51(4):2064-2080.
[17]ESAKI T,DU S,MITANI Y,et al.Development of a shear-flow test apparatus and determination of coupled properties for a single rock joint[J].International Journal of Rock Mechanics and Mining Sciences,1999,36(5):641-650.
[18]JAVADI M,SHARIFZADEH M,SHAHRIAR K,et al.Critical Reynolds number for nonlinear flow through rough-walled fractures:The role of shear processes[J].Water Resources Research,2014,50(2):1789-1804.
[19]RONG G,YANG J,CHENG L,et al.Laboratory investigation of nonlinear flow characteristics in rough fractures during shear process[J].Journal of Hydrology,2016,541:1385-1394.
[20]BARTON N,BANDIS S,BAKHTAR K.Strength,deformation and conductivity coupling of rock joints[J].International Journal of Rock Mechanics and Mining Sciences&Geomechanics Abstracts,1985,22(3):121-140.
[21]DURHAM W B,BONNER B P.Self-propping and fluid flow in slightly offset joints at high effective pressures[J].Journal of Geophysical Research,1994,99(B5):9391-9399.
[22]ZHANG Z Y,NEMCIK J.Fluid flow regimes and nonlinear flow characteristics in deformable rock fractures[J].Journal of Hydrology,2013,447(1):139-151.
[23]YIN Q,MA G W,JING H W,et al.Hydraulic properties of 3D rough-walled fractures during shearing:An experimental study[J].Journal of Hydrology,2017,555:169-184.
[24]TSE R,CRUDEN DM.Estimating joint roughness coefficients[J].International Journal of Rock Mechanics and Mining Sciences&Geomechanics Abstracts,1979,16(5):303-307.
[25]WANG M,CHEN Y F,MA G W,et al.Influence of surface roughness on nonlinear flow behaviors in 3Dself-affine rough fractures:Lattice Boltzmann simulations[J].Advances in Water Resources,2016,96:373-388.
[26]LIU R C,YU L Y,JIANG Y J.Quantitative estimates of normalized transmissivity and the onset of nonlinear fluid flow through rough rock fractures[J].Rock Mechanics and Rock Engineering,2016,50(4):1063-1071.