基于分形理论的岩石裂隙非线性渗流各向异性研究
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摘要
针对裂隙岩体非达西渗流问题,开展了不同粗糙裂隙非线性渗流特性的研究。将完整的方形岩块采用劈裂法制成裂隙试件,用三维光学扫描系统量测裂隙表面形貌,并采用Kulatilake提出的自仿射分形维度方法计算表面的分形维度来表征粗糙表面的各向异性特征。根据裂隙流的曲折效应,在Forchheimer定律基础上,提出了水文弯曲度和表面分形幂律关系来表征非线性特点,并由此提出了新的粗糙裂隙非线性分形模型。对各组裂隙试件在2个方向(0°,90°)上进行饱和渗流试验,发现流动符合Forchheimer定律且存在各向异性特点,最后由分形模型,提出了区分达西流与Forchheimer流的新判据。
Aiming at the issue of Non-Darcy seepage flow in fracture,the seepage characteristics in different rough fractures were studied. The test speciment of fracture rock mass were obtained by splitting the integrated cubic rock mass,and the fracture surface topographies of rock mass were measured by stereotopometric scanning system. Surface roughness anisotropy was quantified by self-affine fractal dimension D using measured data. According to tortuosity effect of flow in fracture,the non-linear flow was characterized by a power law relationship of hydraulic tortuosity and fractal dimension based on Forchheimer law. Fracture seepage tests were conducted from two incidence directions (0°and 90°). The results showed that non-linear flow with anisotropy could be well described by Forchheimer law. Finally,a new formula was proposed,which can distinguish the linear flow and Forchheimer flow.
Aiming at the issue of Non-Darcy seepage flow in fracture,the seepage characteristics in different rough fractures were studied. The test speciment of fracture rock mass were obtained by splitting the integrated cubic rock mass,and the fracture surface topographies of rock mass were measured by stereotopometric scanning system. Surface roughness anisotropy was quantified by self-affine fractal dimension D using measured data. According to tortuosity effect of flow in fracture,the non-linear flow was characterized by a power law relationship of hydraulic tortuosity and fractal dimension based on Forchheimer law. Fracture seepage tests were conducted from two incidence directions (0°and 90°). The results showed that non-linear flow with anisotropy could be well described by Forchheimer law. Finally,a new formula was proposed,which can distinguish the linear flow and Forchheimer flow.
引文
[1]许凯,雷学文,孟庆山,等.非达西渗流系数研究[J].岩石力学与工程学报,2012,31(1):164-170.
[2]Schrauf T W,Evans D D.Laboratory studies of gas flow though a single natural fracture[J].Water Resources Research,1986,22(7):1038-1050.
[3]Zimmerman R W,Al-Yaarubi A,Pain C C,et al.Nonlinear regimes of fluid flow in rock fractures[J].International Journal of Rock Mechanics and Ming Sciences,2004,41(3):163-169.
[4]Zhang Z,Nemcik J.Fluid flow regimes and nonlinear flow characteristics in deformable rock fractures[J].Journal of Hydrology,2013(477):139-151.
[5]Zhou J Q,Hu S H,Fang S,et al.Nonlinear flow behavior at low Reynolds numbers though rough-walled fractures subjected to normal compressive loading[J].International Journal of Rock Mechanics and Ming Sciences,2015(80):202-218.
[6]Chen Y F,Zhou J Q,Hu S H,et al.Evaluation of Forchheimer equation coefficients for non-Darcy flow in deformable rough-walled fractures[J].Journal of Hydrology,2015(529):993-1006.
[7]金毅,郑军领,董佳斌,等.自仿射粗糙割理中流体渗流的分形定律[J].科学通报,2015,60(21):2036-2047.
[8]Tsang Y W.The effect of tortuosity on fluid flow through a single fracture[J].Lubric Technology,1984,20(9):1209-1215.
[9]肖维民,夏才初,王伟,等.考虑曲折效应的粗糙节理渗流计算公式研究[J].岩石力学与工程学报,2011,30(12):2416-2425.
[10]谢和平.分形几何及其在岩土力学中的应用[J].岩土工程学报,1992,14(1):14-24.
[11]谢和平,周宏伟.岩体断裂面渗流特性的分形研究[J].煤炭学报,1998,23(6):585-589.
[12]Murata S,Saito T.Estimation of tortuosity of fluid flow through a single fracture[J].Journal of Canadian Petroleum Technology,2003,42(12):39-45.
[13]王刚,黄娜,蒋宇静,等.考虑分形特征的节理面渗流计算模型[J].岩石力学与工程学报,2014,33(S2):3397-3405.
[14]Ju Y,Zhang Q G,Yang Y M,et al.An experimental investigation on the mechanism of fluid flow through single rough fracture of rock[J].Science China Technological Sciences,2013(56):2070-2080.
[15]Develi K,Babadagli T.Experimental and visual analysis of singlephase flow through rough fracture replicas[J].International Journal of Rock Mechanics and Ming Sciences,2015(73):139-155.
[16]郭建春,庄园,刘超.考虑非达西效应酸蚀裂缝流场数值模拟[J].岩土力学,2015,36(11):3315-3321.
[17]Clarke K C.Computation of the fractal dimension of topographic surfaces using the triangular prism surface area method[J].Computers and Geosciences,1986,12(5):713-722.
[18]Xie H P,Wang J A.Direct fractal measurement of fractal surfaces[J].International Journal Solids and Structures,1999(36):3073-3084.
[19]周宏伟,谢和平,Kwansniewski M A.粗糙表面分维计算的立方体覆盖法[J].摩擦学学报,2000,20(6):455-459.
[20]Kulatilake P H S W,Balasingam P,Park J,Morgan R.Natural rock joint roughness quantification through fractural techniques[J].Geotechnical and Geological Engineering,2006(24):1181-1202.
[21]Kulatilake P H S W,Park J,Balasingam P,et al.R.Quantification of aperture and relations between aperture,normal stress and fluid flow for natural single rock fractures[J].Geotechnical and Geological Engineering,2008(26):269-281.
[22]Javadi M,Sharifzadeh M,Shahriar K,et al.Crital Reynolds number for nonlinear flow through rough-walled fractures:The role of shear processes[J].Water Resources Research,2014,50(2):1789-1804.
[23]王媛,顾智刚,倪小东.光滑裂隙高流速非达西渗流运动规律的试验研究[J].岩石力学与工程学报,2010,29(7):1404-1407.
[2]Schrauf T W,Evans D D.Laboratory studies of gas flow though a single natural fracture[J].Water Resources Research,1986,22(7):1038-1050.
[3]Zimmerman R W,Al-Yaarubi A,Pain C C,et al.Nonlinear regimes of fluid flow in rock fractures[J].International Journal of Rock Mechanics and Ming Sciences,2004,41(3):163-169.
[4]Zhang Z,Nemcik J.Fluid flow regimes and nonlinear flow characteristics in deformable rock fractures[J].Journal of Hydrology,2013(477):139-151.
[5]Zhou J Q,Hu S H,Fang S,et al.Nonlinear flow behavior at low Reynolds numbers though rough-walled fractures subjected to normal compressive loading[J].International Journal of Rock Mechanics and Ming Sciences,2015(80):202-218.
[6]Chen Y F,Zhou J Q,Hu S H,et al.Evaluation of Forchheimer equation coefficients for non-Darcy flow in deformable rough-walled fractures[J].Journal of Hydrology,2015(529):993-1006.
[7]金毅,郑军领,董佳斌,等.自仿射粗糙割理中流体渗流的分形定律[J].科学通报,2015,60(21):2036-2047.
[8]Tsang Y W.The effect of tortuosity on fluid flow through a single fracture[J].Lubric Technology,1984,20(9):1209-1215.
[9]肖维民,夏才初,王伟,等.考虑曲折效应的粗糙节理渗流计算公式研究[J].岩石力学与工程学报,2011,30(12):2416-2425.
[10]谢和平.分形几何及其在岩土力学中的应用[J].岩土工程学报,1992,14(1):14-24.
[11]谢和平,周宏伟.岩体断裂面渗流特性的分形研究[J].煤炭学报,1998,23(6):585-589.
[12]Murata S,Saito T.Estimation of tortuosity of fluid flow through a single fracture[J].Journal of Canadian Petroleum Technology,2003,42(12):39-45.
[13]王刚,黄娜,蒋宇静,等.考虑分形特征的节理面渗流计算模型[J].岩石力学与工程学报,2014,33(S2):3397-3405.
[14]Ju Y,Zhang Q G,Yang Y M,et al.An experimental investigation on the mechanism of fluid flow through single rough fracture of rock[J].Science China Technological Sciences,2013(56):2070-2080.
[15]Develi K,Babadagli T.Experimental and visual analysis of singlephase flow through rough fracture replicas[J].International Journal of Rock Mechanics and Ming Sciences,2015(73):139-155.
[16]郭建春,庄园,刘超.考虑非达西效应酸蚀裂缝流场数值模拟[J].岩土力学,2015,36(11):3315-3321.
[17]Clarke K C.Computation of the fractal dimension of topographic surfaces using the triangular prism surface area method[J].Computers and Geosciences,1986,12(5):713-722.
[18]Xie H P,Wang J A.Direct fractal measurement of fractal surfaces[J].International Journal Solids and Structures,1999(36):3073-3084.
[19]周宏伟,谢和平,Kwansniewski M A.粗糙表面分维计算的立方体覆盖法[J].摩擦学学报,2000,20(6):455-459.
[20]Kulatilake P H S W,Balasingam P,Park J,Morgan R.Natural rock joint roughness quantification through fractural techniques[J].Geotechnical and Geological Engineering,2006(24):1181-1202.
[21]Kulatilake P H S W,Park J,Balasingam P,et al.R.Quantification of aperture and relations between aperture,normal stress and fluid flow for natural single rock fractures[J].Geotechnical and Geological Engineering,2008(26):269-281.
[22]Javadi M,Sharifzadeh M,Shahriar K,et al.Crital Reynolds number for nonlinear flow through rough-walled fractures:The role of shear processes[J].Water Resources Research,2014,50(2):1789-1804.
[23]王媛,顾智刚,倪小东.光滑裂隙高流速非达西渗流运动规律的试验研究[J].岩石力学与工程学报,2010,29(7):1404-1407.