Abstract
The study on seepage flow passing through single fractures is essential and critical for understanding of the law of seepage flow passing through fracture networks and the coupling mechanisms of seepage field and stress field in rock masses. By using the fractal interpolation to reconstruct a natural coarse fracture, as well as taking into account the microstructure of the fracture, the numerical simulation of seepage flow passing through the coarse fractures with two distinct vertical scaling factors is conducted based on the MRT-LBM model of the lattice Boltzmann method. Then, after obtaining the length of the preferential flow pathway, the permeability of the two kinds of fractures is estimated respectively. In view of difficulties in locating the preferential flow pathway of natural fracture networks, by numerical tests a transect permeability weighted algorithm for estimating the fracture network permeability is proposed. The algorithm is not specific to one or more particular preferential flow pathways, but considers the contribution of each section to hinder the fluid passing through the medium. In order to apply the new algorithm, by capturing the structure of fracture networks based on the image-processing technique, the numerical simulations of seepage flow passing through two groups of natural fracture networks is carried out, the permeability is forecasted and the partial flows are reproduced for both cases. It is found that the preferential flow pathway emerges at the beginning of evolution, then is strengthened subsequently, and finally reaches a steady status. Furthermore, by using the proposed method some details on local flow can be clearly observed such as backflows and vortices at local branches can exist simultaneously and so forth, suggesting the validness of the proposed method for multiscale simulations of seepage flow.
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References
Lomize G M. Flow in Fractured Rock (in Russian). Gosemergoizdat, Moscow, 1951. 127–129
Su B Y, Zhan M L, Zhao J. Study on fracture seepage in the imitative nature rock (in Chinese). Chinese J Geotech Eng, 1995, 17(5): 19–24
Tian K M. The hydraulic properties of crossing-flow in an intersected fracture (in Chinese). Acata Geologica Sinica, 1986, 2: 202–214
Tsang Y W, Tsang C F. Channel model of flow through fractured media. Water Resour Res, 1987, 23(3): 467–479
Dahan O, Nativ R, Adar E M, et al. On fracture structure and preferential flow in unsaturated chalk. Ground Water, 2000, 38(3): 444–451
Barton, Bandiss, Bakhtark. Strength deformation and conductivity coupling of rock joints. Inter J Rock Mech Mining Sci Geomech Abstracts, 1985, 22(3): 121–140
Louis C. Rock Hydraulics in Rock Mechanics. New York: Springer-New Verlag, 1974
Iwai K. Fundamental Studies of Fluid Flow Through a Single Fracture. Berkely: University of California, 1976
Yang M J, Chen M X, Ho Y N. The effect of tortuosity on the flow through a fracture (in Chinese). Rock Soil Mech, 2001, 22(1): 78–82
Wang Y, Su B Y. Research on the behavior of fluid flow in a single fracture and its equivalent hydraulic aperture (in Chinese). Adv Water Sci, 2002, 13(1): 61–68
Zhang W J, Zhou C B, Li J P, et al. Research progress of experiment study on seepage characteristic of fractured rock masses (in Chinese). Rock Soil Mech, 2005, 26(9): 1517–1524
Xu G X, Zhang Y X, Ha Q L. Super-cubic and sub-cubic law of rough fracture seepage and its experiments study (in Chinese). Shuili Xuebao, 2003, 3: 74–79
Zhou C B, Xiong W L. A generalized cublic law for percolation in rock joints (in Chinese). Rock Soil Mech, 1996, 17(4): 1–7
Wang E Z. Network analysis and seepage flow model of fractured rockmass (in Chinese). Chinese J Rock Mech Eng, 1993, 12(3): 214–221
Chai J R, Xu W S. Coupling analysis of unsteady seepage and stress fields in discrete fractures network of rock mass in dam foundation. Sci China Tech Sci, 2011, 54(Suppl. 1): 133–139
Zheng H, Liu D F, Lee C F, et al. A new formulation of Signorini’s type for seepage problems with free surfaces. Int J Numer Meth Eng, 2005, 64: 1–16
Jiang Q H, Ye Z Y, Yao C, et al. A new variational inequality formulation for unconfined seepage flow through fracture networks (in Chinese). Sci China Tech Sci, 2012, 42(11): 1339–1350
Jiang Q H, Ye Z Y, Yao C, et al. A new variational inequality formulation for unconfined seepage flow through fracture networks. Sci China Tech Sci, 2012, 55: 3090–3101
Ye Z Y, Jiang Q H, Yao C, et al. Formulation and simulation of non-steady seepage flow through fracture network in rock masses (in Chinese). Rock Soil Mech, 2013, 34(4): 1171–1178
Jiang Q H, Yao C, Ye Z Y, et al. Seepage flow with free surface in fracture networks. Water Resour Res, 2013, 49: 176–186
Yao C, Jiang Q H, Wei W, et al. The variational inequality formulation for unconfined seepage through three-dimensional dense fracture networks. Sci China Tech Sci, 2013, 56: 1241–1247
Lu W, Xiang Y Y, Tang C. Model experiment and numerical simulation of flow and heat transfer for sand-filled fractured rock model (in Chinese). Rock Soil Mech, 2011, 32(11): 3448–3454
Li X Q, Chen Z Y. Boundary element method for 3-D fracture network seepage flow and its programming (in Chinese). J China Institute Water Resources Hydropower Res, 2006, 4(2): 81–87
Li X C, Chen J P, Shi B F, et al. A study on the meshless method on seepage of intersected fractures (in Chinese). Rock Soil Mech, 2007, 28Z: 371–374
Wang J X, Wu Y F, Bai C F. Numerical manifold element method for seepage with free surface problem (in Chinese). Water Resources Power, 2003, 21(4): 23–25, 57
Jiang Q H, Deng S S, Zhou C B, et al. Modeling unconfined seepage flow using three-dimensional numerical manifold method. J Hydrodynamics, 2010, 22(4): 554–561
Zhao Y S, Ma Y, Duan K L. Study on the co-relation law of fracture distribution of crack in rock stratum (in Chinese). Chinese J Rock Mech Eng, 2002, 21(2): 219–222
Zhou H W, Xie H. Direct estimation of the fractal dimensions of a fracture surface of rock. Surface Rev Lett, 2003, 10(5): 751–762
Koyama T, Fardin N. Numerical simulation of shear-induced flow anisotropy and scaling-dependent aperture and transmissivity evolution of rock fracture replicas. Inter J Rock MechMin Sci, 2006, 43: 89–106
Sun H Q, Xie H P. Fractal simulation of rock fracture surface (in Chinese). Rock Soil Mech, 2008, 29 ( 2): 347–352
Succi S, Foti E, Higuera F. Three dimensional flows in complex geometries with the lattice Boltzmann method. Europhys Lett, 1989, 10: 433–438
Dardis O, McCloskey J. Lattice Boltzmann scheme with real numbered solid density for the simulation of flow in porous media. Phys Rev E, 1998, 57: 4834–4837
Pan C, Luo L S, Miller C T. An evaluation of lattice Boltzmann scheme for porous medium flow simulation. Comput Fluids, 2006, 35: 898–909
Qian Y H, d’Humières D, Lallemand P. Lattice BGK model for Navier-Stokes equation. Europhys Lett, 1992, 17: 479
Lallemand P, Luo L S. Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability. Phys Rev E, 2000, 61: 6546
Xie H P, Sun H Q, Ju Y, et al. Study on generation of rock fracture surfaces using fractal interpolation. Inter J Solid Struct, 2001, 38: 5765–5787
Inamuro T, Yoshino M, Ogino F, A non-slip boundary condition for lattice Boltzmann simulations. Phys Fluids, 1995, 7: 2928–2930
Cui B. Complicated Rock Fracture Image Processing and Geometry Complicity Analysis (in Chinese). Dissertation of Masteral Degree. Chongqing: Chongqing University of Posts and Telecommunications, 2007
Peng T, Wang W X. The segmentation of color rock fracture based on fractal (in Chinese). Microcomputr Inf, 2008, 24(2-1): 261–299
Wang E Z, Yang C T. Numerical model of groundwater flow in fracture networks and water flow in disconnected fracture networks. (in Chinese). Hydrogeology Eng Geology, 1992, 19(1): 12–14
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Fan, H., Zheng, H. MRT-LBM-based numerical simulation of seepage flow through fractal fracture networks. Sci. China Technol. Sci. 56, 3115–3122 (2013). https://doi.org/10.1007/s11431-013-5402-3
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DOI: https://doi.org/10.1007/s11431-013-5402-3