Abstract
Nuclear waste repositories have extremely stringent requirements for geological environment. However, natural fractures in rock mass can be potential channels for nuclide migration, therefore, the influence of fractures on the permeability of rock mass must be assessed. In this paper, a well research was conducted on well-exposed granite outcrops in the Xinchang site (the Chinese high-level radioactive waste repository). The high-precision three-dimensional model of a typical outcrop is built to obtain fracture information combined with field measurement, and then the three-dimensional fracture network model is generated using the relevant parameters by Monte Carlo method. To obtain more comprehensive fracture connectivity while avoiding the traditional method of searching the connectivity path in the complicated 3D fracture model taking up a lot of storage space and costing a lot of time, this paper presents an approach using MATLAB cell array instead of traditional adjacency matrix to search and store fracture network connectivity paths. In DFN model, the fracture disc with certain thickness is equivalent to three-dimensional pipe network model (EPNM) with variable diameter, and the equivalent path permeability coefficient (EPC) is proposed to objectively study the permeability characteristics of the seepage path in fractured rock mass based on that. Especially noteworthy is that some fractures in a certain strike range belong to open type, while those in another range belong to cemented closed fractures, when fresh fractures were exposed by cutting off the surface rock to a certain depth. The calculation of EPC under different conditions shows that the order of magnitude of EPC mean value is 1e−7m/s and 1e−3m/s, respectively, when fractures are cemented and not partly. On this basis, the size of the representative elementary volume (REV) of the fractured rock mass in the study area is determined to be about 25 m. By rotating the matrix in model, the spatial permeability tensor of the region (including permeability principal value and main direction) is obtained, which is within the range of borehole data. The predicted results may provide some reference for the related projects in the future.
Similar content being viewed by others
References
Adler PM, Thovert JF, Mourzenko VV (2013) Fractured porous media. Oxford University Press, Oxford
Bagalkot N, Kumar GS (2016) Numerical modeling of two species radionuclide transport in a single fracturematrix system with variable fracture aperture. Geosci J 20(5):627–638
Barenblatt GI, Zheltov IP, Kochina IN (1960) Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata]. PMM J Appl Math Mech 24(5):1286–1303
Berkowitz B (2002) Characterizing flow and transport in fractured geological media: a review. Adv Water Resour 25(8):861–884
Berrone S, Pieraccini S, Scialò S (2013) On simulations of discrete fracture network flows with an optimization-based extended finite element method. SIAM J Sci Comput 35(2):A908–A935
Bruderer-Weng C, Cowie P, Bernabé Y, Main I (2004) Relating flow channelling to tracer dispersion in heterogeneous networks. Adv Water Resour 27(8):843–855
Cacas MC, Ledoux E, Marsily GD, Tillie B, Barbreau A, Durand E (1990) Modeling fracture flow with a stochastic discrete fracture network: calibration and validation: 1. The flow model. Water Resour Res 26(3):479–489
Cai J, Sun S (2013) Fractal analysis of fracture increasing spontaneous imbibition in porous media with gas-saturated. Int J Mod Phys C24(08):1350056
Chen SH, Feng XM, Isam S (2010) Numerical estimation of rev and permeability tensor for fractured rock masses by composite element method. Int J Numer Anal Methods Geomech 32(12):1459–1477
Clemo T, Smith L (1997) A hierarchical model for solute transport in fractured media. Water Resour Res 33(8):1763–1784
Dershowitz WS, Fidelibus C (1999) Derivation of equivalent pipe network analogues for three-dimensional discrete fracture networks by the boundary element method. Water Resour Res 35(9):2685–2691
Dessirier B, Tsang CF, Niemi A (2018) A new scripting library for modeling flow and transport in fractured rock with channel networks. Comput Geosci 111:181–189
Durlofsky LJ (1991) Numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media. Water Resour Res 27(5):699–708
Dverstorp B, Andersson J, Nordqvist W (1992) Discrete fracture network interpretation of field tracer migration in sparsely fractured rock. Water Resour Res 28(9):2327–2343
Esmaieli K, Hadjigeorgiou J, Grenon M (2010) Estimating geometrical and mechanical rev based on synthetic rock mass models at brunswick mine. Int J Rock Mech Min Sci 47(6):915–926
Fadakar-A Y (2017) ADFNE: open source software for discrete fracture network engineering, two and three dimensional applications. Comput Geosci 102:1–11
Fisher NI (1993) Statistical analysis of circular data[M]. Cambridge University Press, Cambridge
Goc RL, Dreuzy JRD, Davy P (2010) An inverse problem methodology to identify flow channels in fractured media using synthetic steady-state head and geometrical data. Adv Water Resour 33(7):782–800
Guo L, Li XZ, Zhou YY, Zhang YY (2015) Generation and verification of three-dimensional network of fractured rock masses stochastic discontinuities based on digitalization. Environ Earth Sci 73(11):7075–7088
Gylling B (1997) Development and applications of the channel network model for simulations of flow and solute transport in fractured rock. PhD Thesis, Royal Institute of Technology, Stockholm, Sweden
Haneberg WC (2008) Using close range terrestrial digital photogrammetry for 3-d rock slope modeling and fracture mapping in the united states. Bull Eng Geol Environ 67(4):457–469
Huang N, Jiang Y, Li B, Liu R (2016) A numerical method for simulating fluid flow through 3-d fracture networks. J Nat Gas Sci Eng 33:1271–1281
Hyman JD, Aldrich G, Viswanathan H, Makedonska N, Karra S (2016) Fracture size and transmissivity correlations: implications for transport simulations in sparse three-dimensional discrete fracture networks following a truncated power law distribution of fracture size. Water Resour Res 52(8):6472–6489
Hyman JD, Hagberg A, Srinivasan G, Mohd-Yusof J, Viswanathan H (2017) Predictions of first passage times in sparse discrete fracture networks using graph-based reductions. Phys Rev E 96(1):013304
Karra S, O’malley D, Hyman JD, Viswanathan HS, Srinivasan G (2018) Modeling flow and transport in fracture networks using graphs. Phys Rev E 97(3):033304
Klimczak C, Schultz RA, Parashar R, Reeves DM (2010) Cubic law with aperture-length correlation: implications for network scale fluid flow. Hydrogeol J 18(4):851–862
Koike K, Liu C, Sanga T (2011) Incorporation of fracture directions into 3D geostatistical methods for a rock fracture system. Environ Earth Sci 66(5):1403–1414
Kristinof R, Ranjith PG, Choi SK (2010) Finite element simulation of fluid flow in fractured rock media. Environ Earth Sci 60(4):765–773
Kulatilake PHSW, Wu TH (1984) The density of discontinuity traces in sampling windows. Int J Rock Mech Min Sci Geomech Abstr 21(6):345–347
Lang PS, Paluszny A, Zimmerman RW (2014) Permeability tensor of threeâdimensional fractured porous rock and a comparison to trace map predictions. J Geophys Res Solid Earth 119(8):6288–6307
Lee CI, Song JJ (2003) Rock engineering in underground energy storage in Korea. Tunn Undergr Sp Tech 18(5):467–483
Lee T, Kim K, Lee K, Lee H, Lee W (2018) Development of fluid flow and heat transfer model in naturally fractured geothermal reservoir with discrete fracture network method. Geosci J 22(3):477–485
Li H, Zhang G, Zhu Y (2010) Three-dimensional seepage network searching of fractured rock mass and steady seepage field analysis. Chin J Rock Mech Eng 29:3447–3454
Liou TS, Lee YH, Chiang LW (2010) Alternative water resources in granitic rock: a case study from Kinmen Island Taiwan. Environ Earth Sci 59(5):1033–1046
Liu R, Jiang Y, Li B, Wang X (2015) A fractal model for charactering fluid flow in fractured rock masses on randomly distributed rock fracture networks. Comput Geotech 65:45–55
Liu R, Li B, Jiang Y (2016) A fractal model based on a new governing equation of fluid flow in fractures for characterizing hydraulic properties of rock fracture networks. Comput Geotech 75:57–68
Long JCS, Witherspoon PA (1985) The relationship of the degree of interconnection to hydraulic conductivity in fracture networks. Geophys Res 90(B4):3087–3098
Long JCS, Remer JS, Wilson CR, Witherspoon PA (1982) Porous media equivalents for networks of discontinuous fractures. Water Resour Res 18(3):645–658
Long J, Gilmour P, Witherspoon PA (1985) A model for steady fluid flow in random three-dimensional networks of disc-shaped fractures. Water Resour Res 21(8):1105–1115
Maryska J, Severyn O, Vohralik M (2005) Numerical simulation of fracture flow with a mixed-hybrid fem stochastic discrete fracture network model. Comput Geosci 8(3):217–234
Mauldon M (1998) Estimating mean fracture trace length and density from observations in convex windows. Rock Mech Rock Eng 31(4):201–216
Mourzenko VV, Bogdanov II, Thovert JF, Adler PM (2011) Original article: three-dimensional numerical simulation of single-phase transient compressible flows and well-tests in fractured formations. Math Comput Simul 81(10):2270–2281
Neuman SP (1988) Stochastic continuum representation of fractured rock permeability as an alternative to the REV and fracture network concepts. Groundwater flow and quality modelling. Springer, Dordrecht
Neuman SP (2005) Trends, prospects and challenges in quantifying flow and transport through fractured rocks [J]. Hydrogeol J 13(1):124–147
Nordqvist AW, Tsang YW, Tsang CF, Dverstorp B, Andersson J (1992) A variable aperture fracture network model for flow and transport in fractured rocks. Water Resour Res 28(6):1703–1713
Olson JE (2003) Sublinear scaling of fracture aperture versus length: an exception or the rule. J Geophys Res-Sol Ea. https://doi.org/10.1029/2001JB000419
Pouya A (2012) Three-dimensional flow in fractured porous media: a potential solution based on singular integral equations. Adv Water Resour 35(1):30–40
Priest SD (1993) Discontinuity analysis for rock engineering. Chapman & Hall, London
Rong G, Peng J, Wang X, Liu G, Hou D (2013) Permeability tensor and representative elementary volume of fractured rock masses. Hydrogeol J 21(7):1655–1671
Spence GH, Finch E (2014) Influences of nodular chert rhythmites on natural fracture networks in carbonates: an outcrop and two-dimensional discrete element modelling study. Geol Soc Lond Spec Publ 374(1):211–249
Tonon F, Chen S (2007) Closed-formand numerical solutions for the probability distribution function of fracture diameters. Int J Rock Mech Min Sci 44(3): 332–350
Tsang YW, Tsang CF (1987) Channel model of flow through fractured media. Water Resour Res 23(3):467–479
Tsang YW, Tsang CF (1989) Flow channeling in a single fracture as a two-dimensional strongly heterogeneous permeable medium. Water Resour Res 25(9):2076–2080
Vu MN, Pouya A, Seyedi DM (2014) Theoretical and numerical study of the steady-state flow through finite fractured porous media. Int J Numer Anal Method 38(3):221–235
Wang FY, Chen JP (2006) Research on method of distilling trace length information of rock mass crevice by digital close-range photogrammetry. Glob Geol 25(1):39–42 (in Chinese)
Wang M, Kulatilake PHSW, Um J, Narvaiz J (2002) Estimation of rev size and three-dimensional hydraulic conductivity tensor for a fractured rock mass through a single well packer test and discrete fracture fluid flow modeling. Int J Rock Mech Min Sci 39(7):887–904
Wang JL, Chen X, Huang YY, Zhang ZC (2013) A study of stochastic generation and connectivity of fracture network in rock mass. Hydrogeol Eng Geol 40(2):30–35 (in Chinese)
Wang P, Cai M, Ren F, Li C, Yang T (2017a) A digital image-based discrete fracture network model and its numerical investigation of direct shear tests. Rock Mech Rock Eng 50(7):1801–1816
Wang Y, Dong Q, Chen Y (2017b) Seepage simulation using pipe network flow model in a discrete element system. Comput Geotech 92:201–209
Wang J, Chen L, Su R, Zhao X (2018) The beishan underground research laboratory for geological disposal of high-level radioactive waste in china: planning, site selection, site characterization and in situ tests. J Rock Mech Geotech Eng 10(3):411–435
Warren JE, Root PJ (1963) The behavior of naturally fractured reservoirs. Soc Pet Eng 3(3):245–255
Witherspoon PA, Wang JSY, Iwai K, Gale JE (1980) Validity of cubic law for fluid flow in a deformable rock fracture. Water Resour Res 16(6):1016–1024
Wu FQ (1993) Principles of statistical mechanics of rockmasses[M]. Wuhan. China University of Geosciences Press 30-63 (in Chinese)
Xia L, Zheng Y, Yu Q (2016) Estimation of the rev size for blockiness of fractured rock masses. Comput Geotech 76:83–92
Xu C, Dowd P (2010) A new computer code for discrete fracture network modelling. Comput Geotech 36(3):292–301
Xu C, Fidelibus C, Dowd P (2014) Realistic pipe models for flow modelling in discrete fracture networks. International Discrete Fracture Network Engineering Conference
Yeo IW, Freitas MHD, Zimmerman RW (1998) Effect of shear displacement on the aperture and permeability of a rock fracture. Int J Rock Mech Min 35(8):1051–1070
Yu B, Lee LJ, Cao H (2002) A fractal in-plane permeability model for fabrics. Polym Compos 23(2):201–221
Zhang R, Ai T, Zhou HW (2015) Fractal and volume characteristics of 3D mining-induced fractures under typical mining layouts. Environ Earth Sci 73(10):6069–6080
Zheng J, Zhang YS, Shi XX, Li XZ (2014) Estimation of mean trace length based on trace maps measured by GPS-RTK. Appl Mech Mater 638–640:2141–2145
Zheng J, Zhang YS, Li XZ, Shi XX (2015) Digital method for acquiring fracture 2d density based on 3d digital traces model. Appl Mech Mater 738–739:526–530
Acknowledgements
This study was financially supported by the National Basic Research Program of China (973 Program, No. 2013CB036001), the National Defense Key Program (No. [2015] 297), and the National Natural Science Foundation of China (No. 40872172). The support received for this project from the Beijing Research Institute of Uranium Geology is greatly appreciated.
Author information
Authors and Affiliations
Corresponding authors
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Xu, W., Zhang, Y., Li, X. et al. Study on three-dimensional fracture network connectivity path of rock mass and seepage characteristics based on equivalent pipe network. Environ Earth Sci 78, 516 (2019). https://doi.org/10.1007/s12665-019-8505-8
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12665-019-8505-8