Numerical simulations of seepage flow in rough single rock fractures

Abstract

To investigate the relationship between the structural characteristics and seepage flow behavior of rough single rock fractures, a set of single fracture physical models were produced using the Weierstrass-Mandelbrot functions to test the seepage flow performance. Six single fractures, with various surface roughnesses characterized by fractal dimensions, were built using COMSOL multiphysics software. The fluid flow behavior through the rough fractures and the influences of the rough surfaces on the fluid flow behavior was then monitored. The numerical simulation indicates that there is a linear relationship between the average flow velocity over the entire flow path and the fractal dimension of the rough surface. It is shown that there is good a agreement between the numerical results and the experimental data in terms of the properties of the fluid flowing through the rough single rock fractures.

Keywords

Seepage flow / Single fracture / Rough surface / Fractal dimension / Fractured rock

Acknowledgments

The Authors are grateful to the National Natural Science Funds for Distinguished Young Scholars of China (Grant No 51125017), the National Natural Science foundation of China (Grant No 51374213), the Creative Research Group Program of Jiangsu Province (Grant No 2014-27), the Priority Academic Program Development of Jiangsu Higher Education Institutions (Grant No PAPD-2014-12), the Open Research Project of State Key Laboratory for Geomechanics and Underground Engineering (Grant No SKLGDUEK1318) and the Science Fund for Creative Research Groups of the National Natural Science foundation of China (Grant No 51421003) for their financial supports.

References

[1] Y. Ju, Q.G. Zhang, Y.M. Yang, H.P. Xie, et al., An experimental investigation on the mechanism of fluid flow through single rough fracture of rock, Sci. China Ser. E Technol. Sci. 56 (8) (2013) 2070-2080.

[2] X.W. Xiong, C.H. Zhang, E.Z. Wang, A review of steady state seepage in a single fracture of rock, Yanshilixue Yu Gongcheng Xuebao 28 (9) (2009) 1839-1847.

[3] A. Baghbanan, L.R. Jing, Hydraulic properties of fractured rock masses with correlated fracture length and aperture, Int. J. Rock Mech. Min. Sci. 44 (5) (2007) 704-719.

[4] H.C. Zhang, Seepage-stress coupled model of heterogeneous and random fractured rock mass, J. China Coal Soc. 34 (11) (2009) 1460-1464.

[5] J.S. Liu, J.C. Sheng, A. Polak, et al., A fully e coupled hydrological e mechanical e chemical model for fracture sealing and preferential opening, Int. J. Rock Mech. Min. Sci. 43 (1) (2006) 23-36.

[6] Li Y.J. Jiang T. Koyama L.R. Jing Y. Tanabashi, Experimental study of the hydro-mechanical behavior of rock joints using a parallel-plate model containing contact areas and artificial fractures, Int. J. Rock Mech. Min. Sci. 45 (3) (2008) 362-375.

[7] Y.W. Tsang, C.F. Tsang, Channel model of flow through fractured media, Water Resour. Res. 23 (3) (1987) 467-479.

[8] Y.W. Tsang, P.A. Witherspoon, The dependence of fracture mechanical and fluid flow properties on fracture roughness and sample size, J. Geophys. Res. 88 (B3) (1983) 2359-2366.

[9] J. Feder, Fractals, Plenum Press, New York, 1988.

[10] B.B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman, New York, 1982.

[11] R.D. Maudin, in: G. Mayer-Kress (Ed.), On the Hausdorff Dimension of Graphs and Random Recursive Objects in Dimensions and Entropies in Chaotic Systems, Springer Verlag, Berlin, 1986, pp. 28-33.

[12] Y.T. Zhang, The Movement of Water Fractured Rock Mass and the Interaction of Hydraulic Structure, Water Conservancy and Water Science Research Institute, 1992.

[13] N. Barton, V. Houbey, The shear strength of rock joints in theory and practice, Rock Mech. (Austria) 10 (1-2) (1977) 1-54.

[14] F.Q. Wu, Statistics Principle of Rock Mass Mechanic, China University of Geosciences Press, Beijing, 1993, p. 5.

[15] Y.H. Lee, et al., Fractal dimension as a measure of the roughness of rock discontinuity profiles, Int. J. Rock Mech. Min. Sci. 27 (6) (1990) 453-464.

[16] H.P. Xie, G. William, Fractal estimation of joint roughness coefficient, J. Geosci. Transl. 9 (1) (1992) 85-90.