Connectivity and Flowrate Estimation of Discrete Fracture Network Using Artificial Neural Network

Document Type : Regular Article


1 Urmia University of Technology, Urmia, Iran

2 Amirkabir University of Technology, Tehran, Iran


Hydraulic parameters of rock mass are the most effective factors that affect rock mass behavioral and mechanical analysis. Aforementioned parameters include intensity and density of fracture intersections, percolation frequency, conductance parameter and mean outflow flowrate which flowing perpendicular to the hydraulic gradient direction. In order to obtain hydraulic parameters, three-dimensional discrete fracture network generator, 3DFAM, was developed. However, unfortunately, hydraulic parameters obtaining process using conventional discrete fracture network calculation is either time consuming and tedious. For this reason, in this paper using Artificial Neural Network, a tool is designed which precisely and accurately estimate hydraulic parameters of discrete fracture network. Performance of designed optimum artificial neural network is evaluated from mean Squared error, errors histogram, and the correlation between artificial neural network predicted value and with discrete fracture network conventionally calculated value. Results indicate that there is the acceptable value of mean squared error and also a major part of estimated values deviation from the actual value placed in acceptable error interval of (-1.17, 0.85). On the other hand, excellent correlation of 0.98 exists between the predicted and actual value that proves the reliability of the designed artificial neural network.


Google Scholar


Main Subjects

[1]     Andersson J, Dverstorp B. Conditional simulations of fluid flow in three-dimensional networks of discrete fractures. Water Resour Res 1987;23:1876–86. doi:10.1029/WR023i010p01876.
[2]     Cacas MC, Ledoux E, de Marsily G, Tillie B, Barbreau A, Durand E, et al. Modeling fracture flow with a stochastic discrete fracture network: calibration and validation: 1. The flow model. Water Resour Res 1990;26:479–89. doi:10.1029/WR026i003p00479.
[3]     Long JCS, Witherspoon PA. The relationship of the degree of interconnection to permeability in fracture networks. J Geophys Res 1985;90:3087. doi:10.1029/JB090iB04p03087.
[4]     Ni P, Wang S, Wang C, Zhang S. Estimation of REV Size for Fractured Rock Mass Based on Damage Coefficient. Rock Mech Rock Eng 2017;50:555–70. doi:10.1007/s00603-016-1122-x.
[5]     Li Y, Chen J, Shang Y. Connectivity of Three-Dimensional Fracture Networks: A Case Study from a Dam Site in Southwest China. Rock Mech Rock Eng 2017;50:241–9. doi:10.1007/s00603-016-1062-5.
[6]     Lee C-H, Yu J-L, Hwung H-H. Fluid flow and connectivity in fractured rock. Water Resour Manag 1993;7:169–84. doi:10.1007/BF00872480.
[7]     Xu C, Dowd P. A new computer code for discrete fracture network modelling. Comput Geosci 2010;36:292–301. doi:10.1016/j.cageo.2009.05.012.
[8]     Reeves DM, Parashar R, Pohll G, Carroll R, Badger T, Willoughby K. The use of discrete fracture network simulations in the design of horizontal hillslope drainage networks in fractured rock. Eng Geol 2013;163:132–43. doi:10.1016/j.enggeo.2013.05.013.
[9]     Zhang Q-H, Yin J-M. Solution of two key issues in arbitrary three-dimensional discrete fracture network flow models. J Hydrol 2014;514:281–96. doi:10.1016/j.jhydrol.2014.04.027.
[10]    Karvounis D, Jenny P. Modeling of flow and transport in enhanced geothermal systems. Proc. 36th Work. Geotherm. Reserv. Eng. Stanford Univ. Stanford, California, 2011, p. 8.
[11]    Kvartsberg S. Hydrogeological characterisation of a fracture network, MSc Thesis, Chalmers University of Technology, Sweden. MSc Thesis, Chalmers University of Technology, Sweden, p 95, 2010.
[12]    Singhal BBS, Gupta RP. Applied Hydrogeology of Fractured Rocks. Dordrecht: Springer Netherlands; 2010. doi:10.1007/978-90-481-8799-7.
[13]    Fadakar-A Y, Xu C, Dowd PA. Connectivity index and connectivity field towards fluid flow in fracture-based geothermal reservoirs. Proc. 38 Work. Geotherm. Reserv. Eng. Stanford Univ. Stanford, Calif., 2013, p. 417–27.
[14]    Seifollahi S, Dowd PA, Xu C, Fadakar AY. A Spatial Clustering Approach for Stochastic Fracture Network Modelling. Rock Mech Rock Eng 2014;47:1225–35. doi:10.1007/s00603-013-0456-x.
[15]    Robinson PC. Connectivity of fracture systems-a percolation theory approach. J Phys A Math Gen 1983;16:605–14.
[16]    Englman R, Gur Y, Jaeger Z. Fluid Flow Through a Crack Network in Rocks. J Appl Mech 1983;50:707. doi:10.1115/1.3167133.
[17]    Charlaix E, Guyon E, Rivier N. A criterion for percolation threshold in a random array of plates. Solid State Commun 1984;50:999–1002. doi:10.1016/0038-1098(84)90274-6.
[18]    Stauffer D. Introduction to Percolation Theory. 1985.
[19]    Bour O, Davy P. Connectivity of random fault networks following a power law fault length distribution. Water Resour Res 1997;33:1567–83. doi:10.1029/96WR00433.
[20]    Bour O, Davy P. On the connectivity of three-dimensional fault networks. Water Resour Res 1998;34:2611–22. doi:10.1029/98WR01861.
[21]    Darcel C, Bour O, Davy P, de Dreuzy JR. Connectivity properties of two-dimensional fracture networks with stochastic fractal correlation. Water Resour Res 2003;39. doi:10.1029/2002WR001628.
[22]    Xu C, Dowd PA, Mardia K V., Fowell RJ. A Connectivity Index for Discrete Fracture Networks. Math Geol 2007;38:611–34. doi:10.1007/s11004-006-9029-9.
[23]    Xu C, Dowd PA, Mohais R. Connectivity analysis of the Habanero enhanced geothermal system. Proceeding, 37-th Work. Geotherm. Reserv. Eng. Stanford Univ. Stanford, Calif., 2012.
[24]    Alghalandis YF, Dowd PA, Xu C. Connectivity Field: a Measure for Characterising Fracture Networks. Math Geosci 2015;47:63–83. doi:10.1007/s11004-014-9520-7.
[25]    He J, Chen S, Shahrour I. Back Analysis of Equivalent Permeability Tensor for Fractured Rock Masses from Packer Tests. Rock Mech Rock Eng 2011;44:491–6. doi:10.1007/s00603-011-0149-2.
[26]    Benardos AG, Kaliampakos DC. Modelling TBM performance with artificial neural networks. Tunn Undergr Sp Technol 2004;19:597–605. doi:10.1016/j.tust.2004.02.128.
[27]    Bowden GJ, Dandy GC, Maier HR. Input determination for neural network models in water resources applications. Part 1—background and methodology. J Hydrol 2005;301:75–92. doi:10.1016/j.jhydrol.2004.06.021.
[28]    Kingston GB, Maier HR, Lambert MF. Bayesian model selection applied to artificial neural networks used for water resources modeling. Water Resour Res 2008;44. doi:10.1029/2007WR006155.
[29]    Kung TC, Hsiao CL, Schuster M, Juang CH. A neural network approach to estimating excavation-induced wall deflection in soft clays. Comput Geotech 2007;34:385–96.
[30]    Kim CY, Bae GJ, Hong SW, Park CH, Moon HK, Shin HS. Neural network based prediction of ground surface settlements due to tunnelling. Comput Geotech 2001;28:517–47. doi:10.1016/S0266-352X(01)00011-8.
[31]    Padmini D, Ilamparuthi K, Sudheer KP. Ultimate bearing capacity prediction of shallow foundations on cohesionless soils using neurofuzzy models. Comput Geotech 2008;35:33–46. doi:10.1016/j.compgeo.2007.03.001.
[32]    Kulatilake PHSW, Qiong W, Hudaverdi T, Kuzu C. Mean particle size prediction in rock blast fragmentation using neural networks. Eng Geol 2010;114:298–311. doi:10.1016/j.enggeo.2010.05.008.
[33]    Monjezi M, Amiri H, Farrokhi A, Goshtasbi K. Prediction of Rock Fragmentation Due to Blasting in Sarcheshmeh Copper Mine Using Artificial Neural Networks. Geotech Geol Eng 2010;28:423–30. doi:10.1007/s10706-010-9302-z.
[34]    Nejati HR, Ghazvinian A, Moosavi SA, Sarfarazi V. On the use of the RMR system for estimation of rock mass deformation modulus. Bull Eng Geol Environ 2014;73:531–40. doi:10.1007/s10064-013-0522-3.
[35]    Gokceoglu C, Sonmez H, Kayabasi A. Predicting the deformation moduli of rock masses. Int J Rock Mech Min Sci 2003;40:701–10. doi:10.1016/S1365-1609(03)00062-5.
[36]    Fausett L V. Fundamentals of neural networks: architectures, algorithms, and applications, Prentice-Hall, Englewood Cliffs, New Jersey. Prentice-hall Englewood Cliffs; 1994.
[37]    Demuth H, Beale M, Hagan M. Neural Network Toolbox for use with MATLAB. User’s Guid Version 5 MathWorks, Inc 2015.
[38]    Shahin MA. State-of-the-art review of some artificial intelligence applications in pile foundations. Geosci Front 2016;7:33–44. doi:10.1016/j.gsf.2014.10.002.
[39]    Zurada JM. Introduction to artificial neural systems. West Publishing Company, St. Paul; 1992.
[40]    Zheng J, Deng J, Zhang G, Yang X. Validation of Monte Carlo simulation for discontinuity locations in space. Comput Geotech 2015;67:103–9. doi:10.1016/j.compgeo.2015.02.016.
[41]    Rouleau A, Gale JE. Statistical characterization of the fracture system in the Stripa granite, Sweden. Int J Rock Mech Min Sci Geomech Abstr 1985;22:353–67. doi:10.1016/0148-9062(85)90001-4.
[42]    Leung CTO, Zimmerman RW. Estimating the Hydraulic Conductivity of Two-Dimensional Fracture Networks Using Network Geometric Properties. Transp Porous Media 2012;93:777–97. doi:10.1007/s11242-012-9982-3.
[43]    Kemeny J, Post R. Estimating three-dimensional rock discontinuity orientation from digital images of fracture traces. Comput Geosci 2003;29:65–77. doi:10.1016/S0098-3004(02)00106-1.
[44]    Baghbanan A. Scale and stress effects on hydro-mechanical properties of fractured rock masses, Ph. D. Dissertation, KTH land and water Resources Engineering, Swede. KTH, 2008.