Introducing a MATLAB Code as a Statistical Approach for Fracture Networks Modelling

Document Type : Research Paper


1 1:School of Mining, College of Engineering, University of Tehran, Iran 2:Mine Environment and Hydrogeology Research Laboratory (MEHR Lab), University of Tehran, Iran

2 Mine Environment and Hydrogeology Research Laboratory (MEHR Lab), University of Tehran, Iran


Fracture network modeling is important in simulating fluid flow, identifying reservoir storage areas, recognizing aquifers, and managing the groundwater pathway to prevent wall failure in mine stability consideration. In other words, precise estimation of mass transport and hydrology parameters depends on the accuracy of fracture modeling. This study presents a new iterative fracture network-modeling MATLAB code that directly models the statistical geometry of the fractures. The code is employed to simulate the parameters of fractures in terms of density, orientation, and length distribution. The method is applied to a real 2-Dimensional fracture network image from an exposed wall to demonstrate the effectiveness of the presented code. Its performance is assessed by three criteria, including fracture length distribution, producing fracture orientation, and fracture density. According to the assessment results, the statistical method can reproduce the length distribution and density of the fracture network similar to the reference. In addition, the method performs almost well in modeling the orientation of fractures. 


  1. Berkowitz B (2002) Characterizing flow and transport in fractured geological media: A Review (25), Advances in Water Resources, 25, 8-12: 861-884,
  2. Rzonca B (2008) Carbonate aquifers with hydraulically non-active matrix: A case study from Poland, Journal of Hydrology, 355, 1-4: 202-213, ##
  3. Wang X, Jardani A, Jourde H, Lonergan L, Cosgrove J, Gosselin O, Massonnat G (2016) Characterisation of the transmissivity field of a fractured and karstic aquifer, southern France, Advances in Water Resources 87: 106–121, ##
  4. Agar S, Geiger S (2015) Fundamental controls on fluid flow in carbonates: Current workflows to emerging technologies, Geological Society London Special Publications, 406, 1: 1-59. ##
  5. Lamarchea J, Lavenua P C, Gauthierc B D M, GuglielmiaY, Jayet O (2012) Relationships between fracture patterns, geodynamics and mechanical stratigraphy in Carbonates (South-East Basin, France), Tectonophysics, 581:, 231–245. ##
  6. Prabhakaran R, Bruna P, Bertotti G, Smeulders D (2019) An automated fracture trace detection technique using the complex shearlet transform, Solid Earth, 10, 6: 2137-2166, ##
  7. Zhang F, Damjanac B, Maxwell S (2019) Investigating hydraulic fracturing complexity in naturally fractured rock masses using fully coupled multiscale numerical modelling, Rock Mechanics and Rock Engineering, 52, 5137–5160, ##
  8. Bisdom K, Nick H M, Bertotti G (2017) An integrated workflow for stress and flow modelling using outcrop-derived discrete fracture networks, Computers and Geosciences, 103: 21-35, ##
  9. Dutler N, Valley B, Gischig V, Villiger L, Krietsch H, Doetsch J, Brixel B, Jalali M, Amann F (2019) Hydraulic fracture propagation in a heterogeneous stress field, Solid Earth, 10: 1877–1904, ##
  10. Ngo T D, Fourno A, Noetinger B (2017) Modelling of transport processes through large-scale discrete fracture networks using conforming meshes and open-source software, Journal of Hydrology, 554: 66-79, ##
  11. Masihi M, King P R (2007) A correlated fracture network: Modelling and percolation properties, Water Resources Research, 43: 7, ##
  12. Wilson M, Grutzik S, Chandross M (2019) Continuum stress intensity factors from atomistic fracture simulations, Computer Methods in Applied Mechanics and Engineering, 354: 732-749, ##
  13. Watkins H, Butler R W H, Bond C E, Healy D (2015) Influence of structural position on fracture networks in the Torridon Group, Achnashellach fold and thrust belt, NW Scotland, Structural Geology, 74: 64–80, ##
  14. Su N, Zou L, Shen X, Guo F, Ren Y, Xie Y, Li J, Wu J (2014) Fracture patterns in successive folding in the western Sichuan basin, China, Asian Earth Science, 81, 65–76,
  15. Lacazette A (2009) Paleostress analysis from image logs using pinnate joints as slip indicators, American Association of Petroleum Geologists Bulletin, 93: 1489–1501, ##
  16. Prioul R, Jocker J (2009) Fracture characterization at multiple scales using borehole images, sonic logs, and walkaround vertical seismic profile, American Association of Petroleum Geologists Bulletin, 93: 11 1503–1516, ##
  17. Hart B S (2006) Seismic expression of fracture-swarm sweet spots, Upper Cretaceous tight-gas reservoirs, San Juan Basin, American Association of Petroleum Geologists Bulletin, 90: 1519–1534, ##
  18. Lohr T, Krawczyk C M, Tanner D C, Samiee R, Endres H, Thierer P O, Oncken O, Trappe H, Bachmann R, Kukla P A (2008) Prediction of subseismic faults and fractures: integration of three-dimensional seismic data, three-dimensional retrode, American Association of Petroleum Geologists Bulletin, 92: 4: 473-485, ##
  19. Masaferro J L, Bulnes M, Poblet J, Casson N (2003) Kinematic evolution and fracture prediction of the Valle Morado structure inferred from 3-D seismic data, Salta province, northwest Argentina, American Association of Petroleum Geologists Bulletin, 87: 1083–1104, ##
  20. Shakiba S, Asghari O, Keshavarz Faraj Khahb N, Zabihi S, Tokhmechi B (2015) Fault and non-fault areas detection based on seismic data through min/max autocorrelation factors and fuzzy classification, Journal of Natural Gas Science and Engineering, 26: 51-60, ##
  21. Assteerawatt A, Hægland H, Helmig R, Bárdossy A, Dahle H K (2019) Simulation of flow and transport processes in a discrete fracture-matrix system I. geostatistical generation of fractures on an aquifer analogue scale, Water Resources Research, Impressed paper. ##
  22. Shah S, Møyner O, Tenea M, Lie K, Hajibeygi H (2016) The multiscale restriction smoothed basis method for fractured porous media (F-MsRSB), Journal of Computational Physics, 318: 36-57,
  23. Guardiano F, Srivastava M (1993) Multivariate geostatistics: Beyond bivariate moments, Geostatistics-Troia, 133-144, doi: 10.1007/978-94-011-1739-5_12.##
  24. Lepillier B, Bruna P, Bruhn D, Bastesen E, Daniilidis A, Garcia Ó Torabi A, Wheeler W (2020) From outcrop scanlines to discrete fracture networks, an integrative workflow, Journal of Structural Geology, 133, Lepillier B, Bruna P, Bruhn D, Bastesen E, Daniilidis A, Garcia Ó Torabi A, Wheeler W (2020) From outcrop scanlines to discrete fracture networks, an integrative workflow, Journal of Structural Geology, 133,
  25. Shakiba S, Doulati Ardejani F (2022) A comparative study of novel object-based geostatistical algorithm and direct sampling method on fracture network modeling, Stochastic Environmental Research and Risk Assessment, 1-17, doi: 10.22078/PR.2022.4960.3210.##
  26. Mariethoz G, Renard P, Straubhaar J (2010) The Direct Sampling method to perform multiple‐point, Water Resources Research, 46: 11536,
  27. Mahmoodpour S, Masihi M (2016) An improved simulated annealing algorithm in fracture network modelling, Journal of Natural Gas Science and Engineering, 33: 538-550,