Isam Shahoor

Numerical estimation and prediction of stress-dependent permeability tensor for fractured rock masses Ji He a,n , Sheng-hong Chen a,b , Isam Shahrour a,b a State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, 430072 Wuhan, China b Laboratoire Ge ńie Civil et ge ó-Environnement, University Lille 1, 59650 Villeneuve d’Ascq, France a r t i c l e i n f o Article hi story: Received 16 June 2011 Received in revised form 1 December 2012 Accepted 17 December 2012 Available online 19 January 2013 Keywords: Fractured rock Permeability tensor Hydro–mecha nical coupling Composite element method Discrete fracture network Artificial neural network a b s t r a c t The numerical experiment based on the Composite Element Method (CEM) is extended to study the stres s-dependent permeabili ty tens or for fractured rock masses. The CEM allows rock meshing regardless of fractures, and the fractures are automatically formulated with an explicit representation. An equivalent filled fracture model is introduced into the CEM to realize a hydro–mechanical coupling simulation for the numerical experiment. This model assumes the hydraulic properties both along and normal to the fracture plane dependent on the fracture normal stress with an exponential relation. Large numbers of rock specimens with different sizes and orientations are modeled and their hydro– mech anical coupl ing behaviors under various stress states are simul ated by the CEM. From the simulated results, the stress-dependent permeability tensors are calculated from the flow rates through the rock specimen boundaries. In order to predict the permeability tensor for any in situ stress state, a load/ perme ability databas e is deve loped using the Artifi cial Neur al Netwo rk (ANN) . The datab ase establishes the mapping from the stress state to the permeability tensor, based on the powerful data modeling capacity of the ANN. Inputting any in situ stress state into the database, the database output is the relevant permeability tensor predicted. The above algorithms are verified by comparison with an analytical solution and successfully used in a stochastic fracture system. & 2012 Elsevier Ltd. All rights reserved. 1. Intr oduc tion Hydr o–me chanic al coup ling in fract ured rock masses is an imp ortant issue. It is believed to res ult in a series of eve nts including dam failures, landslides, and injection-induced earth- quakes. The stress-dependency of fracture behavior is regarded as the main process during coupling [1]. Fractures often play the role of mec han ical wea kne sses and main flow pathways in roc k masses . The fracture ape rtu re can be signifi cantly change d due to bot h extern al loa ds and int ernal hyd rau lic pre ssures. The defo rmat ion of the fract ure aper ture leads to consi dera ble variation in hydraulic fracture behavior. With fractures distrib- uted anisotropically and heterogeneously, the hydraulic property of rock masses has complicated stress-dependency. The numeri cal met hod s for hyd rau lic fra cture simulatio n mainl y have two categ ories: an expl icit (or discr ete) approa ch [2,3] and an implicit (or equivalent continuum) approach [4–6]. The former realizes the geometry of fract ures individu ally and simulates their behavior s discr etel y, while the latter negle cts the exact posit ion of fra ctures and puts the ir eff ects int o the parameter of equivalent permeability tensor by regarding frac- tur ed rock mas ses as a con tin uum medium. App arentl y, the explicit approach is more accurate in fracture simulation. How- ever, if large quantities of fractures exist, the explicit approach is difficult and even impossible to be applied due to the problems such as comple x model ing, time-consumi ng calculation and diffic ult conve rgenc e. Cont raril y, the impl icit appr oach is more sui tab le for this case, and thus it is wid ely used in pract ice engineeri ng. The key issue to use the imp lic it app roach is to obtain the permeability tensor as well as the hydraulic Repre- sentative Elementary Volume (REV) of fractured rock masses. The REV existence is the prerequisite to regard fractured rock masses as a continuum medium [7] . If the hydraulic REV does not exist, the permeabil ity tenso r is mean ingles s to calcul ate. However, both of them are difficult to obtain due to the anisotropy and stress-dependency of hydraulic behavior in fractured rock masses. The expe rime ntal methods for the permeabil ity tenso r are mainly either a pumping test or a packer test. A highly hetero- geneous and anisotropic rock mass often requires a number of test wells placed in different directions and at different locations [8,9]. Such experiments are quite costly, but still have difficulty to dea l wit h the rock per meabil ity anisot rop y, let alone stress- depe ndenc y. Some analytic al solut ions were prop osed for the rocks containing orthogonal or continuous fractures in an attempt Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/ij rmms International Journal of Rock Mechanics & Mining Sciences 1365-1609 /$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijrmms.2012.12.001 n Corresponding author. Tel./fax: þ 86 27 6877 2086. E-mail address: [email protected] (J. He). International Journal of Rock Mechanics & Mining Sciences 59 (2013) 70–79

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Isam Shahoor