Excavation Damaged Zone - 1...CLAYS IN NATURAL & ENGINEERED BARRIERS FOR RADIOACTIVE WASTE...

Session 9

Excavation Damaged Zone - 1Chair: Peter Blumling / Jean-François Aranyossy

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Page 137INTERNATIONAL MEETING, SEPTEMBER 17...>...18, 2007, LILLE, FRANCECLAYS IN NATURAL & ENGINEERED BARRIERSFOR RADIOACTIVE WASTE CONFINEMENT

AUTOCHTHONOUS AND COLONIZINGMICROORGANISMS IN ARGILLACEOUS

UNDERGROUND ENVIRONMENTSS. Poulain1,2, C. Sergeant1, C. Le Marrec3, M.-H. Vesvres1, A. Vinsot4,

S. Dewonck4, M. Simonoff1, S. Altmann2

1. University of Bordeaux I and II/CNRS and GdR FORPRO 0788, Nuclear Analytical and Bio-environmental Chemistry, B.P.120, F-33175 Gradignan cedex, France([email protected])

2. National Agency for Radioactive Waste Management (ANDRA),1/7 Rue Jean Monnet, F-92298Châtenay-Malabry cedex, France

3. ISTAB, University of Bordeaux I/INRA, UMR Oenologie - ISVV, F-33405 Talence cedex, France4. ANDRA, Laboratoire de recherche souterrain de Meuse/Haute-Marne, BP9, F-55290 Bure

INTRODUCTIONFeasibility of geological repositories for high activity and long-lived radioactive waste in argillaceousformations relies on the ability for the host rock to limit radionuclide transfer through the geosphere andwithin the biosphere for hundreds of thousands years. Considering that autochthonous or colonizingmicroorganisms may influence radionuclide chemistry and migration in these environments by catalyzingtheir chemical form transformation, the potential presence of microorganisms was investigated inundisturbed Opalinus Clay (Mont Terri, Switzerland) and Callovo-Oxfordian argilite (Meuse/Haute-Marne,France) samples. In addition, colonizing microbes have been identified at the Meuse/Haute-MarneUnderground Research Laboratory (URL).

METHODSSamples dedicated to detection of autochthonous cells were recovered under aseptic conditions from PC-C (Opalinus Clay), PAC2001 and PAC2002 (Callovo-Oxfordian) cores by nitrogen drilling, withpreliminary decontamination of drilling equipment. Colonizing microorganisms were collected in theMeuse/Haute-Marne URL by exposing solidified cultivation media to ambient air, and by scrapping offgallery wall surfaces at different times after excavation. Circulating water samples were also recoveredfrom geochemical experiments in boreholes PAC2001 (Vinsot and Mettler, 2005) and DIR1001, DIR1002,DIR1003 (Dewonck, 2005) for characterization ofmicrobial contamination and indigenous cellspotentially originating from the geological Callovo-Oxfordian formation.

Microbial identifications were based on ribosomalDNA (rDNA) sequencing of cells grown oncultivation media of diverse compositions, andadditional characterization was completed by electronmicroscopy observations and phylogenetic analyses,in order to determine if, from an evolutionary point ofview, DNA sequences of isolates could support thehypothesis of their origin.

RESULTS AND DISCUSSIONFor the first time, a double molecular biology and cultivation-based approach indicated the presence of afew sparse autochthonous cells in the Opalinus Clay. DNA sequencing suggested the isolation of at leasttwo unknown bacterial species related to genera Sphingomonas and Alicyclobacillus (less than 97% 16SrDNA sequence similarity with validly published sequences). Phylogenetic analyses indicated that an early

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Page 138 INTERNATIONAL MEETING, SEPTEMBER 17...>...18, 2007, LILLE, FRANCECLAYS IN NATURAL & ENGINEERED BARRIERS

FOR RADIOACTIVE WASTE CONFINEMENT

genetic divergence, occurring after physical isolation of bacterial ancestors in the geosphere by thesedimentation process, may have resulted in the generation of particular taxa in the subsurface. The sameexperimental procedure did not result in the detection of any indigenous microorganism in undisturbedCallovo-Oxfordian argilite samples, which suggest that cell density is there inferior to microbialconcentration in the Opalinus Clay, or that our methods (enrichment media, DNA detection) are for themoment unsuited for microbial exploration of this formation.

The FORPRO EDZ(Excavation Damaged Zone) Interdisciplinary Observatory initiative allowed us toisolate numerous bacterial and fungal strains from air and wall clay samples, 48 hours after excavation, andthen after exposition to ambient atmosphere, ventilation and human activity in the laboratory for 3, 6, 9and 18 months. A microbial collection was assembled, and most isolates could be identified by rDNAsequencing. These experiments indicated a regular and massive introduction of microorganisms in theunderground environment of Meuse/Haute-Marne laboratory, and suggested that a minority of cultivablemicroorganisms are highly prevailing on argilite surfaces.

Microbial monitoring of geochemical experiments PAC 2001 and DIR1001, DIR1002 and DIR1003indicated that microbial contamination occurred at different levels along the experimental procedure.Although microbial precautions were taken regarding exogenous introduction, several microbial specieswere brought in experimental intervals through the synthetic water injected into the boreholes, or bycontamination of the circulation equipment before starting the experiments. Nevertheless, particularmicrobial strains showed a genetic singularity suggesting that autochthonous species may have beenbrought by the Callovo-Oxfordian itself.

ReferencesPoulain S., (2006). Caractérisation microbiologique de l’argile à Opalinus du Mont Terri et de l’argilite duCallovo-Oxfordien de Meuse/Haute-Marne. Thesis Univ. Bordeaux I, (FORPRO n°2006/18)

Stroes-Gascoyne, S., Schippers, A., Schwyn, B., Poulain, S., Sergeant, C., Le Marrec, C., Simonoff, M.,Altmann, S., Nagaoka, T., Mauclaire, L., Mckenzie, J. A., Daumas, S., Vinsot, A., Beaucaire, C. &Matray, J.-M. (2007).Microbial community analysis of Opalinus Clay drill core samples from theMontTerri URL, Switzerland. Geomicrobiology Journal 24:1-17.

Poulain, S., Sergeant, C., Le Marrec, C., Simonoff, M. & Altmann, S. (2007): Opalinus Clay, anargillaceous formation under evaluation for radioactive waste repository, contains viable, potentiallyancient microbial cells. Submitted to Environmental Microbiology (FORPRO n°2006/17 A).

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DISCRETE FRACTURE NETWORKMODELLING OF THE HG-A EXPERIMENT

AT THE MONT TERRI ROCK LABORATORYG.W. Lanyon1, P. Marschall2, T. Vietor2

1. Fracture Systems Ltd, Tregurrian, Ayr, St Ives, Cornwall, UK ([email protected])2. NAGRA - National Cooperative for the Disposal of Radioactive Waste, Hardstrasse 73, CH 5430

Wettingen, Switzerland ([email protected])

INTRODUCTIONIn low permeability rocks, such as the Opalinus Clay (NAGRA 2002) of Northern Switzerland, fracturesin the Excavation Damage Zone (EDZ) around emplacement tunnels create a network of discrete pathwaysthat may enhance fluid migration. This abstract describes work to develop discrete fracture network (DFN)models of the EDZ around the HG-A microtunnel at the Mont Terri underground research laboratory. TheHG-A experiment focuses on water and gas flow through the EDZ and is currently in progress. The HG-A experiment is described in detail in the paper by Marschall et al (2006). Its aims are:

• Demonstration of the self-sealing capacity of the EDZ around a sealed disposal tunnel.

• Demonstration of gas escape from a sealed disposal tunnel .

• Estimation of gas transport properties of the Opalinus clay on the tunnel scale.

DFN MODELSThe DFN models follow on from those described in Lanyon et al (2005) of the EDZ around emplacementtunnels in a proposed repository in the Opalinus Clay and have been developed using data from geologicalmapping of borehole cores and tunnel surfaces together with predictions from geomechanical models.

The DFN models of the rock around the HG-A microtunnel contain features representing:

• pre-existing structures (healed faults and fractures) that have been reactivated by the excavation process;and

• induced structures - unloading joints and shear surfaces (largely due to bedding slip).

Figure 1: Schematic of HG-A micro tunnel with a total length of 13 m, comprising a backfilled test section(yellow), a seal section with the megapacker (green) and a steel liner (red).

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The extent of the EDZ within the DFN models is based on geomechanical simulations of the excavationprocess using the FLAC3D code (Itasca 2005). The predictions of the FLAC3D model have been comparedwith observations from core and tunnel mapping.

Water injection tests into the backfilled test section were simulated with the DFN model. Figure 2 showsthe predicted pressure change at an injection pressure of 2 bar (differential pressure). The development ofthe flow field along the EDZ occurs relatively quickly (~10 hours) however pressure responses do notdevelop in monitoring boreholes (located in the intact rock at 1.1-1.7 m from the microtunnel) for ~100sof days. The connection from the EDZ to the monitoring boreholes is represented within the models byuniform low permeability planes that extend from the EDZ to the borehole intervals (clearly seen in Figure2b). Calibrations of the DFN models to the observed pressure responses to hydraulic testing wereconducted. Furthermore the influence of the inflation of the “megapacker” on the hydraulics of the EDZ(fracture opening/closure) was examined using the loosely coupled scheme applied to the models ofemplacement tunnels in Lanyon et al (2005).

References:Itasca (2005). FLAC3D, Fast Lagrangian Analysis of Continuea in 3 Dimensions, Version 3.0. ItascaConsulting Group, Minneapolis, Minnesota.

Lanyon G.W., Marschall, P., Blümling,P (2005). Modelling of Groundwater Flow along the ExcavationDamage Zone of a tunnel in the Opalinus Clay. 2nd meeting on Clays in natural and engineered barriersfor radioactive waste confinement, Tour 2005.

Marschall, P., Distinguin, M., Shao, H., Bossart, P., Enachescu, C., Trick, T. (2006). Creation andEvolution of Damage Zones Around a Microtunnel in a Claystone Formation of the Swiss JuraMountains. SPE Paper 98537-PP.

NAGRA (2002). Projekt Opalinuston – Synthese der geowissenschaftlichen Untersuchungsergebnisse.Entsorgungs-nachweis für abgebrannte Brennelemente, verglaste hochaktive sowie langlebigemittelaktive Abfälle. Nagra Technical Report NTB 02-03. Nagra, Wettingen, Switzerland.

Figure 2: DFN model of hydraulic test. Fractures coloured by change in pressure. Only fractures wheredP>0.5 kPa at a) time~10 hours and b) t~100 days show.

a) b)

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DISCRETE MODELLING OF DRIFTBEHAVIOUR IN THEMEUSE/HAUTE-MARNE

URL (FRANCE)

C. Bourdeau1, F. Dedecker1, D. Billaux1

1. ITASCA Consultants, S.A.S., 64 Chemin des Mouilles, FR 69134 Ecully Cedex, France([email protected])

INTRODUCTIONThe French national radioactivewaste management agency, ANDRA, has built an underground experimentallaboratory in Callovo-Oxfordian argillite at a depth of 490meters to study the feasibility of thismaterial as ahost formation of deep radioactive wastes disposal. A the present time, the experimental drifts drilled at themain level (-490 m) show the development of major damage zones in shear, tensile and mixed modes bothahead and behind the excavation front (Figure 1). Indeed, excavating part of the rock causes a redistributionof the stress field around the excavation that can lead to micro-cracking and even to the failure of some rockvolume in the vicinity of the shaft/drift. In order to be able to foresee the fracture network, to understand theorigin of such damage around the excavation and to identify the main factors controlling the frequency andproperties of the fractures, discrete modeling of drift excavation is realized.

NUMERICAL CONCEPTITASCA Consultants, S.A.S. created discontinuum models with the PFC3D software (developed by Itasca)to study rock damage by building particle assemblies bonded together at contacts and checking thebreakage of bonds under stress. Indeed, fracturing occurs via bond breakage either in tensile or shear modewhenever the magnitude of the tensile/shear contact force equals or exceeds the normal/shear contact bondstrength.

Such models are limited in size because of the very large number of particles needed to model even acomparatively small volume of rock. Thus, we used a coupled, three-dimensional, continuum /discontinuum modelling approach, recently developed by Itasca (Billaux et al., 2004). This new approach,termed Adaptive Continuum/Discontinuum Code (AC/DC), is based on the use of a periodic discontinuum‘‘base brick’’ for which more or less simplified continuum equivalents are derived. Depending on the levelof strain in each part of the model, the AC/DC code can dynamically select the appropriate brick type tobe used.

Figure 1: Conceptual model of the damage zones around the drift at 490 m depth.

σH

σhσH

σh

σv

σv

shear

failure

limit of the fractured

zone due to destressing

tensile and/or

mixed (shear +

tensile) failures

limit of the fractured zone

due to destressing

shear

failure

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RESULTS AND INTERPRETATIONIn the first part of the paper, we will describe the particle model developed to reproduce the short-termbehavior of the Callovo-Oxfordian argillite as well as the calibration process used to define the short-termparameters. Then, we will present the numerical models built to simulate shaft excavation. Taking intoaccount the principal stress orientation applied along the shaft axis and perpendicular to the shaft axis aswell as its geometry (horseshoe-shaped), we reduced the size of the numerical model by considering onlyhalf of it. We created two numerical models of the drift: the first one was dug along the minor principalstress direction while the second one was dug along the major principal stress direction. A minimum ofsix one-meter-length excavations was performed in order to develop a repetitive failure pattern all alongthe drift. Finally, the results obtained on both models were compared to field observations andmeasurements in terms of fractured zones (Dedecker et al., 2006) as well as evolution of convergencemeasurements versus time.

ReferencesDedecker, F., Cundall P., Billaux D. & Gröeger T. (2006): “Evaluation of Damage-induced permeabilityusing a three dimensional Adaptive Continuum / Discontinuum Code”, Physics and Chemistry of theEarth (2006), doi:10.1016/j.pce.2006.01.006.

Billaux, D., Dedecker F. & Cundall P. (2004): “A novel approach to studying rock damage: the threedimensional Adaptive Continuum / Discontinuum Code,” Proceedings of EUROCK 2004 & 53rdGeomechanics Colloquium, pp. 723-728, Ed. Schubert, 2004.

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FRACTURATION IN CALLOVO-OXFORDIANARGILLITE UNDER TRIAXIAL

COMPRESSION STUDIEDBY X-RAY MICROTOMOGRAPHY

N. Lenoir1,2, J. Desrues1, G. Viggiani1, P. Bésuelle1, M. Bornert3, J.D. Barnichon2

1. Laboratoire 3S-R – Sols Solides Structures-Risques, Domaine Universitaire BP53, 38041Grenoble, France ([email protected])

2. ANDRA, Parc de la Croix Blanche, 1/7 rue Jean Monnet, 92298 Châtenay-Malabry, France([email protected])

3. LMS – Laboratoire de Mécanique des Solides, Ecole Polytechnique 91128 Palaiseau, France([email protected])

INTRODUCTIONThe technique of X-ray computed tomography (CT) allows non destructive imaging and quantification ofinternal features of bulk objects. Within the framework of feasibility studies of underground repositoriesfor radioactive waste, the study of the permeability evolution of the host layer induced by fracturation inthe EDZ requires accurate experimental information on the mechanisms of crack formation. An originaltriaxial device has been developed to characterize damage in Callovo-Oxfordian argillite under deviatoricloading, with X-ray micro tomography on a synchrotron beamline at the European Synchrotron RadiationFacility (ESRF, France). A set of tests under has been performed on specimens issued from the boreholeEST261 (depth 476m) of the Underground Research Laboratory of Bure (France). This paper presents mainresults obtained from a triaxial test performed at 10 MPa confining stress.

EXPERIMENTAL SET-UPThe triaxial apparatus designed specifically for this program includes a small triaxial cell and a loadingframe. It has the same functions as a conventional triaxial testing system, except for several importantdetails : i) a much smaller size, ii) a special design of the confining cell, which has to be transparent tothe X-rays and iii) a special design of the loading frame, with no reaction rods crossing the X-Ray beam[Lenoir 2006]. The rock specimen is a cylinder with height twice the diameter (20 and 10 mm,respectively). A total of four triaxial compression tests were performed, at three different values ofconfining stress (1, 5 and 10 MPa). The tests were carried out under undrained conditions. Specimens wereentirely scanned at different steps of the test. The spatial resolution of the recorded X-ray slices i.e. thevoxel size was 14×14×14µm3.

RESULTS AND INTERPRETATIONDirect observation of X-ray micro tomography images allows for immediately detecting volumetric strain,since dilation (contraction) corresponds to a change of mass density, which in turn results in a decrease(increase) of X-ray attenuation. However, as far as shear (deviatoric) strain is concerned, this does notnecessarily induce any volume change and therefore it cannot be directly detected by measuring changesin X-ray attenuation. In this study, we have used a more general approach for obtaining the distribution ofboth the volumetric and deviatoric components of strain increment between two reconstructions of aspecimen at two different steps of deformation. Tomography images were subsequently analyzed using aVolumetric Digital Image Correlation code developed at the Laboratoire de Mécanique des Solides (LMS)in Palaiseau, France [Lenoir et al. 2007]. Full-field incremental strain measurements were obtained, whichallow to detect the onset of shear strain localization and to characterize its development in a 3D complexpattern. The results are illustrated on the example of a test performed at 10 MPa confining stress. Figure1 shows a vertical cut along the axis of the specimen with the deviatoric incremental strain obtained at theimmediate post-peak increment (left) and the tomographic image obtained at the end of this increment

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(right). On the deviatoric incremental strain field, strain localization is distinctly showed as a narrow zoneof intense shear strain in the lower part of the specimen, while a direct examination of the tomographicimage hardly reveals any trace of localized deformation. Volumetric Digital Image Correlation revealspatterns which cannot be directly observed from the original tomographic images, because the deformationprocess in the zones of localized deformation was essentially isochoric (i.e., without volumetric strain),hence not associated to density changes.

CONCLUSIONLocalized damage and its evolution have been characterized at a fine scale (of order of one hundredmicrons). Digital image correlation techniques, extended to three-dimensional images, have been used tomeasure incremental strain fields from tomographic images. According to the results obtained, thefollowing scenario is proposed: the damage (localized deformation) initiates just before the peak of thedeviatoric stress with a concentration of intense shear strain in a narrow zone of the specimen. Then, thelocalized zone fully develops after the deviatoric stress peak. With increasing axial strain, some zones ofopen crack are created and develop (in length and width) along zones previously dilating. However, it ismainly when the mean stress is decreased to zero that the cracks are found to open significantly in modeI; before this step, they are mode II cracks with limited opening [Bésuelle et al. 2006].

ReferencesLenoir N., Bornert M., Desrues J., Bésuelle P. and Viggiani G. (2007): “Volumetric digital imagecorrelation applied to X-ray microtomography images from triaxial compression tests on argillaceousrock”, Strain, Blackwell, in print.

Bésuelle P., Viggiani G., Lenoir N., Desrues J. and Bornert M. (2006): “X-ray Micro CT for StudyingStrain Localization in Clay Rocks Under Triaxial Compression”, Advances in X-ray Tomography forGeomaterials, ISTE Ltd, pp. 35-52.

Lenoir N. (2006), “Mechanical behavior and rupture of clayey rocks studied by X-ray micro tomography”,PhD dissertation, University ofGrenoble I, in French, available online http://tel.ccsd.cnrs.fr/tel-00011996.

Figure 1: Vertical cut along the axis of the specimen. Left: Deviatoric strain during the post-peakincrement; Right: tomographic cut at the end of the increment. The color scale covers the range : [0,0.15].

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A GENERAL REVIEW OF THE DAMAGEMODELS FOR THE EDZ CREATION

C. Arson1, B. Gatmiri1,2

1. CERMES, Ecole Nationale des Ponts et Chaussées, Cité Descartes, Champs-sur-Marne,6-8 avenue Blaise Pascal, 77455 Marne-la-Vallée cedex 2, France([email protected], [email protected])

2. University of Tehran, IRAN

INTRODUCTIONRisks of radionuclide transport have to be assessed in order to ensure the safety of nuclear wasterepositories. It is thus necessary to characterize the EDZ (Excavation Damaged Zone) surrounding storagegalleries. Two dissipation phenomena can occur in the rocks usually forming the geological barrier: plasticdeformation and fracturing. Plastic strains are generated by sliding microscopic mechanisms. Materialdamage grows with the size of micro-cracks. It would thus be restrictive to identify the plastic and thedamaged zones. Moreover, degraded material properties may be partially recovered by crack closure. Onthe contrary, plastic deformations are irreversible. Due to the complexity of the stress paths that can occurin the EDZ, it is impossible to model damage properly with a single scalar variable. The formulation alsohas to be non-local or gradient-enhanced to avoid localization problems. Last but not least, the theory mustbe thermodynamically consistent.

MICROMECHANICAL DAMAGE MODELSMicromechanical approaches consist in modelling the influence of local damage on the macro-mechanicalbehaviour. The interference of micro-cracks may be taken into account. Damage variables have a physicalmeaning related to the degradation of elastic properties or to the characteristics of the fracture network. Itis assumed that stresses are redistributed due to a decrease of the effective material area. Stress-strainrelationships are thus written in terms of effective variables. Since the micromechanical methods updatemacro-data using micro-data, the theory is non-local.

In differential formulations, a state variable is generally replaced by the first terms of the Taylor series ofthe corresponding averaged quantity, leading to the introduction of a second-gradient in the constitutivelaws. The weighing coefficient of the gradient term depends on a material length related to the dimensionof the zone of influence of local damage.

In integral formulations, it is possible to use non-constant functions of the distance of influence.Constitutive relations are expressed in terms of average state variables. The use of decreasing weighingfunctions allows calculating the averaging integral on the whole volume of the system. Therefore, it is notnecessary to define representative volume elements explicitly, because homogeneization is alreadyincluded in the computation process.

ENERGETIC APPROACH OF DAMAGEThe phenomenological models stem from energetic considerations. The free energy of Gibbs is given aspecific expression, which must be consistent with the assumed elastoplastic behaviour law. Theconstrained problem of maximum dissipation is solved by introducing Lagrangian coefficients playing therole of plastic multipliers. These coefficients can be computed by means of the consistency equations.Solving the Lagrangian minimisation problem provides the behaviour, flowing, and hardening/softeninglaws. Phenomenological formulations are automatically thermodynamically consistent, which simplifiesthe determination of the damage evolution laws. If the length scale associated with the loading systems isclose to the internal length scale of the material, the problem becomes ill-posed and shear bands cannot belocalized in the post-bifurcation regime.

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To solve this localization problem (Lorentz and Andrieux, 1999), gradient-enhanced formulations havebeen used in some damage models, and in plasticity models coupled to damage. Contrary to the averaginggradients used in micromechanical formulations, the introduced space-gradients enrich the description ofthe continuum by considering its microstructure.

Provided that localization phenomena are mainly caused by strain softening, some authors have replacedthe gradient term to be introduced in the expression of the free energy by a term representing residualdeformations (Homand-Etienne et al., 1998 ; Shao et al., 2005).

In some formulations combining micromechanical and phenomenological aspects, an equivalent state isintroduced to suppress the dependency of damage on macroscopic strains (Swoboda and Yang, 1999). Onthe one hand, this equivalent state plays the same role as the spatial configuration introduced in gradient-enhanced plasticity models, and represents the microstructure of the medium. On the other hand, theenergy-based formulation is automatically thermodynamically consistent.

HYDRAULIC PROPERTIES OF A FRACTURED POROUS MEDIUMThe alteration of flow properties due to damage has been equated in Continuous Damage Mechanicsmodels (CDM models), involving a single continuum. Such single-porosity models assume that thespatially variable distribution of hydraulic properties originates preferential pathways. Multi-permeabilityapproaches require at least two sets of flow properties, for the porous matrix and the active connectedfracture network respectively. Due to capillarity effects, the fluid generally flows from the fractures to theporous matrix. These matrix/fracture interactions are represented by a transfer coefficient, modellingexchange flux in Richard’s equation (Gerke and Van Genuchten, 1993 ; Gwo et al., 1995 ; Zimmerman etal., 1996). Authors often resort to the Van Genuchten expressions of capillarity pressure and permeabilityto formulate their constitutive model (Van Genuchten, 1980).

Only flow properties of fractured unsaturated media are taken into account in multi-porosity or multi-permeability models. Mechanical damaging is related to the crack initiation in the matrix and to the growthof the existing fractures. A dual-continuum approach for mechanical aspects of damage would thus implycomplex coupled equations. However, if a single-continuum approach is used, it must be assumed thatfractures can be considered as large-sized pores.

To the authors’ knowledge, the degradation of the stiffness related to suction with the fracture aperture hasnever been formulated. In the coupled hydro-mechanical model of Shao (Shao et al., 2005), the influenceof damage bears only on the mechanical part of stresses. This concept cannot hold if the effective stressesdefined in Biot’s theory are replaced by net stresses.

ReferencesGerke, Van Genuchten, 1993, “Evaluation of a first-order water transfer term for variably saturated dual-porosity flow models”, Water Resources Research, 29, 4, 1225-1238

Gwo, Jardine, Wilson, Yeh, 1995, “A multiple-pore-region concept to modeling mass transfer in subsurfacemedia”, Journal of Hydrology, 164, 217-237

Homand-Etienne, Hoxha, Shao, 1998, “A continuum damage constitutive law for brittle rocks”, Computersand Geotechnics, 22, 2, 135-151

Lorentz, Andrieux, 1999, “A variational formulation for nonlocal damage models”, Int. J. of Plasticity, 15,119-138

Shao, Ata, Ozanam, 2005, “Study of desaturation and resaturation in brittle rock with anisotropic damage”,Engineering Geology, 81, 341-352

Swoboda, Yang, 1999, “An energy-based damage model of geomaterials. I. Formulation and numericalresults”, Int. J. Solids and Struct., 36, 1719-1734

Van Genuchten, 1980, “A closed-form equation for predicting the hydraulic conductivity of unsaturatedsoils”, Soil Science Society of America Journal, 44, 892-898

Zimmerman, Hadgu, Bodvarsson, 1996, “A new lumped-parameter model for flow in unsaturated dual-porosity media”, Advances in Water Resources, 19, 5, 317-327

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