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Page 1: Hydro-Mechanical Processes 3...INTERNATIONAL MEETING, SEPTEMBER 17...>...18, 2007, LILLE, FRANCE CLAYS IN NATURAL & ENGINEERED BARRIERS FOR RADIOACTIVE WASTE CONFINEMENT

Session 12

Hydro-Mechanical Processes - 3Chair: Patrik Sellin / Charles Fairhurst

r

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Page 189INTERNATIONAL MEETING, SEPTEMBER 17...>...18, 2007, LILLE, FRANCECLAYS IN NATURAL & ENGINEERED BARRIERSFOR RADIOACTIVE WASTE CONFINEMENT

INSTALLATION AND EVALUATIONOF A LARGE-SCALE IN-SITU SHAFT SEAL

EXPERIMENT IN BOOM CLAY –THE RESEAL PROJECT

Van Geet M.1,a, Bastiaens W. 1, Volckaert G. 1, Weetjens E.1, Sillen X.1, Gens A.2,Villar M.V.3, Imbert Ch.4, Filippi M.5, Plas F.6

1. SCK-CEN, Waste & Disposal department, Boeretang 200, B-2400 Mol, BELGIUM a Currentlyat ONDRAF/NIRAS, Kunstlaan 14, B-1210 Brussel, BELGIUM

2. UPC, Gran Capitan s/n Edificio d-2, E-08034 Barcelona, SPAIN3. CIEMAT, Avd. Complutense 22, E-28040 Madrid, Spain4. CEA, DPC / SCCME / LECBA, F-91191 Gif-sur-Yvette Cedex, FRANCE5. CEA, DM2S / SFME / MTMS, F-91191 Gif-sur-Yvette Cedex, FRANCE6 ANDRA, Parc de la Croix Blanche, 1-7 Rue Jean Monnet, F-92298 Châtenay-Malabry Cedex,

FRANCE

Geological disposal of high-level radioactive waste and spent fuel is currently considered a safe solutionto ensure the long-term isolation from the biosphere. The backfilling and sealing of shafts and galleries isan essential part of underground repository designs. Any opening created during the repository constructionmight be a preferential pathway for water, gas and radionuclides migration. The demonstration of thefeasibility of the sealing on a representative scale is therefore essential. For more than 10 years theapplicability of highly compacted bentonite has been investigated for this purpose. The low permeabilityand high sorption capacity of bentonite make it a very effective barrier.

The RESEAL project aimed at demonstrating the sealing of a borehole and a shaft in plastic clay on arepresentative scale. The in-situ experiments were performed within the Boom Clay in the HADES URL(Mol, Belgium). The RESEAL I project started in 1996 in the EC 4th framework program on “NuclearFission Safety”. Within this project, a borehole seal and shaft seal on a representative scale were designedand installed. In 2000, the project continued within RESEAL II (5th framework program of EC). There theefficiency of the borehole and shaft seals was tested, up until 2007.

Here, focus will be given on the shaft seal experiment. Within the experimental shaft of the HADES URL,the seal was installed. To this end, the bottom part of that shaft was filled with grout and the concrete linerwas removed at the location of the seal. The seal consists of a mixture of 50% of powder and 50% of highlycompacted pellets of FoCa clay. The sealed section is about 2m in diameter and about 2.2m high. The sealis kept in place with a top concrete lid of about 1m thick. A large amount of sensors including pore waterpressure, total pressure, displacement and relative humidity allowed to follow the hydro-mechanicalevolution of the seal during hydration and during the efficiency tests after saturation. Moreover, severalfilters inside the sealed section enabled artificial hydration to speed up the time to attain full saturation. Intotal about 2000 litres of water were artificially injected. This is about 50% of the expected volume. In thebeginning, hydration goes rather fast. But after about two years, when about 75% of relative humidity isattained, hydration slows down. Moreover, about two years are needed to go from 90% relative humidityto full saturation. In total, some 7 years were needed to reach full saturation.

As the EDZ around the seal was also instrumented, it is possible to make some conclusions on thesurrounding EDZ as well. It could be clearly demonstrated that fractures are created or re-created duringremoval of the concrete lining. These fractures are limited to a cylindrical zone around the sealed part andextent up to at least one meter inside the surrounding host rock. Although the Boom Clay has a fast self-sealing capacity, there are indications that some fractures remain open as long as hydration of the seal is

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ongoing. Only when full saturation is nearly achieved, the fractures within the host rock are sealing. Aradionuclide migration test through the sealed host rock is performed after full saturation of the seal andillustrates that the transport is diffusion dominated and no major effects of the sealed fractures is observedon the transport properties.

After full saturation, the efficiency of the seal was tested. First of all, the hydraulic conductivity of the sealwas tested. The original dry density of 1.4 g/cm3 was chosen as to obtain a hydraulic conductivity equalor less than the one of undisturbed Boom Clay. These tests showed that indeed a hydraulic conductivityof about 1 10-12 m/s is obtained. Next, gas pressure was increased on one of the filters floating within theFoCa seal, as to mimic the effect of a gas pressure build up. This experiment showed that gas breakthroughonly occurs when the gas pressure exceeds the local minimum stress. Although the actual breakthrough isan instant phenomenon, it takes some time for it to occur once the gas pressure is applied. Two weeks aftergas breakthrough, the hydraulic conductivity in the disturbed zone is restored to the undisturbed, saturatedvalue.

Then a hydraulic pulse (~12.5 bar) was initiated at the bottom of the seal. Total pressure sensors and to asomewhat lesser extent pore water pressure sensors throughout the seal responded.

The hydro-mechanical behaviour of the sealing material and the surrounding host rock during hydrationand efficiency testing is evaluated using the CODE_BRIGHT computer code. Laboratory experimentscould be predicted very well using a double porosity model. However, for the large scale in-situexperiment, quite some differences between the predicted and observed values are noticed. The generaltrends of the experimental data is covered with the hydro-mechanical models: CODE_BRIGHT andCAST3M.

Current performance assessment calculations have shown that the use of seals in clay media is notstrictly required. However, a review of recent safety cases illustrates that all countries do consider theemplacement of seals. Therefore, it needs to be demonstrated that it is feasible to install seals and thatthis installation can be performed in a safe way. The in-situ experiments performed within theRESEAL project have demonstrated this aspect on an intermediate scale. Further on, the shaft sealexperiment has illustrated that after full saturation the hydraulic conductivity is equal than or lowerthan the one of undisturbed Boom Clay, that there is no preferential gas breakthrough through the sealand that after gas breakthrough the seal has a fast self sealing capacity. However, it should be notedthat the hydration took much longer than originally foreseen. This hydration time is, amongst othersstrongly linked with the dry density of the sealing material, chosen to obtain a certain hydraulicconductivity and also influencing the (time dependent) gas migration through the sealing material. Thereview of recent safety cases did not provide clear data on the timing at which all or some of thefunctional requirements of the seal should properly function. The RESEAL experiment also illustratedthat a homogenization of the used mixture takes place. Next, we can state that the efforts made duringthe RESEAL project have strongly increased our knowledge in the processes occurring withinhydrating seals. However, for the large scale in-situ shaft seal experiment the general trends of thehydro-mechanical behaviour can be predicted, but are still far from a good fit with the experimentalobservations. Finally, the strict requirement from the safety assessment is limited to ensuring adiffusion dominated transport through the near field. The migration of 125I through the EDZ did notdemonstrate any major relicts of the fractures that jeopardise the diffusive transport within the hostrock.

ACKNOWLEDGEMENTSThe RESEAL project was financially supported by the EC through the 4th and 5th framework programme(project numbers FI4W-CT96-0025 and FIKW-CT2000-00010) and by ONDRAF/NIRAS, ANDRA andENRESA.We also appreciate the stimulating discussion with ONDRAF/NIRAS and ANDRA as end-usersof these research results.

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HYDRO-MECHANICAL RESPONSEOF THE CALLOVO-OXFORDIANMUDSTONE

AROUND A DEEP VERTICAL DRIFTJ. Vaunat1, B. Garitte1, A. Gens1, K. Su2 & G. Armand2

1. Technical University of Catalonia (UPC), Building D2, Campus Nord, c/ J. Girona, 1-3, 08034Barcelona, Spain ([email protected], [email protected], [email protected])

2. ANDRA – Agence Nationale pour la Gestion des Déchets Radioactifs, 1-7 rue Jean Monnet,92298 Châtenay-Malabry, France ([email protected], [email protected])

INTRODUCTIONIn order to obtain information about the hydro-mechanical response of the Callovo-Oxfordian mudstone,the French National Agency for Nuclear Waste Management performed a close monitoring of theperturbation caused by the advance of the access shaft to the underground laboratory of Bure betweendepth 460 and 476 m (Armand & Su, 2006). In parallel, prediction and further interpretation of fieldmeasurements were realized through different numerical models within the framework of Modex-Repproject (Su, 2007). This paper presents results of the modelling provided by UPC during this project.

FIELD MEASUREMENTSA layout of the instrumentation is shown in Figure 1.a. Three boreholes equipped with extensometers (redpoints), one borehole with inclinometer (red squares), four boreholes with pore pressure transducers (bluepoints) and four boreholes with strain gauge cells (green points) were installed from a lateral niche previousto the excavation of the shaft at the considered depth. Instrumentation campaign is completed by wavevelocity survey, hydraulic conductivity measurement by means of pulse tests and installation of radialextensometers after excavation.

MODEL DEVELOPEDExcavation of the access shaft has been modelled by use of Code_bright, a Finite Element code that solves3D thermo-hydro-mechanical problem in geological media. In this particular case, equations of stressequilibrium, water mass balance and solid mass balance are solved simultaneously, which gives naturallya hydro-mechanical coupled formulation of Biot type. Mesh is depicted in Fig. 1.a: it consists of a 2Daxisymmetric mesh where the shaft and the lateral niche are represented (the latter in an approximatemanner due to the assumption of axisymmetry). A damage/elastoplastic law that couples degradation ofmoduli and strength with load has been implemented and parameters calibrated on laboratory tests.

Figure 1: a) Experimental shaft and instrument layout; b) Geometry considered in the numerical model.

a)b)

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RESULTS AND INTERPRETATIONValues of convergence, displacements and pore pressure output by the model at some points are comparedin Figure 2 with field measurements. A very good agreement can be observed. Insights into modellingfeatures evidence the importance of the following points for a good reproduction of field data: vertical andhorizontal values of permeability equal to 10-12 and 10-13 m/s respectively, Young modulus for the intactrock belonging to the lower range of field measurements (7000 MPa), damage evolution controlled by theenergy input to the material (which allows for damage in both compression and shear), increase ofpermeability with damage, damage threshold set to a very low value (which allows for damage-inducedincrease of permeability even for small perturbations) and modelling of the upward drainage due to thepresence of the lateral niche.

References:Armand, G., Su, K. (2006): Hydromechanical coupling phenomena observed during a shaft sinkingexperiment in a deep argillaceous rock, Proc. Geoproc 2006, Nanjing, May 2006, p. 725-731.

Su, K. (2007): “Development and Validation of the Constitutive Hydromechanical Models for Callovo-Oxfordian Argillites: the MODEX-REP Project”. Synthesis report of EC Modex-Rep project.

Figure 2: Comparizon between model and measurements for a) convergence b) inclination in borehole2208; c) pore pressure in the far field and d) pore pressure in the near field.

-5

-4

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-1

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17-feb-05 08-abr-05 28-may-05 17-jul-05 05-sep-05 25-oct-05

Time (days)

Convergence(mm)

-40

-30

-20

-10

0

10

20

Relativefrontelevation(m)

z= -467.40 m; r= 3.18 m

Base 1-8

Base 3-8

Base 3-9

Base 4-10

Base 5-11

Base 1-7

Base 6-12

Shaft relative

advance

Debris relative

advance

Lining relative advance

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

17/02/2005 08/04/2005 28/05/2005 17/07/2005 05/09/2005 25/10/2005

Time (days)

Angularvariation(mm/m)

REP_2208_ICL_01 z= -460.79 m; r= 6.83 m

H(an)M

HM

-7

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-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

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40.00

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Time (days)

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REP2104_PRE_02:

SIM2104_PRE_02

REP2104_PRE_04:

SIM2104_PRE_04

0

10

20

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50

60

17-feb-05 08-abr-05 28-may-05 17-jul-05 05-sep-05 25-oct-05

Time (days)

Porepressure(bars)

-50

-40

-30

-20

-10

0

10

Relativefrontelevation(m)REP2103_PRE_01:

z= -462.67 m; r=5.16 m

Front relative distance

Debris relative distance

Lining relative distance

-7

-6

-5

-4

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-2

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0

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SENSITIVITY OF TOTAL STRESSTO CHANGES IN EXTERNALLY APPLIEDWATER PRESSURE IN KBS-3 BUFFER

BENTONITEJ.F. Harrington1, D.J. Birchall1 and P. Sellin2

1. British Geological Survey, Keyworth, Nottingham, NG12 5GG, UK,([email protected])2. SKB, Box 5864 S-102 40 Stockholm, Sweden, ([email protected])

INTRODUCTIONIn the KBS-3 concept, composite copper and steel canisters containing spent nuclear fuel will be placed inlarge diameter disposal boreholes drilled into the floor of the repository tunnels. The space around eachcanister will be filled with pre-compacted bentonite blocks. Over time, the bentonite blocks will draw inthe surrounding groundwater and swell, closing any construction gaps to encapsulate the waste in a lowpermeability barrier.

From a performance assessment perspective, the effect of glacial loading of a future repository and theresulting change in local porewater pressure is an issue that must be addressed. For a clay-water systemwith the porewater in thermodynamic equilibrium with an external reservoir of pure water at pressure, pw,the total stress acting on the clay, σ, can be expressed as

(1)

where σi is the “interparticle stress” and R and A are the repulsive and attractive stresses respectively(Lambe, 1960). In conventional soil mechanics theory the effective stress σeff (Terzaghi and Peck 1967) isdefined as the difference between the total stress and the measurable pore pressure. Since distilled (pure)water was used in this experiment we can write the relationship:

(2)

For dispersed and highly plastic saturated materials such as bentonite which exhibit no mineral to mineralcontact the interparticle term σi reduces to zero (Lambe and Whitman, 1969), and the effective stressequation simplifies to:

(3)

where R-A is equivalent to the swelling pressure, Π, of the clay. Recent work by Harrington and Horseman(2003) examining the sensitivity of total stress to changes in the externally applied water pressuredemonstrated the general validity of the effective stress law. However, to account for minor departures inideality, Harrington and Horseman introduced a proportionality constant α (equal to dσ/dpw) leading to:

(4)

The observation that α may not be equal to 1 has led to the suggestion that as the externally appliedporewater pressure increases, swelling pressure (in this case equivalent to the effective stress) may actuallydecline to the point where liquefaction of the bentonite occurs. This paper presents the original results fromHarrington and Horseman (2003), outlines some of the uncertainties associated with extrapolation of suchdata and discusses in detail a new test history performed at elevated porewater pressures up to 46 MPa.

RESULTSTwo experimental histories (designated Mx80-10 and Mx80-11) have been undertaken using a custom-designed constant volume and radial flow (CVRF) apparatus (Horseman et al., 2004). In both tests

σ σ= + − +i wR A p

σ σ σeff w ip R A= − = + −

σeff R A= −

σ α= +Π pw

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backpressure was varied in a number of incremental and decremental cycles while total stress, porewaterpressure and volumetric flow rate were continuously monitored.

The swelling pressure of the buffer clay at dry densities of 1.58 Mg.m-3 and 1.61Mg.m-3 was determinedto be around 5.5 MPa and 7.2 MPa respectively. Initial histories of ascending porewater pressure yield αvalues of 0.86 and 0.92 for tests Mx80-10 and Mx80-11 respectively.

During the initial ascending porewater pressure history both tests exhibit a general trend of increasing αwith increasing backpressure. Analysis of the water inflow data for Mx80-11 indicates a similar trend,symptomatic of a reduction in system compressibility. The initial non-ideality of α can be explained by anumber of factors such as interplatelet friction, compression of residual gas, the movement of gas intosolution, sidewall friction and apparatus compliance. However, net inflow data indicates the specimen isfully saturated early in the test history, suggesting an alternative mechanism may exert a dominant role onthe mechanical behaviour of the system.

Asymptotic values of porewater pressure measured on the surface of the specimen are in good agreementwith the externally applied backpressure values. Changes in applied porewater pressure are generallymirrored within the specimen within around 2 to 10 days of the change in boundary condition. Inspectionof data provides no evidence for the development of hydraulic thresholds within KBS-3 bentonite subjectto these test conditions.

Analysis of the stress data clearly demonstrates significant hysteresis exists when externally appliedbackpressure is reduced. Comparison of effective stress data (i.e. swelling pressure) for both test historiesindicates a clear trend between the amount of hysteresis observed and the absolute magnitude of thebackpressure applied to specimen. This suggests that the observed hysteresis results from some form of“stress memory” and not experimental compliance. The strength of this phenomena appears to bedependent on the magnitude of the backpressure applied to the specimen.

At porewater pressures of 46 MPa the bentonite still retains a significant proportion of its original swellingranging between 48 and 67% depending on the test cycle. The data also indicates a reduction in the rateof decline in swelling pressure as backpressure increases, indicative of a rise in α values at high waterpressures. Linear regression suggests α = 1 at a porewater pressure of around 64 MPa.

At the end of test Mx80-11 the average effective stress was 14.4MPa, represents an increase in the totalstress of 100% and is an obvious artefact of the apparent stress memorisation mentioned above. If correct,this has important implications for repository performance assessment.

No evidence of classic liquefaction was found in this experimental study.

ReferencesHarrington, J.F. and Horseman, S.T. (2003). Gas migration in KBS-3 buffer bentonite: Sensitivity of testparameters to experimental boundary conditions. Report TR-03-02. Svensk Kärbränslehantering AB(SKB), Stockholm, Sweden.

Horseman, S.T., Harrington, J.F. and Sellin, P. (2004) Water and gas flow in Mx80 bentonite buffer clay.In: Symposium on the Scientific Basis for Nuclear Waste Management XXVII (Kalmar), MaterialsResearch Society, Vol. 807. 715-720.

Lambe, T.W. (1960). A mechanistic picture of shear strength in clay. Proc. ASCE Res. Conf. ShearStrength of Cohesive Soils, 555-580.

Lambe, T.W. andWhitman, R.V. (1969). Spoil mechanics. JohnWiley, New York.

Terzaghi, K. And Peck, R.B. (1967). Soil mechanics in engineering practice. JohnWiley, New York.

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COMPARISON OF THE POROELASTICBEHAVIOR OF MEUSE/HAUTE MARNE

AND TOURNEMIRE ARGILLITES: EFFECTOF LOADING AND SATURATION STATES

E. Bemer1, A. Noiret1, F. Homand2, A. Rejeb3

1. IFP - Institut Français du Pétrole, 3 et 4 Av. du Bois Préau, 92852 Rueil-Malmaison Cedex,France ([email protected]), ([email protected])

2. INPL - Institut National Polytechnique de Lorraine, LAEGO - Laboratoire Environnement,Géomécanique et Ouvrages, Rue du Doyen Marcel Roubault BP 40, 54501 Vandoeuvre-lès-Nancy, France ([email protected])

3. IRSN - Institut de Radioprotection et de Sûreté Nucléaire, Av. du General Leclerc BP n°17,92262 Fontenay-aux-roses, France ([email protected])

This paper will present a synthesis of the experimental work conducted by IFP on rock samples taken outof the Meuse/Haute Marne and Tournemire underground research laboratories host formations, named“argillites”. The behavior of these clayey rocks is studied within the framework of Biot’s mechanics offluid saturated porous solids. Drained and undrained uniaxial strain tests (“oedometric tests”, Figs. 1 and2) are performed to determine the poroelastic parameters for various applied stresses: drained andundrained bulk moduli Ko and K, shear modulus G, Biot’s coefficient b and Biot’s modulus M.

The theoretical relations used to determine the hydromechanical parameters suppose that the rock issaturated. As the provided plugs are not fully saturated, a particular care is given to preliminary resaturationphase of the samples and the estimation of their final saturation. Swelling effects during the resaturationphase are also characterized.

Preliminary results on Meuse/Haute Marne argillites show an influence of the applied stress on theporoelastic parameters: the measured Biot’s coefficient decreases when the axial stress increases, while thedrained bulk modulus and the shear modulus increase (Figs. 3 and 4). The effect of the applied stress onBiot’s modulus is more difficult to interpret, because the measure of this specific parameter stronglydepends on the saturation state of the sample. Meuse/Haute Marne argillites poromechanical behaviorappears to depend on the rock saturation state: samples with a greater initial saturation seem to show alesser apparent surconsolidation degree and a higher compressibility.

Figure 1: Principle of oedometric test.

O edo m et r ic c o ndi t ion s:

σr = σθ

εr = εθ = 0

Displacement

transducer

D ow n st rea m p or e p re ss ur e

U ps t rea m p or e p re ss ur e

σa

Sint er ed sta inl e ss

st ee l pl a te

M e ta ll ic ce ll

R oc k sam ple Po re p re s su re v a lve s

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Fully coupled hydromechanical behavior ofTournemire argillites has been rather less studiedthan Meuse/Haute Marne argillites. The resultsobtained will then give precious comparison data.

The full paper will describe the followed experi-mental method, including the resaturation phase, thefollowed loading paths and the estimation of thesample saturation. The experimental results will beanalyzed to show the influence of both the satura-tion state and the applied stress and compare thehydromechanical behavior of Meuse/Haute Marneand Tournemire argillites.

Numerical modeling of the oedometric tests willalso be described. Finite element calculationsenable to estimate the permeability of the samplesby fitting the experimental pore pressure equilibrium curves obtained during hydromechanical loading.

References:Bemer E., Longuemare P. and Vincké O. (2004), Poroelastic parameters ofMeuse / Haute-Marne argillites:Effect of loading and saturation states, Applied Clay Science, 26, 359-366

Chiarelli A-S (2000), Etude expérimentale et modélisation du comportement mécanique de l’argile del’Est, Thèse de doctorat de l’Université de Lille 1

Niandou H. (1994), Etude du comportement rhéologique et modélisation de l'argilite de Tournemire,applications à la stabilité des ouvrages, Thèse de doctorat de l’Université des Sciences et Technologiesde Lille

Pham Q.T (2006), Effets de la désaturation et de la resaturation sur l’argilite dans les ouvrages souterrains,Thèse de doctorat de l’Ecole Polytechnique

Valès F., Nguyen Minh D., Gharbi H. and Rejeb A. (2004), Experimental study of the influence of thedegree of saturation on physical and mechanical properties in Tournemire shale (France), Applied ClayScience, 26, 197-207

Vincké O., Longuemare P., Bouteca M. and Deflandre J.P. (1998), Investigation of the poromechanicalbehavior of shales in the elastic domain, Paper SPE/ISRM 47589

Figure 3: Ko+4G/3 as a function of the appliedaxial stress (Meuse/Haute Marne argillites).

Figure 4: b as a function of the applied axial stress(Meuse/Haute Marne argillites).

0

1000

2000

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Effective axial stress (MPa)

0,4

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0,55

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Effective axial stress (MPa)

Figure 2: Oedometric curve of a Meuse/HauteMarne argillites sample.

Oedometric curve

-0.016

-0.014

-0.012

-0.01

-0.008

-0.006

-0.004

-0.002

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1 10 100

Effective axial stress (MPa)

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MULTISCALE MODELLING OFTHE ARGILLITES MECHANICAL BEHAVIOR

A. Abou-Chakra Guéry1,2, F. Cormery2, K. Su2, J.F. Shao2, D. Kondo2

1. Laboratoire de Mécanique of Lille, UMR 8107 CNRS, Cité scientifique, 59655 Villeneuved'Ascq, France, ([email protected])

2. Agence Nationale pour la gestion des déchets radioactifs (ANDRA), 92296 Chatenay Malabry,France

ABSTRACT

This study is performed in the general context of the project of underground disposal of radioactive waste,undertaken by the French National Radioactive Waste Management Agency (Andra). Its objective is toformulate a predictive constitutive model of the Callovo-Oxfordian argillite, chosen as one of possiblegeological barriers. Various phenomenological models have been proposed in the past for this class ofmaterials. For instance we can cite (Chiarelli et al., 2003) who have developed a coupled plastic damagemodelling. This model has been calibrated by using experimental data on the Callovo-Oxfordian clay. Itseems to provide good predictions in term of the macroscopic stress-strain curve. However, in this classof phenomenological models, the link between physical deformation mechanisms and macroscopicbehaviour is not properly taken into account and this seems to be a strong limitation in view of the highheterogeneity of the studied material. Therefore it is interesting to develop a more physical modellingapproach. The methodology followed in the present study consists to develop a constitutive model forargillite by using a nonlinear homogenization approach. Owing to the complexity of loading paths whichare involved in the project of underground storage of radioactive waste, we have adopted an adaptation ofthe incremental formulation of Hill (Hill., 1965) which consists, at each loading step, in determining themacroscopic tangent operator from the local tangent behavior of the different constituents. The objectivehere is mainly to implement the incremental method for the modelling of a three phase composite, namelythe argillite which is composed of a plastic clay matrix and elastic or damaged mineral inclusions. Inaddition to the coupling between plasticity and damage, the specific contributions of the present workinclude the consideration of non associated and pressure dependent plastic flow with volumetric dilationfor the clay matrix and the extensive validation of the homogenized constitutive law by comparison withexperimental data on different loading paths. More precisely, it is shown that, by considering a modifiedversion of the original Hill method based on the use of an isotropization procedure of the local tangentoperator (see for instance, Chaboche and Kanouté 2005; Doghri and Ouaar, 2003; in the case of metalsplasticity), the model predictions are in a very satisfactory agreements with the general trends of argillitebehaviour. Finally, the multi-scale modelling is implemented in the finite element computer code Abaquswith a routine UMAT.

Using the proposed model, laboratory tests with various loading paths have been simulated, includingtriaxial compression tests with different confining pressure, proportional compression tests and lateralextension tests. The comparisons with experimental data have shown that the proposed model correctlypredicts the main properties of argillite behaviour, such as plastic deformation, induced damage, pressuresensitivity, volumetric dilatancy, degradation of elastic properties. An example of simulation is given inFig. 1 for a uniaxial compression test. Further, compared with the classic phenomenological models, themulti-scale model not only predicts macroscopic responses but also gives relevant information in eachphase at microscopic scale. For instance, it is interesting to observe that the amplitude of the degradationof the elastic stiffness at local and macroscopic scales is significantly different. Moreover, anotheradvantage of the micromechanical model over the classic phenomenological ones is underlined by thecapability to properly take into account the evolution of the mineralogy of material with depth.

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An example of application of the proposed micromechanical approach to underground structure analysis isalso presented. It consists of the numerical analysis of mechanical responses of a vertical shaft duringexcavation through different argillite layers. The variation of mineralogical compositions with the depth istaken into account by this multi-scale modelling. The evolution of plastic and damage zones due toexcavation has been analysed.

It is useful to note that even if the macroscopic mechanical effect of damage is limited, the damage cansignificantly affect the overall permeability. This is a crucial point which needs to be investigated in futureworks.

References:Doghri, I., Ouaar, A. (2003): “Homogenization of two-phase elasto-plastic composite materials andstructures: Study of tangent operators, cyclic plasticity and numerical algorithms”, Int. J. of Solidsand Structures, 40(7), pp. 1681-1712.

Chaboche, J.L., Kanouté, P. (2005) : « On the capabilities of mean-field approaches for the descriptionof plasticity in metal matrix composites”, Int. J. Plasticity,21(7) , pp. 1409-1434.

Chiarelli, A.S., Shao, J.F., Hoteit, N. (2003): “Modeling of elastoplastic damage behavior of a claystone”,Int. Journ. Plasticity, 19, pp. 23-45.

Hill, R. (1965): “Continuum Micro-mechanics of elastoplastic polycristals”, Journ. of Mech. Phys.Solids, 13, pp. 89-101.

Figure 1: Simulation of a uniaxial compression (depth 466.8m).