Ré sumé

Depuis le XXe siècle, l'utilisation de l'énergie nucléaire est plus important pour les activités humaines.

Par exemple, selon l'Agence internationale de l'énergie atomique (AIEA), l'énergie nucléaire représente 70,6 % de l'électricité totale en France en 2019 (AIEA 2020). Tout en profitant les avantages de l'énergie nucléaire, la question qui se pose est de savoir comment éliminer les déchets radioactifs en toute sécurité. Pendant des décennies, les pays industrialisés ont mené des recherches approfondies sur le stockage géologique des déchets radioactifs moyenne activité and haute activité (MA & HA). En France, l'argile du bassin de Bure (formation du Callovo-Oxfordien (COx)) est considérée comme la roche hôte. Ce matériau présente une importante capacité de la cicatrisation lors de la resaturation. Bien que des recherches approfondies aient été consacrées d'étanchéité de l'argile du COx, un certain nombre de questions liées à ces phénomènes physico-chimiques ne sont toujours pas complètement résolues.

Cette thèse se concentre sur la cicatrisation de l'argile du COx. Six carottes d'argile COx provenant de différentes profondeurs (du laboratoire de recherche souterrain de Meuse/Haute Marne) ont été testées avec différentes expériences, y compris la diffraction quantitative des rayons X (XRD), l'analyse de la capacité d'échange cationique (CEC), le test d'adsorption d'azote, le test de gonflement et poromécanique, et le test d'auto-étanchéité. Cette recherche a été menée sous trois angles différents, à savoir les mécanismes de gonflement multi-échelle, la mesure des propriétés poro-mécaniques avec de l'eau, et l'évaluation du gonflement et des propriétés de transport du matériau guéri.

Mécanismes de gonflement multi-échelle

Cette étude des mécanismes de gonflement multi-échelle de l'argile COx a été réalisée par une série de tests gonflement, complétés par des mesures quantitatives de XRD, de capacité d'échange cationique (CEC) et d'adsorption d'azote. Le matériau testé provient de cinq sites géologiques différents, fournis par l'Andra. Les analyses de XRD, de CEC et de sorption d'azote ont été réalisées sur des échantillons de poudre, tandis que les tests de gonflement ont été effectués sur des échantillons cylindriques. Les échantillons cylindriques ont été recalibrés à partir de différents cellule T1 et prééquilibrés à 75% d'humidité relative pour éliminer l'effet de la saturation. Les effets des teneurs en minéraux argileux et des états d'endommagement (c'est-à-dire la fissuration) sur le comportement de gonflement (amplitude et cinétique) ont été étudiés. Pendant l'essai de gonflement, l'échantillon a d'abord été placé dans une cellule triaxiale à une pression de confinement constante de 14 MPa.

Lorsque la masse de l'échantillon a été stabilisée, de l'eau synthétique a été injectée par les deux extrémités de l'échantillon à une pression constante de 5 MPa. Les données expérimentales obtenues sont l'évolution de la déformation d'expansion de l'échantillon en fonction du temps. L'amplitude de gonflement et la cinétique de gonflement sont évaluées en comparant les échantillons entre eux. L'analyse de la composition minéralogique montre que la smectite est le seul minéral gonflant dans le COx, et qu'elle est intercalée dans deux types d'agrégats I/S dans le COx, à savoir R1-I/S (contient 30% de smectite) et R0-I/S (contient 78% de smectite). Les données de sorption de l'azote révèlent que le gonflement du COx n'est pas seulement déterminé par la teneur en smectite mais correspond

Mesurer des propriétés poro-mécaniques avec l'eau synthétique

Lorsque l'essai de gonflement susmentionné est terminé, les échantillons sont complètement saturés.

Un test poro-mécanique a été effectué sur le matériau saturé. L'objectif principal de ce travail est de mesurer le coefficient de Biot en utilisant de l'eau synthétique (proche de l'eau in-situ) pour contrôler la pression de pore. Dans le cadre de la poroélasticité, le coefficient de Biot est déterminé par les déformations mesurées pendant le chargement et le déchargement séquentiels de la pression de confinement (Pc) et de la pression de pore (Pi). Ce type d'essai prend beaucoup de temps en raison des longs temps de saturation pour obtenir l'uniformité de la pression. Plusieurs essais ont été réalisés avec succès au cours des deux dernières années, parmi lesquels quatre essais représentatifs sont présentés dans cette étude.

Les résultats ont clairement démontré que, malgré une anisotropie significative du matériau, le tenseur de Biot est isotrope avec une composante unique "b". Ce résultat important, cohérent avec certains calculs théoriques, ne signifie pas que les déformations, dues au changement de pression de pore, sont isotropes. Un autre résultat important est que "b" a été trouvé très proche de 1. Cela signifie que, dans les conditions de laboratoire, l'argile COx se comporte comme un matériau de Terzaghi. Ce résultat crucial a été obtenu sur des échantillons d'argile saturés en eau, qui présentaient une certaine déstructuration après les essais. Il est néanmoins cohérent avec de nombreuses observations faites avec du gaz (hélium) comme étant le fluide permettant de contrôler la pression interstitielle, ce qui conduisait le plus souvent à un tenseur de Biot quasi isotrope avec "b"≈1. Dans ce cas, les expériences avec le gaz ont été réalisées sur des matériaux partiellement saturés (de sec à presque saturé) donc sans la déstructuration observée avec l'eau.

Ce travail complète les résultats obtenus avec du gaz et met en évidence que cette argile saturée transversalement isotrope se comporte toujours comme un matériau de Terzaghi. Il contribue également à clarifier la valeur du coefficient de Biot qui doit être choisie dans les simulations numériques, en particulier celles qui sont cruciales pour lesquelles l'activité thermique des déchets est prise en compte.

Évaluation des propriétés de gonflement et de transport de la COx après la guérison

Une série d'essais d'auto-étanchéité à "faible confinement" a été conçue et réalisée pour étudier les propriétés de gonflement et de transport de l'argile COx rescellée. Grâce à cette expérience, le changement de la pression apparente de gonflement (Papp) et de la perméabilité à l'eau pendant la resaturation et la pression de percée du gaz (GBP) après le scellement ont été mesurés. Ces données de mesure directe fourniraient des références importantes pour la reproduction numérique.

Les résultats montrent que Papp a augmenté avec le temps et que la valeur de l'échantillon UT est d'environ 1 MPa, alors qu'elle varie de 3 à 5 MPa pour les échantillons UA. En comparant les échantillons d'une même carotte, les échantillons macro-fissurés présentent une cinétique plus rapide que l'échantillon intact, tandis que l'échantillon intact présente un Papp légèrement plus élevé que les échantillons macro-fissurés. Cette différence est principalement attribuée à la présence de fissures qui augmentent la surface de contact entre l'eau et les minéraux argileux et génèrent plus d'espace pour le gonflement. La Papp présente également une meilleure linéarité avec R1-I/S qu'avec R0-I/S. Ce résultat est cohérent avec l'observation de la contrainte de gonflement en fonction des minéraux liés à la smectite (chapitre 2). Du point de vue de la technologie des tests, la sorption d'azote est une approche plus simple et plus efficace que la XRD pour évaluer la capacité de gonflement du COx.

Pour les matériaux UT et UA, la présence de macro-fissures entraîne une augmentation significative de la perméabilité, jusqu'à 2 à 4 ordres de grandeur pour Kg et 5 à 6 ordres de grandeur pour Kw. L'autoscellage du COx macro-fissuré peut provoquer des réductions significatives de la perméabilité à l'eau (Kw) de manière synchrone avec l'augmentation de Papp. La perméabilité à l'eau finale des échantillons UA est réduite de cinq ordres de grandeur et proche de celle de l'échantillon intact, tandis que la est réduite de quatre ordres de grandeur. Il convient de souligner que le Kw final de l'échantillon UT est supérieur d'environ deux ordres de grandeur à celui de l'échantillon intact. Ces résultats démontrent que, même en l'absence de confinement, le gonflement des minéraux argileux peut toujours conduire à la rescellation des macro-fissures de l'argile COx dans une certaine mesure. En outre, le COx UA présente une cinétique plus rapide que le COx UT, ce qui peut être attribué à l'impact de la teneur élevée en R1-I/S. Après la guérison, les résultats des tests de percée de gaz illustrent que la valeur GBP du UT COx est d'environ 0-0.2 MPa, tandis que la valeur du UA COx est comprise entre 0.8 et 1.46 MPa. Cela confirme que le UA COx possède une meilleure efficacité d'étanchéité que le UT COx, même pour le transport de gaz, ce qui est cohérent avec l'observation de la diminution du Kw. Comparé à Papp et Kw, GBP est plus sensible à l'intégrité de l'échantillon. En utilisant la loi de Poiseuille, la valeur GBP de l'échantillon scellé est du même ordre de grandeur que la pression capillaire équivalente des fissures résiduelles, ce qui indique que la migration du gaz dans l'argile COx scellée se produirait principalement à travers la fissure scellée résiduelle et serait contrôlée par des phénomènes capillaires.

General introduction

Industrial context

Since the 20 th century, the use of nuclear energy has become increasingly important for human activities. For instance, according to the International Atomic Energy Agency (IAEA) nuclear energy accounts for 70.6% of total France electricity power generation in 2019 (IAEA 2020). While obtaining the benefits of nuclear energy, the ensuing issue is how to safely dispose of radioactive waste.

Radioactive waste refers to the materials produced after nuclear reactions (nuclear fission), which generally remain radioactive and harmful to the environment. Different countries have their own classification methods for radioactive waste. In France, the classification is done with reference to the radioactivity and the half-life duration of nuclear species, which is shown below in Fig. 1 (ANDRA, 2015) For decades, industrialized countries have conducted extensive research on the management and storage of MA and HA-LL radioactive waste. Several management options have been proposed, e.g. deep underground repository (or disposal), waste burning under the seabed or under the Arctic ice sheet [START_REF] Philberth | The Disposal of Radioactive Waste in Ice Sheets[END_REF], or abandonment to space (Coopersmith, 1999). In order to fully account for a number of societal issues, including environmental protection (and in particular an effective isolation from the biosphere for a very long time), deep geological repository has been widely accepted as a privileged method for MA and HA-LL waste. This solution refers to waste storage in a geological formation at a depth of several hundred meters below ground surface, either in clayey materials or in granitic bedrocks. Table 1 briefly summarizes the rock formation choices in several nuclear-industrial countries. Low permeability and availability at a large scale are the two main reasons for choosing suitable formations. Déchets RAdioactifs) to explore plausible storage solutions for different categories of waste, see Figure 2. The HA waste are typically vitrified and placed in steel overpacks, while the MA waste (under the form of hulls and pieces) are directly sealed in overpacks. MA waste are then placed in concrete disposal containers after reception from waste producers. As shown in Figure 2, two different kinds of tunnels are excavated from the main gallery parallel to the claystone formation. One kind of tunnel is of several meters in diameter and supported by a concrete wall; such tunnels are used to store the MA waste concrete containers. After placing the containers inside the tunnels, the vacant space are filled by buffer material (based on bentonite) and sealing by bentonite/sand and concrete plugs. For the HA waste packages, they are stored in the other kind of tunnel, which is of only tens of centimeters in diameter and contains a layer of steel interior wall. The HA waste packages are stored head-to-tail in the tunnel, then sealed by clayey materials (bentonite for instance) and concrete plugs. In terms of geological location, the MA and HA radioactive waste would be stored in a claystone formation of Callovo-Oxfordian (COx) age. The CIGEO repository design for radioactive waste includes two anti-radiation protective barriers, which are the engineered barrier (composed of man-made structures, and mainly high performance concrete) and the natural barrier (i.e. the claystone itself).

This claystone is chosen as the natural barrier thanks to its low permeability, excellent retention of radionuclides, favorable swelling characteristics, and self-sealing properties (Van Geet et al. 2008;Giot et al. 2019).

Preliminarily to any actual industrial storage, the feasibility of building a radioactive waste disposal facility within the COx is analyzed by ANDRA. To this purpose, an Underground Research Laboratory (URL) has been built, which is located in Bure, on the border of the Meuse and Haute-Marne districts of the eastern Paris Basin, France (Fig. 3). Since the start of the URL excavations in August 2000, two shafts have been drilled and provide access to drifts at different depth levels. Numerous COx cores have also been extracted from different depths, and are used for understanding the lithology, mineralogy and other properties of COx claystone. Overall, the URL is established for scientific purposes, which will provide useful knowledge for the future industrial CIGEO project (i.e. the actual repository). On the Bure site, the COx claystone layer was formed 152 -158 million years ago and covers an area of approximately 200 km², the thickness of which is about 130 m and lies at a depth of 422-552 m (Yven et al. 2007). Figure 3 shows the vertical lithological and mineralogical evolution at around 365-560 m depth of the Bure basin. Based on its mineralogy content, the COx formation corresponds to strata sequences C3 and C2, and it can be further subdivided into three lithophysical units, with, in order from shallow to deep, the silty-carbonated unit (USC), the transition unit (UT), and the clay unit (UA), respectively.

The geological distribution of these different units shown in Figure 4. More precisely, the USC is located at depths around 420m and 440m; it generally has the highest carbonate and tectosilicate contents. Beneath the USC is the UT located at about 440m-460m depth in Figure 4; it has a contrasted mineralogy (Conil et al. 2018). The clay unit (UA) is located at the base of the COx formation, at depths ranging approximately from 460m to 550m; it covers two-thirds of the total COx formation thickness.

Compared to the USC and the UT, the UA has the biggest proportion of clay minerals and comprises clay minerals, carbonates and tectosilicates contents of around 45-50%, 27%, and 24%, respectively (Giot et al. 2019). 2, where SD is the standard deviation.

Table 2: Average mineralogical composition of the three different lithophysical units of the COx claystone (Conil et al. 2018)

Self-sealing of COx claystone

During excavation and building of the repository tunnels, an Excavation Damaged Zone (EDZ) is formed in the COx formation (Zhang 2011). The cracks in EDZ could be generated during the excavation and ventilation of underground tunnels. Moreover, the thermal dissipation of radioactive waste during long-term storage may also lead to cracking. After the repository closure, the EDZ will be subjected to re-saturation due to underground water seepage. Thanks to the self-sealing capacity, cracks in EDZ could be partially closed. The self-sealing process is a well-known phenomenon, which have been widely studied during the past 20 years (Blümling et al. 2001;Horseman 2001;[START_REF] Bastiaens | SELFRAC: Experiments and conclusions on fracturing, self-healing and self-sealing processes in clays[END_REF]Davy et al. 2007;Van Geet et al. 2008;Zhang 2011;Giot et al. 2019;Bossart et al. 2019, etc). In presence of underground water and confining pressure, the permeability of damaged COx claystones can be reduced by several orders of magnitude and to levels approaching the permeability of undisturbed material (Figure 5). Compared with granitic rocks, clayey materials have a unique ability to self-seal, which can effectively improve the safety of the repository. Scientists have identified several factors affecting the extent of self-sealing of COx claystone. Such as the effect of confining pressure (e.g. Davy et al. 2007;Zhang and Rothfuchs 2008), the swelling of specific clay minerals (smectite) (e.g. [START_REF] Heidug | Hydration swelling of water-absorbing rocks: a constitutive model[END_REF]Saiyouri et al. 2000), and the dynamic rearrangement of clay and non-clay particles in the microcracks (e.g. Marschall et al. 2005;Desbois et al. 2009Desbois et al. , 2017)). A detailed literature review on the selfhealing of clayey rock will be presented in Chapter 1.

Aims and methodology of the research

Despite extensive research has been focused on the self-sealing of COx claystone, there is still a number of questions related to these physical-chemical phenomena still not completely solved. For instance, it has long been proven that clay (i.e. smectite) swelling has significant impact on the selfsealing. However, since smectite does not exist as a single phase in COx, its content and distribution are highly anisotropic. There is still no quantitative evaluation of the contribution of clay swelling to self-sealing. Another interesting scientific question is that, the claystone exhibits greater swelling potential at high relative humidity (>98% RH) rather than at the moderate and low relative humidity (Saiyouri et al. 2000;[START_REF] Valès | Modes de déformation et d'endommagement de roches argileuses profondes sous sollicitations hydro-mécaniques[END_REF]Wang et al. 2015). There is still no reasonable explanation for the underlying mechanisms. After the repository closure, underground water will infiltrate from the undisturbed zone to the unsaturated zone around the galleries, resulting in the pore pressure redistribution. Whether the hydro-mechanical coupling will affects the poro-mechanical behavior of the material remains unclear.

To sum up, the objectives of this thesis are to provide answers to these questions, by a series of laboratory tests carried out on different COx claystone cores. The experimental program is divided into three main parts, as follows.

Part 1: Mineralogical and microstructural analysis

This part of work focuses on: 1) mineralogical analysis of samples from all the cores tested during the thesis, in order to quantitatively determine the proportions of the principal phases (clay minerals, carbonate or silicate or other minerals, such as pyrite). This work is an extension of (Song et al. 2016).

2) using the SEM imaging techniques to observe the microstructure of cracks, i.e. the spatial rearrangement of the clay and non-clay mineral fragments under the condition of without damage (refer to intact), after micro-and macro-cracked, and after self-sealing. The results obtained from this part of the work will be applied to the subsequent analysis of the swelling tests and self-sealing tests.

Part 2: Swelling of intact and micro-cracked COx claystone

The swelling experiments are carried out on the COx claystone samples from four different geological locations at Bure URL. The tested samples are cylindrical cores with diameter 20mm and height 40mm, all samples are from the UA type (relative high clay mineral content and swelling potential). The swelling tests are carried out in the original designed triaxial cell in our laboratory, and for each test, the confinement is of 14 MPa while the water injection pressure is 5 MPa. The volumetric deformations of the COx claystone are measured by strain gauges (glued on the sample side surface) over time. In this part, the effects of injected fluid, mineralogical composition, damage state, and saturation state on the swelling capacity are investigated. For one micro-cracked sample, the X Ray micro-tomography technique, based on the ISIS4D platform (University of Lille), is used to record the visible cracks with the resolution of the device (5 to 20 microns) before and after sealing, and then analyze the possible cracks evolution of the sample.

Part 3: Poro-mechanical tests -Biot's coefficient measurement

After the swelling tests, the fully saturated sample are keep stay in the triaxial cell and under confinement, and we performed the poromechanics tests on several fully saturated samples (initially intact or micro-cracked) by using water as the pore pressure change fluid. The objective of this kind of test is to measure the Biot's coefficient of fully saturated COx claystone, and to compare with the former works carried out in our laboratory (Cariou et al. 2012;Yuan et al. 2017).

Part 4: Self-sealing of macro-cracked COx claystone -under low confinement

In this part, the macro-cracked COx claystone samples are initially cored as diameter/height = 37mm/40mm and then split by Brazilian splitting tests. The Brazilian splitting tests can provide artificial shear and tensile cracks, which are very close to the in-situ cracks around the tunnel. Two original experimental devices are designed and implemented to investigate: 1) the swelling pressure of macrocracked COx claystone under low confinement and 2) the self-sealing efficiency of COx claystone under (or without) low confinement. These devices are inspired by that used on the swelling pressure measurement of bentonite-sand mixtures (Liu et al. 2014). All sample types tested in part2 are also tested in this part.

The self-sealing tests are carried out with a device especially designed for this work. During the test, the initial gas permeability is first measured before water injection, the apparent swelling pressure (see further) and the water permeability are recorded over time. The gas breakthrough pressure is determined once the self-sealing is achieved. is composed of individual non-clay minerals and clay matrix, massive amounts of pores and microcracks take place in the inter-particle space. When focusing on the nanoscale, the clay mineral particle, e.g. smectite particle in Figure 1.1 left, is composed of stacked layers with a certain space between two neighbor layers (Wang et al. 2015). It should be emphasized that these observation was made under ambient conditions of approx. 300 K and 1 bar, while the underground condition is more complex and far less information is available. Many researchers have conducted extensive studies on the microstructure (both the solid structure and the pore structure) of COx claystone. In this chapter, we will discuss the research methodology and the reported research findings in detail.

Solid Structure

The mineral compositions and distributions have a strong influence on the rock petro-physical properties. As many sedimentary rocks, COx claystone exhibits strong transverse isotropy due to its layered structure. From the perspective of mineralogy, COx claystone includes two main components:

clay minerals and non-clay minerals. The clay minerals refer to the aluminum phyllosilicates that were formed by the weathering and decomposition of igneous rocks. In general, the COx claystone is composed of clay minerals and non-clay minerals. Since the material transport and mechanical properties are highly related to the minerals (particularly the clays), it is important to have comprehensive understanding of the mineralogical compositions and distributions in COx claystone.

For COx claystone, the bulk mineralogical composition and clay composition can be analyzed by quantitative X-Ray Diffraction (XRD), while the chemical activity of clay minerals can be further quantified by Cation Exchange Capacity (CEC) test. Both the Quantitative XRD and CEC analysis are indirect methods since they do not give a visual observation of each mineral.

Quantitative XRD

Based on the Rietveld method, the overall mineralogical composition can be quantified by quantitative XRD [START_REF] Rietveld | A profile refinement method for nuclear and magnetic structures[END_REF][START_REF] Bish | Studies of clays and clay minerals using X-ray powder diffraction and the Rietveld method[END_REF]Zhou et al. 2018). Generally, using the Rietveld method to quantify the non-clay minerals is of high accuracy, with a deviation below 1%. However, it is difficult to assess the accuracy of clay composition due to the lack of standards. The bias of clay minerals quantification is mainly associated with the preferred orientation effects and the mistaken of quantifying illite as smectite as they have very similar structures (Seemann et al. 2017;Zhou et al. 2018). Yven et al. (2007) have reported the XRD results of a bunch of COx claystone samples. It is reported that the non-clay minerals in COx claystone include carbonates (calcite, dolomite, aragonite, ankerite, and siderite, etc.), tectosilicates (quartz, feldspars, and plagioclase), and the clay minerals (illite and muscovite, interstratified illite/smectite, kaolinite, and chlorite). Besides, small quantities of pyrite, oxides (anatase, rutile, and magnetite), and organic matter are presented in COx claystone as well (Andra 2005;Yven et al. 2007;Song et al. 2017). From the viewpoint of geological location, the mass proportions of each mineral vary from the different geological sequences of the COx formation.

Particularly, the content (by weight) of phyllosilicates in the COx formation increasing with depth and varies from 20-60%. The content of carbonates decreasing with depth and varies from 15-80%. The distribution of tectosilicates is irregular, significantly variable and constitutes approximately 10 to 40% of the claystone. One plausible impact factor of these variations is the sea level at the time of the deposit. By recording the maximum flooding surface, the mineral analysis exhibits that higher sea level corresponds to greater clay content and lower carbonate content. The portions of pyrite, oxides and organic matter are less than 5% in total and show no tendency with the depth for the whole COx formation [START_REF] Yven | Geometry and Rock Properties Modelling of the Callovo-Oxfordian Claystone from a 3D High Resolution Seismic Cube[END_REF]Conil et al. 2018;Giot et al. 2019).

We illustrate in the general Introduction that the COx formation can be divided into three units from shallow to deep: the silty-carbonated unit (USC), the transition unit (UT), and the clay-rich unit (UA),

where UA has the highest clay fraction.

Cation Exchange Capacity (CEC)

Cation exchange capacity (CEC), which is an inherent characteristic of clayey material, refers to the ability of a material to hold exchangeable cations in a saline aqueous solution. The common exchangeable cations on the outer surfaces of clay platelets are Ca 2+ , K + , and Na + , etc (Anderson et al. 2010). The value of CEC is quantified in milligram equivalents (meq) of exchangeable cations per 100 grams of dry sample, and in many cases, for easy calculation, CEC is also expressed in millimoles of exchangeable cations per grams (mmol/g) of dry sample. For the COx claystone, CEC is not only determined by the proportions of clay minerals and organic matter but also by the type of clay mineral and the maturity of organic matter (Seemann et al. 2017). Empirically, the exchange capacity of 2:1 type clay minerals is higher than 1:1 type clay minerals. For instance, the CEC of smectite (2:1 type) is approximately 80 -120 meq/100g while it is around 1 -10 meq/100g for kaolinite (1:1 type). For organic matter, the exchange capacity varies from 100 to 300 meq/100g (Meier and Kahr 1999;[START_REF]CLAY AND CLAY MINERALOGY[END_REF][START_REF] Bergaya | Cation and Anion Exchange[END_REF]. In COx claystone, since the organic content is negligible, CEC is considered to be only determined by clay minerals.

The workflows of a CEC test are demonstrated in Figure 1.2. For a sample X-clay, it is firstly titrated by adding solution with index cation A (T1) (repeat several cycles). After the titration, the value of CEC is derived by performing steps E1, E2, and E3. In certain cases, it is necessary to perform another titration (T2) to replace the cations A by the index cations B, and subsequently applying steps E4, E5, and E6. Detailed operation procedures and precautions can be found in [START_REF] Bergaya | Cation and Anion Exchange[END_REF][START_REF] Stanjek | CEC determination with Cu-triethylenetetramine: recommendations for improving reproducibility and accuracy[END_REF].

Figure 1.2. workflows of CEC determination [START_REF] Bergaya | Cation and Anion Exchange[END_REF] Numerous exchange cations have been used to determine the CEC of bulk materials, such as Cuethylenediamine, methylene blue, protons, ammonium acetate, alkali or alkaline-Earth cations, organic cations, etc. [START_REF] Bergaya | Cation and Anion Exchange[END_REF]. Nowadays, the most common index cation for clayey rock is Cu 2+ -Trien as it has sufficient affinity for complete exchange with clay minerals. The reproducibility and accuracy by using Cu 2+ -Trien have been exhaustively analyzed can be found in the literature [START_REF] Stanjek | CEC determination with Cu-triethylenetetramine: recommendations for improving reproducibility and accuracy[END_REF]. which is much lower than the purified 2:1 clay and slightly higher than the purified 1:1 clay. It exhibits a general trend that the CEC value increases with the total clay content, but EST44140 is an exception.

Further research has proven that the CEC of claystone is more related to the swelling clay mineral content. [START_REF] Przelaskowska | Application of the cation exchange capacity parameter (CEC) to the characterisation of the swelling capacity of lower Paleozoic, Carpathian Flysch and Miocene Carpathian Foredeep clay rocks Rietveld HM (1969) A profile refinement method for nuclear and magnetic structures[END_REF] investigated the CEC of various claystone with different interstratified illite/smectite (I/S) layers, and the CEC value increases with the total I/S contents which consist with Song et al. (2017). Moreover, CEC is highly interrelated with the swelling mineral (i.e.

smectite) content. A potential explanation is that the CEC value positively relates to the water-sorption capacity, as smectite adsorbs the most water molecules. Seemann et al. (2017) did the linear regression analysis of the measured CEC value and the water vapor (in moles) uptake of COx claystone at different relative humidity, see Figure 1.3, a good correlation is observed between the two properties. The result demonstrates that when the relative pressure range from 0.1 to 0.7, CEC and the total water sorption capacity have a good linear relationship. The calculated hydration numbers (H2O/cation) range from 2.5 to 12.5 H2O/cation (based on the obtained slope). By measuring different claystone samples, the total effective hydration numbers are calculated between 10.6 to 62.7 H2O/cation (at p/p° of 0.98), such big variation suggests that the water sorption is not attributed exclusively to the interlayer cation hydration of clay minerals, there are still other water sorption regimes during the hydration of claystone. Furthermore, the effect of the exchangeable cation type (essentially refer to the effect of hydration energy) is also discussed in (Seemann et al. 2017). They first utilizing Na + and Mg 2+ to completely exchange cations on the unexchanged COx claystone, the CEC values were then measured on exchanged samples to compare with the value of the unexchanged one.

No distinguished results were observed between exchanged and unexchanged samples. This means that the clay surface cation type is not the major influence factor on the CEC.

Pore-fracture structures

The pore-fracture network has a major effect on the mechanical and transport properties of COx claystone. To this date, the microstructural studies on the claystone are in rapid development. The pore-fracture network is a complex multi-scale system and consists of voids from macroscopic (millimeter-scale) to mesoscopic (micron-scale) and to microscopic (nano-scale). At different scales, various techniques can be used. Table 1.3 exhibits pore-fracture categories of claystone and the corresponding characterization approaches. Generally, investigation techniques can be divided into indirect and direct methods. In Table 1.3, mercury intrusion porosimetry and gas adsorption are indirect methods since they need simplified pores models to be analyzed. Micro-computed tomography (Micro-CT) and Scanning Electron Microscopy (SEM) are direct methods as they can be used to directly observe the real pore-fracture network at different scales. In this section, we will discuss these mainstream techniques and their application to COx claystone characterization. Gas physisorption (0,5 nm-0,35 m)

Micro-computed tomography (m-mm)

Scanning Electron Microscopy (nm-mm)

Mercury intrusion porosimetry

Mercury intrusion porosimetry (MIP) is a well-known technique for measuring the porosity and the pore size distribution of porous materials. Although mercury is metal, it behaves like a non-wetting fluid under atmospheric and vacuum conditions while maintaining extremely strong inter-molecule force. Moreover, mercury does not exhibit irregular thermal motion mass transfer pattern like gas.

Thanks to the abovementioned advantages, one can use the MIP to get pore information. During the test, the invaded volume and the corresponding injection pressure are recorded. Before the test, the sample needs first to be dried to remove all pre-existing porous liquid. Theoretically, the minimum pore diameter that can be detected by MIP is around 3-4 nm, [START_REF] Abell | Mercury Intrusion Porosimetry and Image Analysis of Cement-Based Materials[END_REF][START_REF] Diamond | Mercury porosimetry An inappropriate method for the measurement of pore size distributions in cement-based materials[END_REF]. The test carries out by progressively increasing the intruded mercury pressure on the vacuum sample. The intruded porosity (𝜑 Hg ) can be directly calculated by the ratio of intruded mercury volume 𝑉 Hg to the total specimen volume 𝑉 specimen :

𝜑 Hg = 𝑉 Hg 𝑉 specimen (1.1)
Besides, one can derive the information of pore size distributions (PSD) by linking the cumulative invaded mercury volume to the pore size. To generate the PSD information, a premise is that the pore system consists of numerous cylindrical tubes with various diameters. These cylindrical bundles are not interconnected, and each of them penetrates through the material and enters the outside of the sample. The famous Washburn equation (also called the Young-Laplace equation) is used to determine the intruded pore diameter (𝑑):

𝑑 = -4𝜎 cos 𝜃 𝑃 Hg ⁄ (1.2)
where 𝜎 is the mercury-solid interfacial tension, 𝜃 is the mercury-solid contact angle, and 𝑃 Hg is the mercury intruded pressure. MIP has been widely used in claystone microstructure studies for years.

For instance, ANDRA has charged several research institutions to study the porosity of COx claystone with different mineralogy contents by applying mercury intrusion. Table 1.4 summarized the porosity data of the predecessors, the porosity varies from different geological sequences with an average value equal to 16%. The porosity deduced from the mercury-pressure method is always underestimated. This is due to the limitation of the experiment apparatus allowing pores detection with a diameter greater than 3 nm. Moreover, most pores communicate the outside through a long seepage chain of intermediate pores of varying sizes and shapes, thus some pores connected to very fine necks will not be detected [START_REF] Diamond | Mercury porosimetry An inappropriate method for the measurement of pore size distributions in cement-based materials[END_REF]. [START_REF] Boulin | Experiments to estimate gas intrusion in Callovooxfordian argillites[END_REF] found that the MIP porosity gives around 75% of the total porosity for COx claystone. Menaceur et al. (2016) used MIP to measure the porosity of UA COx claystone is ca.

70% -77% total porosity, this result is consistent with the observation in [START_REF] Boulin | Experiments to estimate gas intrusion in Callovooxfordian argillites[END_REF].

Mercury intrusion test also provides information on pore size distribution, two typical result of COx claystone are shown in Figure 1.4. According to intrusion curves, the mean pore diameter of the UA sample is around 10-20 nm, while the value of the UT sample is around 50-100 nm. This implies that the higher the clay content, the smaller the mean pore diameter. For both UA and UT samples, the mean diameter deduced from extrusion curves is relatively higher than from the intrusion curves. The mean accessible pore size of overall COx formation varies between 3 nm and 60 nm, which belongs to the category of mesopores (Andra 2005;Yven et al. 2007). However, [START_REF] Diamond | Mercury porosimetry An inappropriate method for the measurement of pore size distributions in cement-based materials[END_REF] reported that the PSD calculated based on the Washburn equation (rel.

(1.2)) is typically one orders of magnitude smaller than the actual case. Several factors are proven can lead to this underestimation, such as the intrinsic defect of the cylindrical pores model, water status inside the clay particles, pore geometry effect, etc. (Horseman et al. 1999;Desbois et al. 2009;[START_REF] Houben | Pore morphology and distribution in the Shaly facies of Opalinus Clay (Mont Terri, Switzerland): Insights from representative 2D BIB-SEM investigations on mm to nm scale[END_REF]Klaver et al. 2015;Menaceur et al. 2016).

In summary, MIP can provide pore information between 3nm-300μm, with the mean pore-throat diameter between 3 nm and 60 nm, depends on the clay content. However, due to the intrinsic defect of the method, this is an underestimated value. Therefore, many researchers prefer to use another method with better accuracy, namely gas physisorption.

Gas physisorption

Gas physisorption is a pioneering approach to detect the pore textual properties of geomaterials. It is originally developed and applied in the physical-chemistry field of material sciences disciplines.

Comparing to the Mercury intrusion porosimetry, gas physisorption not only provides a wider range of pore information, but also characterize the pore surface, pore volume, and other structural messages based on some well-established theories.

Principle of the gas physisorption

The term "physisorption" refers to a physical process of gas molecules penetrate into and gather at pore surface under van der Waals forces. Nitrogen is the most common gas that is used in laboratory studies, which has a boiling point at 77K and a corresponding saturation pressure of 101.3kPa. Using nitrogen (at 77K) can access a wide range of pore spectrum, from 0.36nm to 0.35μm (Thommes et al. 2015;Seemann et al. 2017). Recently, other gases such as water vapor (at 303K) and CO2 (at 273K) are also developed for gas physisorption studies (Seemann et al. 2017;Lahn et al. 2020). For clay-rich rock, nitrogen and water vapor are the most common used gases. Therefore, only the results using these two gases are discussed here.

Based on the hypothesis that pore surface properties are homogeneous, the amount of adsorbed gas molecules is a function of relative pressure (p/p°) at a constant ambient temperature, where the p/p° is the ratio of the absolute gas pressure and the saturation pressure. Theoretically, the physisorption is thermodynamically reversible under isothermal conditions, thus the available original data is the adsorption/desorption isotherm.

The adsorption process consists of different stages with the increase of relative pressure (p/p°) and the adsorbed space expanded from ultra-micropores to macropores (Thommes et al. 2015). The dominant adsorption mechanisms with the increase of p/p° successively are: volume filling (0.001<p/p°<0.15), statistical monolayer and multilayer sorption (0.15<p/p°<0.42), capillary condensation (0.42<p/p°<0.99) and the clustering & spilling of molecules (p/p°>0.99). Figure 1.5 gives an exhaustive description of adsorption process by using nitrogen at 77K. When the 0.001<p/p°<0.01, molecules start filling the micropores within the range of 0.35-1nm (i.e., the ultra-micropores), this process is termed "the primary filling". The subsequent process is called "the secondary filling", which occurred at slightly higher relative pressure range (0.01<p/p°<0.15) to fill wider micropores (up to 2nm). When p/p ° increase from 0.15 to 0.42, statistical monolayer and multilayer adsorption successively occurs in the mesopores. Meniscus interfaces appear in the individual pores and move steadily up to the pore entrance [START_REF] Hamamoto | Study on adsorption refrigeration cycle utilizing activated carbon fibers. Part 1. Adsorption characteristics[END_REF]. Capillary condensation start at p/p° =0.42.

Theoretically, all pores are fully filled and molecules start spilling when p/p° exactly equals 1. The concentration of gas is maintained constant in both the surrounding environment and the porous system when p/p° = 1. It is empirically considered that all the macropores are radically filled at a relative pressure p/p° greater than 0.99 (Bertier et al. 2016).

Figure 1.5. Main steps of physisorption of N2 at 77K [START_REF] Hamamoto | Study on adsorption refrigeration cycle utilizing activated carbon fibers. Part 1. Adsorption characteristics[END_REF] Desorption refers to the adsorbed gas molecules escape from the pores when p/p° decreases from 1 to 0. For material with complex pore structures (such as COx claystone), wider pores connect with very narrow throats. During desorption, high pore/throat ratio could result in the wider pores will remain filled until the throats empty at much lower pressures. Such effect is reflected in the isotherm as a hysteresis of the desorption phase. Theoretical and experimental studies reveal that the hysteresis is controlled by the comprehensive effects of several mechanisms [START_REF] Rouquerol | Adsorption by Powders and Porous Solids: Principles, Methodology and Applications[END_REF]Thommes and Cychosz 2014) According to the IUPAC2015 report, network effects and pore blocking are the dominant mechanisms for clayey materials.

Applications on the study of COx claystone

Based on several developed analysis theories, the pore textural properties can be converted from the isotherms (Bertier et al. 2016). The most used properties for characterizing COx claystone are:

Gurvich specific pore volume (𝑉 𝐺𝑢𝑟𝑣𝑖𝑐ℎ ) calculated from the Gurvich rule, specific surface area (𝑆𝑆𝐴)

derived by the Brunauer-Emmett-Teller (BET) theory, and the pore size distributions derived by the combination of Barrett-Joyner-Halenda (BJH) and Dubinin-Astakhov (DA) theories. In the following of this section, we will introduce in detail each theory and the related properties of COx claystone.

Gurvich rule

Assuming all pores are filled and the gas has liquid density at the operational temperature (e.g. -196 °C for N2) at p/p 0 close 1, the up limite adsorbed pore volume is the so-called Gurvich specific pore volume (𝑉 𝐺𝑢𝑟𝑣𝑖𝑐ℎ ), is calculated as follow:

𝑉 𝐺𝑢𝑟𝑣𝑖𝑐ℎ = 𝑄 𝑚𝑎𝑥 1000 𝑉 𝑚 (3)
where 𝑄 𝑚𝑎𝑥 is the maximum sorption capacity of the adsorbate, in unit of mmol/g; 𝑉 𝑚 is the liquid molar volume of the adsorbate, in unit of cm 3 /mmol. If the tested material contains micropores, 𝑉 𝐺𝑢𝑟𝑣𝑖𝑐ℎ is underestimated due to the blocking of micropores (Thommes and Cychosz 2014;Bertier et al. 2016). Unlike porosity, which is expressed as a percentage, 𝑉 𝐺𝑢𝑟𝑣𝑖𝑐ℎ is quantified in cm 3 /g. If the density of the absorber is known, 𝑉 𝐺𝑢𝑟𝑣𝑖𝑐ℎ can be converted to porosity by the following equation: (1.4) where 𝜑 𝐺𝑢𝑟𝑣𝑖𝑐ℎ is the Gurvich porosity, 𝜌 is the grains density of the absorbent. Song et al. (2017) performed the nitrogen adsorption analysis on five dry COx samples, with a total clay content varying between 36.8 and 51.9% (in mass). The measured 𝑉 𝐺𝑢𝑟𝑣𝑖𝑐ℎ varied between 0.044 cm 3 /g and 0.062 cm 3 /g. Moreover, water vapor adsorption was performed on two of the five samples using quick static desiccator method, see Figure 1.6. Results demonstrate that the total adsorbed volume (𝑉 𝐺𝑢𝑟𝑣𝑖𝑐ℎ ) measured by water vapor is larger than that by nitrogen. This can be interpreted as the water-clay interaction increases the pore volume. Lahn et al. (2020) found that the nitrogen 𝑉 𝐺𝑢𝑟𝑣𝑖𝑐ℎ increase with decreasing relative humidities (RH) of the COx claystone. This means the 𝑉 𝐺𝑢𝑟𝑣𝑖𝑐ℎ of COx claystone depends on the water content.

𝜑 𝐺𝑢𝑟𝑣𝑖𝑐ℎ = 𝑉 𝐺𝑢𝑟𝑣𝑖𝑐ℎ 1 𝜌 + 𝑉 𝐺𝑢𝑟𝑣𝑖𝑐ℎ

Brunauer-Emmett-Teller theory

The Brunauer-Emmett-Teller (BET) theory is an optimization of the classic Langmuir theory [START_REF] Brunauer | Adsorption of Gases in Multimolecular Layers[END_REF]. The BET theory follows several assumptions, such as the adsorbent surface is supposed to be uniform, no interactions between the molecules in the same layer, gas molecules can adsorb countless layers on a solid surface (Rouquerol et al. 2007). It considers both mesoporous multilayer adsorption and microporous molecule filling in the model, which is often used to quantify the adsorbable pore surface of the porous material.

From the isotherms, two important properties can be converted according to the BET theory, namely the monolayer capacity (𝑄 𝑚𝑜𝑛𝑜 ) and the specific surface area (𝑆𝑆𝐴). 𝑄 𝑚𝑜𝑛𝑜 is determined by transforming the isotherms into the BET plot (in the form of 1 [𝑄(1-𝑝 𝑝°⁄ )] VS. p/p°) with the following equation:

1 [𝑄(1 -𝑝 𝑝°⁄ )] = 1 𝑄 𝑚𝑜𝑛𝑜 𝐶 + [ (𝐶 -1) 𝑄 𝑚𝑜𝑛𝑜 𝐶 ] (𝑝 𝑝°⁄ ) (1.5)
where 𝑄 is the specific amount of adsorptive (mmol/g) at the relative pressure p/p°, and 𝐶 is an empirical constant that is determined by measuring the adsorbent-adsorbate interaction. Rel. (1.8) illustrates that 𝑄 𝑚𝑜𝑛𝑜 linearly corresponds to the relative pressure (p/p°), thus only data from the straight part of BET plot is used for calculation. For practical purpose, [START_REF] Brunauer | Adsorption of Gases in Multimolecular Layers[END_REF] proposed that the useful data to adapt rel. (1.8) corresponds to p/p° range in [0.05, 0.35], which is can be slightly different from each specific adsorptive and adsorbent (Rouquerol et al. 2007).

The specific surface area (𝑆𝑆𝐴) is determined by a mathematical calculation of knowing 𝑄 𝑚𝑜𝑛𝑜 and the molecule cross-sectional area 𝜎 𝑚 of the adsorptive molecule (e.g. 0.162 nm² for Nitrogen at 77K), expressed as:

𝑆𝑆𝐴 = 𝑄 𝑚𝑜𝑛𝑜 • 𝑁 𝐴 • 𝜎 𝑚 𝑚 (1.6)
where 𝑁 𝐴 is the Avogadro number, 6.022×10 23 /mol; 𝑚 is the mass of the adsorbent. Essentially, 𝑆𝑆𝐴 cannot be treated as the real physical surface area but an "effective (or apparent)" surface area because it is derived from a simplified pore model. However, with the strict operation and wellcontrolled experiment conditions, 𝑆𝑆𝐴 is still useful for characterizing the available adsorption area of porous materials (Rouquerol et al. 2007;Thommes and Cychosz 2014). Yven et al. (2007) reported the nitrogen 𝑆𝑆𝐴 varies between 17 and 39 m²/g for COx claystone samples from different depths. Particularly, samples originate from C2b sequence (belong to UA unit, includes higher clay contents) corresponds to relatively high values (Table 1 .4). That is to say, the material with higher clay contents exhibits higher 𝑆𝑆𝐴.

Table 1.5. the information of pore surface area determined by: N2 adsorption (at 77K) (Yven et al. 2007) Seemann et al. ( 2017) performed nitrogen adsorption measurements on 13 different clayey materials (including COx claystone), by using water vapor at 303K and nitrogen at 77K respectively. For COx claystone, the nitrogen 𝑄 𝑚𝑜𝑛𝑜 and 𝑆𝑆𝐴 are 0.36 mmol/g and 35.1 m²/g, respectively. The corresponding values of water vapor are 0.73mmol/g and 46 m²/g, respectively, which are lower than that of water vapor. However, by comparing all 13 different clayey materials, the use of different adsorbents does not lead to significant differences in the results of 𝑄 𝑚𝑜𝑛𝑜 and 𝑆𝑆𝐴.

Barrett-Joyner-Halenda (BJH) theory + Dubinin-Astakhov (DA) theory

The pore size distribution (PSD) is a very important property. It can be obtained based on two theories: Barrett-Joyner-Halenda (BJH) theory and the Dubinin-Astakhov (DA) theory. The Barrett-Joyner-Halenda (BJH) theory is utilized to calculate PSD of pores larger than 4 nm, and the Dubinin-Astakhov (DA) theory is adopted for deriving the micropore size distribution (pore diameter < 2 nm).

The Barrett-Joyner-Halenda (BJH) theory was first established by [START_REF] Barrett | The Determination of Pore Volume and Area Distributions in Porous Substances. I. Computations from Nitrogen Isotherms[END_REF]. This method has two hypotheses: [START_REF] Keller | Image-Based Upscaling of Permeability in Opalinus Clay[END_REF] all pores are in the shape of cylindrical geometry and (2) the retention of adsorbate is controlled by two mechanisms, namely the multilayer adsorption on the pore walls and the capillary condensation in the capillary bundles. Hence the pore radius (𝑟 𝐵𝐽𝐻 ) is the sum of the statistical multilayer thickness (𝑡) and the Kelvin radius (𝑟 𝑘 ) of the liquidvapor interface:

𝑟 𝐵𝐽𝐻 = 𝑡 + 𝑟 𝑘 (1.7)
The multilayer statistical thickness (𝑡) is deduced from the 𝑡-curve and an empirical equation by linking the reciprocal of multilayer-adsorption-pressure to the statistical multi-layer thickness (𝑡):

𝑡 = 𝑘 ( 1 ln (𝑝°𝑝 ⁄ ) )
1 𝑠 (1.8) where the parameters 𝑘 and 𝑠 are both empirical constants, depending on the pore surface chemistry.

Dependent upon the macroscopic thermodynamic principles, the Kelvin radius (𝑟 𝑘 ) is calculated via the classic Kelvin equation:

𝑟 𝑘 = -2 𝑉 𝑀 • 𝜎 𝑤 • cos 𝜃 ln(𝑝 𝑝°⁄ )𝑅𝑇 ⁄ (1.9)
Using rel. (1.7) -(1.9), Yven et al. (2007) have reported the prevailing pores in COx claystone are restricted to small mesopores (2.5 -3.7 nm). It is worth underlining that these calculated value pore diameters are underestimated because using BJH theory to calculate pore size < 10 nm would yield underestimates of up to 20-30% (Thommes and Cychosz 2014). Nevertheless, 𝑟 𝐵𝐽𝐻 is still useful to compare between samples as the computational errors do not affect the qualitative results.

For the micropores PSD analysis, Dubinin-Astakhov (DA) theory is a prioritized approach recommended by both ISO15901 and IUPAC. Based on the theory of volume filling (micropores)

(TVF(M)), the molar work of adsorption (A) in micropores is defined as equal to the loss of Gibbs free energy (-∆𝐺 ). Thus A can be predicted by involving the thermodynamics principles: A = -∆𝐺 = -𝑅𝑇 ln(𝑝 𝑝°⁄ ) (Seemann et al. 2017). Since 𝐴 and 𝑄 can be derived from the isotherm data, the Dubinin-Astakhov equation gives a mathematical method to determine the pore size distribution (Dubinin and Astakhov 1971):

Θ = 𝑄 𝑄 0 = exp [-( 𝐴 𝐸 ) 𝑛 ] (1.10)
where Θ is the fraction of filled micropore volume, 𝑄 0 is the limiting micropore capacity (cm 3 /g) for a certain pore diameter, 𝐸 is the characteristic energy (KJ/mol) of the adsorption system, 𝑛 is the adjustable exponent. Both 𝑄 0 and 𝐸 are the inherent properties of the adsorbtion system and can be obtained by non-linear curve fitting rel. (1.10) (Seemann et al. 2017). The equivalent micropore radius (𝑟 𝑒 ) can be calculated by the simplified van der Waals equation:

𝑟 𝑒 = √ - 𝑘 ∆𝐺 3 (1.11)
where 𝑘 is the interaction constant. According to Janssen and Van Oorschot (1989), 𝑘 𝑁 2 is estimated to be 2.96 KJ•cm 3 /mol.

In Seemann et al. (2017), both BJH theory and DA theory were used to assess pore size distributions of 13 different claystone samples. Results demonstrate that the most popular pore size measured with nitrogen is slightly below 20 nm, while using water vapor leads to smaller pore size. This can be interpreted by the water vapor adsorption process being highly sensitive to rock properties (such as contact angle) and the BJH theory is not of good accuracy. As shown in Figure 1.7, DA micropore volume (𝑄 0 ) is linearly related to the BET monolayer adsorption volume (𝑄 𝑚𝑜𝑛𝑜 ). This implies that the 𝑄 𝑚𝑜𝑛𝑜 does not only relate to the monolayer adsorption capacity and specific surface area, but also being a quantization parameter of micropore volume. It has been reported that the gas sorption is highly affected by the saturation of clayey materials.

Figure 1.8 shows the cumulative pore-size distribution of COx claystone at different relative humidities (RH). One can find that the adsorption capacity decreases with the increase of RH. Results also demonstrate that nitrogen can be still adsorbed in micropores and narrow small mesopores (diameter lower than 10 nm) at high relative humidity (up to 94%RH), but the adsorbed volume sharply decrease with RH increase. This means that partial microporosity is still accessible even at high saturation. Results indicate that its complex pores system consists of a large amount of mesopores and a small amount of micropores and macropores. The Gurvich pore volume (𝑉 𝐺𝑢𝑟𝑣𝑖𝑐ℎ ) is a property derived based on the Gurvich rule, which can be used to quantify the total adsorption capacity of the material.

The monolayer capacity (𝑄 𝑚𝑜𝑛𝑜 ) and the specific surface area (𝑆𝑆𝐴) (of mesopores) are derived from BET theory. They are both "apparent" rather real properties, but can still be used to compare between samples. The PSD of meso-and micro-pores can be deduced by applying BJH theory and DA theory, respectively. Previous studies also proven that the above mentioned properties are highly affected by saturation states.

Nowadays, the most accurate approaches are density functional theory (DFT) and Monte Carlo simulation, which based on the fundamental principles of statistical mechanics. However, the two methods are based on models with certain homogeneous pore geometry, and none of these is well fitted for complex composite pore systems. Therefore, using the classical theories (i.e. Gurvich, BET, BJH, and DA theory) are still elegant solutions for characterizing gas physisorption on claystone.

Micro-Computed Tomography (Micro-CT)

Micro-Computed Tomography (Micro-CT) is an imaging technique used to observe pore structures from mesoscale (μm) to millimeter-scale (mm). The principle of this technique is to scan the sample horizontally with an X-ray to obtain a series of 2D images with the same spacing in the vertical direction.

The 2D images are then superimposed in the vertical direction to construct a 3D image. The 3D image is composed of two parts: the skeleton and the pore network. Micro-CT is a non-destructive method because there is no need to pre-treat the sample and the sample can remain integrity after scanning.

Scanning Electron Microscopy (SEM)

The size of mineral grains and the inter-mineral pores of COx claystone are often at the meso-even microscale. Hence, the Micro-CT is not sufficient to study these objectives and higher precision technique, i.e. Scanning Electron Microscopy (SEM), is needed.

Using SEM can acquire high-resolution images at very high magnification, thanks to the thermionic incident electrons and the atoms on (or approx. 0.5-1 micron below) the sample surface are interacting.

During the scanning, low currents primary electron beam will slightly sputter and raster the target surface, and generate Secondary Electrons (SE) and BackScattered Electrons (BSE). SE images can characterize the sample topography (three-dimensional appearance), with relatively bright steep surfaces and edges and dark flat surfaces. For the standard thermionic SEM, the SE images can maintain a relatively high resolution at high magnification, which can be up to approx. 50-100 nm (depending on the electrical conductivity of the material surface). BSE are produced by the interactions of atoms down to approximately 0.5-1 micron below the surface. Due to the different chemical properties of the atoms, the BSE exhibit a contrasting brightness in images: the heavier the atom, the brighter the area observed in the images. Therefore, detailed mineral information can be obtained from the BSE images [START_REF] Song | Water retention and fine microstructure of Bure argillite[END_REF]. Generally, the BSE images have a lower resolution than SE images. The processing of the sample surface is a very important part of the scanning test. Broad Ion Beam (BIB) polishing method is often used to acquire neat observe cross-sections. By bombarding the target surface with a heavy ions beam (typically argon), a certain mass of sample material is removed and a truly planar surface with less than 5 nm topography deviation is formed. The polished cross section varies from hundreds microns up to 1-2 millimeters in diameter [START_REF] Philipp | The effect of microstructural heterogeneity on pore size distribution and permeability in Opalinus Clay (Mont Terri, Switzerland): insights from an integrated study of laboratory fluid flow and pore morphology from BIB-SEM images[END_REF]. To this day, it is possible to reconstruct the 3D microstructure of the porous material at nanometric size by combining SEM and Focused Ion Beam (FIB) techniques (Klaver et al. 2015;Song et al. 2016aSong et al. , b, 2019;;[START_REF] Keller | Pore geometry effects on elastic properties of Opalinus Clay[END_REF][START_REF] Davy | Three-scale analysis of the permeability of a natural shale[END_REF][START_REF] Keller | Understanding anisotropic mechanical properties of shales at different length scales: In situ micropillar compression combined with finite element calculations[END_REF][START_REF] Brisard | Mesoscale pore structure of a high-performance concrete by coupling focused ion beam/scanning electron microscopy and small angle X-ray scattering[END_REF][START_REF] Keller | Image-Based Upscaling of Permeability in Opalinus Clay[END_REF][START_REF] Song | A Local-Effective-Viscosity Multirelaxation-Time Lattice Boltzmann Pore-Network Coupling Model for Gas Transport in Complex Nanoporous Media[END_REF]. For the 3D reconstruction, a strong current finely focused ions beam (usually gallium) is used to cut a U-shaped hole to isolate a cube volume on the sample surface, see Figure 1.15 (a).

Then cube-shaped sample is cutted into slices by focused ion beam at a constant thickness of 10-50 nm along z-axis. Once a fresh surface is cut, it will immediately be captured as an SEM image with an inclined angle of 52° to the x-y plane. All 2D images are stacked in order to reconstruct a synthetic 3D image. [START_REF] Boulin | Experiments to estimate gas intrusion in Callovooxfordian argillites[END_REF]Van Geet et al. 2008;Zhang 2011;Wang et al. 2015;[START_REF] Harrington | Gas transport properties through intact and fractured Callovo-Oxfordian mudstones[END_REF]Giot et al. 2019;Bossart et al. 2019). Obviously, the desaturation/resaturation cycles (in the presence of in-situ stress) can lead to a significant impact on the transport and mechanical properties of COx claystone. Therefore, understanding these phenomena is crucial for the stability and safety of the repository.

Shrinkage and swelling

It was generally observed that the volumetric behavior exhibits strong transverse isotropy. The swelling/shrinkage strain amplitude is found to be more pronounced in the direction perpendicular to the beddings. Submitting one COx claystone sample to several drying/wetting cycles [START_REF] Yang | Dependence of elastic properties of argillaceous rocks on moisture content investigated with optical full-field strain measurement techniques[END_REF] )

reveals that the strain induced by hydration is more heterogeneous at the μm-scale than at the millimeter scale. This can be interpreted by minerals having specific orientations at the μm-scale.

Whatever the direction, strain always shows non-linearity and a decreasing trend of amplitude after several drying/wetting cycles, which is attributed to the micro-cracking during the cycles [START_REF] Yang | Study of the Anisotropic Properties of Argillite Under Moisture and Mechanical Loads[END_REF]. Wan et al. (2013) measured the water content and porosity of COx claystone by applying different suctions on the COx claystone. Results demonstrate that for suction varying from 0 to 150 MPa, the water content of such material changes between 12% to 3%, with a porosity range in 16.5% to 23%. The volumetric strain exhibits shrinkage of 1.4% at 150 MPa suction and a 7% swelling at 0 suction. After several drying/wetting cycles, water content and saturation appeared to be reversible while the volumetric strains are observed irreversible (Figure 1.17). 1.19). This swelling mechanism is known as the crystalline swelling. For gel or powder materials, the smectite swelling in the suspension was up to more than 100 Å (Delvaux 1992). That is to say, the swelling amplitude can reach a much greater value than crystalline swelling. Such a swelling mechanism is the so-called osmotic swelling. Essentially, osmotic swelling is attributed to the repulsion effect of neighbor particles. Due to the individual subdivided smectite particle carries negative charges on its surface, the inter-layer spacing will increase when adjacent particles are close enough to each other (Anderson et al. 2010). significant deformation perpendicular to, rather than along, the bedding planes. In particular, the wetting episode typically shows a profound strain variation than the drying episode. Results also indicate that a higher proportion of total clay mineral (including interstratified I/S, illite, muscovite, kaolinite, and chlorite) corresponds to a larger swelling pressure in all directions.

Thanks to the intriguing works of Saiyouri et al. (2000) and other researchers, we can have a basic knowledge of the two swelling mechanisms of smectite. From the viewpoint of the deformation scale, the two mechanisms corresponding to two different pore scales: the crystalline swelling occurs in micropores (3 to 12 Å) while the osmotic swelling occurs in mesopores (up to 10 nm). In the natural word, smectite does not appear as a single-phase but is interspersed in I/S aggregates, and I/S aggregates are mixed with other clay and non-clay minerals in COx claystone. With such a complex microstructure, the current understanding of COx claystone swelling usually remains phenomenological, the underlying relationship between multi-scales swelling mechanisms is still not completely understood.

Poro-mechanical properties

Numerous studies have confirmed that the water content change typically leads to the stiffness change of COx claystone [START_REF] Ibrahim | Caractérisation des propriétés mécaniques des géomatériaux par technique de micro indentation[END_REF]Cariou et al. 2012a;Zhang et al. 2019). COx claystone is known as a transverse isotropic material, thus its mechanical properties analysis should be carried on from two directions: along bedding planes (⊥) and perpendicular to bedding planes (∥). Cariou et al (2012a) reported the drained bulk moduli 𝐾 𝛽 (𝛽 ∈ {⊥, ∥}), which is obtained by a series of "change in pore pressure" poro-mechanical tests, see Figure 1.22. Results demonstrate that 𝐾 ∥ is typically greater than 𝐾 ⊥ , and dried samples exhibit higher values. Since the water dilation coefficient is higher than the COx claystone one, the hydro-mechanical loading on the material may causes different effective tensile stresses due to water overpressure and low rock permeability (10 -20 to 10 -21 m 2 water permeability). Hence, understanding the poro-mechanical properties of COx at different water saturations is crucial for the stability and safety of the nuclear waste repository (Duan et al., 2021;[START_REF] Hu | Influences of Mineralogy and Water Content on the Mechanical Properties of Argillite[END_REF]. For instance, radioactive wastes are thermally active and temperature increase up to 90°C is expected by Andra. This effective stress is obviously linked to the material poro-elastic behavior and particularly to its Biot's tensor.

It has thus long been evidenced that this material exhibits a transverse isotropic behavior (Zhang and Rothfuchs, 2004;[START_REF] Guillon | Response of Callovo-Oxfordian claystone during drying tests: unsaturated hydromechanical behavior[END_REF]Cariou et al., 2012) but most of the (very few) studies related to its poro-mechanical properties do not really take into account this important fact. It is may be due to the extreme difficulty in performing accurate measurements of strains (due to pore pressure) during a very long experimental time (weeks and/or months for a single test -see in the following). For such an anisotropy, the effective stress cannot be "a priori" calculated with a single Biot's coefficient 𝑏 but with a two order Biot's tensor, which contains two independent components in the structural material axes. However, due to major difficulties to measure these components, many researchers simplified the experimental analyses, i.e. the tests were analyzed as if the COx claystone was isotropic [START_REF] Bemer | Poroelastic parameters of Meuse/Haute Marne argillites: effect of loading and saturation states[END_REF][START_REF] Vincke | Investigation of the Poromechanical Behavior of Shales in the Elastic Domain[END_REF]. As a consequence, many experimental studies found in the literature, consider an "isotropic" Biot's tensor within the framework of isotropic poro-elasticity.

The measured Biot's coefficient of COx claystone found in the literature, is scattered in a large range -between 0.26 and 1. The reliability of such results can therefore be questioned. For a long period of time, Andra had used 0.6 as average 𝑏-value as a reference for numerical studies (Andra, 2005). Such disperse values evidence the difficulty to carry out "accurate" measurements. When compared with other rocks or porous materials, Biot's coefficients lower than 0.5 -0.6 seem unlikely. b= 0.2-0.3 is met for some salts (Zhang et al., 2020) with a porosity less than 1%, 0.5 -0.7 are quite common for concrete [START_REF] Pei | Effects of severe heating and rehydration on poromechanical properties of a mortar[END_REF] or sandstones [START_REF] Wang | Experimental study and micromechanical interpretation of the poroelastic behaviour and permeability of a tight sandstone[END_REF] but these kinds of material are far from being comparable to claystone, which remains a soft rock, especially in a fully water saturation state. whereas the back-calculated bulk Biot's modulus leads to Biot's coefficient close to 1. This value is also confirmed by [START_REF] Giot | Multi-stage water permeability measurements on claystone by steady and transient flow methods[END_REF]. More recently, a study of [START_REF] Braun | Transversely Isotropic Poroelastic Behaviour of the Callovo-Oxfordian Claystone: A Set of Stress-Dependent Parameters[END_REF] showed two Biot's tensor components close to 1 and depending on the confining pressure. However, the measurement methods

were not direct and the Biot's coefficients were often obtained from back-calculations.

Our laboratory has carried out a series of poro-mechanical studies on COx claystone during the past decade (Cariou et al., 2012[START_REF] Cariou | An original constitutive law for Callovo-Oxfordian argillite, a two-scale double-porosity material[END_REF]Yuan et al., 2017;Hu et al., 2020). In contrast to many results reported in the literature, these studies clearly showed that, despite the structural anisotropy, the Biot's tensor was isotropic leading to a coefficient very close to 1.

However, these previous works were carried out on partially saturated material and used gas as the fluid to control pore pressure. It was particularly demonstrated by (Cariou et al., 2012) that any increase in gas pressure at both sample ends led to the same increase in pressure for the water and gas phases present into the material porous structure. This showed that gas was theoretically a convenient fluid to perform such experiments. However, doubts remained about their equivalence with measurements using water to control the pore pressure and to maintain a full saturation state.

Due to the low water permeability (about 10 -20 to 10 -21 m²), using water as the pore fluid to change pore pressure of saturated samples can be very time-consuming. Recently, Hu et al (2020) first use water as the pore fluid to identify the Biot's tensor of COx claystone. Results implies that even though the material exhibits anisotropic strain behavior, the Biot's tensor is isotropic and, given inherent experimental uncertainties is lying into the range 0.9 to 1 (Figure 1.23). From a theoretical viewpoint, the in-situ COx claystone can be considered as comprising of an isotropic solid matrix and an anisotropic pore network. The multi-scales swelling plays an important role in the self-sealing of EDZ. In the literature, swelling can lead to the increase of water content and porosity. The swelling amplitude increases with the sample saturation degrees and smectite content. However, the effect of smectite distribution in the interstratified illite/smectite phases has not been reported. Moreover, the link between smectite swelling-clay matrix deformation and macroscopic swelling of COx claystone is still poorly understood.

Therefore, understanding the multi-scales swelling mechanisms of COx claystone at different saturation states is crucial. In this thesis, it is concerned particularly with the underlying dominant swelling mechanisms as saturation changes.

Pore water content can significantly increases during the hydration of COx claystone. Due to the low rock permeability, pore pressure will cause effective tensile stresses on the solid phase during hydromechanical loadings. In the laboratory conditions, the Biot coefficient can be determined by the "change in pore pressure" test. The Biot coefficient of dried and partially saturated COx claystone with gas is confirmed to be isotropic (Hu et al. 2020) and close to 1 (Cariou et al. 2012a;Yuan 2017), while the Biot coefficient of saturated material is still needed to be further investigated. In this thesis, experiments have been designed to complete gas experiments and to verify whether they are consistent with water experiments. Reconstituted synthetic water (close to the in-situ one) was used to measure the Biot's components in the saturated state. Two main results had to be confirmed: Biot's tensor isotropy and a unique coefficient close to 1.

Fluid transport: permeability, self-sealing and gas breakthrough

The continuous heat release of the long-life radioactive waste can reduce the strength of the engineering barrier (Reinhardt and Jooss 2003). Once the engineered barrier is damaged, the radionuclide can dissolve in the groundwater and percolate into the COx formation and causing contamination of the biosphere. On the other hand, degradation of the engineered barrier would allow reverse groundwater infiltration, this will cause a moist reservoir environment inside the repository.

Chemical interactions between groundwater and metal facilities can cause metal corrosion and gases generation (usually hydrogen) around the waste repository. When the gas generation rate is much greater than its dissolution rate, a gas pressure gradient arises and the preferential gas pathways are bound to form and propagate, which may allow the radionuclides migrate through to the formation.

Hence, it is essential to understand, analyze, and quantify the water or gas transport in COx claystone. neglecting the effect of gravity, Darcy's law for water can be simplified as:

𝑄 𝐴 = 𝑉 𝑥 = -( 𝐾 water 𝜇 ) 𝑑𝑃(𝑥) 𝑑𝑥 = 𝐾 water 𝜇 (𝑃 1 -𝑃 2 ) 𝐿 (1.12)
where 𝑉 𝑥 is the average flow velocity in the direction of 𝑥 ⃗, which can be derived by the ratio of volume flow rate 𝑄 and cross-sectional area 𝐴; Kwater is the water permeability along 𝑥 ⃗, 𝜇 is the liquid viscosity. P1 and P2 are respectively the gas pressure at upstream and downstream sides of the sample.

From rel. (1.12), one can find that Kwater is an inherent property of the material that theoretically should not depend on the experimental setting conditions, such as sample size and temperature. In fact, water interacts with clay rock (and also with many low porosity materials -concrete for example) and Kwater is not an intrinsic property. When compared to gas permeabitliy Kgas, orders of magnitude difference can be usually found.

For a gas transport process, the gas flux state is governed by its pressure, volume, and temperature.

Assuming the gas is perfect, the ideal gas law can be used as the mass balance equation:

𝑃𝑉 = 𝑛𝑅𝑇 (1.13)
Assuming the use of an ideal gas and under isothermal conditions rel. (1.13) leads to

𝑃 𝜌 = 𝑑𝑃 𝑑𝜌 = 𝑐𝑠𝑡𝑒 (1.14)
According to rel. (1.12) -(1.13) or (1.14) and the mass balance equation, the Darcy's law for a compressible media (i.e. a gas) (K app gas ) leads to:

𝑄 𝐴 = 𝐾 gas app 2𝜇𝐿 (𝑃 1 2 -𝑃 2 2 )
𝑃 2 (1.15) In rel. (1.15), Q is the volumetric gas flow rate at downstream sample side. Researchers found that the calculated gas permeability using experimental data and rel. (1.15) is not constant but linearly decreases with increasing mean gas pressure [START_REF] Klinkenberg | THE PERMEABILITY OF POROUS MEDIA TO LIQUIDS AND GASES[END_REF][START_REF] Tanikawa | Klinkenberg effect for gas permeability and its comparison to water permeability for porous sedimentary rocks[END_REF][START_REF] Chen | Coupled transport and poro-mechanical properties of a heattreated mortar under confinement[END_REF][START_REF] Song | Water retention and fine microstructure of Bure argillite[END_REF][START_REF] Sabet | An extended Kozeny-Carman-Klinkenberg model for gas permeability in micro/nano-porous media[END_REF]. This phenomenon relates to the pressure-and temperaturedependent mean free path of the gas molecules [START_REF] Klinkenberg | THE PERMEABILITY OF POROUS MEDIA TO LIQUIDS AND GASES[END_REF][START_REF] Sabet | An extended Kozeny-Carman-Klinkenberg model for gas permeability in micro/nano-porous media[END_REF]. When the gas pressure is low and the average pore diameter is small, the mean free path shortens and increases the frequency of collision between gas molecules and pore walls and results in an additional gas slip flow along the wall surface [START_REF] Klinkenberg | THE PERMEABILITY OF POROUS MEDIA TO LIQUIDS AND GASES[END_REF]). This effect is termed "Klinkenberg effect" or "slippage effect"

and can be written as:

𝐾 gas app = 𝐾 gas int (1 + 𝛽 𝑃 𝑚 ) (1.16)
where 𝛽 is the Klinkenberg coefficient, which is related to the temperature and the average pore diameter for gas transport, Pm is the average gas pressure: Pm = (P1 + P2)/2. Generally, a so-called "Klinkenberg correction" method is used to remove the Klinkenberg effect. It is achieved by recording the measured apparent permeability at different average gas pressure i.e. K app gas as a function of (1/Pm). Extrapolating the trend curve to infinite pressure (1/Pm → 0), the intrinsic gas permeability can be estimated, see Figure 1.24.

Experiments confirmed that Klinkenberg coefficient depends on the gas type. [START_REF] Boulin | Experiments to estimate gas intrusion in Callovooxfordian argillites[END_REF] studied the nitrogen flow in COx claystone and found that rel. (1.16) is only valid for gas pressure larger than 5 bar. This reveals that the Darcy's flow is not the dominant transport mechanism at low gas pressure. [START_REF] Chen | Water retention and gas relative permeability of two industrial concretes[END_REF] used argon and helium to study gas transport properties of two concrete materials. Results illustrate that the Klinkenberg effect is less pronounced by using argon than helium (Figure 1.24 (a)). This can be explained by the molecule size of argon is bigger than helium and lead to a less significant slippage effect. Skoczylas (2011) and M'Jahad (2012) used argon to study the permeability of COx claystone and found that the Klinkenberg coefficient appears in a relatively small value when injected gas pressure is between 1 to 3 MPa, regardless the sample cracked or not (Fig. 1.24 (b)). In literature, the water permeability of saturated COx claystone ranges in 10 -20 -10 -21 m², and the Klinkenberg corrected gas permeability of which is found located between 10 -17 m² and 10 -19 m² (Davy et al. 2007a;M'Jahad 2012;Song et al. 2016a;[START_REF] Liu | Gas migration through water-saturated bentonite-sand mixtures, COx argillite, and their interfaces[END_REF]). If a porous material contains two or more immiscible fluids (e.g., water, gas, oil, etc.), the mass transfer in the pore network is called two-phase (or multi-phase) flow. In the context of nuclear waste storage, the two-phase flow in COx claystone is comprised of underground water and corrosioninduced gas. Four transport mechanisms have been documented in the literature that leads to gas migration: diffusion, two-phase capillary flow, dilatancy-controlled flow, and gas fracturing (Horseman et al. 1999;[START_REF] Hildenbrand | Gas breakthrough experiments on fine-grained sedimentary rocks[END_REF]Marschall et al. 2005). Among them, the dilatancy-controlled flow and gas fracturing only occur when the initial gas pressure is extremely high (at least exceed the confining pressure), which is not the potential scenario around the nuclear storage repository. Hence, only diffusion and two-phase flow are discussed here below.

Diffusion refers to gas molecule migration by means of dissolving in pore water, in the dispersed organic matter, and long mineral surfaces. This process can occur at very low gas pressure because it is mainly controlled by the gas concentration difference, the ambient temperature, and the organic matter maturity level [START_REF] Amann-Hildebrand | Transport properties of unconventional gas systems[END_REF][START_REF] Busch | Predicting capillarity of mudrocks[END_REF]. The effective diffusion coefficient (𝐷 eff ) is used to represent the bulk diffusion efficiency of claystone, expressed by Fick's first law:

𝐽 𝐷 = -𝐷 eff 𝑑𝐶 𝑏𝑢𝑙𝑘 𝑑𝑥 (17)
Where 𝐽 𝐷 is the diffusive flux (mol/m²/s), 𝐷 eff is the effective diffusion coefficient (m²/s), 𝐶 𝑏𝑢𝑙𝑘 is the bulk gas concentration (mol/m 3 ) comprising contributions by pore water, organic matter, and matrix mineral surface, 𝑥 is the sample length (m) that along the direction of concentration gradient.

In the claystone, diffusion mainly occurs in the water-saturated pores, and 𝐷 eff can be characterized by the product of the gas diffusion coefficient in free water (𝐷 water ) and the water-saturated porosity (𝜙):

𝐷 eff = 𝜏 • 𝐷 water • 𝜙 (1.18)
 is a corrective factor that is able to take into account the porous network tortuosity.

By definition, diffusion is a continuous and ubiquitous process as long as the gas phase is present.

However, compared with the pressure gradient-driven transport (Darcy's flow), its transport efficiency is very limited. In analogy to heat transport, Amann-Hildenbrand et al. ( 2012) used the dimensionless Peclet number (Pe) (sample length×fluid velocity/effective gas diffusion coefficient) to express the ratio of convective to diffusive transport. Results indicate that pressure-driven flow is the dominating process when Pe >> 1 while diffusion dominates the transport process when Pe << 1. Typically, a Peclet number close to 1 corresponds to an effective permeability coefficient less than 10 -22 m². For most laboratory gas transport tests on COx claystone, the value of Pe is found much larger than 1 even if only a small gas pressure (several bars) is applied.

Two-phase capillary flow refers to a pressure gradient-driven two immiscible fluids volume flow in the porous network. Fluid phases are not synchronized during a two-phase capillary flow, and each fluid phase has its own effective permeability (𝐾 eff ). When the material is 100% saturated by one fluid, 𝐾 eff of the fluid is equal to its intrinsic permeability (𝐾 int ) independent of the fluid type. When the sample is partially saturated, the ratio of 𝐾 eff and 𝐾 int of a certain fluid phase is defined as its relative permeability (𝐾 rel ).

Sometimes, 𝐾 rel is very difficult to measure directly especially if concerning the wetting phase. For example it is quite easy to measure effective gas permeability for a partially water saturated material since effective water permeability is almost non directly measurable for low porosity materials. If the saturation is known, Krel can be estimated by the van Genuchten-Mualem (vGM) model [START_REF] Schaap | Improved Prediction of Unsaturated Hydraulic Conductivity with the Mualem-van Genuchten Model[END_REF]Marschall et al. 2005;[START_REF] M'jahad | Characterization of transport and water retention properties of damaged Callovo-Oxfordian claystone[END_REF] as:

𝐾 rg = (1 -𝑆 𝑤 ) 𝜂 (1 -𝑆 𝑤 1 𝑚 ) 2𝑚 𝐾 rw = 𝑆 𝑤 𝜂 [1 -(1 -𝑆 𝑤 1 𝑚 ) 𝑚 ] 2 (1.19)
where Krg and Krw are the relative gas permeability and relative water permeability, respectively;  and m are empirical shape factors.  describes the pore connectivity of the material while m corresponds to the pore size distribution. Sw is the water saturation degree, which can be determined by weighing the sample or by knowing the capillary pressure (M'Jahad et al. 2017): (1.20) where mcurrent is the present sample mass, mdry is the dry mass, and msaturated is water-saturated mass.

𝑆 𝑤 = 𝑚 current -𝑚 dry 𝑚 saturated -𝑚 dry = (1 + ( 𝑃 cap 𝑃 𝑟 ) 1 1-𝑚 ) 𝑚
Pcap refers to the present capillary pressure, and Pr is interpreted as the gas entry pressure (see section

3.3).

It is worth noticing that the empirical parameters 𝜂 and 𝑚 vary significantly between materials. For COx claystone, is generally pick 0.5 (Marschall et al. 2005) and ANDRA (2005) suggest that m is around 0.329. However, Cariou et al. (2012b) found that using rel. (1.19) to fit Krg vs. saturation data, m equal to 0.817. Such a variation in m can be interpreted by the different clay mineral contents between samples, which in turn affect the geometry of the morphology of pores. In fact, with gas for which direct measurements are available, these two coefficients can be regarded more as fitting properties without real physical meanings.

Self-sealing of COx

One of the favorable properties of the EDZ is that cracks tend to close over time after the repository closure, i.e. self-sealing. In terms of fluid transport, self-sealing leads to a significant decrease in gas/water permeability (Davy et al. 2007a;[START_REF] Delay | Three decades of underground research laboratories: what have we learned?[END_REF]Bossart et al. 2019). Self-sealing is a very important property since it can delay the radionuclides migration along the water and gas flow channels. Although the term "self-healing" is mentioned in some European projects for integrated research on the nuclear waste geological storage (such as SELFRAC and NEA), most observations reveal that the EDZ of COx claystone can only self-sealed or partially self-healed (de La Vaissière et al. 2015). Table 1.7 exhibits an overview of the classical experimentally research on the self-sealing of different clayey materials. We can summarize from Table 1.5 that in both in situ and laboratory experiments, the self-sealing of claystone mainly reflects on the closure of cracks and the decrease in permeabilities.

Table 1.7 also illustrates various artificial fractures that were used to simulate the cracks in laboratory experiments, such as cylindrical tiny holes, hollowed samples, neat cracks cut by diamond saw, and compressed shear cracks. A 3D visualization of the excavation-induced fracture network is shown in In the laboratory experiments, the in-situ stress is reproduced by loading confining pressure on recored samples. Various laboratory techniques (e.g. LVDT, strain gauges, wave velocity, etc.) were used to study the effect of confining pressure on self-sealing. Davy et al (2007) reported that loading confining pressure leads to an irreversible decrease of the crack aperture in COx claystone. Figure 28 exhibits the evolution of crack closure (cc) subjected to cycles of loading/unloading confining pressure (Pc), the corresponding gas permeability (Kg) VS. confining pressure (Pc), and gas permeability (Kg) VS.

crack closure (cc). One can find in Figure 1.27 (a) that despite the close amplitude is different for each sample, Pc VS. cc tends to be linear after the first cycle, and each loading almost identical to the other.

This means that during increasing Pc cracks first irreversibly closed then behaved elastically. Besides the effect of confining pressure and thermal aspects, the clay minerals swelling during resaturation has an important effect on self-sealing also. The principle of volumetric swelling is the interaction between underground water and specific clay mineral (i.e. smectite), which was already discussed in section 2.2. Table 1. By visualizing the cracked zone and the water permeability over time, Giot et al. (2019) proposed a useful conceptual model to describe the self-sealing mechanisms of clay-rich samples (UA type), which involved the crystalline swelling and osmotic swelling and the mineral particle clogging of the crack zone. Technically, the in-situ volume swelling behavior is not as easy to analyze as confining pressure and temperature because it is difficult to evaluate separately from the confining pressure.

To sum up, the self-sealing and (partially) self-healing of EDZ is a complex long-term thermal-hydromechanical coupling process, depending on the morphology of the fracture network, stress filed redistribution, thermal impacts, and swelling capacity of smectite.

Gas breakthrough pressure

Since the instantaneous gas pressure (mainly hydrogen) around the repository is not like to exceed the formation stress (approx. 14 MPa in Bure URL), the dilation of flow passages and gas fracturing are not the plausible dominant gas transport mechanisms in the COx claystone. According to the laboratory experimental data, the equivalent gas permeability of diffusion in COx claystone is orders of magnitude smaller than that of the pressure-driven transport process [START_REF] Hildenbrand | Gas breakthrough experiments on fine-grained sedimentary rocks[END_REF][START_REF] Hildenbrand | Gas breakthrough experiments on pelitic rocks: comparative study with N2, CO2 and CH4[END_REF][START_REF] Amann-Hildebrand | Transport properties of unconventional gas systems[END_REF]. Based on the Laplace's law, the mobility of the gas phase in the pressure-driven transport is determined by capillary process. The capillary process is affected by interfacial tension, wetting angle, and pore geometry [START_REF] Hildenbrand | Gas breakthrough experiments on fine-grained sedimentary rocks[END_REF][START_REF] Hildenbrand | Gas breakthrough experiments on pelitic rocks: comparative study with N2, CO2 and CH4[END_REF][START_REF] Busch | Predicting capillarity of mudrocks[END_REF]. Generally, Young-Laplace's equation (rel. (1.2)) is used to determine the threshold pressures during the gas migration process.

Figure 1.30 illustrates that the relationship between capillary pressure and gas saturation during two-phase flow. Assuming the pore system is initially water-saturated and the gas pressure increase continuously from zero, the gas saturation does not increase until gas starts to enter the porous system at a certain pressure, which is termed capillary entry pressure (PEntry). At PEntry, the gas phase will drive the pore water to start moving towards the largest (not necessarily interconnected) pores. By increasing the gas pressure, the gas will successively invade the porous structure and drive the free water out of the pore network. When the first interconnected gas flow path appears, the corresponding capillary pressure is called gas breakthrough pressure (PBreakthrough). After breakthrough, the gas saturation and effective gas permeability increase with capillary pressure. When no more water is extruded from the rock body, we can obtain the corresponding maximum gas saturation and irreducible water saturation. The maximum gas saturation and the irreducible water saturation correspond to the biggest effective gas permeability and the smallest effective water permeability, respectively. With successive decreases in the capillary pressure from this point, water will gradually refill the pore network. When the last inter-connected gas flow path is closed, the corresponding pressure is called snap-off pressure (Psnap-off) (or residual pressure). Psnap-off is typically smaller than PEntry and PBreakthrough [START_REF] Egermann | A Fast and Accurate Method to Measure Threshold Capillary Pressure of Caprocks Under Representative Conditions[END_REF]). Amann-Hildebrand et al ( 2012) reported that the Psnap-off of limestone and shale are about half the PBreakthrough. Generally, there are two approaches to measured the PBreakthrough: steady-state approach and nonsteady-state approach. For a steady-state approach, the sample is first subjected to a constant confining pressure, then a reservoir is connected to its upstream with constant gas pressure and the downstream connects to the atmosphere. Stepwise increasing the upstream gas pressure, PBreakthrough is determined by a continuous gas flow leading to pressure detected at downstream, see Figure 1.31 (a). For a non-steady-state experiment, both ends of the sample are connected to a gas reservoir. By imposing an instantaneously high gas pressure at upstream (exceeding the expected GBP), the gas will migrate under the pressure gradient, the breakthrough is assessed when the downstream pressure start to increase, see Figure 1.31 (b). With the non-steady-state experiments, we can also get both PBreakthrough and Psnap-off.

(a) (b) Figure 1.31. Schemes of two approaches of the gas breakthrough experiments (a) steady-state experiment with a constant upstream pressure (Song et al. 2016a) (b) non-steady-state experiment with a fixed upstream volume [START_REF] Hildenbrand | Gas breakthrough experiments on fine-grained sedimentary rocks[END_REF] In the field of oil exploration and CO2 storage, both the steady-state approach and the non-steadystate approach are widely used to study the gas transport in various sedimentary rocks (such as claystone, limestone, sandstone, etc.) using different gases. Results reveal that the transport porosity account for a very small fraction of the total porosity regardless the gas type. The study on the COx claystone shows that, the maximum gas effective permeability after breakthrough decreases with capillary pressure, eventually stabilizes at a value one to several orders of magnitude lower than the intrinsic permeability (Zhang 2015). For different gas type, nitrogen have the biggest GBP while CO2 corresponds to a lowest, the interfacial tension and wetting angles of different gases seem to be the key impact factors to the breakthrough pressure [START_REF] Hildenbrand | Gas breakthrough experiments on pelitic rocks: comparative study with N2, CO2 and CH4[END_REF][START_REF] Busch | Predicting capillarity of mudrocks[END_REF]. The snap-off pressure is a rock type-dependent parameter and varies from 0.06 to 6.7 MPa for different claystone [START_REF] Hildenbrand | Gas breakthrough experiments on fine-grained sedimentary rocks[END_REF].

For nuclear waste storage, steady-state approach is used to simulate the gradual accumulation effect of gas pressure around the repository. [START_REF] Davy | Gas migration properties through a bentonite/argillite interface[END_REF] used this method to study gas migration through saturated bentonite/argillite (COx claystone) plugs. The effective swelling pressure after water injection is around 7.5 MPa, while the "gas critical pressure" (i.e. the injection pressure when the first gas bubble is detected at downstream, often called discontinuous PBreakthrough) equal to 4.35 MPa ± 0.95.

Chapter 2 -Experimental study of the multi-scale swelling mechanism of Callovo-Oxfordian claystone

In this chapter, the multi-scale swelling mechanism of Callovo-Oxfordian (COx) claystone was experimentally investigated with samples extracted from different depths of the Bure Underground

Research Laboratory (URL), France. Data from this study demonstrate that two types of illite/smectite (I/S) aggregates act as the swelling phases in COx, namely R1-I/S (contains 30% smectite) and R0-I/S (contains 78% smectite). Compared with R0-I/S, R1-I/S has less smectite proportion but provides more water-accessible void volumes and surface areas (from nano-scale to cm-scale) for water, resulting in R1-I/S is better correlated to the volumetric swelling of this material than R0-I/S. A conceptual model is proposed to characterize the multi-scale swelling mechanism of intact COx claystone based on the experimental data. In addition, the effect of compress-induced micro-cracks on swelling was also studied, demonstrating that micro-cracks can lead to a greater swelling amplitude and higher initial swelling kinetics, more important in the direction perpendicular to the crack orientation.

Clay swelling in COx claystone

In general, COx claystone is considered to be composed of non-clay minerals and clay minerals. The charged on its external surface owing to atom substitutions of the lattice structure. Thus, some cations will exist in the inter-platelet region to achieve the system electric balance. The inter-platelet cations differ between illite and smectite: the illite lattice spaces are filled with K + , whereas the smectite lattice spaces are filled with Na + and Ca 2+ . Early XRD results showed that the larger the inter-platelet cation size is, the stronger its association with the platelet surfaces will be. [START_REF] Mooney | Adsorption of Water Vapor by Montmorillonite. II. Effect of Exchangeable Ions and Lattice Swelling as Measured by X-Ray Diffraction[END_REF][START_REF] Slade | Crystalline Swelling of Smectite Samples in Concentrated NaCl Solutions in Relation to Layer Charge[END_REF][START_REF] Boek | Monte Carlo Molecular Modeling Studies of Hydrated Li-, Na-, and K-Smectites: Understanding the Role of Potassium as a Clay Swelling Inhibitor[END_REF]. Since the diameter of K + is greater than that of Na + and Ca 2+ , the structural stability of illite is therefore weaker than that of smectite. Such a difference in structural stability will result in different sensitivity to water. Compared with smectite, illite is almost insensitive to relative humidity (RH) and exhibits almost no swelling capacity [START_REF] Hensen | Why Clays Swell[END_REF]. This means that the swelling capacity of I/S aggregates is only determined on the smectite. repulsive force between the adjacent smectite platelets, which eventually leads to the decomposition of smectite particles (Anderson et al., 2010;[START_REF] Daab | Onset of Osmotic Swelling in Highly Charged Clay Minerals[END_REF]. Osmotic swelling depends on the surface charge density and localization, the nature of cations in aqueous solutions and the potential swelling space (i.e. pores) [START_REF] Bish | Smectite dehydration and stability: Applications to radioactive waste isolation at Yucca Mountain[END_REF][START_REF] Daab | Onset of Osmotic Swelling in Highly Charged Clay Minerals[END_REF]. If sufficient swelling space is available (e.g.

submerge the material in dilute suspensions), osmotic swelling results in significantly larger amplitude (up to ca. 130 Å) than crystal swelling [START_REF] Michot | Coagulation of Na-Montmorillonite by Inorganic Cations at Neutral pH. A Combined Transmission X-ray Microscopy, Small Angle and Wide Angle X-ray Scattering Study[END_REF][START_REF] Pusch | Degradation Mechanisms in Smectitic Clay for Isolating Radioactive Waste[END_REF]. With the aid of environmental scanning electron microscopy technique, Carrier et al. (2013) and [START_REF] Wang | Micro-scale experimental investigation of the swelling anisotropy of the Callovo-Oxfordian argillaceous rock[END_REF] observed the osmotic swelling mainly involving the deformation of mesopores.

During hydration, smectite exhibits a non-linear free swelling behavior upon wetting (Wang et al., 2015). This is attributed to the fact that the two expansion mechanisms occur at different saturation stages [START_REF] Massat | Swelling pressure development and inter-aggregate porosity evolution upon hydration of a compacted swelling clay[END_REF]. From a scale viewpoint, crystalline swelling and osmotic swelling occur at the microscale and mesoscale, respectively [START_REF] Slade | Crystalline Swelling of Smectite Samples in Concentrated NaCl Solutions in Relation to Layer Charge[END_REF]Dormieux et al., 2003;Menaceur et al., 2016;[START_REF] Daab | Onset of Osmotic Swelling in Highly Charged Clay Minerals[END_REF]. This means that at a macroscopic scale, COx swelling is the consequence of combine multi-scale effects. It should also be underlined that COx claystone exhibits a strong swelling anisotropy (Duan et al., 2021). This can be interpreted by the layered structure of the material leading to swelling heterogeneities (Wang et al., 2017).

Despite smectite swelling mechanisms have been extensively studied, complementary researches on COx swelling of are still necessary, especially at the macroscopic scale. It is commonly believed that the macro-scale swelling of COx is directly determined by smectite content (Menaceur et al., 2016).

However, smectite does not appear as a single-phase but is interspersed in I/S aggregates (Fig 2 .1).

The deformation of these I/S aggregates and structural effects, occurring at larger scales, remain poorly understood. Therefore, this work aims at investigating the multi-scale swelling behavior of COx claystone with a focus at the macroscopic level. To achieve this, the mineralogical compositions, pore structure and the swelling behavior of centimetric samples were analyzed by X-ray diffraction (XRD), cation exchange capacity (CEC), nitrogen sorption tests and a series of specially designed swelling tests. Classified by geological sequences, the core EST51133 comes from the transition unit (UT), drilled perpendicular to bedding planes; the other four cores are from the clay-rich unit (UA) and drilled parallel to the bedding plane. The difference between UT and UA claystone is mainly of the content of clay minerals, which will be detailed in section 2.4.1.

Material and sample preparation

When received in the laboratory, all samples were sealed in the "T1 cells" to maintain a compression state. They were re-cored into small cylinders (detailed in the following section). To avoid water loss before further treatment, these cylinders were wrapped in plastic film and sealed in vacuum bags, then immersed in oil and stored in a temperature-controlled room. An exception is the EST 51133 cylinders, which were actually re-cored in 2016 and are not well protected. It has been dried to 36.7% during the long time storage.

Powders: for Quantitative XRD, CEC, and nitrogen sorption measurements

A small amount of fragments (several grams) from each core was used for quantitative mineralogical characterization and nitrogen sorption. The fragments were micronized in ethanol for 15 minutes and then spray dried. Milling in ethanol can avoid further strain, heat damage and dissolution of the material. This step allows obtaining dried and homogenized powder samples with particle sizes of 400-800 microns. Powders with such particle sizes can be directly used for CEC analysis.

For samples used for XRD analysis, an additional processing step was required prior to milling.

Corundum (Al2O3) is to be added as the internal standard into the COx fragments, with a proportion of 0.2 g/g. The internal standard serves as the precision control material to improve the accuracy of the analysis.

The powder samples used in nitrogen sorption were handled differently from the above two. The fragments of each core were first gently manually crushed and sieved. After sieving, particles with a size between 63 and 400 µm are selected for measurement. The powder samples (several grams) were outgassed in a VacPrep 061 machine (Micromeritics Instrument Corporation, Norcross, Georgia, USA)

for 12 hours at an ambient temperature (22 °C ), then dried at 130 °C for 12 hours (under vacuum) to remove excess water prior to the sorption measurement.

Cylinders: for swelling tests

Each T1 cores were re-cored into several small cylinders (40 mm in length and 20 mm in diameter) using a low-speed diamond saw. Although the sample dimension is smaller than the ASTM (or ISRM) standards, the length/diameter ratio (equal to 2) is still enough to avoid the end effects. Moreover, due to the low permeability of the material (between 10 -20 m² and 10 -21 m²), a relatively small sample size can significantly reduce the testing time (Yuan, 2017). In this study, cylinders without further manipulation are called "intact" samples. It is worth mentioning that "intact" does not mean the sample is perfect because they might have been slightly damaged due to the decompression, desaturation and drilling operation.

As illustrated in Figure 2.2, the cylinders were either cored perpendicular (along axis 3, 2.2. All swelling tests were conducted using synthetic water with a mineralogical composition close to that of the ground water (provided by Andra). Intact samples from different cores were used to study the effect of clay mineral contents (group 1 in Table 2.2 (a)). Mass samples were first stabilized at 75% relative humidity (RH) to minimize the effect of initial pore water condition. The resulting water saturation (𝑆 𝑤 ) is determined by:

𝑆 𝑤 = 𝑚 𝑅𝐻 -𝑚 𝑑𝑟𝑦 𝑚 𝑠𝑎𝑡𝑢𝑟𝑎𝑡𝑒𝑑 -𝑚 𝑑𝑟𝑦 (2.1)
where 𝑚 𝑅𝐻 is the mass at 75% RH, 𝑚 𝑠𝑎𝑡𝑢𝑟𝑎𝑡𝑒𝑑 is the saturated mass weighed after swelling, 𝑚 dry is the stable mass after drying in the oven at 105 °C for 48 hours. For the whole set of samples, the resulting water saturation was measured between 73 and 77%. ones. An intact sample was initially loaded with uniaxial stress until failure to determine its uniaxial compressive strength (UCS). The micro-cracked state was then obtained by uniaxial loading until 80% UCS (Figure 2.3). 2 Bulk mineralogical compositions were analyzed by the Rietveld refinement method [START_REF] Rietveld | A profile refinement method for nuclear and magnetic structures[END_REF]. The BGMN-Profex software was used with customized clay mineral structures based on [START_REF] Ufer | Parametric Rietveld refinement of coexisting disordered clay minerals[END_REF].

The clay-content analysis was performed on the material with a size of below 2 m. Such size particles were obtained by centrifugation after thorough chemical treatment to remove cementing agents of the samples (including carbonates, organic matter, and iron/manganese oxides/hydroxides).

This procedure is also known as the "Jackson treatment" [START_REF] Jackson | Kaolinite Intercalation Procedure for All Sizes and Types with X-Ray Diffraction Spacing Distinctive from Other Phyllosilicates[END_REF]. After centrifugation, only clay minerals were retained. They were then saturated with Ca 2+ to remove other exchangeable cations. Such an exchange greatly facilitates the identification and quantification of the clay minerals in the oriented preparations that were prepared. The oriented preparations were made by sedimentation on a porous ceramic plate. Samples were subsequently analyzed by X-ray diffraction while the first reflections (001) of the clay minerals were recorded.

Due to the lack of standard clay materials, the precision of the subdivided clay mineral content is very difficult to quantify. Through a large number of repetitive experiments, it was found that the accuracy is generally better than 0.001g/g for phases with mass content over 0.02g/g. In this study, the two important minerals used for data analysis are R1-I/S and R0-I/S, which mass contents are greater than 0.02g/g in UA samples and slightly smaller than 0.02g/g in UT samples. This means that the accuracy of XRD results is sufficient to avoid the logical bias of this study.

Cation exchange capacity (CEC)

Cation exchange capacity (CEC) reflects the ability of the material to hold exchangeable cations in the saline aqueous solution. In this study, the CEC was measured using the Co (III)-hexamine method (Meier and Kahr, 1999). The micronized powders (ca. 0.5 g) were dried at 110°C and subsequently exchanged with the Co (III)-hexamine solution. The material was then homogenized after ultrasonic treatment (20 kHz, 400 W, 5 min) and the absorption of the supernatant solution was measured using an ultraviolet-visible (UV-Vis) spectrophotometer. The absorption measurement was repeated several times to guarantee a reliable value of the number of exchangeable cations.

Nitrogen sorption measurements

The nitrogen sorption was carried out on the initially dried and degassed materials, with a cryogenic nitrogen bath (-196 °C ). The physisorption isotherms were obtained by recording 55 relative pressure points within a relative pressure interval of 0.001-0.995 p/p 0 . Precisely, 31 points for adsorption and 24 points for desorption were recorded for each measurement. The saturation pressure (p 0 ) was recalibrated independently for every relative pressure point. The thermodynamic equilibrium of sorbatesorbent was assumed when the pressure fluctuation was less than 0.01% over 10 s. The adsorption/desorption isotherm provides abundant information related to the pore structures. Using the isotherm data, several important textural properties of the material were able to be indirectly deduced. The applied theories and related results are further detailed in section 4.2.

Swelling tests

Unlike many tests using swelling pressure to evaluate the swelling capacity of clayey material, this work uses a specially designed hydrostatic disposal to directly measure the sample strain (Figure 2.4).

The sample was wrapped with a rubber sleeve. Both two sample ends were connected to the ISCO water pump successively through a metallic porous disc, a stainless steel hollow cylinder and a pipe.

This design allowed to apply constant pore water pressure (Pi) from both ends. The assemblage was then placed into a hydrostatic cell and immersed in oil. A Gilson TM -type oil pump was connected to the cell to control the confining pressure (Pc) applied on the sample. The strains were recorded by an external digital strain-meter (with an accuracy of ± 10 -6 m/m). All the tests were carried out in a temperature-controlled room to avoid thermal perturbative effects. For each test, Pc was first slowly loaded to 14 MPa and kept constant. When the strain values were stabilized, 5 MPa pore pressure Pi was applied and kept constant. The swelling strain values were recorded until complete stabilization. depict the correlation between CEC, total smectite, R1-I/S and R0-I/S of both UT and UA samples, with the Pearson coefficients (R 2 ) equal to 96.7%, 94.5% and 83.4%, respectively. From Fig. 2.5 (a), one can note that the smectite in COx is responsible for the chemical interaction with aqueous solutions.

However, the structural effect, i.e. the impacts of different I/S layers on CEC, is observed by comparing demonstrates that the structural effect is more significant when only analyzing UA samples. This implies an unexpected result: R1-I/S has less smectite content but plays a more significant role.

Nitrogen sorption isotherms

The sorption isotherms of different cores are shown in Figure 2.6. According to the IUPAC classification (Thommes et al., 2015), the five isotherms are all classified Type IV, indicating that all these cores contain pores of various sizes. A sample-dependent hysteresis loop (Type H3) is observed on the desorption branches at p/p 0 ≈0.45 for all isotherms. The hysteresis loops are caused by complex pore structures such as narrow throats blocking and cavitation-induced evaporation of larger pores (Bertier et al., 2016). This suggests that the pore system of COx is mainly composed of a large amount of mesopores (2 nm < pore diameters < 50 nm) and a small amount of micropores (pore diameter < 2 nm) and macropores (pore diameters > 50 nm). This result is consistent with the reported values of this material (Seemann et al., 2017;Song et al., 2016). The calculation of 𝑉 𝐺𝑢𝑟 involves two hypotheses: 1) the whole pore system is filled at p/p 0 ≈ 1 and 2) the gas density is close to the liquid one at the operational temperature (-196 °C for N2). According to the Gurvich rule, 𝑉 𝐺𝑢𝑟 is given by:

𝑉 𝐺𝑢𝑟 = 𝑄 𝑡𝑜𝑡𝑎𝑙 1000 • 𝑉 𝑚 (2.2)
where 𝑄 𝑡𝑜𝑡𝑎𝑙 (mmol/g) is the total adsorbed N2 quantity at p/p 0 equal to 0.99; 𝑉 𝑚 is the liquid molar volume of N2, cm shows that 𝑉 𝐺𝑢𝑟 linearly increases with the smectite-related clay contents whatever the clay categories.

This implies that higher clays content results in greater adsorption pore volume. The R 2 of R1-I/S and total smectite are close to each other, equal to 97.8% and 96.7%, respectively. It is unexpectedly found that R0-I/S corresponds to the R 2 value of 86.9%, which is the lowest among all smectite-related clays.

This means that even though R0-I/S includes 78% smectite in mass, it provides less pore space for the connection of water and smectite. This is consistent with the result reported in (Wang et al., 2021a) It is also observed that 𝑉 𝐺𝑢𝑟 increases exponentially with the CEC value (R 2 =98.5%), see Figure 2.7 (b). Such a non-linear tendency can be interpreted by the effect of R0-I/S proportion. As a phase containing a large amount of smectite (78%), R0-I/S accounts for about 50% of the total I/S for low CEC samples i.e. the UT one, while it accounts for only 1/4 of the total I/S for high CEC samples (UA cores) (Table 2.3). This indirectly confirms that compared to R1-I/S, R0-I/S provides less pore spaces for free water molecules to contact with smectite.

BET specific surface area vs. clay contents

The BET theory was used to assess the specific surface area (𝑆𝑆𝐴) (Bertier et al., 2016). Following several assumptions (see Rouquerol et al. (2007)), the isotherm data corresponds to p/p 0 range in [0.05, 0.35] can be transformed into the BET plot:

1 [𝑄(1 -𝑝 𝑝°⁄ )] = 1 𝑄 𝑚𝑜𝑛𝑜 𝐶 + [ (𝐶 -1) 𝑄 𝑚𝑜𝑛𝑜 𝐶 ] (𝑝 𝑝°⁄ ) (2.3)
where 𝐶 is the BET constant, 𝑄 𝑚𝑜𝑛𝑜 is the monolayer adsorbed quantity. Both 𝐶 and 𝑄 𝑚𝑜𝑛𝑜 are determined by using rel. (2.3) to fit isotherm data. The specific surface area (𝑆𝑆𝐴) is given by:

𝑆𝑆𝐴 = 𝑄 𝑚𝑜𝑛𝑜 • 𝑁 𝐴 • 𝜎 𝑚 𝑚 (2.4)
where 𝑁 𝐴 is the Avogadro number, 6.022×10 23 mol -1 ; 𝜎 𝑚 is the N2 molecule cross-sectional area, 0.162 nm²; 𝑚 is the total mass of the adsorbent. The 𝑆𝑆𝐴 of the UT sample EST 51133 is 4.12 m 2 /g, which is significantly smaller than the value of UA samples (32.72-37.98 m 2 /g). See Figure 2.8 (a), 𝑆𝑆𝐴 showed a linear relationship with all smectite-related clay minerals. Similar to the observation in Figure 2.7 (a), the lowest correlation (R 2 = 87.8%) is observed for R0-I/S, while the R 2 values for R1-I/S and total smectite are both equal to 96.8%. This implies that despite R0-I/S contains more smectite, R1-I/S not only provides more pore volume 𝑉 𝐺𝑢𝑟 but also a greater specific surface area for gas adsorption than R0-I/S. An exponential relationship is also observed between CEC and 𝑆𝑆𝐴, with an R 2 of 97.0% ( where 𝑄 0 (cm 3 /g) is the limiting micropore volume, 𝐸 (kJ/mol) is the characteristic energy; and 𝑛 is the adjustable DA exponent. 𝑄 0 , 𝐸 and 𝑛 are all derived from non-linear curve fitting the isotherm data using rel. (2.5).

From Table 2.3, the limiting micropore volume 𝑄 0 of UA samples differed from UT by an order of magnitude while the difference between UA samples is not significant. The relationship between 𝑄 0 and the smectite-related minerals is illustrated in Figure 2.9. Obvious similarities between Figure 2.7 (a) and Figure 2.9 can be underlined. As for Vgur, 𝑄 0 exhibits the best linear correlation with R1-I/S (R 2 =93%), whereas the worst one is observed with R0-I/S (R 2 =76.4%). This seems to suggest that R1-I/S provides more pore volume than R0-I/S for pore sizes < 2 nm when concerning both UT and UA samples, which is quite logical as the UT sample data are significantly smaller than that of UA samples.

However, this tendency of Q0 may be changed when focusing on UA samples only, which are detailed later.

Q 0 (cm 3 /g) R 2 =93.0% R 2 =89.9% R 2 =76.4%
Figure 2.9. Linear relationship between 𝑄 0 and smectite-related mineral contents However, there is no significant difference between the calculated 𝐸 and 𝑛 of different core samples (Table 2.5). This means that samples from different stratigraphic locations have similar micropore surface chemistry. Since the crystalline swelling occurs in micropores, the consistency of 𝐸 and 𝑛 between samples indirectly confirms the fact that only a specific clay (i.e. smectite) has such swelling capacity. Lahn et al. (2020) reported that pores below 10 nm will be blocked or fully filled when the relative humidity exceeds 97% for clayey materials. This means that the inter-platelet crystal swelling (0.96 -2 nm) and the osmotic swelling in small mesopores (2 -10 nm) cease at (or very close to) saturation state. In the meantime, osmotic swelling continues to occur in pores larger than 10 nm since they remain accessible at high relative humidity. Hence, it is concluded that when unsaturated COx starts to hydrate, crystalline swelling immediately occurs and stops close to 100% saturation. In parallel osmotic swelling initiates at high saturation level [START_REF] Massat | Swelling pressure development and inter-aggregate porosity evolution upon hydration of a compacted swelling clay[END_REF] and continues until the system hydro-mechanical equilibrium.

Pore size distributions vs. clay contents

The pore size distribution (PSD) of the material was obtained by two theories: Barrett-Joyner-Halenda (BJH) theory and the DA theory. BJH theory is used to calculate the PSD of pores larger than 4 nm (meso-and macropores) and is the result of the Kelvin equation and a statistical thickness equation [START_REF] Lammers | Sedimentary reservoir oxidation during geologic CO2 sequestration[END_REF]. The calculated pore radius is the sum of Kelvin radius (𝑟 𝑘 ) and a multilayer thickness (𝑡) [START_REF] Barrett | The Determination of Pore Volume and Area Distributions in Porous Substances. I. Computations from Nitrogen Isotherms[END_REF]. Kelvin radius (𝑟 𝑘 ) is calculated by the classic Kelvin's equation (Seemann et al., 2017). The statistical multilayer thickness (𝑡) is a function of the partial pressure p/p 0 [START_REF] Halsey | Physical Adsorption on Non-Uniform Surfaces[END_REF]. In particular, the Harkins-Jura equation (with Faas correction) is used for the nitrogenclaystone system [START_REF] Harkins | Surfaces of Solids. XIII. A Vapor Adsorption Method for the Determination of the Area of a Solid without the Assumption of a Molecular Area, and the Areas Occupied by Nitrogen and Other Molecules on the Surface of a Solid[END_REF]. By definition, the BJH theory is only applicable for p/p 0 > 0.15 to measure the PSD of meso and macropores. At lower relative pressures (p/p 0 < 0.15), the DA theory was used to evaluate the PSD of micropores (pore diameter < 2 nm) (Dubinin and Astakhov, 1971). Assuming gas adsorption in micropores follows the volume filling theory (TVF), the micro-PSD can be derived by combining the Dubinin-Astakhov equation (rel. (2.5)) and the Van Der Waals equation (consider surface effects) (Janssen and Van Oorschot, 1989).

Figure 2.10 (a) shows the cumulative pore size distributions (including micropores to macropores) calculated with a combination of BJH and DA theories. The total pore volume of UA samples is significantly higher than that of the UT sample, implying that clay minerals provide a significant pore volume within a wide size (or radius) range. All samples exhibited a rapid increase in cumulative pore volume between 0 and 45 nm pore size, and then a plateau occurs between around 45-75 nm. Such a plateau indicates the COx has relatively few pores in this size range. Following the plateau, the pore volume smoothly increases (compared with the range of 0-45 nm) until reaching the maximum measurable pore size (ca. 160 nm). Statistically, the volume of 0-45 nm pores represents 78.6%-82.4% total pore volume for UA samples and 69.6% for the UT one. This is consistent with the fact that the majority of pores in COx are micropores and mesopores (Song et al., 2016). From the viewpoint of the clay composition, the differences in adsorption capacity between samples are mainly related to the clay content associated with smectite. Since pores between 0-45 nm correspond to the largest pore volume part, the cumulative PSD in this range was correlated with smectite-related minerals for the analysis, see Figure 2.10 (b). Once again, the mineral with the best correlation is still R1-I/S, with R 2 =98.6%. Combining with Figure 2.7 (a), such a result illustrates that the effect of smectite distribution on adsorption capacity is valid from nano-scale to m-scale. XRD and CEC analysis demonstrate that smectite is the most chemical active mineral in COx, while the structure of R1-I/S is more favorable than that of R0-I/S for the interaction between smectite and pore water. In comparison between UT and UA samples, nitrogen adsorption data demonstrates that all void spaces (from the nanoscale to mesoscale) increase significantly with the clay content, in particular with the R1-I/S. When focusing on UA samples only, the absorptive macro-and mesopore volume are still likely linearly increase with the R1-I/S, while the linear correlation with R0-I/S no longer exists. Meanwhile, the available micropore volume seems not sensitive to the change of smectiterelated clays. Thus, it can be concluded that the structural effect on CEC may be attributed to the fact that compared to R0-I/S, R1-I/S provides more available macro-and mesoscale pores for the smectitewater reaction. To examine the upscaling consequence of this structural effect, a series of swelling tests were carried out to link the microstructure properties to the macroscopic swelling strains.

Q 0 (cm 3 /g) R 2 =3.2% R 2 =7.0% R 2 =26.5% (

Swelling experiments 2.5.1. Accuracy of strains

For each sample, the average strain of the two lateral (or vertical) gauges (see Fig. 2.2) was calculated and called 𝜀 ∥ (or 𝜀 ⊥ ). COx claystone is a transversely isotropic material and more deformable perpendicular to bedding planes during wetting, i.e. 𝜀 ∥ < 𝜀 ⊥ (Minardi et al., 2016). During the sample preparation, there are always some uncertainties about the bedding planes vs. the gauge orientation.

Precisely, the 𝐽 ⊥ of UA samples and the 𝐽 ∥ of the UT one are not strictly perpendicular to bedding planes due to the sample curvature and unavoidable geometrical uncertainties and consequently, the measured 𝜀 ⊥ of UA samples (or 𝜀 ∥ of UT sample EST51133) are inevitably biased. To minimize these uncertainty of results, the 𝜀 ∥ of each sample is therefore used for comparison between different samples and/or sample states. It must be nevertheless mentioned that the strain results for UT did not exhibit significant anisotropy. This is highlighted in Fig. 2.12 in which are plotted the strain measurements on the UT sample. One can find that the measured 𝜀 ∥ and 𝜀 ⊥ of the UT sample are obviously very close to each other, which is far to be the case for UA samples. As the smectite content of the UT sample is much lower than that of other UA ones, the measured 𝜀 ∥ is much smaller than that of UA samples. This denotes that the 𝜀 ∥ value of EST51133 can be logically used for a purpose of comparisons between UT and UA materials. Despite the uncertainty in 𝜀 ⊥ S of UA samples, it is obvious that this strain remains a good tool to evaluate the sample sensitivity for swelling. In this study, they were used to investigate the effect of initial damage states on swelling i.e. of cracks suspected to be present in the bedding planes.

Swelling amplitude vs. clay contents & N2 sorption properties

Figure 2.13 (a) depicts the overall swelling process of the tested samples. As discussed in section 2.3, the pre-stable of sample masses at 75% RH leads to similar initial saturation values between samples, whatever the mineralogical compositions are. A typical test starts with a confining pressure 𝑃 𝑐 loading up to 14 MPa before water injection -see the left small graph of Figure 2.13 (a). Comparing the initial contraction (due to Pc) between samples is not very meaningful, because: (1) differences in mineral contents may affect the mechanical properties, and (2) the possible pre-damage varies among samples (interpreted in section 2.3). Nevertheless, it was generally observed that the contraction of the UT sample is much smaller than that of all UA samples, this means that the material stiffness decreased with increasing clay content. After water injection with Pi = 5 MPa, significant swelling was observed under a "Terzaghi effective pressure" of 9 MPa. Some structural effects occurred during a short time and they were attributed to some transient pore pressure phenomena, see the orange and black curve of Figure. 13 (a). After these, all the samples started to swell after pressurization. The swelling time varied widely between samples, ranging from around 10 to 60 days (Figure 2.13 (b)). It can be underlined that the shortest time (10 days) was obtained for UT sample, which contains less clay than the UA ones. The sample swelling is therefore the superposition of pure swelling and poromechanical effect due to pore pressure increase. It is nevertheless obvious that, even if the Biot's coefficient was found close to one (Wang et al., 2021b), the strain due to this effect is much smaller than the measured swelling observed here. As Pi=5MPa, the maximum strain due to poromechanical effect could be roughly estimated (or capped) at 5/14 time the strain due to Pc=14MPa. Fig. 2.14 shows the linear relations between 𝜀 ∥ and smectite-related clays for both UT and UA materials. Inspections of data suggest that 𝜀 ∥ vs. R1-I/S corresponds to the highest R 2 (96.0%) while the worst correlation is 𝜀 ∥ vs. R0-I/S (R 2 =77.2%). In the comparison of Fig. 2.14 with Fig. 2.7-2.9, one can note that the mm-scale property 𝜀 ∥ has similarities with the m-scale and nm-scale pore properties (i.e. VGur, SSA and Q0). This implies that the structural effect seems to be sitll valid at different scales. This assumption can be confirmed by correlating 𝜀 ∥ to multi-scale pore textural properties, see Fig. 2.15. Fig. 2.15 (a) and (b) show that 𝜀 ∥ is well correlated with two mesoscopic pore properties, i.e. 𝑉 𝐺𝑢𝑟 (R 2 =93.9%) and 𝑆𝑆𝐴 (R 2 =93.1%). This means that the expansion of centimetric samples is highly affected by the meso-and macropore volume and specific surface area. The micropore property 𝑄 0 is also linearly related to 𝜀 ∥ with a relative smaller R 2 that equal to 84.7% (Fig. 2.15 (c)). This indicates that the expansion of micropores, which is a small part of the total pore volume, is also one of the drivers affecting macroscopic swelling strains. Hence, it can be concluded that the multiscale pores swelling in all contribute to macroscopic volume expansion with 'in priori' contrasted swelling amplitudes. UT and UA samples. By excluding the UT samples and only analyzing the UA samples (data highlighted by dash ovals in Fig. 2.14), one can note that the linear quality of all relations decreased, similar to the results presented in section 2.4.2.5. In addition, two general conclusions can be drawn by visual observation. Firstly, 𝜀 ∥ is clearly better linearly correlated with R1-I/S than R0-I/S, which could be explained by the smectite swelling in R1-I/S being more significant than in R0-I/S during re-saturation.

This is a complementary result to section 2.4.2 and gives direct evidence for the structural effect of I/S at the macroscale. Secondary, inspections of data of UA samples in Fig. 2.15 indicate that the linear correlation of 𝜀 ∥ with VGur and SSA still exists while almost no correlation with Q0. One could thus conclude that 𝜀 ∥ is more related to the swelling of meso-and macropores than micropores. However, it should be noted that very little data is available in this study, more data are required for the validation of this conclusion.

Conceptual model for the COx swelling

As re-called in section 1. After the crystalline swelling stops, osmotic swelling continues at high saturation levels. Free water molecules keep diffusing into the interlayer regions and lead to the cleavage of highly stacked interstratified I/S along the smectite inter-platelets. The osmotic swelling process is different in R1-I/S and R0-I/S. Thanks to the large pore volume and a small amount of smectite particles, the stacked R1-I/S layers can evolve to highly disaggregated smectite particles (Figure 2.16 (e)). Such a decomposition process produces many smectite "fragments" inducing more surface area for water molecules sorption.

More importantly, since each smectite "fragment" carries negative charges on its surface, the system will absorb more water molecules to achieve the overall electrical balance. These water molecules cause an increase in the distance between adjacent fragments, which is coming along with an increase in osmotic pressure. In contrast, the decomposition of R0-I/S is less complete. Limited by the pore volume, the stacked R0-I/S is decomposed into illite clusters and smectite clusters (Figure 2.16 (f)).

Apparently, the incomplete decomposition of R0-I/S results in a smaller volume expansion and surface area than that of R1-I/S. Consequently, the swelling amplitude of the centimetric sample with high R1-I/S content (Figure 2.16 (g)) would be greater than the one with high R0-I/S content (Figure 2.16 (h)).

Swelling kinetics vs. clay contents & N2 sorption properties

From Figure 2.13, one can observe that it takes around 10 days to achieve the strain stabilization for the UT sample (EST51133), whereas the time to stabilize UA samples is between 19 and 56 days. It can be logically concluded that materials containing more smectite require longer swelling reaction times.

However, no specific linear relationship was observed between the swelling kinetics and the used pore structure properties. One possible interpretation is that the mineralogical composition of UA material was too close to highlight the differences in swelling rate and time between samples (see the black, blue and pink curves in Figure 2.13 (b)). Although sample EST 58145 (orange one in Figure 2.13) has a longer swelling time than that of other UA samples, this cannot be explained through the available data. Hence, more samples and data are needed for further analysis. For instance, macroscopic properties such as permeability and diffusivity are likely to play a major role in swelling kinetics.

Swelling vs. micro-cracks

In order to study the effect of micro-cracking on the swelling behavior, 𝜀 ∥ and 𝜀 ꓕ were recorded and analyzed, respectively shown in Figure . 2.17 (a) and (b). Despite the existence of micro-cracks, neither 𝜀 ∥ and 𝜀 ꓕ exhibited a significant difference in contraction during confinement loading. The difference is mostly visible after water injection (Pi= 5 MPa),which is followed by a pronounced effect of microcracking. This effect is clearly involved in the swelling amplitude. Both 𝜀 ∥ and 𝜀 ꓕ of micro-cracked samples (MC-1 and MC-2) are greater than the intact ones (I-1 and I-2). 𝜀 ∥ of micro-cracked samples are around twice that of intact samples, while 𝜀 ꓕ of micro-cracked ones are almost three times greater than that of intact ones. The micro-cracking effect is more significant for 𝜀 ꓕ , which is consistent with a more intense micro-cracking parallel to the beddings. This leads to more swelling space and less rigidity (i.e. the material becomes more deformable) perpendicularly to the beddings. For a short period of time after starting water injection (several days), micro-cracked samples (particularly the MC-2) exhibit higher swelling kinetics than the intact samples. This can be attributed to the presence of cracks creates more contact surface for initial water imbibition, allowing pore water to contact the smectite in the clay matrix more rapidly at the beginning of the test. Obviously cracking induces increases in permeability and diffusivity. This reinforces the fact, mentioned before, that these properties play a major role in the swelling kinetics. For engineering implications, in-situ COx claystone swells under a quasi-constant volume, and the presence of micro-cracks can significantly affect the cumulative expansion pressure generated over time. The effect of micro-cracks on swelling was studied showing that micro-cracking causes the material to exhibit a greater swelling amplitude and higher initial swelling kinetics. In particular, the compressinduced micro-cracks are more likely to parallel to the bedding planes, leading to a more pronounced expansion in the direction perpendicular to the bedding planes. Results also indicate the swelling kinetics of intact sample not solely depends on the clay content and pore structures, but is likely to depend on other properties like permeability and diffusivity.

Chapter 3 -Poroelastic experiments on COx claystone: insight from the Biot's coefficient measurement with water

This chapter focuses on Biot's coefficient measurement of saturated COx claystone. The tests were systematically conducted to provide clarification on its value as the available literature indicates quite erratic results from 0.26 to 1. The difficulty of this work mainly lies in the time that is necessary to stabilize each loading step (confining pressure and/or pore pressure) and also in sample preparation.

Two main results were obtained: 1) Whatever the initial conditions were (confining pressure 𝑃 𝑐 amplitude, hydric state, damaged or not…), all samples exhibited a significant anisotropic swelling during the first water injection; 2) even being a transversely isotropic rock, its Biot's tensor is (quasi) isotropic thus leading to a unique coefficient "b" which is very close to 1. Such results are consistent with what was observed with gas as being the fluid to control pore pressure in partially saturated samples.

In contrast to many results reported in the literature, experimental studies carried out in our laboratory clearly showed that, despite the structural anisotropy, the Biot's tensor was isotropic leading to a coefficient very close to 1 (Cariou et al., 2012[START_REF] Cariou | An original constitutive law for Callovo-Oxfordian argillite, a two-scale double-porosity material[END_REF]Yuan et al., 2017;Hu et al., 2020).

These previous works were carried out on partially saturated material and used gas as the fluid to control pore pressure. This showed that gas was theoretically a convenient fluid to perform such experiments. However, doubts remained about their equivalence with measurements using water to control the pore pressure and to maintain a full saturation state. This study had therefore been designed to complete gas experiments and to verify whether they are consistent with water experiments. Reconstituted synthetic water (close to the in-situ one) was used to measure the Biot's components in the saturated state. Two main results had to be confirmed: Biot's tensor isotropy and a unique coefficient close to 1.

Summary of the measurements of the Biot's claystone components using

gas to control pore pressure

Constitutive relations in the case of transverse isotropy claystone

As mentioned before, the COx argillite from Bure is a transverse isotropic material. As shown in Figure 3.1, the isotropic plane is the bedding plane containing the structural axis 1, 2 and 3 being the in-situ vertical axis. Let us suppose that a crossed gauge is glued on a sample like in Figure 3.1. One gauge direction is axis 1 or 2 (gauge J2) and the second one is along a direction "n" (gauge Jn). As the sample is a cylinder, axis 'n' can not exactly match with axis 3. Within the frame of Biot's poro-elastic theory, the behavior of the material can be expressed with respect to its material axis using the following relation (Hu et al., 2020): where compressive strengths are positive, and b, b3 are the Biot's tensor components used for a transverse isotropic behavior. A convenient approach to the identification of these components relies on the application of a hydrostatic loading 𝑃 𝑐 and/or a pore pressure 𝑃 𝑖 . One interesting case arises when b=b3. When this specific case is verified, the following expressions for the three strain terms can be derived:

| | 𝜀 11 𝜀 22 𝜀 33 𝛾 12 𝛾 13 𝛾 23 | | = | | | 1 𝐸 1 -𝜈 𝐸 1 -𝜈′ 𝐸 1 -𝜈 𝐸 1 1 𝐸 1 -𝜈′ 𝐸 1 -𝜈′ 𝐸 1 -𝜈′ 𝐸 1
𝜀 11 = 𝜀 11 (𝑃 𝑐 )(1 -𝛼𝑏) 𝜀 22 = 𝜀 22 (𝑃 𝑐 )(1 -𝛼𝑏) 𝜀 33 = 𝜀 33 (𝑃 𝑐 )(1 -𝛼𝑏) 𝛾 𝑖𝑗 = 0 } (3.2)
where =𝑃 𝑖 /𝑃 𝑐 , and

𝜀 11 (𝑃 𝑐 ) = 𝜀 22 (𝑃 𝑐 ) = 𝑃 𝑐 𝐸 1 [1 -(𝜈 + 𝜈 ′ )] 𝑎𝑛𝑑 𝜀 33 (𝑃 𝑐 ) = 𝑃 𝑐 ( 1 𝐸 3 - 2𝜈 ′ 𝐸 1 ) (3.3)
A gauge Jn, glued in any direction n, will give 𝜀 𝑛𝑛 =𝜀̿ . 𝑛 ⃗⃗. 𝑛 ⃗⃗ , with 𝑛 ⃗⃗: | 𝑛 1 𝑛 2 𝑛 3 |. This leads to:

𝜀 𝑛𝑛 = [𝜀 11 (𝑃 𝑐 )(𝑛 1 ) 2 + 𝜀 22 (𝑃 𝑐 )(𝑛 2 ) 2 + 𝜀 33 (𝑃 𝑐 )(𝑛 3 ) 2 ](1 -𝛼𝑏) (3.4)
Rel. (3.4) shows that, whatever the gauge direction, the Biot's coefficient b can be derived from two measurements, which may be combined: hydrostatic loading with a confining pressure 𝑃 𝑐 and a change in pore pressure 𝑃 𝑖 . This is useful when the direction of axis 3 is not accurately known as it is the case for COx claystone samples. It can also be underlined that an "isotropic" Biot's coefficient does not mean that a change in pore pressure would lead to isotropic strain state (see relations (3.2) and (3.3)).

The use of gas to control pore pressure

In a poro-mechanical test intended to measure Biot's coefficient, loading/unloading 𝑃 𝑖 is always more difficult than controlling 𝑃 𝑐 . As the water permeability of COx claystone is in the range 10 -20 to 10 -21 m² (M' Jahad et al., 2017;Yuan, 2017), reaching a homogeneous pore pressure is not only timeconsuming but very difficult to assess. It will be seen in the following that the strain stabilization due to 𝑃 𝑖 variation can be very long. Another specific property of COx claystone is that the material exhibits significant volumetric swelling from unsaturated to saturated state. Such process can also last for a very long time, depending on the material initial saturation state, swelling mineral content, and confinement (Anderson et al., 2010;[START_REF] Busch | Swelling clay minerals and containment risk assessment for the storage seal of the Peterhead CCS project[END_REF]IAEA, 2013). Another specificity is that experiments with gas do not change the sample saturation level, which allow Biot's coefficient measurements on a dry and/or partially saturated sample. This particular aspect is crucial as it means that gas pressure change 𝑃 𝑖 , applied at both sample ends, leads to the same pressure 𝑃 𝑖 for both gas and water phases inside the sample. This was demonstrated by Cariou and led to a very important consequence: gas pressure 𝑃 𝑖 , even applied on a partially saturated sample, induces a uniform global pore pressure change 𝑃 𝑖  i.e. can be used to perform poro-mechanical experiments on a non-fully saturated material.

In conclusion, gas is a good choice to control pore pressure as it is involved in rel. (3.1). Technically, pore pressure equilibrium is easier to be reached by injecting the gas at both sample ends, which also significantly shortens the test time and avoids the swelling effect. Cariou et al. (2012) were the first to perform this kind of test on COx samples. By using argon as the pore fluid, results showed that the stiffness of COx claystone exhibits noticeable anisotropic property (Figure 3.2). It is evidenced by the strain amplitudes, due to Pc change, along bedding plane or perpendicular to it. This is a common result for all the tests having been performed for more than 10 years.

Results obtained with gas. A summary

- As mentioned before, the results in Figure 3.2 are unambiguous as they indicate different strain values, depending on the direction, due to either 𝑃 𝑐 or 𝑃 𝑖 changes. What is more noticeable is that despite this behavior and whatever the direction is, the ratio 𝜀 𝑖 (∆𝑃 𝑖 )/𝜀 𝑖 (∆𝑃 𝑐 ) is almost the same. This clearly evidences that the Biot tensor is isotropic. This result was also validated on a theoretical point of view (Hu et al., 2020). In the case illustrated in Figure 3.2, the ratio 𝜀 𝑖 (∆𝑃 𝑖 = ∆𝑃 𝑐 )/𝜀 𝑖 (∆𝑃 𝑐 ) is 1 (or very close to 1 -see points M to N and P to Q). This was not a particular case as most of the results obtained in [START_REF] Cariou | Couplage hydro-mécanique et transfert dans l'argilite de Meuse/Haute-Marne: approches expérimentale et multi-échelle[END_REF] and Yuan (2017) confirmed this tendency.

It has been observed that the Biot's coefficient of partially saturated COx claystone is generally around 1, and hardly dependent on confining pressure and pore pressure (Yuan et al., 2017). However, it must be mentioned here that on dry material (or close to be) the measured Biot's components were higher than 1, which is theoretically not possible. This means that the strain due to variation of pore pressure 𝑃 𝑖 , j (𝑃 𝑖 =𝑃 𝑐 ), is higher than the one due to 𝑃 𝑐 , j (𝑃 𝑐 =𝑃 𝑖 ). A concomitant phenomenon was also observed by [START_REF] Song | Water retention and fine microstructure of Bure argillite[END_REF] in porosity experiments performed with argon. This work evidenced argon adsorption in COx claystone. Biot's coefficient higher than 1 means an "over-swelling" due to pore pressure increase. Assuming that this swelling was due to adsorption, Yuan et al., (2017) focused the research to compare the strains obtained either with argon or helium, which is a (quasi) nonadsorbable gas. Using helium led to consistent Biot's coefficient between (slightly higher than) 0,9 and 1 and never higher than 1 (Figure 3.3). Adsorption phenomena only occurred for dry (or quasi dry) material. This is quite logical as dry or quasi dry state means that the smallest pores are now free to be filled with gas whereas it is not true at higher level of water saturation. Adsorption is a surface phenomenon and it is well known that the smallest pores give the highest part of the material specific surface.

Partial conclusion

Measuring Biot's coefficient with gas indicates that COx claystone exhibits a high isotropic Biot's coefficient (close to 1), despite a significant structural anisotropy. This is an inherent property of COx claystone, regardless the sample is dried or partially saturated. In the following section, such property is verified on fully saturated samples with synthetic water.

Measurements of the Biot's components with synthetic water

Sample preparation

COx claystone comes from the Meuse/Haute Marne Underground Research Laboratory (MHM-URL),

France. The material had been initially sealed in a T1 cell (80 mm in diameter, 250 mm height cylinders).

Due to the low permeability of COx, samples were cored into cylinders and of 40 mm in height and 20 mm in diameter in order to shorten the experiment duration i.e. to obtain a uniform pore pressure assessed by strain stability. Such a size is relatively smaller than the ASTM or the ISRM standard, but still sufficient to avoid end effects with a slenderness of 2. For a transversely isotropic material it is important to identify the layer orientation. Hence, a small amount of water was sprayed on a sample end to highlight the layers, see Figure 3.4 left. It should be pointed out that this technique was not used for sample EST 57903-1, which led to a structural anisotropy effect less significant than for other tests. Nevertheless, thanks to rel. (3.4), the measured strains are still useful for the Biot's coefficient measurement.

Four strain gauges (5mm length) were glued on each sample. It should be noted here that this phase occurred after a specific sample surface treatment, which took a very long time to successfully develop so as to ensure a reliable gauge behavior over time (for weeks or months). This point is far to be insignificant as it is one of the main difficulties to conduct poro-mechanical experiments on this water saturated claystone. Two longitudinal gauges (in red) were diametrically placed along the sample bedding plane, while the two transverse gauges (in green) were respectively perpendicular to each longitudinal gauge, see Four samples, retrieved from three boreholes, were used for the tests. Different initial sample states were taken into account in order to evaluate their possible impact on Biot's coefficient measurements (see Table 3.1). A (quasi) dry sample was used (EST 51446) to be compared with highly saturated ones.

A pre-damaged state, obtained with the uniaxial compressive test (UCT), was also considered (EST 58128).

Design of the experiments and measurement strategy

A special dedicated setup (see Figure 3.5) was designed to conduct experiments. It includes a hydrostatic cell, an ISCO syringe pump, a Gilson TM -type oil pump and a digital strain-meter. As the sample size is small, it was decided to simply dip it into oil pressure without linking it to the cell. This is more efficient to ensure the isotropic loading. For tightness and fluid injection purposes, samples were sandwiched between two porous stainless steel disks connected to capillary tubes via two steel hollow cylinders. They allow water pressure control (and injection) at both sample ends. The assembly of "sample + steel disks + steel hollow cylinders" was wrapped into a rubber jacket, then immersed in oil. During experiments, the loading/unloading of confining pressure ( 𝑃 𝑐 ) and interstitial water pressure (𝑃 𝑖 ) were applied by the Gilson TM -type oil pump and the ISCO water pump, respectively.

Strains were measured with a digital strain-meter having an accuracy of ± 10 -6 m/m. Synthetic water, similar to in-situ water, was used in all poro-mechanical experiments. The mineralogical composition is detailed in Table 3.2. There are two different phases in the tests. They are necessary as, whatever the initial state is (dry to almost saturated -confining pressure intensity), there is always a significant swelling due to the first water injection (carried out to fully saturate the sample). This swelling is not only due to pore pressure effect as a large part of it attributed to specific clay swelling due to water molecules adsorption (Anderson et al., 2010;Carrier et al., 2013). Hence the first testing phase is to apply a couple (𝑃 𝑐 , 𝑃 𝑖 ), which represents the initial state from which the so-called poro-mechanical experiment can start. It can be noticed here that this first phase can last weeks until strain stability, depending on the sample initial state and the content of swelling clay. The second phase follows with the measurement of Biot's components with water.

The experimental protocol is given as follows:

• Step 1: Maintaining the pore pressure constant (drained test), the initial isotropic confining pressure (𝑃 𝑐 1 ) is loaded to 𝑃 𝑐 2 , i.e. 𝑃 𝑐 2 = 𝑃 𝑐 1 + ∆𝑃 𝑐 . This step is often irreversible (not elastic) due to plastic deformation and/or micro-crack closure.

•

Step 2: Pore pressure is varied under constant confining pressure. It is firstly increased by ∆𝑃 𝑖 , with ∆𝑃 𝑖 = ∆𝑃 𝑐 . This step is regarded as being a unloading one as it leads to a decrease in effective isotropic pressure. Hence, this phase is likely to be elastic and leads to strain values (𝜀 𝑖 (∆𝑃 𝑖 )) -𝜀 𝑖 is the strain recorded for gauge n°𝑖. As soon as strain values are stabilized, the pore pressure is then decreased (by ∆𝑃 𝑖 ) back to its initial value Pi.

• Step 3: The pore pressure being constant, 𝑃 𝑐 2 is decreased (by ∆𝑃 𝑐 ) down to 𝑃 𝑐 1 . This step is regarded as an elastic unloading path leading to 𝜀 𝑖 (∆𝑃 𝑐 ).

At this step 𝜀 𝑖 (∆𝑃 𝑐 ) and 𝜀 𝑖 (∆𝑃 𝑖 = ∆𝑃 𝑐 ) are compared and if the ratio b = 𝜀 𝑖 (∆𝑃 𝑖 )/𝜀 𝑖 (∆𝑃 𝑐 ) is the same (or almost the same) for every gauge n°𝑖, it can be concluded (rel. (3.2) to rel. (3.4)) that Biot's tensor is isotropic with a single component b, which is then the Biot's coefficient. If the ratio depends on the gauge direction (orientation) then the Biot's tensor is not isotropic and the situation begins to be trickier as the complete identification of this tensor would require other complementary experiments. It is also possible to use some kind of average value of the volumetric strain, which is difficult to measure if the structural axes are not perfectly identified. From this averaging, a mean "Biot's coefficient" can be obtained with the volumetric strains due to 𝑃 𝑐 and 𝑃 𝑖 . Such a method leads to a "mean" coefficient value but is not rigorous from a poro-mechanical point of view.

• Step 4: The Biot's coefficient is calculated by the ratio b = 𝜀 𝑖 (∆𝑃 𝑖 )/𝜀 𝑖 (∆𝑃 𝑐 ) if it is independent on any gauge direction.

Results and discussion

The result presentation is divided into two parts to highlight: the swelling phase due to initial loading (𝑃 𝑐 , 𝑃 𝑖 ) and Biot's coefficient isotropy derived from the poro-mechanical loading phases. For a clearer analysis of strain variation, the average values of two longitudinal or transverse gauges were considered to represent the mean strain parallel or perpendicular to bedding planes.

Swelling due to initial loading (Pc, Pi)

Table 3.3 shows the initial loading (𝑃 𝑐 , 𝑃 𝑖 ) leading to P eff (Terzaghi's effective pressure). The tests were generally performed with a first 𝑃 𝑐 loading followed by water injection in order to obtain 𝑃 𝑖 .

Sometimes both 𝑃 𝑐 and 𝑃 𝑖 were simultaneously applied. An example is given in Figure 3.6. An important phenomenon has to be underlined here, which is linked to COx claystone re-saturation with liquid water. Even if the initial effective stress -indicated by P eff -is isotropic compression, there is always a resulting absolute swelling. This swelling occurred whatever the initial conditions were (𝑃 𝑐 amplitude, hydric state, damaged or not…). It is not the purpose of the present study to focus on this phenomenon as it is still under study in the laboratory. However, in the context of nuclear waste storage in COx rock, such a swelling effect facilitates the crack closure in the Excavation Damaged Zone (EDZ) and leads to "self-sealing" (Wang et al., 2021). The swelling amplitude and kinetics are contrasted and variable. They depend on sample initial state and likely on its mineral composition. Positive strain is expansion Results in Table 3.3 evidence that the absolute swelling amplitude shows significant anisotropy, since 𝜀 ⊥ (along axis 3 in Figure 3.1) is always higher than 𝜀 ∥ (along axis 1 or 2 in Figure 3.1). The ratio r = 𝜀 ⊥ / 𝜀 ∥ is variable and generally higher than the degree of mechanical anisotropy often found between 1.5 and 2 (Zhang et al., 2019). It is obvious that a part of the absolute swelling is a poromechanical effect, induced by pore pressure increase, completed by effects of water absorption of swelling clay. From a microscopic point of view, the SEM image exhibits the elementary swelling-clay particles are layer-stratified in structure (Figure 3.7 left). As mentioned before in §2, during saturation, the water molecules are adsorbed in the inter-particle regions into one to several (up to four) water layers (Figure 3.7 right) (Menaceur et al., 2016). At a macroscopic scale, the material anisotropy results in less stiffness perpendicular to the beddings. It is therefore consistent to observe that 𝜀 ⊥ is greater than 𝜀 ∥ of samples. Moreover, it was also observed at a larger scale (Duan et al., 2021) a preferential cracking parallel to the bedding plane. This cracking, which is mainly due to material manipulation and sometimes drying, is likely to amplify the transverse swelling.

Biot's coefficient measurements, results and discussion

When the swelling phase is completed, the Biot's coefficient measurement was carried out according steps 1-4 (see section 3.2). days. Such a duration is likely to explain why many previous published results had given lower Biot's coefficient. It can be seen in Figure 3.8 that the necessary time to stabilize the strains, due to change in 𝑃 𝑐 and/or in 𝑃 𝑖 , is around 10 days (more or less) -even on these small samples, which are drained at both ends. It is consistent to assume that a large part of this time is controlled by the material water permeability, i.e. the time to obtain a uniform pore pressure inside the sample. It is also clear that, if during injection test, the waiting time was insufficient, this would obviously lead to artificially smaller Biot's coefficient.

Figure 3.8. Strain evolution during poro-mechanical tests

As commented in section 3.2.2, Biot's coefficient has to be identified through elastic loading paths.

It was then assumed that a decrease 𝑃 𝑐 in 𝑃 𝑐 or an increase 𝑃 𝑖 in 𝑃 𝑖 would lead to elastic strain recovery as they give a decrease in Terzaghi's effective pressure. A decrease in 𝑃 𝑐 (in Figure 3.8) results

in strains from D to E (or D' to E') while an increase in 𝑃 𝑖 gives strains from B to C (or B' to C'). If 𝑃 𝑐 is kept constant during the 𝑃 𝑖 test, i.e. increase followed by decrease in 𝑃 𝑖 , then both paths must be elastic. Decrease in 𝑃 𝑖 leads to strains from C to D (or C' to D'). This can be easily verified in Figure 3.8 in which strains at B and D are virtually the same. There is an exception in Figure 3.8 (b) for the red curve. This is attributed to experimental artefact due to gauge malfunctioning. Hence either strain B-C (or B'-C') or strain C-D (or C'-D') can be taken as 𝜀 𝑖 (∆𝑃 𝑖 ) to calculate Biot's coefficient. The 𝑃 𝑐 amplitude was chosen as 𝑃 𝑐 =𝑃 𝑖 . This allows a direct comparison between 𝜀 𝑖 (∆𝑃 𝑖 ) and 𝜀 𝑖 (∆𝑃 𝑐 ).

Results in Fig. 9 show that C and E (resp. C' and E') are virtually at the same level of strains. This is detailed in tables Table 3.4 (1) andTable 3.4 (2).

Table 3.4 Another important point must be mentioned as regards water vs gas measurements. After a complete (and very long) cycle of water saturation and poro-mechanical loading steps, the COx claystone is obviously de-structured, see Figure 3.9. After sample dismounted, water content measurements showed values as high as 9.5% while 7.5% (dry at 105°C) is considered to be the in-situ saturated material value. This means that the material, under these laboratory conditions, is oversaturated and deeply modified compared to the in-situ conditions.

Sample ∆𝑃 𝑐 = ∆𝑃 𝑖 (MPa) B'-C' ( m/m) C'-D' ( m/m) B' -C' C' -D' D'E' ( m/m) C' -D' D' -E' b EST51446 7
Figure 3.9. Image of a sample after test. The sample is full of water and looks "pasty"

The destruction effect was also evidenced in a conventional triaxial test. Figure 3.10 shows the stress & strain behaviors of two COx samples (extracted from the same T1 core) at 9 MPa confining pressure under drained conditions, one is in its initial state (7.5% water content) and the other is over saturated (9.5% water content). Strong mechanical contrasts between the two samples were found, especially on strength and ductility. Hence, it could be supposed that 𝑏≈1 derived from this de-structuration.

From there, the comparison with gas experiments brings new interesting highlights. They were indeed performed on partially saturated (or even dry) samples and with the same experimental technics. The sample is not de-structured under such hydric states and gas pore pressure tests obviously indicated that 𝑏1= 𝑏3 and lies in the range [0.9, 1] as indicated with 'helium' results. As in the 'in-situ' conditions, the material is unlikely destructured as it is during 'water' laboratory experiments, it is plausible to consider that the range [0.9, 1] is the most consistent for COx claystone. This means that for simulations, the choice of Biot's coefficient (between these two values) has to be made to ensure the worst case scenario so as to maximize safety.

Chapter summary

This contribution aimed at measuring the Biot's coefficient of COx claystone in a saturated state. In particular, synthetic water (close to in-situ water) was used as being the fluid to control pore pressure.

The tests were very challenging due to difficulties: sample preparation, long saturation times to obtain pressure uniformity. Several tests were successfully performed for the past two years among which four representative ones are presented in this study. Several essential points can be highlighted.

A significant swelling during the first water injection was observed, regardless the initial sample states (hydric and/or damaged) and the initial loading path (couple 𝑃 𝑐 , 𝑃 𝑖 ). This absolute swelling is due to the pore pressure loading (poro-mechanical effect) and the clay mineral swelling. The swelling amplitude was always found to be anisotropic with higher values perpendicular to bedding than the ones parallel to bedding. Such an anisotropy is consistent with the usual results found for this COx claystone i.e. a lower stiffness in the direction perpendicular to the beddings.

The poro-mechanical part of the tests was performed, after the first swelling stabilization, in order to measure Biot's coefficients on saturated samples. Results clearly demonstrated that, despite a significant material anisotropy, the Biot's tensor is isotropic with a unique component "b". This important result, consistent with some theoretical calculations, does not mean that the strains, due to pore pressure change, are isotropic. An other important result is that "b" was found very close to 1.

This means that, under the laboratory conditions used, the COx claystone behaves as a Terzaghi material. This crucial result was obtained on water saturated claystone samples, which exhibited some kind of de-structuration after the tests. It is nevertheless consistent with numerous observations made with gas (helium) as being the fluid to control pore pressure, which more often led to quasi isotropic Biot's tensor with "b" in the range [0.9, 1]. In this case gas experiments were performed on partially saturated materials (from dry to almost saturated) so without the de-structuration observed with water.

To summarize, this work completes the results obtained with gas and evidences that this saturated transversely isotropic claystone still closely behaves as a Terzaghi's material. It also contributes to clarify the Biot's coefficient value range that has to be chosen in numerical simulations, especially the crucial ones for which thermal activity of wastes is taken into account.

Note: This chapter has been written with a purpose of publication and submitted to 'Engineering For both UT and UA COx, self-sealing can cause significant reductions in water permeability. In particular, UA COx shows higher sealing efficiency and faster kinetics compared to UT COx. After sealing, the equivalent crack aperture (calculated from Poiseuille's law) decreases from tens of microns to less than 1 micron. According to the gas breakthrough tests, the gas breakthrough pressure (GBP) is of re-sealed macro-cracked COx is of the same order of magnitude as the equivalent capillary pressure of residual crack. This indicates that the gas migration in the re-sealed cracked COx claystone mainly occurs through the residual crack and is 'a priori' controlled by capillary processes.

Materials and sample preparation

Origin of COx claystone samples

Six COx claystone samples originating from four cores were used. The four cores, provided by Andra, were extracted at different depths of the COx formation. COx claystone is known as a transversely isotropic material, see Figure 4.1 (Cariou et al., 2012). The isotropic bedding planes contain the structural axis 1 and 2, and axis 3 is perpendicular to the bedding plane. All cores were extracted along the bedding planes (i.e. axis 1) and immediately sealed in T1 cells, which were developed by Andra to (Davy et al., 2007) were conducted on five samples (detailed in Table 4.1). To avoid shattering, the side surfaces of the sample were first wrapped with insulating tapes. The uniaxial stress was applied perpendicularly to the bedding planes to prevent cracks propagation only along the bedding surface. A typical result is shown in Figure 4.2 (a). The Brazilian splitting tests were stopped when the macro crack was created throughout the sample, see An originally designed set-up was used to investigate the sealing efficiency of compacted bentonite/sand plugs (Liu et al. (2014)). Innovatively, by placing the bentonite/sand plug in a stainless steel-epoxy tube, swelling occurred at almost constant volume during hydration. This allowed the asymptotic swelling pressure to be derived from the strain on the external surface of the tube. The system of "sample plug + stainless steel tube" is placed inside a triaxial cell and subjected to confining pressure. Thanks to high rigidity of the metallic tube, it is able to prevent the sample from being subjected to high confining pressure. The same kind of experiment was conducted on the COx argillite since the sample was included in a rigid steel tube+epoxy resin. When water is injected, the sample swelling is partially prevented by the tube. As a consequence, the swelling sample will apply radial stress on the assemblage (tube + resin). This stress can be evaluated by calibration (see section 2.2.3) and be related to a kind of swelling pressure. On the other hand, most of the swelling/sealing tests were usually performed with a significant confining pressure. The combination of the sample swelling (due to re-hydration) and the confining pressure leads to sharp decrease in permeability. It is therefore difficult to evaluate the real role of the only swelling. As shown in Figure 4.3 (a), the system consists of a stainless steel tube with an external diameter of 65 mm and a cylindrical COx claystone sample with a diameter of 37 mm, the length of the whole system is 40 mm. The claystone sample is placed in the center of the tube, and the space between tube and sample is fully filled with degassed liquid epoxy resin. The harden resin sticks strongly to the sample surface and the tube internal surface and is considered impermeable, meanwhile it has a significant compressibility (flexibility). The internal pressure effects in the tube-epoxy structure can be evaluated with two strain gauges (with an accuracy of 10 -6 m/m) symmetrically glued on the tube external surface, see Figure 4.3 (a). Thanks to a calibration process, the strain can be converted into an "apparent swelling pressure" (𝑃 𝑎𝑝𝑝 ), which is an adequate indicator of the swelling process duration and amplitude. Hence, the system (tube-epoxycracked sample) allows to measure the swelling kinetics, and an "apparent swelling pressure". It can also be used to evaluate the self-sealing efficiency with water permeability measurements. On the other hand, the sample is subjected to its own swelling pressure and not to an artificial level of confining pressure. This system needs a calibration phase to obtain the relationship between gas pressure into the tube and the strain. Both calibration and self-sealing tests are carried out with a triaxial cell, see Figure 4.3 (b). The experimental procedures are detailed in section 4.2.3.

. Mineralogical analysis

The mineralogical analysis is determined by two measurements: quantitative X-ray diffraction (QXRD) and Cations Exchange Capacity (CEC). Quantitative X-ray diffraction (QXRD) is used to analyze the bulk mineralogical and the subdivided clay mineral composition. For the purpose of improving the reliability of the results, two different representative parts were extracted from each sample, then BET equation are used for these calculations (Seemann et al., 2017). One should notice that the BET theory is an approach based on several assumptions, thus the derived Qm and SSA cannot be treated as the real physical properties (Lahn et al., 2020;Seemann et al., 2017). However, with well-contolled experimental conditions, they are still useful and effective for characterizing pore structure and to compare different materials (Rouquerol et al., 2007;Thommes and Cychosz, 2014).

Self-sealing experiments

Four results were recorded during the self-sealing measurements: evolution of the "apparent swelling pressure" (Papp), initial gas permeability (Kinigas), change of water permeability (Kw), and gas breakthrough pressure (GBP) after self-sealing. All the experiments were carried out in a temperaturecontrolled room in order to minimize the effect of temperature, with an average value of 21℃. In order to better simulate the interaction between the clay mineral and the underground water, a specially made synthetic water was used in all self-sealing tests. The detailed mineralogical composition is shown in Table 4.2. The self-sealing experiment was carried out with a modified triaxial cell. The system (tube-epoxycracked sample) is first wrapped with a rubber jacket then installed in the triaxial cell (Figure 4.3 (b)).

For saturation purpose, a Gilsons TM pump is used to control the confining pressure (Pc) of 4 MPa, the sample is then subjected to a wetting environment. More precisely, the saturation process is achieved also depends on pore pressure (Ppore). This pressure was of the same value (0.5 MPa) for all tests. Papp can then be decomposed as follow:

𝑃 𝑎𝑝𝑝 = 𝑃 𝑝𝑜𝑟𝑒 + 𝑃 𝑠𝑤𝑒𝑙𝑙 -Π 𝑒𝑝𝑜𝑥𝑦 (4.2)
where Π 𝑒𝑝𝑜𝑥𝑦 represents the suppressing effect of epoxy resin on the transmission of sample swelling pressure to the tube. This value has been revealed to be very low during the calibration test.

In any case, the presence of resin does not affect the comparison of Papp between different samples.

As a consequence, the measured Papp is not the genuine value induced from sample swelling but it is still a reliable result for assessing and comparing the COx claystone swelling behavior (and kinetics).

Permeability assessment techniques

Some transfer properties of the cracked samples were measured: the initial gas permeability (Kinigas)

and the water permeability (Kw) over time. The initial gas permeability is measured with argon gas under steady flow rate. The injection pressure is P1 (at upstream side) since the sample is freely drained at P0 = Patm at the downstream side (see Figure 4.6). A bronkhorst gas flowmeter with an accuracy of 0.01 ml/min is connected to the downstream side for the permeability test. Once a stabilized gas flow is detected, the classic Darcy's law for gas phase is applied to calculate the Kinigas:

𝐾 𝑖𝑛𝑖𝑔𝑎𝑠 = 2𝜇𝑄𝐿𝑃 0 𝐴(𝑃 1 2 -𝑃 0 2 ) (4.3)
Where µ is the dynamic viscosity of argon at 21 ℃, equals to 2.2×10 -5 Pa•s, Q is the volume flow rate measured at the downstream sample side, L is the sample length, A is the cross-sectional area of sample, P1 is the upstream gas pressure, and P0 is the downstream atmospheric pressure. The self-sealing efficiency is accessed via two properties: water permeability and gas breakthrough pressure (GBP). They were selected because they can quite easily be captured for the experimental procedure. Water permeability was periodically measured to be compared to the "intact" one. The latter is often in the range [10 -19 m 2 , 5×10 -21 m 2 ], for laboratory measurements [START_REF] M'jahad | Characterization of transport and water retention properties of damaged Callovo-Oxfordian claystone[END_REF].

Therefore, for assessing the swelling-induced permeability decrease, the change of water permeability (Kw) is recorded over time as the sample hydrates and swells. If the differential pressure between the sample inlet and outlet (∆P) is known, the water permeability can be calculated using Darcy's law for liquid phase by recording the water flow rate Q, the equation is as follows:

𝐾 𝑤𝑎𝑡𝑒𝑟 = 𝜇𝑄𝐿 𝐴∆𝑃 (4.4)
Rel. (4.4) is valid under permanent flow rate. This was assumed in order to get an approximate value the water permeability Kw. Water permeability measurements were performed every one to two days, until the end of swelling. The drainage valve remained open during each permeability evaluation and was closed again as soon as the measurement was completed.

Gas breakthrough measurement techniques

GBP was chosen as being another swelling indicator. The gas breakthrough tests were carried out immediately after the swelling stabilized. It was compared to values obtained on different samples during previous laboratory experiments [START_REF] M'jahad | Characterization of transport and water retention properties of damaged Callovo-Oxfordian claystone[END_REF]. In terms of methodology, two methods are presented in the literature to study the gas migration in (partially) saturated porous materials: the steady-state approach and the non-steady-state approach (Horseman et al., 1999;[START_REF] Amann-Hildebrand | Effective gas permeability of Tight Gas Sandstones as a function of capillary pressure -a non-steady-state approach[END_REF]Liu et al., 2014). The non-steady-state approach leads to shorter test durations and can provide both breakthrough and residual pressures, however, it was chosen to use the steady-state approach in the GBP tests (i.e. slow increase of gas pressure until gas is detected at the downstream sample side). It is often assumed that this technique leads to more accurate GBP value and in the present case, it was thought to better reproduce the in-situ case for which gas pressure is supposed to increase slowly. When both Papp and Kw were stabilized, the ISCO water pump was dismounted and replaced by an argon injection system. To start the GBP test, argon is injected from the upstream side of the saturated sample, with 0.2 MPa increment every 24 h. The downstream (i.e. the drainage valve of the cell in Figure 4.3) is initially closed, which results in downstream pressure increase. This increase may be due to expulsed water from the sample (i.e. "pushed" by the upstream gas pressure) and/or to the gas (argon) breakthrough. A gas detection device was then used to detect (or not) this breakthrough. Detection is performed by placing an argon detector (accurate to ± 0.1 µl/s) close to the drainage valve. This valve is opened and the detector gives an indication whether argon is present at the downstream side. The valve is closed again after this operation. Different physical processes can be successively observed: water expulsion due to gas intrusion, discontinuous (transient) gas flow, and continuous gas flow (Liu et al., 2014). The inlet gas pressure leading to continuous gas flow is defined as being the breakthrough gas pressure of the tested sample. In the 2:1 clay minerals group, the subdivided mineral contents are not consistent with the trend of the overall 2:1 clay minerals content. In other words, the subdivided mineral contents in 2:1 clay minerals are contrasted and there is no dominant mineral. In the presence of aqueous solution, specific minerals among the 2:1 clay minerals will be substituted with exchangeable cations in aqueous solution, and the interlayer spacing of which expands as a result of the adsorption of water molecules which are carried by the exchangeable cations. Therefore, in order to determine the most chemically active (i.e. the most swelling-related) mineral, the Cations Exchange Capacity (CEC) was carried out.

Results and discussion

Results demonstrate that the total smectite contents are linearly related to the CEC value, with the Pearson correlation coefficient (R 2 ) of 0.8035, see After a long period of geological evolution, the COx claystone matrix has been highly compacted and its hydration swelling is essentially due to the increase of pores volume. It was observed that crystalline swelling and osmotic swelling occur in the infra-clay micro-pores and inter-clay particle meso-pores, respectively (Saiyouri et al., 2000;Menaceur et al., 2016). Consequently, the measured As smectite is not present as a single phase in the COx claystone (Andra, 2005), a plausible explanation is that the smectite present in R1-I/S is more favorable for water-smectite contact, because it would bring to the claystone a greater pore volume and a larger specific surface area. Therefore, it can be supposed that the spatial arrangement of smectite seems to be more important than its content. Hence using CEC values to assess the swelling capacity is inaccurate, as regards the macroscopic swelling of COx claystone. swelling strain that observed in Chapter 2.

Permeability assessment

Gas and water permeability (evolution) were used for two different purposes. Coupling gas permeability (Kg) with Poiseuille law is able to evaluate a "mean" crack initial width. Water permeability was mainly recorded to be compared to the water permeability of "intact" COx argillite.

If, after swelling, both values (i.e. macro-cracked sample and intact material) are close to each other, it would evidence an efficient self-sealing. Moreover, if water flow through the crack is assumed after swelling, the permeability can also lead to a "final" crack width. This is developed in the following.

Gas permeability

The initial value of Kg was measured under almost no lateral pressure, thanks to the presence of stainless steel tube. As a consenquence, Kg comes from a gas flow that is supposed to mainly take place through the macro crack. This assumption is logical as the obtained results gave gas permeability 3 to 4 orders of magnitude higher than the intact one, see Table 4.4 (also see Duan et al., 2021). As the lateral stress applied on the cracked sample is very low, the gas permeability occurs in an opened crack and can be analized to evaluate its initial width. The initial Kg of macro-cracked samples (Table 4.4) are between 10 -13 m 2 and 10 -15 m 2 . It is noteworthy that the Kg of UA3-2 is not reported due to experimental measurement problem. For the intact sample UA3-I, the initial Kg is of 1.37×10 -17 m 2 that is consistent with previous tests (Zhang and Rothfuchs (2004)).

Table 4.5. Initial gas permeablity and water permeability of the tested sample

UT-C UA1-C UA2-C UA3-C1 UA3-C2 UA3-I Initial Kg (m 2 )
3.85×10 -13 1.79×10 -13 6.04×10 -14 1.08×10 To this purpose, the crack is simply modeled as two parallel planes and e is the distance between both (Figure 4.11). It is obviously far from reality [START_REF] Chen | Permeability of a Macro-Cracked Concrete Effect of Confining Pressure and Modelling[END_REF], but remains a useful assumption to compare samples and to follow crack aperture evolution.

𝑄 = 𝑄 1 = 𝑄 0 = 𝑑 • 𝑒 3 12𝜇𝐿 (𝑃 1 -𝑃 0 ) (4.5)
And for a compressible perfect gas:

𝑄 0 = 𝑃 1 𝑃 0 𝑄 1 = 𝑑 • 𝑒 3 12𝜇𝐿 • (𝑃 1 2 -𝑃 0 2 ) 2𝑃 0 ( 4

Water permeability

Gas permeability was a unique measure used to quantify the equivalent initial gas aperture.

Water permeability was in fact used and recorded in parallel with Papp to identify the end of the swelling process. The latter is assumed as soon as both Kw and Papp are stable. Evolution of Kw can be found in The UT-C sample exhibited a low swelling pressure (1 MPa) and it final water permeability stabilized at 10 -18 m 2 . This value is one order of magnitude higher than the one measured on intact UT sample. For this sample it can be concluded that the self-sealing is incomplete. They are all almost one order of magnitude less than the initial gas permeability. As a result, the initial crack aperture derived from Kw is smaller than what was calculated with Kg. Contrary to gas, water is chemically active with clay (also the case with concrete) and Kw smaller than Kg is usual with COx claystone. On the other hand, swelling is likely to occur very quickly therefore having an immediate impact on permeability. As aforementioned, the final values at the end of the swelling reveal an efficient self-sealing of the UA samples as they are now close to the intact material permeability.

Gas breakthrough pressure (GBP)

Laboratory results

When 𝑃 𝑎𝑝𝑝 and 𝐾 𝑤 were both stabilized, it was considered that the sample had reached full saturation and the gas breakthrough test was immediately performed. The GBP value of each test is shown in Table 4.5. After sealing, the GBP results for the saturated COx demonstrate distinctive features. The first one is that for macro-cracked samples, a significant difference in GBP values between UA and UT is observed. The GBP of UT COx is around 0 -0.2 MPa, while the value of UA COx range from 0.8 to 1.46 MPa. This confirms that UA COx possesses a better sealing efficiency than UT COx claystone, which is consistent with the observation of the initial 𝐾 𝑤 and equivalent crack aperture.

The other investigation is that by comparing UA3-C1, UA3-C1 and UA3-I, it is found that the GBP of intact sample is 4 -6 times higher than those of sealed macro-cracked samples. This demonstrates for the UA COx that even if the induced self-sealing brings the sample back to a very low 𝐾 𝑤 (close to the intact one), the gas transfer properties do not meet those in the undisturbed state. As a result, coupled with 𝑃 𝑎𝑝𝑝 and 𝐾 𝑤 , GBP reveals to be a strong complementary tool to evaluate the sealing efficiency.

Equivalent capillary pressure

The displacement of a gas phase in a saturated porous media is a complex process. Four gas migration mechanisms have been proposed by (Marschall et al., 2005) Where 𝛾 𝑔𝑤 is the gas-water interfacial tension, 72.9×10 -3 N/m at 20 ℃; 𝛼 is the gas/water contact angle, here it is taken at 0. 𝑃 𝑐𝑎𝑝 is assumed to be the necessary gas pressure to push water away from the crack. It can then be compared with GBP (Table 4.5). Even if lower than the real measured value, it can be underlined that Pcap remains in the same order of magnitude than GBP. Given the simplicity (two parallel planes) of the crack geometry and the fact that the whole sample water permeability is due to water flow in the crack, these results can be regarded as quite convincing. On the other hand, they confirm the hypothesis of GBP due to capillary phenomena. The GBP value of intact sample UA3-I was also measured, which was between 6.2 and 6.4 MPa. A rough calculation with GBP value equal to 𝑃 𝑐𝑎𝑝 , compared with Laplace's Law leads to a mean pore radius of the intact sample around 0.023 µm (23 nm). This result is consistent with what can be found in the literature (Song et al., 2015;[START_REF] Keller | Pore geometry effects on elastic properties of Opalinus Clay[END_REF].

Results observed

The initial gas permeability (Kinigas) is measured with argon gas under steady flow rate. The traditional "downstream method" was used to measure Kinigas. The upstream gas pressure is set to a very low value (i.e. 0.05 MPa) to avoid gas leakage between the silicone-COx sample interface. The measured Kinigas of the partially saturated sample (Sw=53%) is 1.51 × 10 -18 m 2 , which is in the same order of the non-damaged dried material (M'jahad et al., 2017). This means that the initial crack aperture is quite low (even not physically measured).

Based on the relationship between Pinternal & strain, the direct measurement strains data are constantly converted into Papp. Papp is followed until its stabilization. the use of silicone (instead of epoxy) resin is satisfactory, because of its weak stiffness, as the lateral pressure on the sample is considerably reduced (by one order of magnitude). This is also obvious that the swelling pressure is not an intrinsic property but strongly depends on external conditions (oedometric ones for example) -but this fact is very well known! On the other hand, this kind of experiment is likely to be more objective to analyze the self-sealing efficiency as it is almost not "polluted" by additional lateral (or confining) stress. is that the initial value of Kw is around four times higher than the Kinigas value. This can be interpreted that the initial Kw , which is deduced from water volume injected in the sample, is affected not only by the water flow through the sample but also by the water adsorption of material (with a low initial saturation). The stabilized Kw is in the order of 10 -19 m 2 (precisely of 2.48×10 -19 m 2 ), which is more than 10 times less than the initial value, can be regarded as the effective permeability after swelling. This result puts in light that a significant sealing process is still observed in the (quasi) absence of confining pressure. This indicates that the swelling of clay minerals can lead the cracked material to partially recover its water permeability under very low lateral pressure due to swelling. On the other hand, the permeability reduction does not allow the material to meet the values measured with the epoxy device (and are far from the reported intact values generally less than 10 -20 m 2 ). In other words, this test seems very promising as it could be used to evaluate, with a better objectivity, the self-sealing efficiency for sample with different crack (initial) opening or to quantify the confining pressure effect. Another important use should be to compare more accurately, between samples, the effect of their mineralogy. (1) During re-saturation, the apparent swelling pressure (Papp) of both macro-cracked and intact samples are all increased with time. By comparing macro-cracked samples from different geological positions, the Papp of UT COx is approximately 1 MPa, while it varies from 3 to 5 MPa for UA COx. By comparing samples from the same core, macro-cracked samples exhibit faster kinetics than the intact sample, while intact sample exhibits a slightly higher Papp than macro-cracked samples. Such difference is mainly attributed to the presence of cracks that increases the waterclay minerals contact area and generates more space for swelling.

(2) Relating Papp to specific clay mineral content, the smectite (swelling mineral) content does not seem to be the main influential factor, while the content of R1-I/S exhibits good linearity with Papp.

Nitrogen adsorption data demonstrate that both VGurvich and SSA are well linearly related to Papp and R1-I/S content, which implies that the effective water-mineral contact space and specific surface area are the key factors for COx swelling, and not simply the content of smectite fraction.

That is to say, estimating the swelling capacity of COx by CEC values will lead to inaccurate results.

From a viewpoint of testing technology, the VGurvich and SSA that derived from nitrogen adsorption data have been proven to be simple and effective parameters for assessing COx swelling capacity.

This should be verified and completed with other experiments.

(3) For both UT and UA COx, the presence of macro cracks results in a significant increment of permeability, up to 2 -4 orders of magnitude for Kg and 5-6 orders of magnitude for Kw. Selfsealing of macro-cracked COx can cause significant reductions in water permeability (Kw)

synchronously with the increase in Papp. The final water permeability of UA samples is reduced by five orders of magnitude and closed to that of the intact sample, while the final Kw of UT sample is reduced by four orders of magnitude and stabilized at around two orders of magnitude higher than the one for intact sample. Such results demonstrate that even in the absence of confinement, the clay mineral swelling can still lead to the macro-cracked COx claystone reseal to some degree.

Besides, UA COx shows faster kinetics compared to UT COx, which can be attributed to the impact of R1-I/S content.

(4) After sealing, the results of gas breakthrough tests illustrate that the GBP of UT COx is around 0-0.2 MPa, while the value of UA COx range from 0.8 to 1.46 MPa. This confirms that UA COx possesses a better sealing efficiency than UT COx even for gas transport, which is consistent with the observation of Kw decrease. Compared with Papp and Kw, GBP is more sensitive to the sample integrity. Using Poiseuille Law, the GBP value of the sealed sample is in the same order of magnitude as the equivalent capillary pressure of residual cracks, which indicates that the gas migration in the sealed COx claystone would mainly occur through the residual sealed-crack and is controlled by capillary phenomena.

(5) A complementary test, with soft silicone instead of epoxy has brought first and interesting results on the sole effect of sample swelling (almost without any lateral stress). This led to strong reduction in water permeability that is nevertheless far from the intact material value. This promising test seems to be a convenient one to evaluate independently the swelling effect and the confining effect (toward the permeability reduction).

Note: This chapter had been written with a purpose of publication and accepted in 'Rocks Mechanics and Rock Engineering'

Conclusions and perspectives

This thesis focuses on experimentally investigating the self-sealing effect of Callovo-Oxfordian (COx) claystone, which is considered to be the host rock for long-lived and high-level radioactive waste Mineralogical composition analysis illustrate that smectite is the only swelling mineral in COx, interspersing in two types of I/S aggregates in COx, namely R1-I/S (contains 30% smectite) and R0-I/S (contains 78% smectite). Nitrogen sorption data reveal that the swelling of COx is not only determined by the smectite content but also corresponds to the water-accessible pore volume and surface area.

This conclusion is valid from nano-scale to m-scale.

Anisotropic strains were measured during the swelling test. In particular, swelling strain parallel to bedding planes (ε ∥ S ) is used to be related to smectite-related minerals. From the viewpoint of the swelling amplitude, the result reveals that ε ∥ S has the highest correlation with R1-I/S, while has the lowest correlation with R0-I/S. This illustrates that the effect of smectite distribution on the material swelling is still valid on the centimetric scale. Therefore, a conceptual model is proposed to give insights into the multi-scale swelling mechanism of this material. As for the swelling kinetics, there is no correlation was found between expansion time and mineral composition or pore properties, indicating that the kinetics corresponds to a more complex coupling process.

In addition, the effect of micro-cracks on swelling was studied by comparing the swelling of intact and micro-cracked samples. Results implied that micro-cracking causes the material to exhibit a greater swelling amplitude and higher initial swelling kinetics. And the compress-induced micro-cracks are more likely to be parallel to the bedding planes, leading to a more pronounced expansion in this direction.

Poro-mechanical properties measurement with water

When the above-mentioned swelling test is completed, the sample is fully saturated. A following poro-mechanical test was performed on the saturated material. The main objective of this work was to measure the Biot's coefficient using synthetic water (close to in-situ water) to control the pore pressure. Within the framework of poroelasticity, the Biot's coefficient is determined by strains measured during sequentially loading and unloading confining pressure (P c ) and pore pressure (P i ).

This kind of test is very time-consuming due to the long saturation times to obtain pressure uniformity.

Several tests were successfully performed for the past two years among which four representative ones are presented in this study.

Results clearly demonstrated that, despite a significant material anisotropy, the Biot's tensor is isotropic with a unique component "b". This important result, consistent with some theoretical calculations, does not mean that the strains, due to pore pressure change, are isotropic. An other important result is that "b" was found very close to 1. This means that, under the laboratory conditions, the COx claystone behaves as a Terzaghi material. This crucial result was obtained on water saturated claystone samples, which exhibited some kind of de-structuration after the tests. It is nevertheless consistent with numerous observations made with gas (helium) as being the fluid to control pore pressure, which more often led to quasi isotropic Biot's tensor with "b" in the range [0.9, 1]. In this case, gas experiments were performed on partially saturated materials (from dry to almost saturated) so without the de-structuration observed with water. All these important results can now be used in numerical simulations with a high level of confidence as they are also consistent with other recent published works.

Swelling and transport properties evaluation of the sealed COx

A series of "low confinement" self-sealing tests was designed and carried out to investigate the swelling and transport properties of the reseal COx claystone. Through this experiment, the change of apparent swelling pressure (Papp) and water permeability during re-saturation and the gas breakthrough pressure (GBP) after sealing have been measured. These direct measurement data would provide important references for numerical reproduction.

Results demonstrate that Papp increased with time and the value of the UT sample is approximately 1 MPa, while it varies from 3 to 5 MPa for UA ones. By comparing samples from the same core, macrocracked samples exhibit faster kinetics than the intact one, while intact sample exhibits a slightly higher Papp than macro-cracked samples. Such difference is mainly attributed to the presence of cracks that increases the water-clay minerals contact area and generates more space for swelling. Papp also exhibits better linearity with R1-I/S than with R0-I/S. Such a result is consistent with the observation in swelling strain vs. smectite-related minerals (chapter 2). From a viewpoint of testing technology, nitrogen sorption is a simpler and more effective approach for assessing COx swelling capacity than XRD.

For both UT and UA material, the presence of macro cracks results in a significant increment of permeability, up to 2 -4 orders of magnitude for Kg and 5-6 orders of magnitude for Kw. Self-sealing of macro-cracked COx can cause significant reductions in water permeability (Kw) synchronously with the increase in Papp. The final water permeability of UA samples is reduced by five orders of magnitude and closed to that of the intact sample, while the is reduced by four orders of magnitude. It worth underlining that the final Kw of UT sample is at around two orders of magnitude higher than the one for intact sample. Such results demonstrate that even in the absence of confinement, the clay mineral swelling can still lead to the macro-cracked COx claystone reseal to some degree. Besides, UA COx shows faster kinetics compared to UT COx, which can be attributed to the impact of high R1-I/S content.

After sealing, the results of gas breakthrough tests illustrate that the GBP of UT COx is around 0-0.2 MPa, while the value of UA COx range from 0.8 to 1.46 MPa. This confirms that UA COx possesses a better sealing efficiency than UT COx even for gas transport, which is consistent with the observation of Kw decrease. Compared with Papp and Kw, GBP is more sensitive to the sample integrity. Using Poiseuille Law, the GBP value of the sealed sample is in the same order of magnitude as the equivalent capillary pressure of residual cracks, which indicates that the gas migration in the sealed COx claystone would mainly occur through the residual sealed-crack and is controlled by capillary phenomena.

Perspectives

Our originally designed "self-sealing" experiment provides a solution for analyzing the swelling and the sealing effect of COx under certain pore fluid pressure. Experiments under "low confinement"

indicate that the apparent swelling pressure increases simultaneously with the water permeability decrease. This gives us a preliminary concept that even under low confining pressure, the clay swelling (i.e. interstratified illite/smectite) has a certain effect on the sealing efficiency of damaged COx. In perspective, it would be very interesting to study the sealing efficiency of COx with (almost) complete elimination of the confining pressure. This could be performed with the device (with silicone) leading to the 'free' self-sealing test detailed in section 4.4. This is very useful for the better understanding of the sole contribution of clay swelling on sealing efficiency. Such a device would allow to make a clear distinction between the 'intrinsic' self-sealing effect due to the sole re-saturation and its amplification due to confining (or lateral) pressure -for example is there a critical initial crack aperture from which no intrinsic sealing is observed?

In addition, during the desaturation, pore water cations will be accumulated and remained in the clay particles, while only water molecules are evaporated from the material. Therefore, understanding the influence of pore water cations on clay swelling and material sealing during resaturation, is crucial.

This will be an important portion of the continuation work of this thesis.

  . Radioactive waste is divided into four categories: Very Low Activity (VLA or TFA for Très Faible Activité in French), Low Activity (LA or FA for Faible Activité in French), Medium Activity (MA also for Moyenne Activité in French), and High Activity (HA also for Haute Activité in French). Based on the radionuclide half-life period, it is also divided into 3 types: very short-lived (< 100 days, labeled VTC for Vie Très Courte in French), short-lived (≤ 31 years, labeled VC for Vie Courte in French), and Long-Lived (LL or VL for Vie Longue in French, ≥ 31 years and up to hundreds of thousand years).

Figure 1 :

 1 Figure 1: French classification of radioactive waste for their management(ANDRA, 2015)

Figure 2 :

 2 Figure 2: The CIGEO facility for HA and MA nuclear waste storage

Figure 3 :

 3 Figure 3: Meuse/Haute-Marne Underground Research Laboratory (in Bure locality): location and geology (de La Vaissière et al. 2015)

Figure 4 :

 4 Figure 4: Lithology and mineralogy of the entire COx claystone(Yven et al. 2007)

Figure 5 :

 5 Figure 5: Evolution of normal strain and permeability parallel to fractures during

1 .

 1 Microstructure of the COx claystoneCallovo-Oxfordian (COx) claystone consists of solid components (clay minerals and non-clay minerals) and complex porous networks. Understanding the structure of COx claystone is vital for the nuclear waste geological storage. Figure 1.1 gives a sketch of the COx claystone structures from the centimeter scale to the nanometer scale. Under an atmosphere environment, the sporadically visible impurities and cracks can be observed on a centimetric sample. On the m-scale, Figure 1.1 middle, COx claystone

Figure 1 . 1 .

 11 Figure 1.1. Multiscale structures of COx claystone(Wang et al. 2015)

Figure 1 . 3 .

 13 Figure 1.3. Molal water uptake (Q (mmol g21)) at 0.1, 0.3, 0.5 and 0.7 p/p° as a function of CEC (Seemann et al. 2017)

Figure 1 . 4 .

 14 Figure 1.4. Typical pore size distribution of UT (left) unit and UA unit (right) (borehole EST205)(Yven et al. 2007)

Figure 1 .

 1 Figure 1.6. Comparison of the adsorption/desorption isotherms of nitrogen and water vapor(Song et al. 2017)

Figure 1 . 7 .

 17 Figure 1.7. The relationship between Dubinin-Astakhov (DA) micropore volume (𝑄 0 ) and the BET monolayer capacity (𝑄 𝑚𝑜𝑛𝑜 ) of moisture-equilibrated COx claystone (Seemann et al. 2017)

Figure 1 .

 1 Figure 1.8. cumulative pore-size distribution (BJH + DA) derived from nitrogen sorption isotherms of COx claystone at different relative humidities (RH) (Seemann et al. 2017)

Figure 1

 1 Figure 1.9. 3D images of the Oplinus clay sample after triaxial compression tests: (a) acquired via high-speed CT (b) acquired via high-resolution CT (Zacher et al. 2015)

Figure 1 .

 1 Figure 1.10. 3D reconstruction of crack network at subsequent loading stages and spatial distribution of tortuosity at three directions by Micro-CT (Cała et al. 2017)

Figure 1 .

 1 Figure 1.11. 3D shear strain increment field in the post-peak increment, represented by horizontal cuts at different heights (left), and vertical cuts (right) (Bésuelle and Hall 2011)

Figure 1 .

 1 Figure1.12. 3D Micro-CT of the crack volume evolution during the water injection(Giot et al. 2019)

Figure 1 .

 1 Figure 1.13 (a), (b) and (c) exhibits the micropores and micro-cracks within the clay matrix of Opalinus clay that observed by SE-SEM at nanoscale.Figure 1.13 (d) is the BSE-SEM image of the mineral

Figure 1 .

 1 13 (d) is the BSE-SEM image of the mineral composition and spatial distribution of Opalinus clay(μm-scale)[START_REF] Houben | Pore morphology and distribution in the Shaly facies of Opalinus Clay (Mont Terri, Switzerland): Insights from representative 2D BIB-SEM investigations on mm to nm scale[END_REF]).

Figure 1 .

 1 Figure 1.13. SE-SEM images of Opalinus clay: (A) micropores within the clay matrix (B) two different pore types in the clay matrix. (C) the elongated micro-crack with jagged edges in the clay matrix. (D) is the BSE-SEM images overview of the typical microstructure of Opalinus clay[START_REF] Houben | Pore morphology and distribution in the Shaly facies of Opalinus Clay (Mont Terri, Switzerland): Insights from representative 2D BIB-SEM investigations on mm to nm scale[END_REF]

Figure 1 .Figure 1 .

 11 Figure 1.14. BSE-SEM micrographs of the BIB cross section overviews of COx claystone (Desbois et al. 2017)

Figure 1 .

 1 15 (b) shows a The reconstructed raw sample volume (Figure1.15 (b)) can be as small as 61 μm 3 with the voxel sizes of 5.9×7.5×10 nm 3[START_REF] Song | Pore network of cement hydrates in a High Performance Concrete by 3D FIB/SEM -Implications for macroscopic fluid transport[END_REF]).

Figure 1 .

 1 Figure 1.15. (a) principle of alternating action of focused ion and electron beams and a carved cube sample for observing; (b) reconstructed raw FIB/SEM 3D image; (c) reconstructed FIB/SEM 3D image of whole pore network of (Song et al. 2019)

Figure 1 .

 1 Figure 1.16. Multiscale pore structure and mineral composition in COx claystone(Yven et al. 2007)

Figure 1 .Figure 1 .

 11 Figure 1.17. drying/wetting test on the COx claystone (a) water content VS. saturation degree (b)volumetric strain obtained during drying/wetting cycles(Wan et al. 2013)

Figure 1 .

 1 Figure 1.19. the schematic of the smectite interlayer distance changes with suction (Menaceur et al. 2016)

  Saiyouri et al. (2000) proposed a conceptual swelling model that consists of two microscopic mechanisms, demonstrated in Figure1.20. Crystalline swelling results in the subdivision of the initial particles. The crystalline swelling amplitude of two adjacent layers varies from 3 to 12 Å, depends on the saturation level. When the material is close to fully saturated (saturation > 90%), Osmotic swelling occurs. If given enough swelling space, osmotic swelling (d2 in Figure1.20) can lead to an order of magnitude greater expansion than crystalline swelling (d1 in Figure1.20)(Anderson et al. 2010).

Figure 1 .

 1 Figure 1.20. swelling model of smectite including two mechanisms(Saiyouri et al. 2000)

Figure 1 .

 1 Figure 1.21. Water retention properties and volume changes obtained by suction control in terms of changes in degree of saturation and volume changes with respect to i) suction changes (a and c, respectively) and ii) water content (b and d, respectively) (Menaceur et al. 2016)

Figure 1 .

 1 Figure 1.22. Evolution of moduli (K=) and Kzz(K‖) with the isotropic effective stress for samples 33957 (top) and 27404 (bottom) (Cariou et al. 2012a)

  Some researchers have recently taken into account the transverse isotropy to consider the Biot's tensor with two components 𝑏1 (along the bedding planes) and 𝑏3 (in the vertical direction). Suarez-Rivera and Fjӕr (2013) put in light Biot's tensor anisotropy of Haynesville and Bossier shales. He et al. (2016) found that the Biot's tensor components of Bakken shales were between 0.57 and 0.70 and also exhibited a slight anisotropy. Belmokhtar et al. (2017) measured Biot's components of COx claystone between 0.85 and 0.98, with (slightly) higher values perpendicular to the bedding planes. Holt et al. (2018) also measured the anisotropy of Biot's tensor components of saturated soft shales,

Figure 1 .

 1 Figure 1.23. a typical result of the "change in pore pressure" test for COx claystone(Hu et al. 2020)

1. 4 . 1 .

 41 Permeability of COx claystone 1.4.1.1 Mono-phase fluid transport For mono-phase flow, the fluid transport is essentially dominated by the fluid pressure gradient and follows Darcy's law. The analysis of Darcy's law is different for the incompressible fluid (such as water or oil, etc.) and the compressible fluid, i.e. a gas phase. Assuming the flow is unidimensional and

Figure 1 .

 1 Figure 1.24. evolution of apparent gas permeability vs. the inverse of average gas pressure of: (a) CEMV concreate, using helium and argon as the injected gas; (b) COx claystone EST42135, sample A-9 is cracked while samples A-14 and A-24 remain "intact" (Chen et al. 2012; M'Jahad 2012) 1.4.1.2 Two-phase fluid transport

Figure 1 .

 1 Figure 1.25. One can find that the shear cracks are considered to be the closest type to the natural EDZ cracks.

Figure 1 .

 1 Figure 1.25. 3D visualization of typical excavation-induced fracture network (de La Vaissière et al. 2015)

  For instance, ANDRA performed a series of one-year repetitive in-situ hydration tests on the EDZ of COx formation in Bure URL, France. By monitoring the change of hydraulic conductivity around excavated tunnels over time, the hydraulic conductivities of all the observed points decreased and stabilized below 10 -10 m/s, shown in Figure1.26. However, field experiment is limited to the qualitative description of sealing process, the self-sealing mechanisms and quantitative analysis need to be studied by laboratory experiments.

Figure 1 .

 1 Figure 1.26. the change of hydraulic conductivity during the hydration tests (de La Vaissière et al. 2015)

  Figure1.27. confining pressure Pc vs. crack closure cc for three COx samples(Davy et al. 2007a) Thermal impact on self-sealing is studied by measuring the relationship between the intrinsic permeability (𝐾 int ) and temperature. Some researchers noted out that increasing temperature will result in a slight increase of intrinsic permeability which is attributed to the fluid viscosity and density as they will decrease with increasing the temperature(Chen et al. 2014; Zhang 2018).Chen et al. (2014) measured the 𝐾 int of both cracked and un-cracked Boom Clay under different temperatures by using three salt solutions and results showed that temperature has no adverse effect on the self-sealing of Boom Clay (Fig.1.28 (a)). Similar conclusions are also reported in the study of COx claystone[START_REF] Delage | On the Thermal Consolidation of Boom Clay[END_REF][START_REF] Monfared | On the THM behaviour of a sheared Boom clay sample: Application to the behaviour and sealing properties of the EDZ[END_REF] Zhang 2018). However, the self-sealing of Opalinus Clay proved to be more temperature-dependent. Figure1.28 (b) exhibits that by injecting with three different solutions, the permeability of Opalinus Clay reduces by tens times when temperature goes up from 20°C to 80°C.

  8 shows the water permeability measurements of GDR-FORPRO research program, the macro-cracked COx claystone water permeability decreases by one to three orders of magnitude during 4-21 days, with a volumetric swelling amplitude between 0.03-0.18mm. Davy et al (2007) performed pulse water injection tests on the macro-cracked COx claystone samples, results demonstrated that the water permeability decreases by two or three orders of magnitude during 2-10 days, which is in consistency with the results of GDR-FORPRO.Table 1.8. Water permeability tests from GDR-FORPRO research program (Davy et al. 2007)The volumetric swelling is quantitatively analyzed by monitoring the deformation of strain gauges on the sample surface(Zhang 2011(Zhang , 2018;; Minardi et al. 2016). Particularly, Zhang (2011) carried out the water injection and compression tests simultaneously on an axially cracked COx sample, the deformation and water permeability are monitored over time. Figure1.29 illustrates the synthetic impact of hydrostatic stress and water-clay mineral interaction. After water injection, the swelling effect is significant even under hydrostatic stress loading. The swelling-induced sealing reflects on: 1) the non-stop decrease over time of water permeability at each elevated confining stress; 2) by unloading the sample to 1 MPa, the rebounded water permeability is still three orders of magnitude lower than the initial value before self-sealing.

Figure 1 .

 1 Figure 1.29. Evolution of normal strain and water permeability of a axial-parallel cracked COx sample, under the hydrostatic stress loading and water injection (Zhang 2011)

Figure 1 .

 1 Figure 1.30. The capillary pressure of the gas phase as a function of water saturation in a two-phase flow process, modified according to Amann-Hildebrand et al. (2002)

  non-clay minerals (such as calcite-CaCO3, silica-SiO2) are considered as rigid inclusions (Fig.2. 1 left) and will not swell. The clay minerals include illite, muscovite, interstratified illite/smectite aggregates (abbreviated as I/S) and small amounts of kaolinite and chlorite.[START_REF] Massat | Swelling pressure development and inter-aggregate porosity evolution upon hydration of a compacted swelling clay[END_REF] reported that I/S aggregates are the only swelling mineral in COx claystone. From Fig.2.1 middle, one I/S aggregate includes tens (even hundreds) illite and smectite particles, both of them are flake-shaped and consist of numerous elementary platelets. The structure of the elementary platelet is the same for illite and smectite, which is composed of an octahedral sheet between two tetrahedral sheets and with a basal spacing of 9.6 Å(Mitchell and Soga, 2005), see Fig. 2.1 right. Each elementary platelet is negatively

Figure 2 . 1 .

 21 Figure 2.1. Microstructure of swelling clay mineral in COx claystone Another swelling mechanism that occurs in COx claystone is called osmotic swelling. It is driven by

  Figure 2.2 (a)) or parallel (along axis 1 or 2, Figure 2.2 (b)) to the bedding planes. The swelling deformation of samples was measured by the strain gauges. Two cross-strain gauges (5mm length each) were symmetrically glued on each sample side surface. For both core orientations, gauges were glued parallel to axis 1 (or 2) and axis 3, illustrated Figure 2.2 (a) and (b). Before gluing gauges, a small amount of water was sprayed on one sample end (or the side surface of EST51133) to let the bedding plane be visible, see Figure 2.2 (c). In the following, gauges parallel to the bedding planes are called 𝐽 ∥ and gauges perpendicular to the beddings are 𝐽 ⊥ . The swelling strains measured by 𝐽 ∥ and 𝐽 ⊥ are called 𝜀 ∥ S and 𝜀 ⊥ S , respectively.

Figure 2 . 2 .

 22 Figure 2.2. Samples cored (a) perpendicularly to the bedding plane and (b) parallel to the bedding plane; (c) exhibits the bedding structure of the material by spraying water on the sample end surface The effects of clay minerals contents and damage states (i.e.additional cracking) on swelling behavior (amplitude and kinetics) were investigated in this study. Cylindrical samples were divided into two groups depending on the study objectives, as shown inTable 2.2. All swelling tests were conducted

  Figure 2.3 (a) and Figure 2.3 (b). respectively give axial/lateral and volumetric strain changes during loading/unloading. A non-linear stress-strain behavior and a significant volume dilatancy were observed, indicating that micro-cracks occurred within the sample even if no visible cracks appeared on the outer surface.

Figure 2 . 3

 23 Figure 2.3 Uniaxial compression test of sample EST58128: (a) stress-strain behavior and (b) volume strain during loading/unloading unixial stress 2.3. Experimental methodology

Figure 2 . 4 .

 24 Figure 2.4. Diagram of the experimental setup for swelling test 2.4. Results and analysis

Fig. 2

 2 Fig. 2.5 (b) and (c) that the linear quality of CEC vs. R1-I/S is better than that of CEC vs. R0-I/S.

  Figure 2.5. The relationship between CEC, total smectite content, R1-I/S and R0-I/S. (a)-(c) show results for both UT and UA samples; (d)-(f) exhibit results for only UA samples.

Figure 2

 2 Figure 2.6. N2 physisorption isotherms of COx samples from different cores, measured at 77 K.

Figure 2 . 7 .

 27 Figure 2.7. Analysis of the relationship between 𝑉 𝐺𝑢𝑟 and clay mineral contents (a) Different clay mass contents are linearly related to 𝑉 𝐺𝑢𝑟 ; (b) the exponential relationship between CEC and 𝑉 𝐺𝑢𝑟 .

  Figure 2.8. Analysis of the relationship between 𝑆𝑆𝐴 and smectite-related mineral contents (a) Different clay mass contents are linearly related to the 𝑆𝑆𝐴; (b) the exponential relationship between CEC and 𝑆𝑆𝐴.2.5.2.3Micropore textural properties vs. crystalline and osmotic swelling

  Figure 2.10. Cumulative pore-size distributions based on the combination of DA and BJH theories

  11. Relationships between material properties and the smectite-related clays for only UA samples 2.5.2.6Partially conclusion

Figure 2 . 12 .

 212 Figure 2.12. Swelling strains of four gauges of the UT sample EST51133 (initially mass stabilized at 75%RH)

  13. Strains evolution (parallel to bedding planes) of different samples, with Pc =14 MPa and Pi =5 MPa. (a) The overall strain evolution. The small chart on the left illustrates the water injection points after loading Pc; (b) absolute swelling behavior during loading Pi.

  Fig. 2.14. Swelling amplitude vs. smectite-related clay contents for both UT and UA samples

  Fig. 2.15. Correlation between absolute swelling strain 𝜀 ∥ and multi-scale pore textural properties Fig.2.14 and Fig.2.15 clearly show that the data again form two distinguished groups. This is logical because the large difference in clay content leads to significant variations in swelling capacity between

  2, crystalline swelling occurs in the micropores, whereas osmotic swelling takes place in the mesopores. A conceptual model is proposed to give insights into the swelling process of COx claystone, see Figure 2.16. As seen in Figure 2.16 (a) and (b), the inter-platelet region of smectite (in R1-I/S and R0-I/S) initially contains 0, 1, 2, and 3 layers of water molecules at different RH. With the increase of RH, crystalline swelling and osmotic swelling occur successively. Crystalline swelling is the first to appear by increasing the thickness of smectite particles (Figure 2.16 (c) and (d)). As shown in Figure 2.16 (left part), the smectite basal spacing increases with RH due to the increase of inter-platelet water layers. At 100% RH, the basal spacing value reaches the maximum value (21.6 Å) and the crystalline swelling is completed. It should be underlined that both R1-and R0-I/S exhibit an increase in layer thickness until the crystalline swelling is complete, without causing any structural damage.

Figure 2 .

 2 Figure 2.16. Conceptual model of multi-scale swelling mechanism of COx claystone. (a) and (b) illustrate the unsaturated R1-I/S and R0-I/S, respectively. Smectite particles are inserted in the interstratified I/S phases. With the increase of RH, the initial water layer state in the smectite interplatelet space corresponds to 1-3 water layers; (c) and (d) show the crystalline swelling of R1-I/S and R0-I/S, respectively, corresponding to 100% RH. Smectite inter-platelet spaces are filled by four layers of water molecules; (e) and (f) are the osmotic swelling of R1-I/S and R0-I/S. The material saturation maintains 100% RH during the osmotic swelling process; (g) is the sample with high R1-I/S content after swelling, while (h) is the sample with high R0-I/S content after swelling.

  16. Comparison of swelling between intact and micro-cracked samples of sample EST58128 (a) swelling strain parallel to bedding planes (𝜀 ∥ S ) (b) swelling strain perpendicular to bedding planes (𝜀 ⊥ S ) This chapter focuses on investigating the effect of clay minerals (specifically smectite-related clays) and pore structure on the swelling behavior of COx claystone. Five COx samples (one UT sample and four UA sample) originated from different geological locations were tested with different approaches. Quantitative XRD and cation exchange capacity (CEC) analysis indicates that smectite is the only swelling clay in COx. It exists in two types interspersed in I/S aggregates, namely R1-I/S (30% smectite) and R0-I/S (78% smectite). Based on different models, nitrogen isotherms were used to study the pore textual properties, such as Gurvich specific volume (𝑉 𝐺𝑢𝑟 ), BET specific surface area (SSA) and micropore volume (𝑄 0 ). It is found that these pore properties have the highest correlation with R1-I/S and the lowest correlation with R0-I/S. This means that from microscale to macroscale, the interstratified I/S phase with lower smectite content consistently corresponds to greater pore volume and surface. Characteristic energy 𝐸 and Dubinin-Astakhov exponent 𝑛 are the micropore textural properties necessary to apply the Dubinin-Astakhov theory. No apparent difference of the two properties was observed between UT and UA samples, which can be explained by the swelling mechanism in micropores, i.e. crystalline swelling is identical for all COx samples. The cumulative pore size distribution derived from Barrett-Joyner-Halenda + Dubinin-Astakhov theories, indicates that increasing smectite-related clay content mainly increases the pore volume between 0 and 45 nm. This means that the macroscopic volume expansion mainly originates from the swelling of these pores. Within this pore size range, both crystalline swelling and osmotic swelling are promoted. A series of swelling tests were carried out to investigate the anisotropic swelling behavior under constant confining pressure. Swelling strain parallel to bedding planes (𝜀 ∥ S ) is used to analyze the effect of smectite-related minerals, due to it is hardly affected by layered structure. Linear correlation of 𝜀 ∥ S with smectite-related clay minerals revealed that R1-I/S has the highest correlation, while R0-I/S shows the lowest correlation. Combined with the nitrogen sorption data to analyze, it can be concluded that the macroscopic strain amplitude is mainly determined by two microscopic factors: the total content of smectite in interstratified I/S phases and the accessible pores for water-smectite contact. A conceptual model is proposed to describe a multi-scale swelling mechanism of COx claystone.

Figure 3 . 1 .

 31 Figure 3.1. Scheme of the argillite sample with its bedding plane and equipped with crossed strain gages

Figure 3 . 2 .

 32 Figure 3.2. Anisotropic strain variations due to equivalent changes in Pc and Pi

Figure 3 . 3 .

 33 Figure 3.3. Measured Biot's tensor of COx claystone with helium and argon(Yuan et al., 2017)

  Figure 3.4 middle. The two longitudinal gauges measured strains parallel to the beddings (𝜀 ∥ ), and the two transverse gauges were used to measure strains perpendicularly to the beddings (𝜀 ⊥ ). Despite their short length, transverse gauge axis cannot strictly be parallel to axis 3 due to the curvature of the sample. Nevertheless, 𝜀 ⊥ is still useful to be compared with 𝜀 ∥ and to calculate Biot's coefficient b (see rel. (3.4)).

Figure 3 . 4 .

 34 Figure 3.4. Specimen with gauges: two longitudinal gauges and two transverse gauges glued on the sample side surface.

Figure 3 . 5 .

 35 Figure 3.5. Experiment setup used for Biot's components measurement.

Figure 3 .

 3 Figure 3.6. Example of a first loading phase of EST 57903-1: Pc and Pi were simultaneously applied.

Figure 3 . 7 .

 37 Figure 3.7. (a) SEM image of an unpolished surface of COx claystone (EST 58128); (b) an conceptual illustration of water molecules distribution in a swelling clay

Figure 3 .

 3 8 presents the strain evolution during poro-mechanical loadings of the four samples. Red lines with solid squares indicate the average strain 𝜀 ⊥ , whereas black lines with solid circles represent the average strain 𝜀 ∥ . Strain variation A-B (or A'-B') and D-E (or D'-E') correspond to increasing and decreasing 𝑃 𝑐 , respectively; B-C (or B'-C') and C-D (or C'-D') are the strain induced by increasing and decreasing 𝑃 𝑖 , respectively. A complete test cycle can last around 20 to 30

.

  Strains and Biot's coefficient measured by gauges (a) perpendicular to the beddings and

Figure 3 .

 3 Figure 3.10 Conventional triaxial test results for partially and fully saturated COx samples (retrived from the same T-cell plug EST 58128).

  chapter, a dedicated experimental device has been designed to measure the apparent swelling pressure, gas and water permeability, and gas breakthrough pressure of macro-cracked COx claystone. The experimental results are analyzed in parallel with mineralogical (quantitative XRD & CEC) and nitrogen adsorption data. Six COx claystone samples from four different geological locations of the Bure basin (France) are tested, five of which are macro-cracked and one remains intact. Sample swelling occurs, during re-hydration with liquid water, leading to the measurement of an apparent swelling pressure. The latter is continuously recorded with a dedicated device. The asymptotic apparent swelling pressure of macro-cracked UT (transitional unit) COx is approximately 1 MPa, while it varies from 3 to 5 MPa for macro-cracked UA (clayey unit) COx. Quantitative X-ray diffraction (QXRD) analysis demonstrates that the amount of smectite, which is a swelling clay, is weakly correlated with Papp. Meanwhile, the interstratified illite/smectite with higher illite content (R1-I/S) is highly correlated to Papp, and nitrogen isotherms data imply that the Gurvich total pore volume (VGurvich) and specific surface area (SSA) are linearly related to R1-I/S. This provide an easier and more effective technique than QXRD for assessing COx swelling capacity, as both VGurvich and SSA have been proven as effective indicators.

Figure 4 .

 4 Figure 4.2 (b). The numbers and diameter of cracks are significantly different from one sample to another. Apart from the split-cracked samples, an intact sample from EST 58145 was also used as the intact reference in our experiment.

Figure 4 .

 4 Figure 4.2. Photograph of a Brazilian test (left) and the resulting diametral macro-crack (right) 4.1.2.2 Design of the "stainless steel tube-epoxy-sample" system

Figure 4 . 3 .

 43 Figure 4.3. Sketch of the experimental set-up: (a) a system consists of steel-epoxy composite tube and a COx sample, the sample is placed in the tube center and two strain gauges are glued on the tube outer surface; (b) the hydrostatic triaxial cell used for the self-sealing experiments4.2. Experimental methodology

Figure 4 . 4 .

 44 Figure 4.4. Nitrogen adsorption results of tested samples

Figure 4 .

 4 Figure 4.6. Schematic diagram of permeability test

Figure 4 . 7 .

 47 Hence, in COx claystone, smectite can be considered as the most swelling-related mineral among all 2:1 clay minerals. For the whole set of UA samples, the difference in the content of smectite was not significant and results in similar CEC values.The smectite content of the two UT representative samples (EST57257-1 and EST57257-2) is slightly higher than for UA samples. But this cannot generalized as the mineral composition of UT COx claystone varies greatly from one location to another(Andra (2005)).

Figure 4 . 7 .

 47 Figure 4.7. Relation between the CEC value and the Smectite content

  apparent swelling pressure (Papp) is the reaction to the limited volume expansion of the COx sample. It can be considered as the micro scale swelling pressure at the macro scale. The Papp change with time was recorded for each test and given in Figure4.8. For the macro-cracked samples, the difference between Papp value of UA and UT samples is quite significant: the Papp of the UT-C is around 0.99 MPa, while for the four tested UA samples (UA1-C, UA2-C, UA3-C1, and UA3-C2), the value of Papp are in the range of 4.55-5.10 MPa. For comparison purposes, the swelling pressure of intact sample UA3-I was also measured (5.88 MPa) in parallel with the macro-cracked samples. The measured Papp range is smaller than that of samples with an "in-situ" void ratio(Zhang et al. 2020). This is a logical consequence, as the rebound and damage of the claystone during re-coring reduces the swelling capacity of the material. Moreover, the presence of steel tube and epoxy resin also suppressed the swelling strain. From the viewpoint of kinetics, the swelling time of UA3-C1 and UA3-C2 are both around five days, while it is 17 days for the intact sample UA3-I. Such difference in kinetics indicates that the presence of macro cracks creates more water-mineral contact area inside the sample, which accelerates the swelling process. Papp of UA3-I, 5.88 MPa, is relatively higher than Papp for UA3-C1 and UA3-C2. The difference in Papp between macro-cracked and intact samples is around 15%. One plausible interpretation of such difference is that the crack network leads to more swelling space, i.e. there is a logical decrease in Papp.

Figure 4 .

 4 Figure 4.8. Evolution of apparent swelling pressure of the tested COx claystone sample

Figure 4 .

 4 Figure 4.9. Apparent swelling pressure vs. specific clay mineral content

Figure 4 .

 4 Figure 4.10 (c) and (d). As smectite is not present as a single phase in the COx claystone(Andra, 2005),

Figure 4 .

 4 Figure 4.10. Correlation of nitrogen adsorption data with apparent swelling pressure: (a) Papp vs. VGurvich (b) Papp vs. SSA (a) R1-I/S vs. VGurvich (b) R1-I/S vs. SSA Moreover, a nitrogen sorption test is easier to be carried out than QXRD. The linear relationship of VGurvich vs. Papp and SSA vs. Papp is consistent with those of VGurvich vs. swelling strain and SSA vs.

Figure 4 .

 4 Figure 4.11. Simplified cracks consists of two parallel planes with a distance of e Poiseuille Law leads to the fracture calculation of the fluid flow rate Q1 and Q0. For an imcompressible liquid in steady flow rate:

. 6 )

 6 With rel.(4.3) and rel. (4.4) and when the material matrix permeability is low (compared to the crack "permeability"), it comes for both gas and liquid:

Figure 4 .

 4 Figure 4.12 and compared with Figure4.8. On a global point of view, there was a strong and rapid swelling for UA-C type samples, and this is consistent with a sharp drop in permeability. After around 5 days, both phenomena stabilized slowly until 20 -25 days. This observed parallelism is logical as swelling leads to crack closure. At the end of the process, water permeability of UA-C samples has decreased by 5 -6 orders of magnitude. It is still slightly higher than initial values reported for intact sample but all in the range [10 -19 m 2 , 10 -20 m 2 ]. This evidences the swelling efficiency on self-sealing.

Figure 4 . 12 .

 412 Figure 4.12. Variation of water permeability with time Initial values of water permeability (at the beginning of water injection) are given in Table4.4.

Figure 4 . 4 . 4 . 4 . 4 . 1 .

 444441 Figure 4.13. Equivalent single crack aperture evolution of all tested samples

Figure 4 .

 4 Figure 4.14: cross-sectional view of the special designed assemblage of "tube+silicone+sample"

Figure 4 .

 4 15 shows the Papp change with time. It can be found that the measured Papp of the two gauges are very close to each other and both values were stabilized at between 0.3 and 0.4 MPa. Considering the poro-mechanical coupling effect (Pi=0.1 MPa), the absolute swelling pressure is therefore smaller than Papp. This indicates that

Figure 4 .

 4 Figure 4.15. Evolution of apparent swelling pressure (Papp)

Figure 4 .

 4 16exhibits the decrease of Kw with time. The injected water pressure is 0.1 MPa. One unexpected result

Figure 4 .

 4 Figure 4.16. Evolution of water permeability (Kw)

  storage in France. Six COx claystone cores originated from various depths (from the Meuse/Haute Marne Underground Research Laboratory) were tested with different experiments, including quantitative X-ray diffraction (XRD), cation exchange capacity analysis (CEC), nitrogen adsorption test, swelling & poro-mechanical test, and self-sealing test. This research was carried out from three different perspectives, namely multi-scale swelling mechanisms, poro-mechanical properties measurement with water, and the swelling and transport properties evaluation of the sealed material.Multi-scale swelling mechanismsThis multi-scale swelling mechanisms of COx claystone was carried out by a series of swelling tests, supplemented by quantitative XRD, cation exchange capacity (CEC) and nitrogen adsorption. The tested material comes from five different geological locations, provided by Andra. XRD, CEC, and nitrogen sorption analysis were performed on powder samples, while the swelling tests were conducted on cylindrical samples. Cylindrical samples were re-cored from different T1-cores and preequilibrated at 75% RH to eliminate the effect of saturation. The effects of clay minerals contents and damage states (i.e. cracking) on swelling behavior (amplitude and kinetics) were investigated. During the swelling test, the sample was first placed in a triaxial cell at a constant confining pressure of 14 MPa. When the sample mass was stabilized, synthetic water was injected from both sample ends at a constant pressure of 5 MPa. The obtained experimental data is the evolution of sample expansion strain with time. The swelling amplitude and the swelling kinetics are evaluated by comparing between samples.

Table 1 :

 1 Natural barrier options for the long term storage of radioactive waste for different industrial countries Depending on the radioactivity of the waste, different storage solutions and different types of repositories are proposed. For instance, in France, the CIGEO project is operated by the French National Agency for Radioactive Waste Management (ANDRA for Agence Nationale de gestion des

	Countries	Host Rock	Geological location
	France	Callovo-Oxfordian claystone	420-550 m depth
	Switzerland	Opalinus clay	Approx. 300 m depth with a thickness of 90 m
	Belgium	Boom clay (plastic clay)	Approx. 230 m with a thickness of 100 m
	Canada	Stanstead granitic rock	240-420 m depth
	Sweden	Småland granites	200-460 m depth
	China	Beishan granites	Approx. 560 m depth
	Finland	Olkiluoto granitic rock	Approx. 345 m depth

Table 1

 1 .1 and table 1.2 show the representative mineralogy characterization of this unit, extract fromSong et al. (2016Song et al. ( , 2017)). Quantitative XRD and Cationic Exchange Capacity (CEC) analysis were carried out on seven samples from different cores (all from the UA unit, coming from different geological depths within a range between 476m and 507m). The quantitative XRD results of two UA samples (EST27405 and EST26095) only include the general clay minerals content, the tectosilicate content, and the carbonate content. The results of the rest five UA samples are more precise and give more detailed information, see Table1.2. The present results illustrate that the clay minerals (illite, interstratified illite/smectite, kaolinite, and chlorite), calcite and quartz are the primary minerals whereas dolomite, ankerite, siderite, feldspar and pyrite make up together the secondary mineral phases. Besides, the total organic matter (not present in Table1.1 and

Table 1 .

 1 2) also existed and forming less than 1% of the total.

Table 1 .

 1

1. General mineralogy results of seven UA type samples by quantitative XRD (Song et al. 2016a) Table 1.2. Detailed mineralogy results of five UA type samples by quantitative XRD

(Song et al. 2017)

  Song et al. (2017) measured the CEC of five UA-type COx claystone samples, the measured CEC values are shown in Table.2. CEC is ranging between 91 and 138 meq/kg (i.e., 9.1 -13.8 meq/100g),

Table 1 .

 1 3. The definition of claystone pore categories in relation to various detected methods

			Pores radius
	Void category				Fractures
		Micropores	Mesopores	Macropores
	Void size	<2 nm	2-50 nm	50 nm -m	m-mm
			Mercury intrusion porosimetry (3 nm-10 mm)
	Investigation
	techniques
	and
	resolution
	scales

Table 1 . 4

 14

. Water content and porosity of the at different Callovo-Oxfordian claystone sequences

(Conil et al. 2018)

1.3. Deformability of COx claystone: shrinkage, swelling, and poro- mechanics

	Numerous studies have proven that COx claystone shrinks during desaturation and swells during
	hydration. Moreover, the deformation of this material always exhibits strong anisotropy due to the
	inherent layered sedimentary characteristics. During the construction of a radioactive waste repository,
	the tunnel ventilation can lead to shrinkage (even cracking) of the surrounding formation (i.e. EDZ, has
	been illustrated in Introduction). After the repository closure, COx claystone will be subjected to long-
	term hydro-mechanical loading. Such hydro-mechanical loading will lead to the self-sealing of
	desaturated & cracked EDZ, which has been validated by in-situ and laboratory experiments

Table 1 .

 1 [START_REF] Hildenbrand | Gas breakthrough experiments on fine-grained sedimentary rocks[END_REF]. laboratory studies on the self-sealing of claystones Many field experimental studies have been conducted on the effect of self-healing on permeability.

	Category of rock	Source	Damaged state	Experiment conditions	Evaluation parameters
		Davy et al. (2007)	Split-cracked along the beddings	Change confining pressure	Kw VS. Cc; Kg VS. Cc
	COx	Zhang & Rothfuchs (2008) Shearly cracked by deviatoric stress	Re-compression via various loading paths Re-saturation by inject water	Kg VS. Pc; Kg VS. Time
	claystone
		Zhang (2011, 2015, 2017) Compress-cracked parallel to beddings	Deviatoric compressed; Re-saturation under various RH; Thermal loading	Kg VS. Crack aperture Kg VS. Strain; Kw VS. T
		Giot et al. (2019)	Cutted with a diamond saw along the beddings	Re-saturation at constant confinement	Kw VS. Time Geometry of crack (𝜇CT)
		Bernier et al. (2007)	Artificially cracked hollow sample	Acoustic emission/isostastic	Strain VS. Time; Kw VS. Time
		Bastiaens et al. (2007)	Cut fractures parallel to the beddings	Re-saturation at constant confinement; In situ measurement	Pp VS. Time; P-wave VS. Time Geometry of crack (𝜇CT)
	Boom clay &	Van Geet et al. (2008)	Drilled a tiny hole through the axis of the sample & Artificial cracks	Inject various solutions	Kw VS. Time Geometry of crack (𝜇CT)
	Opalinus
	clay	Monfared et al. (2012) Shearly cracked hollow sample	Re-saturation; Heating-cooling loading	Pp VS. T; Strain VS. T
		Chen et al. (2014)	Drilled a tiny hole through the axis of the sample, parallel to the beddings	Perform heating cycles after sealing	Kw VS. Time; Kw VS. T Geometry of crack (𝜇CT)
		Bossart et al. (2019)	EDZ at Mont Rock Laboratory	In situ pneumatic-hydraulic tests In situ miniseismic tests	Kw VS. Location; Pp VS. Time P-wave (S-wave) VS. Depth
	Notions: Kw/Kg: water/gas permeability; Cc: crack closure; Pc/Pp: confining/pore pressure; T: temperature

  Liu et al. (2014) performed similar experiments on bentonite/sand plugs. The effective swelling pressure of such mix material is 7.32 MPa ± 0.11, which is compatible with the value of bentonite/argillite plugs. PBreakthrough is sensitive to the plug saturation state: when the sample is fully

saturated, the continuous PBreakthrough is equivalent or slightly higher than the swelling pressure; when the plug is de-saturated (by imposing gas in one of the end surfaces), both the discontinuous and continuous breakthrough pressure are lower than for the fully saturated cases. M'

Jahad et al. (2017)

found that PBreakthrough is very sensitive to the damage state of COx claystone even under high confining pressure. This means that it is a useful in-situ materials damage detector.

2.2.1. Origination of material

  Five COx claystone samples retrieved from different boreholes of the Meuse/Haute Marne Underground Research Laboratory (URL) (Bure, France) were tested in this study, see Table 2.1.

Table 2 .

 2

		1. Information of the tested material
	Core number	Geological sequence	Initial saturation (before swelling test)
	EST 51133	UT	36.7%
	EST 57903	UA	86.8%
	EST 58128	UA	85.5%
	EST 58145	UA	84.3%
	EST 62665	UA	84.3%

Table 2

 2 Duan et al. (2021) reported that cracks parallel to bedding planes can significantly enlarge the swelling strain, especially the 𝜀 ⊥ S value. To verify this result, two intact and two micro-cracked samples from core EST 58128 were used for studying the effect of the initial damage states, see Table2.2 (b). The micro-cracked samples were obtained by performing uniaxial compression tests on "intact"

	.2: Summary of samples used for swelling tests
	(a) Group 1. Intact samples, dried at 75% RH
	Sample ID	Drilling orientation	Damage state	drying procedure
	EST 51133	Vertical	Intact	75% RH
	EST 57903	Horizontal	Intact	75% RH
	EST 58128	Horizontal	Intact	75% RH
	EST 58145	Horizontal	Intact	75% RH
	EST 62665	Horizontal	Intact	75% RH
	(b) Group 2. Two intact and two micro-cracked samples, initial saturation
	Sample origin Sample ID Damage state	saturation
		I-1	Intact	85.5%
	EST 58128	MC-1 I-2	Micro-cracked Intact	85.5% 85.5%
		MC-2	Micro-cracked	85.5%

Table 2

 2

.3. The XRD result shows that UT and UA samples have similar bulk mineral compositions but only differ in proportions.

Table 2 .

 2 3. Quantitative XRD and CEC analysis of the tested samples (in mass percentage)

	Sample	EST 51133-1

EST 51133-2 EST 57903-1 EST 57903-2 EST 58128-1 EST 58128-2 EST 58145-1 EST58145-2 EST62665-1 EST62665-2

  CEC results are presented in Table2.3. The value of UT material (i.e. EST 51133) is lower than 2 meq/100g, which is much smaller than that of UA materials (13.1 -21.3 meq/100g). Fig.2.5 (a)-(c)

	Geological sequence	UT	UT	UA	UA	UA	UA	UA	UA	UA	UA
	Carbonates	76	82.6	29.5	27.7	22.1	21.0	22.6	22.7	19.6	21.1
	Tectosilicates	17.1	13.5	28.6	26.8	26.9	26.9	29	28.6	25.3	26.9
	Secondary minerals (pyrite, anatase, etc.)	0.5	0.3	1.9	1.8	2.1	1.9	1.7	1.9	1.6	1.9
	Non-clay minerals	93.7	96.3	59.9	56.3	51.0	50.0	53.3	53.2	46.5	49.8
	Kaolinite	/	/	2.2	2.7	3.3	3.4	2.9	3.0	3.4	3.1
	Chlorite	0.1	0.1	1.1	1.4	1.5	1.7	1.7	1.7	1.7	1.6
	Illite & muscovite	2.8	1.6	4.7	12.9	13.1	14.3	18.8	20.2	12.7	13.4
	R1-I/S (70% illite /30% smectite)	1.7	1.2	23.5	20.6	22.6	23.2	24.2	23.4	28.3	25.5
	R0-I/S (22% illite /78% smectite)	1.8	0.7	8.5	6.1	8.5	7.4	6.2	6.0	7.3	6.5
	Total smectite	1.87	0.94	13.7	10.9	13.4	12.7	12.1	11.7	14.2	12.7
	Total clay minerals	6.4	3.6	40.1	43.7	49.0	50.0	46.8	46.7	53.5	50.2
	CEC (meq/100g)	1.9	1.4	14.6	13.1	17.6	16.8	15.2	14.2	21.3	20.8

Table 2 .

 2 4. Texutral properties of tested COx claystone derived from the N2 adsorption isotherms. 𝑉 𝐺𝑢𝑟 is the Gurvich specific pore volume, 𝑆𝑆𝐴 is the BET specific surface area, 𝑄 0 is the Dubinin-Astakhov limiting micropore volume, 𝐸 is the characteristic energy and 𝑛 the Dubinin-Astakhov exponent

	Core numbers	𝑉 𝐺𝑢𝑟 (cm 3 /g)	𝑆𝑆𝐴 (m 2 /g)	𝑄 0 (cm 3 /g)	𝐸 (kJ/mol)	𝑛
	EST 51133	0.013	4.12	0.001	15.4	1.6
	EST 57903	0.069	32.72	0.011	16.7	1.9
	EST 58128	0.076	37.51	0.012	17.2	1.7
	EST 58145	0.073	33.56	0.014	16.2	1.6
	EST 62665	0.079	37.98	0.012	17.1	1.6
	2.5.2.1	Gurvich specific pore volume vs. clay contents

Table 3 .

 3

		1. summary of the samples
	Sample	Depth (m)	Curing	Initial saturation
	EST 51446	-480	65°C	Close to 0
	EST 57903-1	-490	-	86.8%
	EST 57903-2	-490	-	86.8%
	EST 58128	-490	Pre-damaged (UCT)	85.5%

Table 3

 3

				.2. mineral composition of synthetic water
	Mineral	NaCl NaHCO3	KCl	CaSO4,2H2O MgSO4,7H2O CaCl2,2H2O Na2SO4	total
	Concentration (g/L)	1.95	0.130	0.035	0.630	1.020	0.080	0.700	4.545

Table 3 . 3

 33 𝜀 ∥ (𝜀 ⊥ ) is the average of two longitudinal (transverse) gauges for each sample

	Absolute Swelling	Swelling time
	(μm/m)	(days)

. Summary of initial pressure and swelling properties of tested samples Sample 𝑃 𝑐 (MPa) 𝑃 𝑖 (MPa) 𝑃 eff (MPa)

  𝜀 𝑖 (∆𝑃 𝑖 = ∆𝑃 𝑐 )/𝜀 𝑖 (∆𝑃 𝑐 ). FromTable 3.4 (a) and (b) it comes that this ratio is the same for both gauge directions (whatever the gauge direction n°𝑖). This completely confirm what was already observed with gas experiments i.e. b=b3 (isotropic Biot's tensor) despite the global material anisotropy. Once again it should be mentioned here that this does not mean that the strains due to change in pore pressure are the same (i.e. C-D≠C'-D'). This is a first important and interesting point. The second one is that 𝑏1≈𝑏3 ≈ 𝜀 𝑖 (∆𝑃 𝑖 = ∆𝑃 𝑐 )/𝜀 𝑖 (∆𝑃 𝑐 ) ≈1. This second and very important result evidences that, when fully water saturated (and under laboratory conditions), COx claystone behaves like a Terzaghi's material i.e. like a soil. Even if only 4 results are presented, this was observed on several other tests with UA claystone samples (clay-rich material). It is now clear that many previous studies indicated too low Biot's coefficient and, in our opinion, it is mainly due to insufficient waiting times between two loading paths (either in 𝑃 𝑐 or in 𝑃 𝑖 ).

			1650	1655	0.997	1630	1.015
	EST57903-1 EST57903-2	5 5	548 406	541 357	1.013 1.137	511 368	1.059 0.970	≈1
	EST58128	5	587	619	0.948	611	1.013
	In both Tables 3.4 (a) and (b), the ratio B-C/C-D (resp. B'-C'/C'-D') is very close to one despite
	(sometimes) small gauge uncertainties, also leading to 'b' slightly greater than one -obviously
	experimental artefacts. It is nevertheless very clear that these ratio indicate that the path from B to D
	via C (resp. B' to D' via C') is elastic, which is consistent. C-D/D-E (resp C'-D'/D'-E') is the ratio b =

Table 4 .

 4 2. Basic information of the tested COx claystone samples

	Sample label	Core number	Depth	Geological unit	Damage state	Saturation degree	Bulk density
	UT-C	EST 57257	-457 m	UT	Brazilian splitting	-	2.58 g/cm 3
	UA1-C	EST 57903	-490 m	UA	Brazilian splitting	86.8%	2.39 g/cm 3
	UA2-C	EST 58128	-490 m	UA	Brazilian splitting	85.5%	2.37 g/cm 3
	UA3-C1	EST 58145	-490 m	UA	Brazilian splitting	84.3%	2.37 g/cm 3
	UA3-C2	EST 58145	-490 m	UA	Brazilian splitting	84.3%	2.37 g/cm 3
	UA3-I	EST 58145	-490 m	UA	Intact	84.3%	2.37 g/cm 3
	4.1.2. Sample preparation
	4.1.2.1	Macro-cracking by Brazilian splitting test
	Brazilian splitting tests were used to obtain a diametrical crack, which aperture can not be fully
	controlled. Multiple cracks were generated sometimes. After retrieving the 37 mm/40 mm samples
	from the original core, the Brazilian splitting tests

Table 4 .

 4 3. Mineral composition of the synthetic water (provided byAndra)

	Mineral	NaCl NaHCO3	KCl	CaSO4 MgSO4 Na2SO4 CaCl2 Total
	Concentration (g/L)	1.95	0.13	0.035 0.63	1.02	0.08	0.7	4.545

Table 4 .

 4 4. Quantitative XRD and CEC analysis for different cores of the tested COx claystone (in mass percentage)

	Sample	EST 57257-1 EST 57257-2 EST 57903-1 EST 57903-2 EST 58128-1 EST 58128-2 EST 58145-1	EST58145-2
	Geological unit	UT	UT	UA	UA	UA	UA	UA	UA
	Carbonates	33.4	26.6	29.5	27.7	22.1	21.0	22.6	22.7
	Tectosilicates	33.7	32.2	28.6	26.8	26.9	26.9	29	28.6
	Secondary minerals	2.6	1.9	1.9	1.8	2.1	1.9	1.7	1.9
	Kaolinite	/	/	2.2	2.7	3.3	3.4	2.9	3.0
	Chlorite	0.9	1.2	1.1	1.4	1.5	1.7	1.7	1.7
	2:1 clay minerals	29.5	38.1	36.8	39.6	44.1	44.9	42.2	42.0
	of which Illite & muscovite	2.5	9.0	4.7	12.9	13.1	14.3	18.8	20.2
	of which R1 illite/smectite (70/30)	14.2	13.3	23.5	20.6	22.6	23.2	24.2	23.4
	of which R0 illite/smectite (22/78)	12.9	15.8	8.5	6.1	8.5	7.4	6.2	6.0
	Total smectite	14.3	16.3	13.7	10.9	13.4	12.7	12.1	11.7
	Total clay minerals	30.4	39.3	40.1	43.7	49.0	50.0	46.8	46.7
	CEC (meq/100g)	16.8	19.2	14.6	13.1	17.6	16.8	15.2	14.2

Table 4 .

 4 6. Summary of equivalent capillary and gas breakthrough pressure

	Sample label	sealed equivalent aperture (µm) Equivalent capillary pressure (MPa)	GBP (MPa)
	UT-C	2.11	0.06	0-0.2
	UA1-C	0.296	0.49	0.8-0.89
	UA2-C	0.253	0.58	1.3-1.46
	UA3-C1	0.235	0.62	1.00-1.23
	UA3-C2	0.163	0.893	1.0-1.2
	UA3-I	-	-	6.2-6.4
	4.3.4.2

  , including diffusion, viscocapillary flow, pore dilatancy flow, and gas fracturing. A series of experiments carried out in our laboratory (such as M'Jahad et al., 2017) had led us to think that capillary phenomena (i.e. a part of the porous network is emptied from its saturating water by gas pressure) are preponderant for saturated COx claystone. Based on previous studies, it is reasonable to assume that the gas migration mechanism in the resealed macro-cracked COx would be capillary gas transport through the sealed crack. In order to evaluate whether this assumption is plausible, calculation of the equivalent crack aperture 𝑒 𝑔𝑤 were performed with the final Kw (Figure4.13 and Table4.5). One can find that 𝑒 𝑔𝑤 (both UA and UT COx) decreased from tens of microns to below one micron after sealing. Thus it can be supposed that, during a GBP experiment, gas would use the easier path to cross the sample, i.e. the sealed crack. Assuming again that this crack is composed of two parallel planes with a width equal to 𝑒 𝑔𝑤 , Laplace Law is used to calculate the capillary pressure Pcap:

	𝑃 𝑐𝑎𝑝 =	2𝛾 𝑔𝑤 𝑒 𝑔𝑤	• cos 𝛼	(4.9)

également au volume des pores et à la surface accessibles à l'eau. Cette conclusion est valable de l'échelle nanométrique à l'échelle du mètre.Des déformations anisotropes ont été mesurées pendant l'essai de gonflement. En particulier, la dé formation de gonflement parallèle aux plans de litage (ε∥ S ) est utilisée pour être liée aux minéraux lié s à la smectite. Du point de vue de l'amplitude de gonflement, le résultat révèle que ε∥ S a la corrélation la plus élevée avec R1-I/S, alors qu'il a la corrélation la plus faible avec R0-I/S. Cela illustre que l'effet de la distribution de la smectite sur le gonflement du mat ériau est toujours valable à l'échelle centimétrique. Par conséquent, un modèle conceptuel est proposé pour donner un aperçu du mécanisme de gonflement multi-échelle de ce matériau. Quant à la cinétique de gonflement, aucune corrélation n'a été trouvée entre le temps d'expansion et la composition minérale ou les propriétés des pores, ce qui indique que la cinétique correspond à un processus de couplage plus complexe.En outre, l'effet des microfissures sur le gonflement a été étudié en comparant le gonflement d'échantillons intacts et microfissurés. Les résultats impliquent que les microfissures entraînent une plus grande amplitude de gonflement du matériau et une cinétique de gonflement initiale plus élevée.Et les microfissures induites par la compression sont plus susceptibles d'être parallèles aux plans de litage, ce qui entraîne une expansion plus prononcée dans cette direction.

Powder samples originated from the UT core (EST51133) consist of ca. 95% non-clay minerals (ca. 79% carbonates and ca. 15% quartz) and 5% clay minerals (mainly 2:1 clay minerals). For powder samples from UA cores, the non-clay minerals are composed of around 24% carbonates and around 28% quartz, while the clay mineral content is between 40% -50%. The subdivided clay mineral analysis indicates that two types of interstratified illite/smectite phases exist in both UT and UA COx, named R1-I/S and R0 -I/S respectively. The difference between the two I/S phases lies in the content and arrangement of illite and smectite [START_REF] Altaner | Interlayer order in illite/smectite[END_REF]. In terms of proportions, R1-I/S is composed of 70% illite and 30% smectite while R0-I/S has 22% illite and 78% smectite. From a structural viewpoint, in R1-I/S, every smectite particle is sandwiched between two illite particles (e.g. ISII.. or IISI..). In contrast, both smectite and illite particles are randomly distributed in R0-I/S (e.g. ISSI… or SSII…). From Table 2.3, the amounts of R1-I/S and R0-I/S are close to each other in UT COx, while the R1-I/S content is three to four times higher than that of R0-I/S in UA COx.

keep the core under certain stress (Conil et al., 2018). The dimensions of the original core are around 300 mm length and 75 mm diameter. From each original core, several cylindrical samples parallel to the bedding planes were retrieved to obtain representative samples that fit the experimental set-up.

After coring, and before swelling and sealing test, all samples were wrapped in plastic film, sealed in vacuum bags and then immersed in oil in order to minimize their desaturation. The re-cored samples were of a diameter of 37 mm and a length slightly greater than 40 mm. After placing the sample in the experimental device, its length was adjusted to 40mm by machining. The detailed preparation procedure of the sample is provided in the following subsection. 4.1 summarizes the information of all tested samples, including the sample label, geological unit, damaged state, and the initial physical properties. It is worth noticing that, as the COx claystone was subjected to decompression when extracted from T1 cells and slighlty de-saturated during coring, a small extent of cracks would have been generated in the samples (Duan et al., 2021). Nevertheless, these re-cored samples (without further processing or macro-cracking) are referred to "intact samples". analyzed and averaged. The detailed representative sample preparation and measurement procedures are exactly the same as illustrated in chapter 2.

Cation exchange capacity (CEC) is an inherent characteristic of a clayey material (such as soil and claystone), which refers to the ability of the solid to hold exchangeable cations in a saline aqueous solution. This property is mainly impacted by the content of clay minerals and organic matter (Mitchell and Soga, 2005)). Empirically, the CEC value of 2:1 type clay minerals (e.g. smectite) is approx. 80 -120 meq/100 g, which is higher than 1:1 type clay minerals (e.g. kaolinite), around 1 -10 meq/100 g. The CEC varies from 100 to 300 meq/100g for the organic matter [START_REF]CLAY AND CLAY MINERALOGY[END_REF]). In order to determine the most active mineral component of the COx claystone during hydration, CEC analysis was simultaneously performed for each sample subjected to QXRD.

The detailed representative sample preparation and measurement procedures are exactly the same as illustrated in chapter 2.

Nitrogen physisorption measurement

As mentioned before, nitrogen adsorption/desorption experiments are used to obtain pore information of the tested COx samples. The main goal is to acquire the nitrogen isotherms, by recording the adsorbed nitrogen quantity at different relative nitrogen pressures. These isotherms are summarized in Figure 4.4, the sample preparation and measure procedures are already illustrated in chapter 2. These isotherms data can be used and analyzed with different theories to derive a series of textural parameters such as the total pore volume (VGurvich) and the Specific Surface Area (SSA), which were selected for this study. VGurvich is the pore volume that is determined under the validity of Gurvich's rule [START_REF] Ongari | Accurate Characterization of the Pore Volume in Microporous Crystalline Materials[END_REF]): when p/p0 ⩾ 0.995, the adsorbed nitrogen has a molar density of the liquid state at the operational temperature, and have no interaction with the solid framework. The VGurvich is computed by:

Where 𝑛 𝑁 2 𝑎𝑑𝑠 is the adsorbed amount of nitrogen (g of nitrogen/g of COx), 𝜌 𝑁 2 𝑙𝑖𝑞 is the liquid nitrogen density, 0.808 g/cm 3 . Theoretically, VGurvich is an underestimated value of the total connected pore volume as nitrogen cannot fill the micropores with a diameter smaller than the N2 molecules.

Specific Surface

Apparent swelling pressure measurement

Before conducting the self-sealing experiment, the tube was calibrated. This is done with gas pressure into the tube (Pinternal) linked to the corresponding average strain of both gauges 𝜀 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 = (𝜀 1 + 𝜀 2 )/2. A linear relationship between Pinternal & strain is shown in Figure 4.5. To improve the accuracy, several internal pressure loading/unloading cycles were performed on each tube submitted to various confining pressure. A special test was performed for which the gas pressure was applied on the "epoxy resin + stainless steel tube". The strains obtained were close to those recorded when the gas pressure was directly applied in the steel tube. Thanks to the tube calibration, the direct measurement data (strains of the two gauges) are constantly converted into Papp. Papp is followed until its stabilization.

Mineralogical characterization

The bulk mineralogical compositions and the subdivided 2:1 clay minerals are summarized in Moreover, they also demonstrate that, among all clay minerals, the illite/smectite mixed layers R1 and R0 constitute the vast majority. Indeed, the illite/smectite mixed layers are divided into two types: the R1-I/S, with 70% illite and 30% smectite, and the R0-I/S, with a proportion of 22% illite and 78% smectite. In R1-I/S, smectite is arranged in regular alternance with illite. Among these, smectite is the only one reputed to be a swelling clay.

Cicatrisation et colmatage de l'argilite de Bure

Self-sealing and clogging of Bure claystone

In the context of geological storage of radioactive nuclear waste in France, claystone at the Bure basin (formation du Callovo-Oxfordien (COx)) is regarded as the ideal host rock. This material exhibits significant self-sealing capacity during resaturation. However, the contribution of clay mineral swelling to the material sealing efficiency is still not completely understood. In this thesis, six COx claystone cores from different geological locations were studied. The relationship between mineralogical compositions and pore properties was analyzed by quantitative X-ray diffraction (XRD), cations exchanged capacity (CEC) and nitrogen sorption measurement. Results demonstrated that the distribution and location of smectite particles affect the pore structure at m-scale and nano-scale, which is highly associated with the material swelling capacity.

Swelling tests on the centimetric samples directly measured swelling strains during resaturation, giving evidence for the macro scale expansion of COx is affected by the combined effect of multi-scale swelling mechanisms. Poro-mechanical studies were carried out on the saturated samples. It is found that even if the material is strongly transversely isotropic, the Biot's coefficient is consistently isotropic and almost equal to 1. By using a modified triaxial cell, the self-sealing of damaged COx claystone was studied under "low-confinement" conditions. Experimental data indicated that clay mineral swelling results in a significant decrease in water permeability. After sealing, the gas breakthrough pressure (GBP) of the resealed material is in the same order of magnitude as the equivalent capillary pressure of residual cracks, indicating that the gas migration in the sealed COx would mainly occur through the residual sealed-crack and is controlled by capillary phenomena.

Keywords: COx claystone, swelling, poro-mechanics, self-sealing