# Mobility of water and ions in partially water-saturated
compacted MX-80 bentonite in relation with swelling
pressure

S. Savoye, J. Wang, L. Desert, S. Lefevre, J.C. Robinet, P. Gouze

► To cite this version:

S. Savoye, J. Wang, L. Desert, S. Lefevre, J.C. Robinet, et al. Mobility of water and ions in partially water-saturated compacted MX-80 bentonite in relation with swelling pressure. Applied Geochemistry, 2024, 167, pp.105994. 10.1016/j.apgeochem.2024.105994. hal-04732346

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1 Mobility of water and ions in partially water-saturated compacted

2 MX-80 bentonite in relation with swelling pressure

3 **S. Savoye**†, *, **J. Wang**†, ‡, **L. Desert**§, †, ‖, **S. Lefevre**†, **J.C. Robinet**‖, **P. Gouze**‡,

4 †. Université Paris-Saclay, CEA, Service de Physico-Chimie, F-91191 Gif-sur-Yvette

5 ‡. Géosciences Montpellier, CNRS-INSU - Montpellier University, 34095, Montpellier Cedex 5, France

6 §. Université de Poitiers/CNRS, UMR 7285 IC2MP, Equipe HydrASA, 5 rue Albert Turpain, Bât. B8, TSA - 51106, 86073 Poitiers

7 cedex 9, France

8 ‖. R&D Division, Transfer Unit, Andra, 92298 Chatenay-Malabry, France

9

10 *Corresponding author

11 Keywords: compacted bentonite, diffusion, degree of water-saturation, swelling pressure,

12 microstructure

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14 Highlights:

15 - Diffusive rate of water tracer is similar in bentonite for water saturation from 1 to 0.7

16 - Strong reduction of diffusive rate of sodium by a factor of 73 in bentonite for water saturation from 1

17 to 0.7

18 - Strong reduction of adsorption of sodium by a factor of 16 in bentonite for water saturation from 1 to

19 0.7

20 - The tortuosity of iodide diffusive paths in bentonite increases by only 1.4 times for water saturation

21 from 1 to 0.7

22 - Diffusive behavior is linked to the bentonite saturation-dependent microstructure changes

23 - Mechanical data are in agreement with the diffusion findings

24
Many countries are planning to host long-lived high- and intermediate-level radioactive waste in disposal facilities sited in deep argillaceous formations. Bentonite, as a swelling material, is often chosen as engineered buffers due to its low permeability and high swelling capacity. However, its properties can be influenced by the hydraulic/gas conditions prevailing in-situ that are expected to change throughout the duration of the repository. The objective of this work is to estimate the effect of partially water-saturated conditions on the mobility of water and ions in compacted MX-80 bentonite in relation to the evolution of its swelling pressure. For that purpose, (i) diffusion of water and ions ($I^-$ and $Na^+$) and (ii) the swelling pressure of compacted bentonite samples partially water-saturated were studied by means of the osmotic technique that allows controlling the suction from 9 to 0 MPa.

Results showed that (i) water diffusivity remained unchanged independently of the degrees of saturation (70, 84 and 100%) and (ii) iodide diffusivity decreased by a factor of 12 (from 100 to 70%), while (iii) $Na^+$ diffusion was reduced by a factor of more than 70 (from 100 to 70%), associated to a drop of the distribution factor by a factor of 16. Comparison of these results with diffusion data already acquired in clayey materials whose porous structure evolves little with suction (i.e. compacted kaolinite and intact Collovo-oxfordian clay-rocks) underlined how the bentonite porous structure whose organization evolved with the degree of saturation is a key parameter. This statement is supported by mechanical tests, which indicated a distinct evolution of the swelling pressure curves depending on the degree of saturation. At 70% saturation, mechanical tests indicate (i) a preservation of the large inter-aggregate porosity where water can diffuse in both vapor and liquid phases, and (ii) a final swelling pressure 1.5 to 2 times lower than at full water saturation, meaning that a part of swelling clay particles was not accessible to water ingress and so to $^{22}$Na$^+$. Conversely, at 84% and 100% saturation, change in swelling pressure curves was explained by a collapse of bentonite inter-aggregate porosity, in favor of expanding the inter-particle and interlayer porosities where $^{22}$Na$^+$ diffusion is enhanced by surface diffusion phenomenon.

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# 1 Introduction

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Many countries are considering deep geological formations to host a disposal facility dedicated to high level and intermediate level long lived (IL-LL) (Andra, 2016; Nagra, 2022 among others). Such disposal facility concepts generally include swelling clayey materials, such as bentonite as engineered barriers in order to seal the individual waste cells, the access galleries and the shafts in order to prevent release of radionuclides towards the biosphere.

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Being mainly composed of montmorillonite, compacted bentonite is characterized by both nanoporous and mesoporous structure (Yong, 1999; Seiphoori et al., 2014, Keller et al., 2014) with three main types of porosity (inter-aggregate, inter-particle and interlayer porosities) as shown in Figure 1. Such a structure induces a very low water permeability, even at a relatively low compacted dry density. According to Villar (2005) permeability of MX-80 bentonite at a dry density of $1400 \text{ kg} \cdot \text{m}^{-3}$ is in the order of $4.5 \pm 1.5 \times 10^{-20} \text{ m}^2$. Diffusion is consequently the main mechanism for the transport of ions such as radionuclides (Molera et al., 2002, 2003; Kozaki et al., 2005; Van Loon et al., 2007; Melkior et al., 2009, Liu et al., 2022, etc.). Pore surfaces located both around and inside the montmorillonite platelets (Figure 1) are negatively charged thus repulsing anionic species and attracting cationic species. Consequently, as shown by several authors (e.g. Molera et al. 2003 and Van Loon et al., 2007), the diffusive flux of anions is reduced compared to that of neutral species such as tritiated water (HTO), while cations diffusion is enhanced compared to HTO, owing to the so-called surface diffusion phenomena (e.g. Molera et al., 2002 and Melkior et al., 2009). Moreover, the large swelling capacity of montmorillonite when in contact with water is a major factor controlling ions mobility in bentonites. Numerous works investigated the extent of bentonite swelling as a function of parameters such as chemical composition of pore-water, dry density, mineralogical composition of the bentonite, initial water content and temperature (e.g. van Olphen, 1963; Sridharan and Rao, 1973; Villar, 2005; Karland et al., 2007; Zhu et al., 2013; Gatabin et al., 2016; Bernachy-Barbe et al., 2020). In some of these studies, constant volume devices equipped with force sensors were used to characterize the swelling pressure of compacted bentonite. For instance, studies of Villar (2005) and Bernachy-Barbe et al. (2020) indicated that the evolution of the swelling pressure developed by compacted MX-80 bentonite as a function of its dry density could be described by an exponential function, when dry density values range between $1100$ and $1700 \text{ kg} \cdot \text{m}^{-3}$.

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In the French deep geological radioactive waste repository concept, the generation of hydrogen due to the anoxic corrosion of steel material (canisters, reinforced steel bars...) may dehydrate the clayey host rocks (in the near field) and the engineered barriers (including bentonite-based materials) for more than 100,000 years (Andra, 2016). Therefore, such partially water saturated conditions may change the containment properties of these clayey materials. Savoye et al. (2010, 2012a, 2017) studied
how the diffusive flux of water and ions through the Callovo-oxfordian (Cox) claystones (i.e. the selected host rock in the French concept) was impacted when partially water-saturated. In these studies, osmotic technique was used to set the partially water-saturated conditions to the clayrock samples from 81% to 100% of water saturation. In this case, a sharp and distinct decrease of the diffusive flux of water and ions from fully-saturated conditions to 81% water saturation was observed with contrasted behavior depending on the tracer charge. Water tracer showed the lowest decrease, by a factor of 7, while iodide and cesium showed the highest decreases, by factors of 50 and 60 respectively. More recently, the same type of investigation was performed in compacted kaolinite, known to be a very weakly surface-charged clay mineral (Wang et al., 2022). Results indicated that from 100% down to 67% of degree of water saturation, the decrease of diffusive flux of water in kaolinite was also smaller than that observed for anionic and cationic tracers (iodide and sodium). Based on previous results, a conceptual and numerical model was developed for describing the macroscopic diffusion of water tracers in both liquid and gas phases in order to reproduce the decrease by a factor of 7 from 100% down to 67% of the diffusive flux. The diffusion in both liquid and vapor phases explains why water tracer diffuse faster than the ions which only move in water.

Conversely, as far as we know, the diffusion of water and ions in partially water-saturated compacted bentonite was not experimentally measured so far. At the opposite to Cox claystones and compacted kaolinite, bentonite material is known to have a porous structure capable of evolving, as a result of swelling, as a function of the degree of water saturation (van Olphen, 1963; Sridharan and Rao, 1973; Villar, 2005; Seiphoori et al., 2014, Massat et al., 2016, Yigsaw et al., 2016), thus making much more complex the interpretation of diffusion data for partially water-saturated conditions. For instance, Massat et al. (2016) visualized through X-ray microtomography the microstructure evolution of compacted Kunipia bentonite compacted at a dry density of 1400 kg m⁻³, upon hydration from dry state to fully water-saturated conditions. The analyses of X-ray microtomography images showed the progressive reduction of inter-aggregate porosity from almost 40% to less than 1%, in parallel to the measured evolution of swelling pressure that increased until a plateau was reached. Dueck (2008) and more recently Yigsaw et al. (2016) directly measured the swelling pressure exerted by bentonite whose degree of water saturation was imposed either by saline solution technique or by osmotic technique. Yigsaw et al. (2016) showed a sharp drop of swelling pressure values by a factor of more than 2 from fully-saturated conditions to the most dehydrated samples submitted to a suction value of 8.5 MPa. The latter authors interpreted this pattern from micro-structural perspective where the applied suction would limit the interlayer porosity to be connected to external water and thus would reduce the swelling pressure exerted by bentonite. In contrast, when no suction was applied, bentonite upon hydration can fully swell, associated to a strong reorganization of pore-network, with a collapse of inter-aggregate porosity in favor of interlayer and inter-particle porosities. In terms of mobility of water and ions, the bentonite saturation-dependent microstructure should counterbalance the effect of
124 dehydration so that one can expect a decrease of diffusive rates in a lesser extent than in other clay-rich materials such as Cox and compacted kaolinite whose microstructure does not noticeably evolve with saturation. Indeed, a weaker increase of tortuous diffusive pathway is expected under partially 125 water saturated conditions related to the existence of more numerous and larger inter-aggregate pores 126 compared to fully saturation conditions where only smaller inter-particle and interlayer pores drive 127 diffusion mechanism. In addition to tortuosity issue, the adsorptive capacity of bentonite may be also 128 impacted, since the decrease of the swelling pressure for partially water-saturated bentonite compared 129 to the fully saturated one, should also correspond to a reduced cation accessibility to some of the clay 130 platelets that do not fully swell. This potential reduction of cation adsorption could also be associated 131 to a strong decrease of cation mobility, due to a decrease of the extent of the surface diffusion 132 phenomena. 133 134

135 The objective of the current paper is to study the effect of the partially water-saturated conditions on 136 the mobility of water, anion and cation in compacted MX-80 bentonite associated to the change of the 137 swelling pressure bentonite is able to exert. This approach allows studying the relation between 138 diffusion of solutes and evolution of microstructure induced by swelling and suction. For that purpose, 139 diffusion and swelling pressure data were monitored with experimental devices using osmotic 140 technique for controlling the degree of water saturation throughout the duration of the experiments. 141

## 2 Materials and methods
142

### 2.1 Materials and sample preparation
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The bentonite used in this study is a Wyoming bentonite MX-80 (commercial name Gelclay WH2, 144 from supplier Laviosa MPC). It contains around 92% of montmorillonite, and other minerals including 145 quartz and feldspars for the most abundant (Gatabin et al., 2016). The raw MX-80 is provided as 146 granular material, thus grinding and sieving steps are required to obtain the powder material required 147 for our study. The chosen particle size is inferior to 500 µm in order to achieve maximum 148 homogeneity. The bentonite sample, after grinding, is preserved in desiccators hosting saturated saline 149 solution of NaCl, which imposes a relative humidity of 75% at 25°C and sets the initial water content 150 in the non-compacted bentonite material at 18wt%. 151

The 10-mm thick bentonite samples were prepared and compacted directly into the cell body of either 151 the diffusion device or the swelling pressure device (described below) that both have a 36 mm inner 152 diameter. 153

The total porosity of the sample is evaluated from the dry densityρ<sub>dry</sub> according to the following 154 equation: 155

$$ \phi = 1 - \frac{\rho_{dry}}{\rho_s} \qquad \text{Eq(1)} $$
where $\rho_s$ denotes the grain density of MX-80 bentonite 2760 kg·m⁻³ (Tang et al., 2008). In our study, the bentonite sample compacted at a dry density of 1500 kg·m⁻³ leads to a total porosity of 46% (Table 1). The volumetric water content, $\theta$, is given by the following expression (Pearson et al., 2003) :

$$ \theta = \frac{\omega_{dry} \times \rho_{dry}}{\rho_w} \qquad \text{Eq(2)} $$

where $\omega_{dry}$ denotes the gravimetric water content per dry mass of the sample and $\rho_w$ is the density of the pore water. We assume here for simplification reasons a value for the density for pore water equal to 1000 kg·m⁻³, even though recent studies showed that density of water adsorbed on bentonites can be higher (Jacinto et al. 2012; Navarro et al., 2022; Wang, 2023). Finally, the saturation degree ($S_w$) is given by the ratio of volumetric water content $\theta$ to the total porosity $\phi$:

$$ S_w = \frac{\theta}{\phi} \qquad \text{Eq(3)} $$

## 2.2 Technique used for controlling water-saturated conditions

In order to impose partially water-saturated conditions, osmosis technique is used. This technique consists in generating an osmosis force by placing a semi-permeable membrane between the sample and a solution enriched in poly-ethylene-glycol (PEG). Note that in order to avoid any sample shrinkage, a hydration path of wetting type was chosen. For that purpose, the bentonite powder was initially stored at 75% relative humidity, corresponding to an applied suction of 41 MPa (i.e. higher than the suction values imposed by the osmotic technique).

The difference in PEG concentration between the sample pore-water and the bulk solution located in the external reservoirs triggers the osmosis force, counterbalancing the capillary force during the wetting path. As a result, the clayey samples remain partially water-saturated. The applied suction level depends on the concentration of PEG in solution, following the relation given by Delage et al. (1998):

$$ s = 11 \times c^2 \qquad \text{Eq(4)} $$

where $s$ is the suction in MPa and $c$ is the concentration of PEG in g of PEG per g of water ($g_{PEG}/g_w$). Note that, since the semi-permeable membrane is permeable to the salts dissolved in the water, the osmotic technique controls the suction. PEG solutions of molecular weight 6000 Da (1 Da = 1 g/mol) and the semipermeable membrane (Spectra por 3500 Da, Spectrum laboratories) were used in this study. Moreover, in order to facilitate the removal of the gas phase during the wetting path, compacted bentonite samples were firstly flushed with $N_2O$ so that air present in porosity was replaced by $N_2O$ gas whose Henry's constant is almost 40 times higher than that of air (Sander, 2015). Afterwards, bentonite samples were put in contact with solutions as described below in section 2.3. Four concentrations of PEG were chosen for the swelling tests: 0.95 $g_{PEG}/g_w$, 0.42 $g_{PEG}/g_w$, 0.096 $g_{PEG}/g_w$
and 0 gPEG/gw to obtain applied suction levels of 9 MPa, 1.9 Mpa, 1 MPa and 0 Mpa, while for the diffusion tests 3 concentrations were chosen: 0.95 gPEG/gw, 0.42 gPEG/gw, and 0 gPEG/gw (see Savoye et al., 2010 for details).

The determination of the saturation level of the bentonite samples as the function of the imposed suction was carried out on the bentonite samples used for preliminary swelling pressure tests. For that purpose, after the completion of the tests and the dismantlement of the cells, the samples were weighed before and after oven-heating at 105°C until mass stabilization. The mass loss during this heating process over the total dry mass gives the water content of the sample. The values of the degree of water saturation were respectively 0.70±0.045 (n=3), 0.84±0.03 (n=3), 0.91 (n=1) and 1.00±0.03 (n=2), for applied suction values of 9, 1.9, 1 and 0 MPa (no PEG), respectively with n the number of the dedicated test.

In parallel, an assessment of the osmotic method to impose correct water saturation to bentonite was performed by preparing two bentonite samples and submitting them to another saturation method, i.e. the saline solution method (see SI pour details). Comparison of saturation degree values given in Fig S1 of SI shows a very good agreement between the two approaches.

## 2.3 Experimental equipment and procedure

### 2.3.1 Through-diffusion

#### 2.3.1.1. *Description of the through-diffusion tests.*

A schematic view of the through-diffusion set-up is given in Figure 1. The setup consists of a stainless steel diffusion cell and two aqueous reservoirs (i.e. an upstream reservoir and a downstream reservoir). Bentonite powder was statically compacted, at a speed of 1.1 mm/min, to the desired dry density in the rigid steel ring of the diffusion cell by using a hydraulic press. Each cell was loaded with a compacted bentonite sample (diameter = 36 mm, thickness = 10 ± 0.2 mm), sandwiched between two semi-permeable membranes maintained by 2 O-rings, 2 stainless steel filters (thickness = 1.95 mm; porosity = 37%) and closed with 2 end-pieces. Each of the end-pieces of the diffusion cell was connected to a reservoir where the solutions are circulating using a peristaltic pump (Ismatec) (Figure 2). For all the concentrations of PEG, the same volume of water was used, i.e. 50 mL of water without considering PEG mass in the upstream reservoir, and from 5 to 50 mL of water without considering PEG mass in the downstream reservoir, depending on the tracer type. Moreover, in order to mimic the chemical composition of Cox pore-water and limit as much as possible any chemical disturbance, a synthetic solution was used with $[Na^+] = 50$ mM, $[Ca^{2+}] = 0.7$ mM, $[HCO_3^-] = 0.7$ mM and $[Cl^-] = 50$ mM in addition to the PEG contents. AgCl at $10^{-6}$ M was also added serving as bactericidal agent. Before the diffusion tests, the bentonite samples in contact with the two reservoirs filled with the PEG solution were maintained at rest for 4 weeks at ambient temperature (21±1°C) in order to reach
chemical equilibrium and the target values of water saturation degree (see Savoye et al., 2010, 2012 and 2017). Then, the solution in the upstream reservoir was spiked with the desired tracer, first HDO, followed by ¹²⁵I⁻ (labeled CERCA ELSB50-82,731/1) and then ²²Na⁺ (labeled CERCA ELSB45-80,693/1) in order to successively determine diffusion parameters for water and simple anion and cation tracers. The initial activities injected in upstream solution for ¹²⁵I⁻ and ²²Na⁺ were resp 6 kBq/g, 0.3 kBq/g (without considering PEG mass). In the case of ¹²⁵I⁻, in addition to radioactive tracer ¹²⁵I⁻, stable iodide was added to reach a concentration of 10⁻³ M in the upstream reservoir to avoid any uptake of iodine, as previously observed by Bazer-Bachi et al. (2006) for lower concentrations (<10⁻⁴ M). Moreover, thiosulfate at a concentration of 5 x 10⁻⁴ M was also added in both reservoirs to ensure that iodide remains in the same redox state (Descostes et al., 2008). Both reservoirs were periodically sampled. Solutions in the downstream reservoirs were regularly replaced in order to keep the concentration of the tracer in this compartment as low as possible, i.e. < 5% of the concentration in the downstream reservoir. The activity or concentration of tracers collected in both reservoirs was measured using techniques depending on the type of tracer. The concentration of HDO in solution was measured by a liquid water isotope analyzer (LWIA DLT-100 from Los Gatos Research) based on infrared spectroscopy, while activity for ¹²⁵I⁻ and ²²Na⁺ was measured using a gamma counter (Packard 1480, WIZARD).

### 2.3.1.2. Treatment of experimental diffusion results.

At sample scale, the through-diffusion is assumed to be one-dimensional for all tracers. The analysis of through-diffusion experiments is based on the Fick's second law that can be written as:

$$ \frac{\partial C}{\partial t} = \frac{D_e}{\alpha} \frac{\partial^2 C}{\partial x^2} \qquad \text{Eq(5)} $$

where C denotes the concentration or activity per volume unit in the solute phase (mol·m⁻³ or Bq·m⁻³ of synthetic pore water without PEG), t denotes the time (s), Dₑ is the effective coefficient diffusion (m²·s⁻¹) and α is the rock capacity factor:

$$ \alpha = \theta_{diff}^t + \rho_d R_d \qquad \text{Eq(6)} $$

where θ<sub>diff</sub><sup>t</sup> is the volumetric water content accessible to the diffusing tracer (-), ρ<sub>d</sub> is the bulk dry density (kg·m⁻³) and R<sub>d</sub> is the distribution factor (m³·kg⁻³). The capacity factor α can be written as Rθ<sub>diff</sub><sup>t</sup>, with R the retardation factor:

$$ R = 1 + \frac{\rho_d R_d}{\theta_{diff}^t} \qquad \text{Eq(7)} $$

According to van Brakel and Heertjes (1974) and Grathwohl (1998), D<sub>e</sub> can be rewritten as follows:
$$D_e = D_p \theta_{diff}^t = \frac{\delta}{\tau^2} D_0 \theta_{diff}^t = \frac{1}{G} D_0 \theta_{diff}^t \qquad \text{Eq(8)}$$

where $D_p$ is the pore diffusion coefficient (m²·s⁻¹), $D_0$ is the self-diffusion coefficient in water (m²·s⁻¹), $G=\tau^2/\delta$ is the geometry factor (-), with $\delta$ the constrictivity factor (-) and $\tau$ the tortuosity factor.

The boundary and initial conditions for the through diffusion problem when the concentration or activity in the upstream reservoir is left free to decrease, are given by:

$$C(x, t) = 0, t = 0 \qquad \text{Eq(9)}$$

$$C(x, t) = C_0, x = 0, t = 0 \qquad \text{Eq(10)}$$

$$C(x, t) = 0, x = L + 2l, t > 0 \qquad \text{Eq(11)}$$

where $L$ is the sample thickness (m), $l$ is the filter-plate thickness (m), and $C_0$ is the concentration of the tracer in the upstream reservoir (Bq·m⁻³). Note that the value of the filter-plate geometry factor $G$ was independently determined by means of through-diffusion tests using solely the filter-plates, with solutions containing either 0, 0.42 or 0.95 gPEG/gw (see supplementary information for details). $G$ values for the filter-plates were equal to 3.7, 8.71 and 14.8 with solutions containing 0, 0.42 and 0.95 gPEG/gw, respectively.

The analytical solutions for the through-diffusion in the sample and for the reservoir-depletion are obtained in the Laplace space, then numerically inverted to provide the solution in time (Moridis, 1998; Savoye et al., 2012b).

Three diffusion cells at respectively 9 MPa, 1.9 MPa and 0 MPa of suction levels were set up and run simultaneously (see Table1 for an overview). For each of the diffusion cells, the diffusion tests with HDO, ¹²⁵I⁻ and ²²Na⁺ were performed successively. Between the diffusion test for ¹²⁵I⁻ and ²²Na⁺, an out-diffusion step was required to let radiotracers diffuse out of the diffusion cell until no radiotracers were significantly measured in upstream and downstream reservoirs.

### 2.3.2 Swelling pressure tests

The experimental set-up was inspired by the one developed by Yigzaw et al. (2016) (Figure 3) and is similar to the one used for the diffusion tests including a peristaltic pump allowing the circulation of solution (including PEG) at each side of the sample. Semi-permeable membranes are also placed between the stainless steel filter plates and the bentonite sample, the sealing being ensured by O-ring. A force sensor installed inside the top part, in contact with the top surface of the bentonite sample allowed measuring the swelling pressure, after converting force to pressure. Note that, as already mentioned by Yigsaw et al. (2016), the risk of damaging the semi-permeable membranes is very low because of the high rigidity of the porous material and its smooth texture that allow measuring high swelling pressure under constant-volume condition.
281 Bentonite powder was compacted at a speed of 1.1 mm/min at 1500 kg·m⁻³ (dry density) in the cell of diameter 36 mm with a height 10 ± 0.2 mm. A constant temperature was maintained at 21 ± 0.5°C by installing the whole device in a thermostatically-controlled chamber.

284 Two types of swelling tests were performed: one test with a successive decrease of applied suction levels (from 9 MPa to 1.9 MPa, 1 MPa and 0 Mpa), and a set of three tests in parallel, at three levels of applied suction respectively 9 MPa, 1.9 MPa and 0 MPa. Note that a bactericidal agent (AgCl at 10⁻⁶ M) was also added to solutions.

288 Table 1 summarizes the diffusion and mechanical tests performed, including information on the initial conditions of bentonite samples and the chemical composition of external solution.

290

## 3 Results and discussion

292 3.1 Diffusion behaviors of water (HDO), iodide (I⁻) and sodium (Na⁺) in MX-80 bentonite

293

294 The normalized fluxes (in m·s⁻¹) as function of water saturation are given in Figure 4 (4a for HDO, 4b for ¹²⁵I⁻ and 4c for ²²Na⁺). Normalized fluxes were calculated for each tracer using the ratio of instantaneous flux in Bq·m⁻²·s⁻¹ (or mol·m⁻²·s⁻¹ for HDO) to the concentration in the upstream reservoir in Bq·m⁻³ or mol·m⁻³. The corresponding diffusion parameters (Dₑ, α or θ<sub>diff</sub><sup>125I⁻</sup> and Rₐ) for water, anion, and cation tracers determined at three levels of suctions (9 MPa, 1.9 MPa and 0 MPa) are listed in Table 2.

300 3.1.1. Diffusion data at full saturation

301 Values for the effective diffusion coefficient at full water saturation, for HDO and ²²Na⁺ are consistent with those obtained by Melkior et al. (2009) in similar raw MX-80 bentonite samples, but compacted at a slightly higher dry density of 1600 kg·m⁻³. Indeed, in the current study the values for Dₑ range from 4.2 × 10⁻¹¹ to 5.5 × 10⁻¹¹ m²·s⁻¹ and to 2.8 × 10⁻¹⁰ to 5 × 10⁻¹⁰ m²·s⁻¹ for HDO and ²²Na⁺ respectively, while Melkior et al. (2009) estimated values for Dₑ to be equal to 5.8 × 10⁻¹¹ and 1.8 × 10⁻¹⁰ m²·s⁻¹ for HTO and ²²Na⁺ respectively. Discrepancy between ²²Na⁺ diffusive behaviors results can originate from the fact that Melkior et al. (2009) used a synthetic solution with a higher concentration of NaCl at 100 mM while a concentration of 50 mM was used in the current study, thus reducing the contribution of surface diffusion. The diffusive parameters for ¹²⁵I⁻ are in very good agreement with those determined for ³⁶Cl⁻ by Van Loon et al. (2007) on a Volclay KWK bentonite whose chemical composition is very close to MX-80 bentonite, and compacted at a slightly higher dry density of 1600 kg·m⁻³. Indeed, the values for Dₑ and θ<sub>diff</sub><sup>125I⁻</sup> in the current study are equal to 1.55±0.15 × 10⁻¹² m²·s⁻¹ and 0.026±0.003 respectively, while Van Loon et al. (2007) estimated values to be equal to 1.1±0.1 × 10⁻¹² m²·s⁻¹ and 0.016±0.002, respectively with NaCl concentration equal to 50 mM.
To go further in the interpretation of the data and compare the diffusive behavior of tracers with each other, the effective diffusion coefficient, $D_e$, of each tracer was normalized by the diffusion coefficient of the species in bulk water, $D_0$, corresponding to the diffusivity parameter (Figure 5a); HDO, $^{22}$Na$^+$ and $^{125}$I$^-$ displayed noticeably different values of $D_e/D_0$. As already mentioned by Melkior et al. (2009), the diffusion of $^{22}$Na$^+$ is enhanced compared to water tracer due to surface diffusion, while diffusion of $^{125}$I$^-$ is reduced compared to water tracer due to the effect of anion exclusion, as previously shown by numerous authors in bentonite (e.g. Eriksen et al., 1996; Molera et al., 2002; Van Loon et al., 2007; Ishidera et al., 2008) and in pure compacted montmorillonite (Kozaki et al., 2001; Glaus et al., 2010; Tachi et al., 2014).

The diffusivity values determined for the water and ion tracers in bentonite MX-80 were also compared with those obtained in the same range of applied suctions (0 to 9 MPa) in compacted kaolinite at a dry density of 1950 kg cm$^{-3}$ (Wang et al., 2022) and in Callovo-oxfordian argillite (Cox) (Savoye et al., 2010, 2017). Results are summarized in Figure 5b for HDO, Figure 5c for $^{125}$I$^-$ and Figure 6a for $^{22}$Na$^+$. At full-saturation, water tracer diffusivity value in bentonite is intermediate between values reported for kaolinite and Cox argillite (Figure 5b). The swelling developed by bentonite from 41 MPa to 0 MPa of suction, and the associated impact on pore structure would be responsible for the low $D_e$ value compared to kaolinite (see Tertre et al., 2018), whereas the largest tortuosity and smallest porosity in the Cox lead to lowest diffusivity values for HTO in Cox argillite. The solute diffusive behavior is mainly controlled by the presence of surface charges in the montmorillonite for the compacted bentonite. This explains (i) the very low diffusivity for iodide, similar to that in the Cox (Figure 5c), owing to the strong effect of anion exclusion and (ii) the very high diffusivity and distribution ratio values for sodium (Figure 6a and 6b), due to the surface diffusion process.

### 3.1.2. Effect of partially water-saturated conditions on the diffusion process.

As shown in Figure 5a, different evolution of the diffusivity ($D_e/D_0$) as a function of the degree of water saturation was observed depending on the tracer type. Water tracer shows no significant change of its diffusivity from full-saturation to 70% of water saturation, whereas a drop of diffusivity by a factor of 73 is observed for $^{22}$Na$^+$ from 100% to 70% saturation. This diffusivity decrease is associated with a decrease of $R_d$ values by a factor of 16. Note that $R_d$ values were calculated, assuming that the volumetric water content accessible to sodium-22 was equal to the volumetric water content determined from Eq(2). The behavior of $^{125}$I$^-$ is intermediate between those of water and sodium tracers, with a decrease of its diffusivity by a factor of 12, associated to a decrease of $\theta_{diff}^{125I^-}$, the volumetric water content accessible to $^{125}$I$^-$, by a factor of 5.5 from 100% to 70% of water saturation.

### 3.1.2.1. The case of water tracers (HTO and HDO).
Figure 5b shows that the diffusivity for kaolinite and Cox argillite decreases by a factor of 7 from 0 to 9 MPa, (corresponding to water saturation of
67% and 81% for kaolinite and for Cox argillite, respectively), whereas diffusivity for HDO in the bentonite remained unchanged from 100% to 70% of water saturation. However, contrary to compacted bentonite, Cox and compacted kaolinite are two materials that display negligible swelling and pore structure changes as a function of water saturation.

Wang et al. (2022) showed that HTO/HDO diffusion in partially water-saturated kaolinite was facilitated compared to ions, since HTO/HDO can diffuse in both the liquid and vapor phases. Keeping this process in mind, it can be postulated that the constant HDO diffusivity for water saturation ranging from 70% to 100% would result from a saturation-dependence of the bentonite microstructure.

Indeed, as already mentioned in introduction, previous works (Keller et al., 2014; Seiphoori et al., 2014; Massat et al., 2016) indicated that during a wetting path (increasing water saturation) the fraction of inter-aggregate pores in bentonite decreased while the fraction of inter-particle and interlayer pores increased. Thus, the larger amount of inter-aggregate porosity occurring in partially saturated bentonite compared to fully saturated bentonite would enhance the diffusion of HTO/HDO especially in vapor phase, since inter-aggregate porosity is the porosity firstly impacted by suction, owing to its larger size. Moreover, according to Asaad et al (2022) who investigated diffusion at saturation in vermiculite (a swelling clay), HTO/HDO diffusion in interlayer porosity is much lower than in inter-particle porosity and so inter-aggregate porosity. This means that even interlayer porosity is fully water-saturated even at 70% water saturation, the contribution of HDO diffusive rate in the interlayer porosity would remain much lower than that in large inter-aggregate porosity where HDO can diffuse in both liquid and vapor phases.

### 3.1.2.2. The case of anion tracer.
The comparison in Figure 5a of ¹²⁵I⁻ diffusivity between bentonite, kaolinite and Cox indicates a smaller diffusivity decrease with decreasing saturation in bentonite (by a factor of 12) than in kaolinite (by a factor of 19) and in the Cox (by a factor of 50). It is noteworthy that at full saturation, the diffusivity value in bentonite is very close to the one determined in the Cox. However, a stronger diffusivity decrease in bentonite could have been expected than in kaolinite, which is a weakly charged clay, since (i) the diffusion of anion species is limited to the largest pores where anion exclusion is less pronounced and (ii) these largest pores are submitted to the partially saturated conditions for suction levels lower than for the smallest pores. Therefore, like for water tracer, one can postulate that the occurrence of the larger amount of inter-aggregate pores in partially saturated bentonite than at full saturation would counterbalance the effect of unsaturated conditions on diffusion. In order to discuss this assumption, values of the reciprocal of the geometry factor calculated from Eq(8) was reported in Figure 5d as a function of the volumetric water content accessible to anion, θ<sub>diff</sub><sup>125I</sup>-, for the three materials. Figure 5d shows that, for decreasingly values of degree of water saturation, the decrease in the reciprocal of the geometry factor is less and less marked from the case of kaolinite through Cox to bentonite. This trend reflects the fact that tortuosity
increases less and less for decreasing values of water saturation, by a factor of 3.5 for kaolinite, 2.2 for Cox and only 1.4 for bentonite. This very low tortuosity increase for bentonite can be clearly related to the larger amount of inter-aggregate pores in partially saturated bentonite than at full saturation that would lead to a solely slight increase of tortuous diffusive paths for iodide, despite the dehydration effect. Moreover, Figure 5d also shows the strong decrease of the volumetric water content accessible to iodide, $θ_{diff}^{125I-}$, for decreasingly values of degree of water saturation for Cox and bentonite, by factors of 11 and 5.5 resp from 0 to 9 MPa of suction. Such a reduction cannot be explained solely by a decrease in the degree of water saturation, as in the case of kaolinite. This could be explained by the presence of volumes isolated from the iodide diffusive paths, owing to the effect of anion exclusion, as already shown by Savoye et al. (2010) for Cox.

### 3.1.2.3. The case of cation tracer.
The effect of water saturation on $^{22}$Na$^+$ diffusivity is larger in bentonite with a decrease by a factor of 73 than in kaolinite and in the Cox argillite with a decrease by factors of 32 and 12, respectively (Figure 6a). Figure 6b shows the evolution as a function of the degree of water saturation, of the distribution ratio, $R_d$, determined from diffusion tests performed in bentonite, kaolinite and Cox argillite samples. At full saturation, $R_d$ values in the Cox argillite ($R_d$ = 0.79 mL/g) and in kaolinite ($R_d$ = 0.38 mL/g) are more than one order of magnitude lower than in bentonite ($R_d$ = 11.44 mL/g), consistent with the lesser effect of surface diffusion of $^{22}$Na$^+$ in the Cox argillite and its absence in the case of the kaolinite. Indeed, the extent of surface diffusion can be estimated using the ratio of $^{22}$Na diffusivity to water tracer (HDO) diffusivity. The values of the ratio determined at full saturation are equal to 15, 3.5 and 1.3 for bentonite, Cox and kaolinite, respectively, denoting both the strong enhancement of $^{22}$Na$^+$ diffusion with respect to HDO diffusion for bentonite and the negligible enhancement of $^{22}$Na$^+$ diffusion for kaolinite. Moreover, the two graphs of Figure 6 show a similar evolution of diffusivity and $R_d$ values for bentonite, with a small decrease from 100% to 84% (by a factor of 1.3 and 1.5 for $D_e/D_0$ and $R_d$, respectively), and a sharp decrease at 70% of water saturation. This behavior indicates how the enhanced diffusion of cation is linked to the extent of its adsorption on the clay surfaces. The diffusion of $^{22}$Na$^+$ in bentonite at 70% of saturation would mainly occur in the dominant fraction of the inter-aggregate porosity, where the extent of surface diffusion is much less strong than in inter-particle and interlayer porosities. Therefore, the diffusivity drop at 70% of degree of water saturation can be attributed to a reduced access of $^{22}$Na$^+$ to the electrical double layers located mainly in inter-particle and interlayer porosities; most of the adsorption area would be thus isolated from the $^{22}$Na$^+$ flux. These isolated volumes would correspond to volumes of montmorillonite that would not totally swell because they would not be connected to external solutions. Yet, one has to keep in mind that the extent of the adsorptive volume relative to the swelling level for partially-water saturation conditions is not known so far.
425 3.2 Swelling pressure tests under partially-saturated conditions

426 3.2.1. Data obtained in bentonite at three levels of applied suction

427 Figure 7a shows swelling pressure data obtained in three cells at three levels of applied suction, i.e.
428 9 MPa, 1.9 MPa and 0 MPa. The swelling pressure after 4 days is 3.5 MPa at full saturation and
429 around 2.5 MPa for the two partially saturated conditions.

430 For the fully saturated case, a common pattern of swelling pressure development was observed. At the
431 beginning of hydration, the swelling pressure increases, then remains stable or slightly decreases,
432 before a second increase period where swelling pressure reaches an equilibrium value of 3.5 MPa for
433 the fully saturated state. This two-step pattern was already observed by several authors (e.g. Imbert
434 and Villar, 2006; Karland et al., 2007; Zhu et al. 2013, Yigsaw et al., 2016). This two-step pattern was
435 interpreted by the evolution during hydration of the relative contribution between microstructural
436 expansion, related to the interlayer and inter-particle pores, and the collapse of the larger macro-pores
437 (i.e. inter-aggregate pores), owing to the reorganization of the macrostructure. In the very beginning of
438 the test, water ingress induces a progressive swelling of montmorillonite platelets and thus of the
439 compacted bentonite (microstructural expansion), until reaching a threshold above which the bentonite
440 “skeleton” would no longer be able to accommodate the extra pressure without reorganizing. This
441 second regime corresponds to the collapse of most inter-aggregate pores. Afterwards, the continuing
442 ingression of water corresponds to the last period where swelling phenomena are predominant with
443 increasing pressure, reaching a plateau.

444 In the following, using osmotic technique to control suction allows for the investigation of how the
445 hydration process takes place during a wetting path. In this case, water ingress will stop when suction
446 will be equilibrated with the imposed suction (linked to the PEG content in external solution). The
447 osmotic technique acts as stopping the wetting path before reaching full saturation. Regarding this
448 point, the very beginning of the three swelling pressure curves obtained at 0, 1.9 and 9 MPa
449 superimposes, suggesting that during this early period the suction imposed by the osmotic technique
450 does not play a major role. Afterwards, note a distinct pattern for the three swelling pressure curves
451 (Figure 7a). At 1.9 MPa of suction, a two-step pattern was observed, similar to the fully saturated case.
452 The fact that the swelling pressure value observed in the first plateau (~ 2 MPa) is similar to that at full
453 saturation suggests that a sufficient amount of water would have penetrated the clayey material, so that
454 the collapse of larger pores could occur, like at 0 MPa of suction. Conversely, the discrepancy between
455 1.9 and 0 MPa of suction during the transient period and during the final swelling pressure step after 4
456 days (2.5 MPa versus 3.5 MPa) suggests that not enough water would have been allowed to ingress
457 bentonite for inducing the fast and significant swelling pressure evolution observed at 0 MPa of
458 suction. Lastly, the two-step pattern is not observed for the test performed at 9 MPa of suction, even
459 though the final swelling pressure is similar to the one reached at 1.9 MPa of suction. This suggests
that at 9 MPa, the osmotic technique would have limited the water ingress so that the threshold above which collapse of inter-aggregate pores can occur would not have been reached yet. This means that the similar final swelling pressure values observed at 9 and 1.9 MPa of suction could be a coincidence: at 9 MPa, microstructural expansion would mainly play a role, while at 1.9 MPa, both microstructural expansion and collapse of the inter-aggregate porosity would be responsible of the resulting swelling pressure.

### 3.2.2. Data obtained with successive changes of the applied suction

A swelling pressure test was performed with a successive change of applied suction, in order to investigate the swelling process when suction decreases. When the applied suction was changed from 9 MPa to 1.9 MPa, no evolution of swelling pressure was observed (Figure 7b). This is in good agreement with the previous tests performed in parallel where the final swelling pressure values after 4 days were similar at 1.9 and 9 MPa of suction (Figure 7a). Only does the application of 1 MPa of suction induce an increase in the swelling pressure level, since this lower applied suction allows for the ingress of more amount of water. Firstly, a peak was observed at $t = 20$ days, then after a short stage of equilibrium, the swelling pressure began to increase and a sudden increase of swelling pressure was observed at $t = 40$ days. Such a complex pattern of the swelling pressure evolution would reflect the re-organization of the material whose the occurrence and the intensity depend on some mechanical thresholds, as mentioned in section 3.2.1. Afterwards, another sudden increase of the swelling pressure was observed when the applied suction becomes equal to 0 MPa. As proposed by Karnland et al. (2007), the sudden increases of swelling pressure may be induced by the instantaneous osmosis effect. A new amount of water penetrates into the porous structure, inducing further swelling of bentonite.

Yigsaw et al. (2016) already performed the same type of test on MX-80 bentonite compacted at $1400 \text{ kg m}^{-3}$ with a successive change of applied suction levels, 8.5, 3.5, 1.0, 0.5 and 0 MPa. These authors also observed that a suction level lower or equal to 1 MPa was necessary to let the bentonite sample swell more. They observed a high peak value (1.8 MPa of swelling pressure) at 8.5 MPa of suction, followed by a progressive decrease of swelling pressure down to 1.04 MPa. Such a pattern was less marked in the present study, with a peak value at 2 MPa, followed by a fast decrease down to 1.8 MPa (Figure 6b). The difference can be explained by the difference in the initial water content of the bentonite samples. Indeed, Yigsaw et al. (2016) used a lower initial water content of 12.5wt%, while a value of 18.3wt% was used in the current study (see also Table 1). The lower initial water content allows a larger amount of water to penetrate the bentonite, and so to lead to a stronger microstructural expansion. The effect of the initial water content can be also observed when comparing the swelling pressure tests performed either in parallel (Fig. 7a) or in series (Fig. 7b). The compacted bentonite sample used for the test with a successive change of applied suction displayed a
quite high water content of 18.3wt% (Table 1), leading to a value of stabilized swelling pressure at 9
and 1.9 MPa of 1.8 MPa. Conversely, the two compacted bentonite samples used for the tests in
parallel have a lower water content of 16.8wt% and 17.25wt% at 9 and 1.9 MPa of suction,
respectively. In these cases, swelling pressure values after 4 days are higher, at about 2.5 MPa. Note
that several authors drew an opposite conclusion for bentonite at full-saturation, showing
experimentally that the swelling pressure is not affected by the initial water content (Villar et Lloret,
2008; Tanaka et Watanabe, 2019). Such a difference depending on the hydration conditions suggests
that by preventing the bentonite from achieving fully saturated conditions, the suction imposed by
osmotic technique would “freeze” the bentonite material under a microstructural organization
depending on initial water content, contrary to what occurs at full-saturation.

3.3 Discussion on the results of diffusion in light of the swelling pressure data and their
relationship with bentonite porous structure

Diffusion of water is mainly controlled by the pore geometry of the clayey porous media, while
diffusion of solutes is in addition governed by negative surface charges of these media. The three
porous media considered here, are displaying an increasing complexity, from kaolinite, Cox argillite to
bentonite.

In the case of kaolinite, its surface charge is too low to be able to influence the diffusion of ions,
leading to a similar diffusive behavior for water, iodide and sodium at full saturation (Wang et al.,
2022). Under partially water-saturated conditions, kaolinite microstructure did not significantly
evolve. Only did the distribution of remaining water in pores, depending on their sizes and their
connection between each other play a role in the diffusion of water and solutes. Since water can
diffuse in both vapor and liquid phases, its diffusive rate was found higher than iodide and sodium that
behaved in the same manner (Wang et al., 2022).

In Cox argillite, the surface charge is high enough to impact diffusion of ions, with a lower diffusive
rate for iodide than that of water, due to anion exclusion from clay surfaces and a higher diffusive rate
for sodium than that of water, due to surface diffusion process (Savoye et al., 2010, 2017). When
dehydrating Cox argillite, microstructure was also not significantly different from that at full
saturation. Therefore, the way the remaining water is distributed in the different types of pores that are
more or less under the influence of negative surface charges depending on their size, will directly
control the diffusive behavior of ions. In this case, iodide diffusivity was more impacted by the
decrease of the degree of water saturation than sodium one, since most of the pores emptied by suction
were the larger pores, which were at full saturation the pores mainly accessible to iodide due to anion
exclusion from the smallest pores. On the other hand, water was the tracer least impacted by
saturation, since it can diffuse in both vapor and liquid phases (Savoye et al., 2010, 2017).
Finally, bentonite is far the most complex clayey porous medium considered here, with a high surface charge and capability of changing its microstructure (i.e. pore size distribution and its connectivity) as a function of its water saturation due to swelling. In order to illustrate this point, a schematic view of bentonite structure is reported in Figure 8, depending on the applied suction level, from 9MPa to 0 MPa of suction, given the considering wetting path.

At a suction of 9 MPa, the absence of the two-step pattern of the swelling pressure curve observed in Figure 7a would suggest that no strong reorganization of the pore structure would have occurred yet during the first part of the wetting path. This would mean a preservation of most of the inter-aggregate porosity at the expense of increasing the volume of interlayer porosity (Figure 8a). This could account for (i) the drop of the diffusive parameters for sodium (diffusivity and distribution factor) compared to fully saturated conditions, because $ ^{22}Na^+ $ would have a limited access to interlayer and inter-particle pores. This could also explain the slight decrease of diffusivity for iodide compared to the case at 1.9 MPa, associated to a very small increase of tortuosity (Figure 5d). In this case, most of iodide would diffuse in inter-aggregate pores, more numerous than at lower suction but more dehydrated.

Contrary to the 9 MPa case, at a suction of 1.9 MPa, the two-step pattern of the swelling pressure curve revealed by the mechanical test (§ 3.2.1.) indicates a possible collapse of the inter-aggregate porosity. This would suggest a type of pore size distribution close to that at 0 MPa of suction, even though the bentonite does not fully swell (Figure 8b). This can explain the very close diffusive parameter values obtained at 0 and 1.9 MPa for sodium, and in a less extent for iodide which is more impacted by dehydration of larger pores.

At full saturation, corresponding to the end of the wetting path, the two-step pattern of the swelling pressure curve would be clearly related to a collapse of bentonite microstructure (§ 3.2.1.), with a decrease of the proportion of the larger pores, i.e. the inter-aggregate porosity, in favor of increasing the volume occupied by the interlayer pores (Figure 7b). This is in agreement with observations obtained by several authors such as Keller et al. (2014) on MX-80 bentonite. These authors showed by FIB-SEM characterization a quasi-disappearance of the inter-aggregate porosity during swelling with an inter-aggregate porosity close to 0.1% for a sample at a dry density of 1700 kg m$^{-3}$ when almost full water saturation was achieved. Then, the large proportion of interlayer porosity would enhance sodium diffusion by surface diffusion phenomenon and strongly limit the iodide diffusion due to anion exclusion, explaining a diffusive rate for sodium 9 and 280 times higher than those of water and iodide, respectively (Table 2).

Lastly, regarding the water tracer diffusivity values, their similarities independently of the degree of saturation could be also attributed to the evolution of pore size distribution from 9 to 0 MPa of suction. At 9 MPa of suction, i.e. 70% water saturation, water could significantly diffuse in vapor form in gas-filled connected pores through the large proportion of the inter-aggregate pores but with a lower rate in
the liquid phase which is more tortuous. At 1.9 MPa of suction, i.e. 84% water saturation, the decrease of the proportion of inter-aggregate pores would be counterbalanced by an increase of the degree of saturation, allowing more water to diffuse in liquid phase. Lastly, at full-saturation, water diffusion takes place only in liquid phase but finally in a more tortuous pore network (Figure 8c).

## Conclusion

Results obtained in the present study show that the diffusive behavior of water and solutes in bentonite can be related to the changes of the bentonite porous structure as a function of water saturation, unlike what was observed for the compacted kaolinite and for intact Cox claystone, two clayey materials whose microstructure did not noticeably evolve with saturation. In bentonite, the diffusivity value of the water tracer, HDO did not change and that of anion tracer, ¹²⁵I⁻, evolved much less with decreasing saturation from 100% to 70% (by a factor of 12) than in the two other materials. These results indicate that the saturation-dependent microstructure changes, triggered by the montmorillonite swelling, should control the geometry of the diffusion paths. Furthermore, the diffusion experiments performed with the cation (²²Na⁺) tracer showed a larger drop in diffusivity and distribution ratio (Rd) by factors of 73 and 16 from 0 to 9 MPa of suction, respectively, compared to the other two clayey materials. This indicates that the adsorptive capacity of bentonite towards this cation is reduced at the lowest degree of saturation, i.e. 70%, probably due to the existence of some montmorillonite volumes that are not connected to the diffusive paths of ²²Na⁺, and more generally to the external solutions. Such results are consistent with data acquired by the mechanical tests. Indeed, at the highest applied suction, i.e. 9MPa, the swelling pressure curve did not indicate any occurrence of collapse of the inter-aggregate porosity, associated with a swelling pressure 1.5 to 2 times lower than at full water saturation, meaning that a part of swelling clay particles was not accessible to water ingress and so to ²²Na⁺. Conversely, at 1.9 and 0 MPa of suction, the two-step pattern of the swelling pressure curves suggests that a threshold is reached above which the bentonite structure is not anymore capable of accommodating the extra swelling pressure without reorganizing its microstructure, and thus the reduction of the inter-aggregate porosity.

A tentative qualitative interpretation of results involving the redistribution of the interlayer, inter-particle and inter-aggregate porosity hosting preferentially the vapor is proposed in order to explain the evolution of diffusivity of water and solutes with saturation. Yet, further experiments involving other tracers such as cesium (the cation having the highest diffusivity in clay materials) as well as high resolution X ray tomography (Massat et al. 2016) and FIB SEM (Keller et al., 2014) could help us deriving a more quantitative model of the saturation-dependent diffusivity in compacted bentonites.

## Acknowledgement
597 The results presented are part of the Ph.D. thesis of J.W. granted by Andra and CEA. Three
598 anonymous reviewers and the associated editor, Thomas Gimmi, are warmly acknowledged for their
599 fruitful comments on the manuscript.

600
602 Andra, 2016. Dossier d'options de sûreté, partie après fermeture (DOS-AF)

603 {https://www.andra.fr/sites/default/files/2018-04/dossier-options-surete-apres-fermeture_0.pdf}

604

605 Asaad, A., Hubert, F., Ferrage, E., Dabat, T., Paineau, T., Porion, P., Savoye, S., Tertre, E., 2021. Role of Interlayer Porosity and Particle Organization in the Diffusion of Water in Swelling Clays

606
607 Applied Clay Science 207: 106089. https://doi.org/10.1016/j.clay.2021.106089.

608 Bazer-Bachi, F., Tevissen, E., Descostes, M., Grenut, B., Meier, P., Simonnot, M.-O., Sardin, M.,

609 2006. Characterization of iodide retention on Callovo-oxfordian argillites and its influence on

610 iodide migration. Phys. Chem. Earth Parts ABC 31, 517-522.

611 https://doi.org/10.1016/j.pce.2006.04.015

612 Bernachy-Barbe, F., Conil, N., Guillot, W., Talandier, J., 2020. Observed Heterogeneities after

613 Hydration of MX-80 Bentonite under Pellet/Powder Form. Applied Clay Science 189:

614 105542. https://doi.org/10.1016/j.clay.2020.105542.

615 Delage, P, Howat, M.D, Cui. Y.J., 1998. The Relationship between Suction and Swelling Properties in

616 a Heavily Compacted Unsaturated Clay. Engineering Geology 50 (1-2): 31-48.

617 https://doi.org/10.1016/S0013-7952(97)00083-5.

618 Descostes, M., Blin, V., Bazer-Bachi, F., Meier, P., Grenut, B., Radwan, J., Schlegel, M.L., Buschaert,

619 S., Coelho, D., Tevissen, E., 2008. Diffusion of anionic species in Callovo-Oxfordian

620 argillites and Oxfordian limestones (Meuse/Haute-Marne, France). Appl. Geochem. 23, 655-

621 677. https://doi.org/10.1016/j.apgeochem.2007.11.003

622 Dueck, A., 2008. Laboratory Results from Hydro-Mechanical Tests on a Water Unsaturated Bentonite.

623 Engineering Geology 97 (1-2): 15-24. https://doi.org/10.1016/j.enggeo.2007.11.001.

624 Eriksen, T. E., Jansson, M., 1996. Diffusion of I-, Cs+ and Sr2+ in compacted bentonite – Anion

625 exclusion and surface diffusion. SKB Technical Report 96-16.

626 Gatabin, C., Talandier, J., Collin, F., Charlier, R., Dieudonné, A.C., 2016. Competing effects of

627 volume change and water uptake on the water retention behaviour of a compacted MX-80

628 bentonite/sand mixture. Applied Clay Science 121-122, 57-62

629 Glaus, M. A., Frick, S., Rossé, R., Van Loon, L.R., 2010. Comparative Study of Tracer Diffusion of

630 HTO, 22Na+ and 36Cl- in Compacted Kaolinite, Illite and Montmorillonite. Geochimica et

631 Cosmochimica Acta 74 (7): 1999-2010. https://doi.org/10.1016/j.gca.2010.01.010.

632 Grathwohl, P., 1998. Modelling of Diffusion Processes, in: Diffusion in Natural Porous Media.

633 Springer, pp. 43–81.

634 Imbert, C., Villar, M.V., 2006. Hydro-Mechanical Response of a Bentonite Pellets/Powder Mixture

635 upon Infiltration. Applied Clay Science 32 (3-4): 197-209.

636 https://doi.org/10.1016/j.clay.2006.01.005.

637 Ishidera, T., Miyamoto, S., Sato, H., 2008. Effect of Sodium Nitrate on the Diffusion of Cl- and I-

638 in Compacted Bentonite. Journal of Nuclear Science and Technology 45, 610–616.

639 https://doi.org/10.1080/18811248.2008.9711459

640 Jacinto, A.C., Villar, M.V., Ledesma, A., 2012. Influence of water density on the water retention curve

641 of expansive clays. Géotechnique 62, 657–667. https://doi.org/10.1680/geot.7.00127.

642 Karnland, O., Olsson, S., Nilsson, U., Sellin, P., 2007. Experimentally Determined Swelling Pressures

643 and Geochemical Interactions of Compacted Wyoming Bentonite with Highly Alkaline

644 Solutions. Physics and Chemistry of the Earth, Parts A/B/C 32 (1-7): 275-86.

645 https://doi.org/10.1016/j.pce.2006.01.012.
646 Keller, L. M., Seiphoori, A., Gasser, P., Falk, L., Holzer, L., Ferrari, A., 2014. The Pore Structure of
647 Compacted and Partly Saturated MX-80 Bentonite at Different Dry Densities. Clays and Clay
648 Minerals 62 (3): 174–87. https://doi.org/10.1346/CCMN.2014.0620302.

649 Kozaki, T., Inada, K., Sato, S., Ohashi, H., 2001. Diffusion mechanism of chloride ions in sodium
650 montmorillonite. J. Contaminant Hydrol. 47, 159.

651 Kozaki, T., Fujishima, A., Saito, N., Sato, S., Ohashi, H., 2005. Effects of dry density and
652 exchangeable cations on the diffusion process of sodium ions in compacted montmorillonite.
653 Engineering Geology 81 (3), 246–254.

654 Liu, Z., Sun, Y., Kong, J., Lee, C.-P., Hua, R., Liu, W., Wang, Z., Jiang, Q., Li, B., 2022. A sensitive
655 improved method for analyzing diffusion coefficients of Cs in compacted bentonite with
656 different lengths. Radiochimica Acta 110, 363–372. https://doi.org/10.1515/ract-2022-0007

657 Massat, L., Cuisinier, O., Bihannic, I., Claret, F., Pelletier, M., Masrouri, F., Gaboreau, S., 2016.
658 Swelling Pressure Development and Inter-Aggregate Porosity Evolution upon Hydration of a
659 Compacted Swelling Clay. Applied Clay Science 124–125: 197–210.
660 https://doi.org/10.1016/j.clay.2016.01.002.

661 Melkior, T., Gaucher, E.C., Brouard, C., Yahiaoui, S., Thoby, D., Clinard, Ch., Ferrage, E., Guyonnet,
662 D., Tournassat, C., Coelho, D., 2009. Na⁺ and HTO diffusion in compacted bentonite: Effect
663 of surface chemistry and related texture. J. Hydrol. 370, 9–20.
664 https://doi.org/10.1016/j.jhydrol.2009.02.035

665 Molera, M., Eriksen, T., 2002. Diffusion of <sup>22</sup>Na, <sup>85</sup>Sr, <sup>134</sup>Cs and <sup>57</sup>Co in bentonite clay compacted to
666 different densities: experiments and modeling. Radiochim. Acta 90 (9 – 11), 753 – 760

667 Molera, M., Eriksen, T., Jansson, M., 2003. Anion diffusion pathways in bentonite clay compacted to
668 different dry densities. Applied Clay Science 23, 69–76. https://doi.org/10.1016/S0169-1317(03)00088-7

670 Moridis, G. J. 1998. A Set of Semianalytical Solutions for Parameter Estimation in Diffusion Cell
671 Experiments. Water Resources Research 35 (6).

672 Nagra, 2022. Le site pour le dépôt en profondeur : La proposition de la Nagra {https://nagra.ch/wp-content/uploads/2022/09/Rapport-le-site-pour-le-depot-en-profondeur-La-proposition-de-la-Nagra.pdf}

675 Navarro, V., Cabrera, V., Merlo, O., De la Morena, G., Torres-Serra, J., 2022. Density of water
676 adsorbed on bentonites: determination and effect on microstructural void ratio modelling.
677 Appl. Clay Sci. 219, 106343, https://doi.org/10.1016/j.clay.2022.106434.

678 Pearson, F.J., Arcos, D., Boisson, J.-Y., Fernández, A.M., Gäbler, H.E., Gaucher, E., Gautschi, A.,
679 Griffault, L., Hernán, P., Waber, N., 2003. Mont Terri Project—Geochemistry of Water in the
680 Opalinus Clay Formation at the Mont Terri Rock Laboratory. Report of the FOWG, No 5,
681 Geology Series

682 Sander, R., 2015. Compilation of Henry's law constants (version 4.0) for water as solvent. Atmos
683 Chem Phys. 15: 4399–4981.

684 Savoye, S., Page, J., Puente, C., Imbert, C., Coelho, D., 2010. New Experimental Approach for
685 Studying Diffusion through an Intact and Unsaturated Medium: A Case Study with Callovo-
686 oxfordian Argillite. Environ. Sci. Technol. 46, 2633–3704. https://doi.org/10.1021/es903738t

687 Savoye, S., Beaucaire, C., Fayette, A., Herbette, M., Coelho, D., 2012a. Mobility of Cesium through
688 the Callovo-oxfordian Claystones under partially saturated conditions. Environ. Sci. Technol.
689 44, 3698–3704. dx.doi.org/10.1021/es2037433

690 Savoye, S., Frasca, B., Grenut, B., Fayette, A., 2012b. How mobile is iodide in the Callovo–oxfordian
691 claystones under experimental conditions close to the in situ ones? J. Contam. Hydrol. 142–
692 143, 82–92. https://doi.org/10.1016/j.jconhyd.2012.10.003
693 Savoye, S., Lefevre, S., Fayette, A., Robinet, J.-C., 2017. Effect of Water Saturation on the
694 Diffusion/Adsorption of 22 Na and Cesium onto the Callovo-oxfordian Claystones. Geofluids
695 2017, 1–17. https://doi.org/10.1155/2017/1683979

696 Seiphoori, A., Ferrari, A., Laloui, L., 2014. Water Retention Behaviour and Microstructural Evolution
697 of MX-80 Bentonite during Wetting and Drying Cycles. Géotechnique 64 (9): 721–34.
698 https://doi.org/10.1680/geot.14.P.017.

699 Sridharan, A., Rao, G.V. 1973. Mechanisms controlling volume change of saturated clays and the role
700 of effective stress concept. Géotechnique, 23: 359–382.

701 Tachi, Y., Yotsuji, K., 2014. Diffusion and sorption of Cs+, Na+, I- and HTO in compacted sodium
702 montmorillonite as a function of porewater salinity: Integrated sorption and diffusion model.
703 Geochimica et Cosmochimica Acta 132, 75–93. https://doi.org/10.1016/j.gca.2014.02.004

704 Tanaka, Y., Watanabe, Y., 2019. Modelling the effects of test conditions on the measured swelling
705 pressure of compacted bentonite. Soils and Foundations 59, 136–150.
706 https://doi.org/10.1016/j.sandf.2018.09.009

707 Tang, A.M., Cui, Y.J., Le, T.T., 2008. A study on the thermal conductivity of compacted bentonites.
708 Appl. Clay Sci. 41 (3–4), 181–189.

709 Tertre, E., Savoye, S., Hubert, F., Prêt, D., Dabat, T., Ferrage, E., 2018. Diffusion of Water through
710 the Dual-Porosity Swelling Clay Mineral Vermiculite. Environ. Sci. Technol. 52, 1899–1907.
711 https://doi.org/10.1021/acs.est.7b05343

712 van Brakel, J., Heertjes, P.M., 1974. Analysis of diffusion in macroporous media in terms of a
713 porosity, a tortuosity and a constrictivity factor. Int. J. Heat Mass Transf. 17, 1093–1103.
714 https://doi.org/10.1016/0017-9310 (74)90190-2

715 Van Loon, L.R., Glaus, M.A., Müller, W., 2007. Anion exclusion effects in compacted bentonites:
716 Towards a better understanding of anion diffusion. Appl. Geochem. 22, 2536–2552.
717 https://doi.org/10.1016/j.apgeochem.2007.07.008

718 van Olphen, H. 1963. An introduction to clay colloid chemistry:for clay technologists, geologists and
719 soil scientists. Interscience, New York.

720 Villar, M.V., 2005. MX-80 Bentonite. Thermo-Hydro-Mechanical Characterisation Performed at
721 CIEMAT in the Context of the Prototype Project.

722 Villar, M.V., Lloret, A., 2008. Influence of dry density and water content on the swelling of a
723 compacted bentonite. Applied Clay Science 39, 38–49.
724 https://doi.org/10.1016/j.clay.2007.04.007

725 Wang, H. 2023. Pore water density in a saturated bentonite. Géotechnique
726 https://doi.org/10.1680/jgeot.22.00247

727 Wang, J., Savoye, S., Ferrage, E., Hubert, F., Lefevre, S., Radwan, J., Robinet, J.-C., Tertre, E.,
728 Gouze, P., 2022. Water and Ion Diffusion in Partially Water-Saturated Compacted Kaolinite:
729 Role Played by Vapor-Phase Diffusion in Water Mobility. Journal of Contaminant Hydrology
730 248: 103989. https://doi.org/10.1016/j.jconhyd.2022.103989.

731 Yigzaw, Z. G., Cuisinier, O., Massat, L., Masrouri., F., 2016. Role of Different Suction Components
732 on Swelling Behavior of Compacted Bentonites. Applied Clay Science 120 (February): 81–90.
733 https://doi.org/10.1016/j.clay.2015.11.022.

734 Yong, R. N., 1999. Overview of Modeling of Clay Microstructure and Interactions for Prediction of
735 Waste Isolation Barrier Performance. Engineering Geology 54 (1–2): 83–91.
736 https://doi.org/10.1016/S0013-7952(99)00064-2.

737 Zhu, C.-M., Ye, W.M., Chen, Y.G., Chen, B., Cui, Y.J., 2013. Influence of Salt Solutions on the
738 Swelling Pressure and Hydraulic Conductivity of Compacted GMZ01 Bentonite. Engineering
739 Geology 166: 74–80. https://doi.org/10.1016/j.enggeo.2013.09.001.

740
<table><caption>Table 1. Initial conditions of compacted bentonite experiments as well as the values of the applied suction, method used and chemical composition of external solution.</caption><thead><tr><th colspan="8">Initial compaction conditions</th></tr><tr><th></th><th>Water content per dry mass (%)</th><th>Dry density (kg m<sup>-3</sup>)</th><th>Total porosity from Eq(1) (%)</th><th>Applied suction (MPa)</th><th>Method</th><th>Chemical composition of solution</th></tr></thead><tbody><tr><td>DIFF-0MPa</td><td>18.3</td><td>1510</td><td>45.3</td><td>0</td><td>Through-diffusion of HDO, <sup>125</sup>I- & <sup>22</sup>Na<sup>+</sup></td><td>Cox pore-water + 0 g<sub>PEG</sub>/g<sub>w</sub></td></tr><tr><td>DIFF-1.9MPa</td><td>18.3</td><td>1490</td><td>46.0</td><td>1.9</td><td>Through-diffusion of HDO, <sup>125</sup>I- & <sup>22</sup>Na<sup>+</sup></td><td>Cox pore-water + 0.42 g<sub>PEG</sub>/g<sub>w</sub></td></tr><tr><td>DIFF-9MPa</td><td>18.3</td><td>1480</td><td>46.4</td><td>9</td><td>Through-diffusion of HDO, <sup>125</sup>I- & <sup>22</sup>Na<sup>+</sup></td><td>Cox pore-water + 0.95 g<sub>PEG</sub>/g<sub>w</sub></td></tr><tr><td>Swell9to0MPa</td><td>18.3</td><td>1505</td><td>45.5</td><td>9, 1.9, 1 and 0</td><td>Swelling test in const. vol.</td><td>Pure water + 0.95, 0.42, 0.096 and 0 g<sub>PEG</sub>/g<sub>w</sub></td></tr><tr><td>Swell_0Mpa</td><td>15.6</td><td>1485</td><td>46.2</td><td>0</td><td>Swelling test in const. vol.</td><td>Pure water + 0 g<sub>PEG</sub>/g<sub>w</sub></td></tr><tr><td>Swell_1.9Mpa</td><td>17.25</td><td>1520</td><td>44.9</td><td>1.9</td><td>Swelling test in const. vol.</td><td>Pure water + 0.42 g<sub>PEG</sub>/g<sub>w</sub></td></tr><tr><td>Swell_9Mpa</td><td>16.8</td><td>1510</td><td>45.3</td><td>9</td><td>Swelling test in const. vol.</td><td>Pure water + 0.95 g<sub>PEG</sub>/g<sub>w</sub></td></tr></tbody></table>
<table><thead><tr><th rowspan="2">Tracers</th><th colspan="3">Suction: 0MPa</th><th colspan="3">Suction: 1.9MPa</th><th colspan="3">Suction: 9MPa</th></tr><tr><th>D<sub>e</sub><br>(10<sup>-11</sup> m<sup>2</sup> s<sup>-1</sup>)</th><th>α or θ<sup>125I-</sup><sub>diff</sub><br>(-)</th><th>R<sub>d</sub><br>(mL g<sup>-1</sup>)</th><th>D<sub>e</sub><br>(10<sup>-11</sup> m<sup>2</sup> s<sup>-1</sup>)</th><th>α or θ<sup>125I-</sup><sub>diff</sub><br>(-)</th><th>R<sub>d</sub><br>(mL g<sup>-1</sup>)</th><th>D<sub>e</sub><br>(10<sup>-11</sup> m<sup>2</sup> s<sup>-1</sup>)</th><th>α or θ<sup>125I-</sup><sub>diff</sub><br>(-)</th><th>R<sub>d</sub><br>(mL g<sup>-1</sup>)</th></tr></thead><tbody><tr><td>HDO</td><td>5.0<br>(4.2-5.5)</td><td>0.89<br>(0.53-0.89)</td><td>0.29<br>(0.06-0.29)</td><td>6.0<br>(5.3-7)</td><td>0.38<br>(0.38-0.65)</td><td>0.00<br>-</td><td>5.0<br>(3.0-6.0)</td><td>0.30<br>(0.3-0.43)</td><td>0.00<br>(0.04-0.05)</td></tr><tr><td><sup>22</sup>Na<sup>+</sup></td><td>44.0<br>(28.0-50.0)</td><td>17.6<br>(14.08-17.6)</td><td>11.44<br>(9.09-11.44)</td><td>35<br>(20.0-55.0)</td><td>11.9<br>(9.9-15.84)</td><td>7.66<br>(5.00-8.12)</td><td>0.6<br>(0.4-0.75)</td><td>1.36<br>(0.8064-1.8)</td><td>0.70<br>(0.34-0.96)</td></tr><tr><td><sup>125</sup>I<sup>-</sup></td><td>0.1550<br>(0.14-0.17)</td><td>0.0264<br>(0.0231-0.0286)</td><td>-</td><td>0.08<br>(0.074-0.085)</td><td>0.0148<br>(0.01-0.0216)</td><td>-</td><td>0.013<br>(0.0128-0.0137)</td><td>0.0048<br>(0.0044-0.0061)</td><td>-</td></tr></tbody></table>

Table 2 Effective diffusion coefficients, D<sub>e</sub>, rock capacity factor, α or θ<sup>125I-</sup><sub>diff</sub>, and distribution ratio R<sub>d</sub>, for HDO, <sup>22</sup>Na<sup>+</sup> and <sup>125</sup>I<sup>-</sup> evaluated from the experimental data for the 3 suction levels of 0MPa, 1.9MPa and 9MPa corresponding to value of the degree of water saturation equal to 1.00±0.03, 0.84±0.03 and 0.70±0.045 (resp.).
749 Figure 1.

750

<figure><img src="image_2.png" /></figure>

751

<caption>Figure 1. Hierarchy of fabric units and pore spaces of bentonite from Yong (1999)</caption>

752

753
754

755

756

757 Figure 2

<figure><img src="image_3.png" /></figure>

758

759
760
761
Figure 2. Schematic view of the through-diffusion setup used for partially water-saturated bentonite samples.

760

761
<figure><img src="image_4.png" /><figcaption>Figure 3. Schematic view of the experimental setup used for the swelling pressure tests.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Figure 4. Normalized diffusive fluxes for water (a), anion (b) and cation (c) tracers at water saturation degree values of 100% in blue (0 MPa of suction), 84% in green (1.9 MPa of suction) and of 70% in red (9 MPa of suction).</figcaption></figure>
<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>
771 Figure 5. Diffusivity versus degree of water saturation for bentonite, a) for water and solute tracers, b) for water tracer compared with those obtained in kaolinite and Cox, c) for anion tracer compared with those obtained in kaolinite and Cox. d) Reciprocal of the geometry factor as function of volumetric water content accessible to anion for bentonite, kaolinite and Cox.
<figure><img src="image_10.png" /><figcaption>Figure 6. a) Diffusivities of $^{22}$Na$^+$ and b) distribution ratio, R_d, as function of degree of water saturation for the bentonite samples, compared with those obtained for kaolinite and Cox.</figcaption></figure>
<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>
<figure><img src="image_13.png" /><figcaption>Figure 8</figcaption></figure>

Figure 8. a), b) and c) schematic views of bentonite at 9, 1.9 and 0 MPa of suction (resp.) with the associated diffusive and mechanical properties.