# Compressibility of a binary bentonite-based mixture with particular emphasis on pellet orientation

Arisleidy Mesa-Alcantara, Enrique Romero, Joel Torres-Serra, Nadia Mokni

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Arisleidy Mesa-Alcantara, Enrique Romero, Joel Torres-Serra, Nadia Mokni. Compressibility of a binary bentonite-based mixture with particular emphasis on pellet orientation. Applied Clay Science, 2024, 261, pp.107575. 10.1016/j.clay.2024.107575. hal-04876643

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Research Paper

# Compressibility of a binary bentonite-based mixture with particular emphasis on pellet orientation

Arisleidy Mesa-Alcantara<sup>a</sup>, Enrique Romero<sup>b,c,*</sup>, Joel Torres-Serra<sup>b</sup>, Nadia Mokni<sup>d</sup>

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

## ARTICLE INFO

### Keywords:

- Bentonite

- Pellet orientation

- Anisotropy

- Compressibility on loading

- Discrete element method

- Radioactive waste disposal

## ABSTRACT

Binary mixtures of Wyoming-type bentonite, consisting of 80 % mass high-density pellets and 20 % granular bentonite, are currently considered candidate materials for the French concept of vertical sealing systems for deep and long-term disposal of radioactive wastes. At low emplacement water contents, the hydro-mechanical behaviour is primarily controlled by contact forces between pellets, forming a coarse grain-supported structure over which granular bentonite is poured. These pellets were uniaxially compacted at elevated stresses to reach high dry densities. Subsequent pellet unloading resulted in anisotropic features due to fissuring and delamination, followed by water absorption. This study investigated compressibility changes upon loading under laterally confined conditions of a well-oriented pellet-supported structure, mimicking the setup of the *in situ* VSEAL 1 experiment at Tournemire (France). Two pellet orientations at the same dry density and coordination number of pellet contacts were examined in a pure pellet skeleton and a mixture to account for potential heterogeneity during pouring. A discrete element method was used to simulate the compression results with pellets represented as a clump with a heterogeneous void ratio distribution due to fissuring. These simulations were instrumental in understanding the important anisotropic deformation properties of pellet-supported structures under two distinct orientations.

## 1. Introduction

Heterogeneous mixtures containing high-density bentonite pellets or large granules were suggested for shaft seals and horizontal galleries in deep radioactive waste disposal concepts: granular bentonite (Hoffmann et al., 2007; Alonso et al., 2011; Wieczorek et al., 2017) and mixtures of pellets and granular bentonite (Imbert and Villar, 2006; Gens et al., 2011; Mokni et al., 2020). These mixtures offer considerable advantages during emplacement by decreasing technological gaps and reaching adequate dry densities with minimum compaction effort.

In the context of the French deep geological repository concept, the Institute for Radiation Protection and Nuclear Safety (IRSN) launched the VSEAL project (Vertical SEALing; Mokni et al., 2023) to investigate the swelling and sealing properties of a binary pellet-granular bentonite mixture. The current study involves this mixture of high-density Wyoming-type bentonite pellets (80 % mass) and granular bentonite

from crushed pellets prepared at low water content, which were widely characterised, and their complex multi-porosity network investigated (Molinero-Guerra et al., 2020; Navarro et al., 2020; Darde et al., 2021; Mesa-Alcantara, 2021; Yang et al., 2024).

At low water content, the studied mixture displays significant heterogeneity in dry density with an underfilled fabric, in which granular bentonite partially fills the voids between pellets. Mesa-Alcantara et al. (2020) estimated a mean volumetric degree of granular bentonite filling around 0.61 (volume fraction of granular bentonite filling the inter-pellet voids), assuming a dry granular bentonite density of 1.10 Mg/m³, poured after the pellet-supported structure's arrangement. This heterogeneity in the dry density of the mixture arises because some areas have higher granular bentonite filling while others remain empty. Despite these differences, the mechanical contribution of granular bentonite is considered limited compared to the load-bearing capacity of the coarse skeleton with dominant contact forces between pellets, at

<footnote><sup>a</sup> Geomechanics Group, International Centre for Numerical Methods in Engineering CIMNE, 08034 Barcelona, Spain</footnote>

<footnote><sup>b</sup> Department of Civil and Environmental Engineering, Universitat Politècnica de Catalunya UPC, 08034 Barcelona, Spain</footnote>

<footnote><sup>c</sup> Geomechanics Group, International Centre for Numerical Methods in Engineering CIMNE, 08034 Barcelona, Spain</footnote>

<footnote><sup>d</sup> Institut de Radioprotection et de Sûreté Nucléaire IRSN, 92260 Fontenay-aux-Roses, France</footnote>

<footnote>* Corresponding author at: Department of Civil and Environmental Engineering, Universitat Politècnica de Catalunya UPC, 08034 Barcelona, Spain.</footnote>

<footnote>E-mail addresses: arisleidy.mesa@upc.edu (A. Mesa-Alcantara), enrique.romero-morales@upc.edu (E. Romero), joel.torres@upc.edu (J. Torres-Serra), nadia.mokni@irsn.fr (N. Mokni).</footnote>
least close to the initial water content, consistent with the load-bearing limit determined for gap-graded mixtures with fine grain contents below 25 % (de Frias Lopez et al., 2016). This heterogeneous distribution of granular bentonite makes it necessary to consider at least two configurations in the current study: the one corresponding to a pellet skeleton without any bentonite filling and the one concerning a skeleton with a mean granular bentonite filling.

The pellets also display anisotropic features in stiffness and strength since they were one-dimensionally compacted at high stresses starting from dry granular bentonite (Darde et al., 2021; Yang et al., 2022). These pellets underwent significant deformation in one direction on static compaction, inducing the aggregates' particle crushing and preferential orientation. Upon one-dimensional unloading, principal stress rotation induces incipient passive failure, delamination, and fissure opening, further impacting the subsequent anisotropic volume change response on pellet loading.

The paper presents different microstructural complementary techniques, including nitrogen adsorption, mercury intrusion porosimetry, X-ray computed microtomography, and field emission scanning electron microscope, which are used to qualitatively detect, localise, and quantitatively evaluate these pellets' fissures and dry density variations induced on unloading after static compaction and further enhanced by some water absorption (from the as-compacted state to laboratory conditions). Yang et al. (2024) recently quantified the propagation of these fissures on hydraulic paths with microstructural techniques.

The anisotropy induced on the pellets by the processes described above affects the deformational response on loading of the pellet-supported structure (with or without granular bentonite), which depends on the prevailing orientation during installation. Setting the VSEAL 1 *in situ* test (Tournemire, France; Mokni et al., 2023) followed a well-oriented pellet-supported structure layer by layer to ensure homogeneity. In this regard, Molinero-Guerra (2018) studied the mixture's compressibility, considering a single orientation of the pellets. To extend this study and encompass two extreme pellet orientations, the current paper focuses on determining the changes in compressibility on loading under laterally confined conditions of a layer of a well-oriented pellet-supported structure with and without granular bentonite under two orientations of pellets at the same initial dry density and coordination number of the pellet's contacts.

The impact of the pellet's anisotropy and the mixture's heterogeneity on the compressibility under laterally confined conditions of a layer of a well-oriented pellet-supported structure was also numerically analysed in this paper by the discrete element method (DEM) to strengthen its fundamental interpretation. The DEM was recently used in modelling spherical pellet assemblies to study swelling upon hydration (Darde et al., 2021) and the hydro-mechanical coupling of pellet-granular bentonite mixtures (Caulk, 2022). In these studies, granular deformation under stress was typically modelled by the inter-particle overlap considered in the DEM contact laws. Alternatively, particle clumps representing clay aggregates were explored to model the compressibility of a single and a random packing of aggregates (Rapino, 2020). Nonspherical particle shapes were also studied by Torres-Serra et al. (2021). In addition, efforts have been made to characterise the compression behaviour at different hydraulic states of single pellets (Darde et al., 2018; Zhang et al., 2022) and pellet-based arrangements (Yang et al., 2024). Nonetheless, the reported elastic mechanical properties were derived from unconfined uniaxial compression of single pellets. By contrast, the current paper complements these previous studies by presenting the volume change behaviour on confined oedometer-type loading of a single layer of a pellet-supported structure with and without inter-pellet filling of granular bentonite. The study particularly seeks changes in compressibility when loading pellet clustering at two orientations and sharing equivalent initial conditions (equivalent modal coordination number for pellets, equality in dry density, and initial water content). Pellet anisotropy and heterogeneity were explicitly included in modelling the pellet as a clump (a

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Schematic view of the pellet, including the axis of symmetry and dimensions: *D*, diameter; *H*, height; *r*, the radius of the cylinder; *h*, the height of the caps; *R*, the radius of cap curvature.</figcaption></figure>

<table><caption>**Table 1**
Initial state of the pellets, granular bentonite, and the mixture.</caption><thead><tr><th>Initial state</th><th>Pellets</th><th>Granular bentonite</th><th>Mixture</th></tr></thead><tbody><tr><td>Initial water content, w (%)</td><td>6.13–9.36</td><td>8.50–10.5</td><td>6.60–9.57</td></tr><tr><td>Total suction, s (MPa)</td><td>160–110</td><td>89–70</td><td>118–110</td></tr><tr><td>Dry density, ρ<sub>d</sub> (Mg/m<sup>3</sup>)</td><td>1.99–2.12</td><td>1.10</td><td>1.47–1.49</td></tr><tr><td>Void ratio, e</td><td>0.39–0.31</td><td>1.52</td><td>0.88–0.86</td></tr><tr><td>Maximum particle size (mm)</td><td>7.0</td><td>2.0</td><td>7.0</td></tr><tr><td>Minimum particle size (mm)</td><td>7.0</td><td>0.075</td><td>0.075</td></tr></tbody></table>

deformable non-spherical packing of rigid spheres) with mechanical contact parameters and a heterogeneous void ratio of the core and caps according to the measured dry density profiles by X-ray computed microtomography. The numerical model was calibrated and validated against the experimental results, which makes the study undoubtedly helpful for better understanding the directional dependent compressibility of these well-oriented skeletons of pellets and mixtures at a low water content.

## 2. Bentonite-based mixture

The investigated mixture was prepared using Wyoming-type sodium bentonite (commercial name MX-80). The mixture comprised high-density bentonite pellets (80 % mass) and granular bentonite. The bentonite presented a solid density of 2.77 Mg/m³, a liquid limit of 560 % and a plastic limit of 62 % (Saba, 2014; Molinero-Guerra, 2018). The Laviosa-MPC company (France) manufactured the material under the commercial name EXPANGEL (EXPANGEL®SP7 for pellets and SP32 for the granular bentonite produced by crushing pellets). Laviosa Minerals SpA measured a smectite content of 80 % and a cation exchange capacity of 98 meq/100 g, with Na⁺ as the major exchangeable cation (Molinero-Guerra, 2018). The pellets were uniaxially compacted from bentonite powder at approximately 5 % water content. The pellet geometry has a central quasi-cylindrical shape with a vertical axis of symmetry and two spherical caps on the top and bottom, as shown in the schematic of Fig. 1.

Table 1 presents the initial conditions and properties of the pellets, granular bentonite, and mixture. Dry density variations in the pellets are associated with the observed fissuring and some expansion related to water absorption (from approximately 5 % to the values indicated in the table). The initial total suction was measured by a chilled mirror dew point psychrometer (WP4C, METER Group), and the water content was
<figure><img src="image_5.png" /><figcaption>Fig. 2. Axis-oriented (0°) configuration: a) pellet at an angle of 0°, indicating the loading direction; b) arrangement of axis-oriented pellets (P0°); c) coordination number (Z) frequency; and d) polar distribution of Z.</figcaption></figure>

determined by oven-drying at 105 °C for 48 h.

**3. Methodology**

This research is fundamental and combines an experimental meth-
odology (at microstructural and phenomenological scales) to confirm a
phenomenon and numerical analyses through the discrete-element
method DEM to support interpreting the results. The different ap-
proaches are highly interrelated and complement each other. The
microstructural techniques described first allow localising and quanti-
fying the pellet's fissures induced by unloading and water absorption
and the detection of dry density variations between more degraded
pellet's caps and the central core, which are further considered in esti-
mating Young's moduli in the numerical model.

After that, the rationale behind the phenomenological loading tests
under lateral confined conditions (oedometer tests) to study the influ-
ence of pellet's anisotropy and mixture's heterogeneity on the
compressibility of a layer of well-arranged pellet-supported structures is
described. Finally, this section describes the discrete element method
and the constitutive laws used in the numerical analyses, calibrated and
validated against the experimental results.

**3.1. Microstructural techniques**

The pellet's microstructure was analysed using four complementary
techniques: field emission scanning electron microscope (FESEM),
mercury intrusion porosimetry (MIP), X-ray computed micro-
tomography (µ-CT), and nitrogen adsorption using the Barrett, Joyner

and Halenda (BJH) model. Moreover, the pore size density function
(PSD) of granular bentonite was investigated through MIP, BJH tech-
niques and the grain size distribution. Cumulating the void volume using
all these techniques provided a complete characterisation of the initial
pore network of both components of the mixture, covering a wide range
of pore sizes from 1.6 nm to 1.18 mm.

FESEM was performed in a JEOL JSM-7001F scanning electron mi-
croscope to provide topographic information and directly observe the
fissure layout and the localisation of the most damaged areas of the
pellets. The pellet was freeze-dried by rapid immersion into liquid ni-
trogen (–196 °C) for 20 min and then maintained in a vacuum at –50 °C
for 24 h using a Telstar LyoQuest-55 freeze dryer. Before the morpho-
logical observations, a thin conductive material coating was applied to
the sample.

The MIP tests, attaining a maximum intrusion mercury pressure of
228 MPa corresponding to a minimum entrance pore size of 7 nm, were
conducted on freeze-dried samples (following an equivalent procedure
as described above on pellet and granular bentonite) using Micro-
meritics AutoPore IV 9500 (Romero and Simms, 2008). The MIP
determined the material's connected porosity and helped scale com-
plementary techniques to obtain the global pore size distribution. Spe-
cifically, MIP data were complemented with nitrogen adsorption
isotherms (Micromeritics ASAP 2020 system) in the lower range of pore
sizes (non-intruded pores below 7 nm), following a similar procedure
applied to the study of clay phyllites (Garzón et al., 2010). The nitrogen
adsorption data on freeze-dried samples were interpreted using the BJH
model, which assumes that pores have a cylindrical shape and that the
pore radius is equal to the sum of the Kelvin radius and the thickness of
<figure><img src="image_6.png" /><figcaption>Fig. 3. Orthogonally-oriented (90°) configuration: a) pellet at an angle of 90°, indicating the loading direction; b) arrangement of orthogonally-oriented pellets (P90°); c) coordination number (Z) frequency; and d) polar distribution of Z.</figcaption></figure>

the film adsorbed on the pore wall (Webb and Orr, 1997).

The µ-CT technique (Phoenix V/tome/x S240 at CENIEH, Spain) was used in a pellet at initial water content in a range where mercury intrusion did not clearly detect large fissures (Romero and Simms, 2008). ImageJ software (Schneider et al., 2012) allowed the reconstruction of a 3D region of interest (ROI), which provided a 16-bit grayscale image stack with a voxel resolution of 12 × 12 × 12 µm³. The µ-CT data were used to obtain the PSD of the pellet for entrance pore sizes larger than 24 µm, i.e., twice the voxel size of the ROI, which allowed complementing the upper range of MIP (Yuan et al., 2022; Yang et al., 2023; Fraccica et al., 2024). By analysing the histogram of the voxel's grey values spanning from i = 0 to 255, a grey value threshold θ was estimated based on the pellet's void ratio e (refer to Table 1) using the expression below (Vᵢ is the volume of the i-th voxel):

$$e = \frac{V_{\text{pores}}}{V_{\text{solids}}} = \frac{\sum_{i=0}^{i=\theta} V_i}{\sum_{i=255}^{i=\theta} V_i} \quad (1)$$

Next, according to the previously obtained grey value threshold, the binarised ROI was used to simulate mercury intrusion with the ImageJ subroutine proposed by Münch and Holzer (2008), which allows for calculating the PSD function (Fraccica et al., 2024).

A calibration equation (Fig. 6) was also done through µ-CT to define the pellet's density map using different elements of known density, including glass (2.5 Mg/m³), aluminium (2.7 Mg/m³), and air at 20 °C (0.0012 Mg/m³), which were simultaneously scanned with the pellet to

avoid possible X-ray fluctuations.

The µ-CT technique could not be used for granular bentonite since the material's low density affects sample preparation. Hence, the PSD function of granular bentonite for pore sizes higher than 400 µm was derived from the grain size distribution of the material at initial conditions. The pore sizes can be related to the grain sizes by an empirical factor accounting for the material's particle shape and void ratio (Kamiya and Uno, 2000). In addition, the histogram for different particle sizes allowed the corresponding pore histogram to be estimated.

## 3.2. Oedometer tests

Laboratory tests were performed by placing one layer of oriented pellets inside an oedometer cell, ensuring a high coordination number (Figs. 2 and 3). In the tests on mixtures, the granular bentonite was afterwards poured, partially filling the inter-pellet pores at a mean volumetric degree of filling of around 0.61 (Mesa-Alcantara et al., 2020). Pellets were placed in two orientations, considering arrangements where the pellets were axis-oriented (Fig. 2a), i.e. the axis of symmetry of the pellet (Fig. 1) was aligned at 0° with respect to the axis of symmetry of the oedometer cell, and arrangements where pellets were orthogonally-oriented (Fig. 3a), i.e. the axis of the pellet formed an angle of 90° with respect to that of the oedometer cell.

Different axial compression tests of a single layer of laterally confined arrangements of pellets (P) and mixtures (M) at the initial water content, both in well-oriented P0° and P90° configurations, were performed in the oedometer cell (for simplicity, ‘oedometer tests’ will be
<table><caption>**Table 2**
Test initial conditions of axis-oriented (0°) and orthogonally-oriented (90°) arrangements of pellets (P) and mixtures (M).</caption><thead><tr><th>Samples</th><th>Test reference</th><th>Dry density (Mg/m³)</th><th>Void ratio</th><th>Initial water content</th><th>Total suction (MPa)</th></tr></thead><tbody><tr><td rowspan="4">Pellets</td><td>P0°_1</td><td rowspan="4">1.19</td><td rowspan="4">1.33</td><td rowspan="4">7.57 %</td><td rowspan="4">122</td></tr><tr><td>P0°_2</td></tr><tr><td>P90°_3</td></tr><tr><td>P90°_4</td></tr><tr><td rowspan="3">Mixtures</td><td>M0°_5</td><td rowspan="3">1.49</td><td rowspan="3">0.86</td><td rowspan="3">8.56 %</td><td rowspan="3">110</td></tr><tr><td>M90°_6</td></tr><tr><td></td></tr></tbody></table>

used throughout the paper).

The initial conditions of the tests, including the total suction of the material measured by a chilled mirror dew point psychrometer, are summarised in Table 2. The oedometer samples had a diameter of 50 mm and an initial height of around 7 mm, coinciding with the dimensions of a pellet. The vertical stress steps ranged between 100 kPa and 2.19 MPa for the pellet arrangements and 5.0 MPa for the mixture. The successive vertical stress increments were applied after the axial deformation rates reached values smaller than 0.03 %/day.

Pellets present different stiffnesses depending on their orientation at high total suctions (Darde et al., 2018). Therefore, it is essential to ensure approximately the same dry density and coordination number of the different pellet-oriented samples to investigate whether pellet orientation significantly impacts the compressibility behaviour (Figs. 2 and 3). The dry density of the skeleton of pellets varied between 1.19 Mg/m³ and 1.17 Mg/m³ for the well-oriented P0° and P90° configurations, respectively. Assuming a mean dry density of the pellet of 2.06 Mg/m³ (Table 1), inter-grain void ratios of 0.731 for the P0° configuration and slightly higher at 0.761 for P90° were obtained. Regarding the coordination number Z of the samples, a first tessellation was applied to identify the pellet centroids (numbered in Figs. 2b and 3b) using vertical images of one layer of 37 pellets well-arranged inside the oedometer cell. 2D triangulation was then used to determine the regions enclosing each pellet and their connectivity. Contacting neighbours were identified using a threshold distance criterion defining the coordination numbers, with two additional contacts at the top and bottom cell boundaries. The arrangement of pellets was found between a simple cubic configuration of uniform spheres (Z = 6 with inter-grain void ratio 0.91) and a less common cubical-tetrahedral configuration (Z = 8 and inter-grain void ratio 0.65). The most frequent value of six contacts per pellet was found in Z histograms for both configurations (see Figs. 2c and 3c), corresponding to 65 % of particles for P0° and 57 % for P90°.

The in-plane distribution of contact points on each pellet (at the intersections between the tessellations and triangulations in Figs. 2b and 3b) assessed the degree of arrangement of P0° and P90° configurations. A reference contact point and direction (from each pellet centroid) were established for axially symmetric P0°, from which the remaining contact directions were determined. An approximately regular polar dispersion of all in-plane contacts was observed (Fig. 2d). Contact directions of P90° were derived from the in-plane pellet axial directions highlighted with a white dash-dotted line in Fig. 3a. The P90° arrangement presented a higher dispersity in the distribution of contact points, increasing with the coordination number (Fig. 3d). This fact was attributed to a more variable pellet geometry in the axial direction associated with the production process of compacted pellets. Based on the observed regular polar distribution of contacts in Figs. 2d and 3d, especially for the frequently occurring coordination number of six contacts, an idealised cubic representative elementary volume (REV) was employed in the numerical modelling of a single pellet.

### 3.3. DEM model set-up with material and contact parameters

Pellet geometry was modelled as a clumped random packing of

<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Schematic of the sphere clump representing a single pellet with inter-pellet granular bentonite filling and walls delimiting the simulation domain, as used in the DEM modelling of an axis-oriented mixture configuration (Model-M0°).</figcaption></figure>

<table><caption>**Table 3**
Mechanical contact parameters of the DEM model.</caption><thead><tr><th>Parameter</th><th></th><th>Value</th></tr></thead><tbody><tr><td rowspan="2">Pellet core</td><td>Pellet caps</td><td>48</td></tr><tr><td>Granular bentonite</td><td>4.5</td></tr><tr><td>Poisson's ratio, ν (–)</td><td></td><td>0.24</td></tr><tr><td>Friction angle, φ (°)</td><td></td><td>18</td></tr><tr><td>Shear cohesion, C<sub>0</sub> (MPa)</td><td></td><td>1.0</td></tr><tr><td>Elastic limit, ε<sub>0</sub> (–)</td><td></td><td>2.0 • 10<sup>-3</sup></td></tr><tr><td>Relative ductility, ε<sub>f</sub> / ε<sub>0</sub> (–)</td><td></td><td>4.0 • 10<sup>3</sup></td></tr></tbody></table>

spherical particles of radius $r = 0.175$ mm. The average void ratios of the pellet core and caps were calculated from the dry density profiles later described (Section 4.1). The resulting anisotropic particle clump (Fig. 4) has a denser cylindrical core and two spherical caps with a larger void ratio corresponding to the initial fissuring of the pellet caps. Granular bentonite filling the inter-pellet void was modelled as a loose random packing of spheres at the void ratio indicated in Fig. 4.

A cohesive particle model implemented in the open-source code Yade (Šmilauer, 2010; Šmilauer et al., 2021) was used to simulate the progressive fissuring of dry pellets by a damage law D controlled by three parameters (shear cohesion $C_0$, elastic limit $\epsilon_0$, and relative ductility $\epsilon_f / \epsilon_0$) built on top of a conventional elastic-frictional contact law with three more parameters (Young's modulus E, Poisson's ratio $\nu$, and friction angle $\varphi$), detailed in Table 3. The following contact laws describe normal stress $\sigma_n$ and shear stress $\sigma_t$ in terms of the respective contact strains, $\epsilon_n$ and $\epsilon_t$, and including damage D as a function of the maximum normal strain $\epsilon_n^{\max}$ between active contacts

$$ \sigma_n = (1 - DH(-\epsilon_n))k_n\epsilon_n \quad (2) $$

$$ \sigma_t = \min\{(1 - D)C_0 + \sigma_n \tan\varphi : k_t\epsilon_t\} \quad (3) $$

$$ D(\epsilon_n^{\max}) = 1 - \frac{\epsilon_f}{\epsilon_n^{\max}} \exp\left(\frac{\epsilon_0 - \epsilon_n^{\max}}{\epsilon_f}\right) \quad (4) $$

where $H(-\epsilon_n)$ is the Heaviside step function activating damage between particle pairs in contact. The normal contact stiffness between the i-th and j-th particles was defined by
<figure><img src="image_8.png" /><figcaption>Fig. 5. FESEM image of the spherical cap of the as-received pellet with 7 mm diameter, showing fissures between aggregates and around the perimeter.</figcaption></figure>

$$k_n = \frac{E_t E_j}{E_t + E_j} d \qquad (5)$$

with E Young's modulus and d the monodisperse particle size (d = 2r). The shear contact stiffness was given by $k_t = \nu k_n$ considering a uniform Poisson's ratio $\nu$ estimated from data presented by Yang et al. (2022).

Young's moduli, E, were estimated from compressibility data of granular bentonite compacted at different void ratios representative of the pellet and granular bentonite and from oedometer results on the mixture of pellets and granular bentonite in M0° and M90° configurations. Since the adopted values of E were defined from the results of this work's experimental campaign, further details can be found in Section 4.3.

The oedometer compression of the whole pellet-supported structure was modelled by the compression of a single pellet in an initially cubic REV (Fig. 4), in agreement with the most frequent simple cubic configuration found in the pellet arrangements presented in Section 3.2. The respective mechanical contact properties were applied to the pellet core and cap regions, and the granular bentonite filling inside the simulation domain enclosed by walls. A negligible horizontal displacement of the pellets was observed experimentally (see the before and after test images in Figs. 8 and 9 below). This horizontal displacement restriction was modelled by the rectangular prismatic set of walls

<figure><img src="image_9.png" /><figcaption>Fig. 6. X-ray computed microtomography: a) 3D region of interest inside a pellet (left) and density map (right) of the core defined by the calibration equation $\rho_d$ (Mg/m³) = 4.3 · 10⁻⁵ × GV – 0.21, where GV is the integer grey value; b) pellet dry density variation throughout the height (core and caps); and c) pellet dry density variation throughout a horizontal cross-section (core).</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>Fig. 7. Pore size distributions of pellet and granular bentonite using different techniques: a) cumulative void ratio; and b) pore size density functions.</figcaption></figure>

depicted in Fig. 4, and particle-wall interactions were governed using the same particle-particle parameters as the contacting pellet clump spheres. This allowed for a simplified representation of the experimental element-scale test by a numerical particle-scale model of a single pellet. In the axis-oriented configurations (Model-P0°, Model-M0°), the pellet was initially axis-aligned inside a cube of length 7 mm. In the orthogonally-oriented configurations (Model-P90°, Model-M90°), however, the pellet was initially rotated 45° around its X-Axis (Fig. 3a) and placed inside a cuboidal prism of height 7 mm (diameter of the core) and a larger square base of 7.6 mm. Configurations at 90° reproduced the poorer confinement conditions of the orthogonally-oriented arrangement compared to an axis-aligned arrangement of the pellet. Compression was simulated by displacing the top horizontal wall of the simulation domain downward at a constant velocity of 7.0 · 10⁻² m/s.

# 4. Results and discussion

## 4.1. Microstructure of the pellets and granular bentonite

The observations of the as-received pellet shown in Fig. 5 confirmed the presence of compressed and broken aggregates and fissures between them and along the perimeter of the spherical cap. Fissures are also expected to develop during hydration since swelling will progress from the external boundary towards the centre of the pellet. Peripheral detachment may also occur from the pellet's core, possibly along the pre-existing fissures, as observed by Mokni et al. (2020) and Molinero-

## Guerra et al. (2020).

The density map of the pellet obtained by µ-CT is shown in Fig. 6a. Brighter zones represent high-density regions. The pellet dry density variation with distance was analysed from µ-CT images throughout vertical and horizontal cross-sections, as shown in Fig. 6a (vertical Y and horizontal X). Along axis Y (Fig. 6b), the dry density profile shows lower values at the pellet's top and bottom caps (between 1.80 and 2.00 Mg/m³), consistent with the fissuring observed in FESEM images. The denser central quasi-cylindrical core displays dry densities between 2.00 and 2.08 Mg/m³ along the Y axis (Fig. 6c), showing a more homogeneous dry density distribution. Nevertheless, minimum values close to 1.95 Mg/m³ were also observed at the extremes of the quasi-cylindrical core.

Fig. 7a shows that the pellet's cumulative void ratio (µ-CT, MIP and BJH) reached a value around 0.4, closely approaching the maximum value documented in Table 1. It is worth emphasising that while large fissures were observed at the pellet caps through FESEM, these were not identified by µ-CT since the 3D ROI only encompassed fissures within the central quasi-cylindrical core (Fig. 6a to the left). The pellet's PSD (log scale) in Fig. 7b exhibits a multi-modal distribution characterised by pore modes at 3 nm (as identified by BJH and represented as a small peak), 20 nm (identified through MIP), and 20 µm (marked at the transition between MIP and µ-CT). The smallest pore modes indicate pores inside aggregates, while the largest pore mode pertains to the voids between aggregates and fissures.

The cumulative void ratio for granular bentonite (grain size analysis, MIP and BJH) reported in Fig. 7a reaches a maximum of 1.15, slightly lower than the expected value for granular bentonite presented in Table 1 (it appears that the pore volume determined by grain size analysis should suggest a more significant cumulative void ratio). The PSD (log scale) of the granular bentonite shown in Fig. 7b also displays a multi-modal distribution with pore modes at 3 nm (reduced peak observed by BJH), 30 nm (identified through MIP), around 1 to 3 µm (MIP), and between 200 and 300 µm (determined at the transition of MIP and grain size analysis). Pore modes <5 µm indicate pores inside grains (intra-aggregate and inter-aggregate pores inside grains), while the largest pore mode corresponds to the voids between grains.

## 4.2. Oedometer tests and DEM simulations

A significant effect was observed on the compression behaviour depending on the pellets' P0° and P90° orientations (see Fig. 8 for the oriented-pellet arrangements). The P90° orientation was initially stiffer than the P0° configuration, but the trend reverted at higher stresses. Tests were divided into an initial stage (stresses below 0.65 MPa) and a final stage (stresses between 1.62 and 2.19 MPa) to explain this behaviour better. The corresponding secant-constrained moduli (initial for stress range 0.1 to 0.65 MPa, and final for stress range 1.62 to 2.19 MPa) are summarised in Table 4. In the initial stage, P0° presented a constrained modulus lower than P90°, attributed to the pellet cap fissuring orthogonal to the loading direction in the axis-oriented configuration. However, the opposite behaviour was observed towards the final loading stage, when P90° displayed some decrease in the constrained modulus compared to P0°, attributed to reduced pellet confinement leading to a more dominant effect of pellet breakage. Although similar dominant coordination numbers (around six) were observed in Figs. 2c and 3c, particle shape effects also explain the different void ratios of the pellet arrangements (P90° configuration displayed slightly larger voids and void ratios than P0°) and thus the poorer confinement of P90°. In the P0° configuration, the closer arrangement of P0° pellets provided an overall higher stiffness of the samples against diametrical breakage of the pellets in the final loading stage (Table 4). The pellet pictures before and after the tests in Fig. 8 show higher degradations of the pellets in the P90° configuration.

Comparing the numerical compressibility curves against experimental results, both Model-P0° and Model-P90° curves in Fig. 8 captured the trend in the initial loading stage, up to a vertical stress of
<figure><img src="image_11.png" /><figcaption>**Fig. 8.** Experimental and numerical compressibility curves on loading one-layer pellet arrangements at different orientations of the pellets (0° and 90°). Pictures before and after loading with pellet crushing.</figcaption></figure>

<caption>**Table 4**</caption>

Secant-constrained moduli at the initial and final loading stages of the pellet (P) and mixture (M) samples with axis-oriented (0°) and orthogonally-oriented (90°) pellet orientations. The stress intervals for the initial and final stages are indicated in the text.

<table><thead><tr><th rowspan="2">Loading stage</th><th colspan="4">Constrained modulus (MPa)</th></tr><tr><th>P90°</th><th>P0°</th><th>M90°</th><th>M0°</th></tr></thead><tbody><tr><td>Initial</td><td>18.7</td><td>13.9</td><td>26.6</td><td>20.3</td></tr><tr><td>Final</td><td>17.6</td><td>18.6</td><td>42.7</td><td>52.5</td></tr></tbody></table>

0.5 MPa, after which the simulated set-up remained stiffer than the experimental pellet arrangements. In the final loading stage, the Model-P90° curve successfully reproduced the degradation of the orthogonally-oriented pellets. In the transition from initial to final trends (the point at which the compressibility curves intersect), the DEM model overestimated pellet strength, attributed to the simplifications regarding sample geometry and boundary conditions and the reduced number of mechanical parameters described in the contact law. Nonetheless, the numerical curves predicted the observed intersection of 0° and 90° curves at a vertical stress around 2 MPa.

Similar compressibility behaviour depending on the pellet orientation was observed in Fig. 9 for the M0° and M90° mixtures at the constant initial water content indicated in Table 2. Higher constrained moduli were systematically obtained for the mixtures compared to well-arranged pellets because of the lower initial void ratios and the inter-pellet voids filled with granular bentonite (Table 2). This behaviour was significant in the higher-stressed mixture since the granular bentonite filling protected the pellets and reduced their breakage. M90° presented lower compressibility on loading than M0° for vertical stresses

below 0.75 MPa associated with pellet cap fissuring induced on fabrication. Nevertheless, the final loading stage was characterised by a similar axial deformation where M90° underwent higher pellet breakage and tended to join the M0° curve at 5 MPa.

As observed in Fig. 9, mixture simulations followed the experimental trends with larger Model-M0° compressibility throughout the initial loading stage (up to 2 MPa) and despite the higher stiffness in this initial stage compared to experiments. Overall, the Model-M0°/M90° curves showed an increase in the mixture's stiffness compared to Model P0°/P90° results and predicted an intersection of the 0° and 90° curves at vertical stress 4 MPa, which was not recorded in the experiments but can be estimated to occur around 6 MPa. Therefore, the proposed DEM setup provided a helpful tool to validate the presented loading framework at different stages (pellet compressibility and pellet crushing stages), explaining the behaviour of pellet arrangements and mixtures of pellets and granular bentonite and confirming the experimental observations on the effect of pellet orientation.

### 4.3. Model of elastic moduli

Fig. 10a shows compression results under oedometer conditions from granular bentonite compacted at equivalent initial void ratios of the pellet (e = 0.39, see Table 1) and granular bentonite (e = 1.52). These results determined the variation of elastic Young's moduli, *E*, at contrasting void ratios, *e*, presented in Fig. 10b. *E* results as a function of *e* from one-layer pellet samples at the two well-oriented M0° and M90° configurations are also included in Fig. 10b. The mixture compression curves (Fig. 9) evolve coherently with the compressibility curves of the components between the stiffer pellet and the more compressible granular bentonite (Fig. 10a).
<figure><img src="image_12.png" /><figcaption>Fig. 9. Experimental and numerical compressibility curves on loading one-layer mixture arrangements at different orientations of the pellets (0° and 90°). Pictures before and after loading.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 10. a) Evolution of the axial strain on oedometer loading emulating pellet and granular bentonite components. b) Fitting of Young's moduli as a function of the void ratio for different components (pellet and granular bentonite), mixtures at different pellet orientations and zones in a pellet (caps and core).</figcaption></figure>

At any known stress-strain point (ε₁, σ₁) on the compressibility curve, Young's modulus, E(ε₁, σ₁), was determined by the following expression considering a representative Poisson's ratio ν (Table 3)

$$E(\varepsilon_1, \sigma_1) = \frac{\Delta\sigma_1 (1 + \nu)(1 - 2\nu)}{\Delta\varepsilon_1 (1 - \nu)} \quad (6)$$
A bilinear model of E(e) is proposed based on the conventional definition of the logarithmic relation for the tangent coefficient of compressibility

$$ \frac{\Delta\sigma_1}{\Delta\varepsilon_1} = \frac{(1 + e_0)}{\lambda}\sigma_0\exp\left(\frac{e_0 - e}{\lambda}\right) \quad (7) $$

where e₀ is the void ratio at a reference stress σ₀, and λ is the mean slope of the compression line in a natural logarithmic scale. The fitted E values in Table 3 were estimated with the maximum value of the two fitted curves in Fig. 10b given by E(e) = max{E₁(e), E₂(e)}. E₁ fitted the experimental data of the denser material, i.e. the compressed bentonite material in the pellet core and caps, whereas E₂ best fitted the looser packing data corresponding to granular bentonite.

The obtained experimental E values from compressibility tests were significantly lower than Young's moduli, around 600 to 800 MPa, measured from uniaxial compression tests on bentonite pellets with initial void ratio 0.37–0.46 and total suction 89–114 MPa (Darde et al., 2018; Yang et al., 2022). At high suction values, the resulting high stiffness of the pellets (modelled as identical spheres with Hertzian contacts) may have contributed to an overestimation of E, as well as to the initial sharp increase of the swelling pressure under hydration in the DEM simulations reported by Darde et al. (2021). In this work, E moduli estimated from experimental data and included in the DEM model of a pellet as a clump of spheres yielded closer approximations to the measured one-layer pellet compressibility curves.

## 5. Summary and conclusions

This paper presented a combined experimental and numerical study delving into the compression behaviour on loading under laterally confined conditions of well-arranged bentonite pellets and binary mixtures (comprising 80 % pellets and 20 % granular bentonite in mass). Two different orientations of pellets at approximately the same initial dry density, coordination number and initial water content conditions were explored in a single layer of pellets with and without granular bentonite filling to account for potential heterogeneity during pouring.

The oriented fissuring of the pellets, which originated on the unloading stage after static compaction and enhanced subsequently on some water absorption, affected the compressibility of the single-layer pellet skeleton. To comprehensively characterise this fissuring, the microstructure of the pellet was quantified using various techniques at different scales. The pore size density function obtained by mercury intrusion porosimetry was complemented by X-ray computed tomography, revealing the presence of fissures with a dominant pore size of approximately 20 µm at the transition between the techniques and consistent with scanning electron microscope observations. Moreover, µ-CT analyses showed variations in dry density throughout the pellet height (between 1.80 and 2.00 Mg/m³ at the pellet's top and bottom caps and between 2.00 and 2.08 Mg/m³ in the central quasi-cylindrical core).

Distinct initial and final stages were identified throughout the loading process, influencing the stiffness evolution, particularly contingent on pellet orientation. During the initial loading stage (vertical stresses <2 MPa), orthogonally-oriented pellet arrangements (P90°) exhibited higher Young's moduli than axis-oriented pellet arrangements (P0°). This disparity in compressibility was attributed to pellet fissuring orthogonal to the loading direction on fabrication. However, during the final loading stage, the elastic moduli of P90° pellets decreased compared to P0° pellets. This phenomenon was linked to pellet breakage, exacerbated by reduced confinement in P90° arrangements, which presented larger voids than in P0° arrangements. The one-layer pellet mixture responded similarly in the initial and final loading stages. Still, it demonstrated higher Young's moduli than the respective one-layer pellet arrangements and higher vertical stresses on the transition between loading stages (5–6 MPa) due to the granular

bentonite filling the inter-pellet voids.

The discrete element method DEM explicitly included pellet anisotropy and heterogeneity by modelling the pellet as a clump (a deformable nonspherical packing of rigid spheres) with a heterogeneous void ratio of the core and caps according to the observed pellet dry density profiles. The heterogeneity of the pellet was also considered in terms of the mechanical properties of the core and cap materials following a bilinear model of elastic moduli with varying void ratios. A cohesive damage DEM model with six mechanical parameters effectively replicated the overall deformation behaviour of one-layer pellet arrangements and the enhanced stiffness response in mixture samples. Furthermore, the model predicted the intersection of compressibility curves for arrangements at 0° and 90°, driven by clump breakage at higher vertical stress levels.

In summary, this study shed light on the anisotropic compressibility of well-oriented pellet-based mixtures at the same conditions regarding dry density and pellet coordination number, impacting our current understanding of these mixtures used in sealing systems for deep and long-term disposal of radioactive wastes. Therefore, this investigation has implications for the in situ performance of well-arranged pellet-based mixtures, installed layer by layer to ensure controlled dry-density conditions.

### CRediT authorship contribution statement

Arisleidy Mesa-Alcantara: Writing – review & editing, Writing – original draft, Visualization, Methodology, Investigation, Formal analysis, Conceptualization. Enrique Romero: Writing – review & editing, Writing – original draft, Supervision, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Conceptualization. Joel Torres-Serra: Writing – review & editing, Writing – original draft, Visualization, Software, Methodology, Investigation, Formal analysis. Nadia Mokni: Writing – review & editing, Methodology, Investigation, Funding acquisition, Conceptualization.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Enrique Romero Morales reports financial support, article publishing charges, equipment, drugs, or supplies, and travel were provided by Institute of Radiation Protection and Nuclear Safety. Enrique Romero Morales reports financial support, article publishing charges, equipment, drugs, or supplies, and travel were provided by Spanish Ministry of Science. Joel Torres-Serra reports financial support was provided by Spanish Ministry of Science. Arisleidy Mesa-Alcantara reports financial support was provided by Institute of Radiation Protection and Nuclear Safety. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Data availability

Data will be made available on request.

### Acknowledgements

The authors thank the financial support of ‘Institut de Radioprotection et de Sûreté Nucléaire’ IRSN (France) through different collaboration agreements with CIMNE (Spain) within the context of the VSEAL Project ‘Long-term performance of vertical sealing systems and impact of gas migration’ (2016-2023). The second and third authors also thank project PID2022-141429OB-I00, funded by the Spanish Ministry of Science/Research Agency MCIN/AEI/10.13039/501100011 033/FEDER EU (2023-2027) and the Spanish Ministry of Universities, who awarded the third author a ‘Margarita Salas’ post-doctoral
fellowship (2022-2024).

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