Modelling the behaviour of bentonite pellet-powder mixtures upon hydration from dry granular state to saturated homogeneous state
Introduction
Bentonite materials are considered as sealing materials in concepts of deep geological disposal for radioactive waste. These materials are characterised by a low permeability, good radionuclide retention capacity and ability to swell upon hydration. The latter feature allows these materials to fill technological voids and to exert a swelling pressure against the host rock, which confines the excavation damaged zone and thus reduces the fluid flow along the gallery via this zone.
Owing to operational convenience, pellet-based materials have been considered as an alternative to compacted blocks (Bernachy-barbe et al., 2020; Darde et al., 2018; Molinero-Guerra et al., 2017; Navarro et al., 2020a, Navarro et al., 2020b; Sánchez et al., 2016). The material is installed in the galleries in a dry state as a granular assembly. Upon hydration by the pore water of the host rock, the granular material progressively becomes homogeneous. Before homogenisation, the mechanical behaviour of the material is controlled by its granular nature. In fully saturated conditions, the material has totally lost its initial granular structure. Its structure in these conditions is similar to fully saturated compacted blocks (Hoffmann et al., 2007; Imbert and Villar, 2006; van Geet et al., 2005). The behaviour of pellet-based materials is thus controlled by different mechanisms depending on the hydration state.
In mixtures of pellet and crushed pellets (powder), powder fills inter-pellet voids, increasing the total dry density of the sealing material thus its final swelling pressure (Imbert and Villar, 2006; Kaufhold et al., 2015; Lloret et al., 2003; Wang et al., 2012). Considering these mixtures as sealing materials involves challenges. For instance, powder in the inter-pellet porosity may migrate during installation and induce local heterogeneities of density. In addition, depending on the density of the powder phase, this latter can be considered to either participate in the macroscopic mechanical response, or to leave the mechanical behaviour controlled by the pellet assembly.
Existing modelling frameworks do not account for these particular features of pellet-powder mixtures. It is proposed in the present study to: (i) provide experimental evidence of the influence of the granular structure on the macroscopic response of the mixture upon hydration; (ii) use Discrete Element Method (DEM) to study the intrinsic behaviour of pellet assemblies; (iii) propose a conceptual model, based on DEM results and modified existing modelling frameworks, able to satisfactorily reproduce the main features of pellet-powder mixtures upon hydration.
In this respect, the present study is organised as follows. First, swelling pressure tests are carried out in the laboratory on three pellet-powder mixtures, with identical pellet volume fraction and various powder volume fractions, to highlight the influence of the granular structure on the material behaviour. Experimental results are discussed and a conceptual interpretation of the behaviour of pellet mixtures is proposed. Then, DEM simulations are performed to model large pellet assemblies and determine constitutive laws. An elasto-plastic model, based on DEM results and a modified formulation of the Barcelona Basic Model (BBM) (Alonso et al., 1990) is then proposed to describe the hydromechanical behaviour of pellet-powder mixtures in granular and continuous states. The swelling pressure tests are finally simulated using the proposed model.
Section snippets
Tested materials
Pellets are made of MX80 bentonite. Pellets are composed of a cylinder-shaped part with two spherical caps at both ends (Fig. 1). Pellet geometrical properties and physical properties are presented in Table 1.
The material referred to as “powder” is obtained by crushing pellets. Initial suction of the powder is 180 MPa. The average grain diameter of the powder is 0.65 mm (Molinero-Guerra et al., 2017).
Three pellet-powder mixtures are prepared at the same pellet volume fraction and three
Objectives
Existing modelling framework used to describe the behaviour of compacted bentonite materials do not account for the features described in the previous section. Since the pellet assembly can control the mechanical response of the material if Φ2 is below a threshold value, it is proposed in the present section to study the mechanical behaviour of pellet assemblies with no powder.
In this respect, DEM is used to address the mechanical behaviour of pellet assemblies from the mechanical properties of
Conceptual approach
This section presents a conceptual model able to describe the hydromechanical behaviour of pellet-powder mixtures, accounting for relevant features such as a free swelling phase for the powder, influence of granular structure, influence of pellet strength, transition to a continuous state. The approach is based on the scheme presented in Fig. 6.
Following this approach, the material is considered to be either “granular” or “continuous”. In the granular domain, the mechanical behaviour is
Simulations of swelling pressure tests
The model is implemented in the open source finite element method (FEM) code Bil developed by Dangla (Dangla, 2018). The swelling pressure tests carried out in the laboratory are simulated using the model to assess its ability to reproduce the behaviour of pellet-powder mixture.
Distinction of two domains and transition criteria
A hypothesis of the model is the consideration of two distinct domains. The mixture is considered either granular, with powder having no contribution to the mechanical behaviour, or continuous, with pellet and power equally contributing to the mechanical behaviour.
The swelling pressure in SP15 test was very close to, but still slightly higher than, SP0a and SP0b swelling pressure. Even if moderate, powder may have an influence in “loose powder phase” mixtures in the granular domain. The
Conclusion
Bentonite pellet-powder mixtures are candidate materials for the sealing of galleries in radioactive waste disposal concepts. The mechanical behaviour of these materials is influenced by their initial granular structure and the density of the powder phase.
In the present study, swelling pressure tests have been carried out on three mixtures with the same pellet volume fraction and different powder contents. It was highlighted that the initial granular structure has no significant influence on
Funding
This work was funded by École des Ponts ParisTech and the French National Agency for Radioactive Waste Management (Andra).
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.
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