DEEP REPOSITORY R&D FOR RADIOACTIVE WASTE | ROCK TUNNELS


Constitutive Model for the Expansive Core The bentonite powder–pellets mixture is the current preferred material for the sealing core. The technical feasibility of implementing powder–pellets mixtures at large scale has been assessed in the framework of the European DOPAS project with the FSS experiment (Bosgiraud et al. 2015; Noiret et al. 2016). A mixture of 70% bentonite pellets and 30% bentonite powder was successfully installed with an average dry density of around 1500 kg.m-3


(reference value for the described


case). Gens and Alonso (1992) presented the conceptual


bases to model expansive soils, further implemented by Alonso et al. (1999) in the Barcelona Expansive Model (BExM) which has been successfully employed to simulate bentonite powder–pellets mixtures. It is adopted for the core material (Gens et al. 2011; Ruiz 2020). Two structure levels are distinguished in the BExM:


the microstructural level, at which swelling of active minerals takes place; and, the macrostructural level, responsible for major structural rearrangements. The coupling between these levels is accomplished through a strain coupling mechanism that accounts for the macrostructural strains that arise from the deformations that occur at microstructural level. Microstructural behaviour is assumed elastic and


volumetric. On the other hand, macrostructural behaviour is simulated through the Barcelona Basic Model (BBM) developed by Alonso et al. (1990). The stress–strain relationships of the BBM model are established in an elasto-plastic framework. The key element of the BBM is the Loading-Collapse


(LC) mechanism given by the dependency of the yield locus on suction. The direction of macrostructural plastic deformations


that develop is governed by the plastic flow rule. It is assumed that microstructural swelling and shrinkage affect the structural arrangement of the macrostructure, inducing irreversible deformations on the soil structure. To represent such phenomena, a micro–macro


coupling mechanism is introduced defining the increment of volumetric plastic strain. It allows for the macrostructure experiencing irreversible strains when the microstructure swells or shrinks, but activation of the LC surface does not affect the microstructure. Alonso et al. (1999) proposed different coupling


functions depending on whether it is a wetting or drying path. Since only wetting paths are expected in these simulations, only one coupling function is adopted. The hardening rule of the double structure


material is governed by the evolution of the saturated preconsolidation pressure, driven by the macrostructural volumetric plastic strain. In this way, the contributions of both plastic mechanisms (LC and micro–macro coupling) are considered. Finally, the model accounts for the possibility


of permeability reduction due to the decrease of macropores. An exponential law is adopted.


The swelling behaviour of the pellet–powder


mixture used in the FSS experiment was studied by Bernachy-Barbe et al. (2020). Figure 7 shows the results reported by these authors corresponding to constant volume swelling pressure tests carried out on samples at various dry densities ranging between 1200 kg.m-3 and 1600 kg.m-3


. An exponential fitting curve proposed


by these authors is presented. An increase in swelling capacity with increasing dry density was observed, as well as significant loss of swelling potential with a relatively small loss of density. On average, a final swelling pressure of around 4 MPa was obtained for the samples with dry density similar to the FSS experiment, which is assumed as the target value for the case described. Other experiments carried out with this kind of


mixture systematically show that swelling potential of bentonite powder–pellets mixtures strongly depends on material dry density (Imbert and Villar 2006; Hoffmann et al. 2007). The parameters for the BExM were calibrated to reproduce this effect. For this purpose, five different constant volume swelling pressure tests were simulated, considering initial dry densities from 1300 kg.m-3


to 1500 kg.m-3 in 50 kg.m-3 steps. A comparison


between model results and experimental data are shown in Figure 7.


Constitutive Model for the Backfill Material The backfill material consists of disaggregated and recompacted COx claystone. It is to support the compression exerted by the concrete plugs when sliding under the pressure of the swelling core. The reaction of the backfill is governed by its own stiffness and strength, and is an important force component in the final mechanical equilibrium of the concrete plug. Because the backfill is initially unsaturated, BBM


is employed as constitutive law. The BBM is able to represent many of the fundamental features of the behaviour of partially saturated soils under compression, and allows consideration of possible irreversible deformations (collapse) during the hydration of the soil. For the sake of simplicity, since the expansive behaviour of the backfill material is limited, and reversible swelling deformations contemplated in the formulation of the BBM are neglected. Parameters for the backfill material were calibrated


reproducing oedometer tests performed for Andra by LAEGO- ENSG (Laboratoire Environnement, Géomécanique & Ouvrages—Ecole Nationale Supérieure de Géologie). Comparison between experimental results of a reference oedometer test reported by LAEGO-ENSG and the results obtained from the simulation are shown in Figure 8.


Constitutive Model for the Compressible and Concrete Lining The lining consists of two layers: the internal layer of B60 grade concrete (uniaxial compressive strength of 60 MPa); and, the external layer made from a compressible material formed from crushed COx claystone.


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