An elastoplastic model of bentonite free swelling
Introduction
Because of the physical and chemical properties of bentonite clays, they have been considered in several countries for use as buffer and backfill materials in spent nuclear fuel repositories. Specifically, in the KBS-3 disposal concept (developed by the Swedish nuclear fuel and waste management administration, SKB, 1999, and by Posiva, 2006, the Finnish expert organisation responsible for the spent nuclear fuel repository), dry Na-bentonite of the Wyoming type (called “MX-80”; see Karnland et al., 2005, Dueck and Nilsson, 2010) is considered for placement around high level radioactive waste (HLW) canisters in a highly compacted state. A reliable model of the behaviour of these bentonites is needed to assess the safety performance of the barrier. For this purpose, the model should characterise the bentonite free swelling (FS) associated with erosion (see, for instance, Birgersson et al., 2009, Moreno et al., 2010), a process of special interest in the field of designing HLW repositories.
Some authors have proposed sol–gel transition models to describe the soil behaviour close to this extreme situation (Liu et al., 2009). However, despite their value, at the present time these models are not able to describe the entire swelling process of bentonite, from an initial unsaturated (with values of suction on the order of tens to hundreds of MPa) and well structured (both micro and macrostructurally) state to the release of soil particles when it becomes a sol.
This study proposes an elastoplastic formulation that contributes to the characterisation of the saturated and unsaturated FS of bentonites. First, a review of its basic concepts will be presented. Afterwards, an analysis of its application to the simulation of FS is illustrated by several examples.
Section snippets
Theory (1): basis
Since the seminal work of Collins and McGown (1974) and Collins (1984), a number of researchers have observed the existence of two structural levels in compacted clays (Pusch, 1982, Romero et al., 1999, Pusch and Moreno, 2001, Lloret et al., 2003, Romero and Simms, 2008). Thus, the structure of the bentonites analysed in this paper is idealised into two structural levels: macro and micro structures. The microstructural level is associated with both intersheet voids and intra-aggregate pores
Theory (2): propose free swelling as a plastic mechanism
According to Fig. 2 and Eq. (1), the swelling (negative volumetric strains, following the Soil Mechanics signs convention) of the microstructure causes negative plastic volumetric deformations of the macrostructure. Therefore, according to the hardening law (Alonso et al., 2011):microstructural swelling would cause a decrease in the saturated pre-consolidation stress pO⁎, that is, a macrostructural softening. In Eq. (8), e is the total void ratio (e = total volume of voids in
Results and discussion
To study the effect of f2, the first step was to analyse three FS tests carried out in the laboratories of B + Tech in Helsinki, Finland. They used natural MX-80 bentonite samples that were hydrated with de-ionised water (see Sane et al., 2013). Dueck and Nilsson (2010) present a detailed description of the material. The general configuration of the tests is described in Fig. 7. The initial height of the sample was 15.85 mm in test T1, 8.80 mm in test T2 and 40.00 mm in test T3. In all three tests,
Conclusions
The application of an elastoplastic model for the simulation of free swelling (FS) processes in bentonite is reviewed. The inclusion of the kinetics of the water mass exchange process between the macrostructure and the microstructure in the model is advisable. This addition, see Eq. (7), makes it is possible to obtain simulation results that have an evolution that is not only controlled by the advancing macrostructural saturation front.
However, while the inclusion of the water mass exchange
Acknowledgements
This research was financed in part by B + Tech Oy (Finland) under a Posiva Oy project and by the FPU Grant AP2009-2134 of the Spanish Ministry of Education awarded to Dr. Asensio. In addition, the authors gratefully acknowledge the financial support provided by the Spanish Ministry of Economy and Competitiveness in the frame of Innocampus Program 2010. Thanks are also given to Dr. Petri Sane and Dr. Olli Punkkinen for their collaboration in the experimental work.
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