Modelling the FEBEX THM experiment using a state surface approach

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Abstract

Buffer materials being considered as engineered barriers in nuclear fuel waste (NFW) disposal systems possess a pronounced nonlinear behaviour in the unsaturated state. In order to simulate such non-linear responses,the authors adopted an incrementally nonlinear poro-elastic approach where the coefficients of the governing equations are assumed to be functions of suction and the void ratio. These functions are in turn developed from a state-surface equation obtained from suction-controlled oedometric tests. In this paper we show the derivation of the governing equations of the poro-elastic model. A finite element computer code, FRACON, was developed by the authors to numerically solve the above equations. We first use the code to simulate laboratory tests to characterize the swelling properties of a typical bentonite. That same bentonite was used in the FEBEX in-situ heater experiment, conducted at the Grimsel site, Switzerland. The FRACON code was also used to perform blind predictions of the FEBEX heater experiment. It is shown that the model correctly predicts drying of the bentonite near the heaters and re-saturation near the rock interface. The evolution of temperature and the heater thermal output were also reasonably well predicted by the model. The trends in the total stresses developed in the bentonite were correctly predicted; the absolute values however were underestimated probably due to the omission of pore pressure build-up in the rock mass.

Introduction

Concepts for deep geological disposal of nuclear fuel waste (NFW) that are being studied in Canada and other countries rely on the host rock, on clay materials (buffer and backfill) and on the waste containers as barriers against contaminant migration to the biosphere. The focus of this paper is on the modelling of the buffer material. The radiogenic heat released from the waste container results in elevated temperatures around the container, creating a thermal gradient with the attendant thermal stresses and strains in the partially saturated buffer. This thermal gradient also causes moisture movement in the buffer through a diffusive process, resulting in drying near the canister and re-wetting near the buffer-rock interface. The buffer responds mechanically to that change in water content by either shrinking or swelling. These thermo-hydro-mechanical (THM) processes are strongly coupled, and highly nonlinear. In the last decade, much effort has been provided in the laboratory and in-situ experimentation in conjunction with the development of mathematical models to simulate the THM behaviour of unsaturated buffer material. The Kamaishi Mine project in Japan is one such example [1], [2], [3], [4], [5] of a comprehensive experimental and theoretical research program involving international cooperation. The FEBEX project [6] is another research project which was recently completed. The FEBEX in-situ experiment was performed in one section of a horizontal tunnel in a granitic rock formation at Grimsel, Switzerland. The tunnel section was provided with two heaters and filled with pre-fabricated bentonite blocks that were placed around the heaters. The THM response of both the bentonite and the surrounding rock was monitored during the experiment. The authors belonged to the Canadian team, among many international teams, participating in the prediction of the FEBEX experiment within the international DECOVALEX III Project. The present paper describes the development of our mathematical model to simulate the THM behaviour of the bentonite used in the in-situ heater experiment and summarizes the results of the model predictions of the THM response of the bentonite during the FEBEX in-situ experiment.

Section snippets

A brief overview of THM models for unsaturated clays

For completeness, we provide here a brief review of models that have been proposed for examining the THM behaviour of unsaturated clays. This review is by no means comprehensive; a more thorough discussion could be found in Rutqvist et al. [4].

Partially saturated clay materials are basically multiphase materials, consisting of the solid skeleton with a mixture of air and water flowing through the pore space. The air can be dissolved in the liquid water, or be present in a gaseous state; the

Governing equations of the model

The governing equations of the mathematical model developed by the authors are derived from energy balance, mass balance and momentum balance considerations.

THM properties of the FEBEX bentonite

The FEBEX bentonite is a Spanish clay considered as the most suitable material for sealing and backfilling of NFW repositories for the Spanish concept [6] for the following reasons: it has a very high content of montmorillonite, low permeability and good retention properties, and is capable of developing large swelling pressures. The characteristics of the FEBEX bentonite are discussed in details in the reports produced by the Spanish research institutions CIEMAT and UPC-DIT [6], [7], [8], [9],

Simulation of laboratory experiments on FEBEX bentonite

In order to gain confidence in the THM model implemented in the FRACON finite element code, we have used the code to conduct computational simulations of two types of laboratory experiments. It is important to note that no parametric studies have been conducted, but rather, a direct prediction was carried out using the properties described in Section 4. The sources and justification for the values assumed for these properties were also detailed in Section 4.

Prediction of the bentonite response in the FEBEX in-situ experiment

The FEBEX gallery is circular in cross section, with diameter 2.28 m and length 70.4 m. It was excavated at a depth of approximately 450 m, in granitic rock. Two electrically powered heaters, with nominal diameter 0.9 m and length 4.54 m, were emplaced at the end of the gallery. Blocks of compacted bentonite were emplaced around the heaters to form a 17.4 m test section, isolated from the rest of the gallery by a concrete plug (Fig. 7).

The bentonite and heaters were installed between July 1, 1996 and

Conclusions

The FEBEX T-H-M experiment performed at the Grimsel site, Switzerland, is a valuable and important project which should lead to an improvement in the understanding of the behaviour of the bentonite barrier around heat-emitting nuclear fuel waste (NFW) containers. Such large-scale field experiments should always be undertaken with the simultaneous development of constitutive and computational models to interpret the experiments. In our contribution to this work, we have followed the process of

Acknowledgements

The authors sincerely thank the Canadian Nuclear Safety Commission (CNSC) for its financial support; ENRESA for providing experimental data from the FEBEX project; and colleagues in the DECOVALEX International cooperative project and the CNSC for fruitful cooperation, discussion and peer review of our work. The opinions expressed in this paper are those of the authors’ and do not necessarily reflect the opinions of the either the CNSC or McGill University.

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    Currently with ANDRA, Bure, France.

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