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ht. J. Rock Mech. Min. Sci. & Geomeclt. Ahsrr. Vol. 32, No. 5. pp. 409434, 1995 Copyright ‘i: 1995 Elsevier Science Ltd 0148-9062(95)00033-X Printed in Great Britain. All rights reserved 0148-9062195 $9.50 + 0.00

Pergamon

Discrete and Continuum Approaches to Simulate the Thermo-Hydro-Mechanical Couplings in a Large, Fractured Rock Mass A. MILLARD? M. DURINT A. STIETELt A. THORAVALI E. VUILLOD$ H. BAROUDIS F. PLAS§ A. BOUGNOUX7 G. VOUILLET A. KOBAYASHIfl_ K. HARASf T. FUJITATS Y. OHNISHI& The study of coupled thermal, mechanical and hydraulic phenomena in fractured rock mass like granite is of major importance for underground wastes repositories. There exist two possible approaches to model a highly fractured rock mass: either represent each fracture individually or use an equivalent continuum. These two approaches have been compared in the frame of a bench mark test (BMTI) on an hypothetic regularly fractured medium hosting nuclear wastes. The methodologies, as well as the algorithms used by the various research teams who participated in the exercise, are presented in detail. The thermal and mechanical results compare rather well, while hydraulic results show pronounced dtyerences which can be partly attributed to the non-linear dependance of the fracture hydraulic conductivity in terms of the aperture.

NOMENCLATURE Physical parameters

Specified values

rock matrix density rock matrix specific heat rock matrix thermal conductivity rock matrix Young’s modulus rock matrix Poisson’s ratio rock matrix lineic thermal expansion coefficient normal stiffness of fractures

2670 kg/m3 900 J/kg/K 3 W/m/K 60,000 MPa 0.23 9.10-6/K 100 GPa/m

tCEA/DMT, CEN Saclay, 91191 Gif-stir-Yvette, France $INERIS, Part Saurupt, 54000 Nancy, France. §ANDRA, route du Panorama R. &human, BP 38-92266 Fontenayaux-Roses, France. IENSMP, 35 rue St-Honor& 77305 Fontainebleau, France. ttIwate University, Faculty of Agriculture, 3-18-8 Ueda, Morioka, Iwate 020, Japan. $$PNC, 4-33 Muramatsu, Tokai-Mura, Naka-Gun, Ibaraki, Japan. #ICyoto University, School of Civil Engineering, Sakyo, Kyoto 606, Japan.

shear stiffness of fractures tensile strength of fractures cohesion of fractures friction angle of fractures dilatancy angle of fractures distance between fractures thickness of fractures number of fractures initial hydraulic aperture of fractures hydraulic aperture of fractures residual hydraulic aperture of fractures maximum hydraulic aperture of fractures porosity density fracture permeability initial permeability of the medium dynamic viscosity of water =1/p& + QT - To)1 reference temperature reference dynamic viscosity of water coefficient water density

10 GPa/m 0 MPa 0.1 MPa 30’ 0, loom

293 K IO-’ N secjm’ 3.2 IO-?/K

MILLARD et al.:

410 Pw

PW” Il... ” KS? c, g S/dz BQ a

DISCRETE AND CONTINUUM

=P,Il - P,(T - T,)l

reference water density

1000 kg/m’ 6 x l0-4/K

coefficient

bulk compressibility modulus of water fluid heat capacity gravity acceleration geothermal gradient initial value of heat source exponent of decaying function damping coefficient

4200 J/kg/K 9.8 I m/se? O.O3”C/m 0.05 W/m’ O.O2/yr

Mathematical and physical symbols Kronecker’s symbol divergence operator gradient operator trace integration domain positive part of x time increment of time total stress field pressure field effective stress field: a;, = uij + pa,, strain field virtual strain displacement field velocity field acceleration field virtual displacement normal displacement of the fracture shear displacement of the fracture body forces external forces internal forces contact forces surface loads elasticity tensor rock matrix elasticity tensor temperature field volumetric heat source hydraulic head flow rate in a fracture hydraulic gradient Darcy’s velocity in a fracture prescribed flow rate at the boundary Note: In this paper, the usual mechanical sign convention is adopted, i.e. tensile stresses and strains are positive.

1. INTRODUCTION

THM APPROACHES

thermal (T), hydrological (H), mechanical (M), and chemical (C) processes. Coupled processes imply that one process affects the initiation and progress of another and therefore the rock mass response to waste storage cannot be predicted by considering each process independently. The overall objective of the DECOVALEX project is to increase the understanding of various thermo-hydromechanical processes of importance for waste storage and its influence on transport of radionuclides from a repository to the biosphere and how these processes can be described by mathematical models. The most important transport mechanism of radionuclides from a repository to the biosphere is through the groundwater present in the rock. The host rock, where the repository is located, will be subjected to in situ stresses, excavation-induced stresses and thermomechanical stresses resulting from radiogenic heat. These stresses can cause changes in hydraulic properties of the jointed rock masses and along the fracture zones. This could lead to changes in the groundwater flow pattern of the repository area. The bench mark test BMTl simulates the thermohydro-mechanical effects, in the geosphere, of an underground repository of high level nuclear wastes. A large scale (km) rock mass is considered, with a repository located at 500 m in depth. The model is bidimensional (vertical section) and measures 3000 x 1000 m. It contains two sets of intersecting fractures, a hydraulic head and an overburden load are laid down at the surface. The heat flux released by the storage decreases exponentially with time (Fig. 1). The complete specifications of the bench mark are given in Ref. [l]. They will be summarized hereafter for sake of completeness. The primary aim of this paper is to compare the predictions obtained by two different approaches in modelling the coupled THM response of a large fractured rock mass:

I. I. General Considerations

-a

The rock mass response to storage of radioactive waste and spent fuel may be a coupled phenomenon involving

discrete approach, where all the discontinuities are explicitly represented, with their individual THM properties

L70m j_

500m 4

w50,

I-

500) 1-1

3000m

Starting

point for fracture

i ry

_I

generation

Fig. I. Model geometry and fracture sets of the far-field THM model.

MILLARD

-a

et al.:

DISCRETE

AND

continuum approach where the discontinuities and the rock mass are represented by an “equivalent continuum”, with THM properties derived from specific homogenization techniques.

A discrete approach has been followed by the research teams of INERIS (France) and ENSMP (France), while a continuum approach has been used by KPH (Japan) and CEA/DMT (France) research teams. Clearly, the validation of the above two approaches should be done against experimental results for similar problems, but this question is beyond the scope of the present paper.

CONTINUUM

THM

specified, but the various research teams had to determine the corresponding fracture aperture according to their approach. The initial and boundary conditions are as follows: For thermal conditions, the initial temperature field shall be determined from specified boundary conditions such as a constant temperature at the top surface, a zero flux on the lateral boundaries, and a geothermal flux on the bottom surface corresponding to a thermal gradient aT/az. These conditions are depicted in Fig. 3. For mechanical conditions, the initial state of stresses is given as:

1.2. General Description of THA4 Couplings

In this paragraph, we describe the various aspects of THM couplings in general, although some of these couplings were not accounted for in the BMTl analysis. The general THM diagram is shown in Fig. 2. The various possible couplings are explained below, in relation with their symbols on the diagram: variations of solid properties with temperature induced thermal strains variations of thermal properties with mechanical strains heat produced by mechanical intrinsic dissipation variations of fluid properties with temperature heat convection by the fluid mechanical effect of fluid pressure variations variations of porosity and permeability. 1.3. Presentation of the Bench Mark Test Hypothesis

The rock matrix is supposed to be impervious and elastic, and having an isotropic behaviour. The water is flowing only in the fractures which are defined by two parallel, planar surfaces, with an effective hydraulic aperture. The mechanical behaviour of the fractures is described by a Mohr-Coulomb failure criterion with zero tensile strength. Darcy’s law is supposed to be valid for the flow. The thermal conductivity and expansion of the rock matrix are assumed to be isotropic, and heat is perfectly exchanged across the fractures. Due to the heat production, most of the parameters (permeability, porosity, etc.) of the equivalent rock mass will change with time. Their initial values are

r

I

0;: = -[lOOO -z for

Odx