A time-dependent anisotropic model for argillaceous rocks. Application to an underground excavation in Callovo-Oxfordian claystone

doi:10.1016/j.compgeo.2016.11.004

Computers and Geotechnics

Volume 85, May 2017, Pages 341-350

https://doi.org/10.1016/j.compgeo.2016.11.004 Get rights and content

Abstract

The paper presents a constitutive model for argillaceous rocks, developed within the framework of elastoplasticity, that includes a number of features that are relevant for a satisfactory description of their hydromechanical behaviour: anisotropy of strength and stiffness, behaviour nonlinearity and occurrence of plastic strains prior to peak strength, significant softening after peak, time-dependent creep deformations and permeability increase due to damage. Both saturated and unsaturated conditions are envisaged. The constitutive model is then applied to the simulation of triaxial and creep tests on Callovo-Oxfordian (COx) claystone. Although the main objective has been the simulation of the COx claystone behaviour, the model can be readily used for other argillaceous materials. The constitutive model developed is then applied, via a suitable coupled hydromechanical formulation, to the analysis of the excavation of a drift in the Meuse/Haute-Marne Underground Research Laboratory. The pattern of observed pore water pressures and displacements, as well as the shape and extent of the damaged zone, are generally satisfactorily reproduced. The relevance and importance of rock anisotropy and of the development of a damaged zone around the excavations are clearly demonstrated.

Introduction

Argillaceous rocks and stiff clay formations have great potential as possible geological host medium for radioactive waste. These materials have low permeability, significant retardation properties for radionuclide migration, no economic value (with the exception of gas or oil shales) and they often exhibit a significant capacity of hydraulic self-sealing of fractures [1], [2]. Therefore, a proper understanding and an appropriate modelling of their hydromechanical behaviour are of immediate interest. Although there are notable differences between different argillaceous formations [3], [4], reflecting their various origins and geological histories, there are also a number of common key features (e.g. time-dependent behaviour, anisotropy, some degree of softening, variation of permeability with damage) [3], [5], [6], [7] that should be considered in any description of their behaviour.

There have already been quite a number of proposals of constitutive laws that incorporate one or more of those features listed above. From a macroscopic point of view models based on plasticity [8], [9], [10], [11], [12], [13], [14] or coupled damage-plasticity [15] have been widely employed. Also, combined micro- and macro-mechanical approaches have been recently applied via homogenization techniques [16], [17]. All of these models are capable of reproducing a post peak brittle behaviour and some of them also incorporate other features like time dependency [14], [17].

The work presented in this paper has been developed in the context of the activities being carried out in the Meuse/Haute-Marne (MHM) Underground Research Laboratory (URL), located in Eastern France near the town of Bure, constructed and operated by the French national radioactive waste management agency (ANDRA). It consists of two shafts (an access shaft and a ventilation shaft) and a network of drifts, excavated at a depth of 490 m, in which several in situ experiments have been performed [18]. The facility is excavated in Callovo-Oxfordian (COx) claystone, an argillaceous rock that has been intensively studied in recent years [19]; some reference properties are shown in Table 1. Laboratory studies have revealed, among others, the following features of behaviour:

•
Anisotropy of strength and stiffness in the directions parallel and orthogonal to the bedding planes.
•
Significant stress-strain nonlinearity and plastic strains prior to peak strength, with a yield limit identified at about 50% of the maximum deviatoric stress.
•
A quasi-brittle behaviour at the in situ stress range, with a significant strength loss after the peak deviatoric stress.
•
Creep deformations with increasing strain rates for higher deviatoric stresses.

In this paper, a constitutive model is described aimed to reproduce the main features of behaviour of the COx claystone as listed above. Specifically, it incorporates strength and stiffness anisotropy, nonlinear isotropic hardening to account for plastic deformations prior peak strength, softening behaviour after peak, a non-associated flow rule, time-dependent deformations and dependency of permeability on irreversible strains. Although the main objective has been the simulation of the behaviour of the COx claystone, the model can be readily applied to other argillaceous materials since they usually exhibit, as pointed out above, similar features of behaviour.

The constitutive law developed has then been applied to the simulation of an underground excavation in the MHM URL. The work has been developed in the context of the “Transverse Action” benchmark programme [20]. Although all the calculations requested have been performed, for space reasons only the analysis corresponding to the hydromechanical modelling excavation of the GCS drift are reported here as it is the more fully instrumented case. Also, the GCS drift is aligned with the major horizontal principal stress resulting in a nearly isotropic stress state in the cross-section perpendicular to the axis of the opening. Thus, in this case, the effects of material anisotropy can be readily identified.

Section snippets

Hydromechanical constitutive model

Both saturated and unsaturated conditions have been considered in the development of the model. As shown later, consideration of unsaturated condition provides a more realistic setting for modelling laboratory tests. Also, potential desaturation of the rock during excavation can then be readily accommodated in the analysis, if necessary. To this end, a generalized effective stress expression has been adopted: $σ^{'} = σ + S_{e} sB I$ where $σ^{'}$ is the effective stress tensor, $σ$ is the total stress tensor, S_e is

Simulation of COx claystone mechanical behaviour

The constitutive model above has been applied to the reproduction of triaxial and creep tests performed on COx claystone samples. Parameters derived from this exercise are later applied to the analysis of an underground excavation. In all cases (triaxial and creep tests), the major principal stress was orthogonal to the bedding planes of the sample. Due to deconfinement and sample preparation, the specimens became unsaturated with an associated suction that corresponds to a relative humidity of

Theoretical formulation

To apply the constitutive model to a boundary value problem, it was incorporated into a general coupled hydromechanical formulation that is briefly described here. The formulation is a particular case of the general formulation presented in [26] for non-isothermal conditions. Only two phases are considered, solid (s) and liquid (l), corresponding to the two species mineral and water. In this case, the relevant balance equations are:

Balance of solid, $\frac{\partial}{\partial t} [ρ_{s} (1 - ϕ)] + \nabla \cdot (j_{s}) = 0$

Balance of water mass, $\frac{\partial}{\partial t} ($

GCS drift excavation

The GCS drift was excavated at the −490 m level of the MHM URL in the location shown in Fig. 7. The drift alignment was parallel to the major horizontal principal stress. As a result, the state of stress perpendicular to the axis of the tunnel was practically isotropic with σ_v = 12.7 and σ_h = 12.4 MPa. The in situ pore water pressure at that level in zones not affected by excavations is 4.7 MPa. The drift section is circular with a 2.6 m radius and was excavated with a road header. The advances of the

Concluding remarks

This paper presents a constitutive model for argillaceous rocks, developed within the framework of elastoplasticity that includes a number of features that are relevant for a satisfactory description of their hydromechanical behaviour: anisotropy of strength and stiffness, behaviour nonlinearity and occurrence of plastic strains prior to peak strength, significant softening after peak, time-dependent creep deformations and permeability increase due to damage. Both saturated and unsaturated

Acknowledgements

The financial and technical assistance of ANDRA to the work presented is gratefully acknowledged. The first author has been supported by a Conacyt scholarship (Reg. No. 270190).

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Research PaperA time-dependent anisotropic model for argillaceous rocks. Application to an underground excavation in Callovo-Oxfordian claystone

Abstract

Introduction

Section snippets

Hydromechanical constitutive model

Simulation of COx claystone mechanical behaviour

Theoretical formulation

GCS drift excavation

Concluding remarks

Acknowledgements

Soils Found

Comput Geotech

Phys Chem Earth

Mech Mater

Phys Chem Earth

J Rock Mech Geotech Eng

The role of geotechnical engineering for nuclear energy utilisation

Environmental geotechnics and nuclear waste

On the hydromechanical behaviour of argillaceous hard soils-weak rocks

Shear strength and stiffness anisotropy of geologically aged stiff clays

Some properties of a heavily overconsolidated Oxford clay at a site near Bedford

Géotechnique

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Clays Clays Min

A constitutive model for structured soils

Géotechnique

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Can Geotech J

Research Paper
A time-dependent anisotropic model for argillaceous rocks. Application to an underground excavation in Callovo-Oxfordian claystone