The Callovo-Oxfordian (COx) claystone has been selected as the host formation for the French geological nuclear waste disposal project (Cigéo), if it is licensed. The COx layer is located 500 m below the ground surface and has a thickness of 150 m. An exhaustive characterisation of the host rock through laboratory investigations at the sample scale and field experiments performed at the Meuse/Haute-Marne Underground Research Laboratory (MHM URL) has revealed complex hydromechanical (HM) responses of this rock under loading representative of the disposal conditions. Several constitutive models have been proposed to describe the COx claystone behaviour based on characterisation data. This paper aims to review 35 years of developing constitutive models to describe the COx claystone behaviour for the Cigéo project design and optimisation. Two main modelling approaches, including intrinsic and non-intrinsic, have been considered to model the excavation-induced host rock response. The non-intrinsic approach consists of the introduction of excavation-induced fracture zones or excavation disturbed zones (EdZ) with properties less favourable than the intact rock into the model geometry. Both the EdZ and the intact rock are usually described by isotropic models. The predefined EdZ helps to reproduce the anisotropic responses to the excavation similar to the in-situ observation. The intrinsic approach uses phenomenological models to self-reproduce the rock response in comparison to laboratory and field observations. Phenomenological models can be divided into three categories: continuum-based, micromechanical-based, and discontinuity models. The continuum models are formulated via the macroscopic constitutive equations (e.g., elasto-visco-plasticity, damage, weakness plane, and their combinations) or through the variational principle for fracture mechanics (e.g., phase-field method). The micromechanical constitutive equations, including different features, such as elasticity, plasticity, viscoplasticity, damage, and non-saturation, are functions of porosity and inclusion fraction. The discontinuity models include the discrete element method (DEM) and constitutive models governing the behaviour of the blocks and interfaces between them. A modelling application to study the behavior of the GCS drift, within Mause/Haute-Marne Underground Research Laboratory, is considered to illustrate the capabilities of representative modelling approaches developed for COx claystone.

Pre-existing faults cross-cutting caprock formations constitute potential leakage pathways during geological CO(2)sequestration. When the fault filling material is calcite-rich, dissolution of the fault minerals is expected to occur causing the mechanical weakening of the fault or, even worse, its reactivation. In turn, these chemical-mechanical processes influence the distribution of pore pressure in the vicinity of the fault. Hence, a fully coupled approach including the chemically-induced alteration is necessary while investigating fault's mechanical stability. In this paper, we present a simplified set of equations that allows the resolution of the coupled hydro-chemo-mechanical problem of reactive fluid flow inside a fault. Empirical relationships are used to describe the change of the fault's material mechanical properties with porosity. The derived model was used to simulate the evolution of the hydro-chemo-mechanical behavior of a fault following an expected leakage scenario during CO(2)storage in the Dogger formation in the Paris Basin. The simulation results showed that under normal conditions, fault reactivation is unlikely to happen even in the long term (similar to 100 years). Nevertheless, the proposed model is capable of capturing the evolution of fault reactivation and has the potential to become a useful element of the toolbox for assessing the risks related to fault reactivation and leakage for CO(2)storage projects.

In this analysis study, based on the recognition that the primary volume loss in the construction of the shield tunnel is caused by the tail void gap between the segment lining and the ground skin, the tail void gap is modeled as an interface element to analyze the effect of segment lining by stiffness values and spacing 'e' of the interface. These results were evaluated by the member force analysis of a lining and the Convergence Confinement method. If the larger the gap between the tail void interface between the segment lining and the ground and the lower the stiffness value, even if the gap grouting process and the installation of the segment are performed simultaneously, the support stiffness of the actual segment lining is expressed afterward the stiffness combination of the segment lining and the interface. In conclusion, this analysis is required to control the load on the lining.

This study considers the fluid flow through a porous formation containing discontinuities (fault, fracture, crack, microcrack), which is usually much more conductive than the surrounding matrix. The discontinuity is mathematically represented by a 1D smooth function of curvilinear abscise and physically characterized by its aperture. Fluid flow is assumed to obey Poiseuille's law in the discontinuity and Darcy's law in the parent porous rock. The solution for the fluid potential within a finite fractured porous medium is established under a singular integral equation form. Explicit solutions of flow and pressure field around a superconductive discontinuity within an infinite matrix with an anisotropic permeability, are derived by a development of a singular integral in a conventional Cartesian coordinate system. The solution shows that the fluid flow transported by a single crack only depends on the determinant of permeability tensor of the host rock but not on its components. A numerical simulation is performed to show that this result is also true for the discontinuity with a finite conductivity. The case of pressurized crack is also considered, discussed and compared to available numerical solutions in the literature.

Crack propagation associated with two initially symmetrical cracks located at the interface between an inclusion and the surrounding matrix, subjected to remote traction, is studied by means of Griffith’s energy criterion within the framework of linear elastic fracture mechanics. Using Muskhelishvili’s method of complex potentials, we derive semi-analytical expressions of the stress intensity factor and energy release rate at the crack-tip. Based on these results, we discuss the mode of propagation of the cracks. Our analysis points at the possibility of a single-sided, rather than simultaneous, symmetric crack growth, even if both initial configuration and loading are symmetric.

The viscoplastic behavior of coarse and bimodal fine/ultrafine grained (F/UFG) Al5083 alloy was investigated between 20 °C and 200 °C through tensile tests at various strain rates, and stress relaxation tests to deduce the strain rate sensitivity (SRS). The plastic strain fields were measured by correlation of SEM images. In the F/UFG material at high temperature, very high strains were measured in shear bands which sometimes crossed the whole gage width and exhibited intensive grain boundary sliding (GBS). Both the SRS and ductility rose with the temperature, and as the strain rate decreased, mainly due to a rising contribution of GBS, which accommodated a much larger fraction of the global strain in the F/UFG material. The boundary between the temperature–strain rate domains where grain refinement led either to strengthening or to softening was determined. Finite element simulations of tension and relaxation tests with viscoplastic grains and sliding grain boundaries captured the macro-scale behavior of the F/UFG material. It also provided some insight into the mechanisms of correlated and cooperative GBS and grain rotation along percolation paths (both inter and intragranular), probably, responsible for macro shear banding.

Argillaceous rocks are chosen as possible host rocks for underground radioactive nuclear waste disposal. These rocks exhibit complex coupled thermo–hydro–chemo-mechanical behavior, the description of which would strongly benefit from an improved experimental insight on micro-scale. In this work we present some recent observations of the evolution of these rocks upon swelling on the scale of their composite microstructure, essentially made of a clay matrix with embedded grains of calcite and quartz with sizes ranging from a few to several hundreds of micrometers. The micro-scale experimental investigation was based on the combination of high definition and high resolution imaging in an environmental scanning electron microscope (ESEM) and digital image correlation techniques. Samples were held at a constant temperature of 2°C while the vapor pressure in the ESEM chamber was varied from a few to several hundreds of Pascals, generating a relative humidity (RH) ranging from about 10% up to 99%. Results on micro-scale showed strongly heterogeneous deformation fields, which result from complex hydromechanical interactions between different components of argillaceous rocks. The swelling of argillaceous rocks is moderate at low RH but becomes significant at high RH. The observations demonstrated that the nonlinearity is related not only to the micro-cracking upon wetting, but also to the nonlinear swelling of the clay matrix itself that is governed by different mechanisms.

Combining environmental scanning electron microscopy (ESEM) and digital image correlation techniques, the mechanical behaviour of mudstones is studied at the scale of their composite microstructure (that is, grains of carbonate and quartz embedded in a clay matrix). A specially designed apparatus is developed to allow in-situ uniaxial compression tests on samples with controlled humidity states in the ESEM chamber. As the mechanical behavior of mudstones is sensitive to water content, two tests on samples with contrasting water contents (3.8 and 7.4 %) are performed to identify the unified mechanisms of deformation and damage. We illustrate heterogeneous local strain fields that well correlate with the microstructure of mudstones. Three types of deformation bands involving different mechanisms have been classified: orthogonal (compaction of macro-pores and closure of pre-existing cracks), parallel (micro-cracking) and inclined (shear deformation) to the uniaxial compression direction. These deformation modes are activated at different stress levels, and they strongly interact: for instance, a high-strained shear band may result in tensile micro-cracks at its tip. We also illustrate damage phenomena, particularly at the inclusion-matrix interface, which is found to be a hazardous position for nucleation of micro-cracks.

Underground salt cavities used for compressed air energy storage undergo cyclic loads and are subject to a fatigue phenomenon that reduces rock strength and stiffness. Understanding such behaviors and developing relevant constitutive models require a micro-mechanical analysis. This study investigates damage and fatigue in salt rock, the extent of which is influenced by its polycrystalline nature, on the basis of self-consistent upscaling approaches for viscous heterogeneous materials. We develop a model that treats monocrystals as spherical inclusions embedded in an infinite homogeneous matrix with purely elastic inclusion-matrix interactions. To predict grain breakage and its subsequent impact, we also introduce a failure criterion. The model provides micro-mechanical interpretations of the common viscoplastic and fatigue behavior of salt such as damage and accelerated creep from grain breakage and the shakedown effect observed in elastoplastic media. Finite Element (FE) simulations confirmed the macrostrain and microstress predictions obtained by homogenization. The FE program will be used in future studies to simulate inter-granular fracture propagation. This study provides new perspectives on research pertaining to the microscopic origin of fatigue in viscous polycrystalline materials.

SUMMARY This paper deals with analytical and numerical modelling of the internal stress generated in argillaceous rocks during humidification/desiccation processes, which is an essential issue for damage study. This local stress field arises from two mechanisms: (i) complex interactions between free swelling/shrinking clay matrix and non‐strained inclusions of carbonate and quartz and (ii) a self‐restraint effect induced by the moisture gradient during the transient moisture exchange process. The inclusion–matrix interaction is investigated in different cases. Firstly, the analytical solution of the stress around a cylindrical inclusion embedded in an infinite swelling matrix is derived: The inclusion would suffer tension (compression) under humidification (desiccation), and the resulting cracking patterns are discussed. Then, the problem of two inclusions with different distances in an infinite swelling matrix is considered, and it is shown that the local stress around an inclusion will be perturbed and amplified by neighbouring inclusions. Finally, an inclusion outcropping at the free surface of a swelling matrix is modelled as to investigate the effect of free surface: The inclusion–matrix interface undergoes shear stresses of which the maximum is found at the free surface. In addition to the inclusion–matrix interaction, the self‐restraint effect is investigated: The induced stress is maximal at the beginning of humidification/desiccation processes and vanishes gradually with time. The quantity of the self‐restraint stress is strongly controlled by the hydric loading rate. Copyright © 2014 John Wiley & Sons, Ltd.

The stress intensity factor at a fracture tip in a porous medium subjected to a fluid injection is studied. This factor evolves during the transient flow phase and tends to a limit value for the steady state. For simple fracture geometries, the finite element simulations show that for constant injection pressures this factor reaches its maximum value in the steady state regime. This result allows simplifying significantly the study and modeling of hydraulic fracture propagation because the determination of the steady flow solution is much easier and faster than the transient flow. In addition, some couplings between hydraulic and mechanical problems disappear under steady state flow and make it possible to establish some closed-form approximate expressions. These can be useful especially in the context of CO2 sequestration projects where the fluid injection is pressure-controlled.

A possible risk of geomechanical nature related to deep injection of CO2 is the shear reactivation of faults, hence potentially leading to the creation of new leakage pathways and eventually inducing earthquakes felt at the surface. Current practices to evaluate fault stability in the domain of CO2 storage still remain limited regarding two issues: 1. Faults are complex and heterogeneous geological systems, which do not correspond to discrete surfaces as already postulated by many authors. Reservoir-scale faults in a priori low-deformed reservoirs targeted for CO2 storage can present high complex architecture, which might influence the hydro-mechanical behaviour of the fault system; 2. Chemical interactions (dissolution and precipitation processes, chemically-induced weakening, etc.) between CO2-enriched brine and the minerals constituting the fault zone can affect the mechanical stability and the transport properties of the faulted/fractured system. The research project FISIC (www.anr-fisic.fr, funded by the French National research Agency) intends to overcome those limitations by accurately modelling the hydro-chemo-mechanical complexity of a fault zone. The main goal is to improve the stability analysis of a fault both undertaking pressure increase and alteration due to the presence of an acidic fluid. The progress of this research project is presented here.

An equivalent continuum model (ECM) is proposed in order to represent the hydromechanical behaviour of the fractured excavation-damaged zone (EDZ) around deep underground galleries excavated in claystone. The fractures observed in these galleries show a regular trend that makes a possible elaboration of the ECM based on theoretical homogenization methods. The ECM that is first established for plane fracture surfaces is then extended to curved, conical shape fracture surfaces based on some simplification assumptions. Stress and displacement fields have been compared around the EDZ by using the ECM in a numerical simulation or by introducing the fractures individually as discontinuities in the model. The results show that although the size of the EDZ is too small compared with that of the representative elementary volume considered in homogenization approaches, the ECM obtained in this way seems to reproduce a well fractured EDZ behaviour.

During tunnel excavation, stress redistribution produces plastic deformation and damage around the opening. Moreover, the surrounding soil can be either saturated or unsaturated. Suction has a significant influence on the mechanical behaviour of geomaterials. Depending on their stress state and on their moisture content, clay-based materials can exhibit either a ductile or a brittle behaviour. Plasticity leads to permanent strains and damage causes the deterioration of the soil elastic and hydraulic properties. The damage-plasticity model proposed in this work is formulated in terms of a damaged constitutive stress, defined from the principle of Bishop's hydro-mechanical stress (for unsaturated conditions), and from the principle of damaged effective stress used in Continuum Damage Mechanics. The evolution laws are obtained by using the principle of strain equivalence. This hydro-mechanical damage-plasticity model was implemented in a Finite Element code. The excavation of a tunnel is simulated at different constant suctions. The results obtained illustrate the influence of suction on the development of plastic and damaged zones.

In this paper, theoretical and numerical formulations of plane steady-state fluid flow in a fractured porous rock are used to investigate its effective permeability.If the far field inflow is uniform, the theoretical solution shows that the pressure field in the matrix is a function of the discharge in the fracture network.A numerical resolution based on singular integral equations is employed to derive the general problem of many intersected fractures in order to obtain the pressure field in anisotropic matrix.This solution allows computing the flux in the fractures which is the key issue for upscalling the equivalent permeability.This paper presents in detail the method for deriving the equivalent permeability from this solution.This method is applied to two real cases: an Excavation Damage Zone (EDZ) around a deep underground gallery and a geological rock formation presenting several families of fractures.The results of the both cases show that the developed method provides an easy and efficient way to determine the equivalent permeability of the fractured porous rock medium.This equivalent permeability can be implemented in analytical and numerical tools for continuous media towards estimating the flow characteristics in the rock formation.