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International audience; Size-effect in concrete and other quasi-brittle materials defines the relation between the nominal strength and structural size when material fractures. The main cause of size-effect is the so-called energetic size-effect which results from the release of the stored energy in the structure into the fracture front. In quasi-brittle materials and in contrast to brittle materials, the size of the fracture process zone is non-negligible compared to the structural size. As a consequence, the resulting size-effect law is non-linear and deviates from the response predicted by linear elastic fracture mechanics. In order to simulate the size-effect, one needs to rely on numerical modeling to describe the formation, development and propagation of the fracture process zone. Although a number of models have been proposed over the years, it transpires that a correct description of the fracture and size-effect which accounts for boundary effects and varying structural geometry remains challenging. In this study, the Lattice Discrete Particle Model (LDPM) is proposed to investigate the effects of structural dimension and geometry on the nominal strength and fracturing process in concrete. LDPM simulates concrete at the aggregate level and has shown superior capabilities in simulating complex cracking mechanisms thanks to the inherent discrete nature of the model. In order to evaluate concrete size-effect and provide a solid validation of LDPM, one of the most complete experimental data set available in the literature was considered and includes three-point bending tests on notched and unnotched beams. The model parameters were first calibrated on a single size notched beam under three-point bending and on the mechanical response under unconfined compression. LDPM was then used to perform blind predictions on the load-crack mouth opening displacement curves of different beam sizes and notch lengths. Splitting test results on cylinders were also predicted. The results show a very good agreement with the experimental data. The quality of the predictions was quantitatively assessed. In addition, a discussion on the fracturing process and dissipated energy is provided. Last but not least, the Universal Size-Effect Law proposed by Bažant and coworkers was used to estimate concrete fracture parameters based on experimental and numerical data.

An Enhanced Geothermal System (EGS) can be thought of as an underground heat exchanger designed to extract geothermal energy. The performance of these systems can be improved by increasing permeability with hydraulic fracturing, following the same technique used for hydrocarbon reservoirs. To understand hydraulic fracturing, whether it is implemented in an EGS or in a hydrocarbon reservoir, it is important to know the fracture parameters of the rock at stake, e.g., the fracture energy. We report here the use of a method based on an energy balance during hydraulic fracture tests. Specimens were prepared and they have been mechanically and hydromechanically characterized at 20 oC and 100 oC, a temperature representative of actual reservoir conditions. The fracture energy is obtained from a balance of kinetic, potential and pressure energies involved in the hydraulic fracture tests. The method provides fracture energies that are consistent with the literature data on similar materials. It is also found that the fracture energy increases upon heating.

International audience; This paper addresses the calculation of the relative permeability of concrete and rocks with a model that is aimed at being implemented in large scale computations for evaluating the tightness of vessels. To this end, it is necessary to rely on some fast procedure and a random hierarchical capillary approach is used. It is based on the extension of an existing model proposed initially to describe the evolution of the intrinsic permeability of mortar undergoing micro-cracking. First, the efficiency of this existing model is tested on several types of concretes and rocks, with permeability spanning over 6 orders of magnitude. Then, the model is adapted to obtain the relative permeability to gas and liquid as a function of the saturation of the porous solid with respect to the liquid phase. The extended model is shown to provide reasonably accurate predictions for several concretes and rocks tested in the literature.

Submitted to the Journal of petroleum science & engineering; Dynamic excitation of a clogged fracture can increase its permeability. Pressure oscillations inside the fracture are expected to flush out the fine particles blocking the flow. The objective is to improve the performance of gas and oil wells by cleaning the fractures previously generated by hydraulic fracturing as the circulation of sediments during service tend to clog them. Yet, more investigations shall be conducted to understand the mechanism better. This experimental study investigates the unclogging process of a propped fracture previously clogged, using a synthetic dynamic load. Laboratory experiments are presented. Fractures are clogged with crushed natural sand. All the permeability measurements are performed under uniaxial stress of 20 MPa to mirror real operating conditions. After applying the dynamic load, a significant increase of the intrinsic permeability is observed. The highest recovery rate reached was 82%. The influence of the proppant density, of the proppant size, and of the frequency of the dynamic signal are discussed. X-ray CT scans provide images of the fracture before and after the dynamic load has been applied. The results show that a high percentage of fines are flushed out of the fracture.

In materials with a strain-softening characteristic behavior, classical continuum mechanics favors uncontrolled strain localization in numerical analyses. Several methods have been proposed to regularize the problem. Two such localization limiters developed to overcome spurious instabilities in computational failure analysis are examined and compared. A disturbance analysis, on both models, around an initially homogeneous state of strain is performed to obtain the closed-form solution of propagating wave velocities as well as the velocities at which the energy travels. It also shows that in spite of forcing the same stress-strain response on both models, the wave equation does not yield similar results. Both propagations of waves are dispersive, but the internal length of each model is different when equivalent behavior is desired. In fact, the previously suggested derivations of gradient models from nonlocal integral models were not completely rigorous. The localization modes and the influence of the internal length should be different in each limiter. The perturbation analysis is pursued in the discrete space where computations are done, and the closed form solutions for the dispersion equations are also obtained. The finite-element discretization introduces an added dispersion: the usual dispersion introduced by elliptic operators and another associated to the regularization technique. Therefore, the influence of the discretization on the localization limiters can be evaluated. The element size must be in the order of, or smaller than, the internal length of the models in order to obtain sufficient accuracy on the phase velocities of the propagating waves in transient analysis.

International audience; For particular structures like containment buildings of nuclear power plants, the study of the hydraulic behaviour is of great concern. These structures are indeed the third barrier used to protect the environment in case of accidents. The evolution of the leaking rate through the porous medium is closely related to the changes in the permeability during the ageing process of the structure. It is thus essential to know the relation between concrete degradation and the transfer property when the consequences of a mechanical loading on the hydraulic behaviour have to be evaluated. A chained approach is designed for this purpose. The mechanical behaviour is described by an elastic plastic damage formulation, where damage is responsible for the softening evolution while plasticity accounts for the development of irreversible strains. The drying process is evaluated according to a non-linear equation of diffusion. From the knowledge of the damage and the degree of saturation, a relation is proposed to calculate the permeability of concrete. Finally, the non-homogeneous distribution of the hydraulic conductivity is included in the hydraulic problem which is in fact the association of the mass balance equation for gas phase and Darcy law. From this methodology, it is shown how an indicator for the hydraulic flows can be deduced.

International audience; A hydro-mechanical coupled lattice-based model for the simulation of crack propagation induced by fluid injection in porous saturated rocks containing cohesive joints is presented. Rock follows an isotropic damage model for tensile fracture and cohesive joints follow a coupled plasticity- damage model. The discretisation uses a dual lattice approach: a Delaunay triangulation for the solid and the boundaries of the associated Voronoï tesselation for the hydraulic part. A classical poromechanical framework for a materials saturated with a single fluid is implemented. First, predictions of crack propagation are compared with analytical models. Then, the interaction between a propagating crack and an existing joint is analysed. Two configurations are con- sidered: the case of a joint that is orthogonal to the crack path and the case of a joint that is inclined by 45° with respect to the crack path. For the vertical joint, the crack is first arrested because the cohesive joint is weaker than the rock mass. The crack reinitiates at both crack tips and subsequently propagates in one of them. For the inclined joint, the crack follows the joint and therefore its path is deviated. Damage in the rock develops in the back of the crack tip, thereby enhancing the increase of permeability due to damage in the rock mass.

The behaviour of reinforced concrete structures is determined by the steel–concrete bond. Numbers of tests have shown that the nonlinear behaviour of the interface is mainly due to a progressive degradation of a concrete layer around the reinforcement. This chapter is a review of recent works done on the application of damage mechanics to this problem, in particular at the LMT where a nonlocal damage model is used to describe this phenomenon. A comparison with pull-out tests shows its capabilities to give information at the global level (nonlinearity and ultimate strength) as well as at the local level (strain evolutions on R bars). On the same kind of tests we show the ability of the model to predict a size effect consistent with experimental observations. The phenomena related to the realization of the anchorage at the bottom of prestressed concrete members are also described. Finally we present the simulation of the behaviour of an anchor bolt (those correspoding to the 1990 RILEM round-robin) in which the sensitivity of the boundary conditions is particularly pointed out.

International audience; Natural and synthesised porous media are generally composed of a double porosity: a microporosity where the fluid is trapped as an adsorbed phase and a meso or a macro porosity required to ensure the transport of fluids to and from the smaller pores. Zeolites, activated carbon, tight rocks, coal rocks, source rocks, cement paste or construction materials are among these materials.In nanometer-scale pores, the molecules of fluid are confined. This effect, denoted as molecular packing, induces that fluid- fluid and fluid-solid interactions sum at the pore scale and have significant consequences at the macroscale, such as instantaneous deformation, which are not predicted by classical poromechanics. If adsorption in nanopores induces instantaneous deformation at a higher scale, the matrix swelling may close the transport porosity, reducing the global permeability of the porous system. This is important for applications in petroleum oil and gas recovery, gas storage, separation, catalysis or drug delivery.This study aims at characterizing the influence of an adsorbed phase on the instantaneous deformation of micro-to-macro porous media presenting distinct and well-separated porosities. A new incremental poromechanical framework with varying porosity is proposed allowing the prediction of the swelling induced by adsorption without any fitting parameters. This model is validated by experimental comparison performed on a high micro and macro porous activated carbon. It is shown also that a single porosity model cannot predict the adsorption-induced strain evolution observed during the experiment. After validation, the double porosity model is used to discuss the evolution of the poromechanical properties under free and constraint swelling.

International audience; The degradation of quasi-brittle materials encompasses micro-cracks propagation, interaction and coalescence in order to form a macro-crack. These phenomena are located within the Fracture Process Zone (FPZ). This paper aims at providing a further insight in the description of the FPZ evolution with the help of statistical analysis of damage. The statistical analysis relies on the implementation of Ripley’s functions, which have been developed in order to exhibit patterns in image analyses. It is shown how a correlation length may be extracted from the Ripley’s function analysis. Comparisons between experimental and numerical evolutions of extracted correlation lengths are performed.

The purpose of this paper is to analyse the development and the evolution of the fracture process zone during fracture and damage in quasi-brittle materials. A model taking into account the material details at the mesoscale is used to describe the failure process at the scale of the heterogeneities. This model is used to compute histograms of the relative distances between damaged points. These numerical results are compared with experimental data, where the damage evolution is monitored using acoustic emissions. Histograms of the relative distances between damage events in the numerical calculations and acoustic events in the experiments exhibit good agreement. It is shown that the mesoscale model provides relevant information from the point of view of both global responses and the local failure process.

International audience; This paper presents a model capable of providing estimates of the apparent permeability directly from the pore-size distribution and from the properties of the fluid to be considered. The model is based on a hierarchical assembly of capillaries with decreasing diameter, generated randomly. The technique yields a porous network, which mimics the pore space measured experimentally by mercury intrusion. The intrinsic permeability and the evolution of the apparent permeability with mean pressure are provided by equating Darcy’s law and a combination of Poiseuille’s and Knudsen’s laws. Comparisons with experimental data on mortar specimens show that the model provides the intrinsic permeability and its evolution when the material is subjected to mechanical loads. For a given pore-size distribution, the evolution of the apparent permeability is also provided and test data with several types of gases compare quite well with the model.

International audience; Size and shape effects are important issues in predicting the global response of concrete structures. Small-scale tests performed in laboratory to determine the material properties are not enough to simulate large-scale structures. Many models are used to extrapolatesmall scale results to large scale simulations, but only few are able to recover size and shape effects. Recently a model of graded damage (TLS) has been proposed and comparison with cohesive zone models shows that this new model contains a new degree of freedom,the length of transition between totally damaged material and undamaged zone (ie the process zone size). In this paper, the capability of the model (TLS) to represent size and shape effects for two recently published experimental campaigns is studied.

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A model capable of predicting transport properties based solely on the pore size distribution of the material and the fluid characteristics has been developed previously by the authors. This model combines a Darcy description of the fluid flow at the macroscale with a Poiseuille/Knudsen flow at the micro-scale. A stochastic approach is then used with regards to pore network generation, in a manner consistent with mercury intrusion porosimetry (MIP). The present paper extends this model to multi-phase flow in an attempt to model partially saturated porous media. Kelvin's law defines which pore sizes are invaded with liquid and rules for accounting contributions of the pore network to liquid and vapour flows are introduced. The extended model provides data that are consistent with the Van Genuchten approach to liquid and gas relative permeabilities, compares well with experimental data and provides information of the relative permeability to vapour and liquid water upon damage. © ASCE.

International audience; Poromechanics offers a consistent theoretical framework for describing the mechanical response of porous solids fully or partially saturated with a fluid phase. When dealing with fully saturated microporous materials, which exhibit pores of the nanometer size, effects due to adsorption and confinement of the fluid molecules in the smallest pores must be accounted for. From the mechanical point of view, these phenomena result into volumetric deformations of the porous solid, the so-called "swelling" phenomenon. The present work investigates how the poromechanical theory may be refined in order to describe such adsorption and confinement induced effects in microporous solids. Poromechanics is revisited in the context of isotropic microporous materials with generic pore size distributions. The new formulation introduces an effective pore pressure, defined as a thermodynamic variable at the representative volume element scale (mesoscale), which is related to the overall mechanical work of the confined fluid. Accounting for the thermodynamic equilibrium of the system, we demonstrate that the effective pore pressure depends on macroscopic variables, such as the bulk fluid pressure, the temperature and the total and excess adsorbed quantity of fluid. As an illustrating example, we apply the model to compute strains and variations of porosity in the case of the methane and carbon dioxide sorption on coal. Agreement with experimental data found in the literature is observed.

International audience; The purpose of this work is to achieve a better understanding of the coupling between adsorption and swelling in microporous materials. This is typically of utmost importance in the enhancement of non-conventional reservoirs or in the valorization of CO 2 geological storage. We consider here the case of fully saturated porous solids with pores down to the nanometer size (≤ 2nm). Hardened cement paste, tight rocks, activated carbon or coal are among those materials. Experimentally, different authors tried to combine gas adsorption results and volumetric swelling data, especially for bituminous coal. However, most results in the literature are not complete in a sense that the adsorption experiments and the swelling experiments were not performed on the exact same coal sample. Other authors present simultaneous in-situ adsorption and swelling results but the volumetric strain is extrapolated from a local measurement on the surface sample or by monitoring the two-dimensional silhouette expansion. Only elastic and reversible swellings are reported in the literature. Theoretically, most continuum approaches to swelling upon adsorption of gas rely on a coupling between the adsorption isotherms and the mechanical deformation. A new poromechanical framework has been recently proposed to express the swelling increment as a function of the increment of bulk pressure with constant porosity. However, this framework has to be extended to take into account the porosity evolution upon swelling. This paper aims at presenting a new experimental setup where both adsorption and strain are measured in-situ and simultaneously and where the full-field swelling is monitored by digital image correlation. Permanent strain and damage are observed. On the other hand, we present an extended poromechanical framework where the porosity is variable upon swelling. A new incremental nonlinear scheme is proposed where the poromechanical properties are updated at each incremental pressure step, depending on the porosity changes. Interactions between swelling and the adsorption isotherms are examined and a correction to the classical Gibbs formalism is proposed. Predicted swellings are compared with results from the literature.

International audience; The objective of this study is to simulate the propagation of the shock wave in water due to an explosion. The study is part of a global research program on the development of an alternative stimulation technique to conventional hydraulic fracturing in tight gas reservoirs aimed at inducing a distributed state of microcracking of rocks instead of localized fracture. We consider the possibility of increasing the permeability of rocks with dynamic blasts. The blast is a shock wave generated in water by pulsed arc electrohydraulic discharges. The amplitude of these shock waves is prescribed by the electrohydraulic discharges which generate high pressures of several kilobars within microseconds. A simplified method has been used to simulate the injected electrical energy as augmentation of enthalpy in water locally. The finite element code EUROPLEXUS is used to perform fluid fast dynamic computation. The predicted pressure is consistent with the experimental results. In addition, shock wave propagation characteristics predicted with simulation can be valuable reference for design of underwater structural elements and engineering of underwater explosion.

SUMMARY The results reported in this paper deal with the simulation of damage in cohesive geomaterials such as rocks or concrete subjected to dynamic loads. The practical objective is to stimulate the production of tight gas reservoirs with a technique that is an alternative to hydraulic fracturing. The principle is that when subjected to dynamic loads, cohesive materials such as concrete, rocks or ceramics exhibit distributed micro-cracking as opposed to localised cracking observed under static loads. Hence, a low permeability rock containing gas trapped into occluded pores can be fragmented with the help of dynamic loads, and gas can be extracted in a much more efficient way compared with hydraulic fracturing, where only large macro cracks are formed with very few connections between occluded pores. At the stage of laboratory development of this technique, compressive underwater shock waves have been used to increase the intrinsic permeability of concrete specimens. In a previous study, pressure waves generated by pulsed arc electrohydraulic discharges in water were used in order to induce micro-cracking and an increase of average permeability of concrete hollow cylinders subjected to confinement stresses (equivalent to geostatic stresses). We discuss here a 3-D anisotropic constitutive model aimed at describing the dynamic response of these specimens. It is based on rate-dependent continuum damage constitutive relations. Crack closure effects and damage-induced anisotropy are included in the model. The directional growth of damage is related to the directional growth of material intrinsic permeability. Numerical simulations of damage induced by shock waves show good agreement with the experiments for various confinement levels of the specimens. Copyright © 2013 John Wiley & Sons, Ltd.

International audience; A thermodiffusion cell is used in order to perform Soret experiments on binary mixtures at high pressure and in the presence of a porous medium. The cell is validated at atmospheric pressure with toluene/hexane and the tetrahydronaphthalene/dodecane mixtures. The mass separation follows a diffusive behaviour when the cell is filled with a porous medium. At least three times the relaxation time is needed to have a good estimation of the Soret coefficients. From the transient state of the mass separation and using accepted values of the diffusion coefficient, the tortuosity of the porous medium was evaluated, too. Finally, experiments at high pressure were performed with the tetrahydronaphthalene/dodecane system. In these experiments, decreases of the Soret coefficient and of the tortuosity of the porous medium were measured as a function of the pressure.

Modelling failure in geomaterials, concrete or other quasi-brittle materials and proper accounting for size effect, geometry and boundary effects are still pending issues. Regularised failure models are capable of describing size effect on specimens with a specific geometry, but extrapolations to other geometries are rare, mostly because experimental data presenting size effect for different geometries and for the same material are lacking. Three-point bending fracture tests of geometrically similar notched and unnotched specimens are presented. The experimental results are compared with numerical simulations performed with an integral-type non-local model. Comparisons illustrate the shortcomings of this classical formulation, which fails to describe size effect over the investigated range of geometries and sizes. Finally, experimental results are also compared with the universal size effect law.

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International audience; Characterizing the path of a hydraulic fracture in a heterogeneous medium is one of the challenges of current research on hydraulic fracturing. We present here a 2D lattice hydro-mechanical model for this purpose.Natural joints are represented introducing elements with a plastic-damage behaviour. The action of fluid pressure on skeleton is represented using Biot’s theory. The interactions of cracks on fluid flow are represented considering a Poisueille’s flow between two parallel plates. The model is simplified by neglecting the effect of deformation in the equation governing fluid flow. Numerical coupling is achieved with a staggered coupling scheme.We consider first the propagation of fracture restricted to the homogeneous case. The numerical model is compared to analytical solutions. It is found that the model is consistent with LEFM in the pure mechanical case, and with analytical solutions from the literature in the case where the leak off is dominant. In very tight formations, deviations are observed, as expected, because of the assumption in the flow model.Finally, the influence of a natural joint of finite length crossed by the fracture is shown. Two cases are considered, the case of a joint perpendicular to the crack and the case of an inclined joint. In the first case, the crack passes through the joint, which is damaged due to the intrusion of the fluid. In the second case, the crack follows the joint and propagation starts again from the tip.

The degradation of quasi-brittle materials encompasses micro-cracks propagation, interaction and coalescence in order to form a macro-crack. These phenomena are located within the Fracture Process Zone (FPZ). This paper aims at providing a further insight in the description of the FPZ evolution with the help of statistical analysis of damage. The statistical analysis relies on the implementation of Ripley’s functions, which have been developed in order to exhibit patterns in image analyses. It is shown how a correlation length may be extracted from the Ripley’s function analysis. Comparisons between experimental and numerical evolutions of extracted correlation lengths are performed.

The purpose of this work is to achieve a better understanding of the relationship between mechanical damage, pore size distribution and transport properties of cementitious materials. In the literature, analyses are usually restricted to intrinsic permeability of the material and the evolution of the apparent permeability with respect to the pressure gradient and to the nature of the fluid considered are left aside. A new model capable to provide the apparent permeability of a porous material to gas, directly from the pore size distribution and from the properties of the gas is discussed. Comparisons with experimental data on mortar specimens show that the model can reproduce the intrinsic permeability and its evolution when the material is subjected to mechanical damage, provided the pore size distributions are available. Extension to the transport of different phases (e.g. water and water vapor) is discussed, with a view towards the simulation of nuclear accident in containment vessels. It is shown that small pores that are not affected by damage according to the pore size distribution are of great importance in the evaluation of the relative permeability to liquid and vapor as a function of the saturation. A tentative model is discussed and compared with the existing – standard – approach relying on Van Genuchten relationships.

International audience; In this paper, the fracture process zone (FPZ) is investigated on unnotched and notched beams with different notch depths. Three-point bending tests have been realized on plain concrete under crack mouth opening displacement (CMOD) control. Crack growth is monitored by applying the acoustic emission (AE) technique. The comparison with a numerical model is also realized by using a mesoscopic approach. Such an approach is of particular interest in the analysis of interactions between the cementitious matrix and aggregates. Several AE parameters are examined during the entire loading process, and show that the relative notch depth influences the AE characteristics, the process of crack propagation, and the brittleness of concrete. The numerical load-CMOD curves show that the mesoscopic modelling reproduces well the notch effect and concrete failure. In order to improve our understanding of the FPZ, the width and length of the FPZ are followed based on the AE source locations maps in parallel with the numerical damage fields. An important energy dissipation is observed at the crack initiation in unnotched beams.

International audience; In this paper, the fracture process zone (FPZ) is investigated on unnotched and notched beams with different notch depths. Three-point bending tests have been realized on plain concrete under crack mouth opening displacement (CMOD) control. Crack growth is monitored by applying the acoustic emission (AE) technique. The comparison with a numerical model is also realized by using a mesoscopic approach. Such an approach is of particular interest in the analysis of interactions between the cementitious matrix and aggregates. Several AE parameters are examined during the entire loading process, and show that the relative notch depth influences the AE characteristics, the process of crack propagation, and the brittleness of concrete. The numerical load-CMOD curves show that the mesoscopic modelling reproduces well the notch effect and concrete failure. In order to improve our understanding of the FPZ, the width and length of the FPZ are followed based on the AE source locations maps in parallel with the numerical damage fields. An important energy dissipation is observed at the crack initiation in unnotched beams.

This book presents a new fracturing technique that should be considered as a potential alternative, or a companion technique, to hydraulic fracturing of tight gas reservoirs and low permeability rock masses. As opposed to hydraulic fracturing which generates a few numbers of large cracks, electro-hydraulic fracturing induces diffuse micro-cracking and fragmentation of rocks. Laboratory tests demonstrate that increases of permeability by two orders of magnitude can be reached, without major cracking in tested specimens. This book discusses the principles of this new technique, reports experiments which have been developed is order to prove the concept and finally describes the numerical model from which the potentialities of this technique in representative reservoir conditions can be assessed. © ISTE Ltd 2016. All rights reserved.

International audience; The purpose of this paper is to discuss how boundary and emerging boundary effects can be folded into a new non-local damage formulation based on integral models that provides a consistent transition towards discrete cracking. Several enhancements of the original non-local damage model inspired from micromechanics of interacting defects are considered. The goals of the modified non-local formulation are threefold: (1) the distribution of damage at failure should be mesh independent; (2) the model should be able to capture the continuous/discontinuous transition involved in the process of failure due to increasing stresses; (3) the discontinuous displacements fields resulting from complete failure should be approached as closely as possible. A one dimensional example illustrates the capabilities of the original and enhanced models. It is found that a combination of increasing/decreasing interactions and non-local effects during failure provides the most suitable results.

Damage models are capable of representing crack initiation and mimicking crack propagation within a continuum framework. Thus, in principle, they do not describe crack openings. In durability analyses of concrete structures however, transfer properties are a key issue controlled by crack propagation and crack opening. We extend here a one dimensional approach for estimating a crack opening from a continuum based fi nite element calculation to two dimensional cases. The technique operates in the case of mode I cracking described in a continuum setting by a nonlocal isotropic damage model. We used the global tracking method to compute the idealized crack location as a post treatment procedure. The orig inal one dimensional problem devised in Dufour et al . [4] is recovered as pro fi les of deformation orthog onal to the idealized crack direction are computed. An estimate of the crack opening and an error indicator are computed by comparing fi nite element deformation pro fi les and theoretical pro fi les corresponding to a displacement discontinuity. Two estimates have been considered: In the strong approach, the maxima of the pro fi les are assumed to be equal; in the weak approach, the integrals of each pro fi le are set equal. Two dimensional numerical calculations show that the weak estimates perform better than do the strong ones. Error indicators, de fi ned as the distance between the numerical and theoretical pro fi les, are less than a few percentages. In the case of a three point bending, test results are in good agreement with experimental data, with an error lower than 10% for widely opened crack ( > 40 m m )

International audience; The conditions for localization in a material described by a non-local damage-based constitutive relation coupled with a Kelvin type creep relation are derived in a closed form. The inception of a localized mode is considered as a bifurcation into a harmonic mode. The criterion of bifurcation is reduced to the classical form of singularity of a pseudo acoustic tensor; this tensor involves the elasto-damage strain and the total one at the inception of localization and the wavelength of the bifurcation mode through the Fourier transform of the weight function used in the definition of non-local damage. A geometrical approach was adopted to analyze localization for loading paths such that the elastic strain tensor is a fraction of the total strain tensor. Such loading paths include the general triaxial ones for which changes in the loading state occur only under time-independent processes (negligible creep strain during these changes of the stress state) and the uniaxial loading. The proposed coupled model preserves the properties of localization limiters; the minimum wavelength of the localization modes cannot be zero. The critical wavelength which is related to the width of the localization zone increases when the material parameter α (0 < α < 1), which is the fraction of creep strain entering into the evolution of damage, is decreasing. Under a certain condition on the growth of the loading function of damage and the initial state of deformation the critical wavelength decreases as the creep effect (creep strains) increases in accordance with experimental observations—increase of brittleness due to creep. In uniaxial tension, and for a specific yield function of concrete considered in this paper, this condition is fulfilled whenever the initial damage is in a region near the first occurrence of localization.

International audience; This chapter compares uniaxial experiments and tests on hollow cylinders to computations. It evaluates the capacity of the computational model to capture the main features of the experiments, that is the growth of permeability with increasing electrical energy inserted into the system. The model calibration has been carried out using a small set of experiments and comparisons with further simulations on the rest of the data provided some evaluation of the quality of the finite element model. The most demonstrative and quantitative evaluation has been provided by the evolution of permeability with increasing electrical energy. In most approaches, permeability is isotropic and it is calculated according to the maximum principal damage. The average permeability of the specimen is overestimated in the isotropic case compared to the anisotropic case. Losing the effect of the directionality of damage on the permeability yields a severe overestimation of the overall permeability.

International audience; This chapter details the experiments in a representative environment and discusses the results obtained on a model material (mortar), and on sandstone. The permeability is measured on each specimen prior to mechanical testing and serves as a reference value in forthcoming comparisons. The ratio between permeability measured under medium confinement and without confinement is approximately equal to one order of magnitude. The variation of permeability due to electrohydraulic fracturing is much larger than that. Each specimen was scanned in an X-ray tomography facility prior to and after testing. Two sequences of tests have been carried out. In the first one, the mortar specimens were subjected to a single shock under a variable injected electrical energy, for each of the three confinement levels considered. In the second sequence, the specimens were subjected to repeated shocks with a constant injected energy.

International audience; This chapter begins with the investigation of the effect of repetitive shocks. In order to investigate the effect of repeated shocks, it considers the experiments on hollow cylinders under high confinement. The chapter examines the capabilities of electrohydraulic fracturing on representative geometries. Next, it reviews simulations using representative reservoir geometries. After an evaluation of the range of propagation of damage in the context of single shocks, the chapter also looks at an optimization of the process, essentially at the effect of guided pressure waves. Finally, it investigates the influence of the shape of the pressure wave on the extent of the damage. The elastic energy carried by the pressure wave is distributed in a growing volume as it propagates. Therefore, the amplitude of the pressure decays rapidly, and the pressure quickly becomes too low to generate any damage.

International audience; This chapter describes the various ingredients that will be put together in order to achieve numerical simulations of the electrohydraulic fracturing process in the context of hydrocarbon production. It first discusses the theoretical model from which the pressure generated by the pulsed area electric discharge (PAED) can be derived. The chapter then describes the mechanical modeling of the rocks under dynamic loads. In the case of dynamic load, which applies in electrohydraulic fracturing, it is essential to account for the time-dependent response of the material. Finally, the chapter reviews the coupled effects between the growth of damage due to microfracturing and the growth of permeability. In the 3D coordinate system corresponding to the principal axes of damage, damage in one direction is due to cracking in orthogonal directions. Hence, damage growth in one direction generates an increase in permeability in the two orthogonal directions.

International audience; The aim of this study is to predict the mechanical behaviour of beams which were in sea water for 40 years. Mechanical experimentations were carried out after inspection of beams: loading in four-point bending and loading in direct tension. The mechanical behaviour of the beams is modelled before and after being corroded, with the software Eficos. The steel corrosion is taken into account only by a reduction in steel cross section because steels have no anchorage. A good correlation is obtained between simulations and experimental results for bending in the case of reinforced concrete.; Cette étude a pour but de simuler le comportement mécanique des poutres de la Rance qui ont été immergées pendant 40 ans en eau de mer. Ces poutres après auscultation ont été testées mécaniquement en flexion 4-points et en traction directe. Notre travail porte sur la modélisation du comportement mécanique des poutres avant et après corrosion à l'aide du code de calcul Eficos. La prise en compte de la corrosion est limitée aux pertes de sections des aciers qui sont des ronds lisses. On obtient une bonne adéquation entre simulations et résultats expérimentaux, en particulier dans le cas de la flexion en configuration béton armé.

International audience; The fracture process zone (FPZ) was investigated on unnotched and notched beams with different notch depths. Three point bending tests were realized on plain concrete under crack mouth opening displacement (CMOD) control. Crack growth was monitored by applying the acoustic emission (AE) technique. In order to improve our understanding of the FPZ, the width and length of the FPZ were followed based on the AE source locations maps and several AE parameters were studied during the entire loading process. The bvalue analysis, defined as the log-linear slope of the frequency-magnitude distribution of acoustic emissions, was also carried out to describe quantitatively the influence of the relative notch depth on the fracture process. Theresults show that the number of AE hits increased with the decrease of the relative notch depth and an important AE energy dissipation was observed at the crack initiation in unnotched beams. In addition, the relative notch depth influenced the AE characteristics, the process of crack propagation, and the brittleness of concrete.

The purpose of this work is to achieve a better understanding of the relationship between mechanical damage and the transport properties of cementitious materials. In the literature, analyses are usually restricted to intrinsic permeability of the material and the evolution of the apparent permeability with respect to the pressure gradient and to the nature of the fluid considered are left aside. A new model capable to provide the apparent permeability of a porous material to gas, directly from the pore size distribution and from the properties of the gas is discussed. Comparisons with experimental data on mortar specimens show that the model can reproduce the intrinsic permeability and its evolution when the material is subjected to mechanical damage, provided the pore size distributions are available. For a given pore size distribution, the evolution of the apparent permeability is also provided and test data with several types of gases compare quite well with the model. © ASCE.

International audience; It is shown herein that the bending problem of a discrete damage system, also called microstructured damage system or lattice damage system, can be rigorously handled by a nonlocal continuum damage mechanics approach. It has been already shown that Eringen's nonlocal elasticity was able to capture the scale effects induced by the discreteness of a microstructured system. This paper generalizes such results for inelastic materials and first presents some results for engineering problems modelled within continuum damage mechanics. The microstructured model is composed of rigid periodic elements connected by rotational elastic damage springs (discrete damage mechanics). Such a discrete damage system can be associated with the finite difference formulation of a continuum damage mechanics problem, i.e. the Euler-Bernoulli damage beam problem. Starting from the discrete equations of this structural problem, a continualization method leads to the formulation of an Eringen's type nonlocal model with full coupling between nonlocal elasticity and nonlocal continuum damage mechanics. Indeed, the nonlocality appears in this continualized approach both in the constitutive law and in the damage loading function. A comparison of the discrete and the continuous problems for the cantilever shows the efficiency of the new micromechanics-based nonlocal continuum damage modelling for capturing scale effects. The length scale of the nonlocal continuum damage mechanics model is rigorously calibrated from the size of the cell of the discrete repetitive damage system. The new micromechanics-based nonlocal damage mechanics model is also analysed with respect to available nonlocal damage mechanics models.