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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.

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.

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; 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.

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.

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; 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.

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.

International audience; Poromechanics offers a consistent theoretical framework for describing the mechanical response of porous solids. When dealing with fully saturated nanoporous materials, which exhibit pores of the nanometer size, additional 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, and into a change of the apparent permeability. The present work investigates how poromechanics may be refined in order to capture adsorption and molecular-packing-induced effects in nanoporous solids. The revisited formulation introduces an effective pore pressure, defined as a thermodynamic variable at the representative volume element scale (mesoscale), which is related to the mechanical work of the fluid at the pore scale (nanoscale). Accounting for the thermodynamic equilibrium of the system, this effective pore pressure is obtained as a function of the bulk fluid pressure, the temperature, and the total and excess adsorbed masses of fluid. We derive the analytical swelling strains due to sorption and molecular packing. A good agreement in the comparison with experimental data dealing with the swelling of coal due to methane and carbon dioxide sorption is observed, as a preliminary stage toward modeling partially saturated solids and applications to cement paste.

International audience; This paper deals with the stability of a single-degree-of-freedom plastic softening oscillator. Understanding such an elementary model concerns, for instance, the seismic behaviour of concrete or steel structures. The associated dynamic system is a complex hysteretic system. Using appropriate internal variables, it can be written as a singular autonomous system. Liapounov stability of the solutions is then studied. A domain of perturbations associated with a stable solution is exhibited. This domain looks like a truncated cone in the three-dimensional phase space. It can be read as a critical displacement or energy that the oscillator can support during a seismic excitation. The difference with the “equivalent” linearized elastic system is highlighted. The unloading part of the response of the inelastic system has a stabilising effect.

A synthesis of work carried out for several years within our laboratory is presented. The first part includes an experimental study. The tests are performed on hollow cylindrical concrete specimens, subjected to compressive loading. At stress levels lower than 80 % of the peak stress, the variation of permeability is small and it is slightly influenced by the stress, but as the load exceeds 80 % of the peak stress, micro-cracking increases rapidly, causing an increase of the permeability and a greater sensitivity to the applied load. In the post-peak phase the increase of permeability is much larger due to significant crack width growth. The effects of the applied load on permeability are greater with temperature. Finally, the experimental results seem to agree with the format of coupled evolution of the permeability due to damage and temperature assumed by Gawin et al. [10]. The second part of this paper includes a numerical study. The lattice mechanics model is extended to the hydraulic problem and, for this case, it appears that permeability is the size independent variable. Additionally, the evolution of permeability with damage and with stress ratio in the pre-peak phase is compared with experimental results on different types of concrete.

L'auto-cicatrisation des fissures sur un beton a ultra-hautes performances, considere comme materiau modele, est etudiee au travers d'essais mecaniques et acoustiques. Le phenomene, principalement mis en evidence par des essais de permeabilite a l'eau jusqu'a maintenant, est ainsi quantifie. Le comportement mecanique en flexion 3 points d'eprouvettes de beton cicatrisees et une analyse par emission acoustique des mecanismes de fissuration sont proposes. Les essais mecaniques montrent une reprise de raideur globale, dependant du temps de cicatrisation, pour les eprouvettes initialement endommagees et ensuite cicatrisees, et une legere reprise de resistance. En parallele, l'analyse par emission acoustique est menee afin de montrer la precipitation de nouveaux cristaux dans la fissure, responsables de cet apport sur le plan mecanique. La microfissuration de ces cristaux pendant les essais de flexion 3 points est ainsi mise en evidence.

Experimental results for fatigue tests on three size geometrically similar asphalt concrete specimen are presented. Effect on fatigue life is analyzed and compared to trends given by a fatigue damage model. This innovative laboratory campaign points out a size effect on fatigue assessment of asphalt mixture. In a second part, the application of a nonlocal fatigue damage model for asphalt mixtures is presented. A qualitative agreement is obtained between experimental results and non local damage fatigue predictions trends. This agreement validates the nonlocal modelling that allows to model the influence of the heterogeneous nature of the material on fatigue failure. Differences observed between laboratory data and model predictions may be attributed to viscoelasticity induced thermal softening which had to be quantified and coupled to damage in order to properly study these fatigue test data.

International audience; In this paper, we examine the correlation between the width of the fracture process zone, the parameters entering in the description of size effect (related to the dimension of the specimen especially), and the internal length in non local constitutive relations for a model mortar material with a controlled macro-porosity. Experimental investigations on this material in compression, bending, acoustic emission measurements and their analysis are detailed. The experiments show a good agreement between the evolution of Bažant's size effect parameter d0 and the evolution of the width of the FPZ. The internal length obtained with the help of inverse finite element analysis is also proportional to these quantities. This correlation provides a reasonable approximation of the internal length, from an experimental test on specimens of a single size directly, equipped with acoustic emission localization devices.; Dans cet article, nous examinons les corrélations entre la largeur de la zone de microfissuration (FPZ), les paramètres entrant dans la description de l'effet d'échelle et la longueur interne du modèle d'endommagement non local pour un mortier à macro-porosité contrôlée. Des résultats expérimentaux sur ce matériau en comparession, en flexion ainsi que des mesures d'émission acoustiques et leur analyse sont présentés. Les résultats d'essais montrent une bonne corrélation, entre l'évolution du paramètre d0, paramètre de la loi d'effet d'échelle de Bažant, et la largeur de la PFZ. La longueur interne obtenue numériquement par analyse inverse est aussi proportionnelle à ces paramètres. Une bonne approximation de la longueur interne à partir d'essais sur une seule taille d'éprouvette équipée d'un système d'émission, acoustique est aussi obtenue.

International audience; A nonlocal damage model is proposed to predict the behavior of pavement fatigue cracking. This constitutive relation has been implemented in a finite-element code, along with a self-adaptive jump-in-cycle procedure for high cycle fatigue computations. Strain localization analysis shows that during uniaxial fatigue tests, bifurcation due to strain softening occurs much later than in monotonic tests. The incorporation of an internal length into the constitutive model is advocated since the model should encompass loading histories with very different amplitudes of cycles, in which localization may still occur. The influence of the internal length on the fatigue life of bending beams is also investigated. Calibration of the damage model is performed after thermal effects have been evaluated and accounted for in a simplified way, uncoupled to damage. Parameter identification is performed in bending and uniaxial tests. The resulting calibrated constitutive relation is found to yield a good description of several different uniaxial tests.

A simplified computational technique based on a refined global-local method is applied to the failure analysis of concrete structures. The technique distinguishes the scale of the structure, modelled with large size finite elements, from the scale at which material non-linearity occurs due to progressive cracking and macro-crack propagation. The finite element solution is split into two parts: a linear elastic analysis on a coarse mesh over the entire structure and a non-linear analysis over a small part of the structure where a dense finite element grid is employed. In the non-linear calculation, a non-local damage model is implemented. These two computations are coupled with the help of an iterative scheme. The size and location of the region where a non-linear analysis is performed, is adapted to follow the development of the damage zone. Numerical examples of mode I fracture of concrete specimens with straight and curved cracks are presented.

International audience; Continuum damage mechanics is a framework for describing the variations of the elastic properties of a material due to microstructural degradations. This paper presents the application of this theory to the modelling of concrete. Several constitutive relations are devised, including incremental, explicit, and non local damage models. A general framework for damage induced anisotropy is also presented. In the second part of this contribution, computational issues in damage mechanics related to iterative schemes and solution control in non linear computations are considered. The paper concludes with an example of 3D finite element computation of a reinforced concrete beam, as part of a benchmark initiated by Electricité de France.

The paper reports on the discussions at the ONR Workshop on Fracture Scaling, held at University of Maryland in June 1999, under the chairmanship of Z.P. Bažant and Y.D.S. Rajapakse. The workshop dealt with size effects in structural failure and scale bridging in mechanics of materials. The lectures at the Workshop were published in Volume 95 of this Journal. The objective of this paper is to present records and interpretations of the extensive discussions prepared by invited specialists. The records show which are the areas of disagreement among leading researchers and which are those where consensus has been reached.

International audience; Failure of quasi-brittle materials such as concrete needs a proper description of strain softening due to progressive micro-cracking and the introduction of an internal length in the constitutive model in order to achieve non zero energy dissipation. This paper reviews the main results obtained with the non local damage model, which has been among the precursors of such models. In most cases up to now, the internal length has been considered as a constant. There is today a consensus that it should not be the case as models possess severe shortcomings such as incorrect averaging near the boundaries of the solid considered and non local transmission across non convex boundaries. An interaction-based model in which the weight function is constructed from the analysis of interaction has been proposed. It avoids empirical descriptions of the evolution of the internal length. This model is also recalled and further documented. Additional results dealing with spalling failure are discussed. Finally, it is pointed out that this model provides an asymptotic description of complete failure, which is consistent with fracture mechanics.

The degradation of quasi-brittle materials encompasses micro-crack propagation, interaction and coalescence in order to form a macro-crack. These phenomena are located progressively within the so-called Fracture Process Zone (FPZ). The shape and growth of the FPZ, and its interaction with boundaries lead to typical phenomena such as size effects, boundary effects and shielding effects. Classical failure constitutive models involve strain softening due to progressive cracking and a regularization technique for avoiding spurious strain and damage localization. Different approaches have been promoted in the literature such as integral-type non-local models, gradient damage formulations, cohesive cracks models or strong discontinuity approaches. Such macroscale failure models have been applied on a wide range of problems, including the description of damage and failure in strain softening quasi-brittle materials, softening plasticity, creep or composite degradation. An important element of validation of failure models is that they should be able to capture size and boundary effects for various geometries. However, numerical predictions of size effect on different geometries or the description of boundary effects are quite rare in the literature because experimental data on different specimen geometries and on the same material are not available for comparison. If experiments involving size effect are numerous in the literature, they are restricted to a specific geometry and barely consider structures made of the same material, with different geometries. Most of the time, the notch-to-depth ratio tends to zero without reaching zero and unnotched specimens are studied separately, with different materials compared with size effect tests on notched specimens. This paper aims at presenting new experimental and numerical investigations of failure for geometrically similar notched and unnotched concrete specimens made of the same mix. Different geometries (four depth and three notch sizes) have been considered to obtain results involving size and boundary effects at the same time. A mesomodel is used to study the FPZ evolution upon damage depending on the geometry and boundary conditions. A very good agreement with the experimental results is obtained. An analysis of the correlations involved during the fracture process at the mesoscale is performed and a good agreement with acoustic emissions data is revealed.

International audience; In a concrete structure subjected to an explosion, for example a concrete slab, the material is subjected to various states of stress which lead to many modes of rupture. Closer to the explosive, a state of strong hydrostatic compression is observed. This state of stress produces an irreversible compaction of the material. Away from the zone of explosion, con"nement decreases and the material undergoes compression with a state of stress, which is slightly triaxial. Finally, the compression wave can be re#ected on a free surface and becomes a tensile wave, which by interaction with the compression wave, produces scabbing. We present, in this paper, a model aimed at describing these three failure modes. It is based on visco-plasticity and rate dependent damage in which a homogenization method is used in order to include the variation of the material porosity due to compaction. The model predictions are compared with several experiments performed on the same concrete. Computations of split Hopkinson tests on con"ned concrete, a tensile test with scabbing, and an explosion on a concrete slab are presented.

The damage growth in a softening interface connected to an elastic block is analysed. The elastic block, assumed to be infinite, is modelled as a two-dimensional continuum and the interface is one-dimensional with a constitutive response which follows a scalar damage model. The solution technique is based on the equilibrium of the interfacial forces resulting from the deformation of the elastic block and from the interface constitutive response. The interface failure process is compared to that of a hierarchical model which was obtained analytically (Delaplace et al., 1998). The two are found to be similar, without an internal length scaling the distribution of damage at the inception of macro-cracking. Finally, scale effects on the occurrence of bifurcation and instability are considered. It is shown that bifurcation may occur prior to or after the limit point under displacement control, depending on the elastic block height or stiffness.

Fracture mechanics is very often employed in analyses of cracked structural components for civil engineering structures such as bridges, dams, and cooling towers. An alternate technique is presented that is based on the equivalence between a crack, its process zone, and a distribution of damage. It is a simplified method aimed at approximating the distribution of damage around an existing crack. This approximation is based on the analysis of localization with a nonlocal damage model. Finite-element calculations on a compact tension concrete specimen for several initial crack lengths are presented and compared with experiments. The method is shown to yield errors less than 20% on the prediction of the load reduction factor as a function of the initial crack length. The method is also extended to the prediction of the response of fiber-reinforced components with initial damage. The response of cracked fiber-reinforced concrete beams is computed and compared with the results of original experiments, where the loading conditions that created the initial crack are different from those leading to failure.

International audience; This article deals with the development of a technique to stimulate low-permeability reservoirs, a potential alternative to hydraulic fracturing. The practical objective is to increase the intrinsic permeability of rocks around the oil well by dynamic shock waves. Laboratory experiments were carried out on small hollow cylinder specimens under different confinements, which mimic in situ conditions. Shock waves are generated in water by Pulsed Arc Electrohydraulic Discharges (PAED), which then propagate in water and into the specimens. The specimen is damaged by the pressure waves and its permeability increases with the evolution of damage. Specimens were tested mechanically under three stress levels, corresponding to different depths underground. Then the overall permeability to gas of the specimens was measured and correlated to the electrical energy involved into the PAED. For each stress level, the threshold of energy was observed. From the threshold, the increase of permeability is linear. The thresholds of injected electrical energy increase with confinement level. The effect of repeated shocks on permeability is also considered. Tomography X ray scans have been used to analyze the evolution of the microstructure of representative specimens qualitatively. A good correlation is observed between the X-ray tomography results and the permeability. The evolution of cracking and damage due to dynamic mechanical loads are correlated with the intrinsic permeability of the material and with its microstructure.

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 nanometre size, aside from the fluid pressure acting on the pore walls additional 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 should be refined in order to describe adsorption and confinement induced swelling in microporous solids. Firstly, we report molecular simulation results that show that the pressure and density of the fluid in the smallest pores are responsible for the volumetric deformation of the material. Secondly, poromechanics is revisited in the context of a microporous material with a continuous pore size distribution. Accounting for the thermodynamic equilibrium of the fluid phase in the overall pore space, the new formulation introduces an apparent porosity and an interaction free energy. We use a prototype constitutive relation relating these two quantities to the Gibbs adsorption isotherm, and then calculate the induced deformation of the solid matrix. Agreement with experimental data found in the literature is observed. As an illustrating example, we show the predicted strains in the case of adsorption of methane on activated carbon.

International audience; This paper deals with the development of a model for concrete subjected to dynamic loads. Shock waves are generated by Pulsed Arc Electro-hydraulic Discharges in water and applied to mortar samples. A diphasic model (liquid water and vapour) is implemented in order to describe the electrical discharge and the propagation of shock waves in water. An anisotropic damage model is devised, which takes account of the strain rate effect and the crack closure effect. Coupling between anisotropic damage and permeability is proposed in order to assess the variation of material permeability due to shock waves. Comparisons with experiments show a good correlation between the experimental and the numerical results.; Cette étude porte sur développement d'un modèle du béton sous chargement dynamique rapide. Le chargement dynamique est généré par des ondes de chocs dues à la décharge électrohydraulique d'un arc (PAED) sous l'eau. Un modèle actuel diphasique est qualifié et utilisé pour simuler la décharge électrique et la propagation des ondes dans l'eau. Un modèle d'endommagement anisotrope est développé qui prend en compte l'effet de vitesse de la déformation et la refermeture des fissures. Un couplage entre l'endommagement et la perméabilité anisotropique est proposé. Après la comparaison avec l'expérimentation, une bonne corrélation est observée entre les résultats expérimentaux et numériques.

This article discusses the influence of compressive shock waves on the permeability of cementitious materials. Shock waves are generated in water by Pulsed Arc Electrohydraulic Discharges (PAED). The practical aim is to increase the intrinsic permeability of the specimens. The maximum pressure amplitude of the shock wave is 250 MPa. It generates damage in the specimens and the evolution of damage is correlated with the intrinsic permeability of the mortar. A threshold of pressure is observed. From this threshold, the increase of permeability is linear in a semi-log plot. The influence of repeated shocks on permeability is also discussed. Qualitative X Ray Tomography illustrates the evolution of the microstructure of the material leading to the increase of permeability. Comparative results from mercury intrusion porosimetry (MIP) show that the micro-structural damage process starts at the sub-micrometric level and that the characteristic size of pores of growing volume increases. Cement and Concrete Research, ISSN : 0008-8846, DOI : 10.1016/j.cemconres.2010.07.005, Issue : 12, Volume : 40, pp. 1631–1638, December 2010.

International audience; Abstract This paper deals with the dynamics of a single-degree-of-freedom unilateral damage oscillator. Using appropriate internal variables, the hysteretic dynamic system can be written as a nonsmooth autonomous system. The free dynamics of such a nonlinear system are simply reduced to periodic motion, eventually attractive trajectories, and divergent motion. The direct Lyapunov method is used to investigate the stability of the free damage system. A critical energy is highlighted that the oscillator can support while remaining stable. The natural frequency of the periodic motion depends on the stationary value of the damage internal variable. The inelastic forced oscillator, however, can exhibit very complex phenomena. When the damage parameter remains stationary, the dynamics are similar to those of an elastic oscillator with nonsymmetric stiffness. The dynamics appear to be controlled by the initial perturbations. Chaotic motions may appear in such a system, specifically for severely damaged oscillators. It is numerically shown that chaos is observed in the vicinity of the divergence zone (the collapse). This closeness of both behaviors-chaos and divergence-is probably related to the perturbation of the homoclinic orbit associated with the critical energy. © 2010. Journal of Mechanics of Materials and Structures.

International audience; The present contribution aims at providing a closer insight on boundary effects in non local damage modelling. From micromechanics, we show that on a boundary interaction stress components normal to the surface should vanish. These interaction stresses are at the origin of non locality and therefore the material response of points located on the boundary should be partially local. Then, we discuss a tentative modification of the classical non local damage model aimed at accounting for this effect due to existing boundaries and also boundaries that arise from crack propagation. One-dimensional computations show that the profiles of damage are quite different compared to those obtained with the original formulation. The region in which damage is equal to 1 is small. The modified model performs better at complete failure, with a consistent description of discontinuity of the displacement field after failure.

International audience; Some insights on boundary effects in nonlocal damage modelling are addressed. Interaction stresses that are at the origin of nonlocality are expected to vanish at the boundary of a solid, in the normal direction to this boundary. Existing models do not account for such an effect. We introduce tentative modifications of the classical nonlocal damage model aimed at accounting for this boundary layer effect in a continuum modelling setting. Computations show that some nonnegligible differences may be observed between the classical and modified formulations. In a one dimensional spalling test, only the modified formulation provides a spall of finite nonzero thickness, whereas spalls smaller than the internal length cannot be obtained according to the original formulation. For the same set of model parameters, including the internal length, the fracture energy derived from the size effect test method is also very different according to both approaches. Parameters in the size effect laws for notched and unnotched specimens, obtained from computation of geometrically similar bending beams, are more consistent with the modified nonlocal model compared to the original nonlocal formulation.

International audience; The serviceability of concrete structures is a coupled problem in which fracture and damage are coupled with several environmental attacks. In this paper, we start with the description of chemo-mechanical damage and the case of calcium leaching which is relevant to waste containment vessels. The second example of implementation of continuum damage models discussed deals with coupled damage permeability effects. In the case of diffuse damage, the material permeability is controlled by the decrease of average stiffness due to micro-cracking. After a macro-crack has formed, permeability is controlled by a power function of the crack opening (Poiseuille flow). A relationship between permeability and damage, consistent with the two above asymptotic cases, is defined.; La durabilité de structures en béton est un problème dans lequel la rupture et l'endommagement sont couplés aux différentes attaques de l'environnement. Nous commençons par illustrer un tel couplage avec la lixiviation et la modélisation chimiomécanique de l'endommagement dans les bétons. Les couplages entre l'endommagement et les propriétés de transport du béton sont le deuxième exemple traité. Dans le cas d'un endommagement diffus, la perméabilité du matériau est contrôlée par la diminution de raideur moyenne due à la microfissuration. Lorsqu'une macrofissure s'est formée, la perméabilité est contrôlée par une fonction puissance de l'ouverture de fissure (écoulement de Poiseuille). Une relation entre la perméabilité et l'endommagement est définie, en accord avec ces deux cas limites.

International audience; The serviceability of concrete structures is a problem in which creep and damage are coupled. In this paper, we present experimental investigations on concrete that involve tertiary creep. We consider residual capacity tests on notched bending beams and investigate the evolution of size effect due to basic creep. In these experiments, beams are first subjected to a constant load, at a given ratio of the maximum capacity during 90 days. They are then loaded up to failure and their residual capacity is obtained. During the creep phase, acoustic emission is analyzed and it shows that damage develops under creep. The comparison between the size effect test results with and without creep exhibits variations of the fracture properties of the material. The fracture energy and the size of the fracture process zone decrease when creep occurs prior to failure. These results, which include size effect fracture tests, may serve for the development and validation of coupled creep-damage models.

International audience; Experimental tests exhibit a strong interaction between material damage and transport properties of concrete. There are at least two asymptotic cases where some theoretical modeling exists: in the case of diffuse cracking, the material permeability should be controlled by damage, e.g., by the decrease of average stiffness due to microcracking. In the case of localized microcracking, and after a macrocrack has formed, permeability should be controlled by a power function of the crack opening (Poiseuille flow). For quasi-brittle materials with evolving microstructure due to mechanical loads, a transition regime on the evolution of permeability between these two asymptotic cases is expected. In this contribution, we define a relationship between permeability and damage that is consistent with the two above configurations. One of the key issues is to relate the crack opening to the state variables in the continuum approach, so that the two asymptotic cases are expressed in the same variable system and can be matched. A simplified approach is used for this purpose. The permeability law is then derived using a mixing formula that weights each asymptotic regime with damage. To illustrate the influence of the matching law on structural response, finite-element simulations of a Brazilian splitting test and a comparison with existing test data are presented.