Theoretical and practical differences between creep and relaxation Poisson's ratios in linear viscoelasticity

International audiencePoisson's ratio is a well-defined parameter in elasticity. For time-dependent materials , multiple definitions based on the ratios between lateral and axial deformations are available. Here, we focus ourselves on the two most widely used definitions in the time domain, which define time-dependent functions that we call relaxation Poisson's ratio and creep Poisson's ratio. Those two ratios are theoretically different, but are linked in an exact manner through an equation we derive. We show that those two functions are equal at both initial and large times and that their derivatives with respect to time also are. Based on simple rheological models for both the deviatoric and volumetric creep behaviors, we perform a parametric study and show that the difference between those two time-dependent Poisson's ratios can be significant. However, based on creep data available in the literature, we show that, for cementitious materials, this difference can be negligible or not, depending on the case

Retrait et fluage des matériaux cimentaires sous chargement multiaxial : modèle poromécanique pour application dans l’industrie nucléaire

The main interest of the thesis is the long-term mechanical behavior of the containment building of french nuclear power plants. The containment buildings of the power plants are biaxially prestressed concrete structures. Therefore, we summarize the problem of interest into two following key points: biaxiality of load and long-term delayed strain.In order to characterize the delayed strain under biaxial load, our study first concentrates on the viscoelastic Poisson's ratio of concrete. In this purpose, we start by scrutinizing the definition of Poisson's ratio in non-aging linear isotropic viscoelasticity. Then, from the analysis of experimental results from the literature, we can obtain the viscoelastic Poisson's ratio of concrete. As an extension, we use micromechanics to shed some light on the long-term creep mechanism of the C-S-H gel.In a second step, we aim at proposing a poroviscoelastic model without postulating a priori the classical decomposition of delayed strains. We start by identifying the major experimental tendencies and physical phenomena that we aim at capturing with the model. From experimental data of autogenous shrinkage and basic creep from the literature, we analyze the possible physical origin of long-term autogenous shrinkage. In the end, a physics-based poroviscoelastic model is proposed, derived from the poromechanics theory. The prediction of the model is compared with experimental results from literatureL’intérêt principal de la thèse est le comportement mécanique à long terme des enceintes de confinement des centrales nucléaires françaises. Les enceintes de confinements des centrales sont des structures en béton précontrainte biaxiale. Nous résumons donc le problème que nous nous adressons en deux points clés : la biaxialité du chargement et les déformations différées à long terme.Afin de caractériser les déformations différées sous chargement biaxial, nous nous concentrons dans un premier temps au coefficient du Poisson viscoélastique du béton. Dans ce but, nous commençons par examiner minutieusement la définition du coefficient de Poisson dans le cadre de la viscoélasticité linéaire isotrope non-vieillissente. Puis, en analysant les résultats expérimentaux de la littérature, nous obtenons le coefficient de Poisson viscoélastique du béton. Comme extension, nous amenons une analyse micromécanique et essayons d’éclaircir le mécanisme du fluage à long terme du gel de C-S-H.Dans un deuxième temps, nous visons à proposer un modèle poroviscoélastique sans supposer préalablement la décomposition classique des déformations différées. Nous commençons par identifier les tendances expérimentales majeures et phénomènes physiques que nous voulons capturer par le modèle. À partir des résultats expérimentaux du retrait endogène et du fluage propre de la littérature, nous analysons l’origine physique possible du retrait endogène à long terme. À la fin, dérivé de la théorie de la poromécanique, un modèle poroviscoélastique basé sur la physique est proposé. La prédiction du modèle est comparée avec les résultats expérimentaux de la littératur

Thermal Expansion of Cement Paste at Various Relative Humidities after Long-term Drying: Experiments and Modeling

International audienceThe coefficient of thermal expansion (CTE) of cement paste is an essential parameter for estimating cracks of cementbased structures, including under normal operating conditions. The CTE of low-heat Portland cement pastes dried for along term at various relative humidities were measured by applying trapezoidal temperature history. The measured CTEwas a convex function when displayed versus relative humidity and was highest at the relative humidity of 58%. At therelative humidity of 11%, the CTE was similar to the one of the fully dried sample. Based on a drying shrinkage modelin the literature that classifies pore water as free liquid water and adsorbed water, we computed pore pressure change andcorresponding strain, from which the CTEs were estimated. The microstructural rearrangements of cement paste due tolong-term drying were taken into account by obtaining pore size distributions from water vapor sorption isotherm. TheCTEs predicted with the model agree well with the measured ones

Addendum to 'Is long-term autogenous shrinkage a creep phenomenon induced by capillary effects due to self-desiccation?'

Prof. F.-J. Ulm brought to our attention that we forgot to include an important reference in our manuscript. Indeed, Ulm et al. [1] showed that, for 5 concretes that differed in their water-to-cement ratio and for which basic creep and autogenous shrinkage were measured by Le Roy [2], the long-term kinetics of autogenous shrinkage could be explained by creep of the solid skeleton under the action of an internal pore pressure. Their conclusion was based on the observed linearity of the relationship between basic creep compliance and increase in autogenous shrinkage in the long term.From the slope of this linear relationship, they back-calculated an “effective pore pressure” displayed in Fig. 1. Interestingly, this uniaxial “effective pore pressure” – merely calculated from macroscopic observables – is in very good agreement (both in terms of magnitude and in terms of trend with water-to-cement ratio) with the capillary stresses that we estimated at the pore scale with the help of micromechanics (see Fig. 6 in our manuscript). The reason for this agreement lies in Eq. 16 of our manuscript, which reads Σ∞ = σ∞ and shows that, in the linear viscoelastic case with a viscoelastic Poisson's ratio of the matrix equal to 0.2, the long-term “effective” macroscopic stress Σ∞ that acts at the scale of the concrete sample is equal to the long-term microscopic stress σ∞ that acts on the C-S-H gel

Is long-term autogenous shrinkage a creep phenomenon induced by capillary effects due to self-desiccation?

Long-term shrinkage and creep of concrete can impact the lifetime of concrete structures. Basic creep of cementitious materials is now known to be non-asymptotic and evolve logarithmically with time at large times. However, the long-term kinetics of autogenous shrinkage is not systematically analyzed. Here we first aim at finding out how autogenous shrinkage evolves with time at long term. We analyze all experimental data available in the literature and find that autogenous shrinkage evolves logarithmically with respect to time at long term, like basic creep. Then, by considering concrete as a multiscale material, we obtain the bulk creep modulus of the calcium silicate hydrate gel. In the end, we show that the kinetics of long-term autogenous shrinkage can be a viscoelastic response to self-desiccation by comparing the mechanical stress that should be applied to explain this long-term kinetics of autogenous shrinkage with the capillary force due to self-desiccation

A viscoelastic poromechanical model for shrinkage and creep of concrete

International audienceLong-term delayed strain of concrete impacts the lifetime of civil engineering structures such as dams, nuclear power plants, nuclear waste storage tunnels or large bridges. In design practice, the long-term delayed strain of concrete is decomposed into four components: autogenous shrinkage, basic creep, drying shrinkage and drying creep. The four components are first computed separately and then summed up to obtain the total delayed strain of concrete, without wondering about any potential correlation between them. In this work, we aim at modeling the total delayed strain in a unified manner, without assuming this decomposition a priori. Such model is derived in the framework of viscoelastic poromechanics. The influence of relative humidity on the creep properties is taken into account. We assume that drying creep is due to the fact that the mechanical consequences of capillary effects are larger in loaded drying specimens than in non-loaded drying specimens. The model is validated by comparing the prediction with experimental results of delayed strain from the literature and discussed with respect to existing models

Time evolutions of non-aging viscoelastic Poisson's ratio of concrete andimplications for creep of C-S-H

The viscoelastic Poisson's ratio of concrete is an essential parameter to study creep and loss of prestress in biaxially prestressed structures. Here we first aim to scrutinize the various existing definitions of this ratio. We then analyze all creep data of concrete available in literature that make it possible to compute the evolutions of this viscoelastic Poisson's ratio, which, for mature concrete, is found to remain roughly constant or slightly decrease over time, such as to reach a long-term value always comprised between 0.15 and 0.2. Then, the long-term viscoelastic Poisson's ratio of concrete is downscaled to the level of calciumsilicate hydrates (noted C-S-H) with micromechanics. The long-term viscoelastic Poisson's ratio of the C-SH gel is found to range between 0 and 0.2. Finally, the identification of this range is used to discuss various potential creep mechanisms at the level of the C-S-H particles.Le coefficient de Poisson de fluage du béton est un paramètre essentiel pour prédire les déformations différées du béton et les pertes de précontrainte. Ici nous étudions d'abord les différentes définitions de ce coefficient. Puis, nous analysons les différents essais disponibles dans la littérature qui permettent de calculer le coefficient de Poisson. L'analyse des résultats montre qu'il est quasiment constant et que sa valeur à long terme est comprise entre 0.15 et 0.2. A partir d'une approche micromécanique par homogénéisation, cela conduit à estimer le coefficient de Poisson des C-S-H entre 0 et 0.2. Les mécanismes potentiels de fluage du béton sont alors discutés sur la base de ces résultats