Justification and refinements of model B3 for concrete creep and shrinkage 2. Updating and theoretical basis

Following statistical evaluation in part 1, this part deals with the improvement of prediction by updating one or two parameters of the model on the basis of short term tests and theoretical derivation of some formulae. The updating of model parameters is particularly important for high strength concretes and other special concretes containing various admixtures, superplasticizers, water-reducing agents and pozzolanic materials. For the updating of shrinkage prediction, a new method is presented in which the shrinkage half-time is calibrated by simultaneous measurements of water loss. This approach circumvents the ill-posedness of the shrinkage extrapolation problem. Theoretical justifications of various aspects of the model are given and a new formula for the additional creep due to drying (or stress-induced shrinkage) is derived. The new model should allow a more realistic assessment of the creep and shrinkage effects in concrete structures, which significantly affect durability and long term serviceability of civil engineering infrastructure.     

Short form of creep and shrinkage prediction model B3 for structures of medium sensitivity

TC Membership: Chairman: Zdeněk P. Bažant, USA;Secretary: Bernard Espion, Belgium;Members: Paul Acker France; Michel Auperin, France; Ignacio Carol, Spain; Domingo Carreira, USA; José M. R. Catarino, Portugal; Jenn-Chuan Chern, Taiwan; Mario Chirino, Italy; John W. Dougill, UK; Christian Huet, Switzerland; Jan Erik Jonasson, Sweden; Jin-Keun Kim, Korea; Vladimir Kristek Czech Republic; Harald S. Muller, Germany; Byung-Hwan Oh, Korea; Josko Ozbolt, Germany; Stuart G. Ried, Australia; Hans Reinhardt, Germany; Peter Schwesinger, Germany; Bretislav Teply, Czech Republic; Heinrich Trost, Germany; Tatsuya Tsubaki, Japan; Robert F. Warner, Australia; Folker H. Wittmann, Switzerland; J. Francis Young, USA.     

Practical formulation of shrinkage and creep of concrete

Materials and Structures - A set of algebraic formulas is proposed to describe the shrinkage and creep of concrete over the entire range of time durations of interest. The formulas cover: the...     

Sensitivity study of BP-KX and B3 creep and shrinkage models

A numerical study of sensitivity analysis and statistical prediction of concrete creep average compliance function and shrinkage strain is presented. Two advanced models—the BP-KX and the B3—are studied. The influence of uncertainty of the basic input variables is taken into account by considering them as random variables. The statistical correlation is also treated in a simplified form for the assessment of its influence. Utilising the numerical simulation Latin Hypercube Sampling, the statistical and sensitivity analyses are performed. The results using different models are also compared. Two alternative measures of sensitivity analysis are utilised: sensitivity in terms of coefficient of variation and sensitivity in terms of nonparametric rank-order correlation coefficient. The strength of concrete and humidity appear as the most dominant factors with regard to the variability of results. Also, the estimations of distribution functions of the models are shown. They provide the possibility of establishing appropriate confidence limits. The significant difference in their ranges for the models in question is also shown.     

Effect of metakaolin on creep and shrinkage of concrete

The effect of metakaolin (MK) on the creep and shrinkage of concrete mixes containing 0%, 5%, 10%, and 15% MK has been investigated. The results showed that the early age autogenous shrinkage measured from the time of initial set of the concrete was reduced with the inclusion of MK, but the long-term autogenous shrinkage measured from the age of 24 h was increased. At 5% replacement level, the effect of MK was to increase the total autogenous shrinkage considered from the time of initial set. While at replacement levels of 10% and 15%, it reduced the total autogenous shrinkage. The total shrinkage (autogenous plus drying shrinkage) measured from 24 h was reduced by the use of MK, while drying shrinkage was significantly less for the MK concretes than for the control concrete. The total creep, basic creep as well as drying creep were significantly reduced particularly at higher MK replacement levels. Compared with estimated values by the CEB 90 model, total creep of all concretes was overestimated, especially in the mixes containing the higher levels of MK. For basic creep, estimates for low levels of MK were acceptable but, for the higher levels, creep was overestimated.     

Short-term tensile creep and shrinkage of ultra-high performance concrete

The tensile creep and free shrinkage deformations of ultra-high performance concrete (UHPC) were examined through short-term testing to assess the influences of stress/strength ratio, steel fiber reinforcement, and thermal treatment. The use of fibers and the application of thermal treatment decreased 14-day drying shrinkage by more than 57% and by 82%, respectively. Increasing the stress-to-strength ratio from 40% to 60% increased the tensile creep coefficient by 44% and the specific creep by 11%, at 14 days of loading. Incorporating short steel fibers at 2% by volume decreased the tensile creep coefficient by 10% and the specific creep by 40%, at 14 days. Also, subjecting UHPC to a 48-h thermal treatment at 90 °C, after initial curing, decreased its tensile creep coefficient by 73% and the specific creep by 77% at 7 days, as compared to ordinarily cured companion mixes. Comparison of tensile creep behavior to published reports on compressive creep in UHPC reveal that these phenomena differ fundamentally and that further evaluation is necessary to better understand the underlying mechanisms of tensile creep in UHPC. Results from this study also showed that the effects of both thermal treatment and fiber reinforcement were more pronounced in tensile creep behavior than tensile strength results of different UHPC mixes. This emphasizes the importance of conducting tensile creep testing to predict long-term tensile performance.     

Practical prediction of creep and shrinkage of high strength concrete

Model for practical prediction of creep and shrinkage of normal strength concrete, developed previously, is extended to high strength concrete. It is found that only a minor adjustment for the concrete strength effect is needed in the formulas for drying creep. The formulas for basic creep and shrinkage need no adjustment. The prediction model is compared with test data for creep and shrinkage obtained recently by Ngab, Nilson and Slate, and by Collepardi, Corradi and Valente, and a satisfactory agreement is demonstrated. The coefficient of variation of the deviations from test data is not larger than that for the normal cient of variation of the deviations from test data is not larger than that for the normal strength range. However, the existing data are rather limited and further testing is desirable.     

Simulation of shrinkage distress and creep relief in concrete repair

This paper addresses the problem of stress buildup in the repair layer of a concrete patch repair system resulting from moisture diffusion. As moisture evaporates from the repair layer into the surrounding ambience of known relative humidity, the hardened concrete substrate restrains free shrinkage movement of the repair layer. As a consequence, primary tensile stresses are set up in the repair layer together with shear and peeling stresses at the interface of the repair layer-concrete substrate. The repair layer under non-uniformly increasing tensile shrinkage stresses undergoes restrained creep in tension, which results in the development of secondary stresses in the system. The secondary stresses due to restrained creep being of opposite sign to that of restrained shrinkage serve to relieve the primary shrinkage stress field and the net or combined stress buildup as a result is reduced.A finite element based computer program used for computing the time dependent moisture loss profile in the repair system is interfaced with a finite element based 2-D stress analysis program for computing the time dependent restrained shrinkage and creep stresses.Variation of normal and shear stresses across depth and width at critical locations in the patch repair and temporal variation of these stresses are presented. Influence of ultimate free shrinkage strain ε_sh^∞ and the buildup of tensile stresses versus the evolution of tensile strength capacity f′_t of the repair is highlighted. Also, possible zones of failure are identified in the repair layer and at the interface of the patch repair system.     

Constitutive equation for concrete creep and shrinkage based on thermodynamics of multiphase systems

Summary The constitutive equation for creep, shrinkage and thermal expansion, which reflects correctly the effect of variable humidity and temperature, including the effect of size, shape and stress distribution, is derived. Cement paste and concrete are treated as a multi-phase composite material, in which both the static and thermodynamic conditions of equilibrium must be considered.

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Résumé L'action des variations d'humidité et de température sur le béton, compte tenu des facteurs de dimension et de forme, ainsi que de la répartition des contraintes est traduite par l'équation fondamentale du fluage, du retrait et de la dilatation thermique. La pate de ciment et le béton sont étudiés en tant que matériaux composites multiphases dans lesquels les conditions d'équilibre, tant statique que thermodynamique, doivent être considérées.

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Modelling creep and shrinkage of concrete by means of effective stresses

A novel model of mechanical performance of concrete at early ages and beyond, and in particular, evolution of its strength properties (aging) and deformations (shrinkage and creep strains), described in terms of effective stress is briefly presented. This model reproduces such? phenomena known from experiments like drying creep or some additional strains, as compared to pure shrinkage, which appear during autogenous deformations of a maturing, sealed concrete sample. Creep is described by means of the modified microprestress-solidification theory with some modifications to take into account the effects of temperature and relative humidity on concrete aging. Shrinkage strains are modelled by using effective stresses giving a good agreement with experimental data also for low values of relative humidity. Results of four numerical examples based on the real experimental tests are solved to validate the model. They demonstrate its possibilities to analyze both autogenous deformations in maturing concrete, and creep and shrinkage phenomena, including drying creep, in concrete elements of different age, sealed or drying, exposed to external load or without any load.     

Long term deformations by creep and shrinkage in recycled aggregate concrete

The main aim of this work was to determine creep and shrinkage variations experienced in recycled concrete, made by replacing the main fraction of the natural aggregate with a recycled aggregate coming from waste concrete and comparing it to a control concrete. It was possible to state that the evolution of deformation by shrinkage and creep was similar to a conventional concrete, although the results after a period of 180 days showed the influence of the substitution percentage in the recycled aggregates present in the mixture. In the case when 100% coarse natural aggregate was replaced by recycled aggregate there was an increase in the deformations by creep of 51% and by shrinkage of 70% as compared to those experienced by the control concrete. The substitution percentages of coarse natural aggregate by coarse recycled aggregate were 20, 50 and 100%. Fine natural aggregate was used in all cases and the amount of cement and water–cement ratio remained constant in the mixture.     

Sampling analysis of concrete structures for creep and shrinkage with correlated random material parameters

The latin hypercube sampling method, which represents the most efficient way to determine the statistics of the creep and shrinkage response of structures, has previously been developed and used under the assumption that the random parameters of the creep and shrinkage prediction model are mutually independent. In reality they are correlated. On the basis of existing data, this paper establishes, by means of the method of maximum likelihood, the joint multivariate probability distribution of the random parameters involved, tests the hypothesis of mutual dependence of parameters on the basis of the χ²-distribution, and generalizes the latin hypercube sampling method to the case of correlated multinormal random parameters. The generalization is accomplished by an orthogonal matrix transformation of the random parameters based on the eigenvectors of the inverse of the covariance matrix. This yields a set of new random parameters which are uncorrelated (independent) and can be subjected to the ordinary latin hypercube sampling, with samples of equal probabilities. Numerical examples of statistical prediction of creep and shrinkage effects in structures confirm the practical feasibility of the method and reveal a good agreement with the scatter observed in some previous experiments.     

Practical prediction of cyclic humidity effect in creep and shrinkage of concrete

The previously published BP Model for prediction of concrete creep and shrinkage is generalized to cover the increase of creep caused by the cyclic component of environmental relative humidity. A simple formula, which is partly empirical, partly based on the diffusion theory, is proposed and is calibrated by comparisons with test data from the literature.     

Practical prediction model for shrinkage of steel fibre reinforced concrete

A practical prediction model is proposed for predicting the shrinkage of steel fibre reinforced concrete (SFRC) from the composition of concrete mix, strength, age when drying begins, conditions of environment, size and shape of structures, fibre volume, aspect ratio of fibre, etc. The formulas were developed according to an extension of the well-recognized BP prediction model for the shrinkage of plain concrete (OPC). All important features of the BP prediction model, such as the diffusion-type size dependence of humidity effects and the square-root hyperbolic law for shrinkage, are automatically adopted for SFRC. In order to supplement the insufficient test data collected from the literature, a recently finished experimental series was used to expand the databank and hence the authors have a better command of the prediction formulas. Results of shrinkage from the literature and from the test series are reported, together with comparisons with predictions using the proposed model.     

Possible mechanisms of influence of admixtures on drying shrinkage and creep in cement paste and concrete

This paper presents data on the influence of a lignosulphonate admixture, used either with or without the accelerating admixtures calcium chloride and triethanolamine, on drying shrinkage and creep in concrete. The ability of these admixtures to give rise to significant increases in drying shrinkage and creep is discussed in terms of the Feldman and SeredaNew Model for the structure of hydrated Portland cement. It is postulated that the increases in drying shrinkage and creep can be attributed to the influence of the admixtures in altering the initial spacing and degree of layering of the tobermorite gel, which takes place on first dryring.

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Résumé On présente ici des données sur l'action d'un lignosulfonate utilisé comme adjuvant, avec ou sans les accélérateurs de prise que sont le chlorure de calcium et la triéthalonamine, sur le séchage au retrait et le fluage de la pate de ciment et du béton. On montre que le lignosulfonate peut déterminer des valeurs notablement plus grandes des déformations à court terme dues au séchage, et que cette action est ultérieurement renforcée par l'inclusion de chlorure de calcium ou de triéthalonamine. On examine le phénomène conformément auNouveau Modèle de Feldmann et Sereda pour la structure de ciment Portland hydraté. L'accroissement qu'on observe du retrait au séchage est attribué à la propriété de l'adjuvant d'altérer la distribution et l'importance des courbes dugel de tobermorite, tel qu'il s'était constitué lors du premier séchage. On suppose que cette modification de structure facilite un accroissement du retrait au séchage par une augmentation du nombre de sites qui permettent le départ de l'eau intercalée, et par l'accroissement de l'espace interacalaire ou du volume solide de la structure de la pate. On montre de même que le lignosulfonate peut amener un accroissement notable du fluage dans un environment de retrait, cet effet étant là encore renforcé par l'inclusion des accélérateurs que sont le chlorure de calcium ou la triéthalonamine. Cependant, cet effet n'a pas la même importance lorsque les éprouvettes sont maintenues dans les conditions de conservation et chargées dans une chambre à brouillard (et l'on s'approche ainsi du fluage de base). Ce fait vient appuyer l'hypothèse que le mode d'action des adjuvants à base de lignosulfonate sur le fluage de la pate de ciment et du béton est essentiellement similaire à celui qui est considéré pour le retrait de séchage à la différence évidente que les contraintes sont incluses dans les forces qui intervienment.