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[en] A physically based model for auotgenous shrinkage and swelling of portland cement paste is necessary for computation of long-time hydgrothermal effects in concrete structures. The goal is to propose such a model. As known since 1887, the volume of cement hydration products is slightly smaller than the original volume of cement and water (chemical shrinkage). Nevertheless, this does not imply that the hydration reaction results in contraction of the concrete and cement paste. According to the authors’ recently proposed paradigm, the opposite is true for the entire lifetime of porous cement paste as a whole. The hydration process causes permanent volume expansion of the porous cement paste as a whole, due to the growth of C–S–H shells around anhydrous cement grains which pushes the neighbors apart, while the volume reduction of hydration products contributes to porosity. Additional expansion can happen due to the growth of ettringite and portlandite crystals. On the material scale, the expansion always dominates over the contraction, i.e., the hydration per se is, in the bulk, always and permanently expansive, while the source of all of the observed shrinkage, both autogenous and drying, is the compressive elastic or viscoelastic strain in the solid skeleton caused by a decrease of chemical potential of pore water, along with the associated decrease in pore relative humidity. As a result, the selfdesiccation, shrinkage and swelling can all be predicted from one and the same unified model, in which, furthermore, the low-density and high-density C–S–H are distinguished. A new thermodynamic formulation of unsaturated poromechanics with capillarity and adsorption is presented. The recently formulated local continuum model for calculating the evolution of hydration degree and a new formulation of nonlinear desorption isotherm are important for realistic and efficient finite element analysis of shrinkage and swelling. Comparisons with the existing relevant experimental evidence validate the proposed model.
[en] The reporting and evaluation of creep tests of concrete is complicated by the fact that creep is significant even for the shortest observable load durations. Compared to the strain after 0.1 s load duration, the strain at 2 h duration is typically 53% greater. Most experimenters have for decades been unaware of this fact. Consequently, the reported creep curves require correction by a time shift, which ranges from 0 to 2 h. This further implies a vertical shift of entire creep curve, important for all times up to structure lifetime. To filter out the errors, it is argued that, within an initial period during which the advance of hydration is negligible, which is normally about 1 day, the initial basic creep must follow a power law of the time. Creep test data from the literature are used to prove it. Corrections by time and deformation shifts are determined by minimization of the sum of squared deviations of the power law from the creep test data. For a fixed exponent n and time shift s, the optimization is reduced to linear regressions of two kinds, depending on whether the data are given in terms of either the compliance function or the creep coefficient. For both, the linear regression parameters depend nonlinearly on the chosen values of n and s. To avoid nonlinear optimization, which need not converge to the correct result, a set of many discrete values of n and s within their realistic ranges is selected and the (n, s) combination minimizing the objective function is obtained by a search. Enforcing a power law form of the initial creep curve is found to lead to better data fits. The optimum exponent n for the entire database is around 0.3, applicable to the time period cca (10 s, 1 day). After that, the exponent transits to about 0.1, and prior to that it is about 0.08. After filtering out the errors, the corrected database will allow better calibration of the general creep prediction model such as B3 or B4.
[en] The article Statistical filtering of useful concrete creep data from imperfect laboratory tests, written by Mohammad Rasoolinejad, Saeed Rahimi-Aghdam, Zdenek P. Bazant, was originally published online without Open Access. After publication in volume 51, article ID 153 RILEM decided to grant the author to opt for open choice and to make the article an open-access publication.
[en] In modern concretes, the autogenous shrinkage, i.e., the shrinkage of sealed specimens, is much more important than it is in traditional concretes. It dominates the shrinkage of thick enough structural members even if exposed to drying. A database of 417 autogenous shrinkage tests, recently assembled at Northwestern University, is exploited to develop empirical predictive equations, which improve significantly those embedded in RILEM Model B4. The data scatter is high and the power law (time)0.2 is found to be optimal for times ranging from hours to several decades of years, as the test data give no hint of upper bound. Statistics of data fitting yields the approximate dependence of the power law parameters on the water-cement and aggregate-cement ratios, cement type, additives such as the blast furnace slag and silica fume, and curing type and duration. Alternatively, the power law parameters can be reasonably well predicted from the compression strength alone. Since some database entries do not report all these composition parameters and others do not report the compressive strength, and since the concrete strength is often the only material property specified in design, two types of models are formulated—composition based, and strength based. Both are verified by statistical comparisons with individual tests, and optimized by nonlinear statistical regression of the entire database, so as to minimize the coefficient of variation of deviations from the data points normalized by the overall data mean. The regression is weighted so as to compensate for the bias due to crowding of data in the short-time range. Statistical comparisons with the prediction models in the JSCE code, Eurocode and CEB MC90-99 code (identical to fib Model Code 2010) show the present model to give significantly better data fits. Finally it is emphasized that, in presence of external drying and creep, accurate predictions will require treating the autogenous shrinkage as a consequence of pore humidity drop caused jointly by self-desiccation due to hydration and by moisture diffusion, and solving the time evolution of humidity profiles. The present model is proposed as an update for the autogenous shrinkage formula in model B4, although recalibration of the whole B4 would be needed.