Justification and refinements of model B3 for concrete creep and shrinkage 1. statistics and sensitivity

Model B3 for creep and shrinkage prediction in the design of concrete structures, presented as a RILEM Recommendation inMater Struct.28 (1995) 357–365, is calibrated by a computerized data bank comprising practically all the relevant test data obtained in various laboratories throughout the world. The coefficients of variation of deviations of the model from the data are distinctly smaller than for the latest CEB model, and much smaller than for the previous ACI model (which was developed in the mid-1960's). The effect of concrete composition and design strength on the model parameters is identified as the main source of error. The model is simpler than the previous models (BP and BP-KX) developed at Northwestern University, yet it has comparable accuracy and is more rational.     

高强钢管高强混凝土徐变特性试验研究

高强钢管高强混凝土的应用越来越广泛,但目前对于其徐变特性的试验研究较少。该文对15根不同含钢率的高强钢管高强混凝土轴压短柱进行了365 d的收缩和徐变测试,并将试验结果与常用的徐变预测模型MC90、ACI209和MC2010等进行了对比。试验结果表明:高强钢管高强混凝土的徐变系数远小于素混凝土,当加载365 d后,素混凝土的徐变系数是高强钢管高强混凝土的2倍以上;含钢率对钢管混凝土试件的徐变有一定影响,徐变系数随着含钢率的增大而减小。在对比的3种常用徐变预测模型中,MC2010模型的徐变预测结果与试验结果吻合最好,可推荐用于高强钢管高强混凝土的收缩和徐变效应计算。此外,还将高强钢管高强混凝土与普通钢管混凝土的徐变试验结果进行了对比,结果表明,钢管混凝土的徐变随着核心混凝抗压强度的增加而减小。研究成果可为高强钢管高强混凝土轴心受压构件在正常使用阶段的徐变预测及徐变变形控制提供依据。     

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.     

Improved prediction model for time-dependent deformations of concrete: Part 2—Basic creep

The second part of this series presents the formulae for the prediction of basic creep of concrete, i.e. creep at no moisture exchange. The formulae give the secant uniaxial compliance function which depends on the stress level, and, as a special case, the compliance function for linear structural analysis according to the principle of superposition. The formulae are based on the recently developed solidification theory for concrete creep which takes into account simultaneous ageing, satisfies all the basic thermodynamic requirements, and avoids divergence of creep curves. The formulae, which describe both creep and elastic properties, involve only four free material parameters. All four appear linearly, so that optimum data fits can be obtained by linear regression. For the frequent situations where no test data for the particular concrete to be used are available, empirical formulae for predicting these four parameters from the concrete mix composition and the standard compressive strength are given. These formulae, however, involve considerable error. To avoid it, one should, whenever possible, carry out measurements of the elastic modulus and, if possible, also the short-time creep of 7 to 28 days duration. With such measurements, greatly improved predictions can be achieved. The predictions are compared with 17 extensive data sets taken from the literature, and the coefficients of variation of the deviations are found to be smaller than with previous models.     

Practical prediction of time-dependent deformations of concrete

Proposed is a practical model for predicting creep and shrinkage of concrete from the composition of concrete mix, strength, age at loading, conditions of environment, size and shape, etc. The main features are: double power law for basic creep, square-root hyperbolic law for shrinkage, diffusion-type size dependence of humidity effects, additive drying creep term related to shrinkage, and activation energy treatment of thermal effects. Optimization techniques are used to fit numerous test data available in the literature. The work is a continuation of previous investigations and consists of several parts. This first part deals with shrinkage.     

Creep and drying shrinkage of concrete containing GGBFS

Experiments were conducted on 150 × 600 mm cylindrical specimens to investigate creep and drying shrinkage of concrete containing ground granulated blast furnace slag (GGBFS). The creep strain was measured for 150 days under a constant sustained load. The creep strain recovery was measured for one subsequent month after the removal of the sustained load. The shrinkage strain was also measured for 180 days. The amount of cement replacement by GGBFS was 20%, 40% and 60% by weight of cement. The test results indicate that higher GGBFS percentage exhibits higher creep and shrinkage strains. At 150 days of sustained loading, the average creep coefficients of 20%, 40% and 60% GGBFS concrete are 16.3%, 33.3% and 55.2% higher than plain concrete. In the absence of a creep and shrinkage prediction model for GGBFS concrete, a modification factor is suggested for incorporating the effect of GGBFS proportion in the existing models. The available models for predicting creep and shrinkage strain of plain concrete are compared.     

钢骨混凝土短柱在长期轴向荷载作用下的试验研究

钢骨混凝土柱结构在过去几十年间已得到广泛的运用。但是目前关于这种柱结构在长期荷载作用下由于徐变和收缩引起的与时间相关的力学性能研究还开展得很少。该文开展了钢骨混凝土短柱的长期轴向荷载试验研究,还进行了这些柱的极限承载力破坏试验。试验监测了由徐变和收缩引起的柱的轴向长期变形。基于该实测曲线的分析表明,采用ACI 209R-92的收缩模型和CEB-FIP90的徐变模型,利用龄期调整有效模量法可以较好地模拟钢骨混凝土柱在长期轴向荷载作用下的变形发展。经历了长期加载后的试验柱的极限承载力破坏试验还表明,长期轴向荷载对柱的轴压承载力没有显著影响。     

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.     

Improved prediction model for time-dependent deformations of concrete: Part 4—Temperature effects

This Part presents a refinement of the BP model for the effects of temperature on the basic creep and drying creep of concrete. The temperature effect on basic creep is introduced through two different activation energies, one for the effect of temperature increase on the rate of hydration, which causes a decrease of creep, and one for the effect of temperature increase on the rate of creep, which causes an increase of creep. The dichotomy of these two opposing temperature influences is an essential feature, required for good agreement with test data. The greatest error in basic creep is again caused by the prediction of the material parameters from concrete composition and strength. This error can be largely eliminated by conducting limited short-time basic creep tests at different temperatures. Comparisons with 13 different data sets from the literature show a satisfactory agreement, better than that achieved with previous models, while at the same time the scope of the present model is broader. The effect of temperature on the creep of drying specimens is rather different because heating causes a moisture loss from unsealed specimens. The paper presents prediction formulae which modify those for drying creep at room temperature on the basis of the activation energy concept and take into account the effect of heating on the moisture loss. Comparisons with the limited test data that exist show satisfactory agreement. No additional material parameters depending on concrete composition and strength are introduced for drying creep.     

Shrinkage and creep of masonry mortar

Shrinkage and creep results are presented for different types of masonry mortars having a wide range of strength. The range of values implies that the type of mortar has an appreciable influence on deformation of masonry. The results are analysed, together with other data obtained from other investigations carried out over several years in the same laboratory, and predictive models developed. Factors quantified are strength, volume/surface/ ratio, time of exposure to drying (shrinkage) and time under load (creep). While creep is unaffected, for a given strength, shrinkage of water-cured mortar is greater than shrinkage of mortar that is cured under polythene. When based on 28-day strength, the average error of prediction for shrinkage is 19% but if based on the strength at the start of shrinkage, the error coefficient is reduced slightly to 16%. Creep is estimated with an average error of 24%.     

The long-term creep and shrinkage behaviors of green concrete designed for bridge girder using a densified mixture design algorithm

Creep and shrinkage behaviors are critical factors in the precast/prestressed concrete industry because these factors allow engineers to assess the long-term performance of concrete and to develop life-cycle estimates for concrete structures. The current study presents the results of an experimental work that addresses creep and shrinkage behaviors as well as the development of compressive strength in ordinary Portland cement concrete (OPC), high-performance concrete (HPC), and self-consolidating concrete (SCC). The concrete mixtures created for the present study were used to fabricate prestressed bridge girders. A conventional method (ACI) was used to design the mixture proportion for OPC and a densified mixture design algorithm (DMDA) was used to design the mixture proportions for HPC and SCC. All concrete mixtures had the same target strength of 69 MPa (10000 psi) at 56 days. Additionally, a comparative performance in terms of strength development and creep and shrinkage behaviors of ACI and DMDA concrete is performed in the present study. Test results show that all of the samples attained the target strength after 28 days of curing and that the strengths of each continued to increase afterward. Importantly, the incorporation of pozzolanic materials into concrete mixtures affected the propagation of creep strain and shrinkage positively. Furthermore, the DMDA concrete sample delivered better long-term performance than ACI concrete in terms of compressive strength, creep strain, and shrinkage.     

Long-term deflections of reinforced concrete elements: accuracy analysis of predictions by different methods

Long-term deflection response of reinforced concrete flexural members is influenced by the interaction of complex physical phenomena, such as concrete creep, shrinkage and cracking, which makes their prediction difficult. A number of approaches are proposed by design codes with different degrees of simplification and accuracy. This paper statistically investigates accuracy of long-term deflection predictions made by some of the most widely used design codes (Eurocode 2, ACI 318, ACI 435, and the new Russian code SP 52-101) and a numerical technique proposed by the authors. The accuracy is analyzed using test data of 322 reinforced concrete members from 27 test programs reported in the literature. The predictions of each technique are discussed, and a comparative analysis is made showing the influence of different parameters, such as sustained loading duration, compressive strength of concrete, loading intensity and reinforcement ratio, on the prediction accuracy.     

Stress prediction in very early-age concrete subject to restraint under varying temperature histories

Assessing the stress development in concrete requires an appropriate tensile creep model which is capable of incorporating the effect of the field environment conditions. This study quantifies the effect of temperature variation on the very early-age stress developments in restrained concrete by adopting a modified microprestress-solidification (MPS) theory-based creep model. The MPS creep model is first calibrated and verified based on the measured direct tensile creep data under normal and high temperature histories, it is then used to predict the very early-age stress development of the fully restrained concrete specimens under variable temperature history since casting. The predicted results are in good agreement with the experimental results. The tensile stress in restrained specimens can be relaxed by 80 %–87% within the first three days since casting. The predicted stress exhibits an obvious deviation from the measured one if temperature effect is not considered. Therefore, it is of importance to consider the temperature effect on concrete creep when the temperature variation in concrete is significant, and MPS creep model is valid for tensile stress prediction in concrete at very early ages.     

再生混凝土梁时变挠度分析与预测

重点考虑收缩和徐变等因素,对再生混凝土梁的时变挠度进行了理论分析。假定收缩和徐变不会相互影响,通过截面时随分析,得到再生混凝土梁时变相对受压区高度表达式。依据现有文献的试验数据,对分析结果准确性进行了验证。结果表明:对于不同的再生粗骨料取代率,时变挠度的计算结果与试验结果相比,大多数误差可控制在19%以内。该文的工作较好揭示了再生混凝土梁时变挠度的演化特点,可以为今后再生混凝土梁的长期挠度预测提供理论基础。     

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.     

Tests of composite concrete beams with prestressed planks

This paper deals with tests on composite concrete beams with prestressed concrete planks. It describes the separate influences of differential shrinkage and creep as well as stress redistribution due to a great strain difference at the adjoining faces between the prestressed plank and added concrete. Existing formulas relating to differential shrinkage and creep are based on the actual strains to be expected, but in order for the designer to have this information, extensive tests are required. This paper contains qualitative data in this regard and describes means by which information can be satisfactorily obtained, including the effect of stress redistribution.     

混凝土受力状态下超声波传播特性研究

本文研究了混凝土在单轴向压力下超声波速、幅值及主频的变化规律。试验表明，波速对混凝土构件中的应力变化敏感度较低，在７０％的极限应力范围内，波速基本保持稳定。因此在工程实际中利用超声波速－强度率定曲线推测混凝土承力构件的强度时，波速无需修正。与波速相比，超声幅值衰减量对检测裂筵开展则具有较高的灵敏度。为提高超声检测的精度，本文采用波速、幅值、频率综合判断法，提出了损伤系数的概念，对混凝土的损伤程度作出定量评价，文中结果对进一步提高混凝土无损检测精度，评估混凝土结构在受力、收缩、徐变等因素影响下的损伤程度有一定的应用价值。     

钢管混凝土劲性骨架拱桥收缩徐变影响理论研究

采用混凝土徐变理论、变形协调、中值理论及平衡条件,并考虑混凝土的弹性后效及受四周约束作用的徐变特性,导出了混凝土徐变、收缩引起的截面应力重分布的表达式。公式简单,应用方便,并对万县长江大桥收缩、徐变模型试验进行分析,所得结果与模型试验较为吻合,同时指出了影响该桥型应力的主要因素。     

Experimental validation of a framework for hygro-mechanical simulation of self-induced stresses in concrete

An accurate simulation of the internal stresses that develop in concrete structures in service demands the explicit consideration of the internal heat and moisture movements that induce strains, which in turn have the potential to cause relevant internal stresses. Following a previous exploratory work from the authors, in which a thermo-hygro-mechanical simulation framework had been proposed, the present paper focuses on the validation of the proposed methodology through an experimental program targeted to assist prediction of the evolution of bulk drying shrinkage (and the corresponding internal stresses) in three specimens of different sizes. This paper presents the entire experimental program, which involved extensive concrete characterization using three distinct sizes of specimens, namely: moisture diffusion with internal humidity sensors, compressive strength, E-modulus, creep and shrinkage on three distinct specimen sizes. The program also included characterization of cement paste shrinkage, which was accomplished employing a newly proposed methodology based on the use of very thin specimens monitored with a handheld microscope. Finally, the obtained experimental data was used for partial validation of predictive capacities of the above mentioned simulation framework, mostly in regard to the prediction of bulk shrinkage. It is noted that the validation does not focus on thermal modelling, since this is a matter that has been addressed by the authors in previous works.     

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.