B3 Model Research Articles

Modeling early-age stress development of restrained concrete

The B3 Model is a compliance model that was designed and calibrated to estimate the instantaneous and time-dependent strain behavior of concrete with an age of 1 day or more. However, it was not designed to model the rapidly changing viscoelastic and elastic properties of early-age concrete between setting and 1 day. The early-age stress development, free strain, and mechanical property development of 28 concrete mixtures were measured to model the early-age stress development of concrete. The mixtures utilized three water–cement ratios, five coarse aggregate types, two curing temperature scenarios, and densities from 1,390 to 2,320 kg/m3 (87–145 lb/yd3). Modifications were made to the B3 Model to account for the early-age viscoelastic and elastic behavior of concrete. The effect of the modifications made to the B3 Model are limited to improving the early-age response and have minimal effect on the later-age compliance estimated with the original B3 Model. The modifications to the B3 Model significantly improved the unbiased estimate of standard deviation from 0.74 MPa (110 psi) to 0.39 MPa (57 psi) and coefficient of variation from 0.23 to 0.79 compared to the unmodified B3 Model.

Long-Term Deflections of Crushed Limestone Sand Concrete Beams

Creep tests of three crushed limestone sand concrete beams were conducted. The mid-span creep deflections and creep deflection coefficients of the beams in the first six months were measured. The results show that the creep deflection is significantly affected by the environmental humidity and temperature conditions. The formula of the mid-span creep deflection is derived based on the creep coefficients for simple supported beams. The mid-span creep deflections of beams are calculated using the CEB-FIP 90, ACI 209, and B3 models to predict the creep coefficient separately. Comparisons between the calculated values and experimental results indicate that the coefficients obtained using the ACI 209 model fit the results best. The formula of the creep coefficient is derived from the mid-span creep deflection. The creep coefficient of crushed limestone sand concrete is calculated from the measured mid-span creep deflection, and a best-fit formula is proposed for the creep coefficient.

Thermo‐hygro‐mechanical meso‐scale analysis of concrete as a viscoelastic‐damaged material

PurposeKnowledge of the behavior of concrete at mesoscale level requires, as a fundamental aspect, to characterize aggregates and specifically, their thermal properties if fire hazards (e.g. spalling) are accounted for. The assessment of aggregates performance (and, correspondingly, concrete materials made of aggregates, cement paste and ITZ – interfacial transition zone) is crucial for defining a realistic structural response as well as damage scenarios.Design/methodology/approachIt is here assumed that concrete creep is associated to cement paste only and that creep obeys to the B3 model proposed by Bažant and Baweja since it shows good compatibility with experimental results and it is properly justified theoretically.FindingsFirst, the three‐dimensionality of the geometric description of concrete at the meso‐level can be appreciated; then, creep of cement paste and ITZ allows to incorporate in the model the complex reality of creep, which is not only a matter of fluid flow and pressure dissipation but also the result of chemical‐physical reactions; again, the description of concrete as a composite material, in connection with porous media analysis, allows for understanding the hygro‐thermal and mechanical response of concrete, e.g. hygral barriers due to the presence of aggregates can be seen only at this modelling level. Finally, from the mechanical viewpoint, the remarkable damage peak effect arising from the inclusion of ITZ, if compared with the less pronounced peak when ITZ is disregarded from the analysis, is reported.Originality/valueThe fully coupled 3D F.E. code NEWCON3D has been adopted to perform fully coupled thermo‐hygro‐mechanical meso‐scale analyses of concrete characterized by aggregates of various types and various thermal properties. The 3D approach allows for differentiating each constituent (cement paste, aggregate and ITZ), even from the point of view of their rheologic behaviour. Additionally, model B3 has been upgraded by the calculation of the effective humidity state when evaluating drying creep, instead than using approximate expressions. Damage maps allows for defining an appropriate concrete mixture to withstand spalling and to characterize the coupled behaviour of ITZ as well.

Creep analysis of CFT columns subjected to eccentric compression loads

By considering the creep characteristics of concrete core under eccentric compression, a creep model of concrete filled steel tubes (CFT) columns under eccentric compressive loads is proposed based on the concrete creep model B3. In this proposed model, a discrete element method is introduced to transform the eccentric loading into axial loading. The validity of the model is verified by comparing the predicting results with the published creep experiments results on CFT specimens under compressive loading, together with the predicting values based on other concrete creep models, such as ACI209, CEB90, GL2000 and elastic continuation and plastic flow theory. By using the proposed model, a parameters study is carried out to analysis the effects of practical design parameters, such as concrete mix (e.g. water to cement ratio, aggregate to cement ratio), steel ratio and eccentricity ratio, on the creep of CFT columns under eccentric compressive loading.

Carcinogenicity Prediction of Noncongeneric Chemicals by a Support Vector Machine

The ability to identify carcinogenic compounds is of fundamental importance to the safe application of chemicals. In this study, we generated an array of in silico models allowing the classification of compounds into carcinogenic and noncarcinogenic agents based on a data set of 852 noncongeneric chemicals collected from the Carcinogenic Potency Database (CPDBAS). Twenty-four molecular descriptors were selected by Pearson correlation, F-score, and stepwise regression analysis. These descriptors cover a range of physicochemical properties, including electrophilicity, geometry, molecular weight, size, and solubility. The descriptor mutagenic showed the highest correlation coefficient with carcinogenicity. On the basis of these descriptors, a support vector machine-based (SVM) classification model was developed and fine-tuned by a 10-fold cross-validation approach. Both the SVM model (Model A1) and the best model from the 10-fold cross-validation (Model B3) runs gave good results on the test set with prediction accuracy over 80%, sensitivity over 76%, and specificity over 82%. In addition, extended connectivity fingerprints (ECFPs) and the Toxtree software were used to analyze the functional groups and substructures linked to carcinogenicity. It was found that the results of both methods are in good agreement.

Improved Estimation of Long-Term Relaxation Function from Compliance Function of Aging Concrete

Based on asymptotic considerations, this paper develops an improved approximate formula for estimating the relaxation function from the given compliance function of concrete, which is considered as aging, linearly viscoelastic material. Compared with the formula developed in 1979 by Bazant and Kim, the new formula prevents any violation of the thermodynamic requirement of nonnegativeness of the relaxation function. It is significantly more accurate for long-time relaxation of concrete loaded at a young age, and, for this reason, it is particularly useful for compliance functions that correctly describe multidecade creep, which is the case for model B3 compliance function (a 1995 international RILEM recommendation) and not, for example, for the compliance functions of the American, European, Japanese, and Canadian standard recommendations, for which the benefit is smaller. The main application of the new formula is to evaluate the aging coefficient of the age-adjusted effective modulus method (AAEM) from the compliance function specified by the standard recommendation. The AAEM, developed in 1972 at Northwestern University and embodied in most standard design recommendations including those of the American Concrete Institute (ACI) and the Federation internationale du beton ( fib), provides an approximate estimate of the creep effects in structures according to the principle of superposition, which itself is a simplification neglecting nonlinear and diffusion effects.DOI:10.1061/ (ASCE)EM.1943-7889.0000339. © 2013 American Society of Civil Engineers. CE Database subject headings: Creep; Concrete; Relaxation (mechanics); Creep; Aging (material). Author keywords: Creep; Concrete; Stress relaxation; Aging; Creep analysis of structures.

Creep Effects on the Reliability of a Concrete-Filled Steel Tube Arch Bridge

The deterioration and ageing process make the reliability of bridges a time-variant problem. However, most studies about time-dependent reliability focus on material corrosion and damage, less attention is given to the effects of concrete creep on the reliability of bridges. This paper presents a case study to investigate the influence of concrete creep on the serviceability reliability of concrete-filled steel tube (CFST) arch bridges, which have a wide application in China. The structural creep effect was analyzed by Model B3 and the age-adjusted effective modulus method; the reliability analysis was performed by Monte Carlo simulation with the Latin Hypercube sampling method, considering random variables involved in three aspects: creep model uncertainty, and variations of material and geometric properties. The analytic results show that the serviceability reliability of CFST arch bridges decreases due to creep, and creep model uncertainty is the most important factor for the structural creep effects and serviceability reliability.

Excessive Long-Time Deflections of Prestressed Box Girders. I: Record-Span Bridge in Palau and Other Paradigms

The segmental prestressed concrete box girder of Koror-Babeldaob (KB) Bridge in Palau, which had a record span of 241 m (791 ft), presents a striking paradigm of serviceability loss because of excessive multidecade deflections. The data required for analysis have recently been released and are here exploited to show how the analysis and design could be improved. Erected segmentally in 1977, this girder developed a midspan deflection of 1.61 m (5.3 ft) compared with the design camber after 18 years, and it collapsed in 1996 as a consequence of remedial prestressing, after a 3-month delay. Compared with three-dimensional analysis, the traditional beam-type analysis of box girder deflections is found to have errors up to 20%, although greater errors are likely for bridges with higher box-width-to-span ratios than the KB Bridge. However, even three-dimensional finite-element analysis with step-by-step time integration cannot explain the observed deflections when the current American Concrete Institute, Japan Society of Civil Engineers, Comite Euro-International du Beton (or Comite Euro- International du Beton—Federation internationale de la precontrainte), and Gardner and Lockman prediction models for creep and shrinkage are used. These models give 18-year deflection estimates that are 50-77% lower than measured and yield unrealistic shapes of the deflection history. They also predict the 18-year prestress loss to be 46-56% lower than the measured mean prestress loss, which was 50%. Model B3, which is the only theoretically based model, underestimates the 18-year deflection by 42% and gives a prestress loss of 40% when the default parameter values are used. However, in Model B3, several input parameters are adjustable and if they are adjusted according to the long-time laboratory tests of Brooks, a close fit of all the measurements is obtained. For early deflections and their extrapolation, it is important that Model B3 can capture realistically the differences in the rates of shrinkage and drying creep caused by the differences in the thickness of the walls of the cross section. The differences in temperature and possible cracking of the top slab also need to be taken into account. Other paradigms on which data have recently been released are four bridges in Japan and one in the Czech Republic. Their excessive deflections can also be explained. The detailed method of analysis and the lessons learned are presented in Part II. DOI: 10.1061/(ASCE)ST.1943-541X .0000487. © 2012 American Society of Civil Engineers. CE Database subject headings: Creep; Shrinkage; Box girders; Serviceability; Deflection; Span bridges. Author keywords: Prestressed box girder; Bridges; Segmental erection; Shear lag; Design standards; Concrete; Relaxation.

Creep of AFRP Confined High-Strength Concrete Columns under Low-Level Stress

This paper investigates the creep of fiber-wrapped high-strength concrete (HSC) columns (FWHSCCs) under low level axial stress by testing and modeling. Firstly, an experimental work on the creep of four FWHSCCs is presented. Secondly, by introducing modified coefficients about compressive strength, water-cement ratio and silica fume content of concrete, a modified model suitable for predicting the creep of HSC, based on Bažant's B3 model for normal concrete creep prediction, is proposed. Thirdly, considering the state of triaxial stresses of the concrete core, the autogenous shrinkage of HSC, and the interaction stress history, an analytical model based on the proposed model for HSC creep and the power law for fiber reinforced polymer (FRP) creep is developed for predicting the creep of FWHSCC. The prediction results agree well with the test data. This investigation also shows the creep of FWHSCCs is lower than that of FRP wrapped normal strength concrete column.

Modeling of Concrete Creep Based on Microprestress-solidification Theory

Creep of concrete is strongly affected by the evolution of pore humidity and temperature, which in turn depend on the environmental conditions and on the size and shape of the concrete member. Current codes of practice take that into account only approximately, in a very simplified way. A more realistic description can be achieved by advanced models, such as model B3 and its improved version that uses the concept of microprestress. The value of microprestress is influenced by the evolution of pore humidity and temperature. In this paper, values of parameters used by the microprestress-solidification theory (MPS) are recommended and their influence on the creep compliance function is evaluated and checked against experimental data from the literature. Certain deficiencies of MPS are pointed out, anda modified version of MPS is proposed.

Prediction of Creep Deformation in Concrete Using Some Design Code Models

The tendency of a concrete material to deform under stress is often responsible for excessive deflection at service loads which can compromise the performance of elements with a structure. Hence, the realistic prediction of both the magnitude and rate of creep strain is an important requirement of the design process. Therefore, relatively simple empirically based national design Code models are analyzed in order to predict the magnitude of creep strain. The models assessed are ACI 209 (1992), AS 3600 (1988), BS 8110 (1985), CEB-FIP (1978), CEB-FIP (1990), SAB 0100 (1992) and the RILEM Model B3 (1995).

Influence of Fly Ash Content in Cement Paste on Size of Creep

The cement paste is basic part of concrete and can contain a various additives. Fly ash is one of the materials useable as an admixture in the cement paste and concrete. The changes of properties of the cement paste mixed with fly ash were observed during several months. Creep of dried and saturated cement paste was measured for one complete month. The preparation of the cement paste and specimens is described in paper, too. From tests were obtaining two different kinds of data, about water dried and saturated specimens. The measured data was evaluated and compared with results of computational model with a creep model B3. © 2012 The Authors. Published by Elsevier Ltd.

Overall Memory Impairment Identification with Mathematical Modeling of the CVLT-II Learning Curve in Multiple Sclerosis.

The CVLT-II provides standardized scores for each of the List A five learning trials, so that the clinician can compare the patient's raw trials 1–5 scores with standardized ones. However, frequently, a patient's raw scores fluctuate making a proper interpretation difficult. The CVLT-II does not offer any other methods for classifying a patient's learning and memory status on the background of the learning curve. The main objective of this research is to illustrate that discriminant analysis provides an accurate assessment of the learning curve, if suitable predictor variables are selected. Normal controls were ninety-eight healthy volunteers (78 females and 20 males). A group of MS patients included 365 patients (266 females and 99 males) with clinically defined multiple sclerosis. We show that the best predictor variables are coefficients B3 and B4 of our mathematical model B3 ∗ exp(−B2 ∗ (X − 1)) + B4 ∗ (1 − exp(−B2 ∗ (X − 1))) because discriminant functions, calculated separately for B3 and B4, allow nearly 100% correct classification. These predictors allow identification of separate impairment of readiness to learn or ability to learn, or both.

Effects of Humidity Field on Creep of Reinforced Concrete Beams

Creep, as one of the most important properties of concrete, has important influences on concrete structures. In present domestic researches, studies on humidity diffusion in concrete are relative inadequate; and few models can take comprehensive consideration on humidity factors. According to humidity diffusion theory of concrete, this paper studied the distribution of humidity field within concrete at constant humidity condition by using finite element method. Based on the drying creep of the Model B3, this paper analyzes the effects of humidity field on creep of RC beams.

Creep effects on dynamic behavior of concrete filled steel tube arch bridge

Long-term properties of concrete affect structures in many respects, not excepting dynamic behaviors. This paper investigates the influence of concrete creep on the dynamic behaviors of concrete filled steel tube (CFT) arch bridges, by means of combining the analytical method for the creep of axially compressed CFT members, which is based on Model B3 for concrete creep, with the finite element model of CFT arch bridges. By this approach, the changes of the stress and strain of each element in the bridge with time can be obtained and then transformed into damping and stiffness matrices in the dynamic equation involved in the finite element model at different times. A numerical example of a long-span half- through CFT arch bridge shows that creep influences the natural vibration characteristics and seismic responses of the bridge considerably, especially in the early age. In addition, parameter analysis demonstrates that concrete composition, compressive strength and steel ratio have an obvious effect on the seismic response of the CFT arch bridge.

Aging coefficient, creep coefficient and extrapolating aging coefficient from short term test for sealed concrete

Aging coefficient and creep coefficient are important parameters for creep analysis of any structure. With the aim to obtain those parameters, an experimental investigation is carried out on sealed concrete. Altogether ten specimens were tested, out of which four were for creep, two for shrinkage and remaining four for relaxation test. A year of relaxation test and two years of creep test results were analyzed to compute aging coefficient and creep coefficient. From regression analysis of observed and calculated aging coefficient using formula of Bazant and Kim, modification for aging coefficient is performed and extrapolation equations are generated. Instead of ACI model, B3 model has been used to obtain compliance function as the parameters of B3 model seems more relevant to creep mechanism of concrete compared to that of ACI model.

Pervasiveness of Excessive Segmental Bridge Deflections: Wake-Up Call for Creep

An obsolete standard recommendation for creep design led to significant underestimation of the observed 18-year deflections of the Koror-Babeldaob (KB) Bridge in the island nation of Palau. A search for data on similar bridges revealed that 56 other large-span, prestressed concrete, segmentally erected box girders (66 by the time of proof) have been found to exhibit excessive long-time deflections. There are probably many more in existence. The observed deflections give no sign of approaching a finite bound, as implied in the empirical ACI Committee 209, CEB-fib, and GL models for creep. They were found to evolve approximately logarithmically beginning at about 1000 days after span closing. While sufficient data for the finite element creep analysis of these deflections were not obtainable, comparisons with accurate deflection solutions for the KB Bridge showed that the terminal logarithmic deflection trend can be predicted well by a simple extrapolation of the measured 1000-day deflection under the hypothesis of proportionality to the compliance function increment since the time of span closing. Comparisons of the extrapolations according to various creep models show that the underestimation of long-time deflections is much less severe for the theoretically based Model B3 than it is for the three other models, and that the terminal trend is logarithmic. A simple update of this model that gives the same mean terminal trend as the 56 bridges is devised that should allow for improving the durability of segmental bridges.

Evaluation of prestress losses in nuclear reactor containments

The most critical safety barrier in a nuclear power plant, the concrete containment, is prestressed by hundreds of tendons, both horizontally and vertically. The main purpose of the containment is to prevent radioactive discharge to the environment in the case of a serious internal accident. Due to creep and shrinkage of concrete and relaxation of the prestressing steel, tendon forces decrease with time. These forces are thus measured in Swedish containments with unbonded tendons at regular in-service inspections. In this paper, the prestress losses obtained from these in-service inspections are compared to losses estimated using several prediction models for creep, shrinkage and relaxation. In an attempt to increase the accuracy of these models, existing expressions for the development of shrinkage were modified using previous findings on the humidity and temperature inside two Swedish containments. The models which were used and modified for predicting creep and shrinkage were CEB-FIP Model Codes 1990 and 1999, ACI 209, Model B3 and GL2000. Eurocode 2 was used for the prediction of relaxation. The results show that the most accurate of the models were CEB/FIP MC 99 and ACI 209. Depending on the model, the accuracy of the prediction models was increased by 0.5–1.2 percentage points of prestress losses when using the modified development of shrinkage. Furthermore, it was found that the differences between the different models depend mainly on the prediction of creep. Possible explanations for the deviation between the calculated and measured models can be the influence of reinforcement on creep and shrinkage of concrete and the influence of friction on horizontal tendons.

Creep Modeling for Concrete Filled Steel Tubular Members Compressed with a Large Eccentricity

Based on concrete creep calculation model B3 and mechanical characteristics of concrete-filled steel tube (CFT) beam-column members of large eccentricity, a creep calculation model of CFT beam-column members of large eccentricity is constructed, which accords with mechanisms of concrete creep, and creep characteristics of concrete core of CFT beam-column members of large eccentricity have been taken into account. The model is verified against previous creep experiments for CFT beam-column specimens, by changing model B3 for ACI209, CEB90, GL2000 model, elastic continuation and plastic flow theory. The results show that introduction of model B3 to predicting creep of CFT beam-column members with a large eccentricity is necessary. Using the model, a study is then carried out on the effects of practical design parameters, such as concrete mix (e.g. water to cement ratio ( ), aggregate to cement ratio ( )), steel ratio and eccentricity ratio, on creep of CFT beam-column members with a large eccentricity.

Uncertainty and sensitivity analysis of creep models for uncorrelated and correlated input parameters

The intention of this paper is to evaluate the uncertainties and sensitivities of creep prediction models of standard concrete. The development of creep prediction models has been a field of extensive research and many different models have already been proposed. The four major models are: model GL2000 by Gardner and Lockman, model MC90 according to CEB-FIP Model Code 1990, model ACI209 according to the American Concrete Institute and model B3 by Bažant and Bajewa. First, a sensitivity study is performed in order to determine the parameters which mostly contribute to the uncertainties of the model prediction. This is done for uncorrelated and correlated input parameters and the differences are pointed out. Due to high parameter correlation, most standard sensitivity methods are not applicable and, therefore, a new method developed by Xu and Gertner is applied. Second, the uncertainties of the creep prediction for all of the models are compared and reveal significant differences. Due to the consideration of parameter and model uncertainties, a measure for the total variation of the model response is achieved. A special FEM code is developed to include the existing creep models in structural analysis. Utilising the FEM application, arbitrarily distributed creep strains, non-linear creep and single reinforcement bars can be taken into account. Finally, this FEM code is used and the prescribed creep models and uncertainty method are applied to a pre-stressed concrete bridge. The uncertainties of the loss of pretensioning force and axial shortening are calculated and show a reduction in comparison to uncertainties of pure creep strain. Together, the presented method proves its ability to determine uncertainties and sensitivities of models of time-dependent behaviour for uncorrelated and correlated parameters in an efficient way.