Rate-type creep law of aging concrete based on maxwell chain

Bažant, Zdeněk P.; Wu, Spencer T.

doi:10.1007/bf02482679

Cited by 96 publications

(102 citation statements)

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“…According to figure 2, the concrete is represented through a viscoelastic model, corresponding to a chain composed by five Maxwell´s elements in parallel. Bazant and Wu (1974) presented an algorithm to automatically determinate the parameters E µ (t) and η µ (t) for each age, t, of concrete, from experimental results or standard concrete values. According to Aurich (2008) where:…”

Section: Mechanical Analysismentioning

confidence: 99%

Modelagem por elementos finitos do comportamento do concreto nas primeiras idades

Aurich

Filho

Bittencourt

et al. 2009

Rev. IBRACON Estrut. Mater.

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ResumoIn this work a computational model, based on the finite element method was implemented, to simulate the early age concrete behavior, having as a special feature, the evaluation of the cracking risk. The finite element analysis encloses the computational modeling of the following phenomena: chemical, thermal, diffusion and mechanical which occur at the first days after the concrete cast. The developed software results were compared with experimental values found in the literature, demonstrating an excellent agreement for all the implemented analysis. Keywords: Concrete. Early age. Thermal analysis. Diffusion analysis. Mechanical Analysis.Neste trabalho é apresentado um modelo computacional, baseado no método dos elementos finitos, para a simulação do comportamento de peças de concreto nas primeiras idades, tendo, em especial, o propósito de avaliar o potencial risco de fissuração. A análise por elementos finitos abrange a modelagem computacional dos fenômenos químicos, térmicos, de difusão de umidade e mecânicos que ocorrem nos primeiros dias após o lançamento do concreto. Os resultados desta modelagem computacional foram comparados com valores experimentais encontrados na literatura, demonstrando excelente aproximação em todas as etapas de solução implementadas. Palavras-chave:Concreto. Primeiras Idades.

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Section: Mechanical Analysismentioning

confidence: 99%

Modelagem por elementos finitos do comportamento do concreto nas primeiras idades

Aurich

Filho

Bittencourt

et al. 2009

Rev. IBRACON Estrut. Mater.

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“…There exist numerous methods to model the creep behaviour in young concrete (see for example Trost 1967, Bažant 1972, Bažant and Wu 1974, Bažant and Panula 1978, Bažant and Wittmann 1982, Bažant and Chern 1985aand 1985b, Bažant 1988, Emborg 1989, Kanstad 1990, Bažant and Xi 1999, Westman 1999, De Schutter 2001, Gutsch 2001, Pane and Hansen 2001, Sakata et al 2001, Zi and Bažant 2001or Hagihara et al 2002. Many of these models are complex mathematical formulations including sets of parameters that have no direct relation to the material behaviour and thereby are complicated to understand and use in a more practical context.…”

Section: How Creep Influences Thermal Stressesmentioning

confidence: 99%

Linear Logarithmic Model for Concrete Creep

Larson

Jonasson

2003

ACT

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Control of thermal cracking in young concrete is of great importance to ensure a desired service lifetime and function of a structure. Young concrete is here defined as the period up to approximately 100 days after casting. Making reliable predictions about thermal stresses, and thereby cracking risks, the creep behaviour forms an important part of the material modelling. Up until now few studies have been made to investigate how different creep modelling influences calculated thermal stresses. Existing creep models for young concrete are often pure mathematical expressions with no direct relation to the material behaviour and thereby complicated to understand and use in a more practical context.In this paper a new basic creep model primarily aimed for early age purposes is outlined. The formulation with its model parameters, which have an easy to understand meaning in the material behaviour, is based on piece-wise linear curves in logarithm of time and therefore denoted the Linear Logarithmic Model (LLM). Comparison with experimental creep data and other more commonly used creep formulations for young concrete is made to achieve an opinion about the accuracy of the new model. The new model is a flexible and robust formulation that can model the behaviour of both young and mature concrete. The robustness enables it to make reliable creep modelling with very few test data.Another advantage with the LLM formulation is that the appearance of negative relaxation in linear viscoelastic modelling is very small and negligible with respect to thermal stresses. This means that the original formulation may be used directly in a thermal stress analysis for young concrete without any adjustment for negative relaxation.The LLM formulation shows very good agreement directly with experimental creep data and indirectly with measured thermal stresses, whereby the formulation has been used to model the viscoelastic behaviour of the concrete. The formulation also has the best correlation with experimental data compared to other commonly used creep models that have been analysed in this paper.

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Section: Introductionmentioning

confidence: 99%

“…Instead of storing during step-by-step computation the values of stresses or strains in all previous steps, it suffices to store only the current values of several internal variables. The number of arithmetic operations also gets significantly reduced (3,5,6,10,11,19).The existing rate-type formulation of the aging creep law of concrete consists of a system of first or second-order linear differential equations with the actual time as an independent variable. This paper examines the question whether the rate-type formulation can be made more efficient by means of introducing as the independent variable a certain monotonically increasing function of time, called the reduced time.…”

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Rate‐Type Concrete Creep Law with Reduced Time

Bažant¹,

Chern²

1984

J. Eng. Mech.

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For creep analysis of large structural systems, the linear aging integral-type creep law needs to be converted to a rate-type form which consists of a system of first-order linear differential equations with age-dependent coefficients. The system may be visualized by the Kelvin chain model with agedependent elastic moduli and viscosities. In the existing formulation, the independent variable is actual time. It is shown that, by using as the independent variable a certain reduced time which increases with time at a gradually declining rate, one reduces the number of differential equations needed to describe creep within the given time range, thereby making numerical structural analysis more efficient. An algorithm for identifying the material parameters from given creep data, based on minimization of a sum of squared deviations, is also presented. Thermodynamic restrictions on the material coefficients are analyzed. Finally, the capability of closely approximating available creep data is demonstrated. INTRODUCTIONFor numerical creep analysis of large structural systems, particularly finite element analysis, the rate-type form of a linear aging creep law is far more efficient than the integral-type form based directly on the principle of superposition. Instead of storing during step-by-step computation the values of stresses or strains in all previous steps, it suffices to store only the current values of several internal variables. The number of arithmetic operations also gets significantly reduced (3,5,6,10,11,19).The existing rate-type formulation of the aging creep law of concrete consists of a system of first or second-order linear differential equations with the actual time as an independent variable. This paper examines the question whether the rate-type formulation can be made more efficient by means of introducing as the independent variable a certain monotonically increasing function of time, called the reduced time.Linear Aging Creep Law Based on Principle of Superposition.-For stresses less than about one-half of the strength, the creep law of concrete may be approximately considered as linear, i.e., obeying the principle of superposition. The linearity assumption greatly simplifies structural analysis, and is generally used in practice. According to the principle of superposition, the uniaxial creep law of concrete may be written in the form Vol. 110, No.3, March, 1984. ©ASCE, ISSN 0733-9399/84/0003-0329/$01.00. Paper No. 18621. 329 in which CT, E = uniaxial stress and strain; EO = prescribed stress-independent strain representing shrinkage and thermal dilatation; and J (t, It may now be checked by substitution into Eqs: ~ and 1 that the ~ol lowing linear differential equations are always satisfied by the precedmg expression for ElL:dy~ dYIL CIL(t) dYIL Expressing the derivative d'YlL/dYIL from Eq. 5, we may verify that functions "I IL always satisfy the differential equationVariables EILand "I IL are related to E by the differential equations . (8 )It can be further shown that int...

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Rate-type creep law of aging concrete based on maxwell chain

Cited by 96 publications

References 5 publications

Modelagem por elementos finitos do comportamento do concreto nas primeiras idades

Modelagem por elementos finitos do comportamento do concreto nas primeiras idades

Linear Logarithmic Model for Concrete Creep

Rate‐Type Concrete Creep Law with Reduced Time

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