Keywords: concrete, cracking, creep, finite element method, shrinkage, visco-elasticity.

Time-dependent analysis of concrete structures is crucial for the assessment of possible long-term shrinkage and creep movements, identification of highly stressed regions at different time, recognition of areas which are prone to cracking, and evaluation of alternative construction schemes and concrete placement scheduling so as to mitigate the shrinkage cracking problem [1,2]. For general structures, the time-dependent analyses are most suitably conducted using the finite element method. In accordance with the conventional concrete creep models (including the prevalent codified formulations, for example, Model Code 1990 [3]), when the stresses in concrete vary with time, the corresponding creep strains at any time have to be determined as the summation of individual creep responses due to stress increments in preceding time intervals [4,5]. However, such summation process entails the memorisation of stress histories for all finite elements, thus leading to prohibitive computer storage requirements and computational effort demand for large analysis problems.

In the present study, a new visco-elastic creep model is developed for concrete, whereby the concrete creep is modelled by a set of rheological elements and the creep strain is expressed in terms of a set of remnant creep strains carried by visco-elastic units. By connecting specially designed visco-elastic units in parallel, the proposed model possesses a multi-layer configuration. In this paper, the associated governing equations and mathematical derivations are expounded. The proposed model successfully circumvents the need of memorising the stress histories of concrete, thereby greatly facilitates the computer analyses of time-dependent effects on concrete structures.

The multi-layer visco-elastic creep model is completely general in the sense that it is capable to reproduce any creep function by expressing the function in the form of Dirichlet series, i.e. a series of real exponentials. Herein, reference has been made to the Model Code 1990 [3] in the valuation of the model parameters. Excellent agreement is achieved between the Model Code 1990 and the proposed creep model. To demonstrate the general applicability of the proposed model, numerical examples on restrained concrete prism and concrete podium structure are presented. The authors advocate the use of the multi-layer visco-elastic model in time-dependent analyses for construction projects.

1

Kwan, A.K.H., Au, F.T.K. and Lee, P.K.K., "Minimizing shrinkage cracks in concrete structures for better serviceability and durability", Proceedings, Innovative Buildings Symposium, Hong Kong, 117-136, 2002.

2

Kwan, A.K.H., Au, F.T.K. and Lee, P.K.K., "High-performance concrete buildings for the new millennium", Progress in Structural Engineering and Materials, 5(4), 263-273, 2003. doi:10.1002/pse.158

3

Comite Euro-International du Beton, CEB-FIP Model Code 1990: Model Code for Concrete Structures, Thomas Telford, London, UK, 1993, 437pp.

4

Gilbert, R.I., Time Effects in Concrete Structures, Elsevier Science Publishers B.V., Amsterdam, The Netherlands, 1988, 321pp.

5

Ghali, A., Favre, R. and Elbadry, M., Concrete Structures: Stresses and Deformation, Third Edition, Spon Press, London, UK, 2002, 584pp.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £120 +P&P)