Keywords: high strength concrete, microplane model, simulation, finite element modeling.

High strength and high performance concretes belong to the group of up-to-date structural materials which are used in multiple engineering structures. Such materials find wide application, for example, at high rise buildings, especially for their high bearing capacity in columns.

However, using of high strength concretes brings not only positive aspects of higher strength but usually also less ductility. Thus, special attention must be paid to the post peak behavior of such columns, because reduction of ductility can lead to the significant reduction of the overall load bearing capacity of the structure.

The paper deals with the numerical simulation of high strength concrete columns which is connected to the experimental program of which results are interpreted and used for verification of the model.

The model of reinforced column is based on the microplane model M4 [1,2]. Model parameters are found using standard experimental procedure - uniaxial compression test on cylinders. Results from tests on cylinders are fitted by the microplane model and appropriate material parameters are detected. Reduced ductility of the base material can be found already at this level of testing and the model must be accommodated to this situation. The obtained material parameters are used for subsequent simulations of columns.

The key role in the modeling of concrete structures plays the constitutive model of concrete. As concrete is a quasi brittle material whose fracture and ductility properties depend on the stress state in the structure. The microplane model was found to be suitable tool for such calculations due to its basic features which are following. The microplane model M4 is a triaxial material model for concrete which is capable to describe concrete in different loading and unloading situations and it incorporates anisotropy of the material by a natural way of assessing the response from different spatial orientations.

Calibration of the material model parameters is based on the optimal fitting of several experimental test procedures. Due to the lack of triaxial tests, only uniaxial compression tests were used in our case, but sufficient results have been obtained.

The finite element model of the column consists of several parts. Concrete is modeled using the microplane model and the end parts are elastic for saving computational costs which are rather high for computation with the microplane model. Explicit integration is used for structural analysis of the problem. This choice also contributes to saving of computational times and less computational demands in case of the microplane model. The problem is solved using finite element package OOFEM [5] developed at the Department of Structural Mechanics, CTU Prague.

Detailed description of the model and the comparison of measured and computed responses is presented. The main observed parameters of the responses were as follows: load-displacement diagrams, ultimate loads and displacements, stress development, failure modes, time of the computation.

Numerical simulation showed that the model is capable to describe properly the type of a failure and character of loading diagram. The ultimate stress (peak load) was also reproduced well. The reduction of ductility (i.e. post peak behavior) with respect to the normal strength concretes is also captured well in agreement with experiments. However, differences have been encountered in the post-peak behavior - different slope of the post-peak branch of the loading diagram. These differences can be explained by inaccurate modeling of concrete-steel contact in case of RC column or by insufficient fitting of material parameters of the material model as only data from uniaxial compression tests were available for calibration. Numerical implementation of the model involves time consuming operations in comparison with classical models which yielded in long computationl times even on a fast single processor computer.

1

Z. P. Bazant, I. Carol, A. D. Adley, S. A. Akers, "Microplane Model M4 for Concrete I: Formulation with Work-Conjugate Deviatoric Stress", Journal of Engineering Mechanics 2000; 126(9), 944-953. doi:10.1061/(ASCE)0733-9399(2000)126:9(944)

2

F. C. Caner, Z. P. Bazant, "Microplane Model M4 for Concrete. II: Algorithm and Calibration.", Journal of Engineering Mechanics 2000; 126(9), 954-961. doi:10.1061/(ASCE)0733-9399(2000)126:9(954)

3

J. Nemecek, "Modeling of Compressive Softening of Concrete", CTU Reports - Ph. D. Thesis. Prague : CTU, 2000, pp. 3-145. ISBN 80-01-02298-6.

4

J. Nemecek, B. Patzák, D. Rypl, Z. Bittnar, " Microplane Models: Computational Aspects and Proposed Parallel Algorithm", Computers and Structures, Elsevier, 80 (2002) pp. 2099-2108. doi:10.1016/S0045-7949(02)00242-0

5

http://ksm.fsv.cvut.cz/oofem/ "Finite element software OOFEM", Dept. of structural mechanics, CTU Prague.

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