Keywords: verification, microplane model, finite element modeling, concrete.

This paper is focused on numerical simulations of different engineering structures using the microplane model M4 [1,2]. The model is calibrated according to a standard experimental procedure (uniaxial compression test). The obtained material parameters are used for subsequent simulations of several different specimens loaded differently.

General performance and capabilities of the model to capture different loading cases and conditions in different structures is studied and the quality of the reproduction of experimental data is shown.

The microplane model M4 is a powerful triaxial material model for concrete. The basic idea of the model consists in the projection of the macroscopic strain tensor into a number of spatial orientations. Constitutive relations are evaluated for these directions. Final macroscopic stress tensor is then obtained from these contributions using the principle of virtual work. Constitutive laws of the microplane model are based on a large set of material parameters (21 plus Young's modulus and Poisson's ratio). Nevertheless, only a few of them (six) have to be adjusted for a specific type of concrete. The rest of the parameters have been identified from numerous experimental data for usual types of concrete and they are preset in the model. Identification of free parameters (i.e. the calibration of the model) is based on the optimal fitting of several experimental test procedures. In particular, free parameters can be obtained by an optimal fitting of hydrostatic compression tests, uniaxial compression tests (unconfined) and triaxial compression tests (confined). However, a complete set of these tests is often unavailable. In this case, at least uniaxial compression tests must be used for the calibration.

The paper describes the results of the simulation of several examples, where parameters have been determined from uniaxial compression test only. The studied cases were following:

• uniaxial compression test on a cylinder,
• torsion of a cylinder,
• three-point bending of a notched specimen,
• four-point bending of a reinforced concrete prism,
• eccentrically loaded reinforced concrete column.

If experimental data were available, the comparison of measured and computed responses was 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 based on the same set of material parameters showed that the model is capable to describe properly the type of a failure and character of loading diagram in all cases. The ultimate stress (peak load) was also reproduced well. On the other hand, significant differences have been found in post-peak behavior mainly for three-point bending and RC column. These differences can be explained by inaccurate modeling of concrete-steel contact in case of RC column, but in case of three-point bending, where only plain concrete is modeled, the situation is worse. Bad agreement with experiment is caused either by insufficient fitting of material parameters or by improper setting of internal parameters of the model. As only data from uniaxial compression tests were available for calibration, we were not able to correct material parameters and decide, what is the reason for incorrect results in case of three-point bending and RC column.

Found differences bring us to the future need of more complex identification of the free material parameters and/or readjusting constitutive laws (so called boundary curves in the microplane model M4).

Acknowledgments

Support of the Grant Agency of the Czech Republic (contract No. 103/02/1273) and of the Ministry of Education of Czech Republic under contract No. 210000003 is gratefully acknowledged.

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

B. Patzák, J. Nemecek, D. Rypl, Z. Bittnar, "Computational Aspects of Microplane Models and Proposed Parallel Algorithm", Computational Concrete Structures Technology. Edinburgh : Civil-Comp Press, pp. 1-8, 2000. doi:10.4203/ccp.69.1.1

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 £125 +P&P)