Ingeniero

SIZE EFFECT

IN

CONCRETE COLUMNS: FINITE-ELEMENT ANALYSIS WITH MICROPLANE MODEL

By Michele Brocca1 and Zdenek P. Bazant,2 Fellow, ASCE ˘ ˇ
ABSTRACT: Failure of concrete structures due to concrete failing in compression was recently shown to exhibit a size effect. This is not taken into account by current design codes based on failure criteria expressed in terms of strength or plasticity.But compressive failure of concrete cannot be described by strength criteria, since it is brittle and is caused by release of elastic strain energy stored in the structure. In this sense, it is similar to tensile failure governed by fracture mechanics. The paper presents a finite-element study of the size effect of compressive failure of geometrically similar concrete columns of different sizes.The test columns considered here are reduced-scale specimens made with micro-concrete of maximum aggregate size 3.35 mm and are loaded eccentrically. The analysis employs the microplane model for concrete. It is based on the crack-band concept and is shown to capture with good approximation the size effect observed experimentally.

INTRODUCTION The current design codes for reinforced concretecolumns, based on failure criteria expressed in terms of strength or yield surfaces, exhibit no size effect, i.e., no dependence of the nominal strength on the size of the structure. (As standard in mechanics, the term ‘‘nominal strength’’ is here used to mean the load divided by the cross-section area, and not the ultimate axial force, as used by ACI. In mechanics, the ‘‘strength’’ always has thedimension of stress.) However, the failure of concrete columns is not plastic, but brittle, as confirmed by the fact that the observed load-deflection diagrams of columns have no yield plateau but descend after the peak. Under extremely high confining pressures (Bazant et al. 1999; Brocca ˇ and Bazant 1999), compressive failure of concrete can be ducˇ tile, without any significant postpeak decrease ofapplied load. But such pressures can develop only when the concrete is confined in very strong steel tubes. Thus, the description of structural behavior of concrete in terms of plastic limit states is in general not correct. Mathematical modeling of such behavior should be based on fracture mechanics, which predicts size effect, such that the nominal strength at failure, N, decreases with anincrease of the characteristic dimension of the structure, D, provided that the structures of different sizes are geometrically similar. In the concrete fracture community, it is now generally accepted that size effects must occur in all the failures of concrete structures that are due to concrete rather than to steel. This is true not only of those failures that are due to concrete failing in tension(punching shear of slabs, torsion, anchor pullout, bar pullout, splice failure, etc.) but also of the failures that are due to concrete failing in compression. This includes the bending of prestressed concrete beams, anchor pullout, and diagonal shear failure of reinforced concrete beams, and all the cases analyzed by the strut-and-tie model, in which failure is due to crushing of the so-called‘‘compression strut’’ of concrete. Most importantly, this includes reinforced concrete columns, which will be studied in this paper from the size effect viewpoint. Experimental results documenting a size effect in compres1 Grad. Res. Asst., Northwestern Univ., Evanston, IL 60208; currently at Boston Consulting Group, Chicago. 2 Walter P. Murphy Prof. of Civ. Engrg. and Materials Sci., Northwestern Univ.,Evanston, IL 60208. E-mail: z-bazant@northwestern.edu Note. Associate Editor: John Wallace. Discussion open until May 1, 2002. To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on December 28, 1999; revised May 24, 2001. This paper is part of the Journal of...