Compression Field Modeling of Confined Concrete:
Constitutive Models
Esneyder Montoya
1
; Frank J. Vecchio, M.ASCE
2
; and Shamim A. Sheikh, M.ASCE
3
Abstract: It has been widely recognized that the behavior of confined concrete depends upon the level of confinement. Brittleness or
ductility is a function of the state of compressive stresses, unconfined concrete strength, volumetric expansion, and concrete softening.
Constitutive models for strength enhancement, concrete dilatation, and a new stress-strain relationship for concrete in triaxial compression
are proposed. The load-carrying capacity of confined concrete is predicted by utilizing an Ottosen-type surface with newly developed
coefficients that account for a wide range of confinement levels lateral pressures up to 100% of the unconfined concrete strength and
unconfined concrete strengths from 20 to 130 MPa. Concrete dilatation is modeled as a function of the lateral pressure ratio and concrete
strength and can reach values beyond the limit of uncompressibility. Experimental results are used to corroborate the new models at the
material level, producing accurate agreement.
DOI: 10.1061/ASCE0899-1561200618:4510
CE Database subject headings: Concrete; Constitutive models; Triaxial compression; Stress strain relations.
Introduction
Triaxial compressive stresses delay expansion and damage propa-
gation in concrete. As concrete stresses become larger, the inter-
nal structures of paste, aggregates, and pores change. Cracks
develop through the aggregates, pores collapse, and the failure
mode transforms from brittle to ductile Sfer et al. 2002. It is also
well known that confinement increases the strength and ductility
of concrete. After peak strength, low-confined concrete exhibits
softening and decreasing capacity, whereas high-confined con-
crete exhibits continuous hardening behavior with little or no soft-
ening until failure.
Concrete subassemblies, elements, and structures subjected to
triaxial stresses can be found in many civil engineering applica-
tions. In prestressed beams, anchorage of strands at the ends cre-
ates disturbed zones D zones that require stirrups around
prestressed cables to prevent the concrete from spalling off explo-
sively. Anchor fasteners embedded in concrete and subjected to
tension produce high axisymmetric triaxial compressive stresses
in the concrete in the vicinity of the bolt head Pivonka et al.
2000. Concrete in massive dams is subjected to triaxial compres-
sion due to its self-weight and to restraints at the dam’s base and
lateral supports. Finally, reinforced concrete columns are pas-
sively confined by either steel, fiber-reinforced polymer FRP
fabric, or a combination of both. The behavioral enhancement of
FRP composites for structural retrofitting has long been investi-
gated e.g., Demers and Neale 1999.
Several types of formulations have been used in the analysis of
concrete columns confined by steel stirrups or spirals, from
simple empirical models e.g., Sheikh and Uzumeri 1980;
Mander et al. 1988 that utilize physical variables stirrup and
longitudinal reinforcement arrangements, section dimensions, and
material properties to finite-element analysis techniques e.g.,
Sankarasubramanian and Rajasekaran 1996; Montoya et al.
2001; Sfer et al. 2002 based on nonlinear elasticity, plasticity,
fracture mechanics, or continuum damage mechanics.
The work of several researchers has contributed to calibrating
the behavior of confined concrete and has added to the database
of experimental results. Measured lateral and axial strains at ulti-
mate on concrete specimens have shown ratios of lateral to axial
strain greater than 1.0 Candappa et al. 1999; ratios larger than
6.0 in some uniaxial compression tests had also been found Lee
et al. 1997. It had also been observed that concrete dilatation
depends on the level of lateral pressure Assa et al. 2001a.
Several computational models for confined concrete had been
proposed. Some of the proposed failure and loading surfaces of
plasticity-type models used Drucker-Prager models Karabinis
and Rousakis 2002; Pivonka et al. 2000, which did not reproduce
accurately the volumetric strain behavior. Many of the models
require a large number of parameters to be calibrated, and the
parameters applied to certain types of analyses had to be redeter-
mined for other loading paths Ghazi et al. 2002. These param-
eters are generally based on experimental results for one type of
concrete e.g., normal strength concrete or high-strength concrete
and could only be applied according to their constraints. Analyti-
cal stress-strain curves obtained by Sankarasubramanian and Ra-
jasekaran 1996 were stiffer than the experiments, some of the
curves did not reach peak stress, and either the analytical model
was not able to trace the postpeak behavior, or the postpeak be-
havior did not follow that of the test.
Models based on compatibility of deformations and simple
formulations for concrete strength e.g., Assa et al. 2001a,b
1
Senior Structural Designer, CHM Structural Engineers, Miami, FL
33156. E-mail: esneyder@chm.cc
2
Professor, Dept. of Civil Engineering, Univ. of Toronto, 35 St.
George St. Office 213, Canada M5S 1A4.
3
Professor, Dept. of Civil Engineering, Univ. of Toronto, 35 St.
George St. Office 213, Canada M5S 1A4.
Note. Associate Editor: Kiang-Hwee Tan. Discussion open until
January 1, 2007. Separate discussions must be submitted for individual
papers. To extend the closing date by one month, a written request must
be filed with the ASCE Managing Editor. The manuscript for this paper
was submitted for review and possible publication on December 20,
2004; approved on May 20, 2005. This paper is part of the Journal of
Materials in Civil Engineering, Vol. 18, No. 4, August 1, 2006. ©ASCE,
ISSN 0899-1561/2006/4-510–517/$25.00.
510 / JOURNAL OF MATERIALS IN CIVIL ENGINEERING © ASCE / JULY/AUGUST 2006