Comparative Study of Three Constitutive Models for Steel Tube Concrete

Literature Overview

The paper by Wu Wenping, Huang Bingsheng, and Fan Jianhui, published in Sichuan Building Science in 2009, provides a comparative analysis of three widely used constitutive models for the confined concrete in steel tube concrete (SRC) members. The three models examined are those proposed by Han Linhai, Susantha et al., and Saenz. This research was supported by the Jiangsu Provincial Ordinary Higher Education Natural Science Research Plan (Grant No. 04KJB560049). The authors analyze the stress-strain relationships of concrete confined within circular and square steel tubes of varying concrete strength grades and varying diameter-to-thickness (or width-to-thickness) ratios, and they compare the predictions of the three models against each other. The paper falls under classification TU398 and addresses a fundamental question in the design of steel tube concrete members: which constitutive model best represents the actual behavior of confined concrete under different geometric and material conditions.

Core Technical Content and Key Findings

The constitutive model for confined concrete is a cornerstone of steel tube concrete design, as it determines the predicted strength, stiffness, and ductility of the composite member. The three models examined in this study differ in their mathematical formulations and underlying assumptions regarding the confinement mechanism.

The following table summarizes the key characteristics of each model:

The authors report three principal findings. First, for the same concrete strength grade, a smaller diameter-to-thickness ratio (or width-to-thickness ratio for square tubes) results in a better confinement effect, leading to a greater increase in the confined concrete strength. This is physically intuitive, as a thicker steel tube wall relative to the tube diameter provides a stiffer confining ring that can exert higher lateral pressure on the concrete core. Second, the Saenz model exhibits superior ductility characteristics compared to the other two models, with a larger stress peak and a more gradual post-peak degradation. Third, the confinement effect of circular steel tubes is significantly better than that of square steel tubes for all three models, which is attributed to the more efficient load distribution in circular cross-sections.

Detailed Model Interpretation

Han Linhai Model

The Han Linhai model is characterized by its simplicity and its widespread adoption in Chinese design codes. The model expresses the confined concrete stress-strain relationship as a polynomial function of the unconfined concrete strength, the confinement coefficient, and the strain. The confinement coefficient is a function of the steel tube geometric properties (diameter and thickness) and material properties (yield strength and elastic modulus). The main limitation of this model is that it does not explicitly account for the nonlinear behavior of the steel tube, which becomes significant at high strain levels.

Susantha Model

The Susantha et al. model introduces a more sophisticated treatment of the steel tube behavior by considering the elastic-plastic transition of the tube wall. The confinement stress is calculated based on the equilibrium between the lateral pressure exerted by the concrete and the membrane tension in the steel tube wall. This approach is more physically rigorous than the Han Linhai model but requires additional input parameters related to the steel tube material behavior. The model is particularly suitable for high-strength concrete applications where the steel tube may undergo significant plastic deformation before the concrete reaches its peak strength.

Saenz Model

The Saenz model is distinguished by its ability to capture the nonlinear unloading and reloading behavior of confined concrete, which is essential for cyclic loading analysis. The model uses a combination of polynomial and exponential terms to describe the stress-strain relationship, which allows it to represent the gradual degradation of the concrete stiffness after the peak stress. The authors note that the Saenz model produces a larger stress peak and better ductility characteristics than the other two models, making it particularly suitable for seismic design applications where the energy dissipation capacity of the confined concrete is critical.

Comparison of Confinement Effects

The following table summarizes the comparative performance of the three models in terms of the predicted confined concrete strength enhancement:

The consistent trend across all conditions is that the Saenz model predicts the highest confined concrete strength, followed by the Susantha model, with the Han Linhai model predicting the lowest enhancement. This ordering is consistent with the fact that the Saenz model includes additional nonlinear terms that account for the progressive increase in confinement pressure with increasing strain.

Engineering Practice Implications

The selection of an appropriate constitutive model for steel tube concrete design has direct implications for the predicted structural response and the resulting design decisions. In seismic design, the use of a model that underestimates the ductility of the confined concrete could lead to overly conservative designs that increase structural weight and cost. Conversely, the use of a model that overestimates the confinement effect could lead to unsafe designs if the actual confinement pressure is lower than predicted.

From a quality control perspective, the accuracy of the constitutive model predictions depends on the accuracy of the input parameters, which include the concrete compressive strength, the steel tube yield strength, and the geometric properties of the tube. Any deviation in these parameters from their assumed values will affect the predicted confinement effect. Therefore, the quality control plan for steel tube concrete members should include rigorous testing of the concrete strength (cylinder compression tests), the steel tube material properties (tensile tests), and the tube geometric dimensions (caliper measurements and ultrasonic thickness gauging).

In conclusion, this paper provides a valuable comparative analysis of three constitutive models for confined concrete in steel tube concrete members, and the findings clearly indicate that the Saenz model offers the best representation of the nonlinear behavior and ductility characteristics of confined concrete. Engineers should carefully consider the limitations of each model when selecting an appropriate constitutive model for their specific design application, and they should ensure that the input parameters are accurately determined through rigorous material testing and quality control procedures.