Comparative Study of Three Constitutive Models for Concrete-Filled Steel Tubes

Literature Overview

This paper by Wu Wenping, Huang Bingsheng, and Fan Jianhui (2009), published in Sichuan Building Science, provides a systematic comparison of three widely-used constitutive models for the confined concrete core in concrete-filled steel tubes (CFST): the Han Linhai model, the Susantha model, and the Saenz model. The research was supported by the Jiangsu Provincial Natural Science Research Fund for Higher Education Institutions (Grant No. 04KJB560049). The study analyzes the stress-strain relationships for different concrete strength grades and different diameter-to-thickness ratios (or width-to-thickness ratios for square tubes).

Core Technical Findings

The three constitutive models represent different theoretical approaches to describing the confined concrete behavior in CFST members:

Model	Developer/Origin	Confinement Stress Expression	Peak Strain Behavior	Ductility Representation
Han Linhai	Tsinghua University	Empirical fit to test data	Moderate post-peak strain	Moderate ductility
Susantha	Sri Lankan research	Theoretical confinement model	Higher post-peak strain	Good ductility
Saenz	Spanish research	Simplified confinement formula	Highest post-peak strain	Best ductility

Key comparative findings:

For the same concrete grade, smaller D/t (or B/t) ratios produce better confinement effects and greater concrete strength enhancement
The Saenz model exhibits superior ductility characteristics and higher peak stress values compared to the other two models
Circular steel tubes provide significantly better confinement effects than square steel tubes across all three models

Interpretation of Key Technical Points

Confinement Mechanism and Constitutive Modeling

The confinement effect in CFST columns arises from the lateral restraint provided by the steel tube to the concrete core. As the concrete expands laterally under axial compression (governed by Poisson's ratio), the steel tube develops hoop stresses that resist this expansion, creating a confining pressure on the concrete. This confining pressure increases both the compressive strength and the ductility of the concrete beyond its unconfined values.

The mathematical expression of this confinement varies significantly between models:

Han Linhai Model: Uses an empirical approach where the confined concrete strength is expressed as a function of the confinement stress ratio, calibrated against experimental data from Chinese test programs.

Susantha Model: Employs a more theoretical framework considering the equilibrium between the confining pressure from the steel tube and the lateral pressure exerted by the concrete.

Saenz Model: Uses a simplified formulation that captures the essential physics while maintaining mathematical tractability for practical engineering applications.

Effect of D/t Ratio on Confinement

The diameter-to-thickness ratio (D/t) is a fundamental geometric parameter that controls the confinement efficiency:

D/t Ratio	Confinement Effect	Practical Implication
< 20	Very high	Maximum strength enhancement; thick-walled tubes
20–30	Moderate	Standard design range for most applications
30–40	Reduced	Thin-walled tubes; limited confinement benefit
> 40	Minimal	Confinement effect negligible; tube may buckle before concrete crushes

This finding has direct implications for steel pipe selection in CFST applications—thinner walls provide less confinement benefit, reinforcing the economic rationale for optimizing wall thickness rather than simply maximizing it.

Circular vs. Square Tube Confinement

The study confirms what has been established in the broader literature: circular steel tubes provide superior confinement compared to square tubes. This is attributed to:

Uniform hoop stress distribution in circular sections under uniform internal pressure
Corner concentration effects in square sections that reduce effective confinement
More efficient stress transfer in circular geometries

From a steel pipe manufacturing perspective, this finding favors the use of circular seamless or HFW tubes for CFST applications where maximum confinement is required, although square tubes remain popular for architectural and connection reasons.

Connection with Steel Pipe Engineering Practice

Material Specification Implications

The constitutive model comparison has direct implications for material specifications in CFST design:

Steel grade selection: Higher-strength steels (e.g., Q345, Q390, Q420) provide greater confining pressure but may exhibit reduced ductility in the tube wall
Concrete grade: The models show that confinement benefits are proportional to the unconfined concrete strength; high-strength concrete (C60 and above) benefits more from confinement in absolute terms
Tube geometry: The D/t ratio optimization must balance confinement effectiveness against structural weight and cost

Welding Quality and Confinement Integrity

For welded CFST columns (LSAW or UOE tubes), the longitudinal weld seam represents a potential weak point in the confinement system:

Weld Quality Factor	Effect on Confinement	Inspection Method
Weld toe geometry	Stress concentration; crack initiation	MT, PT
HAZ softening	Reduced hoop stress capacity	Hardness testing, UT
Lack of fusion	Loss of hoop continuity	RT, PAUT
Porosity	Reduced effective wall thickness	UT, RT

Finite Element Analysis Applications

The constitutive model selection directly affects the accuracy of finite element analysis (FEA) used in design verification. The Saenz model's superior ductility representation makes it particularly suitable for nonlinear FEA where post-peak behavior is critical, such as:

Seismic performance assessment
Progressive collapse analysis
Fatigue life estimation

Key Questions and Reflections

The comparison of three constitutive models raises important questions about model applicability:

Model calibration: Each model was developed based on specific test databases with particular ranges of D/t ratios, concrete grades, and steel grades. Extrapolation beyond these ranges may lead to inaccurate predictions.
Temperature effects: None of the three models adequately addresses the degradation of confinement effects at elevated temperatures, which is critical for fire resistance design of CFST members.
Long-term behavior: The models describe monotonic loading behavior but do not capture time-dependent effects such as creep and shrinkage, which affect the long-term confinement pressure in CFST columns.
Multi-axial stress state: The models simplify the confined concrete to a uniaxial stress-strain relationship with an equivalent confinement stress, which may not accurately represent the complex stress state near tube corners in square sections.

Study Insights and Engineering Implications

This comparative study provides valuable guidance for engineers selecting appropriate constitutive models for CFST analysis. The recommendation to use the Saenz model for applications requiring accurate ductility prediction is well-founded, as it provides the most conservative representation of post-peak behavior. For steel pipe manufacturers, the finding that confinement effectiveness decreases with increasing D/t ratio reinforces the importance of providing accurate dimensional data (particularly wall thickness) to designers. The study ultimately underscores that the mechanical performance of CFST columns is a system property dependent on the interaction between steel tube geometry, steel material properties, concrete properties, and the quality of the steel-concrete bond—all of which must be carefully controlled during manufacturing and construction.