Modified damaged plasticity and variable confinement modelling of rectangular CFT columns

Highlights

• A novel algorithm is developed to determine the dilation angles and the stress-strain characteristics of confined concrete.

• A solution dependent field variable (SDFV) is used for the modelling of confined concrete in the modified CDP model.

• The proposed modelling technique is validated with test results of RC, CFT and RCFT columns under axial loads.

• Tension stiffening effect of concrete is considered in the modelling of eccentrically loaded CFT columns.

Abstract

Concrete damage plasticity (CDP) model is widely used to represent the constitutive behaviour of confined concrete in finite element analysis of concrete-filled tube (CFT) columns. This model requires a constant dilation angle and a stress-strain base curve of concrete as the main input parameters. However, in the case of rectangular CFT columns, the variation in the level of confinement across the cross-section makes both the dilation angle and stress-strain base curve to be solution-dependent. In this study, a novel algorithm has been developed to estimate the dilation angles and to generate the multiple stress-strain curves of concrete under various confining pressures. A numerical technique has been proposed for the modelling of confined concrete in the modified CDP model through the implementation of a solution dependent field variable (SDFV). The efficacy of the proposed modelling technique has been verified through finite element validation of twenty previously tested reinforced concrete (RC), CFT and reinforced-CFT (RCFT) columns under both concentric and eccentric axial loads. Tension stiffening effect of concrete has also been considered in the modelling of eccentrically loaded CFT columns. The proposed numerical models accurately predicted the load-deformation behaviour of CFT columns with and without confining reinforcement under concentric and eccentric axial monotonic loads.

Introduction

Composite columns consisting of structural steel and concrete offer numerous benefits in terms of high axial resistance and stiffness by combining the advantages of the constituent materials [1]. These columns can be broadly divided into two categories, namely, concrete-filled steel tubes (CFT), and steel tube reinforced concrete (TRC). In CFT columns, both concrete and steel tubes are loaded simultaneously. Thus, steel tubes contribute to the axial resistance capacity of CFT columns besides providing the passive confinement to the core concrete. The core concrete, in turn, helps in delaying the compression buckling of steel tubes. In the case of TRC columns, external axial loads are only applied to the core concrete region and the steel tubes primarily act as the confining devices [2,3]. However, the steel tubes of non-greased TRC columns resist the axial load partially due to the friction between the concrete infill and steel tube [[4], [5], [6]]. If the friction is removed by greasing the inner surface of steel tubes, the steel tube acts perfectly as a confining device and does not resist any axial load [[7], [8], [9], [10]].

Past experiments [[11], [12], [13], [14]] have demonstrated that the strength and ductility of both of CFT and TRC columns are enhanced by the confinement provided by the steel tubes. The presence of the axial-strain gradient across the cross-section of rectangular reinforced concrete (RC) columns improves the displacement ductility in comparison to those with the relatively uniform strain distribution [15]. The axial-strain gradient affects the confinement pressure generated by the transverse reinforcement [16] and may lead to the gradual reduction in the post-peak stiffness of the stress-strain response of concrete. Fattah [17] proposed a stress-strain relationship for confined concrete under eccentric loading by considering two extreme cases, namely, infinite eccentricity (bending) and zero eccentricity (uniformly confined concrete). The peak stress of concrete corresponding to the infinite eccentricity was considered the same as that of unconfined concrete. However, the strain at the peak stress for infinite eccentricity case was considered to be 1.5 times the axial strain at peak stress in unconfined concrete (ε_cu).

Two different models are widely adopted to define the uniaxial compressive stress-strain response of confined concrete, namely, (a) design-oriented models, and (b) analysis-oriented models. The design-oriented models [[18], [19], [20]] provide the empirical equations for the stress-strain relationship of the confined concrete, which are derived from a limited data set. As the name suggests, these models are intended for design purposes. The analysis-oriented models, on the other hand, are more versatile and are generated through an incremental procedure. Ahmad and Shah [21] first used the incremental approach to obtain the stress-strain curve for passively confined concrete. In this procedure, the axial strain is increased gradually in small increments and a series of stress-strain curves of actively confined concrete are used to compute the confinement pressure at each step based on the interaction between the concrete core and the confining device. It is worth mentioning that the test specimens representing the actively confined concrete are subjected to constant hydrostatic lateral pressure. However, the concrete in CFT or TRC columns under axial compression is passively confined in which the lateral confining pressure varies with the magnitude of compressive stress. Chen et al. [22] developed a path-dependent analytical model for the confined concrete and concluded that loading path affects the axial stress but have negligible effects on the magnitude of axial strain. Recently, Lin et al. [23] also proposed confinement stress path dependent analytical models for the circular CFT columns for high strength concrete. Patel [24] developed fibre-based models for round ended CFT columns under uniaxial loadings. The effect of local buckling of the steel tube was also considered in the fibre models.

Finite element (FE) method is used as an alternative to expensive and time-consuming experiments to investigate the behaviour of composite columns. Three-dimensional (3D) FE models using commercial software, e.g., ABAQUS [25], are capable of exhibiting the composite action between the concrete and steel components of columns [[26], [27], [28]]. However, the accurate prediction of the behaviour of composite columns is largely dependent on the input uniaxial stress-strain characteristics of unconfined and confined concrete. With unconfined uniaxial stress-strain curve as the input base model for concrete, the CDP model can predict the increase in peak strength of concrete with sufficient accuracy for the varying degrees of confinement. However, the CDP model does not accurately capture the increase in strain at the peak strength of confined concrete [29,30], and the predicted strain at the peak strength is underestimated in comparison to the experimental observations [31,32]. The increase in the magnitude of axial strain at peak strength due to confinement may be about 5 times of the corresponding increase in compressive strength of concrete [19]. Also, the change in the post-peak slope of the stress-strain curve of the confined concrete is also not well captured using the CDP model. Past studies [[32], [33], [34]] have reported that the post-peak strain softening becomes more gradual with the increasing confining pressure. The errors in the prediction of post-peak strain as well as the post-peak slope of stress-strain curve increase with the increase in compressive strength and the level of confinement of concrete. If the confined uniaxial stress-strain curve is used as the input base model for concrete, to account for the deficiency of the CDP model in capturing the increase in strain at peak strength and change in post-peak slope due to confinement, the peak strength of concrete would be overestimated. Thus, Yang and Su [35] concluded that it is wrong to use the confined stress-strain curve as the input base model for the modelling concrete using concrete damaged plasticity (CDP) constitutive model [36].

To solve this problem, Tao et al. [26] developed a constitutive model based on the statistical analysis of existing experimental results of circular and rectangular CFT columns. The peak strength in this model was kept same as the unconfined strength of concrete, although the axial strain corresponding to the peak stress and the slope of the post-peak branch of the stress-strain curve was increased based on the effective confinement ratio depending on geometric properties of the test specimen. The main limitation of this approach is that this technique may not be suitable to simulate the effect of confinement in any general column section or under eccentric axial loading, as this method is developed based on experimental data of CFT columns under concentric axial loading only.

The modified CDP constitutive model developed by Lee and Fenves [36] and adopted in ABAQUS [25], considers the effect of confinement in estimating the shear strength of concrete. However, the flow rule, hardening-softening rule, and damaged variable are not confinement dependent [37]. In order to predict the post-peak branch of actively or passively confined concrete, these parameters should be made confinement dependent [37]. Yu et al. [37,38] developed user-defined subroutines for the modelling of fibre-reinforced polymer (FRP) jacketed columns. The basic difference between the FRP jacketed column and the CFT column is that the FRP as a confining material behaves linearly till rupture, whereas the steel tube demonstrates a nonlinear force-deformation behaviour in the post-yielding stage. Hence, it is necessary to develop a FE modelling technique capable of efficiently simulating the post-peak stress-strain behaviour of concrete of CFT columns for varying confining pressure to accurately predict the strain ductility of CFT columns. The modelling of concrete confined by the non-linear confining device is the main focus of the present study.