# Effect of Concrete Age and Creep on the Behavior of Concrete-Filled Steel Tube Columns

Authors: HaiYang Wang; XiaoXiong Zha; Wei Feng
Journal: Advances in Materials Science and Engineering
 (2016)

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## Abstract

The influence of concrete age and creep on the ultimate axial loading capacity of concrete-filled steel tube (CFST) columns is experimentally and numerically investigated. After validation of numerical models, a parametric study is conducted and the results are used to formulate empirical formulas for predicting the ultimate axial load-bearing capacity of the columns. Formulas are also proposed for predicting both the composite creep and aging coefficients of the CFST columns, which consider the confinement action of steel tubes on concrete. Then, the proposed formulas are validated independently by comparing their predictions with existing test results performed by other researchers. The comparisons show that the empirical formulas have the potential to be used in the practical design of CFST columns.


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## Body

## 1. Introduction

Concrete-filled steel tube (CFST) columns have been extensively used in civil engineering structures over the past few decades. Extensive experimental and theoretical investigations on CFST components have been conducted and are well documented in the literature. The experimental work includes tests reported by O’Shea and Bridge [1] and Giakoumelis and Lam [2], who conducted research on the bearing capacity of short CFST columns. Zhong [3] and Zha [4] also reported their works on short and long CFST columns. Han et al. [5] and Wang [6] also studied property of the CFST under long-time load, while these results cannot be implemented conveniently considering the new code (GB50936-2014). Although significant work has been conducted on the properties of matured CFST columns, less emphasis has been placed on the influence of concrete age. Tan and Qi [7] have worked systematically by testing the effect of creep on columns under axially applied eccentric compressive load. Terry et al. [8] and Luo et al. [9] tested the creep of CFST columns and plain concrete in order to investigate the influence of steel tube reinforcement. Ichinose et al. [10] also reported a series of similar tests to obtain creep coefficients. Naguib and Mirmiran [11] and Liu et al. [12] developed an algorithm for the time-dependent behavior of CFST using the rate of flow method and the double power law functions for the creep of concrete. Shrestha and Chen [13] worked on the aging and creep coefficients of confined concrete, but the effect of steel tube was excluded in their formulas.This study investigates the effect of concrete age and creep by experimental test and FEM modeling. Then, empirical formulas are proposed by treating a CFST column as a structural component made of a single material through homogenization.


## 2. Simulation and Methods

After pouring concrete into the steel tube, the elastic modulus of concrete increases with age. At the early stage, the steel tube is subjected to higher values of load than that specified by the design code. Thus, the ultimate bearing capacity of the CFST column is lower than the designed value. In this section, laboratory tests and FEM model are used to obtain the time-dependent load-bearing capacity. An empirical formula is established to provide a simple form of calculation for estimating the age-related ultimate load-bearing capacity.


### 2.1. FEM Modeling of CFST Columns

The numerical model is implemented in ABAQUS eight-node quadrilateral in-plane continuum shell elements which are used for the steel tube whereas the concrete is modeled employing eight-node linear brick element. The bilinear material model is adopted for the steel, with tangent modulus being 5% of the elastic modulus of2.06e5 MPa. The material model used for the concrete is the damaged plasticity model, and hardening of concrete at different ages follows the curves proposed by Yi et al. [14], as shown in Figure 1. Other mechanical and geometrical parameters of the column are given in Table 1. FE meshes of both concrete and steel are shown in Figure 2. The contact between the steel tube and concrete is assumed to be perfect; here the nodes on the interface between solid and shell elements are tied.Table 1
Geometrical and mechanical properties of the specimens.
D (mm) T (mm) L (mm) f y (MPa) f c k (MPa) E s (MPa) 219 4.5 766 345 40.7 2.06 e 5Figure 1
Stress strain relations of concrete at different ages.Figure 2
Finite element mesh of (a) concrete and (b) steel tube.
(a) (b)Different meshing schemes are tested in order to assess the convergence of the FEM model, and the details are listed in Table2, where N_Ring, N_Radius, and N_Axial are, respectively, the numbers of elements in the circumferential, radial, and axial directions. E_Section and E_Total are the total number of elements on a cross section and of the whole column, respectively. N_3 d and N_28 d are the ultimate axial loads of the column at ages of 3 days and 28 days.Table 2
Meshes parameter and results.
Model N_Ring N_Radius N_Axial E_Section E_Total N_3 d (kN) N_28 d (kN) M1 12 2,3 18 56 1120 2240 2868 M2 12 3,4 18 68 1224 2256 2904 M3 16 3,4 18 96 1728 2285 2942 M4 20 3,4 18 104 1872 2358 2965 M5 24 3,4 18 132 2376 2372 2972 M6 28 3,4 18 160 2880 2377 2979Figure3 shows terms of load against relative displacement of the different meshing FE model for concrete at the age 3 of and 28 days. With the increase in the number of elements, from M1 to M6, Table 2 shows the convergence of the ultimate load. When the elements number is more than that of M4, the difference between the different meshing schemes is nonsignificant. Therefore, meshing scheme M4 will be used in the following numerical simulations.Figure 3
The load curve for different meshes at the (a) age of 3 days and (b) age of 28 days.
(a) (b)Laboratory tests have been conducted (see Figure4) on the column specified in Table 1 in order to verify the FEM model. Load-bearing capacity tests are conducted at ages equal to 3, 7, 14, 21, 28, and 49 days.Figure 4
Load-bearing capacity test of the CFST column.The experimental test results of the time-dependent elastic modulus at different ages are shown in Table3, and the load-bearing capacity of the CFST column is shown in Figure 5 as a function of the considered ages. Comparison between experimental and numerical results shows that the FE model can clearly predict the age-dependent load-bearing capacity.Table 3
Elastic modulus of the concrete at different age.
Age (days) 3 7 14 21 28 E c (MPa) 30680 32319 34053 35101 35905Figure 5
Load-bearing capacity of the CFST column at different ages.


### 2.2. Empirical Formula of the Age-Related Load-Bearing Capacity

Parametric studies on a variety of CFST columns presented in Table4 are conducted to derive an empirical formula for the load-bearing capacity of the CFST columns, whose numerical results are presented in Table 5.Table 4
Axially compressed short columns.
Number D × T × L (mm) f y (MPa) f c k (MPa) α ξ 1 1000 × 12 × 3000 345 40.7 0.050 0.422 2 1000 × 18 × 3000 345 40.7 0.076 0.645 3 1000 × 24 × 3000 345 40.7 0.103 0.876 4 1000 × 30 × 3000 345 40.7 0.132 1.117 5 1000 × 36 × 3000 345 40.7 0.161 1.366 α is the area ratio of the steel with respect to that of concrete (α=As/Ac), whereas ξ is the hoop effect coefficient (ξ=Asfy/Acfck).Table 5
Ultimate load-bearing capacity of the axially compressed columns.
N k (kN) N u t (×103 kN) ( N u t - N k ) / ( N u 28 - N k ) Concrete age (day) 0 1 3 7 14 28 1 3 7 14 Number 1 13.070 30.876 43.497 49.731 52.161 54.934 0.425 0.727 0.876 0.934 Number 2 19.235 38.841 51.250 57.432 59.979 63.839 0.440 0.718 0.856 0.913 Number 3 25.238 45.828 58.000 64.098 66.483 70.591 0.454 0.722 0.857 0.909 Number 4 31.084 52.171 64.129 70.131 72.343 76.533 0.464 0.727 0.859 0.908 Number 5 36.770 58.070 69.795 75.706 77.777 81.960 0.471 0.731 0.862 0.907 N k = A s f y; Nu28 is the load-bearing capacity when the concrete age is equal to 28 days.Supposing that the age-strength relationship of concrete in the steel tube has the same form as when it is unconfined, according to ACI-209 [15], the following equation can be established:(1)Nut-NkNu28-Nk=ta+bt,where the two unknown constants in the equation can be estimated by fitting FE results presented in Table 5. Then, a=1.243 and b=0.977 are obtained with the maximum error of 3.4%. Therefore, the ultimate load-bearing capacity of the CFST column is obtained as follows:(2)Nut=Nk+Nu28-Nkt1.243+0.977t.The previously presented equation is validated through its application on the specimen defined in Table1, and a comparison between experimental and numerical results is shown in Figure 6. F(exp) and F(FEM) are obtained applying (2) to the experimental and numerical results, respectively, shown in Figure 5. The predicted ultimate loading capacities obtained from the formula are consistent with those obtained from the experimental tests and FE modeling.Figure 6
Comparison with the experimental and numerical results.


## 2.1. FEM Modeling of CFST Columns

The numerical model is implemented in ABAQUS eight-node quadrilateral in-plane continuum shell elements which are used for the steel tube whereas the concrete is modeled employing eight-node linear brick element. The bilinear material model is adopted for the steel, with tangent modulus being 5% of the elastic modulus of2.06e5 MPa. The material model used for the concrete is the damaged plasticity model, and hardening of concrete at different ages follows the curves proposed by Yi et al. [14], as shown in Figure 1. Other mechanical and geometrical parameters of the column are given in Table 1. FE meshes of both concrete and steel are shown in Figure 2. The contact between the steel tube and concrete is assumed to be perfect; here the nodes on the interface between solid and shell elements are tied.Table 1
Geometrical and mechanical properties of the specimens.
D (mm) T (mm) L (mm) f y (MPa) f c k (MPa) E s (MPa) 219 4.5 766 345 40.7 2.06 e 5Figure 1
Stress strain relations of concrete at different ages.Figure 2
Finite element mesh of (a) concrete and (b) steel tube.
(a) (b)Different meshing schemes are tested in order to assess the convergence of the FEM model, and the details are listed in Table2, where N_Ring, N_Radius, and N_Axial are, respectively, the numbers of elements in the circumferential, radial, and axial directions. E_Section and E_Total are the total number of elements on a cross section and of the whole column, respectively. N_3 d and N_28 d are the ultimate axial loads of the column at ages of 3 days and 28 days.Table 2
Meshes parameter and results.
Model N_Ring N_Radius N_Axial E_Section E_Total N_3 d (kN) N_28 d (kN) M1 12 2,3 18 56 1120 2240 2868 M2 12 3,4 18 68 1224 2256 2904 M3 16 3,4 18 96 1728 2285 2942 M4 20 3,4 18 104 1872 2358 2965 M5 24 3,4 18 132 2376 2372 2972 M6 28 3,4 18 160 2880 2377 2979Figure3 shows terms of load against relative displacement of the different meshing FE model for concrete at the age 3 of and 28 days. With the increase in the number of elements, from M1 to M6, Table 2 shows the convergence of the ultimate load. When the elements number is more than that of M4, the difference between the different meshing schemes is nonsignificant. Therefore, meshing scheme M4 will be used in the following numerical simulations.Figure 3
The load curve for different meshes at the (a) age of 3 days and (b) age of 28 days.
(a) (b)Laboratory tests have been conducted (see Figure4) on the column specified in Table 1 in order to verify the FEM model. Load-bearing capacity tests are conducted at ages equal to 3, 7, 14, 21, 28, and 49 days.Figure 4
Load-bearing capacity test of the CFST column.The experimental test results of the time-dependent elastic modulus at different ages are shown in Table3, and the load-bearing capacity of the CFST column is shown in Figure 5 as a function of the considered ages. Comparison between experimental and numerical results shows that the FE model can clearly predict the age-dependent load-bearing capacity.Table 3
Elastic modulus of the concrete at different age.
Age (days) 3 7 14 21 28 E c (MPa) 30680 32319 34053 35101 35905Figure 5
Load-bearing capacity of the CFST column at different ages.


## 2.2. Empirical Formula of the Age-Related Load-Bearing Capacity

Parametric studies on a variety of CFST columns presented in Table4 are conducted to derive an empirical formula for the load-bearing capacity of the CFST columns, whose numerical results are presented in Table 5.Table 4
Axially compressed short columns.
Number D × T × L (mm) f y (MPa) f c k (MPa) α ξ 1 1000 × 12 × 3000 345 40.7 0.050 0.422 2 1000 × 18 × 3000 345 40.7 0.076 0.645 3 1000 × 24 × 3000 345 40.7 0.103 0.876 4 1000 × 30 × 3000 345 40.7 0.132 1.117 5 1000 × 36 × 3000 345 40.7 0.161 1.366 α is the area ratio of the steel with respect to that of concrete (α=As/Ac), whereas ξ is the hoop effect coefficient (ξ=Asfy/Acfck).Table 5
Ultimate load-bearing capacity of the axially compressed columns.
N k (kN) N u t (×103 kN) ( N u t - N k ) / ( N u 28 - N k ) Concrete age (day) 0 1 3 7 14 28 1 3 7 14 Number 1 13.070 30.876 43.497 49.731 52.161 54.934 0.425 0.727 0.876 0.934 Number 2 19.235 38.841 51.250 57.432 59.979 63.839 0.440 0.718 0.856 0.913 Number 3 25.238 45.828 58.000 64.098 66.483 70.591 0.454 0.722 0.857 0.909 Number 4 31.084 52.171 64.129 70.131 72.343 76.533 0.464 0.727 0.859 0.908 Number 5 36.770 58.070 69.795 75.706 77.777 81.960 0.471 0.731 0.862 0.907 N k = A s f y; Nu28 is the load-bearing capacity when the concrete age is equal to 28 days.Supposing that the age-strength relationship of concrete in the steel tube has the same form as when it is unconfined, according to ACI-209 [15], the following equation can be established:(1)Nut-NkNu28-Nk=ta+bt,where the two unknown constants in the equation can be estimated by fitting FE results presented in Table 5. Then, a=1.243 and b=0.977 are obtained with the maximum error of 3.4%. Therefore, the ultimate load-bearing capacity of the CFST column is obtained as follows:(2)Nut=Nk+Nu28-Nkt1.243+0.977t.The previously presented equation is validated through its application on the specimen defined in Table1, and a comparison between experimental and numerical results is shown in Figure 6. F(exp) and F(FEM) are obtained applying (2) to the experimental and numerical results, respectively, shown in Figure 5. The predicted ultimate loading capacities obtained from the formula are consistent with those obtained from the experimental tests and FE modeling.Figure 6
Comparison with the experimental and numerical results.


## 3. Influence of Creep on CFST Columns

In this section, a composite creep coefficient of CFST columns is proposed, in order to consider steel confinement, and the factor of the effective aging coefficient is obtained by regression on the FEM results.


### 3.1. Creep Coefficient of the CFST Column

Yi et al. [14] proposed the age-adjusted effective modulus method, also known as BT theory, which represents an effective method to analyze the long-term effect of concrete creep. An aging coefficient was introduced in order to consider the effect of concrete aging on the ultimate creep, and the integral equation for creep was transformed into an algebraic equation by employing the integral mean value theorem.When stress varies with time, the corresponding total strain at timet can be expressed as follows:(3)εcct=σc10τ0Ecτ01+φt,τ0+1Ecτ0∫τ0tdσc1τdτ1+φt,τdτ,where εcc(t) is the strain of concrete when creep is with no steel confinement at age t days, σc10(τ0) is the stress of the concrete at τ0 days, Ec(τ0) is the elastic modulus of concrete at τ0 days, and φ(t,τ0) is the creep coefficient at t when loaded at τ0 days.Applying the integral mean value theorem on formula (3) leads to(4)εcct=σc10τ0Ecτ01+φt,τ0+σc1t-σc10τ0Eφ.Consider (5)Eφ=Ecτ01+ρφt,τ0,where σc1(t) is the stress of concrete at age of t days. Eφ is the age-adjusted effective modulus. ρ is the aging coefficient of concrete that is calculated as follows:(6)ρ=Ecτ01-e-φt,τ0-1φt,τ0.The following calculation is based on the assumption of plane section and superposition principle of creep regardless of the toroidal shrinkage and strain. The axial strains of concrete and steel tube at age ofτ0 are denoted as εc10 and εs10, respectively, whereas σc10 and σs10 represent the related stresses. The creep of concrete with no steel confinement is εcc=εc0φ(t,τ0) at the age of t. As a result of the effect of the steel tube confinement, the concrete creep is reduced to εc1c, as shown in Figure 7.Figure 7
Creep strain of CFST member under axial compression.It is clear that the strain increment of the steel tube is the actual concrete creep. Hence,(7)εsc1c=εs1c,εs1c=εcc-εc1c,εs10=εc10,where εsc1c is the axial creep strain of the CFST column, εs1c is the axial strain of steel tube due to concrete creep, εcc is the creep strain of the concrete with no steel confinement, εc1c is the reduced strain of the concrete considering the steel tube confinement, εs10 is the strain of the steel tube when loaded at τ0 days, and εc10 is the strain of the concrete when loaded at τ0 days.The total strain of CFST, or concrete in the steel tube, is derived as follows:(8)εt=εc10+εcc-εc1c.From (3), it becomes(9)εt=σc10Ecτ01+φt,τ0+1Ecτ0∫τ0tdσc1τdτ1+φt,τdτ,εc10=σc10Ecτ0,εcc=σc10Ecτ0φt,τ0.From (8) and (9), it is obtained that(10)εc1c=-1Ecτ0∫τ0tdσc1τdτ1+φt,τdτand by considering (4) and (5) (11)εc1c=-1+ρφt,τ0σc1t-σc10Ecτ0=-1+ρφt,τ0σc1cEcτ0,where σc1c is the stress change of the concrete due to creep. In spite of extensive microcracks that will be induced in the core as reported by previous researchers and splitting cracks that can occur at 30% to 40% stress [16–18], the cracks could close if they are subject to an outer sustained compression load at an early age. The confining stress would delay the formation of splitting cracks and restrict the widening of splitting cracks [19, 20], and the confinement effect appears based on the splitting cracks formation [21]. There will be no or little splitting cracks in the core concrete under the maximum sustained load after seven stages at an early age that is 40% bearing capacity of the specimens in the experiment and this had been contained naturally in the total creep. Therefore, the effect of splitting cracks on the creep was not considered separately here.The equilibrium force condition in the axial direction satisfies the following equations:(12)σc1cAc+σs1cAs=0,σc1c=-Asσs1cAc=-ασs1c,where σs1c is the stress change of steel tube due to creep.Not considering the creep of the steel tube and taking steel as elastic modulus value a constant give(13)εs1c=σs1cEs=-σc1cαEsand (11) becomes (14)σc10Ecτ0φt,τ0+1+ρφt,τ0σc1cEcτ0=-σc1cαEs;letting n=Es/Ec(τ0) in (14), the change in stresses on concrete and steel tube because of the concrete creep is expressed as follows:(15a)σc1c=-αnσc10φt,τ01+αn1+ρt,τ0φt,τ0,(15b)σs1c=nσc10φt,τ01+αn1+ρt,τ0φt,τ0.Consider the following equations:(16)σs1c=εs1cEs=εsc1cEs,σc10=Ecτ0εsc10=Esεsc10n.Equations (16) are introduced into (15a) and (15b) to obtain the total creep strain εsc1c of the CFST column, as follows:(17)εsc1c=εsc10φt,τ01+αn1+ρt,τ0φt,τ0.Here the creep prediction functionφt,τ0 employed the equation from ACI-209 [15]. Then, the composite creep coefficient of the CFST, φsc(t,τ0)=εsc1c/εsc0, is obtained as follows:(18a)φsct,τ0=φt,τ01+αn1+ρsct,τ0φt,τ0,(18b)φt,τ0=t-τ00.610+t-τ00.6φcu,(18c)φcu=2.35γlaγhγψγsγλγa,where φcu is the ultimate creep of concrete; γla is the influence coefficient of loading age; γh is influence coefficient of average thickness or the ratio of volume and area of the component; γψ is influence coefficient of the fine aggregate content; γs is influence coefficient of the concrete slump; γλ is influence coefficient of the ambient humidity; γa is influence coefficient of the air content.In this study,ρsc(t,τ0) represents the aging coefficient that introduce the effect of not only concrete age but also the steel tube confinement when the CFST column is considered as a single homogeneous material, which is distinguished by ρ(t,τ0), the aging coefficient of concrete.Experimental test and FEM creep analysis of the CFST column are conducted in order to determine the aging coefficient,ρsc(t,τ0).


### 3.2. Experimental Test and FEM Simulation of the Creep Model during Construction

A special loading device was designed and manufactured in order to simulate the loading process during construction, as shown in Figure8. Six columns, divided into two groups, were tested. The three columns in the first group are filled with concrete with recycled aggregates, whereas the other three columns in the second group are filled with concrete with conventional aggregates. The volume percentage of the expansive agent is 0%, 5%, and 10% for the three columns in each group, respectively. The design details of the columns are shown in Table 6.Table 6
Geometrical and mechanical properties of tests columns.
Number D (mm) T (mm) H (mm) f y (MPa) f c k (MPa) Aggregate kind Percent of expansive 1# 133 4.5 400 345 30.4 Recycled 0 2# 133 4.5 400 345 30.4 Recycled 5 3# 133 4.5 400 345 30.4 Recycled 10 4# 133 4.5 400 345 30.4 Conventional 0 5# 133 4.5 400 345 30.4 Conventional 5 6# 133 4.5 400 345 30.4 Conventional 10Figure 8
Experimental testing devices.The ultimate bearing capacity of the columns is designed as 1,100 kN, whose 40% represents the maximum dead load of 350 kN reached at the final stage of loading. The entire loading process is divided into seven stages and the load at each stage is recorded by the force sensor, as shown in Table7 and Figure 9. An initial load of approximately 50 kN is applied to all columns of the two groups when concrete is three days old. Dead load increases by approximately 50 kN at each stage with a three-day interval, until it reaches 350 kN.Table 7
Registered load at each stage (kN).
Number 1st stage 2nd stage 3rd stage 4th stage 5th stage 6th stage 7th stage 1# 53.05 102.45 154.42 204.31 253.60 306.10 355.20 2# 53.31 103.40 153.87 203.30 252.75 305.05 354.28 3# 53.54 102.70 152.94 202.90 252.58 303.37 349.58 4# 54.48 103.40 151.44 208.40 253.92 305.79 355.70 5# 52.90 103.16 150.71 204.46 253.00 304.43 354.28 6# 49.40 103.50 152.39 205.95 255.11 306.54 355.99Figure 9
The dead load applied at related time.The creep deformation of the columns is measured by excluding the instantaneous displacements from the total displacement, as shown in Figure10. Instantaneous displacements from the dead load are recorded immediately after such a load is applied, at each stage of the loading process. From Figure 10, the longitudinal deformation of the columns caused by the creep is notable and an increase in the expansion agent results in a larger creep deformation.Figure 10
Longitudinal creep deformation curve obtained by FE model.Column 4 is modeled by ABAQUS using a user-supplied subroutine of the creep effect. The creep model of ACI-209 [15], which considers the moist-cured condition, is adopted in the subroutine, where the progression method proposed by Gao et al. [22] is used to consider the change in concrete elastic modulus with age.Creep deformation of column 4 obtained from the FE analysis is compared with the experimental results shown in Figure11. In general, the FE solutions are consistent with the experimental test results.Figure 11
Experimental and numerical longitudinal creep deformation curves of specimen 4#.After validating the FE analysis, the model is used to evaluate the aging coefficientρsc(t,τ0) of the columns specified in Table 8; here the composite creep coefficient φsc(t,τ0) is obtained by ratio between creep and instantaneous displacements from the numerical result, shown in Figure 12.Table 8
Parameters of column needed in calculation.
D (mm) T (mm) H (mm) f y (MPa) f c k (MPa) τ 0 (day) TL (day) φ c u 1000 12~36 4000 345 40.7 7 50 2.12 TL is the time of the load duration;φcu is the ultimate creep coefficient of concrete according to Terry et al. [8].Figure 12
Composite creep coefficient.ρ s c ( t , τ 0 ) can be back calculated employing (18a), (18b), and (18c) with known φsc(t,τ0) in Figure 12. Figure 13 shows the resulting aging coefficients, which are almost linear for the steel ratio α ranging from 0.05 to 0.20, representing the typical reinforcement ratio of practical designs. Thus, the aging coefficient within this range can be approximately computed as follows:(19)ρsct,τ0=0.848+0.16α.Figure 13
Aging coefficient of CFST column.Then, the composite creep coefficientφsc(t,τ0) of a CFST column can be calculated employing (18a), (18b), (18c), and (19).Predictions by (18a), (18b), and (18c) are compared with the test results from the studies of Terry et al. [8], in order to verify such equations, as shown in Figure 14, where Equ(Terry-1) is the equation result obtained by (18a), (18b), and (18c) related to the experimental test of Terry-1. A quite agreement can be seen, with some differences due to the different value adoptions of the ultimate creep of concrete and the loading duration.Figure 14
Composite creep coefficient compared with results of Terry et al. [8].


## 3.1. Creep Coefficient of the CFST Column

Yi et al. [14] proposed the age-adjusted effective modulus method, also known as BT theory, which represents an effective method to analyze the long-term effect of concrete creep. An aging coefficient was introduced in order to consider the effect of concrete aging on the ultimate creep, and the integral equation for creep was transformed into an algebraic equation by employing the integral mean value theorem.When stress varies with time, the corresponding total strain at timet can be expressed as follows:(3)εcct=σc10τ0Ecτ01+φt,τ0+1Ecτ0∫τ0tdσc1τdτ1+φt,τdτ,where εcc(t) is the strain of concrete when creep is with no steel confinement at age t days, σc10(τ0) is the stress of the concrete at τ0 days, Ec(τ0) is the elastic modulus of concrete at τ0 days, and φ(t,τ0) is the creep coefficient at t when loaded at τ0 days.Applying the integral mean value theorem on formula (3) leads to(4)εcct=σc10τ0Ecτ01+φt,τ0+σc1t-σc10τ0Eφ.Consider (5)Eφ=Ecτ01+ρφt,τ0,where σc1(t) is the stress of concrete at age of t days. Eφ is the age-adjusted effective modulus. ρ is the aging coefficient of concrete that is calculated as follows:(6)ρ=Ecτ01-e-φt,τ0-1φt,τ0.The following calculation is based on the assumption of plane section and superposition principle of creep regardless of the toroidal shrinkage and strain. The axial strains of concrete and steel tube at age ofτ0 are denoted as εc10 and εs10, respectively, whereas σc10 and σs10 represent the related stresses. The creep of concrete with no steel confinement is εcc=εc0φ(t,τ0) at the age of t. As a result of the effect of the steel tube confinement, the concrete creep is reduced to εc1c, as shown in Figure 7.Figure 7
Creep strain of CFST member under axial compression.It is clear that the strain increment of the steel tube is the actual concrete creep. Hence,(7)εsc1c=εs1c,εs1c=εcc-εc1c,εs10=εc10,where εsc1c is the axial creep strain of the CFST column, εs1c is the axial strain of steel tube due to concrete creep, εcc is the creep strain of the concrete with no steel confinement, εc1c is the reduced strain of the concrete considering the steel tube confinement, εs10 is the strain of the steel tube when loaded at τ0 days, and εc10 is the strain of the concrete when loaded at τ0 days.The total strain of CFST, or concrete in the steel tube, is derived as follows:(8)εt=εc10+εcc-εc1c.From (3), it becomes(9)εt=σc10Ecτ01+φt,τ0+1Ecτ0∫τ0tdσc1τdτ1+φt,τdτ,εc10=σc10Ecτ0,εcc=σc10Ecτ0φt,τ0.From (8) and (9), it is obtained that(10)εc1c=-1Ecτ0∫τ0tdσc1τdτ1+φt,τdτand by considering (4) and (5) (11)εc1c=-1+ρφt,τ0σc1t-σc10Ecτ0=-1+ρφt,τ0σc1cEcτ0,where σc1c is the stress change of the concrete due to creep. In spite of extensive microcracks that will be induced in the core as reported by previous researchers and splitting cracks that can occur at 30% to 40% stress [16–18], the cracks could close if they are subject to an outer sustained compression load at an early age. The confining stress would delay the formation of splitting cracks and restrict the widening of splitting cracks [19, 20], and the confinement effect appears based on the splitting cracks formation [21]. There will be no or little splitting cracks in the core concrete under the maximum sustained load after seven stages at an early age that is 40% bearing capacity of the specimens in the experiment and this had been contained naturally in the total creep. Therefore, the effect of splitting cracks on the creep was not considered separately here.The equilibrium force condition in the axial direction satisfies the following equations:(12)σc1cAc+σs1cAs=0,σc1c=-Asσs1cAc=-ασs1c,where σs1c is the stress change of steel tube due to creep.Not considering the creep of the steel tube and taking steel as elastic modulus value a constant give(13)εs1c=σs1cEs=-σc1cαEsand (11) becomes (14)σc10Ecτ0φt,τ0+1+ρφt,τ0σc1cEcτ0=-σc1cαEs;letting n=Es/Ec(τ0) in (14), the change in stresses on concrete and steel tube because of the concrete creep is expressed as follows:(15a)σc1c=-αnσc10φt,τ01+αn1+ρt,τ0φt,τ0,(15b)σs1c=nσc10φt,τ01+αn1+ρt,τ0φt,τ0.Consider the following equations:(16)σs1c=εs1cEs=εsc1cEs,σc10=Ecτ0εsc10=Esεsc10n.Equations (16) are introduced into (15a) and (15b) to obtain the total creep strain εsc1c of the CFST column, as follows:(17)εsc1c=εsc10φt,τ01+αn1+ρt,τ0φt,τ0.Here the creep prediction functionφt,τ0 employed the equation from ACI-209 [15]. Then, the composite creep coefficient of the CFST, φsc(t,τ0)=εsc1c/εsc0, is obtained as follows:(18a)φsct,τ0=φt,τ01+αn1+ρsct,τ0φt,τ0,(18b)φt,τ0=t-τ00.610+t-τ00.6φcu,(18c)φcu=2.35γlaγhγψγsγλγa,where φcu is the ultimate creep of concrete; γla is the influence coefficient of loading age; γh is influence coefficient of average thickness or the ratio of volume and area of the component; γψ is influence coefficient of the fine aggregate content; γs is influence coefficient of the concrete slump; γλ is influence coefficient of the ambient humidity; γa is influence coefficient of the air content.In this study,ρsc(t,τ0) represents the aging coefficient that introduce the effect of not only concrete age but also the steel tube confinement when the CFST column is considered as a single homogeneous material, which is distinguished by ρ(t,τ0), the aging coefficient of concrete.Experimental test and FEM creep analysis of the CFST column are conducted in order to determine the aging coefficient,ρsc(t,τ0).


## 3.2. Experimental Test and FEM Simulation of the Creep Model during Construction

A special loading device was designed and manufactured in order to simulate the loading process during construction, as shown in Figure8. Six columns, divided into two groups, were tested. The three columns in the first group are filled with concrete with recycled aggregates, whereas the other three columns in the second group are filled with concrete with conventional aggregates. The volume percentage of the expansive agent is 0%, 5%, and 10% for the three columns in each group, respectively. The design details of the columns are shown in Table 6.Table 6
Geometrical and mechanical properties of tests columns.
Number D (mm) T (mm) H (mm) f y (MPa) f c k (MPa) Aggregate kind Percent of expansive 1# 133 4.5 400 345 30.4 Recycled 0 2# 133 4.5 400 345 30.4 Recycled 5 3# 133 4.5 400 345 30.4 Recycled 10 4# 133 4.5 400 345 30.4 Conventional 0 5# 133 4.5 400 345 30.4 Conventional 5 6# 133 4.5 400 345 30.4 Conventional 10Figure 8
Experimental testing devices.The ultimate bearing capacity of the columns is designed as 1,100 kN, whose 40% represents the maximum dead load of 350 kN reached at the final stage of loading. The entire loading process is divided into seven stages and the load at each stage is recorded by the force sensor, as shown in Table7 and Figure 9. An initial load of approximately 50 kN is applied to all columns of the two groups when concrete is three days old. Dead load increases by approximately 50 kN at each stage with a three-day interval, until it reaches 350 kN.Table 7
Registered load at each stage (kN).
Number 1st stage 2nd stage 3rd stage 4th stage 5th stage 6th stage 7th stage 1# 53.05 102.45 154.42 204.31 253.60 306.10 355.20 2# 53.31 103.40 153.87 203.30 252.75 305.05 354.28 3# 53.54 102.70 152.94 202.90 252.58 303.37 349.58 4# 54.48 103.40 151.44 208.40 253.92 305.79 355.70 5# 52.90 103.16 150.71 204.46 253.00 304.43 354.28 6# 49.40 103.50 152.39 205.95 255.11 306.54 355.99Figure 9
The dead load applied at related time.The creep deformation of the columns is measured by excluding the instantaneous displacements from the total displacement, as shown in Figure10. Instantaneous displacements from the dead load are recorded immediately after such a load is applied, at each stage of the loading process. From Figure 10, the longitudinal deformation of the columns caused by the creep is notable and an increase in the expansion agent results in a larger creep deformation.Figure 10
Longitudinal creep deformation curve obtained by FE model.Column 4 is modeled by ABAQUS using a user-supplied subroutine of the creep effect. The creep model of ACI-209 [15], which considers the moist-cured condition, is adopted in the subroutine, where the progression method proposed by Gao et al. [22] is used to consider the change in concrete elastic modulus with age.Creep deformation of column 4 obtained from the FE analysis is compared with the experimental results shown in Figure11. In general, the FE solutions are consistent with the experimental test results.Figure 11
Experimental and numerical longitudinal creep deformation curves of specimen 4#.After validating the FE analysis, the model is used to evaluate the aging coefficientρsc(t,τ0) of the columns specified in Table 8; here the composite creep coefficient φsc(t,τ0) is obtained by ratio between creep and instantaneous displacements from the numerical result, shown in Figure 12.Table 8
Parameters of column needed in calculation.
D (mm) T (mm) H (mm) f y (MPa) f c k (MPa) τ 0 (day) TL (day) φ c u 1000 12~36 4000 345 40.7 7 50 2.12 TL is the time of the load duration;φcu is the ultimate creep coefficient of concrete according to Terry et al. [8].Figure 12
Composite creep coefficient.ρ s c ( t , τ 0 ) can be back calculated employing (18a), (18b), and (18c) with known φsc(t,τ0) in Figure 12. Figure 13 shows the resulting aging coefficients, which are almost linear for the steel ratio α ranging from 0.05 to 0.20, representing the typical reinforcement ratio of practical designs. Thus, the aging coefficient within this range can be approximately computed as follows:(19)ρsct,τ0=0.848+0.16α.Figure 13
Aging coefficient of CFST column.Then, the composite creep coefficientφsc(t,τ0) of a CFST column can be calculated employing (18a), (18b), (18c), and (19).Predictions by (18a), (18b), and (18c) are compared with the test results from the studies of Terry et al. [8], in order to verify such equations, as shown in Figure 14, where Equ(Terry-1) is the equation result obtained by (18a), (18b), and (18c) related to the experimental test of Terry-1. A quite agreement can be seen, with some differences due to the different value adoptions of the ultimate creep of concrete and the loading duration.Figure 14
Composite creep coefficient compared with results of Terry et al. [8].


## 4. Conclusion

In this study, the effect of concrete age and creep on the ultimate loading capacity of CFST columns had been experimentally and numerically investigated. The validated numerical models were employed in order to propose a set of empirical equations that can be used to predict the axial loading capacity of CFST columns with different concrete ages and composite creep coefficients.According to the analysis of formula derivation and verification by experimental test and FE method, the ultimate bearing capacity considering the age of the CFST column can be calculated using (2). When treating the CFST column as a single material, both the unity creep and the aging coefficient, determined by employing (18a), (18b), (18c), and (19), respectively, can be used for long-term property analysis.Equations in this study will be simplified to a certain degree on the design and time-dependent analysis of the CFST column. More studies considering the step upload will be conducted in the future.



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