Performance of recycled aggregate concrete–filled square steel tubular columns exposed to fire

Abstract

Experimental and theoretical investigation on the fire performance of concentrically loaded recycled aggregate concrete–filled square steel tubular columns with or without fire protective coating is reported in this article. Tests of nine specimens were conducted with the variation in the recycled coarse aggregate replacement ratio, axial compressive load ratio and thickness of fire protective coating. The failure pattern, typical temperature development, axial displacement and fire resistance of the tested specimens are presented and analysed. The experimental results reveal that the temperatures of the core concrete decrease with increasing recycled coarse aggregate replacement ratio and decreasing thickness of fire protective coating under the same fire exposure time. In general, the specimens with the recycled coarse aggregate replacement ratio of 50% have a similar behaviour as the corresponding specimen with normal concrete; however, the performance of specimens with the recycled coarse aggregate replacement ratio of 100% is clearly different from the reference specimen with normal concrete. Moreover, the fire resistance of recycled aggregate concrete–filled square steel tubular columns increases with an increase in the thickness of fire protective coating and a decrease in axial compressive load ratio. A finite element analysis model was developed for simulating the performance of recycled aggregate concrete–filled square steel tubular columns exposed to fire, and the finite element analysis model was validated against the experimental results.

Keywords

composite column finite element analysis model fire protective coating fire resistance recycled aggregate concrete–filled steel tube square section

Introduction

Recycling of waste concrete as aggregates in new concrete, which helps to save natural aggregate resources and to establish an environment-friendly construction industry, has attracted more and more attention of researchers (Evangelista and De Brito, 2014; Safiuddin et al., 2013). However, the properties of recycled aggregate concrete (RAC) might be not as good as those of normal concrete (NC) using natural aggregates due to the old mortar attaching to the original aggregate particles in recycled aggregates (Hansen, 1986). To improve the performance of RAC, Yang and Han (2006) proposed to fill RAC into the steel tube to form composite members and investigated the response of the RAC-filled steel tube (RACFST) members under various load cases and found that the structural performance of core RAC was enhanced due to the confinement provided by the steel tube. However, comparing with normal concrete–filled steel tube (CFST) members, the structural behaviour of RACFST members was generally worse due to the properties of RAC being worse than those of its NC counterpart (Yang and Hou, 2015).

CFST column has better structural performance than bare steel or plain concrete column due to the interaction between the steel tube and the concrete core, which makes it widely used in buildings (Zhao et al., 2010). During the last three decades, a considerable amount of experimental and theoretical work has been performed to investigate the fire behaviour of CFST columns (Kodur, 2007; Rush et al., 2012), and the simplified formulae for the fire resistance and thickness of fire protective coating of CFST columns have also been proposed (Comité Européen de Normalisation (CEN), 2005; Han et al., 2003; Kodur, 2007; Twilt et al., 1995; Zhao et al., 2010). Recently, Ibañez et al. (2015) presented a method for the realistic cross-sectional temperature prediction and the simplified fire resistance design of circular CFST columns under axial compression. Moliner et al. (2013) reported the fire test results of 24 slender circular CFST columns under eccentric compression, and both normal and high-strength concrete were considered in the tests. Tao and Ghannam (2013) carried out a numerical calculation for the temperature development in concrete-filled carbon and stainless steel tubes based on the new proposed models for thermal conductivity of concrete and thermal contact conductance at the interface. Wang and Young (2013) numerically studied the fire resistance of concrete-filled high-strength steel tubular columns using finite element model. Yang et al. (2013) experimentally and theoretically investigated the performance of concrete-filled rectangular steel tubular columns exposed to fire on three sides. Rush et al. (2015) conducted the furnace tests and thermal modelling of the unprotected and protected concrete–filled steel hollow sections. However, for the moment, only few studies are found in the literature concerning the behaviour of RACFST members exposed to fire attack. Liu (2012) conducted fire resistance tests for three RACFST and three reference CFST columns with circular section and the results showed that the fire resistance of RACFST columns was slightly higher than that of their CFST counterparts under the same conditions. Yang and Hou (2012) investigated experimentally the post-fire behaviour of concentrically loaded RACFST stub columns after exposure to high temperatures. The analysis of the existing literature highlights that the fire performance of RACFST columns has received less attention than that of CFST columns.

The aim of this article is thus to experimentally and theoretically assess the behaviour of the RAC-filled square steel tubular columns exposed to fire, including the failure pattern, typical temperature development, displacement versus time relationship and fire resistance. Nine concentrically loaded specimens having variable recycled coarse aggregate replacement ratio, axial compressive load ratio and thickness of fire protective coating were tested. The experimental results were further used to evaluate the accuracy of the predicted fire behaviour of the RAC-filled square steel tubular columns using the finite element analysis (FEA) model developed in this study.

Experimental programme

Material properties

The steel tube of the specimens was cold-formed steel square hollow section (SHS). The properties of the steel were obtained by testing three tensile coupons randomly cut from the flat portion of the tube. The nominal yield strength, ultimate strength, modulus of elasticity, Poisson’s ratio and elongation at rupture of the steel were 345.0 MPa, 411.2 MPa, 1.83 × 10⁵ N/mm², 0.279 and 20.1%, with standard deviation of 33.7 MPa, 26.9 MPa, 0.11×10⁵ N/mm², 0.014 and 1.9%, respectively.

In this study, only the recycled coarse aggregate (RCA) was partially or fully used to replace the natural coarse aggregate (NCA) when producing RAC, and the RCA was obtained by crushing concrete debris from the demolition of the concrete basement walls. The cube compressive strength of the waste concrete was about 40 MPa. The natural coarse and fine aggregate were calcareous stone and river sand, respectively, and the fineness modulus of natural fine aggregate was 2.7. The physical properties of natural and RCA are illustrated in Table 1. It can be seen that the grading range of RCA is larger than that of NCA, and RCA has lower density and higher water absorption compared with NCA due to the attachment of old mortar (Hansen, 1986). To consider the effect of higher water absorption of RCA than NCA, additional water was added while producing RAC based on the difference in water absorption. The crushing index, which is defined in GB/T 14685 (2011) for evaluating the crushing resistance subject to compression, was 6.4% (Grade I) and 19.9% (Grade II) for NCA and RCA, respectively. This indicates that RCA is suitable for adoption in new concrete, although it has lower compressive strength comparing with NCA.

Table 1.

Physical properties of natural and recycled coarse aggregate.

Type	Grading (mm)	Bulk density (kg/m³)	Apparent density (kg/m³)	Water absorption (%)
NCA	5–25	1430	2670	1.22
RCA	5–40	1320	2640	5.49

NCA: natural coarse aggregate; RCA: recycled coarse aggregate.

Three types of concrete with the desired workability class S1 designated in EN 206-1 (CEN, 2000), including NC with NCA, RAC with 50% RCA (RAC1) and RAC with 100% RCA (RAC2), were considered in the tests, as presented in Table 2. It can be seen that all slumps of fresh concrete generally belong to class S1 and the slump of RAC is slightly higher than that of NC due to incorporation of the additional water. Several 150 mm cubes and 150 mm × 150 mm × 300 mm prisms were prepared to obtain the cube compressive strength and elastic modulus of concrete, respectively. The measured cube compressive strength ( $f_{cu}$ ) and modulus of elasticity ( $E_{c}$ ) are given in Table 2, where $f_{cu, 28}$ and $f_{cu, test}$ are the cube compressive strength at 28 days and specimen testing date, respectively. It is found that RAC has lower cube compressive strength and elastic modulus compared with NC, and the larger the amount of RCA in RAC, the lower the cube compressive strength and elastic modulus.

Table 2.

Mix proportions and properties of new concrete.

Label	Cement (kg/m³)	Fine aggregate (kg/m³)	Coarse aggregate (kg/m³)		Water (kg/m³)	Slump (mm)	f _cu,28 (MPa)	f _cu,test (MPa)	E _c (N/mm²)
Label	Cement (kg/m³)	Fine aggregate (kg/m³)	Natural	Recycled	Water (kg/m³)	Slump (mm)	f _cu,28 (MPa)	f _cu,test (MPa)	E _c (N/mm²)
NC	473	636	1072	0	236.5	32	38.3	53.2	32,400
RAC1	473	636	536	536	259.4	35	37.1	49.4	29,800
RAC2	473	636	0	1072	282.3	42	36.3	44.2	27,600

NC: normal concrete; RAC: recycled aggregate concrete.

For specimens with fire protective coating, a kind of thick fireproof coating for structural steel having a thermal conductivity of 0.116 W/(m K), a specific heat of 1047 J/(kg K), a density of (400 ± 20) kg/m³ and a water content of 1% was sprayed on the surface of the tube before conducting fire tests, and the smoothness and uniformity of the protective coating were guaranteed.

Specimen preparation

Fire performance of nine square composite columns, including eight RACFST specimens and one normal CFST specimen as reference, was experimentally studied as subjected to constant axial compressive load. The parameters varied in the tests are as follows:

RCA replacement ratio (r, which is defined as the weight percentage of RCA within the whole coarse aggregate): 0%, 50% and 100%

Axial compressive load ratio (n): 0.2, 0.3, 0.4 and 0.5

Thickness of fire protective coating (a): 0, 3, 6 and 9 mm

The axial compressive load ratio (n) is defined as follows

n = \frac{N_{0}}{N_{u}}

(1)

where $N_{0}$ is the constant axial compressive load applied to the top of specimens during the tests, and $N_{u}$ is the bearing capacity of specimens at ambient temperature (Yang and Hou, 2015), which is given by the following equation

N_{u} = φ \cdot f_{scy, r} \cdot A_{sc}

(2)

where $φ$ and $f_{scy, r}$ are the stability factor and strength index, respectively (Yang and Hou, 2015), and $A_{sc}$ is the cross-sectional area of composite column.

Four cross sections in the longitudinal direction of the specimen with interval of 0.75 m were selected to measure the thickness of fire protective coating and there were eight measuring points symmetrically distributed at each cross section. Finally, the average value of all the measured results was adopted as the thickness of fire protective coating.

To monitor the development of temperatures at typical locations, four thermocouples were installed at the mid-height section of the specimens by a welded reinforcement bracket. The details are shown in Figure 1.

Figure 1.

Arrangement of thermocouples: (a) without fire protective coating and (b) with fire protective coating.

A summary of the tested specimens is presented in Table 3, where B is the outside width of square steel tube, $t_{s}$ is the wall thickness of the steel tube, L_e is the buckling length of specimen, $λ (= 2 \sqrt{3} L_{e} / B)$ is the slenderness ratio and $t_{R, e}$ and $t_{R, p}$ are the experimental and predicted fire resistance, respectively. The height of the specimens is 3750 mm. There were no separate end plates in the specimens, but the supporting devices serving as pinned bearings were assembled directly to the ends of the specimen to implement pinned–pinned boundary conditions, and the distance from the end of specimens to the pin bearing is 30 mm. As a result, the buckling length of specimen (L_e) is 3810 mm. Two semicircle vents of 20 mm in diameter located at the junction near the top and bottom end were drilled to release water vapour pressure produced under high temperatures.

Table 3.

Summary of the tested specimens.

No.	Label	B (mm)	t _s (mm)	L _e (mm)	λ	r (%)	n	N ₀ (kN)	a (mm)	t _R,e (min)	t _R,p (min)	t _R,p/t_R,e
1	NC-0.34-0	300	5.9	3810	44.0	0	0.34	1555.6	0	36	37	1.028
2	RAC1-0.35-0	300	5.9	3810	44.0	50	0.35	1542.9	0	40	38	0.950
3	RAC2-0.37-0	300	5.9	3810	44.0	100	0.37	1535.0	0	29	32	1.103
4	RAC1-0.24-0	300	5.9	3810	44.0	50	0.24	1028.6	0	80	85	1.062
5	RAC1-0.47-0	300	5.9	3810	44.0	50	0.47	2057.2	0	23	26	1.130
6	RAC1-0.59-0	300	5.9	3810	44.0	50	0.59	2571.5	0	16	18	1.125
7	RAC1-0.59-3	300	5.9	3810	44.0	50	0.59	2571.5	3	52	46	0.885
8	RAC1-0.59-6	300	5.9	3810	44.0	50	0.59	2571.5	6	71	80	1.127
9	RAC1-0.59-9	300	5.9	3810	44.0	50	0.59	2571.5	9	87	128	1.471

NC: normal concrete; RAC: recycled aggregate concrete.

Test set-up

Before conducting fire tests, the top and bottom surfaces of the columns were ground flat using a grinding wheel machine to ensure that the axial compressive load could be applied to the steel tube and core concrete simultaneously. The test set-up is shown in Figure 2. The specimens were installed in a vertical position and both ends were inserted into the directional supports which acted as the hinged bearings. The bottom support and part of the specimens close to the two supports were protected by fire cotton, and thus, a fire exposure height of 2750 mm was attained. The axial compressive loads were applied by a 4000-kN hydraulic jack controlled by a regulator device. The furnace chamber had a floor area of 3000 mm × 2000 mm and a height of 3300 mm. The heating was achieved by eight liquefied petroleum gas burners on two sides of the furnace chamber, and the control precision of temperatures in the furnace was ±10°C. The furnace temperatures were measured with five nickel chromium–nickel silicon thermocouples, and the temperatures measured were averaged automatically to control the temperatures in the furnace approximately following the ISO 834 standard fire curve (International Standards Organization (ISO), 1999). The ambient temperature was about 20°C at the beginning of the fire tests.

Figure 2.

Schematic diagram of the test set-up.

The testing procedure consisted of two stages: first, the axial compressive loads were applied smoothly to the specimen at ambient temperature, and second at a prescribed ratio the constant axial compressive load was maintained during heating. Four displacement transducers (DTs), symmetrically located at four corners of the top support, were used to measure the axial displacements, as illustrated in Figure 2. The average value of four measured displacements was adopted as the axial displacement ( $δ$ ) of the tested specimens. According to the relevant provisions of ISO 834 (ISO, 1999), the fire resistance of the specimens is reached when the axial displacement rate is greater than (3h/1000)/min (mm/min), where h is the fire exposed height of the column in millimetres.

Results and discussion

Overall observations and failure pattern

It was observed that similar to normal CFST specimens under fire attack in literature (Han et al., 2003; Kodur, 2007; Rush et al., 2012) and this paper, RACFST specimens behaved in a relatively ductile manner, and the tests proceeded in a smooth and controlled way due to the existence of the core concrete. In the early phase of fire exposure, the specimens kept straight and no noticeable damage was found. With rising furnace temperature, the specimen gradually exhausted steam from its top end and this process generally continued for 10–15 min. Meanwhile, the colour of steel surface of the unprotected specimens gradually changed from primary to dark red, and for specimens with fire protective coating the colour of spray material surface gradually changed from original to flame and the rough surface of spray material gradually became glazed. In the later phases of the fire exposure, vertical cracks appeared at four corners of the spray material. The spray material did not fall off until the end of fire tests; however, with the gradual cooling of the specimen, the spray material first began to shrink in the vertical direction of the specimen, then partially peeled off from the steel tube and eventually fell off completely after reaching room temperature.

Figure 3 illustrates the failure modes of various specimens showing the buckling waves in the walls of the steel tube as well as flexural buckling of the specimen, depending on the parameters n, r and a. It can be seen that in general, both compression failure mechanism and overall buckling occurred in the tested specimens, that is, when the lateral displacements are relatively small, considerable number of local buckles appear on each side of the tube of the specimens, and meanwhile, the lateral displacements of the specimens are relatively small. Figure 3(a) shows that there is no difference in the failure mode of specimens with r = 0 and r = 50%, whereas the specimen with r = 100% shows lateral deflection and the local buckles concentrate on the side of the tube where the flexural compression effects are the greatest. This can be explained by the fact that when subjected to high temperatures, the damage of RAC with r = 100% is more serious than that of NC and RAC with r = 50% due to its larger amount of interfacial transition zone (ITZ) between RCA and hydration products, and a higher vapour pressure is produced for RACFST specimen with r = 100% due to its larger moist content. Figure 3(b) shows that generally, the higher the axial compressive load ratio (n), the less the number of tube buckling and the larger the lateral deflection. This means that the failure progression is accelerated due to the second-order effect of axial compressive force. It can be seen from Figure 3(c) that generally, the tube buckling of the unprotected specimens is more evident than that of specimens with fire protective coating. This may be due to the fact that for the unprotected specimens, a higher temperature of materials was reached when specimen failed and resulted in a more serious buckling of the steel tube. However, for specimen with a of 9 mm, only a concentrated buckling of the steel tube appeared at the compressive side. This may be attributed to the premature failure in the partial ITZ of the core concrete and the rapid strength loss of materials under high temperatures due to the cracking of the spray material in advance after the appearance of the centralized buckles of the steel tube.

Figure 3.

Failure modes of various specimens: (a) RCA replacement ratio, (b) axial compressive load ratio and (c) thickness of fire protective coating.

The typical failure modes of the core concrete on two sides of the specimens are shown in Figure 4. It can be seen that in general, the colour of concrete surface is yellow and grey at positions with and without steel tube buckling, respectively. This follows from the air gap between the tube inner surface and concrete core in the positions of local buckles, leading to lower local temperatures at the surface of the core concrete. Figure 4(a) shows that with the increase in r, the number and width of cracks increase and the crushing and flaking of concrete become more and more evident. This is possibly due to the fact that the damage to ITZ between RCA and hydration products becomes more serious for increasing r. It can be found from Figure 4(b) that for the unprotected specimens, diagonal cracks mainly appear at the failure zone and part of concrete is crushed within the buckling position of the steel tube; however, for specimens with fire protective coating, there are larger lateral deflections at the failure zone and a more severe crushing of concrete. Because the protective coating of the column affects the distribution of the temperatures in the core concrete as well as the vapour pressure there, and thus a more serious damage to the core concrete is caused due to the different internal vapour pressure and loading effects at high temperatures compared with the unprotected column.

Figure 4.

Typical failure modes of core concrete: (a) RCA replacement ratio and (b) thickness of fire protective coating.

Temperature development

Figure 5 shows the comparison between the recorded temperature (T) versus fire exposure time (t) curve in the furnace chamber and the ISO 834 fire curve (ISO, 1999). It shows that there is a divergence between the furnace chamber $T - t$ curve and the ISO 834 curve in the initial 5 min. This is because that the initial gas supply cannot completely meet the requirement of the heating rate of the standard fire curve. After that, the furnace chamber $T - t$ curve is in close proximity to the ISO 834 curve.

Figure 5.

Comparison of fire curves.

The measured typical $T - t$ curve of the specimens is demonstrated in Figure 6. It can be seen that, in general, the shorter the distance away from the centre of the cross section, the lower the temperatures, and the specimens with fire protective coating have a lower temperature than the unprotected specimens under the same fire exposure time.

Figure 6.

Comparison of the predicted and measured $T - t$ curves: (a) NC-0.34-0, (b) RAC1-0.35-0, (c) RAC2-0.37-0, (d) RAC1-0.24-0, (e) RAC1-0.47-0, (f) RAC1-0.59-0, (g) RAC1-0.59-3, (h) RAC1-0.59-6 and (i) RAC1-0.59-9.

The effect of the parameters considered in the tests on typical $T - t$ curves is demonstrated in Figure 7. It can be seen from Figure 7(a) that in general, the temperatures decrease with an increase in r under the same fire exposure time. This can be explained that RCA has more pores than NCA and the density of RAC is also lower than that of its NC counterpart (Hansen, 1986), which results in a lower thermal conductivity of RAC than that of the corresponding NC. Figure 7(b) shows that n has a moderate influence on $T - t$ curves. This means that the mutual effect between the loads and temperatures is not evident. It can also be observed from Figure 7(c) that similar to the protected CFST specimens under fire attack (Han et al., 2003), the thinner the fire protective coating, the higher the temperatures are under the same fire exposure time.

Figure 7.

Effect of parameters on typical $T - t$ curves: (a) a = 0 mm, (b) r = 50% and a = 0 mm and (c) r = 50% and n = 0.59.

Axial displacement

The variation in the axial displacement ( $δ$ ) of the tested specimens as a function of fire exposure time (t) is shown in Figure 8. It can be seen that $δ - t$ curve of RACFST specimens is generally similar to that of CFST specimens in this study and in the literature (Han et al., 2003; Kodur, 2007). In the early stage of fire exposure, $δ$ increases with increasing time because the expansion of the steel section is larger than that of the concrete core under high temperatures. Generally, the time of reaching the maximum axial elongation which varies between 3 and 9 min decreases with an increase in r and n and a decrease in a. This may be explained that a quicker damage to ITZ between RCA and hydration products causes a quicker strength loss of the core concrete for specimen with r = 100%, and meanwhile, a higher constraint to the expansion of the materials is produced for specimens with a larger n. Furthermore, for specimens with a thicker fire protective coating, a slower temperature increase results in a slower increase in expansion. After reaching the maximum axial elongation, the steel section yields gradually due to its strength decrease under high temperatures, and more and more axial compressive loads are transferred from the steel section to the core concrete. During this stage, the contraction of the specimens occurs and increases with increasing t. In general, r has a moderate effect on the trend of $δ - t$ curve; however, the propagation of contraction increases with an increase in n and a decrease in a. These can be attributed to the influence of the second-order effect and the difference in temperature development for specimens with and without fire protective coating. Finally, fire resistance of the specimens is reached when its bearing capacity is no longer larger than the applied axial compressive load, and at the same time, the axial contraction rate rapidly exceeds its limitation prescribed in ISO 834 (ISO, 1999).

Figure 8.

Axial displacement of the tested specimens as a function of fire exposure time: (a) RCA replacement ratio, (b) axial compressive load ratio and (c) thickness of fire protective coating.

Fire resistance

The experimental fire resistance ( $t_{R, e}$ ) of the specimens is presented in Table 3, and the relationship of $t_{R, e}$ versus recycled aggregate replacement ratio (r), axial compressive load ratio (n) and thickness of fire protective coating (a) is demonstrated in Figure 9. It can be seen from Figure 9(a) that under a similar value of n, the unprotected RACFST specimen with r = 50% has a slightly higher $t_{R, e}$ than the reference normal CFST specimen ( $r = 0$ ); however, $t_{R, e}$ of RACFST specimen with r = 100% is lower than that of its normal CFST counterpart. This may be due to the fact that for RACFST specimen with r = 50%, the beneficial effect of rougher surface of the coarse aggregate is larger than the adverse effect of deterioration of ITZ between the coarse aggregate and hydration products compared with normal CFST counterpart. However, for RACFST specimen with r = 100%, the adverse effect of deterioration of ITZ is more severe than the beneficial effect of rougher surface of the coarse aggregate compared with RACFST specimen with r = 50%. The deterioration of ITZ between the coarse aggregate and hydration products may be caused by the vapour pressure produced under high temperatures. Generally, RACFST specimen with a larger moist content possesses a higher vapour pressure than normal CFST specimen, and the vapour pressure increases with the increase in moist content. Moreover, n and a have a more significant effect on $t_{R, e}$ than r. Similar to CFST specimens in fire (Han et al., 2003), $t_{R, e}$ of RACFST specimens decreases with an increase in n and a decrease in a. The lower $t_{R, e}$ can be attributed to the larger second-order effect and the quicker temperature rising.

Figure 9.

Relationship of fire resistance versus recycled aggregate replacement ratio, axial compressive load ratio and thickness of fire protective coating: (a) RCA replacement ratio, (b) axial compressive load ratio and (c) thickness of fire protective coating.

FEA model

General description

To simulate the performance of the RAC-filled square steel tubular columns exposed to fire, a nonlinear FEA model was developed using ABAQUS (2007). The FEA model consists of two main parts: the thermal part for the simulation of temperature development and the mechanical part for the analysis of failure pattern, displacement and fire resistance, and both parts have the same element meshing.

Thermal analysis

The basic theory for uncoupled heat transfer analysis can be found in ABAQUS (2007). The effects of heat convection and radiation on RACFST columns are considered in the heat transfer model as boundary conditions, the details of which are described in the report of the European Convention for Construction Steelwork (ECCS) (1988) Technical Committee 3. Furthermore, the thermal contact resistance between the steel tube and core RAC is also considered based on the suggestion in Ghojel (2004), and the value of 0.01 m² °C/W for normal CFST is temporarily used in this analysis.

The thermal properties of the steel are those provided in Lie (1994), which have also been successfully adopted in previous temperature distribution analysis of normal CFST columns (Han et al., 2003; Yang et al., 2013). The thermal properties of RAC derived from the equations suggested in Huang (2006) are obtained by revising the formulae for NC in Eurocode 4 (CEN, 2005) with the effect of RCA replacement ratio (r), and the details are as follows:

Thermal conductivity ( $λ_{c}$ )

\begin{array}{l} λ_{c} = f_{λ} (r) - 0.2 (\frac{T}{100}) + 0.008 {(\frac{T}{100})}^{2} \\ (20 ° C \leq T \leq 1200 ° C) \end{array}

(3)

where $f_{λ} (r) = 1.556 - 0.215 r + 0.04 r^{2}$ .

Specific heat ( $c_{c}$ )

\begin{array}{l} c_{c} = f_{c} (r) + 42 (\frac{T}{100}) - 2 {(\frac{T}{100})}^{2} \\ (20 ° C \leq T \leq 1200 ° C) \end{array}

(4)

where $f_{c} (r) = 892.5 + 44.2 r - 1.7 r^{2}$ .

The density of RAC ( $ρ_{c}$ ) is 2210 kg/m³ (Huang, 2006). The core concrete in RACFST columns contains a certain amount of free water, and the existence of free water will affect the thermal properties of the concrete (Lie, 1994). Moreover, as mentioned before, the water content in RAC is higher than that in NC and increases with the increase in r. In this study, the effect of free water expressed using the moisture content of the concrete is taken into account on the level of the heat balance by the revision of $ρ_{c} c_{c}$ . The revised thermal properties of RAC are as follows

ρ'_{c} c'_{c} = {\begin{matrix} (1 - η_{w}) \cdot ρ_{c} c_{c} + η_{w} \cdot ρ_{w} c_{w} (T \leq 100 \circ C) \\ ρ_{c} c_{c} (T > 100 \circ C) \end{matrix}

(5)

where $ρ'_{c}$ and $c'_{c}$ are the revised density and specific heat of concrete, respectively; $η_{w}$ is the moisture content of the concrete and equals to 5%, 7.5% and 10% for NC, RAC with 50% RCA and RAC with 100% RCA, respectively; and $ρ_{w}$ and $c_{w}$ are the density and specific heat of water, respectively (Lie, 1994).

In the heat transfer model, the steel tube was modelled by four-node quadrilateral three-dimensional shell elements (DS4), and the core concrete and fire protective coating were simulated by eight-node linear three-dimensional brick elements (DC3D8). The height of the columns affected by fire is the same as that in the tests (i.e. 2750 mm). For a modelled column, there are 51 layers of finite elements in the longitudinal direction and 36, 32 and 96 finite elements in the cross section of each layer for the fire protective coating, steel tube and core concrete, respectively, as shown in Figure 10.

Figure 10.

Meshing and boundary conditions: (a) longitudinal direction, (b) cross section with protective coating and (c) cross section without protective coating.

Mechanical analysis

The plasticity model in ABAQUS (2007) is adopted to simulate the mechanical behaviour of steel under high temperatures. The model uses von Mises yield surfaces with associated plastic flow, which allows for isotropic yielding. The nonlinear relationship of true stress versus logarithmic plastic true strain is required to be defined for steel component, which can be converted from the engineering stress versus engineering strain relationship in Lie (1994).

The damaged plasticity model in ABAQUS (2007) is adopted to simulate the complicated nonlinear behaviour of the core concrete under high temperatures. The nonlinear relationship of stress versus inelastic strain needs to be defined, which can also be converted from the engineering stress versus engineering strain relationship. Similar to NC (Song et al., 2010), the compressive engineering stress versus engineering strain relationship of RAC under high temperatures can be derived from the model of RAC at ambient temperature presented in Yang (2015) by considering the effect of T on the peak stress and the peak strain

σ_{0, T} = \frac{σ_{0}}{1 + 1.986 {(T - 20)}^{3.21} \times 10^{- 9}}

(6)

ε_{0, T} = ε_{0} \cdot [1 + 3.6 \times 10^{- 4} (T - 20) + 4.22 \times 10^{- 6} {(T - 20)}^{2}]

(7)

where $σ_{0, T}$ and $ε_{0, T}$ are the peak stress and strain, respectively, under high temperatures, and $σ_{0}$ and $ε_{0}$ are the respective peak stress and strain at ambient temperature, respectively. Moreover, the influence of the temperature on the confinement factor of concrete core determining the second branch of the engineering stress–strain curve needs to be considered (Song et al., 2010), and the yield strength of steel under high temperatures, which is used to calculate the confinement factor with the effect of temperature, can be determined according to Eurocode 4 (CEN, 2005).

For the concrete in tension, the stress versus fracture energy model in ABAQUS was adopted to describe the tension stiffening effect. The cracking stress is defined as 10% of peak compressive stress, and the fracture energy ( $G_{f}$ ) can be determined using the following equation (Song, 2010)

\begin{array}{l} G_{f} = 0.26 \times (1.25 f_{c}^{'})^{2 / 3} (1 - T / 1000) \\ (20 ° C \leq T \leq 1000 ° C) \end{array}

(8)

where $f'_{c}$ is the cylinder compressive strength of the concrete.

In the simulation, the elastic modulus of steel and concrete under high temperatures was the initial tangent modulus of the engineering stress versus engineering strain curves, and the Poisson’s ratio of steel and concrete was set to be 0.3 and 0.2, respectively. The coefficient of thermal expansion for steel and concrete in Lie (1994) was adopted in the FEA model. Moreover, the creep of steel under high temperatures was further considered based on the model in Fields and Fields (1991).

In the model, the directional support adopted in the tests was treated as a rigid plate. The steel tube was modelled by four-node reduced-integration three-dimensional shell elements (S4R), and the core concrete and rigid plate were simulated by eight-node reduced-integration three-dimensional brick elements (C3D8R). The ‘hard contact’ and ‘Coulomb friction’ were selected to be the contact properties along the normal and tangential directions of the interface between the steel tube and core concrete, respectively, and the friction coefficient between the three types of concrete cores (NC, RAC1 and RAC2) and the steel tube was set to be 0.25, which was within the range of 0–0.6 suggested in ABAQUS (2007). The hard contact was adopted to define the interaction between the end plates and core concrete, and the coupling between the shell and solid elements was defined as the interaction between the end plates and steel tube. The dilation angle of the three types of concrete cores was the same and set to be 30°. The mesh convergence studies showed that local mesh encryption was necessary in the corner part of the column to ensure the computational efficiency and to improve the accuracy of prediction. Furthermore, to consider the effect of global geometric imperfections, an initial eccentricity ( $e_{i}$ ) of $L_{0} / 1000$ with respect to the centroidal axis was applied at both the end plates of the column as shown in Figure 10, $L_{0}$ being the effective length of the member.

The boundary conditions at the end plates are shown in Figure 10, indicating ‘pinned’ with all displacements constrained in the centroidal line of the bottom end plate, and at the top end plate, the only allowed displacements at the centroidal line are the vertical ones. Furthermore, the geometric nonlinearity (large displacement) was assumed to take into account the large lateral deflections. The constant axial compressive load was first applied on the top of the column, and then thermal distribution was employed by reading nodal temperatures obtained from the thermal analysis.

Verifications of the FEA model

The predicted temperature (T) versus fire exposure time (t) curves of the tested specimens are given in Figure 6. It can be seen that at the interface between the steel tube and core concrete (position 4), the predicted $T - t$ curves of the specimens are slightly higher than the experimental curves. For other monitoring positions, the predicted $T - t$ curves generally agree well with the experimental results. The difference between the predicted and experimental $T - t$ curves might be caused by the discrepancy between the design location of the thermocouples and their real positions in the tests.

Figure 11 demonstrates the typical predicted failure modes, where the maximum principal plastic strain is presented for the core concrete. It can be seen that in general, the predicted failure patterns and positions of buckles in the steel tube accord well with the experimental results and appear at the crushing position of the core concrete. The comparison between the predicted and experimental $δ - t$ curves is illustrated in Figure 12. It can be found that a reasonably good agreement is obtained between both the results. However, the predicted $δ - t$ curve at the expanding stage (i.e. the expansion of the specimens under high temperatures is larger than the contraction subjected to axial compression) has a more clear difference from the experimental result. This might be caused by the unexpected environmental factors and material drawbacks in the experiments, which cannot be completely reproduced in the FEA model. The predicted fire resistance ( $t_{R, p}$ ) of the RAC-filled square steel tubular columns is given in Table 3, and the comparison between the predicted fire resistance ( $t_{R, p}$ ) and experimental results ( $t_{R, e}$ ) is demonstrated in Figure 13. It can be found from Table 3 and Figure 13 that in general, a good agreement between the predicted and experimental results with $t_{R, p} / t_{R, e}$ between 0.885 and 1.130 is attained, except for one specimen with a of 9 mm as the premature failure appeared in this test in the local ITZ of the core concrete under high temperatures due to the cracking of the protective coating in advance.

Figure 11.

Typical predicted failure modes: (a) unprotected column and (b) protected column (a = 6 mm).

Figure 12.

Comparison of $δ - t$ curves between the predicted and experimental results: (a) NC-0.34-0, (b) RAC1-0.35-0, (c) RAC2-0.37-0, (d) RAC1-0.24-0, (e) RAC1-0.47-0, (f) RAC1-0.59-0, (g) RAC1-0.59-3, (h) RAC1-0.59-6 and (i) RAC1-0.59-9.

Figure 13.

Correlation of the predicted and experimental fire resistance.

Summary and conclusion

An experimental and theoretical investigation on fire performance of the RAC-filled square steel tubular columns with or without fire protective coating is presented in this study. According to the results of observations and comparison study, the following conclusions can be drawn:

The RAC-filled square steel tubular columns exposed to fire behaved in a ductile manner and the tests proceeded in a smooth and controlled way. Under the same heating curve and fire exposure time, the temperatures of the core concrete increase with a decrease in RCA replacement ratio (r) and increase in the thickness of fire protective coating (a), and the axial compressive load ratio (n) has a moderate effect on temperature development.

In general, the failure pattern, axial displacement development and fire resistance of specimens with r = 50% are similar to the reference CFST specimen; however, the behaviour of specimen with r = 100% is clearly different from the CFST counterpart.

Similar to CFST columns under fire, the fire resistance of the RAC-filled square steel tubular columns increases with increasing a and decreasing n.

The predicted response of the RAC-filled square steel tubular columns exposed to fire by the FEA model developed in this article is generally in good agreement with the experimental observations.

No doubt the findings presented in this article complement the research area of RACFST members subjected to extreme load conditions. However, further research is needed to confirm and justify the effect of various parameters on the fire resistance. In addition, further parametric study using the FEA model is needed to find the effective thickness of fire protective coating for different RACFST columns.

Footnotes

Acknowledgements

The authors wish to thank Prof. Xiao-Yong Mao for his assistance in the experiments.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship and/or publication of this article: The studies in this article are financially supported by the National Natural Science Foundation of China (50908034, 51421064). The financial support is gratefully acknowledged.

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