Influence of high temperature on the residual physical and mechanical properties of foamed concrete

Construction and Building Materials 135 (2017) 203–211

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Influence of high temperature on the residual physical and mechanical properties of foamed concrete Xianjun Tan a,b,c,⇑, Weizhong Chen a,b, Jiuhong Wang d, Diansen Yang a, Xianyin Qi a, Yongshang Ma a, Xu Wang d, Shaosen Ma a, Changjun Li a a

State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, Hubei 430071, China Research Center of Geotechnical and Structural Engineering, Shandong University, Jinan, Shandong 250061, China Post-Doctoral Scientific Research Station, Yankuang Group Company Limited, Zoucheng, Shandong 273500, China d Yankuang Group Company Limited Nan-Tun Coal, Zoucheng, Shandong 273515, China b c

h i g h l i g h t s
The appearances for all samples were not changed obviously when the temperature lower than 200 °C.
With the increasing of temperature, the density became lower and lower for all samples.
A function among compressive strength, temperature and density was obtained.
A prediction model to reflect the change law of elastic modulus with the densities and temperatures was deduced.

a r t i c l e

i n f o

Article history: Received 17 September 2016 Received in revised form 9 December 2016 Accepted 30 December 2016 Available online 10 January 2017 Keywords: Foamed concrete High temperature Compressive strength Elastic modulus Fire resistance

a b s t r a c t To study the influence of high temperature on the properties of foamed concrete, four densities of foamed concrete (300 kg/m3, 450 kg/m3, 600 kg/m3 and 800 kg/m3) were taken into account in a series of tests. The change laws of appearance, mass, compressive strength and elastic module at ambient temperature and after undergoing different high temperatures (200 °C, 400 °C and 600 °C) were presented. The results indicate that the appearances for all of four different densities were different. The cracks to be observed at the higher densities foamed concretes (i.e., 800 kg/m3 and 600 kg/m3). However, the pore connectivity and surface spalling phenomenon are easier to be observed at lower densities foamed concretes (i.e., 300 kg/m3 and 450 kg/m3). With temperature increasing, the density, compressive strength and elastic modulus became lower and lower for all samples, however some details are different. Furthermore, two predicting models to reflect the change laws of compressive strength and elastic modulus with different densities and temperatures are obtained and are verified by comparing the results with the experimental data and other proposed models in previous works. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction 1.1. Significance Fire disaster is one of the major disasters to destroy building structures. The stability of the building components are greatly weakened under high temperature, including compressive strength, tensile strength and so on [1–3]. Foamed concrete is either cement paste or mortar, classified as lightweight concrete, ⇑ Corresponding author at: State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, Hubei 430071, China. E-mail address: [email protected] (X. Tan). http://dx.doi.org/10.1016/j.conbuildmat.2016.12.223 0950-0618/Ó 2017 Elsevier Ltd. All rights reserved.

in which air-voids are entrapped in mortar by suitable foaming agent [4]. It is now widely used as exterior wall thermal insulation material or non-load bearing wall, since it has many featured advantages, such as excellent thermal insulation, low cost and fireproof [5,6]. However, foamed concrete has the characteristics of high porosity, the structure performance is easy to change under fire condition [7,8]. Therefore, it is of great significance to study the influence of high temperature on the properties of foamed concrete. 1.2. Research status Fire resistance of foamed concrete has attracted a lot of researchers. Researchers have been investigating for many years,

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and the main contributions include: Mydin and Wang [8] reported the results of experimental and analytical studies to investigate the mechanical properties of foamed concretes with two different densities (650 and 1000 kg/m3) under high temperatures. The experimental results consistently demonstrated that the loss in stiffness of foamed concrete at elevated temperatures occurring predominantly after about 90 °C, regardless of density as water expands and evaporates from the porous body. This research has also found that the mechanical properties of foamed concrete can be predicted using the mechanical property models of normal weight concrete. Kearsley and Mostert [9] studied the effect of cement composition on the behaviour of foamed concrete at high temperature, and concluded that foamed concrete containing hydraulic cement with an Al2O3/CaO ratio can withstand temperatures as high as 1450 °C without any damage. Sayadi et al. [10] and Vilches et al. [11] demonstrated the effects of expanded polystyrene particles (EPS) on fire resistance, and concluded that the volume of EPS increasing caused a significant reduction of fire endurance. Jones and McCarthy [12] summarized that, as compared to vermiculite concrete, lower densities of foamed concrete exhibited better fire resistance. Othuman and Wang [13] presented two methods to determine thermal conductivity values of lightweight foamed concrete (LFC) at elevated temperature, furthermore, they concluded that LFC offers a feasible alternative to gypsum as the construction material for partition walls.

2.2. Mix proportions There is no standard method for proportioning foamed concrete. Here we design them according to their dry density. The mix proportioning method used in the study described as follows:

qd ¼ Sa Mc

where, qd is the dry density of the designed foamed concrete (kg/ m3), Sa is the empirical coefficient, 1.2 is usually used for standard 425# Portland cement, M c is the mass of cement (kg/m3). The foam volume can be obtained by the following equation


 Mc Mw V 2 ¼ Kð1  V 1 Þ ¼ K 1  þ

qc

The objectives in the previous works aimed at mid to high densities of foamed concrete (>500 kg/m3). However, it all known that when the foamed concrete is used as insulation material, its density should be as low as possible on the premise of ensuring other properties to reach the insulation effect. What about the fire resistance for low densities (<500 kg/m3) foamed concrete? Furthermore, the existed theory present that at high temperature the heat transfer through porous materials is influenced by radiation, which is an inverse function of the number of air–solid interfaces traversed. With its lower thermal conductivity and diffusivity, the foamed concrete may result in better fire resistance properties, whether is it suitable for low density (<500 kg/m3) foamed concrete. There is no established theory for these two questions. Therefore, four densities of foamed concrete (300 kg/m3, 450 kg/ m3, 600 kg/m3 and 800 kg/m3) were prepared, and asset of tests were carried out, and the change laws of appearance, mass, compressive strength and elastic module at ambient temperature and after undergoing different high temperatures (200 °C, 400 °C and 600 °C) were presented.

qw

ð2Þ

where, V 1 and V 2 are the volume of cement paste and foam, respectively; qc and qw are the densities of cement and water respectively, which equal to 3100 and 1000 kg/m3; Mc and Mw are the cement and water respectively. In this paper, Mw =0.45Mc, as the binder ratio is constant 0.45; K is a coefficient, it is decided by the foam quality, generally ranging from 1.1 to 1.3, the stability of the foam agent used in our tests is good enough, so 1.1 is used in this paper. The mass of foaming agent can be obtained by the following equations

My ¼ V 2 qf Mp ¼

1.3. Objectives

ð1Þ

My

aþ1

ð3Þ ð4Þ

where, M y and qf are the mass and densities of foam, respectively; Mp is the mass of foaming agent, a is the dilution ratio, 20 is used in this paper. Four densities of foamed concrete, 300, 450, 600 and 800 kg/m3, were cast and tested. Further details of the mix constituent proportions of all densities are outlined in Table 2. 2.3. Specimen preparation According to Table 2, the measured cement and water were added into blender and mixed at first, meanwhile the foam was manufactured, after the cement paste mixing finished. The chosen amounts of the foam were added into the slurry, and mix 2– 3 min in a high-speed (about 60–120 r/min). When the cement slurry and foam are mixed evenly, the foam slurry preparation is completed. Then, it was poured into the moulds. The specimens were removed from moulds after 24 h of casting and then seal cured in curing tank for 28 days. After that, the specimens were removed out and shaped to standard samples to further tests (Ø 50 mm  100 mm). 2.4. Heating of specimens

2. Experimental details 2.1. Constituent materials Combinations of the following constituent materials were used to produce the foamed concrete. (1) Ordinary Portland cement (OPC): the cement used in this study is a Chinese standard (GB175-2007) 425# Portland cement [14]. (2) Water: the common tap water. (3) Foaming agent: one type of commercial composite foaming agent is chosen from Hua-tai building materials development Co., LTD, Henan province of China. The foaming performance is shown in Table 1.

The heating cabinet dimension is 80 cm  60 cm  60 cm, and the heating function is realized by the 8 heating resistance wires at both side. Its maximum operating temperature can reach 800 °C. From this figure it can be seen that if we want to heat to 200 °C, 400 °C and 600 °C, the required time is 9 min, 40 min and 150 min, respectively. In these heating tests, to show the influence of high temperature sufficiently, all of the heated samples undergoing 60 min constant temperature after they reached the target temperature. 2.5. Mass measurement and density calculation 1) Ambient temperature: Choosing three standard specimens (Ø 50 mm  100 mm), gauging their actual dimensions to obtain their volume, and then putting the specimens into

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X. Tan et al. / Construction and Building Materials 135 (2017) 203–211 Table 1 Foaming performance of the foaming agent. Expansion ratio

Half-life (min)

Foam density (kg/m3)

Foam diameter (lm) 5 min

30 min

1h

30

60

33.8

390

480

580

Table 2 Mix proportions for different densities of FC. Mix code

Target density(kg/m3)

Cement (kg/m3)

Water (kg/m3)

Foaming agent (kg/m3)

M1 M2 M3 M4

300 450 600 800

250.00 375.00 500.00 666.67

125.00 168.75 225.00 300.00

1.41 1.26 1.09 0.86

the oven for 24 h at 65 °C. After 24 h, baking these three specimens at 105 °C till to constant weight and then cooling to ambient temperature, after all of these, measuring the mass of each specimen. Their densities can be obtained by the following expression:

q¼

M V

ð5Þ

where, M, V and q are the mass, volume and density of foamed concrete, respectively. 2) High temperature: after the ambient temperature measurement, the chosen three specimens were put into the electric furnace, the mass of the specimens is measured after undergoing 200 °C, 400 °C and 600 °C, respectively. The densities were obtained in the same way with the samples at ambient temperature. Furthermore, the density ratio undergoing different high temperature was calculated using the following equation:

b¼

q2  100% q1

ð6Þ

where, b is the density ratio,% q1 and q2 are the density of foamed concrete before and after undergoing different high temperature, respectively, kg/m3. 2.6. Compressive test The compressive tests were carried out at the multi-function rock mechanics test (RMT) machine. More details relating to this machine can be found in the previous publications [15]. The compressive strength can be expressed as follows:

rc ¼

F S

ð7Þ

where, rc is the compression strength, MPa; F is the destroyed load, N; S is the compression area, mm2. The compressive strength ratio undergoing different high temperature can be calculated using the following equation:

v¼

rc2  100% rc1

ð8Þ

where, v is the compressive strength ratio,%; rc1 and rc2 are the compressive strength of foamed concrete before and after undergoing different high temperature, respectively, MPa. 3. Experimental results and analysis 3.1. Influence of high temperature on appearance of specimens The typical appearances of the foamed concrete for four different densities at ambient temperature, 200 °C, 400 °C and 600 °C

were presented in Figs. 1–4. It is indicated that the appearances for the four different densities were not changed obviously at ambient temperature, 200 °C. However, when the temperature higher than 400 °C, they were quite different from each other. The visible cracks begin to appear at 400 °C for higher densities (i.e., 800 kg/m3 and 600 kg/m3). However, the appearances at 600 °C were different, in which many cracks occurred for 800 kg/ m3 density while much lesser for 600 kg/m3 density. The crack seems not easier to appear for lower densities (i.e., 450 kg/m3 and 300 kg/m3), only one invisible crack was found for 450 kg/m3 density at 600 °C and 300 kg/m3 density at 400 °C. But we observed pore connectivity and surface spalling phenomenon for 300 kg/m3 density at 600 °C, which may mean the mass and compressive strength will drop considerably. 3.2. Influence of high temperature on mass The actual density at ambient temperature and remaining density after undergoing different temperatures presented were obtained by directly weighing samples, as shown in Fig. 5. To directly reveal the change law, the average value of each phase was used. From Fig. 5 it can be seen that all samples experienced a slight monotonous decrease in density with temperature, and with density increasing, this trend become more and more evident. The reason for this is that foamed concrete contains free water and chemically bond water, and the free water content in foamed concrete depends on the density (i.e., the greater the density, the greater the water content). With temperature increasing, the chemically bond water in foamed concrete will evaporate and dehydrate, in which the density of foamed concrete decreases. According to previous research, the dehydration process can be divided into four stages [8]: 1) In the range of 90–170 °C: the evaporable free water and part of the chemically bond water escapes. The evaporable free water may be considered to completely eliminate by 170 °C. Chemically bond water is also lost through decomposition of the calcium silicate hydrates (C-S-H) gel, that takes place between 120 °C and 140 °C, and the decomposition of ettringite around 120 °C [16]. 2) In the range of 200–400 °C: chemically bond water is released from further decomposition of the C-S-H gel and the sulfoaluminate phases of the cement paste [16,17]. 75% of the chemically combined water is vaporized at this stage. 3) In the range of 400–650 °C: further dehydration occurs at around 450 °C, which corresponds to decomposition of Ca (OH)2 to CaO and H2O and it is completed at 530 °C. The remaining 25% of the chemically combined water is then

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X. Tan et al. / Construction and Building Materials 135 (2017) 203–211

Fig. 1. Appearance of foamed concrete of 800 kg/m3 density at different temperatures.

Fig. 2. Appearance of foamed concrete of 600 kg/m3 density at different temperatures.

Fig. 3. Appearance of foamed concrete of 450 kg/m3 density at different temperatures.

evaporated in this stage [8,16]. And the crystalline transformation from a-quartz to b-quartz occurs between 500 and 650 °C [18]. 4) In the range of 650–1000 °C: the further weight loss stage can be assigned to the release of carbon dioxide (CO2) from calcium carbonate (CaCO3) (i.e., CaCO3 decompose to CaO and CO2), mainly occurring between 750 °C and 850 °C.

The fourth stage was not observed in this paper because the electric furnace cannot reach this temperature. But the first three stages were reflected clearly in Fig. 5. To descript this decreasing trend quantitatively, the density ratio obtained by Eq. (5) was used, and the details was demonstrated in Fig. 6. It was found that the ratio is different with density and temperature. For the foamed concrete of 800 kg/m3 density, the value is

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X. Tan et al. / Construction and Building Materials 135 (2017) 203–211

Fig. 4. Appearance of foamed concrete of 300 kg/m3 density at different temperatures.

1000

Density (kg/m3)

800

800kg/m3

600kg/m3

450kg/m3

300kg/m3

600

400

200

0 0

200

400

600

Temperature (°C)

some details are different, for the foamed concrete of both 800 kg/m3 and 600 kg/m3 densities, the decreasing trend become smaller and smaller with the temperature increasing from ambient to 600 °C. This law is also suitable for the foamed concrete of both 450 kg/m3 and 300 kg/m3 densities when the temperature lower than 400 °C. While after 400 °C, the density ratio decreased sharply, especially for the 300 kg/m3 density foamed concrete. This phenomenon cannot be explained by the above-mentioned four stage dehydration processes. The possible reason is that high temperature can cause pore connectivity and cement spalling for low density foamed concrete, it can be confirmed by Fig. 4 (d). Moreover, the results exhibited in Fig. 10 were a bit different from Mydin [8], it may because the foamed concrete density used by them is much higher than ours, as Sayadi [10] also reported that lower densities of foamed concrete showed worse fire resistance compared to foamed concrete with higher densities after they compared the results among 150 kg/m3, 250 kg/m3 and 450 kg/m3.

Fig. 5. Density change values at different temperature.

3.3. Influence of high temperature on mechanical properties 3.3.1. Influence of high temperature on compressive strength The compressive strength at ambient temperature and remaining density after undergoing different temperatures were presented in Fig. 7. As same in Section 3.2, to directly reveal the change law, the average value of each phase was used, as the three duplicate tests of each series gave very consistent results.

105

density ratio (%)

100

800kg/m3

600kg/m3

450kg/m3

300kg/m3

95 90 85

8 80

800kg/m3

600kg/m3

450kg/m3

300kg/m3

75 70 0

200

400

600

Temperature (°C) Fig. 6. Percentage of original density at different temperature.

86.9%, 78.6% and 74.6% at 200 °C, 400 °C and 600 °C, respectively; for the 600 kg/m3 density, the value is 91.0%, 84.0% and 78.7%, respectively. For the 450 kg/m3 density, the values are 93.2%, 87.5% and 81.5%, respectively; for the 300 kg/m3 density, the values are 94.5%, 91.0% and 83.4%, respectively. These data indicated that, with temperature increasing, the density became lower and lower for all samples, this trend is identical with Fig. 5. However,

Compressive strength (MPa)

7 6 5 4 3

2 1 0 0

200

400

600

Temperature (°C) Fig. 7. Compressive strength change values at different temperature.

X. Tan et al. / Construction and Building Materials 135 (2017) 203–211

It was also demonstrated that the samples experienced a slight monotonous decreasing with the raise of temperature, which is accordance with the change law of density. It means that the four stages evaporation and dehydration processes of free and chemically bond water in foamed concrete also has substantial effect on compressive strength, as high temperature made the sample crack for higher densities foamed concrete and spall for lower densities (the phenomenon has been shown in Figs. 1–4). To descript this decreasing trend quantitatively, the compressive strength ratio obtained by Eq. (7) was used, and the details was demonstrated in Fig. 8. It indicated that the compressive strength reduction at 200 °C is not significant. All of samples still retained 87% larger, compared to the original unheated value. This is because the decrease in compressive strength between 20 and 150 °C corresponds to a reduction of the cohesion of the Van der Waal forces between the calcium silicate hydrate layers. This decreases the surface energy of calcium silicate hydrate, which leads to the formation of silanol groups (Si–OH: OH–Si) presenting weaker bonding strength. However, this change only affects the concrete superficially [19]. Between 200 °C and 400 °C, decomposition of C-S-H gel and the sulfoaluminate phases caused cracks in the specimens [16]. These cracks had significant effect on the compressive strength of foamed concrete [20]. Furthermore, from Fig. 8, it can be found that the impact degree of temperature become greater and greater with density decreasing. To deeply reveal the relationship among compressive strength, temperature and density, deducting a prediction model is a useful way. Nowadays several models have been proposed for normal strength concrete [8,21–23], here we follow their research ideas, the generally expression are as follows:

rc ¼ r0 DðrT Þ

ð9Þ

where, rc is the compressive strength considering the influence of density and high temperature; r0 is the compressive strength at ambient temperature, DðrT Þ is a temperature damage function. 3.3.1.1. The establishment of r0 . Many achievements have proposed the development law of r0 , it is usually considered as a function of porosity or density [4,7,24]. The mathematic expression laws are different: linear, power, exponential, logarithmic and so on. The relationship between compressive strength and density is shown in Fig. 9. After analyzed these data carefully, we found exponential is more suitable to fit, and the expression is given below

r0 ¼ 0:095e

0:0053q

ð10Þ

Compressive strength rao (%)

where, q is the density of foamed concrete.

100

800kg/m3

600kg/m3

90

450kg/m3

300kg/m3

80 70

8 7 Compressive strength (MPa)

208

6 5 4

3 R² = 0.9974 2 1 0

200

400

600 Density (kg/m3)

800

Fig. 9. The relationship between compressive strength and density (test data and fitting curve).

3.3.1.2. The establishment of DðrT Þ. D(rT)is very complicated, and its function forms also different from each other. According to Fig. 8, the ORIGIN software is utilized to fit the relation. Firstly, according to the characteristics of the data in Fig. 8, we determined the function form by ORIGIN software. It is shown from the fitting analysis that quadratic polynomial is more suitable, and some of the parameters can be established, namely,

DðrT Þ ¼ a  bT  106 T 2

ð11Þ

where, T is the temperature, a and b is the parameters, which changes with density. So we separately fit the curves under each density condition, and obtain 4 groups of different values for a and b.

8 1:0078 > > > < 1:0105 a¼ > 1:0109 > > : 1:0139

800 kg=m3 3

600 kg=m

3

450 kg=m

3

300 kg=m

8 > 3:06  104 > > > < 3:67  104 b¼ > 4:07  104 > > > : 5:24  104

800 kg=m3 600 kg=m3 450 kg=m3 300 kg=m3 ð12Þ

From Eqs. (11) and (12) we can found that parameter a changes little and has a limited influence on D(rT),So here the average value is adopted, that is a = 1.01. Although the value of parameter b seems small, it has significant impact after multiplying with T. We further fit the different values of the 4 groups in Eq. (12) and obtained the expression of b:

b ¼ 0:0109  q0:534

ð13Þ 2

The fitted curve is related to the actual values (R = 0.9909), which shown in Fig. 10. Substituting Eqs. (12) and (13) into Eq. (11), the expression of DðrT Þ can be obtained:

60

DðrT Þ ¼ ð1:01  0:0109q0:534 T  106 T 2 Þ

50 40 30 20 0

200

400 Temperature (°C)

Fig. 8. Percentage of original density at different temperature.

600

ð14Þ

To validate proposed model, Eq. (14) and other models from literatures [18,22,23] were used to compare with the experimental results of Mydin et al. [8]. The comparison results were shown in Fig. 11, it can be seen that, as expected, our proposed model seem to give good results. It is found that both of the Eurocode 2 [18] and Li [23] models are suitable for foamed concrete, while the Hertz [22] model gave much higher results than the test results, which means it was not appropriate for foamed concrete.

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X. Tan et al. / Construction and Building Materials 135 (2017) 203–211

1400

0.06

1200

Elasc modulus (MPa)

0.05

b

0.04 0.03

y = 0.0109x-0.534 R² = 0.9909

0.02

800kg/m3

600kg/m3

450kg/m3

300kg/m3

1000 800

600 400

200

0.01

0

0

0

300

400

500

600

700

200

800

400

600

Temperature (°C)

Density (kg/m3) Fig. 12. Elastic modulus change values at different temperature. Fig. 10. The fitted curve of parameter b in Eq. (13).

Eqs. (9), (10) and (14) were integrated, and the final function relation among compressive strength, temperature and density can be described as follows:

ð15Þ

3.3.2. Influence of high temperature on elastic modulus The elastic modulus at ambient temperature and remaining density after undergoing different temperatures were presented in Fig. 12. It was also demonstrated that the samples experienced a slight monotonous decrease with the raise of temperature, which is accordance with the change law of density and compressive strength, it means that the four stages evaporation and dehydration process of free and chemically bond water in foamed concrete also has substantial effect on elastic modulus. The elastic modulus ratio was demonstrated in Fig. 13. It indicated a liner decrease and the change law for all of the densities are similar, which was different from compressive strength’s. Here we also deduced a prediction model to reflect the change law of elastic modulus with different densities and temperatures. Generally expression was defined similar with Eq. (9), that is:

Ec ¼ E0  DðET Þ

ð16Þ

where, Ec is the elastic modulus considering the influence of density and high temperature; E0 is the elastic modulus at ambient temperature, DðET Þ is the function of temperature E0 damage.

600kg/m3

450kg/m3

300kg/m3

60

40

20

0 0

200

600

400 Temperature (°C)

Fig. 13. Percentage of original elastic modulus at different temperature.

3.3.2.1. The establishment of E0 . Several models have been proposed forE0, it was usually considered as a function of compressive strength, porosity or density [12,24–26]. After carefully analyzed the data in Figs. 11 and 16, we found there was close correlation between elastic modulus and compressive strength, which was shown in Fig. 14. The expression is given below:

E0 ¼ 481:09r0:5458 0

ð17Þ

1.2

Temperature damage funcon

1.2

Temperature damage funcon

800kg/m3

80

Elasc modulus rao (%)

rc ¼ 0:095e0:0053q ð1:01  0:0109q0:534 T  106 T 2 Þ

100

1 0.8 0.6

Our proposed model Eurocode 2

0.4

Li and Purkiss model Herz model

0.2

Test results

0

1 0.8 0.6

Our proposed model Eurocode 2

0.4

Li and Purkiss model Herz model

0.2

Test results

0 0

200

400

600

0

200

400

Temperature (°C)

Temperature (°C)

(a) 650 kg/m 3

(b) 1000 kg/m3

Fig. 11. Compared results of compressive strength model damage with temperature for different densities from Mydin et al. [8].

600

210

X. Tan et al. / Construction and Building Materials 135 (2017) 203–211

3.3.2.2. The establishment of DðET Þ. From the existed literatures [18,23,27–29], it is found that the function forms of DðET Þ is simple relatively, most of them are linear. Combining with the change law in Fig. 13, a liner function was proposed as follows:

1400

Elasc modulus (MPa)

1200 1000

DðET Þ ¼ 1  0:00154  T

y = 481.09x0.5458 R² = 0.994

800 600

400 200

0

1

2

3 4 5 Compressive strengh (MPa)

6

ð19Þ 2

7

8

Fig. 14. The relationship between elastic modulus and compressive strength (test data and fitting curve).

The fitted curve is related to the actual values (R = 0.9897), which shown in Fig. 15. To validate proposed model, Eq. (19), other models from literatures [23,27–29] were used to compare with the experimental results of Mydin et al. [8]. The comparison results were shown in Fig. 16. It can be seen that all of the models can reflect the elastic model damage variation with temperature. The damage degree are slightly larger in our proposed model compared to the test results, maybe because the density is lower than the Mydin et al. [8]. Substituting Eqs. (17) and (19) into Eq. (16), the final function relation among elastic modulus, compressive strength and temperature can be described as follows:

Ec ¼ 481:09r0:5458  ð1  0:00154  TÞ 0

ð20Þ

100

4. Conclusions Elasc modulus rao (%)

80

To study the Influence of high temperature on the properties of foamed concrete, a set of tests were carried out. According to these tests, the following conclusions were obtained:

60 40

R² = 0.9897

20 0 0

200 400 Temperature (°C)

600

Fig. 15. The fitted curve of Eq. (19).

It can be seen from Fig. 14 that Eq. (16) is related to the actual values (R2 = 0.994). Furthermore, when we put Eq. (10) into Eq. (17), the relationship between elastic modulus and density can be obtained:

E0 ¼ 133:13  ð1:0029Þq

ð18Þ

(1) The appearances for all of the four different densities were not changed obviously at ambient temperature and 200 °C. The visible cracks begin to appear at 400 °C for higher densities (i.e., 800 kg/m3 and 600 kg/m3). Cracks seems not easy to appear for lower densities (i.e., 450 kg/m3 and 300 kg/m3). However, pore connectivity and surface spalling phenomenon were observed for 300 kg/m3 density at 600 °C, which may mean the mass and compressive strength will drop considerably. (2) With temperature increasing, the density became lower for all samples. However, some details are different, for the foamed concrete of both 800 kg/m3 and 600 kg/m3 densities. The decreasing trend become smaller and smaller with the temperature increasing from ambient to 600 °C. This law is also suitable for the foamed concrete of both 450 kg/m3 and 300 kg/m3 densities when the temperature lower than 400 °C. While after 400 °C, the density ratio decreased sharply, especially for the 300 kg/m3 density foamed concrete.

1.4

1.4

1.2

1.2

Lu et al

Lu et al

1

1 0.8

0.8

Test results

0.6

0.6

0.4

0.4

0.2

0.2

Test results

0

0 0

200

400

(°C)

600

0

200

400

(°C)

Fig. 16. Compared results of elastic model damage with temperature for different densities from Mydin et al. [8].

600

X. Tan et al. / Construction and Building Materials 135 (2017) 203–211

(3) It was also demonstrated that the samples experienced a slight monotonous decreasing with the raise of temperature, which is accordance with the change law of density. The function among compressive strength, temperature and density was obtained and described as follows:

rc ¼ 0:095e0:0053q ð1:01  0:0109q0:534 T  106 T 2 Þ: (4) A prediction model to reflect the change law of elastic modulus with the densities and temperatures was deduced, Ec ¼ 481:09r0:5458  ð1  0:00154  TÞ. By comparing the 0 results of the model with the experimental data and other proposed models, it is able to accurately simulate the elastic modulus under the different density and temperature conditions. Although the two proposed models were verified by ours and other peoples, one model maybe most suitable for one material. These two model maybe only suitable for foamed concrete with density range from 300 to 1000 kg/m3. Acknowledgements This work was supported by the National Program on Key Basic Research Project (973 Program) (Grant Nos. 2015CB057906 and 2013CB036006), the National Natural Science Foundation of China (Grant Nos. 51208499 and 51579238), the Postdoctoral Science Foundation of China (2014M550365, 2015T80718), and Youth Innovation Promotion Association CAS. Authors also thank the anonymous reviewers for their constructive comments which helped to modify the manuscript in current form. References [1] A. Agarwal, A.H. Varma, Fire induced progressive collapse of steel building structures: the role of interior gravity columns, Eng. Struct. 58 (2014) 129–140. [2] C. Fang, B.A. Izzuddin, A.Y. Elghazouli, D.A. Nethercot, Robustness of steelcomposite building structures subject to localised fire, Fire Saf. J. 46 (6) (2011) 348–363. [3] H.R. Baum, Simulating fire effects on complex building structures, Fire Saf. Sci. 8 (2005) 3–18. [4] K. Ramamurthy, E.K.K. Nambiar, G.I.S. Ranjani, A classification of studies on properties of foamed concrete, Cem. Concr. Compos. 31 (6) (2009) 388–396. [5] T.S. Gu, L.Y. Xie, G. Chen, Building energy conservation and wall thermal insulation, Eng. Mech. 23 (S2) (2006) 167–184.

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