# Temperature Effect on Mechanical Properties and Damage Identification of Concrete Structure

Authors: Yubo Jiao; Hanbing Liu; Xianqiang Wang; Yuwei Zhang; Guobao Luo; Yafeng Gong
Journal: Advances in Materials Science and Engineering
 (2014)

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## Abstract

Static and dynamic mechanical properties of concrete are affected by temperature effect in practice. Therefore, it is necessary to investigate the corresponding influence law and mechanism. This paper demonstrates the variation of mechanical properties of concrete at temperatures from −20°C to 60°C. Temperature effects on cube compressive strength, splitting tensile strength, prism compressive strength, modulus of elasticity, and frequency are conducted and discussed. The results indicate that static mechanical properties such as compressive strength (cube and prism), splitting tensile strength, and modulus of elasticity have highly linear negative correlation with temperature; this law is also applied to the first order frequency of concrete slab. The coupling effect of temperature and damage on change rate of frequency reveals that temperature effect cannot be ignored in damage identification of structure. Mechanism analysis shows that variation of elastic modulus of concrete caused by temperature is the primary reason for the change of frequency.


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## Body

## 1. Introduction

As widely used construction material in civil engineering structures, the properties of concrete have direct relationship with structural safety. Standard concrete specimens are usually cured and tested under ideal conditions according to specifications. However, concrete structures are exposed to external environment in service; the mechanical (static and dynamic) properties of concrete are complicated as they are affected by environmental conditions such as temperature and moisture [1, 2].Numerous researches have been conducted to investigate the relationships between concrete performances and environmental conditions. Peng et al. [3] present environmental investigations to obtain the relationship between explosive spalling occurrence and residual mechanical properties of high-performance concrete and high temperature ranging from 200 to 800°C. Cülfik and Özturan [4] investigated the temperature effect on mechanical properties of both normal and high strength concrete. Residual compressive and splitting tensile strength, as well as the static modulus of elasticity of specimens, were obtained under elevated temperatures (50, 100, 150, 200, and 250°C). The residual mechanical properties started to decrease at 100°C for normal strength concrete and high strength concrete performed better under different temperature cycles. Fares et al. [5] conducted an experimental study on performance of self-consolidating concrete under high temperature effect. Mechanical properties such as compressive strength and flexural strength are tested at different temperatures (150, 300, 450, and 600°C). The performance of concrete under transient temperature conditions has been comprehensively investigated, particularly under actions such as high temperatures from fire. However, most of concrete structures are exposed to external temperature between −20°C and 60°C in practical situation; relative little literature is available for properties of concrete under this condition. Shoukry et al. [6] investigated static mechanical properties of concrete under temperature ranging from −20°C to 50°C and relative humidity between 40% and 60%. The results indicated that concrete strength in compression, tension, and corresponding modulus of elasticity decreased with temperature increasing. However, the dynamic properties of concrete structure are not investigated.Dynamic-based methods have been widely applied for health monitoring and damage identification of structures [7–9], because the dynamic properties (frequency, mode shape, and damping) are closely related to structural parameters such as stiffness and mass [10–12]. At present, most researches are focused on the effect of damage on dynamic properties without considering temperature effect [13]. However, if the effects are not rationally taken into account and removed, the damage identification results cannot be reliable. Farrar et al. [14] present the monitoring results of Alamosa Canyon Bridge. They found that the first eigenfrequency of the structure varies approximately 5% over a 24-hour time period. Askegaard and Mossing [15] found that the variation of frequency for a three-span footbridge was 10% over the year. Wahab and de Roeck [16] observed a change of 4%~5% in natural frequencies of a prestressed concrete bridge in spring and winter from dynamic test. Moser and Moaveni [17] demonstrated that significant variability in natural frequencies was identified from a continuous monitoring system installed on Dowling Hall Footbridge, and these changes in natural frequencies are strongly correlated with temperature. Extensive research results reveal that temperature will lead to frequencies changes of structure, but explicit investigation of the effect of temperature is not obtained in experiments.In this paper, static mechanical properties such as cube compressive strength, split tensile strength, prism compressive strength, and modulus of elasticity of concrete are conducted under different temperatures from −20°C to 60°C. The relationships between properties and temperatures are determined. Meanwhile, the temperature effect on first order natural frequency of concrete slab is also observed and corresponding influence mechanism is discussed.


## 2. Experimental Details

### 2.1. Materials and Mixtures

PO 42.5 type Portland cement confirming the requirements of GB175-2007 [18] is used in this study. Crushed stone with diameters ranging from 5 mm to 20 mm and natural sand with fineness modulus of 2.7 are adopted as coarse and fine aggregates, respectively. The mixture proportions of concrete are listed in Table 1. These ingredients are mixed for about 4 min. Slump results of concrete are tested with 38 mm, which indicate that the mixture is with favorable cohesiveness and meets the requirements of GB/T 50081-2002 [19] and GB 50164-2011 [20].Table 1
Mixture proportions.
Materials
Nominal proportions
Cement
(kg/m3)
336
Coarse aggregate
(kg/m3)
1221
Fine aggregate
(kg/m3)
658
Water
(kg/m3)
185
Water/cement ratio
0.55


### 2.2. Specimens

Concrete specimens are 150 mm cubes (produced for testing cube compressive strength and splitting tensile strength) and 150 mm × 150 mm × 300 mm prisms (produced for testing prism compressive strength and modulus of elasticity) which are casted horizontally in steel molds and compacted by vibrating machine. All specimens are removed from the molds 24 h after casting and cured in a curing room (20±3°C and 95% RH (relative humidity)) for 28 days (GB/T 50082-2009) [21].Slabs with length 60 cm, width 15 cm, and height 5 cm are also prefabricated, and they are also cured in a curing room (20±3°C and 95% RH (relative humidity)) for 28 days.


### 2.3. Testing Machines

Two different compression testing machines are used to obtain the static properties of concrete. Both cube and prism compressive strength and modulus of elasticity are tested through machine 1 (shown in Figure1) with maximum load 2000 kN. Splitting tensile strength is measured by machine 2 (shown in Figure 2) with maximum load 1000 kN, which can realize the dynamic monitoring of force and output the force-displacement curves.Figure 1
Compression testing machine 1 (2000 kN).Figure 2
Compression testing machine 2 (1000 kN).The temperatures are jointly controlled by refrigerator and oven. The former is used for −50°C–0°C, while the latter is for 20°C–300°C.Piezoelectric acceleration sensor is applied for measuring acceleration response signals for slabs, and DH 5920 type dynamic signal measurement system is used to obtain the natural frequency from the measured signals.As for the damage of slab, it is achieved by cutting machine (shown in Figure3).Figure 3
Damage simulation of slab using cutting machine.


### 2.4. Testing Procedures

The cube compressive strength, splitting tensile strength, prism compressive strength, modulus of elasticity, and frequency of concrete structures are tested under temperatures −20°C, 0°C, 20°C, 40°C, and 60°C. In order to eliminate the influence of moisture, the concrete specimens are wrapped by preservative film to maintain humidity stability. Each specimen is placed in temperature control apparatus for 4 h to make the core temperature of concrete consistent with environmental temperature before testing.


#### 2.4.1. Cube Compressive Strength

Totally fifteen 150 mm × 150 mm × 150 mm specimens are tested for calculating the cube compressive strength (i.e., three specimens at each temperature). In the process of cube compressive strength testing, machine 1 imposes loads at the speed of 0.5–0.8 MPa/s [19]. The loads are recorded until the failure of specimens. The cube compressive strength of each specimen can be calculated by
(1)fcui=FcuiAcui,
where fcui is cube compressive strength of the ith concrete specimen, Fcui is the corresponding failure load under compression, Acui is bearing area of specimens, and i=1,2,3 in this paper.The final cube compressive strengthfcu of concrete can be determined by the following regulations [19].(1)
The average value of cube compressive strength for three specimens is treated as final compressive strength.(2)
If one of maximum and minimum value of cube compressive strength for three specimens exceeds the medium one by 15%, the medium value of cube compressive strength is used as final cube compressive strength.(3)
If all of maximum and minimum values of cube compressive strength for three specimens exceed the medium one by 15%, the results are considered to be invalid and another group of specimens should be retested.


#### 2.4.2. Splitting Tensile Strength

Another fifteen 150 mm × 150 mm × 150 mm specimens are measured for calculating the splitting tensile strength (i.e., three specimens at each temperature). In the process of splitting tensile strength testing, machine 2 applied loads at the speed of 0.05–0.08 MPa/s [19] until the failure of specimens. The splitting tensile strength of concrete can be obtained by
(2)ftsi=2Ftsi(π×Atsi),
where ftsi is splitting tensile strength of the ith concrete specimen, Ftsi is the corresponding failure load under splitting, and Atsi is splitting area of specimens.Final splitting tensile strengthfts can be calculated according to the same rules of getting fcu.


#### 2.4.3. Prism Compressive Strength

Totally fifteen 150 mm × 150 mm × 300 mm prisms are tested for measuring the prism compressive strength of concrete. In the process of prism compressive strength testing, machine 1 imposes loads at the speed of 0.5–0.8 MPa/s [19]. The loads are recorded until the failure of specimens. The prism compressive strength of each specimen can be calculated by
(3)fcpi=FcpiAcpi,
where fcpi is prism compressive strength of the ith concrete specimen, Fcpi is the corresponding failure load under compression, Acpi is bearing area of specimens, and i=1,2,3 in this paper.Final prism compressive strengthfcp can be calculated according to the same rules of getting fcu.


#### 2.4.4. Modulus of Elasticity

Totally fifteen 150 mm × 150 mm × 300 mm prisms are tested for calculating the modulus of elasticity; it can be calculated by(4)Eci=Fai-F0iAei×LΔdi,
where Eci is modulus of elasticity of the ith concrete specimen; Fai and F0i are loads corresponding to the stress of one-third prism compressive strength and 0.5 MPa, respectively; L is gauge length of specimen, L=150 mm in this paper; Δdi is average value of deformation for concrete from Fo to Fa, and it can be obtained by
(5)Δdi=εai-ε0i,
where εai is the average value of deformation for concrete specimens under Fai and ε0i is the average value of deformation for concrete specimens under F0i. εai and ε0i are tested through dial gauges.Final modulus of elasticityEc can be calculated according to GB/T 50081-2002 [19].


#### 2.4.5. Frequency and Damage Identification

Three concrete slabs are prefabricated and tested for frequency under temperatures −20°C, 0°C, 20°C, 40°C, and 60°C. The concrete slabs are also wrapped by preservative film to maintain humidity stability to eliminate the influence of moisture. Firstly, the slabs are measured under intact condition and temperature effect on frequency for undamaged slab is discussed. Secondly, the midspan sections of slabs are cut by special machine to simulate damage. Damage severity is represented by cutting depth; it can be calculated by(6)δ=WcW×100%,
where δ is damage severity and Wc and W are widths of damaged and intact midspan sections, respectively.


## 2.1. Materials and Mixtures

PO 42.5 type Portland cement confirming the requirements of GB175-2007 [18] is used in this study. Crushed stone with diameters ranging from 5 mm to 20 mm and natural sand with fineness modulus of 2.7 are adopted as coarse and fine aggregates, respectively. The mixture proportions of concrete are listed in Table 1. These ingredients are mixed for about 4 min. Slump results of concrete are tested with 38 mm, which indicate that the mixture is with favorable cohesiveness and meets the requirements of GB/T 50081-2002 [19] and GB 50164-2011 [20].Table 1
Mixture proportions.
Materials
Nominal proportions
Cement
(kg/m3)
336
Coarse aggregate
(kg/m3)
1221
Fine aggregate
(kg/m3)
658
Water
(kg/m3)
185
Water/cement ratio
0.55


## 2.2. Specimens

Concrete specimens are 150 mm cubes (produced for testing cube compressive strength and splitting tensile strength) and 150 mm × 150 mm × 300 mm prisms (produced for testing prism compressive strength and modulus of elasticity) which are casted horizontally in steel molds and compacted by vibrating machine. All specimens are removed from the molds 24 h after casting and cured in a curing room (20±3°C and 95% RH (relative humidity)) for 28 days (GB/T 50082-2009) [21].Slabs with length 60 cm, width 15 cm, and height 5 cm are also prefabricated, and they are also cured in a curing room (20±3°C and 95% RH (relative humidity)) for 28 days.


## 2.3. Testing Machines

Two different compression testing machines are used to obtain the static properties of concrete. Both cube and prism compressive strength and modulus of elasticity are tested through machine 1 (shown in Figure1) with maximum load 2000 kN. Splitting tensile strength is measured by machine 2 (shown in Figure 2) with maximum load 1000 kN, which can realize the dynamic monitoring of force and output the force-displacement curves.Figure 1
Compression testing machine 1 (2000 kN).Figure 2
Compression testing machine 2 (1000 kN).The temperatures are jointly controlled by refrigerator and oven. The former is used for −50°C–0°C, while the latter is for 20°C–300°C.Piezoelectric acceleration sensor is applied for measuring acceleration response signals for slabs, and DH 5920 type dynamic signal measurement system is used to obtain the natural frequency from the measured signals.As for the damage of slab, it is achieved by cutting machine (shown in Figure3).Figure 3
Damage simulation of slab using cutting machine.


## 2.4. Testing Procedures

The cube compressive strength, splitting tensile strength, prism compressive strength, modulus of elasticity, and frequency of concrete structures are tested under temperatures −20°C, 0°C, 20°C, 40°C, and 60°C. In order to eliminate the influence of moisture, the concrete specimens are wrapped by preservative film to maintain humidity stability. Each specimen is placed in temperature control apparatus for 4 h to make the core temperature of concrete consistent with environmental temperature before testing.


### 2.4.1. Cube Compressive Strength

Totally fifteen 150 mm × 150 mm × 150 mm specimens are tested for calculating the cube compressive strength (i.e., three specimens at each temperature). In the process of cube compressive strength testing, machine 1 imposes loads at the speed of 0.5–0.8 MPa/s [19]. The loads are recorded until the failure of specimens. The cube compressive strength of each specimen can be calculated by
(1)fcui=FcuiAcui,
where fcui is cube compressive strength of the ith concrete specimen, Fcui is the corresponding failure load under compression, Acui is bearing area of specimens, and i=1,2,3 in this paper.The final cube compressive strengthfcu of concrete can be determined by the following regulations [19].(1)
The average value of cube compressive strength for three specimens is treated as final compressive strength.(2)
If one of maximum and minimum value of cube compressive strength for three specimens exceeds the medium one by 15%, the medium value of cube compressive strength is used as final cube compressive strength.(3)
If all of maximum and minimum values of cube compressive strength for three specimens exceed the medium one by 15%, the results are considered to be invalid and another group of specimens should be retested.


### 2.4.2. Splitting Tensile Strength

Another fifteen 150 mm × 150 mm × 150 mm specimens are measured for calculating the splitting tensile strength (i.e., three specimens at each temperature). In the process of splitting tensile strength testing, machine 2 applied loads at the speed of 0.05–0.08 MPa/s [19] until the failure of specimens. The splitting tensile strength of concrete can be obtained by
(2)ftsi=2Ftsi(π×Atsi),
where ftsi is splitting tensile strength of the ith concrete specimen, Ftsi is the corresponding failure load under splitting, and Atsi is splitting area of specimens.Final splitting tensile strengthfts can be calculated according to the same rules of getting fcu.


### 2.4.3. Prism Compressive Strength

Totally fifteen 150 mm × 150 mm × 300 mm prisms are tested for measuring the prism compressive strength of concrete. In the process of prism compressive strength testing, machine 1 imposes loads at the speed of 0.5–0.8 MPa/s [19]. The loads are recorded until the failure of specimens. The prism compressive strength of each specimen can be calculated by
(3)fcpi=FcpiAcpi,
where fcpi is prism compressive strength of the ith concrete specimen, Fcpi is the corresponding failure load under compression, Acpi is bearing area of specimens, and i=1,2,3 in this paper.Final prism compressive strengthfcp can be calculated according to the same rules of getting fcu.


### 2.4.4. Modulus of Elasticity

Totally fifteen 150 mm × 150 mm × 300 mm prisms are tested for calculating the modulus of elasticity; it can be calculated by(4)Eci=Fai-F0iAei×LΔdi,
where Eci is modulus of elasticity of the ith concrete specimen; Fai and F0i are loads corresponding to the stress of one-third prism compressive strength and 0.5 MPa, respectively; L is gauge length of specimen, L=150 mm in this paper; Δdi is average value of deformation for concrete from Fo to Fa, and it can be obtained by
(5)Δdi=εai-ε0i,
where εai is the average value of deformation for concrete specimens under Fai and ε0i is the average value of deformation for concrete specimens under F0i. εai and ε0i are tested through dial gauges.Final modulus of elasticityEc can be calculated according to GB/T 50081-2002 [19].


### 2.4.5. Frequency and Damage Identification

Three concrete slabs are prefabricated and tested for frequency under temperatures −20°C, 0°C, 20°C, 40°C, and 60°C. The concrete slabs are also wrapped by preservative film to maintain humidity stability to eliminate the influence of moisture. Firstly, the slabs are measured under intact condition and temperature effect on frequency for undamaged slab is discussed. Secondly, the midspan sections of slabs are cut by special machine to simulate damage. Damage severity is represented by cutting depth; it can be calculated by(6)δ=WcW×100%,
where δ is damage severity and Wc and W are widths of damaged and intact midspan sections, respectively.


## 2.4.1. Cube Compressive Strength

Totally fifteen 150 mm × 150 mm × 150 mm specimens are tested for calculating the cube compressive strength (i.e., three specimens at each temperature). In the process of cube compressive strength testing, machine 1 imposes loads at the speed of 0.5–0.8 MPa/s [19]. The loads are recorded until the failure of specimens. The cube compressive strength of each specimen can be calculated by
(1)fcui=FcuiAcui,
where fcui is cube compressive strength of the ith concrete specimen, Fcui is the corresponding failure load under compression, Acui is bearing area of specimens, and i=1,2,3 in this paper.The final cube compressive strengthfcu of concrete can be determined by the following regulations [19].(1)
The average value of cube compressive strength for three specimens is treated as final compressive strength.(2)
If one of maximum and minimum value of cube compressive strength for three specimens exceeds the medium one by 15%, the medium value of cube compressive strength is used as final cube compressive strength.(3)
If all of maximum and minimum values of cube compressive strength for three specimens exceed the medium one by 15%, the results are considered to be invalid and another group of specimens should be retested.


## 2.4.2. Splitting Tensile Strength

Another fifteen 150 mm × 150 mm × 150 mm specimens are measured for calculating the splitting tensile strength (i.e., three specimens at each temperature). In the process of splitting tensile strength testing, machine 2 applied loads at the speed of 0.05–0.08 MPa/s [19] until the failure of specimens. The splitting tensile strength of concrete can be obtained by
(2)ftsi=2Ftsi(π×Atsi),
where ftsi is splitting tensile strength of the ith concrete specimen, Ftsi is the corresponding failure load under splitting, and Atsi is splitting area of specimens.Final splitting tensile strengthfts can be calculated according to the same rules of getting fcu.


## 2.4.3. Prism Compressive Strength

Totally fifteen 150 mm × 150 mm × 300 mm prisms are tested for measuring the prism compressive strength of concrete. In the process of prism compressive strength testing, machine 1 imposes loads at the speed of 0.5–0.8 MPa/s [19]. The loads are recorded until the failure of specimens. The prism compressive strength of each specimen can be calculated by
(3)fcpi=FcpiAcpi,
where fcpi is prism compressive strength of the ith concrete specimen, Fcpi is the corresponding failure load under compression, Acpi is bearing area of specimens, and i=1,2,3 in this paper.Final prism compressive strengthfcp can be calculated according to the same rules of getting fcu.


## 2.4.4. Modulus of Elasticity

Totally fifteen 150 mm × 150 mm × 300 mm prisms are tested for calculating the modulus of elasticity; it can be calculated by(4)Eci=Fai-F0iAei×LΔdi,
where Eci is modulus of elasticity of the ith concrete specimen; Fai and F0i are loads corresponding to the stress of one-third prism compressive strength and 0.5 MPa, respectively; L is gauge length of specimen, L=150 mm in this paper; Δdi is average value of deformation for concrete from Fo to Fa, and it can be obtained by
(5)Δdi=εai-ε0i,
where εai is the average value of deformation for concrete specimens under Fai and ε0i is the average value of deformation for concrete specimens under F0i. εai and ε0i are tested through dial gauges.Final modulus of elasticityEc can be calculated according to GB/T 50081-2002 [19].


## 2.4.5. Frequency and Damage Identification

Three concrete slabs are prefabricated and tested for frequency under temperatures −20°C, 0°C, 20°C, 40°C, and 60°C. The concrete slabs are also wrapped by preservative film to maintain humidity stability to eliminate the influence of moisture. Firstly, the slabs are measured under intact condition and temperature effect on frequency for undamaged slab is discussed. Secondly, the midspan sections of slabs are cut by special machine to simulate damage. Damage severity is represented by cutting depth; it can be calculated by(6)δ=WcW×100%,
where δ is damage severity and Wc and W are widths of damaged and intact midspan sections, respectively.


## 3. Static Mechanical Properties

### 3.1. Cube Compressive and Splitting Tensile Strength

The testing arrangements of cube compressive and splitting tensile strength are shown in Figures4 and 5, respectively.Figure 4
Compression test.Figure 5
Splitting tensile test.The testing results of concrete under different temperatures are listed in Table2. The relationship between cube compressive strength, splitting tensile strength, and temperatures is shown in Figures 6 and 7.Table 2
Results of cube compressive strength and splitting tensile strength for concrete under different temperatures.
Temperature (°C)
F
cu
i (kN)
f
cu
i (MPa)
F
ts
i (kN)
f
ts
i (MPa)
f
cu (MPa)
f
ts (MPa)
−20
1264
56.18
238
6.738
53.75
5.889
1244
55.29
208
5.889
1120
49.78
168
4.756
0
980
43.56
164
4.643
44.33
4.454
1020
45.33
156
4.417
992
44.09
152
4.303
20
940
41.78
140
3.964
41.18
3.888
910
40.44
134
3.794
930
41.33
138
3.907
40
660
29.33
98
2.774
28.56
2.812
648
28.80
96
2.718
620
27.56
104
2.944
60
624
27.73
80
2.265
26.84
2.529
600
26.67
100
2.831
588
26.13
88
2.491Figure 6
Temperature effect on cube compressive strength of concrete.Figure 7
Temperature effect on splitting tensile strength of concrete.Linear formulas are applied to simulate the relationship between cube compressive strength, splitting tensile strength, and temperature. They are listed in the following equations, respectively:(7)fcu=-0.348T+45.89,R2=0.9541-20C°≤T≤60C°,(8)fts=-0.041T+4.750,R2=0.9545-20C°≤T≤60C°.As can be seen from Figures6 and 7 and Table 2, the cube compressive strength and splitting tensile strength both decrease with the increasing of temperature. The cube compressive strength improves by 100.3% from 60°C to −20°C, while it is 132.9% for splitting tensile strength.


### 3.2. Prism Compressive Strength and Modulus of Elasticity

Prism compressive strengths of specimens under temperatures −20°C, 0°C, 20°C, 40°C, and 60°C are measured and calculated. The results are listed in Table3 and Figure 8.Table 3
Results of prism compressive strength for concrete under different temperatures.
Temperature (°C)
F
cp
i (N)
f
cp
i (MPa)
f
cp (MPa)
−20
904
40.18
40.47
864
38.40
964
42.84
0
780
34.67
34.43
760
33.78
784
34.84
20
626
27.82
28.92
682
30.31
644
28.62
40
572
25.42
26.00
585
26.00
598
26.58
60
498
22.13
23.70
522
23.20
580
25.78Figure 8
Temperature effect on prism compressive strength.The relationship between prism compressive strength and temperature is listed in(9)fcp=-0.209T+34.90,R2=0.9593-20C°≤T≤60C°.The relationship reveals that prism compressive strength decreases with the increasing of temperature and presents linear character. The prism strength decreases by 70.76% from −20°C to 60°C.The testing arrangements of modulus of elasticity are shown in Figure9.Testing arrangement of modulus of elasticity.
(a)
Gauge length
(b)
Modulus of elasticity testThe measurement results and temperature effects on modulus of elasticity are listed in Table4 and Figure 10.Table 4
Modulus of elasticity for concrete under different temperatures.
Temperature (°C)
F
0 (kN)
F
a (kN)
Δ
d (mm)
E
c
i (GPa)
E
c (GPa)
−20
11.52
245.01
0.050
31.132
31.928
11.30
245.90
0.048
32.583
11.70
247.40
0.049
32.067
0
12.24
249.35
0.045
35.127
28.397
11.50
245.80
0.061
25.607
11.70
246.50
0.064
24.458
20
12.87
244.68
0.057
27.112
27.184
10.90
245.32
0.059
26.488
11.60
242.21
0.055
27.953
40
11.40
245.50
0.065
24.010
24.091
11.30
245.60
0.069
22.638
18.14
252.60
0.061
25.624
60
11.80
243.77
0.067
23.082
21.533
11.80
244.90
0.068
22.853
16.21
262.60
0.088
18.666Figure 10
Temperature effect on modulus of elasticity.Regression analysis is conducted through linear formula to represent the relationship between modulus of elasticity and temperature; it is listed in(10)Ec=-0.125T+29.13,R2=0.9852-20C°≤T≤60C°.From Table4 and Figure 10, modulus of elasticity increases with the decreasing of temperature, and a good linear relationship is presented. The modulus of elasticity improves by 48.3% from 60°C to −20°C.


## 3.1. Cube Compressive and Splitting Tensile Strength

The testing arrangements of cube compressive and splitting tensile strength are shown in Figures4 and 5, respectively.Figure 4
Compression test.Figure 5
Splitting tensile test.The testing results of concrete under different temperatures are listed in Table2. The relationship between cube compressive strength, splitting tensile strength, and temperatures is shown in Figures 6 and 7.Table 2
Results of cube compressive strength and splitting tensile strength for concrete under different temperatures.
Temperature (°C)
F
cu
i (kN)
f
cu
i (MPa)
F
ts
i (kN)
f
ts
i (MPa)
f
cu (MPa)
f
ts (MPa)
−20
1264
56.18
238
6.738
53.75
5.889
1244
55.29
208
5.889
1120
49.78
168
4.756
0
980
43.56
164
4.643
44.33
4.454
1020
45.33
156
4.417
992
44.09
152
4.303
20
940
41.78
140
3.964
41.18
3.888
910
40.44
134
3.794
930
41.33
138
3.907
40
660
29.33
98
2.774
28.56
2.812
648
28.80
96
2.718
620
27.56
104
2.944
60
624
27.73
80
2.265
26.84
2.529
600
26.67
100
2.831
588
26.13
88
2.491Figure 6
Temperature effect on cube compressive strength of concrete.Figure 7
Temperature effect on splitting tensile strength of concrete.Linear formulas are applied to simulate the relationship between cube compressive strength, splitting tensile strength, and temperature. They are listed in the following equations, respectively:(7)fcu=-0.348T+45.89,R2=0.9541-20C°≤T≤60C°,(8)fts=-0.041T+4.750,R2=0.9545-20C°≤T≤60C°.As can be seen from Figures6 and 7 and Table 2, the cube compressive strength and splitting tensile strength both decrease with the increasing of temperature. The cube compressive strength improves by 100.3% from 60°C to −20°C, while it is 132.9% for splitting tensile strength.


## 3.2. Prism Compressive Strength and Modulus of Elasticity

Prism compressive strengths of specimens under temperatures −20°C, 0°C, 20°C, 40°C, and 60°C are measured and calculated. The results are listed in Table3 and Figure 8.Table 3
Results of prism compressive strength for concrete under different temperatures.
Temperature (°C)
F
cp
i (N)
f
cp
i (MPa)
f
cp (MPa)
−20
904
40.18
40.47
864
38.40
964
42.84
0
780
34.67
34.43
760
33.78
784
34.84
20
626
27.82
28.92
682
30.31
644
28.62
40
572
25.42
26.00
585
26.00
598
26.58
60
498
22.13
23.70
522
23.20
580
25.78Figure 8
Temperature effect on prism compressive strength.The relationship between prism compressive strength and temperature is listed in(9)fcp=-0.209T+34.90,R2=0.9593-20C°≤T≤60C°.The relationship reveals that prism compressive strength decreases with the increasing of temperature and presents linear character. The prism strength decreases by 70.76% from −20°C to 60°C.The testing arrangements of modulus of elasticity are shown in Figure9.Testing arrangement of modulus of elasticity.
(a)
Gauge length
(b)
Modulus of elasticity testThe measurement results and temperature effects on modulus of elasticity are listed in Table4 and Figure 10.Table 4
Modulus of elasticity for concrete under different temperatures.
Temperature (°C)
F
0 (kN)
F
a (kN)
Δ
d (mm)
E
c
i (GPa)
E
c (GPa)
−20
11.52
245.01
0.050
31.132
31.928
11.30
245.90
0.048
32.583
11.70
247.40
0.049
32.067
0
12.24
249.35
0.045
35.127
28.397
11.50
245.80
0.061
25.607
11.70
246.50
0.064
24.458
20
12.87
244.68
0.057
27.112
27.184
10.90
245.32
0.059
26.488
11.60
242.21
0.055
27.953
40
11.40
245.50
0.065
24.010
24.091
11.30
245.60
0.069
22.638
18.14
252.60
0.061
25.624
60
11.80
243.77
0.067
23.082
21.533
11.80
244.90
0.068
22.853
16.21
262.60
0.088
18.666Figure 10
Temperature effect on modulus of elasticity.Regression analysis is conducted through linear formula to represent the relationship between modulus of elasticity and temperature; it is listed in(10)Ec=-0.125T+29.13,R2=0.9852-20C°≤T≤60C°.From Table4 and Figure 10, modulus of elasticity increases with the decreasing of temperature, and a good linear relationship is presented. The modulus of elasticity improves by 48.3% from 60°C to −20°C.


## 4. Frequency and Damage Identification of Slab

### 4.1. Temperature Effect on Frequency

The test process is illustrated in Figure11. Testing results of first order natural frequency for three slabs (A, B, and C) are listed in Table 5.Table 5
First order natural frequency for intact concrete slab.
Temperature(°C)
Slabs
A
B
C
−20
201.66
201.66
196.77
0
192.38
196.77
193.85
20
189.94
192.38
186.53
40
184.28
189.91
182.99
60
178.22
187.01
173.83Testing arrangement of frequency.
(a)
Concrete slab
(b)
Frequency testTemperature effect on frequency of slabs is also demonstrated in Figure12. It can be concluded that the influence of temperature on first order frequency is obvious. The frequency decreases with the increasing of temperature, and it shows clear negative correlation.Figure 12
Temperature effect on first order natural frequency.


### 4.2. Temperature Effect on Damage Identification

The results of slabA are used as examples to investigate the variation of frequency under the integrated effect of temperature and damage. Five damage severities including 0% (undamaged), 10%, 20%, 30%, and 40% are simulated, and the measurement results are listed in Table 6 and Figure 13.Table 6
The first order natural frequencies under coupling effect of temperature and damage (Hz).
Damage severity (%)
Temperature (°C)
−20
0
20
40
60
0
201.655
192.380
189.935
184.280
178.220
10
195.800
188.925
180.170
176.265
172.360
20
183.185
177.245
174.800
172.850
166.985
30
177.240
173.335
169.915
164.050
158.685
40
173.335
169.355
165.075
160.905
156.000Figure 13
Integrated effect of temperature and damage on the first order natural frequency.As can be seen from Table6 and Figure 13, the first order natural frequency decreases with the increasing of damage severity under the same temperature, while it decreases with the increasing of temperature under the same damage severity.In damage identification of structures, change rate of natural frequency is an effective damage indicator. According to dynamic theory, damage of structure will lead to the reduction of frequencies. In order to illustrate the effect of temperature in damage identification of concrete slab, the baseline natural frequency of undamaged structure is assumed to be measured under temperature 40°C, and the damaged ones are tested under temperatures −20°C, 0°C, 20°C, 40°C, and 60°C. The corresponding change rates of first order frequency are calculated by (10), and the results are listed in Table 7 and Figure 14. Consider
(11)αδT=fδT-fδ40fδ40×100%,
where f is the measured first order natural frequency, α is the change rate of frequency, δ is damage severity (δ=0%, 10%, 20%, 30%, and 40%), and T is testing temperature (T=-20°C, 0°C, 20°C, 40°C, and 60°C).Table 7
Change rate of the first order natural frequency (%).
Damage severity (%)
Temperature (°C)
−20
0
20
40
60
Range caused by temperature
0
9.429
4.395
3.069
0.000
−3.288
12.717
10
6.251
2.521
−2.230
−4.349
−6.468
12.719
20
−0.594
−3.818
−5.144
−6.203
−9.385
8.791
30
−3.820
−5.939
−7.795
−10.978
−13.889
10.069
40
−5.939
−8.099
−10.422
−12.685
−15.346
9.407
Range caused by damage
15.368
12.494
13.491
12.685
12.058Figure 14
Integrated effect of temperature and damage on change rate of natural frequency.In theory, damage of structure will lead to the reduction of frequency. Therefore, the change rate of frequency is a negative value. However, the change rates of frequency for damage severity 10% at temperatures −20°C and 0°C are positive. Reasons for this phenomenon lie in the fact that frequencies increase from temperature 40°C to −20°C and 0°C, and the recruitments due to temperatures are greater than the decreasing value caused by damage. It reveals that frequency changes caused by damage have been submerged by temperature effect, and damage identification results will be unreliable in practice. The range analysis is also conducted and listed in Table7. As can be seen from this table, the maximum range caused by damage is 15.368%, while it is 12.720% for temperature. The temperature effect is not negligible.


### 4.3. Mechanism Analysis

For a simply supported uniform beam with lengthl, height h, density ρ, and modulus of elasticity E, the undamped flexural vibration frequency of order n can be calculated by [22–24]
(12)fn=n2πh2l2E12ρ.Temperature effect on modulus of elasticity has been tested and listed in Table8. Theoretical calculation results of the first order frequency can be obtained based on (11); they are shown in Table 8 and Figure 15.Table 8
Theoretical and measured results of the first order frequency for concrete slab.
Temperature(°C)
E (GPa)
Theoretical results (Hz)
Measured results (Hz)
−20
31.928
224.95
201.66
0
28.397
212.15
192.38
20
27.184
207.57
189.94
40
24.091
195.40
184.28
60
21.533
184.74
178.22Figure 15
Relationship between theoretical and measured frequency of concrete slab.As can be seen from Table8 and Figure 15, the calculated frequencies based on measured modulus of elasticity and dynamic theory are consistent with the measured ones. The results indicate that temperature effect on frequency is mainly caused by the influence of temperature on modulus of elasticity. It can provide reference for damage identification of structures.


## 4.1. Temperature Effect on Frequency

The test process is illustrated in Figure11. Testing results of first order natural frequency for three slabs (A, B, and C) are listed in Table 5.Table 5
First order natural frequency for intact concrete slab.
Temperature(°C)
Slabs
A
B
C
−20
201.66
201.66
196.77
0
192.38
196.77
193.85
20
189.94
192.38
186.53
40
184.28
189.91
182.99
60
178.22
187.01
173.83Testing arrangement of frequency.
(a)
Concrete slab
(b)
Frequency testTemperature effect on frequency of slabs is also demonstrated in Figure12. It can be concluded that the influence of temperature on first order frequency is obvious. The frequency decreases with the increasing of temperature, and it shows clear negative correlation.Figure 12
Temperature effect on first order natural frequency.


## 4.2. Temperature Effect on Damage Identification

The results of slabA are used as examples to investigate the variation of frequency under the integrated effect of temperature and damage. Five damage severities including 0% (undamaged), 10%, 20%, 30%, and 40% are simulated, and the measurement results are listed in Table 6 and Figure 13.Table 6
The first order natural frequencies under coupling effect of temperature and damage (Hz).
Damage severity (%)
Temperature (°C)
−20
0
20
40
60
0
201.655
192.380
189.935
184.280
178.220
10
195.800
188.925
180.170
176.265
172.360
20
183.185
177.245
174.800
172.850
166.985
30
177.240
173.335
169.915
164.050
158.685
40
173.335
169.355
165.075
160.905
156.000Figure 13
Integrated effect of temperature and damage on the first order natural frequency.As can be seen from Table6 and Figure 13, the first order natural frequency decreases with the increasing of damage severity under the same temperature, while it decreases with the increasing of temperature under the same damage severity.In damage identification of structures, change rate of natural frequency is an effective damage indicator. According to dynamic theory, damage of structure will lead to the reduction of frequencies. In order to illustrate the effect of temperature in damage identification of concrete slab, the baseline natural frequency of undamaged structure is assumed to be measured under temperature 40°C, and the damaged ones are tested under temperatures −20°C, 0°C, 20°C, 40°C, and 60°C. The corresponding change rates of first order frequency are calculated by (10), and the results are listed in Table 7 and Figure 14. Consider
(11)αδT=fδT-fδ40fδ40×100%,
where f is the measured first order natural frequency, α is the change rate of frequency, δ is damage severity (δ=0%, 10%, 20%, 30%, and 40%), and T is testing temperature (T=-20°C, 0°C, 20°C, 40°C, and 60°C).Table 7
Change rate of the first order natural frequency (%).
Damage severity (%)
Temperature (°C)
−20
0
20
40
60
Range caused by temperature
0
9.429
4.395
3.069
0.000
−3.288
12.717
10
6.251
2.521
−2.230
−4.349
−6.468
12.719
20
−0.594
−3.818
−5.144
−6.203
−9.385
8.791
30
−3.820
−5.939
−7.795
−10.978
−13.889
10.069
40
−5.939
−8.099
−10.422
−12.685
−15.346
9.407
Range caused by damage
15.368
12.494
13.491
12.685
12.058Figure 14
Integrated effect of temperature and damage on change rate of natural frequency.In theory, damage of structure will lead to the reduction of frequency. Therefore, the change rate of frequency is a negative value. However, the change rates of frequency for damage severity 10% at temperatures −20°C and 0°C are positive. Reasons for this phenomenon lie in the fact that frequencies increase from temperature 40°C to −20°C and 0°C, and the recruitments due to temperatures are greater than the decreasing value caused by damage. It reveals that frequency changes caused by damage have been submerged by temperature effect, and damage identification results will be unreliable in practice. The range analysis is also conducted and listed in Table7. As can be seen from this table, the maximum range caused by damage is 15.368%, while it is 12.720% for temperature. The temperature effect is not negligible.


## 4.3. Mechanism Analysis

For a simply supported uniform beam with lengthl, height h, density ρ, and modulus of elasticity E, the undamped flexural vibration frequency of order n can be calculated by [22–24]
(12)fn=n2πh2l2E12ρ.Temperature effect on modulus of elasticity has been tested and listed in Table8. Theoretical calculation results of the first order frequency can be obtained based on (11); they are shown in Table 8 and Figure 15.Table 8
Theoretical and measured results of the first order frequency for concrete slab.
Temperature(°C)
E (GPa)
Theoretical results (Hz)
Measured results (Hz)
−20
31.928
224.95
201.66
0
28.397
212.15
192.38
20
27.184
207.57
189.94
40
24.091
195.40
184.28
60
21.533
184.74
178.22Figure 15
Relationship between theoretical and measured frequency of concrete slab.As can be seen from Table8 and Figure 15, the calculated frequencies based on measured modulus of elasticity and dynamic theory are consistent with the measured ones. The results indicate that temperature effect on frequency is mainly caused by the influence of temperature on modulus of elasticity. It can provide reference for damage identification of structures.


## 5. Conclusions

Temperature effects on cube compressive strength, splitting tensile strength, prism compressive strength, modulus of elasticity, and frequency are conducted and the following conclusions can be drawn.(1)
Compressive strength (cube and prism), splitting tensile strength, and modulus of elasticity change obviously under temperature effect. These static mechanical properties all decrease with the increasing of temperature, and linear formulas can effectively simulate their relationships. The compressive strength improves by 100.3% from 60°C to −20°C; it is 132.9% and 48.3% for splitting tensile strength and modulus of elasticity, respectively.(2)
Influence of temperature on the first order frequency of concrete slab is significant and the frequency decreases with the increasing of temperature; a good negative relationship is present. Under the coupling effect of damage and temperature, the frequency change caused by damage would be submerged by temperature effect. Therefore, it is necessary to consider the influence of temperature in damage identification of structure. The range analysis reveals that the temperature effect cannot be neglected in practice. Mechanism analysis of temperature effect on frequency is also conducted. The results demonstrated that it is mainly caused by the influence of temperature on modulus of elasticity.



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*Source: 191360-2014-11-25.xml*