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A fundamental study on compressive strength, static and dynamic elastic moduli of young concrete
Construction and Building Materials 98 (2015) 137–145
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A fundamental study on compressive strength, static and dynamic elastic moduli of young concrete Yong Zhou a,⇑, Jie Gao a, Zhihui Sun b, Wenjun Qu a a b
Department of Structural Engineering, Tongji University, 1239 Siping Road, Shanghai 20092, PR China Department of Civil and Environmental Engineering, University of Louisville, Louisville, KY 40292, USA
h i g h l i g h t s Relationship between static and dynamic moduli of elasticity is linear. Aggregate volume content, water-to-cement ratio and curing temperature affect E. Aggregate volume content and maximum size are dominant factors on Ec–Ed.
a r t i c l e
i n f o
Article history: Received 25 April 2015 Received in revised form 6 July 2015 Accepted 12 August 2015 Available online 24 August 2015 Keywords: Early age Impact resonance test Influential factors Multiple regression analysis
a b s t r a c t This study investigates the influence of volume content of aggregates, maximum size and type of coarse aggregates, water-to-cement ratio and curing temperature on mechanical properties, i.e. prismatic compressive strength (fc), static modulus of elasticity (Ec) and dynamic modulus of elasticity (Ed) of concrete at early age. A new equation is proposed to correlate prismatic compressive strength and elastic moduli of concrete. Based on the experimental data and the analysis results, the Ec–Ed relationship is also proposed. It is found that the relationship between Ec and Ed is linear, and the coefficients of linear relationship are analyzed by multiple regression analysis, considering aggregate content, maximum size of the coarse aggregate, water-to-cement ratio and curing temperature. It is found that the volume content of aggregates is the most significant factor that influences the Ec–Ed relationship. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction The construction of concrete structures greatly depends on the mechanical properties of concrete, among which compressive strength and modulus of elasticity are mostly concerned. For example, the proper time to remove formwork and the proper time to apply pre-stress on concrete members are completely controlled by these two properties. If anything improper is done before concrete has developed its desired properties, large deformation, crushing of concrete or even catastrophic collapse may happen. Therefore, knowing the early-age compressive strength and the elastic modulus of concrete is critical to guarantee its life-time performance. For concrete, both the compressive strength and the elastic modulus increase rapidly during its early age [1–3]. The design code recommends estimating concrete’s elastic modulus based on its 28th day’s compressive strength [4–9]. This recommended relationship may not be applicable to concrete at early age. ⇑ Corresponding author. E-mail address: [email protected] (Y. Zhou). http://dx.doi.org/10.1016/j.conbuildmat.2015.08.110 0950-0618/Ó 2015 Elsevier Ltd. All rights reserved.
There are many influential factors on compressive strength and modulus of elasticity of concrete. Stock et al. [10] presented that the modulus of elasticity is proportional to the volume content of aggregate. Ranchero [11] indicated that volume content of aggregates, type of coarse aggregate and water-to-cement ratio were the most important influential factors. Johnson and Bawa [12] found that the modulus of elasticity increases with the increase in volume content of aggregates and decreases with the increase in water-to-cement ratio. Yıldırım and Sengul [13] pointed out that the modulus of elasticity could be lower if smaller aggregates were used. All the above researches focused on concrete at the age of 28 days or older. It is not clear that how these factors influence the modulus of elasticity at early age. When design a concrete structure, its compressive strength and the static Young’s modulus are used as recommended by the design codes. However, for field measurement, concrete quality is normally estimated via in situ non-destructive testing (NDT) methods, among which the ultrasonic pulse velocity, the wave reflection, and the impact echo methods are commonly used [14–17]. These methods are dynamic methods, measuring the dynamic modulus of concrete. Therefore, a good model to correlate
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static and dynamic moduli of concrete is needed to correlate structure design and field measurement. Although the relationship between the static and the dynamic moduli of concrete has been suggested by some researchers [11,18–20], a model based on design parameters, such as aggregate size and volume, water-tocement ratio and curing temperature is needed to close the gap between structure design and field measurement. This paper presents the results of a study on the development of prismatic compressive strength and modulus of elasticity, and the relationships between static and dynamic moduli of elasticity of concrete within the age of 12 h to 28 days. Meanwhile, the influences of the material parameters used in designing mix proportions (such as water-to-cement ratio, maximum coarse aggregate size, coarse aggregate type, and coarse aggregate volume content, etc.) on the relationship between static modulus (Ec) and dynamic modulus (Ed) are investigated. Fig. 1. Gradation curves of coarse aggregate.
2. Materials and experiments 2.1. Raw materials
respectively. The maximum diameter of gravel was 20 mm. The aggregate gradation complied with GB/T14684-2011 [21] and GB/T14685-2011 [22]. In Table 1, the cumulative particle size distributions, the specific gravity under the saturatedsurface-dry condition and the absorption capacities of the sand, gravel and crushed limestone are listed in details. The gradation curves of all the coarse aggregates that used in this study are plotted in Fig. 1.
Ordinary type I Portland cement was used in all the experiments. The specific gravity of the cement was assumed to be 3.15. River sand, gravel and crushed limestone were used as fine and coarse aggregates. To study the influence of maximum coarse aggregate size on the mechanical properties of concrete, the maximum diameters of crushed limestone were chosen as 16 mm, 20 mm and 31.5 mm,
Table 1 Properties of aggregates.
Crushed limestone with the diameter 5~31.5mm (C1) Sieve size (mm)
37.5
Mass retained (%)
0
Density (SSD)
31.5
19.0
9.5
4.75
2.36
0
26
93*
100
100
3
2634 kg/m
Absorption capacity
1.05%
Crushed limestone with the diameter 5~20mm (C2) Sieve size (mm)
26.5
19.0
9.5
4.75
2.36
Mass retained (%)
0
5
72
98
100
Density (SSD)
2638 kg/m3
Absorption capacity
0.94%
Crushed limestone with the diameter 5~16mm (C3) Sieve size (mm)
19.0
Mass retained (%)
0
Density (SSD)
16.0
9.5
4.75
2.36
9
55
96
100
3
2630 kg/m
Absorption capacity
1.01%
Gravel with the diameter 5~20mm (G) Sieve size (mm)
26.5
19.0
9.5
4.75
2.36
Mass retained (%)
0
9
66
96
100
Density (SSD)
2587 kg/m3
Absorption capacity
1.02%
River sand Sieve size (mm)
9.50
4.75
2.36
1.18
0.6
0.3
0.15
Mass retained (%)
0
5
15
28
43
90
98
Fineness modulus Density (SSD) *
2.63- medium sand 2604 kg/m3
Absorption capacity
1.81%
Note: mass retained should be 90% at the sieve size 9.5 mm according to GB/T14685-2011.
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Y. Zhou et al. / Construction and Building Materials 98 (2015) 137–145 2.2. Mixture design In order to investigate the influence of aggregate volume content, maximum size of coarse aggregate, aggregate type, water-to-cement ratio and curing temperature on the mechanical properties of concrete, 15 mix proportions were designed and listed in Table 2. The mass ratio of fine aggregate to total aggregate was 0.33 for all mixture proportions. Specimen SVCA0–0.75 were designed for studying the influence of volume content of aggregates by using the same crushed limestone with the diameter 5–16 mm and the water-to-cement ratio of 0.5. The coarse aggregates of SMSCA16–31.5 were the crushed limestone with maximum size of 16 mm, 20 mm and 31.5 mm, respectively. The coarse aggregate of SCL20 and SG20 were the crushed limestone with the maximum diameter of 20 mm and the gravel with the same size, respectively. SWC0.35–0.6 were designed for studying the influence of water-to-cement ratio from 0.35 to 0.6 by using the same volume content of aggregate (0.65). All these concrete were moisture cured under 21 °C throughout the study. In order to study the temperature effect, for the concrete with aggregate volume content equals 0.65, two other curing temperatures (12.5 °C and 33.5 °C) were also used. And they are listed as the ‘‘SCT series” in Table 2. Naphthalenebased superplasticizer was added in SVCA0.75 and SWC0.35 to achieve similar slump to other mixtures. The mass ratio of superplasticizer to cement was 0.8% in SVCA0.75 and 0.75% in SWC0.35. 2.3. Sample preparation ASTM C305-06 [23] and C192-06 [24] were followed during the mixing of SVCA0 and all others, respectively. Freshly mixed concrete was cast into 100 100 300 mm steel molds, then sealed and put into the curing chamber within 30 min after mixing. 24 h later, the molds were removed and the specimens were directly submerged in saturated lime water to prevent the leaching of Ca(OH)2 in concrete. Constant temperatures of 12.5 ± 1 °C, 21 ± 0.5 °C and 33.5 ± 1 °C were used. 50 specimens were made from each mix proportion. 2.4. Test methods The specimens of each mix proportions were tested at the age of 12 h, 1 day, 2 days, 3 days, 7 days, 14 days and 28 days. Six specimens were tested at each age: 3 specimens for the prismatic compressive strength tests and 3 specimens for the static and dynamic elastic modulus tests. For the moduli tests, because the dynamic test is a NDT-test, the specimens used for this test can be used again for the static test. Details for each test are specified as follows. 2.4.1. Impact resonance tests Impact resonance tests were performed according to ASTM C215-08 [25], using the longitudinal mode. Fig. 2 shows a schematic of the impact resonance test used in this study. A miniature piezoelectric accelerometer that has a flat response from 1 to 12,000 Hz with a sensitivity of 10 mV/g at 160 Hz (LC0159 manufactured by Lance) was mounted at the center of one end surface of the prism. A steel ball with a diameter of 12 mm was used as the impact source and applied at the center of the opposite end surface. The dynamic modulus of elasticity is obtained from the following equations:
Ed ¼ DMn2
ð1Þ
D ¼ 4ðL=btÞ
ð2Þ
Fig. 2. Schematic of the impact resonance test.
where Ed is the dynamic modulus of elasticity, L is the length of the specimen, b and t are the dimensions of the prism cross section, M is the mass of the specimen, and n is the measured fundamental longitudinal frequency. 2.4.2. Static tests The static tests were conducted following GB/T 50081-2002 [26], using a 50 kN universal testing machine at the age of 12 h and 1 day and a 500 kN universal testing machine at the age of 2–28 days. Firstly, three replicas were used to obtain the prismatic compressive strength, and the compressive load was applied continuously at the specified loading rate. Although both cylindrical strength and prismatic strength can be tested, the prismatic strength was chosen in this study. This is because the Chinese code for static modulus estimation at 28 days requires the 28-day prismatic compressive strength. To keep the consistency, prisms were used in the tests to obtain compressive strength at different ages. After the strength tests, another three replicas (also used for dynamic tests) were prepared for static modulus of elasticity. When measuring the static modulus, two 100 mm linear extensometers were attached to two opposite sides of the specimen to measure the axial deformation, in Fig. 3. Both extensometers were manufactured by Epsilon, model 3542RA2-100M-600M-ST with the measuring range of ±6 mm. The specimen was preloaded and unloaded once firstly, then loaded and unloaded thrice to approximately 33% of the prismatic compressive strength before loaded to failure. The stress–strain curves were plotted for each specimen. And the slope of the stress–strain curve (up to 33% of the strength) was determined as the static elastic modulus via linear regression.
3. Test results and analysis 3.1. Development of the mechanical properties 3.1.1. Prismatic compressive strength – fc Due to the size effect [27,28], the prismatic compressive strength is different from the cylindrical strength. This difference is influenced by size, shape and placement direction of specimens [29]. According to GB 50010-2010 [30], the ratio of the cylindrical strength to the prismatic compressive strength is 1.18 for ordinary concrete. Fig. 4 plots the prismatic strength development for concrete SMSCA20 from 12 h to 28 days. It can be seen that the compressive
Table 2 Mixture proportions. No.
Quantity (kg/m3)
Mixture proportion by weight
Mixture proportion by volume
0.0 702.5 1141.6 1317.2
1:0.5:0:0 1:0.5:0.48:0.97 1:0.5:1.35:2.74 1:0.5:2.21:4.49
0.38:0.61:0:0 0.23:0.36:0.13:0.27 0.13:0.21:0.22:0.43 0.09:0.15:0.25:0.50
562.3 563.4 562.9
1141.6 1143.9 1142.8
1:0.5:1.35:2.74 1:0.5:1.35:2.75 1:0.5:1.35:2.75
0.13:0.21:0.22:0.43 0.13:0.21:0.22:0.43 0.13:0.21:0.22:0.43
208.0 208.0
563.4 556.1
1143.9 1129.1
1:0.5:1.35:2.75 1:0.5:1.34:2.71
0.13:0.21:0.22:0.43 0.13:0.21:0.22:0.43
509.4 415.9 370.6
178.3 208.0 222.4
562.3 562.3 562.3
1141.6 1141.6 1141.6
1:0.35:1.10:2.24 1:0.5:1.35:2.74 1:0.6:1.52:3.08
0.12:0.22:0.22:0.43 0.13:0.21:0.22:0.43 0.16:0.18:0.22:0.43
415.9 415.9 415.9
208.0 208.0 208.0
562.3 562.3 562.3
1141.6 1141.6 1141.6
1:0.5:1.35:2.74 1:0.5:1.35:2.74 1:0.5:1.35:2.74
0.13:0.21:0.22:0.43 0.13:0.21:0.22:0.43 0.13:0.21:0.22:0.43
Cement
Water
Sand
Coarse aggregate
1211.1 721.7 415.9 293.6
605.5 360.9 208.0 146.8
0.0 346.0 562.3 648.8
SMSCA16 SMSCA20 SMSCA31.5
415.9 415.9 415.9
208.0 208.0 208.0
SCL20 SG20
415.9 415.9
SWC0.35 SWC0.5 SWC0.6 SCT12.5 SCT21 SCT33.5
SVCA0 SVCA0.4 SVCA0.65 SVCA0.75
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Y. Zhou et al. / Construction and Building Materials 98 (2015) 137–145 Table 3 Regression coefficients of prismatic compressive strength. Specimens
f0 (MPa)
A1
A2
t1
t2
SVCA0 SVCA0.4 SVCA0.65 SVCA0.75
25.702 26.662 26.166 25.625
18.521 21.346 17.855 14.676
12.103 20.703 20.929 22.671
19.416 9.981 6.328 5.712
0.881 0.402 0.583 0.746
SMSCA16 SMSCA20 SMSCA31.5
26.166 25.053 23.657
17.855 14.241 12.948
20.929 19.047 19.550
6.328 6.069 7.621
0.583 0.941 0.836
SCL20 SG20
25.053 23.307
14.241 10.075
19.047 17.560
6.069 10.681
0.941 1.787
SWC0.35 SWC0.5 SWC0.6
47.502 26.166 23.529
30.716 17.855 10.972
65.654 20.929 16.179
14.694 6.328 17.947
0.368 0.583 1.937
SCT12.5 SCT21 SCT33.5
33.132 26.166 31.513
14.743 17.855 11.376
23.896 20.929 23.512
9.985 6.328 11.178
2.689 0.583 1.618
maximum coarse aggregate size. Through this multiple regression analysis, it can also be seen that the water-to-cement ratio is most important influential factor to f0, as the f0 value of SWC0.35 is twice as much as that of SWC0.6. A1 and A2 are two coefficients that control the converging rate of the curve. They are also influenced by water-to-cement ratio the most. t1 and t2 are two decay constants. They are influenced by both the volume content of aggregates, the water-to-cement ratio and curing temperature.
Fig. 3. Test setups for static modulus measurement.
3.1.2. Static modulus of elasticity (Ec) and dynamic modulus of elasticity (Ed) Fig. 5 plots the static and the dynamic moduli for concrete SMSCA20 from 12 h to 28 days, respectively. As shown in the figure, both moduli increase rapidly at the age of 12 h through 3 days, while they increase slowly at the age of 3–28 days. Both Ec and Ed at the age of 3 days reach 80% of the values of 28 days. Meanwhile, the increasing rates of both Ec and Ed are faster than that of fc during the age of 12 h to 3 days. Similar results were found by Lew and Reichard [31]. All other specimens used in this study showed the same trend. Therefore an exponential equation is proposed to represent the development tendency of Ec an Ed with age: Fig. 4. Development of prismatic compressive strength of SMSCA20.
Ec ðtÞ or Ed ðtÞ ¼ E0 þ B1 et=g1 þ B2 et=g2
strength increases rapidly at the age of 12 h to 7 days, while it increases slowly at the age of 7–28 days. And the compressive strength at the age of 7 days was approximately 80% of that at 28 days. All other specimens used in this study showed the same characteristics. To further study the development of strength growth, an exponential equation shown as Eq. (3) was proposed to simulate the development trend.
f c ðtÞ ¼ f 0 þ A1 et=t1 þ A2 et=t2
where t represents the hydration age (in days), E0, B1, B2, g1 and g2 are coefficients.
ð3Þ
where t represents the hydration age (in days), f0, A1, A2, t1 and t2 are coefficients from regression. It is clearly seen that Eq. (3) can depict the development tendency of prismatic compressive strength, and the fitted result of Adj.R2 is close to 1. For all the tested concrete, the regression coefficients f0, A1, A2, t1 and t2 are listed in the following Table 3. From both Eq. (3) and the Table 3, it can be seen that the coefficient f0 represents the ultimate strength of the concrete (when t ? 1, which has a value pretty close to the 28 days strength. By comparing specimens SVCA0 through SVCA0.75, it can be seen that changing the volume content of aggregates does not affect the ultimate strength gains of concrete. The f0 values of SMSCA16 through SMSCA31.5 indicate a decrease of the strength with an increase of
ð4Þ
Fig. 5. Development of the static and the dynamic modulus for SMSCA20.
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Apparently, the curve of Eq. (4) is closer to the experimental data, and the fitted result of Adj.R2 is close to 1. Therefore, Eq. (4) can depict the development tendency of the modulus of elasticity. Similar to the compressive strength, the E0 in the equation indicate the ultimate modulus of concrete (when t ? 1; B1 and B2 are two shape factors that control the converge rate of the curve; and g1 and g2 are two decay constants. The curve fitting results are listed in Tables 4 and 5 for all the coefficients. From the tables, it can be seen that E0 has a value pretty close to the 28 days modulus of elasticity. To be different from the compressive strength, the volume content of aggregates is the most significant influencing factor on the E0 values. B1 and B2 are also affected by aggregate volume content the most. g1 and g2 are more sensitive to the water-to-cement ratio and the curing temperature.
Table 6 Estimating equations in different codes. Code ACI 318-08 ACI 363-08 NZS 3101-2006 CSA A23.3-04 EC-2 GB 50010
Estimating equation pffiffiffiffiffi Ec ¼ 4700 f c pffiffiffiffiffi Ec ¼ 3300 f c þ 6900 pffiffiffiffiffi Ec ¼ 3320 f c þ 6900 pffiffiffiffiffi Ec ¼ 4500 f c Ec = 22(fc/10)0.3 2
10 Ec ¼ 2:2þ34:7=f
Units fc: MPa, Ec: MPa fc: MPa, Ec: MPa fc: MPa, Ec: MPa fc: MPa, Ec: MPa fc : MPa, Ec : GPa fc: MPa, Ec: MPa
c
3.2. Ec and Ed vs. fc The relationship between Ec and fc has been recommended by design codes of many countries [4–9], shown in Table 6. Fig. 6 compares the values estimated by the equations in different codes with the experimental data of SWC0.5. The calculated values of ACI 318 and CSA A23.3 at the age of 12 h, and EC-2 at the age of 1 day, are closest to the experimental data, respectively. After the age of 2 days, all the calculated values are smaller than the experimental data.
Table 4 Regression coefficients of the static modulus of elasticity. Specimens
E0 (GPa)
B1
B2
g1
g2
SVCA0 SVCA0.4 SVCA0.65 SVCA0.75
12.35 25.11 35.91 38.80
5.57 15.53 12.69 11.47
14.77 68.66 122.14 110.87
10.17 4.64 6.41 4.14
0.56 0.26 0.27 0.34
SMSCA16 SMSCA20 SMSCA31.5
35.91 37.89 35.29
12.69 10.00 10.60
122.14 48.84 61.09
6.41 14.43 4.03
0.27 0.69 0.49
SCL20 SG20
37.89 32.43
10.00 12.32
48.84 70.97
14.43 5.38
0.69 0.39
SWC0.35 SWC0.5 SWC0.6
40.89 35.91 37.92
9.60 12.69 14.03
128.32 122.14 48.29
7.78 6.41 18.74
0.32 0.27 0.65
SCT12.5 SCT21 SCT33.5
38.78 35.91 37.19
9.66 12.69 10.40
45.62 122.14 39.98
17.63 6.41 5.63
1.16 0.27 0.51
g1
g2
Table 5 Regression coefficients of the dynamic modulus of elasticity. Specimens
E0 (GPa)
B1
B2
SVCA0 SVCA0.4 SVCA0.65 SVCA0.75
13.53 28.55 41.93 45.01
6.11 15.51 13.39 15.04
15.76 64.76 99.86 177.47
7.74 4.71 6.37 3.29
0.56 0.30 0.34 0.26
SMSCA16 SMSCA20 SMSCA31.5
41.93 40.82 40.80
13.39 10.80 16.42
99.86 65.68 82.23
6.37 6.44 2.91
0.34 0.51 0.36
SCL20 SG20
40.82 39.09
10.80 16.40
65.68 81.50
6.44 4.37
0.51 0.35
SWC0.35 SWC0.5 SWC0.6
46.89 41.93 41.01
9.86 13.39 14.35
130.75 99.86 66.98
7.68 6.37 9.62
0.33 0.34 0.48
SCT12.5 SCT21 SCT33.5
41.94 41.93 43.93
6.47 13.39 8.92
48.79 99.86 43.02
8.91 6.37 13.94
1.33 0.34 0.62
Fig. 6. Comparison of the calculated values and the experimental data of SWC0.5.
All other mix proportions have similar characteristics. Therefore, Ec would be underestimated by using the abovementioned codes. Previous research found that during its early age, concrete compressive strength is mainly governed by the strength of its paste matrix, the flaw size, and the ITZ properties. However, the elastic modulus of concrete is more influenced by its aggregate contents and properties [32]. This hints that using one-fit-all equations to correlate compressive strength and elastic modulus will not lead to reliable results. Influencing factors, such as aggregate volume fraction, maximum aggregates size (dominant influence on ITZ), water-to-cement ratio, and hydration age, etc. should be included. Different from Venkiteela et al. [32], the relationship between Ed and fc was studied. The equations in Table 6 can be modified to accommodate the dynamic modulus of elasticity because of the linear relationship between Ec and Ed (in GPa). The equations can be rewritten as follows: n
Ec or Ed ¼ af c þ b
ð5Þ
where a, b and n are coefficients. Fig. 7 shows the result of Eq. (5) and experimental data of SWC0.5. The regression data are very close to experimental data, and both R2 values are so close to 1. Coefficient n is nearly 0.295, and is not subjected to the influential factors. Coefficient a governs the shape and converging rate of the relationship. As shown in Table 7, a is more related to the volume content of aggregate (Vagg) and maximum coarse aggregate size (Magg). Coefficient b is influenced by the volume content of aggregate, maximum coarse aggregate size and water-to-cement ratio (w/c). Both this research and previous research [32] show that curing temperature does not affect fc–Ec (or fc–Ed) relationships. The detailed relationships are expressed as follows:
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Fig. 8. Relationship between Ec and Ed of SMSCA31.5.
Fig. 7. Relationship between Ec or Ed and fc of SWC0.5.
Table 7 Coefficients a and b for each specimen. Specimens
Ec (GPa) and fc (MPa) a
b
Table 8 Coefficient c and d for the relationship between Ec and Ed.
Ed (GPa) and fc (MPa) n
a
b
n
SVCA0 SVCA0.4 SVCA0.65 SVCA0.75
7.00 12.89 18.51 20.27
5.63 9.21 12.03 13.49
0.302 0.301 0.292 0.294
7.87 14.72 20.02 22.66
6.07 9.56 11.17 11.27
0.301 0.299 0.300 0.282
SMSCA16 SMSCA20 SMSCA31.5
18.51 18.62 19.54
12.03 13.40 14.03
0.292 0.298 0.299
20.02 20.32 21.56
11.17 12.34 13.00
0.300 0.298 0.296
SCL20 SG20
18.62 18.07
13.40 11.51
0.298 0.286
20.32 20.19
12.34 10.16
0.298 0.289
SWC0.35 SWC0.5 SWC0.6
18.25 18.51 18.42
12.49 12.03 12.04
0.293 0.292 0.297
20.03 20.02 20.41
9.86 11.17 10.76
0.285 0.300 0.297
SCT12.5 SCT21 SCT33.5
18.16 18.51 18.11
12.22 12.03 12.39
0.292 0.292 0.298
20.19 20.02 20.01
11.02 11.17 10.65
0.280 0.300 0.286
a ¼ 17:88V agg þ 0:08M agg þ 5:27
ð6Þ
b ¼ 7:41V agg 4:23V 2agg 0:12Magg þ 1:79ðw=cÞ 4:60
ð7Þ
3.3. Relationship between Ec and Ed The study shows that the dynamic modulus of elasticity is always greater than the static modulus of elasticity at each specific age. Taking SMSCA31.5 as an example, a linear relation between Ec and Ed can be observed as shown in Fig. 8. This relationship can be described by Eq. (8):
Ec ¼ cEd þ d
ð8Þ
where c and d are regression coefficients. For all the used concrete, this relationship fit. The values of coefficients c and d are listed in Table 8. From the Table 8, it can be seen that the c and d values are certainly influenced by the volume content of aggregate, maximum coarse aggregate size, water-tocement ratio and curing temperature. The details are discussed in the following sections. 3.4. Influential factors on Ec–Ed relationship Fig. 9(a) shows the influence of volume content of aggregate on elastic moduli. Because aggregate is generally more rigid than fresh
Specimens
c
d
SVCA0 SVCA0.4 SVCA0.65 SVCA0.75
0.894 0.885 0.887 0.951
0.023 0.089 0.134 0.401
SMSCA16 SMSCA20 SMSCA31.5
0.887 0.917 0.921
0.260 0.211 0.238
SCL20 SG20
0.917 0.882
0.211 0.229
SWC0.35 SWC0.5 SWC0.6
0.951 0.887 0.901
0.390 0.134 0.230
SCT12.5 SCT21 SCT33.5
0.914 0.887 0.971
0.243 0.134 0.353
paste in ordinary concrete, increasing the volume content of aggregate will lead to the increase of both Ec and Ed. The elastic modulus of SVCA0.65 is far greater than SVCA0 and SVCA0.4. This indicates that the volume content of aggregates is the most important influential factors on Ec and Ed. From the Table 8 and Fig. 9(b), it can be seen that the value of c increased significantly when the volume concrete of aggregates was increased from 65% to 75%. The d values keep decreasing with the increase of aggregate contents. This indicates that compared to Ec, Ed is more sensitive to the change in aggregate volume content. Fig. 10 plots the influence of maximum coarse aggregate size on Ec, Ed, and Ec–Ed relationship. As shown in Fig. 10(a), it seems that reducing the maximum aggregate size from 31.5 mm to 20 mm or 16 mm do not substantially affect the Ec and Ed. In Fig. 10(b), the experimental curves of SMSCA16, SMSCA20 and SMSCA31.5 are almost overlapped. From Table 8, it can be seen that the slope (c value) increases with the increase of aggregate size, however, the intercept (d value) does not change much with the aggregate size. Therefore, the maximum aggregate size would only affect the slope of the Ec–Ed relationship. Fig. 11 shows the influence of coarse aggregate type on Ec, Ed, and Ec–Ed relationship. Ec and Ed of the specimens with crushed limestone are greater than those with gravel. The reason could be that the used limestone has relatively higher modulus than that of the gravel. It could also due to better ITZ in SCL 20 specimens,
Y. Zhou et al. / Construction and Building Materials 98 (2015) 137–145
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Fig. 9. Influence of volume content of aggregate.
Fig. 10. Influence of maximum size of coarse aggregate.
because the surface of crushed limestone is rougher than that of gravel, so a better adhesion between crushed limestone and cement paste is ensured. However, the aggregate type does not affect the relationship between Ec and Ed. One can notice that the two lines in Fig. 11(b) are almost overlapped. This can also be reflected by the similar values of c and d (for SLG20 and SG20) in Table 8. Fig. 12 shows the influence of water-to-cement ratio on Ec, Ed, and Ec–Ed relationship. From Fig. 12(a), it can be seen that for a given age, both Ec and Ed decrease with the increase of the water-to-cement ratio within the studied range. A lower waterto-cement ratio will lead to a stronger paste matrix, which enhances the elastic moduli of concrete. As shown in Fig. 12(b) and Table 8, the values c and d are not influenced by the waterto-cement ratio. This hints that the aggregates are the dominant phase that governs the Ec–Ed relationship. The temperature influences on Ec, Ed, and Ec–Ed relationship are given in Fig. 13. In Fig. 13(a), it shows that for a lower curing
temperature (e.g. 12.5 °C) both Ec and Ed would approach their ultimate values much slower than those cured under higher temperatures. For the specimens cured in 33.5 °C, higher increase rates of Ec and Ed can be expected during its early age that leads to a quick converge to their final values. SCT21 represents the specimens cured in normal temperature (21 °C). One should notice that in Table 8, although the values c and d varied a lot, a direct correlation between temperature and c, d values cannot be found. This again indicates that aggregate is the dominant phase that affect the Ec– Ed relationship, as temperature mainly influence the hydration of the cement paste. According to the above analysis, the linear coefficients c and d in Eq. (8) are influenced by volume content of aggregate and the maximum aggregate size. Multiple regression analysis was applied to establish the relationship between the linear coefficients c and d and the above influential factors. They are listed as follows:
c ¼ 0:048V agg þ 0:0005Magg þ 0:8755
ð9Þ
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Y. Zhou et al. / Construction and Building Materials 98 (2015) 137–145
Fig. 11. Influence of type of coarse aggregate.
Fig. 12. Influence of water-to-cement ratio.
Fig. 13. Influence of curing temperature.
Y. Zhou et al. / Construction and Building Materials 98 (2015) 137–145
d ¼ 0:855V 3agg 0:023
ð10Þ
where Vagg is volume content of aggregate, ranges from 0 to 0.75, Magg is maximum size of coarse aggregate, ranges from 16 mm to 31.5 mm. 4. Conclusion The study confirms that prismatic compressive strength, static modulus of elasticity and dynamic modulus of elasticity are influenced by volume content of aggregate, maximum size and type of coarse aggregate, water-to-cement ratio and curing temperature. The following conclusions can be drawn: (1) Prismatic compressive strength, static modulus of elasticity and dynamic modulus of elasticity increase rapidly at very early age, and then increase slowly. The development tendency with age can be fit with an exponential decay equation. (2) The relationship between static (or dynamic) modulus of elasticity and prismatic compressive strength is recommended by a polynomial equation. (3) Aggregate volume content, water-to-cement ratio and curing temperature affect the development of both the static and the dynamic moduli of elasticity. However, waterto-cement ratio and curing temperature does not affect the correlation between Ed and Ec. (4) A linear relationship between static modulus Ec and the dynamic modulus Ed can be found. The relationship is mainly governed by the aggregate phase in concrete. Aggregate volume content and maximum size are the two dominant factors that govern the Ec–Ed correlation. It should be noted that the above mentioned results are only applicable to the given conventional concrete. Other types of concrete may have different relations and parameters of correlation. Acknowledgments This study was financially supported by National Natural Science Foundation of China (Grant No. 51208373) and the Natural Science Foundation of Shanghai, China (Grant No. 14ZR1443300). The support from the Civil and Environmental Engineering Department, University of Louisville, is also appreciated. References [1] M.a.a Abd elaty, Compressive strength prediction of Portland cement concrete with age using a new model, HBRC J. 10 (2) (2014) 145–155. [2] J.K. Kim, Y.H. Moon, S.H. Eo, Compressive strength development of concrete with different curing time and temperature, Cem. Concr. Res. 28 (12) (1998) 1761–1773. [3] R. Madandoust, J.H. Bungey, R. Ghayidel, Prediction of the concrete compressive strength by means of core testing using GMDH-type neural network and ANFIS models, Comput. Mater. Sci. 51 (1) (2012) 261–272.
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[4] American Concrete Institute, ACI 318-08 Building Code for Structural Concrete, Detroit, USA, 2008. [5] American Concrete Institute, ACI 363R-08 State of the Art Report on High Strength Concrete, Detroit, USA, 2008. [6] New Zealand Standard, Concrete Structures Standard, NZS 3101:2006, The Design of Concrete Structures, Wellington, New Zealand, 2006. [7] CSA Technical Committee, Reinforced Concrete Design, A23.3-04, Design of Concrete Structures, Rexdale, Ontario, Canada, 2004. [8] European Committee for Standardization, Eurocode 2: Design of Concrete Structures, Brussels, Belgium, 2004. [9] Code For Design of Concrete Structures (GB 50010-2010), State Development Planning Commission of the People’s Republic of China, Beijing. [10] A.F. Stock, D.J. Hannantt, R.I.T. Williams, The effect of aggregate concentration upon the strength and modulus of elasticity of concrete, Mag. Concr. Res. 31 (109) (1979) 225–234. [11] J.L. Ranchero, Analyzing and determining relationships in elastic properties of concrete using wave propagation and vibration and uniaxial compression (a thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Civil Engineering), University of Illinois at UrbanaChampaign, Urbana, Illinois, 2005. [12] J.W.S. de Graft-Johnson, N.S. Bawa, Effect of mix proportion, water-cement ratio, age and curing conditions on the dynamic modulus of elasticity of concrete, Build. Sci. 3 (3) (1969) 171–177. [13] H. Yıldırım, O. Sengul, Modulus of elasticity of substandard and normal concretes, Constr. Build. Mater. 25 (4) (2011) 1645–1652. [14] G. Trtnik, F. Kavcic, G. Turk, Prediction of concrete strength using ultrasonic pulse velocity and artificial neural networks, Ultrasonics 49 (1) (2009) 53–60. [15] S.V. Kolluru, J.S. Popovics, S.P. Shah, Determining elastic properties of concrete using vibrational resonance frequencies of standard test cylinders, Cem. Concr. Aggr. 22 (2) (2000) 81–89. [16] Z. Sun, T. Voigt, S.P. Shah, Temperature effects on strength evaluation of cement-based materials with ultrasonic wave reflection technique, ACI Mater. J. 102 (4) (2005) 272–278. [17] T. Voigt, Z. Sun, S.P. Shah, Comparison of ultrasonic wave reflection method and maturity method in evaluating early-age compressive strength of mortar, Cem. Concr. Compos. 28 (4) (2006) 307–316. [18] A.M. Neville, Properties of Concrete, Pitman Books Limited, New York, 1981. [19] S.H. Han, J.K. Kim, Effect of temperature and age on the relationship between dynamic and static elastic modulus of concrete, Cem. Concr. Res. 34 (7) (2004) 1219–1227. [20] F.D. Lydon, R.V. Balendran, Some observations on elastic properties of plain concrete, Cem. Concr. Res. 16 (3) (1986) 314–324. [21] Sand for Construction (GB/T14684-2011), China Building Materials Federation, Beijing. [22] Pebble and Crushed Stone for Construction (GB/T14685-2011), China Building Materials Federation, Beijing. [23] American Society for Testing Material, ASTM C305-06 Standard Practice for Mechanical Mixing of Hydraulic Cement Pastes and Mortars of Plastic Consistency, West Conshohocken, Pennsylvania, USA, 2006. [24] American Society for Testing Material, ASTM C192-06 Standard Practice for Making and Curing Concrete Test Specimens in the Laboratory, West Conshohocken, Pennsylvania, USA, 2006. [25] American Society for Testing Material, ASTM C215-08 Standard Test Method for Fundamental Transverse, Longitudinal, and Torsional Resonant Frequencies of Concrete Specimens, West Conshohocken, Pennsylvania, USA, 2008. [26] Standard for Test Method of Mechanical Properties on Ordinary Concrete (GB/ T 50081-2002), China Academy of Building Research, Beijing. [27] Z.P. Bazant, Y.J. Xiang, Size effect in compression fracture: splitting crack band propagation, J. Eng. Mech. ASCE 123 (2) (1997) 162–172. [28] J.K. Kim, S.T. Yi, Application of size effect to compressive strength of concrete members, Sadhana Acad. Proc. Eng. Sci. 27 (2002) 467–484. [29] S.T. Yi, E.K. Yang, J.C. Choi, Effect of specimen sizes, specimen shapes, and placement directions on compressive strength of concrete, Nucl. Eng. Des. 236 (2) (2006) 115–127. [30] Code for Design of Concrete Structures (GB 50010-2010), China Academy of Building Research, Beijing. [31] H.S. Lew, T.W. Reichard, Mechanical properties of concrete at early ages, ACI J. Proc. 75 (10) (1978) 533–542. [32] G. Venkiteela, Z. Sun, H. Najm, Prediction of early age normal concrete compressive strength based on dynamic shear modulus measurements, J. Mater. Civ. Eng. 25 (1) (2013) 30–38.
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
A fundamental study on compressive strength, static and dynamic elastic moduli of young concrete Yong Zhou a,⇑, Jie Gao a, Zhihui Sun b, Wenjun Qu a a b
Department of Structural Engineering, Tongji University, 1239 Siping Road, Shanghai 20092, PR China Department of Civil and Environmental Engineering, University of Louisville, Louisville, KY 40292, USA
h i g h l i g h t s Relationship between static and dynamic moduli of elasticity is linear. Aggregate volume content, water-to-cement ratio and curing temperature affect E. Aggregate volume content and maximum size are dominant factors on Ec–Ed.
a r t i c l e
i n f o
Article history: Received 25 April 2015 Received in revised form 6 July 2015 Accepted 12 August 2015 Available online 24 August 2015 Keywords: Early age Impact resonance test Influential factors Multiple regression analysis
a b s t r a c t This study investigates the influence of volume content of aggregates, maximum size and type of coarse aggregates, water-to-cement ratio and curing temperature on mechanical properties, i.e. prismatic compressive strength (fc), static modulus of elasticity (Ec) and dynamic modulus of elasticity (Ed) of concrete at early age. A new equation is proposed to correlate prismatic compressive strength and elastic moduli of concrete. Based on the experimental data and the analysis results, the Ec–Ed relationship is also proposed. It is found that the relationship between Ec and Ed is linear, and the coefficients of linear relationship are analyzed by multiple regression analysis, considering aggregate content, maximum size of the coarse aggregate, water-to-cement ratio and curing temperature. It is found that the volume content of aggregates is the most significant factor that influences the Ec–Ed relationship. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction The construction of concrete structures greatly depends on the mechanical properties of concrete, among which compressive strength and modulus of elasticity are mostly concerned. For example, the proper time to remove formwork and the proper time to apply pre-stress on concrete members are completely controlled by these two properties. If anything improper is done before concrete has developed its desired properties, large deformation, crushing of concrete or even catastrophic collapse may happen. Therefore, knowing the early-age compressive strength and the elastic modulus of concrete is critical to guarantee its life-time performance. For concrete, both the compressive strength and the elastic modulus increase rapidly during its early age [1–3]. The design code recommends estimating concrete’s elastic modulus based on its 28th day’s compressive strength [4–9]. This recommended relationship may not be applicable to concrete at early age. ⇑ Corresponding author. E-mail address: [email protected] (Y. Zhou). http://dx.doi.org/10.1016/j.conbuildmat.2015.08.110 0950-0618/Ó 2015 Elsevier Ltd. All rights reserved.
There are many influential factors on compressive strength and modulus of elasticity of concrete. Stock et al. [10] presented that the modulus of elasticity is proportional to the volume content of aggregate. Ranchero [11] indicated that volume content of aggregates, type of coarse aggregate and water-to-cement ratio were the most important influential factors. Johnson and Bawa [12] found that the modulus of elasticity increases with the increase in volume content of aggregates and decreases with the increase in water-to-cement ratio. Yıldırım and Sengul [13] pointed out that the modulus of elasticity could be lower if smaller aggregates were used. All the above researches focused on concrete at the age of 28 days or older. It is not clear that how these factors influence the modulus of elasticity at early age. When design a concrete structure, its compressive strength and the static Young’s modulus are used as recommended by the design codes. However, for field measurement, concrete quality is normally estimated via in situ non-destructive testing (NDT) methods, among which the ultrasonic pulse velocity, the wave reflection, and the impact echo methods are commonly used [14–17]. These methods are dynamic methods, measuring the dynamic modulus of concrete. Therefore, a good model to correlate
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static and dynamic moduli of concrete is needed to correlate structure design and field measurement. Although the relationship between the static and the dynamic moduli of concrete has been suggested by some researchers [11,18–20], a model based on design parameters, such as aggregate size and volume, water-tocement ratio and curing temperature is needed to close the gap between structure design and field measurement. This paper presents the results of a study on the development of prismatic compressive strength and modulus of elasticity, and the relationships between static and dynamic moduli of elasticity of concrete within the age of 12 h to 28 days. Meanwhile, the influences of the material parameters used in designing mix proportions (such as water-to-cement ratio, maximum coarse aggregate size, coarse aggregate type, and coarse aggregate volume content, etc.) on the relationship between static modulus (Ec) and dynamic modulus (Ed) are investigated. Fig. 1. Gradation curves of coarse aggregate.
2. Materials and experiments 2.1. Raw materials
respectively. The maximum diameter of gravel was 20 mm. The aggregate gradation complied with GB/T14684-2011 [21] and GB/T14685-2011 [22]. In Table 1, the cumulative particle size distributions, the specific gravity under the saturatedsurface-dry condition and the absorption capacities of the sand, gravel and crushed limestone are listed in details. The gradation curves of all the coarse aggregates that used in this study are plotted in Fig. 1.
Ordinary type I Portland cement was used in all the experiments. The specific gravity of the cement was assumed to be 3.15. River sand, gravel and crushed limestone were used as fine and coarse aggregates. To study the influence of maximum coarse aggregate size on the mechanical properties of concrete, the maximum diameters of crushed limestone were chosen as 16 mm, 20 mm and 31.5 mm,
Table 1 Properties of aggregates.
Crushed limestone with the diameter 5~31.5mm (C1) Sieve size (mm)
37.5
Mass retained (%)
0
Density (SSD)
31.5
19.0
9.5
4.75
2.36
0
26
93*
100
100
3
2634 kg/m
Absorption capacity
1.05%
Crushed limestone with the diameter 5~20mm (C2) Sieve size (mm)
26.5
19.0
9.5
4.75
2.36
Mass retained (%)
0
5
72
98
100
Density (SSD)
2638 kg/m3
Absorption capacity
0.94%
Crushed limestone with the diameter 5~16mm (C3) Sieve size (mm)
19.0
Mass retained (%)
0
Density (SSD)
16.0
9.5
4.75
2.36
9
55
96
100
3
2630 kg/m
Absorption capacity
1.01%
Gravel with the diameter 5~20mm (G) Sieve size (mm)
26.5
19.0
9.5
4.75
2.36
Mass retained (%)
0
9
66
96
100
Density (SSD)
2587 kg/m3
Absorption capacity
1.02%
River sand Sieve size (mm)
9.50
4.75
2.36
1.18
0.6
0.3
0.15
Mass retained (%)
0
5
15
28
43
90
98
Fineness modulus Density (SSD) *
2.63- medium sand 2604 kg/m3
Absorption capacity
1.81%
Note: mass retained should be 90% at the sieve size 9.5 mm according to GB/T14685-2011.
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Y. Zhou et al. / Construction and Building Materials 98 (2015) 137–145 2.2. Mixture design In order to investigate the influence of aggregate volume content, maximum size of coarse aggregate, aggregate type, water-to-cement ratio and curing temperature on the mechanical properties of concrete, 15 mix proportions were designed and listed in Table 2. The mass ratio of fine aggregate to total aggregate was 0.33 for all mixture proportions. Specimen SVCA0–0.75 were designed for studying the influence of volume content of aggregates by using the same crushed limestone with the diameter 5–16 mm and the water-to-cement ratio of 0.5. The coarse aggregates of SMSCA16–31.5 were the crushed limestone with maximum size of 16 mm, 20 mm and 31.5 mm, respectively. The coarse aggregate of SCL20 and SG20 were the crushed limestone with the maximum diameter of 20 mm and the gravel with the same size, respectively. SWC0.35–0.6 were designed for studying the influence of water-to-cement ratio from 0.35 to 0.6 by using the same volume content of aggregate (0.65). All these concrete were moisture cured under 21 °C throughout the study. In order to study the temperature effect, for the concrete with aggregate volume content equals 0.65, two other curing temperatures (12.5 °C and 33.5 °C) were also used. And they are listed as the ‘‘SCT series” in Table 2. Naphthalenebased superplasticizer was added in SVCA0.75 and SWC0.35 to achieve similar slump to other mixtures. The mass ratio of superplasticizer to cement was 0.8% in SVCA0.75 and 0.75% in SWC0.35. 2.3. Sample preparation ASTM C305-06 [23] and C192-06 [24] were followed during the mixing of SVCA0 and all others, respectively. Freshly mixed concrete was cast into 100 100 300 mm steel molds, then sealed and put into the curing chamber within 30 min after mixing. 24 h later, the molds were removed and the specimens were directly submerged in saturated lime water to prevent the leaching of Ca(OH)2 in concrete. Constant temperatures of 12.5 ± 1 °C, 21 ± 0.5 °C and 33.5 ± 1 °C were used. 50 specimens were made from each mix proportion. 2.4. Test methods The specimens of each mix proportions were tested at the age of 12 h, 1 day, 2 days, 3 days, 7 days, 14 days and 28 days. Six specimens were tested at each age: 3 specimens for the prismatic compressive strength tests and 3 specimens for the static and dynamic elastic modulus tests. For the moduli tests, because the dynamic test is a NDT-test, the specimens used for this test can be used again for the static test. Details for each test are specified as follows. 2.4.1. Impact resonance tests Impact resonance tests were performed according to ASTM C215-08 [25], using the longitudinal mode. Fig. 2 shows a schematic of the impact resonance test used in this study. A miniature piezoelectric accelerometer that has a flat response from 1 to 12,000 Hz with a sensitivity of 10 mV/g at 160 Hz (LC0159 manufactured by Lance) was mounted at the center of one end surface of the prism. A steel ball with a diameter of 12 mm was used as the impact source and applied at the center of the opposite end surface. The dynamic modulus of elasticity is obtained from the following equations:
Ed ¼ DMn2
ð1Þ
D ¼ 4ðL=btÞ
ð2Þ
Fig. 2. Schematic of the impact resonance test.
where Ed is the dynamic modulus of elasticity, L is the length of the specimen, b and t are the dimensions of the prism cross section, M is the mass of the specimen, and n is the measured fundamental longitudinal frequency. 2.4.2. Static tests The static tests were conducted following GB/T 50081-2002 [26], using a 50 kN universal testing machine at the age of 12 h and 1 day and a 500 kN universal testing machine at the age of 2–28 days. Firstly, three replicas were used to obtain the prismatic compressive strength, and the compressive load was applied continuously at the specified loading rate. Although both cylindrical strength and prismatic strength can be tested, the prismatic strength was chosen in this study. This is because the Chinese code for static modulus estimation at 28 days requires the 28-day prismatic compressive strength. To keep the consistency, prisms were used in the tests to obtain compressive strength at different ages. After the strength tests, another three replicas (also used for dynamic tests) were prepared for static modulus of elasticity. When measuring the static modulus, two 100 mm linear extensometers were attached to two opposite sides of the specimen to measure the axial deformation, in Fig. 3. Both extensometers were manufactured by Epsilon, model 3542RA2-100M-600M-ST with the measuring range of ±6 mm. The specimen was preloaded and unloaded once firstly, then loaded and unloaded thrice to approximately 33% of the prismatic compressive strength before loaded to failure. The stress–strain curves were plotted for each specimen. And the slope of the stress–strain curve (up to 33% of the strength) was determined as the static elastic modulus via linear regression.
3. Test results and analysis 3.1. Development of the mechanical properties 3.1.1. Prismatic compressive strength – fc Due to the size effect [27,28], the prismatic compressive strength is different from the cylindrical strength. This difference is influenced by size, shape and placement direction of specimens [29]. According to GB 50010-2010 [30], the ratio of the cylindrical strength to the prismatic compressive strength is 1.18 for ordinary concrete. Fig. 4 plots the prismatic strength development for concrete SMSCA20 from 12 h to 28 days. It can be seen that the compressive
Table 2 Mixture proportions. No.
Quantity (kg/m3)
Mixture proportion by weight
Mixture proportion by volume
0.0 702.5 1141.6 1317.2
1:0.5:0:0 1:0.5:0.48:0.97 1:0.5:1.35:2.74 1:0.5:2.21:4.49
0.38:0.61:0:0 0.23:0.36:0.13:0.27 0.13:0.21:0.22:0.43 0.09:0.15:0.25:0.50
562.3 563.4 562.9
1141.6 1143.9 1142.8
1:0.5:1.35:2.74 1:0.5:1.35:2.75 1:0.5:1.35:2.75
0.13:0.21:0.22:0.43 0.13:0.21:0.22:0.43 0.13:0.21:0.22:0.43
208.0 208.0
563.4 556.1
1143.9 1129.1
1:0.5:1.35:2.75 1:0.5:1.34:2.71
0.13:0.21:0.22:0.43 0.13:0.21:0.22:0.43
509.4 415.9 370.6
178.3 208.0 222.4
562.3 562.3 562.3
1141.6 1141.6 1141.6
1:0.35:1.10:2.24 1:0.5:1.35:2.74 1:0.6:1.52:3.08
0.12:0.22:0.22:0.43 0.13:0.21:0.22:0.43 0.16:0.18:0.22:0.43
415.9 415.9 415.9
208.0 208.0 208.0
562.3 562.3 562.3
1141.6 1141.6 1141.6
1:0.5:1.35:2.74 1:0.5:1.35:2.74 1:0.5:1.35:2.74
0.13:0.21:0.22:0.43 0.13:0.21:0.22:0.43 0.13:0.21:0.22:0.43
Cement
Water
Sand
Coarse aggregate
1211.1 721.7 415.9 293.6
605.5 360.9 208.0 146.8
0.0 346.0 562.3 648.8
SMSCA16 SMSCA20 SMSCA31.5
415.9 415.9 415.9
208.0 208.0 208.0
SCL20 SG20
415.9 415.9
SWC0.35 SWC0.5 SWC0.6 SCT12.5 SCT21 SCT33.5
SVCA0 SVCA0.4 SVCA0.65 SVCA0.75
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Y. Zhou et al. / Construction and Building Materials 98 (2015) 137–145 Table 3 Regression coefficients of prismatic compressive strength. Specimens
f0 (MPa)
A1
A2
t1
t2
SVCA0 SVCA0.4 SVCA0.65 SVCA0.75
25.702 26.662 26.166 25.625
18.521 21.346 17.855 14.676
12.103 20.703 20.929 22.671
19.416 9.981 6.328 5.712
0.881 0.402 0.583 0.746
SMSCA16 SMSCA20 SMSCA31.5
26.166 25.053 23.657
17.855 14.241 12.948
20.929 19.047 19.550
6.328 6.069 7.621
0.583 0.941 0.836
SCL20 SG20
25.053 23.307
14.241 10.075
19.047 17.560
6.069 10.681
0.941 1.787
SWC0.35 SWC0.5 SWC0.6
47.502 26.166 23.529
30.716 17.855 10.972
65.654 20.929 16.179
14.694 6.328 17.947
0.368 0.583 1.937
SCT12.5 SCT21 SCT33.5
33.132 26.166 31.513
14.743 17.855 11.376
23.896 20.929 23.512
9.985 6.328 11.178
2.689 0.583 1.618
maximum coarse aggregate size. Through this multiple regression analysis, it can also be seen that the water-to-cement ratio is most important influential factor to f0, as the f0 value of SWC0.35 is twice as much as that of SWC0.6. A1 and A2 are two coefficients that control the converging rate of the curve. They are also influenced by water-to-cement ratio the most. t1 and t2 are two decay constants. They are influenced by both the volume content of aggregates, the water-to-cement ratio and curing temperature.
Fig. 3. Test setups for static modulus measurement.
3.1.2. Static modulus of elasticity (Ec) and dynamic modulus of elasticity (Ed) Fig. 5 plots the static and the dynamic moduli for concrete SMSCA20 from 12 h to 28 days, respectively. As shown in the figure, both moduli increase rapidly at the age of 12 h through 3 days, while they increase slowly at the age of 3–28 days. Both Ec and Ed at the age of 3 days reach 80% of the values of 28 days. Meanwhile, the increasing rates of both Ec and Ed are faster than that of fc during the age of 12 h to 3 days. Similar results were found by Lew and Reichard [31]. All other specimens used in this study showed the same trend. Therefore an exponential equation is proposed to represent the development tendency of Ec an Ed with age: Fig. 4. Development of prismatic compressive strength of SMSCA20.
Ec ðtÞ or Ed ðtÞ ¼ E0 þ B1 et=g1 þ B2 et=g2
strength increases rapidly at the age of 12 h to 7 days, while it increases slowly at the age of 7–28 days. And the compressive strength at the age of 7 days was approximately 80% of that at 28 days. All other specimens used in this study showed the same characteristics. To further study the development of strength growth, an exponential equation shown as Eq. (3) was proposed to simulate the development trend.
f c ðtÞ ¼ f 0 þ A1 et=t1 þ A2 et=t2
where t represents the hydration age (in days), E0, B1, B2, g1 and g2 are coefficients.
ð3Þ
where t represents the hydration age (in days), f0, A1, A2, t1 and t2 are coefficients from regression. It is clearly seen that Eq. (3) can depict the development tendency of prismatic compressive strength, and the fitted result of Adj.R2 is close to 1. For all the tested concrete, the regression coefficients f0, A1, A2, t1 and t2 are listed in the following Table 3. From both Eq. (3) and the Table 3, it can be seen that the coefficient f0 represents the ultimate strength of the concrete (when t ? 1, which has a value pretty close to the 28 days strength. By comparing specimens SVCA0 through SVCA0.75, it can be seen that changing the volume content of aggregates does not affect the ultimate strength gains of concrete. The f0 values of SMSCA16 through SMSCA31.5 indicate a decrease of the strength with an increase of
ð4Þ
Fig. 5. Development of the static and the dynamic modulus for SMSCA20.
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Apparently, the curve of Eq. (4) is closer to the experimental data, and the fitted result of Adj.R2 is close to 1. Therefore, Eq. (4) can depict the development tendency of the modulus of elasticity. Similar to the compressive strength, the E0 in the equation indicate the ultimate modulus of concrete (when t ? 1; B1 and B2 are two shape factors that control the converge rate of the curve; and g1 and g2 are two decay constants. The curve fitting results are listed in Tables 4 and 5 for all the coefficients. From the tables, it can be seen that E0 has a value pretty close to the 28 days modulus of elasticity. To be different from the compressive strength, the volume content of aggregates is the most significant influencing factor on the E0 values. B1 and B2 are also affected by aggregate volume content the most. g1 and g2 are more sensitive to the water-to-cement ratio and the curing temperature.
Table 6 Estimating equations in different codes. Code ACI 318-08 ACI 363-08 NZS 3101-2006 CSA A23.3-04 EC-2 GB 50010
Estimating equation pffiffiffiffiffi Ec ¼ 4700 f c pffiffiffiffiffi Ec ¼ 3300 f c þ 6900 pffiffiffiffiffi Ec ¼ 3320 f c þ 6900 pffiffiffiffiffi Ec ¼ 4500 f c Ec = 22(fc/10)0.3 2
10 Ec ¼ 2:2þ34:7=f
Units fc: MPa, Ec: MPa fc: MPa, Ec: MPa fc: MPa, Ec: MPa fc: MPa, Ec: MPa fc : MPa, Ec : GPa fc: MPa, Ec: MPa
c
3.2. Ec and Ed vs. fc The relationship between Ec and fc has been recommended by design codes of many countries [4–9], shown in Table 6. Fig. 6 compares the values estimated by the equations in different codes with the experimental data of SWC0.5. The calculated values of ACI 318 and CSA A23.3 at the age of 12 h, and EC-2 at the age of 1 day, are closest to the experimental data, respectively. After the age of 2 days, all the calculated values are smaller than the experimental data.
Table 4 Regression coefficients of the static modulus of elasticity. Specimens
E0 (GPa)
B1
B2
g1
g2
SVCA0 SVCA0.4 SVCA0.65 SVCA0.75
12.35 25.11 35.91 38.80
5.57 15.53 12.69 11.47
14.77 68.66 122.14 110.87
10.17 4.64 6.41 4.14
0.56 0.26 0.27 0.34
SMSCA16 SMSCA20 SMSCA31.5
35.91 37.89 35.29
12.69 10.00 10.60
122.14 48.84 61.09
6.41 14.43 4.03
0.27 0.69 0.49
SCL20 SG20
37.89 32.43
10.00 12.32
48.84 70.97
14.43 5.38
0.69 0.39
SWC0.35 SWC0.5 SWC0.6
40.89 35.91 37.92
9.60 12.69 14.03
128.32 122.14 48.29
7.78 6.41 18.74
0.32 0.27 0.65
SCT12.5 SCT21 SCT33.5
38.78 35.91 37.19
9.66 12.69 10.40
45.62 122.14 39.98
17.63 6.41 5.63
1.16 0.27 0.51
g1
g2
Table 5 Regression coefficients of the dynamic modulus of elasticity. Specimens
E0 (GPa)
B1
B2
SVCA0 SVCA0.4 SVCA0.65 SVCA0.75
13.53 28.55 41.93 45.01
6.11 15.51 13.39 15.04
15.76 64.76 99.86 177.47
7.74 4.71 6.37 3.29
0.56 0.30 0.34 0.26
SMSCA16 SMSCA20 SMSCA31.5
41.93 40.82 40.80
13.39 10.80 16.42
99.86 65.68 82.23
6.37 6.44 2.91
0.34 0.51 0.36
SCL20 SG20
40.82 39.09
10.80 16.40
65.68 81.50
6.44 4.37
0.51 0.35
SWC0.35 SWC0.5 SWC0.6
46.89 41.93 41.01
9.86 13.39 14.35
130.75 99.86 66.98
7.68 6.37 9.62
0.33 0.34 0.48
SCT12.5 SCT21 SCT33.5
41.94 41.93 43.93
6.47 13.39 8.92
48.79 99.86 43.02
8.91 6.37 13.94
1.33 0.34 0.62
Fig. 6. Comparison of the calculated values and the experimental data of SWC0.5.
All other mix proportions have similar characteristics. Therefore, Ec would be underestimated by using the abovementioned codes. Previous research found that during its early age, concrete compressive strength is mainly governed by the strength of its paste matrix, the flaw size, and the ITZ properties. However, the elastic modulus of concrete is more influenced by its aggregate contents and properties [32]. This hints that using one-fit-all equations to correlate compressive strength and elastic modulus will not lead to reliable results. Influencing factors, such as aggregate volume fraction, maximum aggregates size (dominant influence on ITZ), water-to-cement ratio, and hydration age, etc. should be included. Different from Venkiteela et al. [32], the relationship between Ed and fc was studied. The equations in Table 6 can be modified to accommodate the dynamic modulus of elasticity because of the linear relationship between Ec and Ed (in GPa). The equations can be rewritten as follows: n
Ec or Ed ¼ af c þ b
ð5Þ
where a, b and n are coefficients. Fig. 7 shows the result of Eq. (5) and experimental data of SWC0.5. The regression data are very close to experimental data, and both R2 values are so close to 1. Coefficient n is nearly 0.295, and is not subjected to the influential factors. Coefficient a governs the shape and converging rate of the relationship. As shown in Table 7, a is more related to the volume content of aggregate (Vagg) and maximum coarse aggregate size (Magg). Coefficient b is influenced by the volume content of aggregate, maximum coarse aggregate size and water-to-cement ratio (w/c). Both this research and previous research [32] show that curing temperature does not affect fc–Ec (or fc–Ed) relationships. The detailed relationships are expressed as follows:
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Fig. 8. Relationship between Ec and Ed of SMSCA31.5.
Fig. 7. Relationship between Ec or Ed and fc of SWC0.5.
Table 7 Coefficients a and b for each specimen. Specimens
Ec (GPa) and fc (MPa) a
b
Table 8 Coefficient c and d for the relationship between Ec and Ed.
Ed (GPa) and fc (MPa) n
a
b
n
SVCA0 SVCA0.4 SVCA0.65 SVCA0.75
7.00 12.89 18.51 20.27
5.63 9.21 12.03 13.49
0.302 0.301 0.292 0.294
7.87 14.72 20.02 22.66
6.07 9.56 11.17 11.27
0.301 0.299 0.300 0.282
SMSCA16 SMSCA20 SMSCA31.5
18.51 18.62 19.54
12.03 13.40 14.03
0.292 0.298 0.299
20.02 20.32 21.56
11.17 12.34 13.00
0.300 0.298 0.296
SCL20 SG20
18.62 18.07
13.40 11.51
0.298 0.286
20.32 20.19
12.34 10.16
0.298 0.289
SWC0.35 SWC0.5 SWC0.6
18.25 18.51 18.42
12.49 12.03 12.04
0.293 0.292 0.297
20.03 20.02 20.41
9.86 11.17 10.76
0.285 0.300 0.297
SCT12.5 SCT21 SCT33.5
18.16 18.51 18.11
12.22 12.03 12.39
0.292 0.292 0.298
20.19 20.02 20.01
11.02 11.17 10.65
0.280 0.300 0.286
a ¼ 17:88V agg þ 0:08M agg þ 5:27
ð6Þ
b ¼ 7:41V agg 4:23V 2agg 0:12Magg þ 1:79ðw=cÞ 4:60
ð7Þ
3.3. Relationship between Ec and Ed The study shows that the dynamic modulus of elasticity is always greater than the static modulus of elasticity at each specific age. Taking SMSCA31.5 as an example, a linear relation between Ec and Ed can be observed as shown in Fig. 8. This relationship can be described by Eq. (8):
Ec ¼ cEd þ d
ð8Þ
where c and d are regression coefficients. For all the used concrete, this relationship fit. The values of coefficients c and d are listed in Table 8. From the Table 8, it can be seen that the c and d values are certainly influenced by the volume content of aggregate, maximum coarse aggregate size, water-tocement ratio and curing temperature. The details are discussed in the following sections. 3.4. Influential factors on Ec–Ed relationship Fig. 9(a) shows the influence of volume content of aggregate on elastic moduli. Because aggregate is generally more rigid than fresh
Specimens
c
d
SVCA0 SVCA0.4 SVCA0.65 SVCA0.75
0.894 0.885 0.887 0.951
0.023 0.089 0.134 0.401
SMSCA16 SMSCA20 SMSCA31.5
0.887 0.917 0.921
0.260 0.211 0.238
SCL20 SG20
0.917 0.882
0.211 0.229
SWC0.35 SWC0.5 SWC0.6
0.951 0.887 0.901
0.390 0.134 0.230
SCT12.5 SCT21 SCT33.5
0.914 0.887 0.971
0.243 0.134 0.353
paste in ordinary concrete, increasing the volume content of aggregate will lead to the increase of both Ec and Ed. The elastic modulus of SVCA0.65 is far greater than SVCA0 and SVCA0.4. This indicates that the volume content of aggregates is the most important influential factors on Ec and Ed. From the Table 8 and Fig. 9(b), it can be seen that the value of c increased significantly when the volume concrete of aggregates was increased from 65% to 75%. The d values keep decreasing with the increase of aggregate contents. This indicates that compared to Ec, Ed is more sensitive to the change in aggregate volume content. Fig. 10 plots the influence of maximum coarse aggregate size on Ec, Ed, and Ec–Ed relationship. As shown in Fig. 10(a), it seems that reducing the maximum aggregate size from 31.5 mm to 20 mm or 16 mm do not substantially affect the Ec and Ed. In Fig. 10(b), the experimental curves of SMSCA16, SMSCA20 and SMSCA31.5 are almost overlapped. From Table 8, it can be seen that the slope (c value) increases with the increase of aggregate size, however, the intercept (d value) does not change much with the aggregate size. Therefore, the maximum aggregate size would only affect the slope of the Ec–Ed relationship. Fig. 11 shows the influence of coarse aggregate type on Ec, Ed, and Ec–Ed relationship. Ec and Ed of the specimens with crushed limestone are greater than those with gravel. The reason could be that the used limestone has relatively higher modulus than that of the gravel. It could also due to better ITZ in SCL 20 specimens,
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Fig. 9. Influence of volume content of aggregate.
Fig. 10. Influence of maximum size of coarse aggregate.
because the surface of crushed limestone is rougher than that of gravel, so a better adhesion between crushed limestone and cement paste is ensured. However, the aggregate type does not affect the relationship between Ec and Ed. One can notice that the two lines in Fig. 11(b) are almost overlapped. This can also be reflected by the similar values of c and d (for SLG20 and SG20) in Table 8. Fig. 12 shows the influence of water-to-cement ratio on Ec, Ed, and Ec–Ed relationship. From Fig. 12(a), it can be seen that for a given age, both Ec and Ed decrease with the increase of the water-to-cement ratio within the studied range. A lower waterto-cement ratio will lead to a stronger paste matrix, which enhances the elastic moduli of concrete. As shown in Fig. 12(b) and Table 8, the values c and d are not influenced by the waterto-cement ratio. This hints that the aggregates are the dominant phase that governs the Ec–Ed relationship. The temperature influences on Ec, Ed, and Ec–Ed relationship are given in Fig. 13. In Fig. 13(a), it shows that for a lower curing
temperature (e.g. 12.5 °C) both Ec and Ed would approach their ultimate values much slower than those cured under higher temperatures. For the specimens cured in 33.5 °C, higher increase rates of Ec and Ed can be expected during its early age that leads to a quick converge to their final values. SCT21 represents the specimens cured in normal temperature (21 °C). One should notice that in Table 8, although the values c and d varied a lot, a direct correlation between temperature and c, d values cannot be found. This again indicates that aggregate is the dominant phase that affect the Ec– Ed relationship, as temperature mainly influence the hydration of the cement paste. According to the above analysis, the linear coefficients c and d in Eq. (8) are influenced by volume content of aggregate and the maximum aggregate size. Multiple regression analysis was applied to establish the relationship between the linear coefficients c and d and the above influential factors. They are listed as follows:
c ¼ 0:048V agg þ 0:0005Magg þ 0:8755
ð9Þ
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Fig. 11. Influence of type of coarse aggregate.
Fig. 12. Influence of water-to-cement ratio.
Fig. 13. Influence of curing temperature.
Y. Zhou et al. / Construction and Building Materials 98 (2015) 137–145
d ¼ 0:855V 3agg 0:023
ð10Þ
where Vagg is volume content of aggregate, ranges from 0 to 0.75, Magg is maximum size of coarse aggregate, ranges from 16 mm to 31.5 mm. 4. Conclusion The study confirms that prismatic compressive strength, static modulus of elasticity and dynamic modulus of elasticity are influenced by volume content of aggregate, maximum size and type of coarse aggregate, water-to-cement ratio and curing temperature. The following conclusions can be drawn: (1) Prismatic compressive strength, static modulus of elasticity and dynamic modulus of elasticity increase rapidly at very early age, and then increase slowly. The development tendency with age can be fit with an exponential decay equation. (2) The relationship between static (or dynamic) modulus of elasticity and prismatic compressive strength is recommended by a polynomial equation. (3) Aggregate volume content, water-to-cement ratio and curing temperature affect the development of both the static and the dynamic moduli of elasticity. However, waterto-cement ratio and curing temperature does not affect the correlation between Ed and Ec. (4) A linear relationship between static modulus Ec and the dynamic modulus Ed can be found. The relationship is mainly governed by the aggregate phase in concrete. Aggregate volume content and maximum size are the two dominant factors that govern the Ec–Ed correlation. It should be noted that the above mentioned results are only applicable to the given conventional concrete. Other types of concrete may have different relations and parameters of correlation. Acknowledgments This study was financially supported by National Natural Science Foundation of China (Grant No. 51208373) and the Natural Science Foundation of Shanghai, China (Grant No. 14ZR1443300). The support from the Civil and Environmental Engineering Department, University of Louisville, is also appreciated. References [1] M.a.a Abd elaty, Compressive strength prediction of Portland cement concrete with age using a new model, HBRC J. 10 (2) (2014) 145–155. [2] J.K. Kim, Y.H. Moon, S.H. Eo, Compressive strength development of concrete with different curing time and temperature, Cem. Concr. Res. 28 (12) (1998) 1761–1773. [3] R. Madandoust, J.H. Bungey, R. Ghayidel, Prediction of the concrete compressive strength by means of core testing using GMDH-type neural network and ANFIS models, Comput. Mater. Sci. 51 (1) (2012) 261–272.
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