Study of Ultra-High Performance Concrete Mechanical Behavior under High Temperatures
Abstract
:1. Introduction
2. Materials and Methods
2.1. Composition of UHPC
2.2. Factorial Design
2.3. Combination of Study Factors
2.4. Mixing and Casting Procedure
- (1)
- Add 50% of the cement + 100% of the silica + 100% of the water, and mix for 5 min at low speed;
- (2)
- Add 25% of the cement + 100% of the additive, and mix for 5 min at medium speed;
- (3)
- Add 25% of the cement and mix for 5 min at high speed;
- (4)
- Add 100% of the sand + 100% of the quartz powder, and mix for 5 min at high speed;
- (5)
- Add fibers evenly and mix for 5 min, with the speed being low during fiber insertion and high soon after.
2.5. Description of the Drying Process and Application of High Temperatures
2.6. Tests Performed
3. Results and Discussion
3.1. Consistence Index
- Ca: UHPC, which may be self-compacting (diameter 270 mm). Generally able to be placed without vibration or use of a mechanical flow aid;
- Cv: viscous UHPC (230 mm diameter < 270 mm). Generally able to be placed without vibration but which requires the use of a mechanical flow aid;
- Ct: UHPC exhibiting a flow threshold (diameter < 230 mm). Generally able to flow under the effect of dynamic shearing but whose free surface at rest may keep sloping.
1611.1337948474 × P − 883.33333333313 × P2 − 751.11111111085 × A × P
3.2. Compressive Strength and Elasticity Modulus
- A factorial 23 design was used to determine an initial response surface;
- The response surface equation from the previous step was used to determine the fc values of the missing cells to carry out two 22 factorial designs, wherein the PVA fiber was set at 0.25% and the steel fiber was set at 1.75%. In this way, the fc values were determined for a temperature equal to 310 °C;
- Once the fc values for a temperature equal to 310 °C were obtained, a 23 factorial design was carried out in order to determine the remaining fc values (for temperatures equal to 482 °C and 600 °C);
- Finally, a final 23 factorial design was performed using all tests and estimated values to construct the response surface to be analyzed.
3.2.1. Compressive Strength
1849.9247355629 × A − 505.4942376002 × A2 + 678.7990434340 × P + 0.0017623997 × P2 −
0.0000006460 × T × P − 367.5148148148 × A × P
3.2.2. Elasticity Modulus
A − 0.0003231396 × A2 + 84.7319703553 × P + 220,5596768604 × P2 −
0.0000000311 × T × A − 0.2717441860 × T × P − 75.77777778 × A × P
4. Conclusions
Author Contributions
Funding
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Cement | Silica Fume | Quartz Sand | Quartz Powder | Superplasticizer | Water |
---|---|---|---|---|---|
922.880 | 179.160 | 1015.168 | 92.288 | 36.915 | 179.160 |
Variable | Symbol | Type | Value Range | |
---|---|---|---|---|
Minimum | Maximum | |||
Temperature (°C) | T | Independent | 20 | 600 |
Steel fiber (%) | FA | Independent | 1.5 | 2.0 |
PVA fiber (%) | FPVA | Independent | 0 | 0.5 |
Fluidity (mm) | Vr1 | Dependent | - | - |
Compressive strength (MPa) | Vr2 | Dependent | - | - |
Elasticity modulus (GPa) | Vr3 | Dependent | - | - |
Variable | Coded Variable | ||||
---|---|---|---|---|---|
−α | −1 | 0 | 1 | α | |
T | 20 | 138 | 310 | 482 | 600 |
FA | 1.50 | 1.60 | 1.75 | 1.90 | 2.00 |
FPVA | 0.00 | 0.10 | 0.25 | 0.40 | 0.50 |
Mix | Coded Variable | Experimental Values | |||||
---|---|---|---|---|---|---|---|
T | FA | FPVA | T (°C) | FA (%) | FPVA (%) | ||
Factorial points | T1 | −1 | −1 | −1 | 138 | 1.60 | 0.10 |
T2 | −1 | −1 | 1 | 138 | 1.60 | 0.40 | |
T3 | −1 | 1 | −1 | 138 | 1.90 | 0.10 | |
T4 | −1 | 1 | 1 | 138 | 1.90 | 0.40 | |
T5 | 1 | −1 | −1 | 482 | 1.60 | 0.10 | |
T6 | 1 | −1 | 1 | 482 | 1.60 | 0.40 | |
T7 | 1 | 1 | −1 | 482 | 1.90 | 0.10 | |
T8 | 1 | 1 | 1 | 482 | 1.90 | 0.40 | |
Axial points | T9 | −1.682 | 0 | 0 | 20 | 1.75 | 0.25 |
T10 | 1.682 | 0 | 0 | 600 | 1.75 | 0.25 | |
T11 | 0 | −1.682 | 0 | 310 | 1.50 | 0.25 | |
T12 | 0 | 1.682 | 0 | 310 | 2.00 | 0.25 | |
T13 | 0 | 0 | −1.682 | 310 | 1.75 | 0.00 | |
T14 | 0 | 0 | 1.682 | 310 | 1.75 | 0.50 | |
Center points | T15 | 0 | 0 | 0 | 310 | 1.75 | 0.25 |
T16 | 0 | 0 | 0 | 310 | 1.75 | 0.25 |
Mix | Consistence Index (Flow Table) | |
---|---|---|
Diameter (mm) | Classes (NF P-18 470 [17]) | |
1 and 5 | 203.33 | Ct |
2 and 6 | 175.40 | Ct |
3 and 7 | 257.93 | Cv |
4 and 8 | 162.40 | Ct |
9 | 278.05 | Ca |
10 | 251.70 | Cv |
11 | 204.45 | Ct |
12 | 191.23 | Ct |
13 | 250.80 | Cv |
14 | 215.08 | Ct |
15 and 16 | 328.53 | Ca |
Mix | Temp. (°C) | Steel (%) | PVA (%) | Resp. Surface fc* (MPa) | Experimental fc (MPa) |
---|---|---|---|---|---|
1 | 138 | 1.60 | 0.10 | 169.86 | 169.47 |
2 | 138 | 1.60 | 0.40 | 196.70 | 196.71 |
3 | 138 | 1.90 | 0.10 | 182.78 | 182.66 |
4 | 138 | 1.90 | 0.40 | 177.13 | 176.81 |
5 # | 482 | 1.60 | 0.10 | 156.15 | 155.76 |
6 # | 482 | 1.60 | 0.40 | 182.99 | 183.00 |
7 # | 482 | 1.90 | 0.10 | 169.07 | 168.95 |
8 # | 482 | 1.90 | 0.40 | 163.42 | 163.10 |
9 | 20 | 1.75 | 0.25 | 186.22 | 186.22 |
10 | 600 | 1.75 | 0.25 | 163.10 | 163.10 |
11 # | 310 | 1.50 | 0.25 | 163.25 | 163.25 |
12 # | 310 | 2.00 | 0.25 | 157.66 | 157.66 |
13 # | 310 | 1.75 | 0.00 | 183.14 | 229.29 |
14 # | 310 | 1.75 | 0.50 | 200.96 | 249.91 |
15 | 310 | 1.75 | 0.25 | 192.05 | 195.00 |
16 | 310 | 1.75 | 0.25 | 192.05 | 189.10 |
Factors | Sum of Squares (SS) | Degree of Freedom (df) | Mean Square (MS) | Fcalculated | p |
---|---|---|---|---|---|
(1) Temperature (°C) (L) | 643.130 | 1 | 643.130 | 221.45 | 0.000 |
Temperature (°C) (Q) | 315.872 | 1 | 315.872 | 121.16 | 0.000 |
(2) Steel (%) (L) | 38.150 | 1 | 38.150 | 13.14 | 0.011 |
Steel (%) (Q) | 1168.896 | 1 | 1168.896 | 402.50 | 0.000 |
(3) PVA (%) (L) | 387.631 | 1 | 387.631 | 133.48 | 0.000 |
PVA (%) (Q) | 0.000 | 1 | 0.000 | 0.00 | 1.000 |
1 L by 2 L | 0.000 | 1 | 0.000 | 0.00 | 1.000 |
1 L by 3 L | 0.000 | 1 | 0.000 | 0.00 | 1.000 |
2 L by 3 L | 547.022 | 1 | 547.022 | 188.36 | 0.000 |
Error | 17.425 | 6 | 2.904 | - | - |
Total SS | 3144.827 | 15 | - | - | - |
SS | df | MS | Fcalculated | Ftable | |
---|---|---|---|---|---|
Regression (SSR) | 3190.222 | 9 | 354.469 | 122.06 | 4.10 |
Residual | 17.425 | 6 | 2.904 | - | - |
Total (SST) | 3207.646 | 15 | - | - | - |
Author | Steel Fiber (%) | PVA Fiber (%) | 20 °C | 100 °C | 200 °C | 300 °C | 400 °C | 500 °C | 600 °C | 700 °C | 1049 °C |
---|---|---|---|---|---|---|---|---|---|---|---|
Sanchayan and Foster (2016) [27] | 2.00 | 0.00 | 170.00 | 176.15 | 188.68 | 172.87 | - | - | - | - | - |
1.50 | 0.50 | 150.00 | 158.88 | 183.06 | 187.50 | 143.59 | 87.34 | 80.92 | 41.94 | - | |
1.00 | 1.00 | 158.00 | 163.20 | 170.46 | 161.12 | 141.89 | 50.93 | 48.51 | 30.14 | - | |
0.50 | 1.50 | 145.00 | 143.57 | 163.60 | 150.72 | 117.81 | 87.29 | 59.62 | 31.00 | - | |
0.00 | 2.00 | 134.00 | 146.34 | 152.07 | 134.88 | 92.57 | 72.29 | - | - | - | |
Park et al. (2019) [15] | 1.50 | 0.20 | 192.00 | - | - | - | - | - | - | - | 11.80 |
1.50 | 0.30 | 194.00 | - | - | - | - | - | - | - | 17.40 | |
Equation (3) | 2.00 | 0.00 | 165.88 | 170.97 | 173.60 | 172.09 | - | - | - | - | - |
1.50 | 0.50 | 189.30 | 194.38 | 197.02 | 195.51 | 189.87 | 180.10 | 166.19 | 148.14 | - | |
1.00 | 1.00 | 143.73 | 148.81 | 151.44 | 149.94 | 144.30 | 134.52 | 120.61 | 102.57 | - | |
0.50 | 1.50 | 29.17 | 34.25 | 36.88 | 35.38 | 29.74 | 19.96 | 6.05 | −11.99 | - | |
0.00 | 2.00 | −154.38 | −149.30 | −146.67 | −148.17 | −153.81 | −163.58 | - | - | - | |
1.50 | 0.20 | 151.04 | - | - | - | - | - | - | - | 14.50 | |
1.50 | 0.30 | 163.80 | - | - | - | - | - | - | - | 27.25 |
Mix | Temp. (°C) | Steel (%) | PVA (%) | Resp. Surface E* (GPa) | Experimental E (GPa) |
---|---|---|---|---|---|
1 | 138 | 1.60 | 0.10 | 48.78 | 48.83 |
2 | 138 | 1.60 | 0.40 | 59.53 | 59.71 |
3 | 138 | 1.90 | 0.10 | 46.92 | 46.98 |
4 | 138 | 1.90 | 0.40 | 50.97 | 51.04 |
5 # | 482 | 1.60 | 0.10 | 17.76 | 17.93 |
6 # | 482 | 1.60 | 0.40 | 0.72 | - |
7 # | 482 | 1.90 | 0.10 | 15.89 | 16.08 |
8 # | 482 | 1.90 | 0.40 | −7.85 | - |
9 | 20 | 1.75 | 0.25 | 44.27 | 44.27 |
10 # | 600 | 1.75 | 0.25 | −31.47 | - |
11 # | 310 | 1.50 | 0.25 | 38.27 | 38.27 |
12 # | 310 | 2.00 | 0.25 | 29.50 | 29.50 |
13 | 310 | 1.75 | 0.00 | 53.13 | 53.13 |
14 | 310 | 1.75 | 0.50 | 42.21 | 42.21 |
15 | 310 | 1.75 | 0.25 | 33.89 | 36.91 |
16 | 310 | 1.75 | 0.25 | 33.89 | 30.86 |
Factors | Sum of Squares (SS) | Degree of freedom (df) | Mean Square (MS) | Fcalculated | p |
---|---|---|---|---|---|
(1) Temperature (°C) (L) | 6904.215 | 1 | 6904.215 | 2263.52 | 0.000 |
Temperature (°C) (Q) | 878.985 | 1 | 878.985 | 288.17 | 0.000 |
(2) Steel (%) (L) | 93.762 | 1 | 93.762 | 30.74 | 0.001 |
Steel (%) (Q) | 0.000 | 1 | 0.000 | 0.00 | 1.000 |
(3) PVA (%) (L) | 145.481 | 1 | 145.481 | 47.70 | 0.000 |
PVA (%) (Q) | 222.534 | 1 | 222.534 | 72.96 | 0.000 |
1 L by 2 L | 0.000 | 1 | 0.000 | 0.00 | 1.000 |
1 L by 3 L | 393.233 | 1 | 393.233 | 128.92 | 0.000 |
2 L by 3 L | 23.256 | 1 | 23.256 | 7.62 | 0.033 |
Error | 18.301 | 6 | 3.050 | - | - |
Total SS | 9381.874 | 15 | - | - | - |
SS | df | MS | Fcalculated | Ftable | |
---|---|---|---|---|---|
Regression (SSR) | 9363.572 | 9 | 1040.397 | 341.09 | 4.10 |
Residual | 18.301 | 6 | 3.050 | - | - |
Total (SST) | 9381.874 | 15 | - | - | - |
Author | Steel Fiber (%) | Polymeric Fiber (%) | Elasticity Modulus, in GPa (Exposure Temperature in °C) | |||
---|---|---|---|---|---|---|
Room Temperature | 20 °C~200 °C | 200 °C~400 °C | 400 °C~600 °C | |||
Sanchayan and Foster (2016) [27] | 2.00 | - | 46.30 | 45.92 (200 °C) | 43.09 (300 °C) | - |
1.00 | 1.00 (PVA) | 42.10 | 42.27 (200 °C) | 36.94 (300 °C) | 6.53 (600 °C) | |
- | 2.00 (PVA) | 40.80 | 37.30 (200 °C) | 33.64 (300 °C) | - | |
Rasul, M.; Ahmad, S.; Adekunle, S.K.; Al-Dulaijan, S.U.; Maslehuddin, M.; Ali, S.I. [36] | - | 0.26 (PP) | 47.81 | - | 45.00 (300 °C) | - |
- | 0.52 (PP) | 47.25 | - | 43.13 (300 °C) | - | |
- | 0.78 (PP) | 43.50 | - | 43.88 (300 °C) | - | |
- | 1.04 (PP) | 46.13 | - | 39.38 (300 °C) | - |
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Sumitomo, G.S.; Pimentel, L.L.; Jacintho, A.E.P.G.A.; Forti, N.C.S. Study of Ultra-High Performance Concrete Mechanical Behavior under High Temperatures. Materials 2024, 17, 4212. https://doi.org/10.3390/ma17174212
Sumitomo GS, Pimentel LL, Jacintho AEPGA, Forti NCS. Study of Ultra-High Performance Concrete Mechanical Behavior under High Temperatures. Materials. 2024; 17(17):4212. https://doi.org/10.3390/ma17174212
Chicago/Turabian StyleSumitomo, Guilherme S., Lia L. Pimentel, Ana Elisabete P. G. A. Jacintho, and Nadia C. S. Forti. 2024. "Study of Ultra-High Performance Concrete Mechanical Behavior under High Temperatures" Materials 17, no. 17: 4212. https://doi.org/10.3390/ma17174212
APA StyleSumitomo, G. S., Pimentel, L. L., Jacintho, A. E. P. G. A., & Forti, N. C. S. (2024). Study of Ultra-High Performance Concrete Mechanical Behavior under High Temperatures. Materials, 17(17), 4212. https://doi.org/10.3390/ma17174212