The Nature-Inspired Metaheuristic Method for Predicting the Creep Strain of Green Concrete Containing Ground Granulated Blast Furnace Slag
Abstract
:1. Introduction
2. Experimental Setup
2.1. Materials
2.2. Methods
2.3. Statistical Analysis of the Database
3. Numerical Analysis
3.1. Selection of the Optimum Structure of the ANN Model
3.2. Results of Learning, Testing and Cross-Validation of the FA-ANN
3.3. Validation of the FA-ANN Model
4. Conclusions
- It is possible to predict the creep strain of green concrete with GGBFS using artificial neural networks (ANN) and the nature-inspired metaheuristic firefly algorithm (FA).
- A reliable prediction can be conducted based on the parameters of GGBFS concrete, which characterize the composition of the concrete mixture and selected rheological properties. For this purpose, the cement content, GGBFS content, water-to-binder ratio, fine aggregate content, coarse aggregate content, slump, the compaction factor of concrete and the age after loading were used as the input parameters, and in turn the creep strain (εcr) of GGBFS concrete was considered as the output parameter.
- The ANN model optimized by the FA was able to predict the value of εcr with a very high level of accuracy. The obtained values of determination coefficient (R2) were equal to 0.99 in training, cross-validation and testing.
- The performance of the FA-ANN was compared with other commonly used algorithms such as the imperialist competitive algorithm (ICA), genetic algorithm (GA) and particle swarm optimization (PSO). The obtained results indicated that the ANN model optimized by the FA was more accurate and provided more precision than other models.
Author Contributions
Funding
Conflicts of Interest
References
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Characteristic | Experimental Value | |
---|---|---|
Cement | GGBFS | |
Blaine’s fineness (m2/kg) | 245 | 340 |
Specific gravity | 3.15 | 2.86 |
Soundness (mm) | 1.5 | 1.5 |
Compressive strength (MPa) | 45.9 | 40 (with 30% GGBFS) |
Normal Consistency (%) OPC + 0% GGBFS OPC + 20% GGBFS OPC + 40% GGBFS OPC + 60% GGBFS | 27.0 28.5 29.5 31.0 |
Name of Oxide | Cement (%) | GGBFS |
---|---|---|
CaO SiO2 Al2O3 Fe2O3 MgO Na2O K2O P2O5 TiO2 MnO Glass content | 63.71 22.18 07.35 03.82 0.95 0.28 0.11 0.05 0.27 0.04 - | 38.01 37.88 14.23 0.38 9.1 0.26 0.15 0.01 0.34 0.07 91.0 |
Mix Group | Mix Designation | Cement | GGBFS | Aggregates (kg/m3) | Water-Binder Ratio | |
---|---|---|---|---|---|---|
(kg/m3) | (kg/m3) | Fine | Coarse | |||
M1 | M10 M11 M12 M13 | 400 320 240 160 | 0 80 160 240 | 665 | 1107 | 0.45 |
M2 | M20 M21 M22 M23 | 350 280 210 140 | 0 70 140 210 | 680 | 1132 | 0.50 |
M3 | M30 M31 M32 M33 | 320 256 192 128 | 0 64 128 192 | 688 | 1145 | 0.55 |
No. | Age t (days) | Cement Content C(kg/m3) | GGBFS Content G(kg/m3) | Water-to-Binder Ratio w/b (-) | Fine Aggregate Content Fa (kg/m3) | Coarse Aggregate Content Ca (kg/m3) | Slump S(mm) | Compaction Factor CF (-) | Creep Strain |
---|---|---|---|---|---|---|---|---|---|
1 | 0 | 400 | 0 | 0.45 | 665 | 1107 | 41 | 0.9 | 106 |
2 | 1 | 400 | 0 | 0.45 | 665 | 1107 | 41 | 0.9 | 123 |
3 | 3 | 400 | 0 | 0.45 | 665 | 1107 | 41 | 0.9 | 145 |
4 | 7 | 400 | 0 | 0.45 | 665 | 1107 | 41 | 0.9 | 162 |
5 | 14 | 400 | 0 | 0.45 | 665 | 1107 | 41 | 0.9 | 181 |
6 | 21 | 400 | 0 | 0.45 | 665 | 1107 | 41 | 0.9 | 196 |
7 | 28 | 400 | 0 | 0.45 | 665 | 1107 | 41 | 0.9 | 204 |
8 | 56 | 400 | 0 | 0.45 | 665 | 1107 | 41 | 0.9 | 235 |
9 | 90 | 400 | 0 | 0.45 | 665 | 1107 | 41 | 0.9 | 261 |
… | … | … | … | … | … | … | … | … | … |
132 | 150 | 128 | 192 | 0.55 | 688 | 1145 | 61 | 0.96 | 937 |
Symbol and Name of Parameter | Statistical Characteristics | Shapiro–Wilk Test Results W | |||
---|---|---|---|---|---|
Mean | Minimum | Maximum | Standard Deviation | ||
t - age after loading (days) | 44.54 | 0.00 | 150.00 | 50.26 | 0.796 |
C - cement content (kg/m3) | 249.67 | 128.00 | 400.00 | 83.67 | 0.905 |
G – GGBFS content (kg/m3) | 107.00 | 0.00 | 240.00 | 80.70 | 0.793 |
w/b – water-to-binder ratio (-) | 0.50 | 0.45 | 0.55 | 0.04 | 0.769 |
Fa - fine aggregate content (kg/m3) | 677.67 | 665.00 | 688.00 | 9.53 | 0.767 |
Ca - coarse aggregate content (kg/m3) | 1128.00 | 1107.00 | 1145.00 | 15.77 | 0.937 |
S - slump (mm) | 50.33 | 41.00 | 61.00 | 5.78 | 0.834 |
CF - compaction factor (-) | 0.92 | 0.90 | 0.96 | 0.02 | 0.935 |
-creep strain (μm/m) | 358.98 | 106.00 | 937.00 | 172,55 | 0.937 |
Symbol and Name of Parameter | ρs | τ | F |
---|---|---|---|
t - age after loading (days) | 0.597 | 0.453 | 66.34 |
C - cement content (kg/m3) | 0.788 | 0.612 | 13.14 |
G – GGBFS content (kg/m3) | −0.473 | −0.345 | 11.36 |
w/b – water-to-binder ratio (-) | 0.282 | 0.199 | 27.17 |
Fa - fine aggregate content (kg/m3) | 0.437 | 0.342 | 27.16 |
Ca - coarse aggregate content (kg/m3) | 0.437 | 0.342 | 27.16 |
S - slump (mm) | 0.437 | 0.342 | 27.25 |
CF - compaction factor (-) | 0.543 | 0.405 | 26.67 |
FA | GA | ICA | PSO | ||||
---|---|---|---|---|---|---|---|
Attraction coefficient | 0.5 | Population | 150 | Number of initial countries | 500 | Swarm size | 100 |
Mutation coefficient | 0.9 | Mutation rate | 15 | Number of initial imperialists | 50 | ||
Number of fireflies | 10 | Crossover rate | 50 | Assimilation angle coefficient(β) | 2 | Cognition coefficient | 2 |
Radius reduction factor | 0.95 | Angle coefficient (γ) | 0.5 | Social coefficient | 2 | ||
Generation | 50 | Generation | 50 | Generation | 50 | Generation | 50 |
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Sadowski, Ł.; Nikoo, M.; Shariq, M.; Joker, E.; Czarnecki, S. The Nature-Inspired Metaheuristic Method for Predicting the Creep Strain of Green Concrete Containing Ground Granulated Blast Furnace Slag. Materials 2019, 12, 293. https://doi.org/10.3390/ma12020293
Sadowski Ł, Nikoo M, Shariq M, Joker E, Czarnecki S. The Nature-Inspired Metaheuristic Method for Predicting the Creep Strain of Green Concrete Containing Ground Granulated Blast Furnace Slag. Materials. 2019; 12(2):293. https://doi.org/10.3390/ma12020293
Chicago/Turabian StyleSadowski, Łukasz, Mehdi Nikoo, Mohd Shariq, Ebrahim Joker, and Sławomir Czarnecki. 2019. "The Nature-Inspired Metaheuristic Method for Predicting the Creep Strain of Green Concrete Containing Ground Granulated Blast Furnace Slag" Materials 12, no. 2: 293. https://doi.org/10.3390/ma12020293