Experimental and Statistical Analysis of Concrete Eco-Cobble Using Organic and Synthetic Fibers
Abstract
:1. Introduction
1.1. Overview
1.2. Literature Review
1.2.1. Coconut Fiber in Concrete
1.2.2. Synthetic Fibers in Concrete
1.2.3. Natural Fibers and Composite Materials in Concrete
1.3. Aim of This Work and Scientific Contributions
2. Materials and Methods
2.1. Main Properties of the Materials Used
2.2. Fiber Properties and Impact
2.3. Technical Standards Used
2.4. Experimental Design
- Concrete: 90% (low) to 100% (high), with a 10% variation (∆%).
- Coconut Fiber: 0% (low) to 10% (high).
- PET Fiber: 0% (low) to 10% (high).
- ➢
- Fiber Type and Dosage: The design mixes were selected to evaluate the effects of different types and amounts of fibers on the performance of the eco-cobble. Various fiber dosages were tested, ranging from 0% to 10% for both coconut and PET fibers, to assess their influence on strength, durability, and workability. This approach allowed us to identify the optimal mix that balances mechanical performance and sustainability.
- ➢
- Comparative Analysis: The mixes were selected to provide a comparative analysis between different fiber combinations. This selection enabled a direct comparison between the effects of PET fibers (synthetic) and coconut fibers (natural) on the material’s properties, offering insights into the advantages and limitations of each fiber type.
- ➢
- Consistency in Testing: Some design mixes are repeated to ensure testing consistency and verify the reproducibility of results. Repeated testing of specific mixes helps confirm the reliability of the data and identify any variability that might occur during the experimentation process.
- ➢
- Quality Control: Repeating mixes also serves as a quality control measure to ensure that the results are robust and not affected by anomalies in the preparation or testing procedures. This repetition helps validate the experimental results and refine the conclusions drawn from the data.
- ➢
- Incremental Analysis: Repeating certain mixes with slight variations allows for a detailed comparative evaluation of how different fiber content affects the performance metrics. This point is particularly useful for analyzing the incremental impact of adding or altering fiber types in the mixture.
2.5. Granulometric Analysis of Coarse and Fine Aggregates (INV E-213)
- The sieves with openings of 1 ½″, 1″, 3/4″, 1/2″, 3/8″, No. 4, and bottom are used to separate the coarse aggregate.
- Then, the retained weights on each sieve are obtained, which is the amount of material in grams retained on each sieve.
- The retained percentage is calculated using Equation (1), which indicates that the retained weight of each sieve should be divided by the total weight of the sample. For the sample under study, a weight of 6010.6 gr was used. Below is the step-by-step calculation for the retained percentage for the 1 ½″ and 1″ sieves.
- The accumulated withheld percentage is the sum of the previous withheld percentages.
- The percentage that passes (% Pass) subtracts 100% minus each accumulated percentage withheld.
- The use of sieves with openings of 3/4″, 1/2″, 3/8″, No. 4, No. 8, No. 16, No. 30, No. 50, No. 100, No. 200, and background is used for fine aggregate.
- Afterward, the weight retained in each sieve is obtained. This weight is the amount of grams of material retained in each sieve.
- The percentage retained is calculated by dividing the retained weight of each sieve by the total weight of the sample, with a total weight of 1556.2 gr. Then, Equation (1) is used again.
- The accumulated withheld percentage is the sum of the previous withheld percentages.
- The percentage that passes is the subtraction of 100% minus each accumulated percentage withheld.
2.6. Cobble Development
2.7. Mechanical Tests
2.8. Statistical Analysis
- ➢
- Design of Experiments: A central composite design (CCD) was used to systematically vary the levels of PET and coconut fibers in the mixtures. This design allows for the evaluation of quadratic effects and interaction effects between the variables.
- ➢
- Model Fitting: The collected data were fitted to a second-order polynomial model to create response surfaces. This model aids in visualizing how changes in fiber dosages affect the mechanical properties and in identifying optimal conditions for desired performance.
- ➢
- Optimization: RSM was used to identify the optimal combination of PET and coconut fiber dosages that maximize the desired properties (e.g., compressive strength, flexural strength) while minimizing undesirable attributes (e.g., water absorption); this analysis is based on predictive equations.
3. Results and Discussions
3.1. Mechanical Test Results
3.2. Statistical Analysis Results
3.2.1. ANOVA for the Analyzed Variables
3.2.2. Quadratic of Results for Model Adjustment
3.2.3. Response Surface Methodology (RSM)
Response Surface Methodology (RSM) for Compression at 14 and 28 Days
RSM for Flexure at 14 and 28 Days
RSM for Absorption
3.3. Response Optimization According to Statgraphics
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Symbology Lists
PET: Polyethylene Terephthalate |
COMP: Compressive Strength |
CAR.MAX: Maximum Load Capacity |
TEN: Tension/Flexure |
E = Modulus of elasticity (MPa) |
ν = Poisson’s ratio |
fc′ = Compressive strength (MPa) |
ϵ = Unit strain |
σ = Stress (MPa) |
τ = Shear stress (MPa) |
G = Shear modulus (MPa) |
ρ = Density (kg/m3) |
ϕ = Diameter (mm) |
d = Effective diameter (mm) |
A = Area (mm2) |
L = Length (mm) |
V = Volume (mm3) |
t = thickness (mm) |
P = Load (N) |
M = Bending moment (N mm) |
Q = Shear force (N) |
k = Thermal conductivity coefficient (W/m K) |
Cp = Heat capacity (J/kg K) |
α = Coefficient of thermal expansion (1/K) |
T = Temperature (K) |
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Mixture | Concrete (%) | F. Coconut (%) | F. PET (%) |
---|---|---|---|
1 | 95.0 | 5.0 | 0.0 |
2 | 100.0 | 0.0 | 0.0 |
3 | 95.0 | 0.0 | 5.0 |
4 | 91.667 | 1.667 | 6.667 |
5 | 93.333 | 3.333 | 3.333 |
6 | 90.0 | 5.0 | 5.0 |
7 | 90.0 | 0.0 | 10.0 |
8 | 96.667 | 1.667 | 1.667 |
9 | 90.0 | 10.0 | 0.0 |
10 | 91.667 | 6.667 | 1.667 |
11 | 100.0 | 0.0 | 0.0 |
12 | 90.0 | 10.0 | 0.0 |
13 | 90.0 | 0.0 | 10.0 |
14 | 95.0 | 5.0 | 0.0 |
15 | 95.0 | 0.0 | 5.0 |
16 | 90.0 | 5.0 | 5.0 |
17 | 93.333 | 3.333 | 3.333 |
18 | 100.0 | 0.0 | 0.0 |
19 | 90.0 | 10.0 | 0.0 |
20 | 90.0 | 0.0 | 10.0 |
Mixture | Dosage (Kg%) | Cobble Number | Test Amount | 14 Days | 28 Days |
---|---|---|---|---|---|
1 | 95 + 5 + 0 | 2 | 3 | 6 | 6 |
2 | 100 + 0 + 0 | 3 | 3 | 9 | 9 |
3 | 95 + 0 + 5 | 2 | 3 | 6 | 6 |
4 | 91.6 + 1.6 + 6.6 | 1 | 3 | 3 | 3 |
5 | 93.3 + 3.3 + 3.3 | 2 | 3 | 6 | 6 |
6 | 90 + 5 + 5 | 2 | 3 | 6 | 6 |
7 | 90 + 0 + 10 | 3 | 3 | 9 | 9 |
8 | 96.6 + 1.6 + 1.6 | 1 | 3 | 3 | 3 |
9 | 90 + 10 + 0 | 3 | 3 | 9 | 9 |
10 | 91.6 + 6.6 + 1.6 | 1 | 3 | 3 | 3 |
- | - | - | Total | 60 | 60 |
Property | Equation | Equation No. | Result | |
---|---|---|---|---|
Fine | Coarse | |||
Density | (2) | 1281.234 kg/m3 | ||
Degradation resistance | (3) | 9.04% | ||
Relative density | (4) | 1.227 | 1.4528 | |
Apparent density | (5) | 1548.484 | 1456.653 | |
Absorption | (6) | 17.046 | 1127 |
Mixture | Concrete (%) | F. Coconut (%) | F. PET (%) | Compression Resistance | Flexural Strength | Absorption (%) | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
14 Days (MPa) | Max. Load. (Psi) | 28 Days (MPa) | Max. Load. (Psi) | 14 Days (MPa) | Max. Load. (Psi) | 28 Days (MPa) | Max. Load. (Psi) | |||||
1 | 95 | 5 | 0 | 16.6 | 339.7 | 14.9 | 311.5 | 7.6 | 19.9 | 1.4 | 8.1 | 5.75 |
2 | 100 | 0 | 0 | 19.3 | 386.5 | 14.5 | 303.9 | 2.8 | 6.9 | 3.4 | 19.8 | 6.22 |
3 | 95 | 0 | 5 | 26.8 | 561.7 | 17.2 | 361.1 | 2.4 | 19.9 | 3.7 | 20.7 | 4.07 |
4 | 92 | 2 | 7 | 14.7 | 301.5 | 16.3 | 344.0 | 2.5 | 7.0 | 3.2 | 19.0 | 4.93 |
5 | 93 | 3 | 3 | 17.2 | 363.6 | 19.7 | 414.1 | 3.0 | 8.4 | 3.5 | 18.2 | 4.36 |
6 | 90 | 5 | 5 | 14.1 | 297.7 | 9.10 | 187.6 | 6.3 | 17.0 | 3.2 | 17.5 | 5.34 |
7 | 90 | 0 | 10 | 15.1 | 318.0 | 19.1 | 392.7 | 2.1 | 17.7 | 2.9 | 18.4 | 3.50 |
8 | 97 | 2 | 2 | 12.4 | 255.0 | 13.0 | 270.5 | 6.6 | 17.1 | 3.2 | 17.8 | 5.73 |
9 | 90 | 10 | 0 | 15.1 | 310.3 | 19.8 | 414.0 | 6.5 | 17.3 | 3.5 | 18.0 | 6.05 |
10 | 92 | 7 | 2 | 20.6 | 412.7 | 19.9 | 415.8 | 5.7 | 15.4 | 3.2 | 19.0 | 5.65 |
11 | 100 | 0 | 0 | 18.9 | 379.5 | 14.5 | 307.1 | 6.4 | 16.1 | 3.4 | 18.8 | 5.90 |
12 | 90 | 10 | 0 | 14.1 | 295.0 | 21.1 | 442.9 | 5.7 | 15.4 | 3.1 | 17.1 | 6.25 |
13 | 90 | 0 | 10 | 11.9 | 249.2 | 19.0 | 389.5 | 2.2 | 17.4 | 3.2 | 19.0 | 3.28 |
14 | 95 | 5 | 0 | 11.5 | 235.0 | 20.3 | 423.7 | 6.5 | 17.6 | 3.6 | 21.0 | 5.54 |
15 | 95 | 0 | 5 | 21.1 | 440.1 | 28.7 | 598.9 | 1.4 | 12.0 | 3.6 | 21.0 | 4.39 |
16 | 90 | 5 | 5 | 16.7 | 348.8 | 12.5 | 267.2 | 5.7 | 17.4 | 3.4 | 19.6 | 5.06 |
17 | 93 | 3 | 3 | 15.6 | 327.0 | 20.1 | 413.4 | 6.4 | 18.6 | 3.1 | 17.5 | 4.68 |
18 | 100 | 0 | 0 | 19.0 | 391.0 | 15.2 | 316.3 | 6.0 | 14.8 | 3.6 | 20.2 | 6.06 |
19 | 90 | 10 | 0 | 12.8 | 259.8 | 13.0 | 273.5 | 5.5 | 16.3 | 3.1 | 19.4 | 6.15 |
20 | 90 | 0 | 10 | 13.9 | 284.9 | 13.6 | 280.0 | 2.6 | 20.1 | 3.2 | 18.5 | 3.39 |
Test | Source | Sum of Squares | Gl | Middle Square | F-Ratio | p-Value | |
---|---|---|---|---|---|---|---|
COMPRESSION (MPa) | 14 days | Half | 5388.06 | 1 | 5388.06 | - | - |
Linear | 54.64 | 2 | 27.32 | 2.18 | 0.1438 | ||
Quadratic | 83.21 | 3 | 27.73 | 2.99 | 0.0672 | ||
Special Cubic | 8.31 | 1 | 8.31 | 0.89 | 0.3634 | ||
Error | 121.74 | 13 | 9.36 | - | - | ||
Total | 5655.97 | 20 | - | - | - | ||
28 days | Half | 5855.73 | 1 | 5855.73 | - | - | |
Linear | 0.78 | 2 | 0.39 | 0.02 | 0.9813 | ||
Quadratic | 149.62 | 3 | 49.87 | 3.42 | 0.0471 | ||
Special Cubic | 4.68 | 1 | 4.68 | 0.30 | 0.5902 | ||
Error | 199.65 | 13 | 15.36 | - | - | ||
Total | 6210.47 | 20 | - | - | - | ||
FLEXURE (MPa) | 14 days | Half | 448.31 | 1 | 448.31 | - | - |
Linear | 42.49 | 2 | 21.24 | 10.48 | 0.0011 | ||
Quadratic | 14.18 | 3 | 4.73 | 3.27 | 0.0532 | ||
Special Cubic | 0.24 | 1 | 0.25 | 0.16 | 0.6935 | ||
Error | 20.01 | 13 | 1.54 | - | - | ||
Total | 525.25 | 20 | - | - | - | ||
28 days | Half | 199.27 | 1 | 199.27 | - | - | |
Linear | 0.44 | 2 | 0.22 | 0.60 | 0.5616 | ||
Quadratic | 5.21 | 3 | 1.74 | 21.45 | 0.0000 | ||
Special Cubic | 0.60 | 1 | 0.60 | 14.70 | 0.0021 | ||
Error | 0.53 | 13 | 0.04 | - | - | ||
Total | 206.06 | 20 | - | - | - | ||
ABSORPTION (%) | Half | 523.26 | 1 | 523.26 | - | ||
Linear | 16.08 | 2 | 8.04 | 53.76 | 0.0000 | ||
Quadratic | 1.17 | 3 | 0.39 | 4.00 | 0.0298 | ||
Special Cubic | 0.05 | 1 | 0.05 | 0.57 | 0.4648 | ||
Error | 1.31 | 13 | 0.10 | - | - | ||
Total | 541.89 | 20 | - | - | - |
Test | Source | Sum of Squares | Gl | Middle Square | F-Ratio | p-Value | |
---|---|---|---|---|---|---|---|
COMPRESSION (MPa) | 14 | Quadratic Model | 137.85 | 5 | 27.57 | 2.97 | 0.0495 |
Total error | 130.05 | 14 | 9.28 | - | - | ||
Total (corr.) | 267.91 | 19 | - | - | - | ||
28 | Quadratic Model | 150.41 | 5 | 30.08 | 2.06 | 0.1316 | |
Total error | 204.33 | 14 | 14.59 | - | - | ||
Total (corr.) | 354.74 | 19 | - | - | - | ||
FLEXURE (MPa) | 14 | Quadratic Model | 56.68 | 5 | 11.33 | 7.830 | 0.0011 |
Total error | 20.26 | 14 | 1.44 | - | - | ||
Total (corr.) | 76.94 | 19 | - | - | - | ||
28 | Quadratic Model | 5.65 | 5 | 1.13 | 13.97 | 0.0001 | |
Total error | 1.13 | 14 | 0.08 | - | - | ||
Total (corr.) | 6.79 | 19 | - | - | - | ||
ABSORPTION (%) | Quadratic Model | 17.25 | 5 | 3.45 | 35.31 | 0.0000 | |
Total error | 1.36 | 14 | 0.09 | - | - | ||
Total (corr.) | 18.62 | 19 | - | - | - |
Test | Parameter | Error | Statistics | |||
---|---|---|---|---|---|---|
Estimated | Standard | T | p-Value | |||
COMPRESSION | 14 days | A | 18.63 | 1.73 | - | - |
B | 14.84 | 1.73 | - | - | ||
C | 13.53 | 1.73 | - | - | ||
AB | −13.18 | 9.08 | −1.45 | 0.1687 | ||
AC | 23.60 | 9.08 | 2.59 | 0.0210 | ||
BC | 4.80 | 9.08 | 0.52 | 0.6054 | ||
28 days | A | 14.10 | 2.17 | - | - | |
B | 18.35 | 2.17 | - | - | ||
C | 17.10 | 2.17 | - | - | ||
AB | 7.17 | 11.38 | 0.63 | 0.5387 | ||
AC | 27.96 | 11.38 | 2.45 | 0.0277 | ||
BC | −23.05 | 11.38 | −2.02 | 0.0624 | ||
FLEXURE | 14 days | A | 5.29 | 0.68 | - | - |
B | 5.90 | 0.68 | - | - | ||
C | 2.24 | 0.68 | - | - | ||
AB | 6.04 | 3.58 | 1.68 | 0.1139 | ||
AC | −7.22 | 3.58 | −2.01 | 0.0636 | ||
BC | 6.34 | 3.58 | 1.76 | 0.0985 | ||
28 days | A | 3.47 | 0.16 | - | - | |
B | 3.26 | 0.16 | - | - | ||
C | 3.06 | 0.16 | - | - | ||
AB | −6.25 | 0.84 | −7.36 | 0.0000 | ||
AC | 2.52 | 0.84 | 2.97 | 0.0100 | ||
BC | 1.43 | 0.84 | 1.69 | 0.1119 | ||
ABSORPTION | A | 6.09 | 0.17 | - | - | |
B | 6.14 | 0.17 | - | - | ||
C | 3.45 | 0.17 | - | - | ||
AB | −2.07 | 0.93 | −2.22 | 0.0432 | ||
AC | −1.93 | 0.93 | −2.07 | 0.0564 | ||
BC | 1.58 | 0.93 | 1.70 | 0.1110 |
Statistic | COMPRESSION (MPa) | FLEXURE (MPa) | ABSORPTION (%) | ||
---|---|---|---|---|---|
14 | 28 | 14 | 28 | ||
R2 (%) | 51.45 | 42.39 | 73.66 | 83.30 | 92.65 |
R2 (adjusted by G.l.)% | 34.11 | 21.82 | 64.26 | 77.33 | 90.03 |
Standard Error | 3.04 | 3.82 | 1.20 | 0.28 | 0.31 |
MAE | 1.87 | 2.69 | 0.77 | 0.20 | 0.18 |
Durbin-Watson Statistic | 1.63 | 2.01 | 1.23 | 2.29 | 2.31 |
p = 0.2131 | p = 0.5151 | p = 0.0434 | p = 0.7395 | p = 0.7501 |
Days | Compression (MPa) | Max. Load (MPa) |
---|---|---|
14 | ||
28 |
Days | Compression (MPa) | Max. Load (MPa) |
---|---|---|
14 | ||
28 |
Test | Concrete (%) | F. Coconut (%) | F. PET (%) |
---|---|---|---|
Compression 14 days | 96.08 | 1.8 × 10−8 | 3.92 |
Compression 28 days | 94.46 | 5.53 × 10−9 | 5.55 |
Flexure 14 days | 94.49 | 5.50 | 3.51 × 10−9 |
Flexure 28 days | 95.82 | 1.96 × 10−9 | 4.17 |
FLEXURE (MPa) | 14 | |
28 | ||
COMPRESSION (MPa) | 14 | |
28 | ||
ABSORPTION (%) |
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García-León, R.A.; Trigos-Caceres, J.; Castilla-Quintero, N.; Afanador-García, N.; Gómez-Camperos, J. Experimental and Statistical Analysis of Concrete Eco-Cobble Using Organic and Synthetic Fibers. Processes 2024, 12, 1936. https://doi.org/10.3390/pr12091936
García-León RA, Trigos-Caceres J, Castilla-Quintero N, Afanador-García N, Gómez-Camperos J. Experimental and Statistical Analysis of Concrete Eco-Cobble Using Organic and Synthetic Fibers. Processes. 2024; 12(9):1936. https://doi.org/10.3390/pr12091936
Chicago/Turabian StyleGarcía-León, Ricardo Andrés, Jorge Trigos-Caceres, Natalia Castilla-Quintero, Nelson Afanador-García, and July Gómez-Camperos. 2024. "Experimental and Statistical Analysis of Concrete Eco-Cobble Using Organic and Synthetic Fibers" Processes 12, no. 9: 1936. https://doi.org/10.3390/pr12091936
APA StyleGarcía-León, R. A., Trigos-Caceres, J., Castilla-Quintero, N., Afanador-García, N., & Gómez-Camperos, J. (2024). Experimental and Statistical Analysis of Concrete Eco-Cobble Using Organic and Synthetic Fibers. Processes, 12(9), 1936. https://doi.org/10.3390/pr12091936