# Multi-Objective Taguchi Optimization of Cement Concrete Incorporating Recycled Mixed Plastic Fine Aggregate Using Modified Fuller’s Equation

^{*}

## Abstract

**:**

^{4}) Taguchi orthogonal array with four three-level design factors was adopted to optimize the fresh, durability, and mechanical properties of MPFA concrete. The results showed that MPFA concrete produced with 400 kg/m

^{3}cement content, 0.43 water/cement ratio, 0.43 fine aggregate/total aggregate ratio, and 10 vol% MPFA content exhibited the highest quality. Findings from the present work also revealed that MPFA concrete produced with tailored particle size distribution of MPFA NS fine aggregate system achieved superior, if not comparable, qualities to those of conventional concrete.

## 1. Introduction

#### 1.1. Plastic Waste in Concrete

#### 1.2. Past Optimization Studies

#### 1.3. Research Significance

## 2. Materials and Methods

#### 2.1. Materials

^{2}/g was supplied by EnGro Co. Limited, Singapore. The chemical composition of the PC provided by the supplier is listed in Table 1. NS and 20-mm granite gravel with a specific gravity ranging between 2.60 and 2.65, provided by Buildmate (Singapore) Pte Ltd., were used as fine (FA) and coarse aggregate (CA). A polycarboxylate-based high-range water-reducer superplasticizer (SP) manufactured by Mapei Singapore was used in this study. The plastic wastes of different polymer types were sourced from local plastic recycling companies and mixed into a predetermined concoction to replicate the composition of mixed plastic waste in the postconsumer waste streams. The blended mixed plastic waste was then extruded and pelletized into MPFA with sizes ranging between 2 to 4 mm using a twin-screw thermal extruder, as shown in Figure 1.

#### 2.2. Sample Preparation

#### 2.3. Laboratory Tests

#### 2.4. BWM–Taguchi Multi-Objective Optimization Framework

**Step 1.**Define optimization objectives and quality criteria (QC) $({qc}_{1},q{c}_{2},\dots ,q{c}_{n})$ to facilitate the multi-criteria decision-making process. Specify appropriate design factors and levels with overarching impacts on QC for the design of the experiment.

**Step 2.**Identify one best (highest priority) and one worst (lowest priority) criterion based on experts’ preferences. Carry out a pairwise comparison between the best criterion against other criteria and other criteria against the worst criterion by assigning a number between 1 to 9 to obtain the best-to-others (BO) and others-to-worst (OW) vectors, respectively. The resultant BO and OW vectors are expressed in Equations (3) and (4), respectively.

**Step 3.**Compute optimal weights $({w}_{1}^{\prime},{w}_{2}^{\prime},\dots ,{w}_{n}^{\prime})$ of QC using the BWM linear model shown below with respect to BO and OW vectors determined in Step 2.

**Step 4.**Select Taguchi orthogonal array (OA) for the design of the experiment based on the number of design factors $DF$ and levels $L$ proposed in the study. The OA must ensure all levels $L$ to be tested at least once of $(DF-1)$ design factors. Else, the next higher OA should be selected for the design of the experiment.

**Step 5.**Collect experimental responses by conducting experimental runs based on selected OA. For each QC, repeat Step 2 to compute the optimal weights for an individual experimental response using the BWM linear model. The selection of best and worst criteria should be based on the target performance of individual QC.

**Step 6.**Compute the total weight (overall quality) of each experimental run as a composite of vectors between optimal weights of QC (${w}_{1\times 9}^{\prime})$ and optimal weights of individual experimental response with respect to each QC $\left({w}_{9\times 9}^{\prime}\right)$. This is an important step to convert a multi-objective optimization problem into a single-objective optimization problem, which is then solvable using the Taguchi method.

**Step 7.**Calculate the SN ratio and determine the optimal level of design factors that correspond with the highest SN ratio obtained. The larger-the-better Taguchi loss function, expressed in Equation (9), shall be used to appraise the effects of the total weight of each experiment since the underlying single optimization objective is to maximize the overall quality. Conduct a confirmation experiment if the optimal level of design factors is not covered in the experimental runs of the selected OA.

## 3. Results

#### 3.1. Optimization of MPFA Concrete

**Step 1.**Define optimization objectives and quality criteria (QC) $({qc}_{1},q{c}_{2},\dots ,q{c}_{n})$ to facilitate the multi-criteria decision-making process. Specify appropriate design factors and levels with overarching impacts on QC for the design of the experiment.

**Step 2.**Identify one best (highest priority) and one worst (lowest priority) criterion based on experts’ preferences. Carry out a pairwise comparison between the best criterion against other criteria and other criteria against the worst criterion by assigning a number between 1 to 9 to obtain the best-to-others (BO) and others-to-worst (OW) vectors, respectively.

**Step 3.**Compute optimal weights $({w}_{1}^{\prime},{w}_{2}^{\prime},\dots ,{w}_{n}^{\prime})$ of QC using the BWM linear model with respect to BO and OW vectors determined in Step 2.

**Step 4.**Select Taguchi orthogonal array (OA) for the design of the experiment based on the number of design factors $DF$ and levels $L$ proposed in the study.

^{4}) design factors proposed in this study. The corresponding mix specifications of MPFA concrete for each experimental run are summarized in Table 6.

**Step 5.**Collect experimental responses by conducting experimental runs based on selected OA. For each QC, repeat Step 2 to compute the optimal weights for an individual experimental response using the BWM linear model. The selection of best and worst criteria should be based on the target performance of individual QC.

**Step 6.**Compute the total weight (overall quality) of each experimental run as a composite of vectors between optimal weights of QC (${w}_{1\times 9}^{\prime})$ and optimal weights of individual experimental response with respect to each QC $\left({w}_{9\times 9}^{\prime}\right)$.

**Step 7.**Calculate the SN ratio and determine the optimal level of design factors that correspond with the highest SN ratio obtained.

**P1Q1R1S1**, which translates to 400 kg/m

^{3}cement content (P), 0.43 W/C ratio (Q), 0.43 FA/TA ratio (R) and 10 vol% MPFA content (S). The optimal level with the highest SN ratio corresponds to the mix specification of the experimental run MP1; hence no confirmation test was required.

#### 3.2. Performance Benchmark of Material Tailoring Strategies

- Reference cement concrete with continuous graded NS only and 0% MPFA (Ref)
- MP1 cement concrete containing mixed plastic waste in loose form with an identical concoction instead of pelletized MPFA (MP1-LMP)
- MP1 cement concrete made with MPFA NS fine aggregate system with as-received NS instead of continuous graded NS (MP1-arNS).

## 4. Concluding Remarks

^{3}cement content, 0.43 W/C ratio, 0.43 FA/TA ratio, and 10 vol% MPFA content.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**Main effect plot for SN ratios of total weight (the red circle denotes the optimal level).

Binder | CaO | SiO_{2} | Al_{2}O_{3} | Fe_{2}O_{3} | SO_{3} | MgO |
---|---|---|---|---|---|---|

PC | 65.08 | 19.72 | 5.18 | 3.22 | 2.07 | 1.64 |

QC | Description | Target Performance |
---|---|---|

X1 | Air content (%) | Smaller the better |

X2 | Water absorption at 28 days (%) | Smaller the better |

X3 | Water permeability (mm) | Smaller the better |

X4 | Chloride permeability (C) | Smaller the better |

X5 | Ultrasonic pulse velocity at 28 days (km/s) | Larger the better |

X6 | Compressive strength at 7 days (MPa) | Larger the better |

X7 | Compressive strength at 28 days (MPa) | Larger the better |

X8 | Flexural strength at 28 days (MPa) | Larger the better |

X9 | Splitting tensile strength at 28 days (MPa) | Larger the better |

Factor | Description | Levels | ||
---|---|---|---|---|

1 | 2 | 3 | ||

P | Cement content (kg/m^{3}) | 400 | 415 | 430 |

Q | Water/cement ratio: w/c | 0.43 | 0.45 | 0.47 |

R | Fine aggregate/total aggregate ratio: FA/TA (wt%) | 0.43 | 0.44 | 0.45 |

S | MPFA content (vol% of FA) | 10 | 15 | 20 |

QC | Description | BO (OW) |
---|---|---|

X1 | Air content (%) | 4 (6) |

X2 | Water absorption at 28 days (%) | 6 (4) |

X3 | Water permeability (mm) | 5 (5) |

X4 | Chloride permeability (C) | 8 (2) |

X5 | Ultrasonic pulse velocity at 28 days (km/s) | 9 (1) |

X6 | Compressive strength at 7 days (MPa) | 7 (3) |

X7 | Compressive strength at 28 days (MPa) | 1 (9) |

X8 | Flexural strength at 28 days (MPa) | 2 (8) |

X9 | Splitting tensile strength at 28 days (MPa) | 3 (7) |

QC | Description | Critical Weights |
---|---|---|

X1 | Air content (%) | 0.0958 |

X2 | Water absorption at 28 days (%) | 0.0638 |

X3 | Water permeability (mm) | 0.0766 |

X4 | Chloride permeability (C) | 0.0479 |

X5 | Ultrasonic pulse velocity at 28 days (km/s) | 0.0274 |

X6 | Compressive strength at 7 days (MPa) | 0.0547 |

X7 | Compressive strength at 28 days (MPa) | 0.3146 |

X8 | Flexural strength at 28 days (MPa) | 0.1915 |

X9 | Splitting tensile strength at 28 days (MPa) | 0.1277 |

Total | 1 |

Mix No. | Taguchi L9 (3^{4}) Orthogonal Array | Mix Specification | ||||||
---|---|---|---|---|---|---|---|---|

P | Q | R | S | P | Q | R | S | |

MP1 | 1 | 1 | 1 | 1 | 400 | 0.43 | 0.43 | 10 |

MP2 | 1 | 2 | 2 | 2 | 400 | 0.45 | 0.44 | 15 |

MP3 | 1 | 3 | 3 | 3 | 400 | 0.47 | 0.45 | 20 |

MP4 | 2 | 1 | 2 | 3 | 415 | 0.43 | 0.44 | 20 |

MP5 | 2 | 2 | 3 | 1 | 415 | 0.45 | 0.45 | 10 |

MP6 | 2 | 3 | 1 | 2 | 415 | 0.47 | 0.43 | 15 |

MP7 | 3 | 1 | 3 | 2 | 430 | 0.43 | 0.45 | 15 |

MP8 | 3 | 2 | 1 | 3 | 430 | 0.45 | 0.43 | 20 |

MP9 | 3 | 3 | 2 | 1 | 430 | 0.47 | 0.44 | 10 |

QC | MP1 | MP2 | MP3 | MP4 | MP5 | MP6 | MP7 | MP8 | MP9 |
---|---|---|---|---|---|---|---|---|---|

X1 (%) | 1.70 | 2.15 | 2.75 | 2.65 | 1.95 | 2.50 | 2.60 | 1.65 | 2.15 |

X2 (%) | 3.82 | 4.52 | 5.20 | 4.53 | 3.80 | 3.90 | 4.08 | 4.74 | 4.36 |

X3 (mm) | 14.8 | 14.7 | 14.7 | 12.7 | 15.3 | 21.2 | 13.6 | 13.4 | 7.90 |

X4 (C) | 224 | 237 | 153 | 233 | 156 | 228 | 234 | 220 | 165 |

X5 (km/s) | 4.45 | 4.42 | 4.41 | 4.41 | 4.53 | 4.47 | 4.44 | 4.38 | 4.44 |

X6 (MPa) | 52.0 | 43.7 | 35.8 | 42.3 | 44.4 | 38.5 | 42.8 | 44.7 | 42.9 |

X7 (MPa) | 59.7 | 49.3 | 42.9 | 48.2 | 54.1 | 49.9 | 58.2 | 52.1 | 44.9 |

X8 (MPa) | 5.95 | 6.05 | 5.15 | 5.40 | 5.18 | 4.98 | 5.41 | 5.37 | 5.28 |

X9 (MPa) | 4.85 | 4.55 | 3.90 | 4.05 | 4.10 | 4.10 | 4.00 | 4.00 | 3.45 |

QC | MP1 | MP2 | MP3 | MP4 | MP5 | MP6 | MP7 | MP8 | MP9 |
---|---|---|---|---|---|---|---|---|---|

X1 | 2 (8) | 4 (6) | 9 (1) | 8 (2) | 3 (7) | 6 (4) | 7 (3) | 1 (9) | 4 (6) |

X2 | 2 (8) | 6 (4) | 9 (1) | 7 (3) | 1 (9) | 3 (7) | 4 (6) | 8 (2) | 5 (5) |

X3 | 7 (3) | 6 (4) | 5 (5) | 2 (8) | 8 (2) | 9 (1) | 4 (6) | 3 (7) | 1 (9) |

X4 | 5 (5) | 9 (1) | 1 (9) | 7 (3) | 2 (8) | 6 (4) | 8 (2) | 4 (6) | 3 (7) |

X5 | 3 (7) | 6 (4) | 8 (2) | 7 (3) | 1 (9) | 2 (8) | 4 (6) | 9 (1) | 4 (6) |

X6 | 1 (9) | 4 (6) | 9 (1) | 7 (3) | 3 (7) | 8 (2) | 6 (4) | 2 (8) | 5 (5) |

X7 | 1 (9) | 6 (4) | 9 (1) | 7 (3) | 3 (7) | 5 (5) | 2 (8) | 4 (6) | 8 (2) |

X8 | 2 (8) | 1 (9) | 8 (2) | 4 (6) | 7 (3) | 9 (1) | 3 (7) | 5 (5) | 6 (4) |

X9 | 1 (9) | 2 (8) | 8 (2) | 5 (5) | 3 (7) | 3 (7) | 6 (4) | 6 (4) | 9 (1) |

QC | MP1 | MP2 | MP3 | MP4 | MP5 | MP6 | MP7 | MP8 | MP9 |
---|---|---|---|---|---|---|---|---|---|

X1 | 0.188 | 0.192 | 0.055 | 0.077 | 0.125 | 0.315 | 0.315 | 0.192 | 0.303 |

X2 | 0.094 | 0.064 | 0.064 | 0.027 | 0.063 | 0.096 | 0.064 | 0.315 | 0.184 |

X3 | 0.027 | 0.027 | 0.077 | 0.315 | 0.047 | 0.027 | 0.027 | 0.048 | 0.046 |

X4 | 0.047 | 0.055 | 0.192 | 0.055 | 0.054 | 0.055 | 0.055 | 0.096 | 0.073 |

X5 | 0.125 | 0.315 | 0.048 | 0.192 | 0.309 | 0.128 | 0.128 | 0.055 | 0.122 |

X6 | 0.063 | 0.128 | 0.027 | 0.064 | 0.188 | 0.048 | 0.077 | 0.027 | 0.122 |

X7 | 0.054 | 0.096 | 0.096 | 0.048 | 0.094 | 0.064 | 0.192 | 0.128 | 0.061 |

X8 | 0.309 | 0.048 | 0.128 | 0.096 | 0.027 | 0.192 | 0.096 | 0.077 | 0.061 |

X9 | 0.094 | 0.077 | 0.315 | 0.128 | 0.094 | 0.077 | 0.048 | 0.064 | 0.027 |

Mix No. | Total Weight |
---|---|

MP1 | 0.233 |

MP2 | 0.130 |

MP3 | 0.052 |

MP4 | 0.075 |

MP5 | 0.127 |

MP6 | 0.072 |

MP7 | 0.120 |

MP8 | 0.111 |

MP9 | 0.082 |

Mix No. | SN Ratio |
---|---|

MP1 | −12.648 |

MP2 | −17.720 |

MP3 | −25.735 |

MP4 | −22.536 |

MP5 | −17.949 |

MP6 | −22.849 |

MP7 | −18.455 |

MP8 | −19.108 |

MP9 | −21.771 |

Mix No. | MP1 | Ref | $\Delta (\mathbf{\%})$ | MP1-LMP | $\Delta (\mathbf{\%})$ | MP1-arNS | $\Delta (\mathbf{\%})$ |
---|---|---|---|---|---|---|---|

X1 (%) | 1.70 | 2.45 | −44.1 | 3.00 | −76.5 | 2.60 | −52.9 |

X2 (%) | 3.82 | 1.66 | 56.54 | 4.38 | −14.7 | 3.79 | 0.79 |

X3 (mm) | 14.8 | 17.5 | −18.6 | 18.4 | −24.8 | 13.85 | 6.10 |

X4 (C) | 224 | 237 | −5.80 | 232 | −3.57 | 217 | 3.13 |

X5 (km/s) | 4.45 | 4.53 | −1.80 | 4.52 | −1.57 | 4.64 | −4.27 |

X6 (MPa) | 52.0 | 53.8 | −3.44 | 47.6 | 8.39 | 46.25 | 11.0 |

X7 (MPa) | 59.7 | 63.8 | −6.91 | 5.85 | 1.25 | 59.51 | 0.25 |

X8 (MPa) | 5.95 | 6.28 | −5.55 | 5.85 | 1.68 | 6.13 | −3.03 |

X9 (MPa) | 4.85 | 4.15 | 14.43 | 4.40 | 9.28 | 4.56 | 5.98 |

Parameters | LOR | Ref | MP1 |
---|---|---|---|

Arsenic (As) | 0.01 | <0.01 | <0.01 |

Cadmium (Cd) | 0.001 | <0.001 | <0.001 |

Chromium (Cr) | 0.01 | <0.01 | <0.01 |

Lead (Pb) | 0.01 | 0.02 | <0.01 |

Mercury (Hg) | 0.001 | 0.002 | <0.001 |

Selenium (Se) | 0.01 | <0.01 | <0.01 |

Silver (Ag) | 0.01 | <0.01 | <0.01 |

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© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Lee, K.J.L.; Wong, S.F. Multi-Objective Taguchi Optimization of Cement Concrete Incorporating Recycled Mixed Plastic Fine Aggregate Using Modified Fuller’s Equation. *Buildings* **2023**, *13*, 893.
https://doi.org/10.3390/buildings13040893

**AMA Style**

Lee KJL, Wong SF. Multi-Objective Taguchi Optimization of Cement Concrete Incorporating Recycled Mixed Plastic Fine Aggregate Using Modified Fuller’s Equation. *Buildings*. 2023; 13(4):893.
https://doi.org/10.3390/buildings13040893

**Chicago/Turabian Style**

Lee, Kevin Jia Le, and Sook Fun Wong. 2023. "Multi-Objective Taguchi Optimization of Cement Concrete Incorporating Recycled Mixed Plastic Fine Aggregate Using Modified Fuller’s Equation" *Buildings* 13, no. 4: 893.
https://doi.org/10.3390/buildings13040893