# Development of Concrete Mixture Design Process Using MCDM Approach for Sustainable Concrete Quality Management

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emission and natural resources consumption through optimum cement and water use in concrete production. Concrete mixture factors such as water/cement (w/c) ratio, density, ratio of fine aggregate to cement (FA/c), ratio of coarse aggregate and cement (CA/c), and cost of concrete may be used to satisfy the socioeconomic indicators of sustainable concrete. Concrete mixture factors such as water/cement (w/c) ratio, density, ratio of fine aggregate and total aggregate (FA/T), ratio of total aggregate to cement (T/c), and ratio of fine aggregate to cement (FA/c) can be used to satisfy the environmental indicators of sustainable concrete. Proper concrete proportioning along with optimum ratios of ingredients results in high durability of structures [2] and helps to resolve the environment and socioeconomic issues. Alam et al. [3] identified the factors concerning the quality of concrete production and pointed out that a proper concrete mix is one of the key factors which affects the quality of concrete. Ahmad [4] studied concrete mixture proportion from the quality of concrete point of view and suggested that there exists an optimum ratio of fine aggregate and total aggregate (FA/T) and cement/fine aggregate (c/FA) ratio for improved quality. Zavadskas et al. [5] emphasized that the application of Multicriteria Decision-Making (MCDM) techniques have great potential and sustainable decision-making in structural engineering, design, and building technology. An extensive body of literature is available in which MCDM approaches are used to tackle the selection of the right stackholder, the best practice or option, an optimum measure of right materials in concrete construction project management, and sustainable construction engineering. Zavadskas et al. [6] present a summary of published research related to the application of basic decision-making frameworks and processes, along with advanced MCDM techniques for sustainability in the construction engineering discipline. A broader review of MCDM approaches and their applications in civil engineering are due to Kabir et al. [7]. Stojcic et al. [8] discussed the application of MCDM for sustainability in the engineering field. Monghasemi et al. [9] introduced a new MCDM model to optimize the construction time, construction cost, and construction quality of projects. Alhumaidi [10] proposed an MCDM technique considering a multi-attribute fuzzy weighted average approach for project contractor selection. Taylon et al. [11] used a hybrid fuzzy Analytic Hierarchy Process (fuzzy-AHP) and fuzzy TOPSIS MCDM technique for assessing the selection criteria and risk criteria of construction projects. Hamdia et al. [12] develop the reinforced cement concrete (RCC) building damage assessment criteria using the fuzzy analytic hierarchy process. The application of the MCDM technique to structural retrofitting procedures for buildings and bridges repairs is due to Caterino et al. [13] and Rashidi et al. [14]. They conclude that technique for order preference by similarity to ideal solution (TOPSIS) and the methodology of VIKOR (Vlse Kriterijumska Optimizacija I Kompromisno Resenje in Serbian) are more suitable for selecting retrofit procedures. Zhao et al. [15] propose a coupled MCDM method, intervalued trapezoidal intuitionistic fuzzy number (IVTIFN), and a TOPSIS method to support the selection of pipe materials in building projects. The Fuzzy extended analytical hierarchy process (FEAHP) technique is proposed by Akadiri et al. [16] for ranking building materials. Falqi et al. [17] apply a TOPSIS method in a fuzzy environment for siliceous material management for sustainable concrete construction. Ahmed et al. [18] propose a hybrid MCDM approach to select a concrete mixture design method for the production of high-performance concrete. Bera et al. [19] suggested multi-attribute decision-making (MADM) to choose an appropriate proportion of silty sand and artificial clay for soil stabilization based on a mixing design approach.

## 2. Multicriteria Decision-Making Based on Fuzzy Sets Theory

## 3. Fuzzy TOPSIS Method

_{1}, A

_{2}, …, A

_{n}, is given, in order to rate their individual capabilities concerning various sub-criteria already set aside. The overall performance of each mixture design method was assessed based on their sustainable performance and the opinion of experts collected earlier in linguistic variables viz., very good, good, fair, poor, and very poor, along with triangular fuzzy numbers. This method’s algorithm is defined in the following section.

#### 3.1. Fuzzy Decision Matrix Construction for a Sustainable Quality Concrete Production Problem

_{1}, A

_{2}, …, A

_{m}are the alternatives to be chosen, C

_{1}, C

_{2}, …, C

_{n}denote the evaluation criteria for preferential mix design method, and ${\tilde{D}}_{ij}$ represents the rating of alternative A

_{i}with respect to criterion C

_{j}evaluated by k decision-makers”. Since the interpretation of the preferential mix design approach depends on an individual’s expertise, this study uses the mean value method to combine fuzzy output score ${\tilde{x}}_{ij}$ for k decision-makers with the same assessment criteria, i.e.,

_{i}with respect to criterion C

_{j}evaluated by the kth decision-maker and ${\tilde{x}}_{ij}^{k}=({a}_{ij}^{k},{b}_{ij}^{k},{c}_{ij}^{k})$”.

#### 3.2. Fuzzy Decision Matrix Normalization for a Sustainable Quality Concrete Production Problem

#### 3.3. Weighted Normalized Fuzzy Decision Matrix Construction for a Sustainable Quality Concrete Production Problem

#### 3.4. FPIRP and FNIRP Determination

#### 3.5. Determination of Each Concrete Mixture Construction Process Distances to FPIRP and FNIRP

_{i}from FPIRP, and ${d}_{i}^{-}$ is the distance of alternative A

_{i}from FNIRP”.

#### 3.6. Development of Closeness Coefficient (CC) and the Potential Alternatives Order

_{i}.

## 4. Concrete Mixture Design Method Assessment for Sustainable Quality Concrete Production

#### 4.1. Determination of the Synthetic Importance Weights of Assessment Criteria

#### 4.2. Fuzzy Decision Matrix Construction

#### 4.3. Fuzzy Decision Matrix Normalization and Weighted Normalized Matrix

_{1}documented in Table 7 as 0.290 = 0.580 × 0.500; 0.546 = 0.700 × 0.780; 0.8084 = 0.860 × 0.940.

#### 4.4. Fuzzy Positive and Fuzzy Negative Ideal Reference Points

#### 4.5. Distance of Each Preferential Concrete Mix Design Method to FPIRP and FNIRP

#### 4.6. Closeness Coefficient (CC) for Selection Order of Concrete Mixture Design Method

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**QUESTIONNAIRE FOR FUZZY TOPSIS**

_{1})?

_{2})?

_{3})?

_{4})?

_{5})?

_{6})?

_{7})?

With Respect to: The Sub-Criteria Criteria for Sustainable Concrete Quality | Importance (or Preference) of Each Criterion (Workability etc.) | |||||

Questions | Sub-criteria Criteria | (0, 0.1, 0.3) Very Low | (0.1, 0.3, 0.5) Low | (0.3, 0.5, 0.7) Medium | (0.5, 0.7, 0.9) High | (0.7, 0.9, 1) Very High |

Q1 | w/c | √ | ||||

Q2 | Density | √ | ||||

Q3 | CA/c | √ | ||||

Q4 | T/c | |||||

Q5 | FA/c | √ | ||||

Q6 | FA/T | √ | ||||

Q7 | Cost | √ |

## Appendix B

**QUESTIONNAIRE FOR FUZZY TOPSIS**

With Respect to the Potential Mixture Design Methods (ACI) for Sustainable Concrete Quality | Performance of Each Mixture Design Methods (ACI) Alternative with Respect to Each Sub-Criterion | ||||||

Questions | Sub-Criteria | mixture design methods | (0, 1, 3) Very Poor | (1, 3, 5) Poor | (3, 5, 7) Fair | (5, 7, 9) Good | (7, 9, 10) Very Good |

Q11 | w/c | ACI | √ | ||||

Q12 | Density | ACI | √ | ||||

Q13 | CA/c | ACI | √ | ||||

Q14 | T/c | ACI | |||||

Q15 | FA/c | ACI | √ | ||||

Q16 | FA/T | ACI | √ | ||||

Q17 | Cost | ACI | √ |

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**Figure 2.**Hierarchical structure to select the mixture design method for sustainable quality concrete production.

**Figure 6.**Potentiality order of mixture design methods for obtaining sustainable quality concrete based on the closeness coefficient.

Mixture Factors | DOE Method | ACI Method | Concrete Mixture Optimum Value with Lowest Cost | |||
---|---|---|---|---|---|---|

Ratio of FA/T | 0.41 [27] | 0.43 [27] | 0.42 [31] | 0.45–0.4 [30] | 0.39 [29] | 0.38 [1,4] |

Ratio of T/c | 4.26 [27] | 4.31 [27] | -- | 3–3.6 [30] | 4.3–5.1 [29] | 4.88 [1,4] |

Ratio of w/c | 0.5 [27] | 0.5 [27] | -- | -- | 0.4–0.43 [29] | -- |

Ratio of CA/c | 2.51 [27] | 2.43 [27] | -- | -- | -- | -- |

Ratio of FA/c | 1.75 [27] | 1.88 [27] | -- | -- | -- | -- |

**Table 2.**Weight of fuzzy importance, BNP, and rank of each sub-criteria with respect to workability.

Sub-Criteria | Weight of Fuzzy Importance | BNP | Rank |
---|---|---|---|

(C_{1}) w/c | (0.5800, 0.7800, 0.9400) | 0.7667 | 1 |

(C_{2}) Density | (0.1400, 0.3400, 0.5400) | 0.3400 | 5 |

(C_{3}) CA/c | (0.5000, 0.7000, 0.9000) | 0.7000 | 2 |

(C_{4}) T/c | (0.5000, 0.7000, 0.8600) | 0.6867 | 3 |

(C_{5}) FA/c | (0.1200, 0.2600, 0.4600) | 0.2800 | 7 |

(C_{6}) FA/T | (0.1400, 0.3400, 0.5400) | 0.3400 | 6 |

(C_{7}) Cost | (0.2200, 0.4200, 0.6200) | 0.4200 | 4 |

Sub-Criteria | Fuzzy Importance Weight | BNP | Rank |
---|---|---|---|

(C_{8}) w/c | (0.7000, 0.9000, 1.0000) | 0.8667 | 1 |

(C_{9}) Density | (0.5800, 0.7800, 0.9400) | 0.7667 | 3 |

(C_{10}) CA/c | (0.4200, 0.6200, 0.8200) | 0.6200 | 6 |

(C_{11}) T/c | (0.4600, 0.6600, 0.8600) | 0.6600 | 4 |

(C_{12}) FA/c | (0.4600, 0.6600, 0.8400) | 0.6533 | 5 |

(C_{13}) FA/T | (0.1200, 0.3000, 0.5000) | 0.3067 | 7 |

(C_{14}) Cost | (0.6600, 0.8600, 0.9800) | 0.8333 | 2 |

Sub-Criteria | Fuzzy Importance Weight | BNP Values | Rank |
---|---|---|---|

(C_{15}) w/c | (0.6600, 0.8600, 0.9800) | 0.8333 | 1 |

(C_{16}) Density | (0.6200, 0.8200, 0.9600) | 0.8000 | 2 |

(C_{17}) CA/c | (0.2600, 0.4600, 0.6600) | 0.4600 | 5 |

(C_{18}) T/c | (0.2400, 0.4200, 0.6200) | 0.4267 | 6 |

(C_{19}) FA/c | (0.5000, 0.7000, 0.8800) | 0.6933 | 4 |

(C_{20}) FA/T | (0.2200, 0.4200, 0.6200) | 0.4200 | 7 |

(C_{21}) Cost | (0.5400, 0.7400, 0.9200) | 0.7333 | 3 |

**Table 5.**Overall order of sub-criteria using BNP value with respect to sustainable concrete quality.

Sub-Criteria | BNP Value | Rank |
---|---|---|

C_{1} | 0.7667 | 5 |

C_{2} | 0.3400 | 18 |

C_{3} | 0.7000 | 8 |

C_{4} | 0.6867 | 10 |

C_{5} | 0.2800 | 21 |

C_{6} | 0.3400 | 18 |

C_{7} | 0.4200 | 16 |

C_{8} | 0.8667 | 1 |

C_{9} | 0.7667 | 5 |

C_{10} | 0.6200 | 13 |

C_{11} | 0.6600 | 11 |

C_{12} | 0.6533 | 12 |

C_{13} | 0.3067 | 20 |

C_{14} | 0.8333 | 2 |

C_{15} | 0.8333 | 2 |

C_{16} | 0.8000 | 4 |

C_{17} | 0.4600 | 14 |

C_{18} | 0.4267 | 15 |

C_{19} | 0.6933 | 9 |

C_{20} | 0.4200 | 16 |

C_{21} | 0.7333 | 7 |

Criteria | ACI | DOE | FM |
---|---|---|---|

C_{1} | (5.0000, 7.0000, 8.6000) | (7.0000, 9.0000, 10.000) | (5.0000, 7.0000, 9.0000) |

C_{2} | (5.8000, 7.8000, 9.2000) | (7.0000, 9.0000, 10.000) | (5.0000, 7.0000, 9.0000) |

C_{3} | (5.8000, 7.8000, 9.4000) | (5.0000, 7.0000, 9.0000) | (7.0000, 9.0000, 10.000) |

C_{4} | (4.6000, 6.6000, 8.4000) | (5.0000, 7.0000, 9.0000) | (7.0000,9.0000, 10.000) |

C_{5} | (4.6000, 6.6000, 8.4000) | (7.0000, 9.0000, 10.000) | (5.0000, 7.0000, 9.000) |

C_{6} | (4.6000, 6.6000, 8.4000) | (5.4000, 7.4000, 9.2000) | (7.0000, 9.0000, 10.000) |

C_{7} | (2.6000, 4.6000, 6.6000) | (5.0000, 7.0000, 9.0000) | (3.0000, 5.0000, 7.0000) |

C_{8} | (2.6000, 4.6000, 6.6000) | (5.0000, 7.0000, 8.8000) | (2.6000, 4.6000, 6.4000) |

C_{9} | (3.0000, 5.0000, 7.0000) | (5.8000, 7.8000, 9.2000) | (1.8000, 3.8000, 5.8000) |

C_{10} | (3.0000, 5.0000, 7.0000) | (5.8000, 7.8000, 9.2000) | (2.6000, 4.6000, 6.4000) |

C_{11} | (5.8000, 7.8000, 9.4000) | (6.0000, 8.0000, 9.5000) | (4.8000, 6.8000, 8.8000) |

C_{12} | (5.8000, 7.8000, 9.4000) | (5.2000, 7.2000, 9.1000) | (4.4000, 6.4000, 8.4000) |

C_{13} | (5.4000, 7.4000, 9.2000) | (4.8000, 7.2000, 8.5000) | (4.8000, 6.8000, 8.4000) |

C_{14} | (5.0000, 7.0000, 9.0000) | (5.0000, 6.8000, 8.8000) | (4.8000, 6.8000, 8.4000) |

C_{15} | (4.6000, 6.6000, 8.6000) | (4.8000, 7.0000, 8.6000) | (4.2000, 6.2000, 8.2000) |

C_{16} | (4.2000, 6.2000, 8.2000) | (4.8000, 6.8000, 8.5000) | (4.8000, 6.8000, 8.5000) |

C_{17} | (5.8000, 7.8000, 9.4000) | (5.2000, 7.2000,9.0000) | (4.2000, 6.2000, 8.2000) |

C_{18} | (3.4000, 5.4000, 7.2000) | (5.6000, 7.6000, 9.3000) | (3.0000, 5.0000, 6.9000) |

C_{19} | (3.4000, 5.4000, 7.4000) | (6.4000, 8.4000, 9.7000) | (2.2000, 4.2000, 6.2000) |

C_{20} | (3.4000, 5.4000, 7.4000) | (5.8000, 7.8000, 9.4000) | (3.6000, 5.6000, 7.3000) |

C_{21} | (2.2000, 4.2000, 6.2000) | (6.0000, 8.0000, 9.5000) | (3.6000, 5.6000, 7.5000) |

Criteria | ACI | DOE | FM |
---|---|---|---|

C_{1} | (0.5000, 0.7000, 0.8600) | (0.7000, 0.9000, 1.0000) | (0.5000, 0.7000, 0.9000) |

C_{2} | (0.5800, 0.7800, 0.9200) | (0.7000, 0.9000, 1.0000) | (0.5000, 0.7000, 0.9000) |

C_{3} | (0.5800, 0.7800, 0.9400) | (0.5000, 0.7000, 0.9000) | (0.7000, 0.9000, 1.0000) |

C_{4} | (0.4600, 0.6600, 0.8400) | (0.5000, 0.7000, 0.9000) | (0.7000, 0.9000, 1.0000) |

C_{5} | (0.4600, 0.6600, 0.8400) | (0.7000, 0.9000, 1.0000) | (0.5000, 0.7000, 0.9000) |

C_{6} | (0.4600, 0.6600, 0.8400) | (0.5400, 0.7400, 0.9200) | (0.7000, 0.9000, 1.0000) |

C_{7} | (0.2889, 0.5111, 0.7333) | (0.5556, 0.7778, 1.0000) | (0.3333, 0.5556, 0.7778) |

C_{8} | (0.2955, 0.5227, 0.7500) | (0.5682, 0.7955, 1.0000) | (0.2955, 0.5227, 0.7273) |

C_{9} | (0.3261, 0.5435, 0.7609) | (0.6304, 0.8478, 1.0000) | (0.1957, 0.4130, 0.6304) |

C_{10} | (0.3261, 0.5435, 0.7609) | (0.6304, 0.8478, 1.0000) | (0.2826, 0.5000, 0.6957) |

C_{11} | (0.6105, 0.8211, 0.9895) | (0.6316, 0.8421, 1.0000) | (0.5053, 0.7158, 0.9263) |

C_{12} | (0.6170, 0.8298, 1.0000) | (0.5532, 0.7660, 0.9681) | (0.4681, 0.6809, 0.8936) |

C_{13} | (0.5870, 0.8043, 1.0000) | (0.5217, 0.7826, 0.9239) | (0.5217, 0.7391, 0.9130) |

C_{14} | (0.5556, 0.7778, 1.0000) | (0.5556, 0.7556, 0.9778) | (0.5333, 0.7556, 0.9333) |

C_{15} | (0.5349, 0.7674, 1.0000) | (0.5581, 0.8140, 1.0000) | (0.4884, 0.7209, 0.9535) |

C_{16} | (0.4941, 0.7294, 0.9647) | (0.5647, 0.8000, 1.0000) | (0.5647, 0.8000, 1.0000) |

C_{17} | (0.6170, 0.8298, 1.0000) | (0.5532, 0.7660, 0.9574) | (0.4468, 0.6596, 0.8723) |

C_{18} | (0.3656, 0.5806, 0.7742) | (0.6022, 0.8172, 1.0000) | (0.3226, 0.5376, 0.7419) |

C_{19} | (0.3505, 0.5567, 0.7629) | (0.6598, 0.8660, 1.0000) | (0.2268, 0.4330, 0.6392) |

C_{20} | (0.3617, 0.5745, 0.7872) | (0.6170, 0.8298, 1.0000) | (0.3830, 0.5957, 0.7766) |

C_{21} | (0.2316, 0.4421, 0.6526) | (0.6316, 0.8421, 1.0000) | (0.3789, 0.5895, 0.7895) |

Sub-Criteria | ACI | DOE | FM |
---|---|---|---|

C_{1} | (0.290, 0.540, 0.809) | (0.406, 0.702, 0.940) | (0.290, 0.546, 0.846) |

C_{2} | (0.081, 0.265, 0.497) | (0.098, 0.306, 0.540) | (0.070, 0.238, 0.486) |

C_{3} | (0.290, 0.546, 0.846) | (0.250, 0.490, 0.810) | (0.350, 0.630, 0.900) |

C_{4} | (0.230, 0.462, 0.723) | (0.250, 0.490, 0.774) | (0.350, 0.630, 0.860) |

C_{5} | (0.055, 0.172, 0.387) | (0.084, 0.234, 0.460) | (0.060, 0.182, 0.414) |

C_{6} | (0.065, 0.225, 0.454) | (0.076, 0.252, 0.497) | (0.098, 0.306, 0.540) |

C_{7} | (0.064, 0.215, 0.455) | (0.122, 0.327, 0.620) | (0.073, 0.233, 0.482) |

C_{8} | (0.207, 0.471, 0.750) | (0.398, 0.716, 1.000) | (0.207, 0.471, 0.727) |

C_{9} | (0.189, 0.424, 0.715) | (0.366, 0.661, 0.940) | (0.114, 0.322, 0.593) |

C_{10} | (0.137, 0.337, 0.624) | (0.265, 0.526, 0.820) | (0.119, 0.310, 0.571) |

C_{11} | (0.281, 0.542, 0.851) | (0.291, 0.556, 0.860) | (0.233, 0.473, 0.797) |

C_{12} | (0.284, 0.548, 0.840) | (0.255, 0.506, 0.813) | (0.215, 0.449, 0.751) |

C_{13} | (0.071, 0.241, 0.500) | (0.063, 0.235, 0.462) | (0.063, 0.222, 0.457) |

C_{14} | (0.367, 0.669, 0.980) | (0.367, 0.650, 0.958) | (0.352, 0.650, 0.915) |

C_{15} | (0.353, 0.660, 0.980) | (0.368, 0.700, 0.980) | (0.322, 0.620, 0.934) |

C_{16} | (0.306, 0.598, 0.926) | (0.350, 0.656, 0.960) | (0.350, 0.656, 0.960) |

C_{17} | (0.161, 0.382, 0.660) | (0.553, 0.766, 0.957) | (0.116, 0.303, 0.576) |

C_{18} | (0.088, 0.244, 0.480) | (0.602, 0.817, 1.000) | (0.077, 0.226, 0.460) |

C_{19} | (0.175, 0.390, 0.671) | (0.660, 0.866, 1.000) | (0.114, 0.303, 0.563) |

C_{20} | (0.080, 0.241, 0.488) | (0.617, 0.830, 1.000) | (0.084, 0.251, 0.482) |

C_{21} | (0.125, 0.327, 0.604) | (0.6326, 0.842, 1.000) | (0.205, 0.436, 0.726) |

Alternatives | ${\mathit{d}}_{\mathit{i}}^{+}$ | ${\mathit{d}}_{\mathit{i}}^{-}$ | CC_{i} | Selection Order |
---|---|---|---|---|

ACI | 12.9556 | 9.8633 | 0.4322 | 2 |

DOE | 11.5653 | 11.4510 | 0.4975 | 1 |

FM | 13.0164 | 9.7581 | 0.4285 | 3 |

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## Share and Cite

**MDPI and ACS Style**

Ahmed, M.; Mallick, J.; AlQadhi, S.; Ben Kahla, N.
Development of Concrete Mixture Design Process Using MCDM Approach for Sustainable Concrete Quality Management. *Sustainability* **2020**, *12*, 8110.
https://doi.org/10.3390/su12198110

**AMA Style**

Ahmed M, Mallick J, AlQadhi S, Ben Kahla N.
Development of Concrete Mixture Design Process Using MCDM Approach for Sustainable Concrete Quality Management. *Sustainability*. 2020; 12(19):8110.
https://doi.org/10.3390/su12198110

**Chicago/Turabian Style**

Ahmed, Mohd., Javed Mallick, Saeed AlQadhi, and Nabil Ben Kahla.
2020. "Development of Concrete Mixture Design Process Using MCDM Approach for Sustainable Concrete Quality Management" *Sustainability* 12, no. 19: 8110.
https://doi.org/10.3390/su12198110