# Optimization of Pervious Geopolymer Concrete Using TOPSIS-Based Taguchi Method

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^{2}

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## Abstract

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^{3}, dune sand addition of 20%, AAS/B of 0.60, and SH molarity of 12 M. Meanwhile, the optimum mix for the permeability-dominant scenario included a 400 kg/m

^{3}of binder content, 0% of dune sand addition, 0.60 of AAS/B, and 12 M of SH molarity. For a balanced performance scenario (i.e., equal weights for the responses), the optimum mix was similar to the permeability scenario with the exception of a 10% dune sand addition. An ANOVA showed that the binder content and dune sand addition had the highest contribution toward all the quality criteria. Multivariable regression models were established to predict the performance of the PGC using the mix design factors. Experimental research findings serve as a guide for optimizing the production of PGC with a superior performance while conducting minimal experiments.

## 1. Introduction

_{2}) footprint and the consumption of nearly 1.6 tons of natural resources per ton of cement produced [1,3]. Thus, there is a need to lessen the utilization of cement in concrete by identifying alternative sustainable binders that reduce the CO

_{2}footprint and replenish natural resources.

_{2}emissions and the consumption of natural resources, and beneficially recycling industrial wastes [4,5,7].

_{2}emissions compared to ordinary Portland cement [17,18,19]. Even though PC is mainly made with cement, several studies have reported the integration of geopolymers in PC [20,21]. The results showed that fly ash-based geopolymers possessed high early strength, reduced shrinkage, and a good resistance to sulfate attack [22,23]. Additionally, pervious geopolymer concrete (PGC) made with FA or GBFS displayed superior strength and durability responses compared to its cement-based counterparts [23,24,25,26,27]. When cured at 60 °C, the PGC produced with GBFS and FA exhibited an improved compressive strength, signifying an increased polymerization rate at higher curing temperatures [28]; however, this practice is not feasible on-site. In PGC made with a blended geopolymer binder of GBFS and FA, a higher content of GBFS yielded higher strength responses. Indeed, respective increases of 19, 49, and 47% in compressive, tensile, and flexural strengths were reported, respectively, when the GBFS content increased from 450 to 490 kg/m

^{3}[29]. Accordingly, PGC is considered a promising material in concrete industries, yet further studies are needed to explore the effect of mixture design factors on the strength, durability, and hydraulic properties of PGC.

## 2. Materials and Methods

#### 2.1. Materials

^{3}, 2.77/2.82, 141.5/2.49 cm

^{2}/g, and 1.45/6.82. The sodium silicate (SS) and sodium hydroxide (SH) solutions were blended to form the alkaline activator solution (AAS). The Grade N SS solution had a composition of H

_{2}O:SiO

_{2}:Na

_{2}O of 6.2:2.5:1.0, by mass. SH solutions, with different molarities of 8, 10, and 12 M, were obtained by dissolving 97% SH flakes in tap water.

#### 2.2. Development of Pervious Concrete Mixes

^{3}. Dune sand was added to the mix in replacement of the coarse aggregates to study its effect on the properties of PGC. It ranged between 0 and 20%, by mass of the total aggregate. Furthermore, the AAS/B represented the quantity of solution added to the mix with respect to the binder content, ranging from 0.5 to 0.6. The SH solution molarity was the last factor considered in the design phase, ranging from 8 to 12 M. The suggested levels were based on typical values adopted in previous work on geopolymer concrete and the ACI 522R-10 guide on pervious concrete [43,44,45]. The ratio of SS-to-SH was fixed to 1.5, by mass, as this mix design parameter was found to have a limited impact on the properties of slag-fly ash geopolymer concrete [28]. Accordingly, an L9 orthogonal array consisting of four factors, each at three levels, was developed, as shown in Table 3. If the selected approach were a factorial design, the mixes required to attain the optimum would have been 81 (3

^{4}). This underlines the importance of utilizing the Taguchi method for designing the mixes and minimizing the experimental work.

#### 2.3. Sample Preparation

#### 2.4. Test Methods

_{cu}) was determined using 100 mm cubes, as per BS EN-12390-3 [46]. This was defined as the ultimate compressive strength of the cubic samples tested using a Wykeham Farrance compression machine with a loading capacity up to 2000 kN and at a loading rate of 2 kN/s, as shown in Figure 1b. Three replicate samples were tested for each mix to compute the average f

_{cu}value. The preliminary test results showed limited change in the strength between 7 and 28 days; therefore, the analysis was carried out on 7-day f

_{cu}only. Other past work had also implemented this approach [47,48,49].

#### 2.5. Framework for the Selection of Optimum PGC Mixes

#### 2.5.1. Taguchi Analysis

_{i}is the optimized response, and Y

_{0}characterizes the response mean.

#### 2.5.2. TOPSIS Analysis

- The decision matrix was normalized to develop a comparison within the results of the different criteria. The S/N ratios obtained from the Taguchi method were utilized in the process, as per Equation (6):$${r}_{ij}=\frac{{a}_{ij}}{\sqrt{{\sum}_{i=1}^{m}{a}_{ij}^{2}}}$$
_{ij}is the S/N ratio for a performance criterion (response), and r_{ij}denotes the normalized vector of the a_{ij}vector. - After normalization, the weights of the performance criteria were assigned relevant to their importance. Different scenarios could be developed accordingly. The highest weight was given to the most desired or significant criteria to the user, and equal weights were assigned when the criteria were equally important to the user. A weighted normalized matrix was obtained by multiplying the normalized matrix values by the corresponding assigned weights.
- Furthermore, the maximum and minimum weighted normalized matrices were allotted as the positive (v
_{j}^{+}) and negative (v_{j}^{−}) ideal solutions, respectively, and calculated as per Equations (7) and (8):$${v}_{j}{}^{+}=\left\{\left({\mathrm{max}v}_{ij}|j\in J\right),\left({\mathrm{min}v}_{ij}|j\in J\right)\right\}$$$${v}_{j}{}^{-}=\left\{\left({\mathrm{min}v}_{ij}|j\in J\right),\left({\mathrm{max}v}_{ij}|j\in J\right)\right\}$$ - Respective separation measures from the ideal solutions, S
^{+}and S^{−}, were further obtained using Equations (9) and (10):$${S}^{+}=\sqrt{{\displaystyle \sum}_{j=1}^{n}{\left({v}_{ij}-{v}_{j}{}^{+}\right)}^{2}}$$$${S}^{-}=\sqrt{{\displaystyle \sum}_{j=1}^{n}{\left({v}_{ij}-{v}_{j}{}^{-}\right)}^{2}}$$ - The optimal mix was then deduced from the ranking score or closeness coefficient (C
_{i}) obtained using Equation (11). The values of C_{i}for each scenario, ranging from 0 to 1, were then inputted as Taguchi responses. Using the “larger-is-better” characteristic, the Taguchi method analysis was performed to determine the S/N ratios, whereby the maximum S/N ratio for each level corresponded to the optimum mix:$${C}_{i}=\frac{{S}^{-}}{{S}^{+}{+S}^{-}}$$

## 3. Results and Discussion

#### 3.1. Properties of PGC

#### 3.1.1. Compressive Strength

^{3}and dune sand addition of 0%, exhibited a low strength response of less than 15 MPa. Conversely, mix 6, with a binder content of 450 kg/m

^{3}, dune sand addition of 20%, AAS/B of 0.50, and SH solution molarity of 10 M, exhibited the highest strength response of 40.7 MPa. For each group of mixes with a constant binder content (400, 450, and 500 kg/m

^{3}), those made with a 0% dune sand addition experienced the lowest strength, i.e., mixes 1, 4, and 7, respectively. Similarly, in each group of mixes, the highest strength was attained with a 20% dune sand addition (i.e., mixes 3, 6, and 9). Such a finding is independent of the AAS/B or SH molarity, indicating the critical influence of dune sand compared to these two factors.

^{3}of the binder content, 10–20% of a dune sand addition, 0.50–0.55 of AAS/B, and 8–12 M of SH molarity. The use of a high binder content (i.e., ≥450 kg/m

^{3}) led to an increase in strength, owing to a higher hydraulic reaction capacity with the presence of more CaO in the binding matrix [54]. On the other hand, a low AAS/B ratio and the addition of dune sand (10–20%) increased the strength responses due to the improved particle packing density and reduced void content [46,55]. The contribution of the dune sand to strength can be also attributed to its fineness, leading to a denser and more homogenous geopolymer concrete. In fact, mortar and concrete made with dune sand had an equivalent strength to that of their counterparts made with natural aggregates [56,57]. Lastly, the incorporation of a SH solution with a molarity of 10 M led to a higher dissolution of hydroxide ions, reflecting higher strength responses (>35 MPa) [28]. Higher or lower molarities reduced the strength response. It is noteworthy that adopting one level of factors without considering the others could lead to inferior strength responses. For example, the use of a low binder content of 400 kg/m

^{3}with a 0% dune sand addition in the PGC yielded inferior strength responses below 15 MPa.

#### 3.1.2. Permeability

^{3}of the binder, a 0% dune sand addition, AAS/B of 0.50, and SH solution of 8 M, attained the highest permeability of 7.23 mm/s. Conversely, mix 6, including a binder content of 450 kg/m

^{3}, dune sand addition of 20%, AAS/B of 0.50, and SH molarity of 10 M, achieved the lowest permeability response of 3.02 mm/s. The results show that incorporating a higher binder content decreased the permeability, owing to the refinement of the pore structure that hindered the ease of water percolation [59]. Furthermore, the addition of dune sand to the PGC mixes reduced the permeability. In fact, for each group of binder content (400, 450, and 500 kg/m

^{3}), the mixes made with a 20% dune sand addition had the lowest permeability. These findings highlight the more significant impact of binder content and dune sand addition on the permeability of PGC compared to AAS/B and SH molarity, evidenced by the contribution shown in the ANOVA section later. Analogous findings have been noted in conventional pervious concrete made with cement, where the hydraulic performance was greatly affected by the amount of fine aggregate and binder incorporated into the mix [60]. In addition, the permeability results were in line with those of compressive strength. As such, an exponential relationship was developed between the two properties, as shown in Figure 4. This correlation can be used to predict the permeability of PGC from its f

_{cu}values with a high accuracy (coefficient of determination, R

^{2}= 0.99).

^{3}, 0–10%, 0.50–0.55, and 8–10 M, respectively. Further increases in the binder content, dune sand addition, AAS/B, and SH molarity led to lower permeability responses, with values lower than 4 mm/s being attained. Such a response could be owed to the higher hydraulic reaction capabilities with the increase in binder content, which leads to less pores in the binding matrix [56,61]. Similarly, the increase in dune sand content lowered the percolation capacity of the PGC due to the granular structure and void-filling capacity of the dune sand [57]. Additionally, the permeability was reduced to below 4 mm/s when the SH solution molarity increased and AAS/B decreased, owing to an increase in the dissolution of hydroxide ions and poor packing density, respectively [62]. Nevertheless, all 9 mixes tested herein had permeability coefficients between 3.02 and 7.23 mm/s, which are acceptable for pervious concrete applications [7,57]. Moreover, it is worth noting that designing a PGC mix with one suitable factor while neglecting others may lead to insufficient permeability. For example, using 500 kg/m

^{3}of binder content with a dune sand addition of 10–20% resulted in a permeability value below 4 mm/s.

#### 3.1.3. Abrasion Resistance

_{cu}were correlated through a linear equation that could be used in predicting one performance criterion or response from the other with a high accuracy (R

^{2}= 0.90).

^{3}of the binder content, a 10–20% dune sand addition, 0.50–0.55 of AAS/B, and 8–12 M of SH solution. It can be noticed that these levels of mix design factors are similar to those for attaining a compressive strength exceeding 30 MPa. Furthermore, a decrease in the abrasion resistance was noted when a lower binder content and dune sand addition were employed. Meanwhile, the variation in SH molarity and AAS/B did not seem to significantly impact the abrasion resistance responses, evidenced by their low contributions presented in the ANOVA section later.

#### 3.2. Optimization Results

#### 3.2.1. Taguchi Analysis

^{3}, a dune sand addition of 20%, AAS/B of 0.50, and SH molarity of 12 M. Conversely, the optimum mix to secure the best permeability corresponded to a 400 kg/m

^{3}binder content, dune sand addition of 0%, AAS/B of 0.60, and SH solution molarity of 8 M. Hence, the Taguchi method revealed that a particular combination of levels was essential to provide either a superior strength and abrasion resistance or permeability of the PGC.

#### 3.2.2. Analysis of Variance (ANOVA)

#### 3.2.3. TOPSIS Analysis

^{3}, dune sand addition of 20%, AAS/B of 0.60, and SH molarity of 12 M.

^{3}, 0%, 0.60, and 12 M, respectively. Meanwhile, the levels of the factors for optimization based on the fourth scenario (i.e., the three quality criteria were assigned equal weights of 0.33) were A1B2C3D3 (Figure 10d). Hence, the TOPSIS optimization process produced a mix of PGC having a binder content of 400 kg/m

^{3}, dune sand addition of 10%, AAS/B of 0.60, and SH molarity of 12 M with a balanced performance among the compressive strength, permeability, and abrasion resistance.

#### 3.3. Prediction of PGC Properties

^{3}for the binder content, 0 to 20% for the dune sand addition, 0.50 to 0.60 for AAS/B, and 8 to 12 M for SH solution molarity. The form of the proposed quadratic model is given in Equation (12). Table 8 lists the coefficients of the established models for each quality criterion. The R

^{2}and root-mean-square-error (RMSE) values were in the respective ranges of 0.98–0.99 and 0.37–1.20. Accordingly, these models could be employed in predicting the properties of PGC with a high accuracy. Additionally, the properties of the optimum mixes (based on the TOPSIS analysis) could be estimated using the newly-developed regression models. Indeed, mixes A3B3C3D3, A1B1C3D3 and A1B2C3D3, i.e., the optimum mixes for scenarios 1/3, 2, and 4, were characterized by a compressive strength of 39.1, 10.5, and 15.6 MPa, respectively. Their corresponding permeability was 3.4, 7.7, and 6.9 mm/s, while their respective abrasion resistances were 52.8, 12.8, and 20.9%.

_{0}(A) + α

_{1}(B) + α

_{2}(C) + α

_{3}(D) + α

_{4}(A

^{2}) + α

_{5}(B

^{2}) + α

_{6}(C

^{2}) + α

_{7}(D

^{2})

## 4. Conclusions

- A compressive strength and abrasion resistance higher than 30 MPa and 40%, respectively, could be achieved for PGC mixtures made with 450–500 kg/m
^{3}of binder content, a 10–20% dune sand addition, 0.50–0.55 of AAS/B, and 8–12 M of SH molarity. The abrasion resistance could be accurately predicted from the compressive strength using a newly-developed regression model with a high coefficient of determination of R^{2}= 0.90. - High permeability values, exceeding 6 mm/s, were obtained in PGC mixes made with a binder content, dune sand addition, AAS/B, and SH solution of 400–450 kg/m
^{3}, 0–10%, 0.50–0.55, and 8–10 M, respectively. An analytical regression model was established to predict the permeability of the PGC from the compressive strength with a high accuracy (R^{2}= 0.99). - Using the Taguchi method, the optimum mixes for superior compressive strength and abrasion resistance were made with a binder content, dune sand addition, AAS/B, and SH molarity of 500 kg/m
^{3}, 20%, 0.50, and 12 M, respectively. Contrarily, the optimized mix design for superior permeability was made with a binder content of 400 kg/m^{3}, dune sand addition of 0%, AAS/B of 0.6, and SH molarity of 8 M. - An ANOVA revealed that the binder content and dune sand addition had the highest contributions to the compressive strength, permeability and abrasion resistance, while the AAS/B and SH solution molarity had lower contributions toward the performance of the PGC.
- A TOPSIS-based Taguchi method was employed in optimizing the mixes in accordance with four optimization scenarios. For the scenarios where the compressive strength and abrasion resistance were more important to the user, the optimum mix comprised a binder content of 500 kg/m
^{3}, dune sand addition of 20%, AAS/B of 0.60, and SH molarity of 12 M. As for the permeability-dominant scenario, the optimum mix had a binder content of 400 kg/m^{3}, dune sand addition of 0%, AAS/B of 0.60, and SH Molarity of 12 M. Meanwhile, the balanced performance scenario, i.e., equal weights for the three criteria, had an optimum mix comprised of a binder content of 400 kg/m^{3}, dune sand addition of 10%, AAS/B of 0.60, and SH Molarity of 12 M. - Multivariable regression models were established to predict the compressive strength, permeability, and abrasion resistance from the binder content, dune sand addition, AAS/B, and SH solution molarity with a high accuracy. The R
^{2}and RMSE values ranged from 0.98 to 0.99 and 0.37 to 1.20, respectively. The optimum mixes, namely, A3B3C3D3, A1B1C3D3, and A2B2C3D3, had compressive strengths of 39.1, 10.5, and 15.6 MPa, permeability of 3.4, 7.7, and 6.9 mm/s, and abrasion resistance of 52.8, 12.8, and 20.9%, respectively.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Images of the (

**a**) representative cubic sample, (

**b**) compression machine, (

**c**) permeability setup [50], and (

**d**) abrasion machine.

**Figure 8.**S/N ratios of Taguchi analysis for (

**a**) compressive strength, (

**b**) permeability, and (

**c**) abrasion resistance.

**Figure 9.**Contribution of factors toward Taguchi optimization of the mix for superior (

**a**) compressive strength, (

**b**) permeability, and (

**c**) abrasion resistance.

Component, Unit | FA | GBFS | Dune Sand |
---|---|---|---|

SiO_{2}, (wt.%) | 48.0 | 27.8 | 64.9 |

CaO, (wt.%) | 3.3 | 58.6 | 14.1 |

Al_{2}O_{3}, (wt.%) | 23.1 | 8.1 | 3.0 |

Fe_{2}O_{3}, (wt.%) | 12.5 | 1.3 | 0.7 |

MgO, (wt.%) | 1.5 | 6.0 | 1.3 |

Na_{2}O, (wt.%) | 0.0 | 0.2 | 0.4 |

Others, (wt.%) | 10.5 | 0.3 | 15.5 |

LOI, (wt.%) | 1.1 | 0.9 | 0.0 |

Specific gravity | 2.32 | 2.70 | 2.77 |

Unit weight, kg/m^{3} | 1262 | 1209 | 1660 |

Factor | Level 1 | Level 2 | Level 3 |
---|---|---|---|

Binder content (kg/m^{3}) | 400 | 450 | 500 |

Dune sand addition (wt.%) | 0 | 10 | 20 |

AAS/B ratio | 0.50 | 0.55 | 0.60 |

SH Molarity (M) | 8 | 10 | 12 |

Mix No. | Binder Content (kg/m^{3}) | Dune Sand Addition (wt.%) | AAS/B Ratio | SH Molarity (M) |
---|---|---|---|---|

1 | 400 | 0 | 0.50 | 8 |

2 | 400 | 10 | 0.55 | 10 |

3 | 400 | 20 | 0.60 | 12 |

4 | 450 | 0 | 0.55 | 12 |

5 | 450 | 10 | 0.60 | 8 |

6 | 450 | 20 | 0.50 | 10 |

7 | 500 | 0 | 0.60 | 10 |

8 | 500 | 10 | 0.50 | 12 |

9 | 500 | 20 | 0.55 | 8 |

Mix No. | Binder Content (kg/m^{3}) | Dune Sand Addition (wt.%) | AAS/B Ratio | SH Molarity (M) | Compressive Strength (MPa) | Permeability (mm/s) | Abrasion Resistance (%) |
---|---|---|---|---|---|---|---|

1 | 400 | 0 | 0.50 | 8 | 12.7 | 7.23 | 14.4 |

2 | 400 | 10 | 0.55 | 10 | 16.5 | 6.62 | 21.2 |

3 | 400 | 20 | 0.60 | 12 | 26.4 | 5.15 | 35.3 |

4 | 450 | 0 | 0.55 | 12 | 22.1 | 5.63 | 28.1 |

5 | 450 | 10 | 0.60 | 8 | 22.8 | 5.41 | 29.6 |

6 | 450 | 20 | 0.50 | 10 | 40.7 | 3.02 | 55.0 |

7 | 500 | 0 | 0.60 | 10 | 21.4 | 5.76 | 27.5 |

8 | 500 | 10 | 0.50 | 12 | 32.2 | 4.25 | 43.5 |

9 | 500 | 20 | 0.55 | 8 | 38.6 | 3.23 | 50.0 |

Response Criterion | Normalized Weights for Each Criterion | ||||
---|---|---|---|---|---|

Target Values | Scenario 1 | Scenario 2 | Scenario 3 | Scenario 4 | |

Compressive Strength | Larger is better | 0.80 | 0.10 | 0.10 | 0.33 |

Permeability | Larger is better | 0.10 | 0.80 | 0.10 | 0.33 |

AbrasionResistance | Larger is better | 0.10 | 0.10 | 0.80 | 0.33 |

Mix No. | S/N 1 (Compressive Strength) | S/N 2 (Permeability) | S/N 3 (Abrasion Resistance) |
---|---|---|---|

1 | 22.08 | 17.18 | 23.17 |

2 | 24.35 | 16.42 | 26.53 |

3 | 28.43 | 14.24 | 30.96 |

4 | 26.89 | 15.01 | 28.97 |

5 | 27.16 | 14.66 | 29.43 |

6 | 32.19 | 9.60 | 34.81 |

7 | 26.61 | 15.21 | 28.79 |

8 | 30.16 | 12.57 | 32.77 |

9 | 31.73 | 10.18 | 33.98 |

Mix No. | Scenario 1 | Scenario 2 | Scenario 3 | Scenario 4 |
---|---|---|---|---|

1 | 0.1552 | 0.8903 | 0.1472 | 0.5035 |

2 | 0.2654 | 0.8690 | 0.3147 | 0.5589 |

3 | 0.6282 | 0.6127 | 0.6670 | 0.6305 |

4 | 0.4840 | 0.7096 | 0.5042 | 0.5971 |

5 | 0.5084 | 0.6651 | 0.5410 | 0.5933 |

6 | 0.8448 | 0.1097 | 0.8528 | 0.4965 |

7 | 0.4586 | 0.7347 | 0.4899 | 0.5976 |

8 | 0.7778 | 0.3992 | 0.8017 | 0.5839 |

9 | 0.8444 | 0.1308 | 0.8419 | 0.5015 |

Compressive Strength | Permeability | Abrasion Resistance | |
---|---|---|---|

α_{0}(A) | 1.122 | −0.179 | 1.687 |

α_{1}(B) | 0.194 | −0.035 | 0.447 |

α_{2}(C) | −921.000 | 176.000 | −1457.000 |

α_{3}(D) | 0.800 | 0.220 | 4.400 |

α_{4}(A^{2}) | −0.001 | 0.001 | −0.002 |

α_{5}(B^{2}) | 0.032 | −0.004 | 0.036 |

α_{6}(C^{2}) | 791.000 | −154.000 | 1261.000 |

α_{7}(D^{2}) | −0.015 | −0.014 | −0.168 |

R^{2} | 0.99 | 0.98 | 0.99 |

RMSE | 1.04 | 0.37 | 1.20 |

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## Share and Cite

**MDPI and ACS Style**

Anwar, F.H.; El-Hassan, H.; Hamouda, M.; El-Mir, A.; Mohammed, S.; Mo, K.H.
Optimization of Pervious Geopolymer Concrete Using TOPSIS-Based Taguchi Method. *Sustainability* **2022**, *14*, 8767.
https://doi.org/10.3390/su14148767

**AMA Style**

Anwar FH, El-Hassan H, Hamouda M, El-Mir A, Mohammed S, Mo KH.
Optimization of Pervious Geopolymer Concrete Using TOPSIS-Based Taguchi Method. *Sustainability*. 2022; 14(14):8767.
https://doi.org/10.3390/su14148767

**Chicago/Turabian Style**

Anwar, Faiz Habib, Hilal El-Hassan, Mohamed Hamouda, Abdulkader El-Mir, Safa Mohammed, and Kim Hung Mo.
2022. "Optimization of Pervious Geopolymer Concrete Using TOPSIS-Based Taguchi Method" *Sustainability* 14, no. 14: 8767.
https://doi.org/10.3390/su14148767