# Engineering Properties of Engineered Cementitious Composite and Multi-Response Optimization Using PCA-Based Taguchi Method

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Work

#### 2.1. Materials

#### 2.2. Mix Design

_{PVA}) were selected as the mix design factors. The combinations of these mix factors with five levels were reduced from 625 (25 × 25) possible trials to 25 mix proportions using an orthogonal array (L

_{25}), as summarized in Table 2. The mass fraction of superplasticizer for each mix proportion is also presented in Table 2.

#### 2.3. Test Method

## 3. Results and Discussion

#### 3.1. Engineering Properties of ECC

_{PVA}. Despite the possible shape change in fly ash particles resulting from the milling procedure [36], the degeneration of flowability is not observed for ECC mixtures containing ground fly ash. The possible reason is the higher packing density brought about by the ground fly ash that releases the water to lubricate the particles [37,38]. Meanwhile, the micro fly ash particles tend to bind with water, leading to the formation of compounds with a larger volume than the water itself. Therefore, the inter-particle spacing between the rough cement grains is increased [39]. The maximum flow expansion was obtained with A5B1C5D1 (FA: 0.700, S/B: 0.250, W/B: 0.5000, V

_{PVA}: 0).

_{PVA}: 0.005–0.015) on the compressive strength is exhibited in Figure 6b. The most significant improvement in the compressive strength was achieved with FA ranging from 0.375 to 0.525, which could be the result of relatively early pozzolanic reaction between the fly ash and calcium hydroxide. In terms of the PVA fiber reinforcement, the bridging effect acts as the lateral constraint for the specimens subjected to the vertical loading. While the ECC specimen split into parts and experienced spalling due to the absence of fibers (Figure 7a), the specimen reinforced with PVA fibers did not disintegrate even at the stage of failure in compression (Figure 7b). However, there is a risk of strength degradation resulting from the increase in fiber content, as shown in Figure 6b. The pores induced by excessive fibers are likely to worsen the density of specimens. Additionally, the compressive strength of ECC can obviously benefit from the moderate S/B (around 0.500) and low W/B (0.2500–0.3125). The maximum compressive strength was obtained with A3B3C2D3 (FA: 0.350, S/B: 0.500, W/B: 0.3125, V

_{PVA}: 0.010).

_{PVA}> 1.5% (Figure 6c) and the relatively poor post-cracking performance of Mix. 25 was observed (Figure 8). The maximum flexural strength was obtained with A3B3C1D4 (FA: 0.350, S/B: 0.500, W/B: 0.2500, V

_{PVA}: 0.015).

_{PVA}= 2.0% (lower than the S/N ratio at V

_{PVA}= 0) due to the difficulties in providing a homogeneous distribution of numerous fibers in the ECC mixtures. Moreover, the ECC became obviously more permeable with the ascending W/B. Both the hydration progress and the evaporation of free water induce some deficiencies in the paste and the interfaces, thereby weakening the resistance to chloride ion penetration. It can be observed from Figure 6d that the A3B3C1D3 (FA: 0.350, S/B: 0.500, W/B: 0.2500, V

_{PVA}: 0.010) provided the minimum amount of charge passed.

_{PVA}= 2.0%. Reasonable S/B also helps the ECC materials gain adequate density and strength prior to the frost exposure. Nevertheless, higher sand content is against the freeze–thaw resistance since the paste ratio is simultaneously decreased. Furthermore, the ground fly ash was found to be beneficial to the freeze–thaw resistance, especially at a replacement rate of 35%. The optimum condition under the frost exposure was A3B3C1D4 (FA: 0.350, S/B: 0.500, W/B: 0.2500, V

_{PVA}: 0.015).

#### 3.2. Principal Component Analysis of Test Data

_{i,j}(i = 1, 2, …, q; j = 1,2, …, p) is the S/N ratio of the jth response collected from the ith trial, q is the number of trials under each test condition, and p is the number of responses. The S/N ratios were normalized as follows to eliminate the difference among units:

_{i,j}is the normalized S/N ratio, R

_{j}

_{,max}is the maximum S/N ratio of the jth response, and R

_{j}

_{,min}is the minimum S/N ratio of the jth response. Thus, the normalized multi-response array can be expressed by

_{l,k}as follows:

_{i,l}, N

_{i,k}) denotes the covariance of N

_{i,l}and N

_{i,k}; Var (N

_{i,l}) and Var (N

_{i,k}) are the variance of N

_{i,l}and N

_{i,k}, respectively. The eigenvalues and eigenvectors can be defined as follows:

_{1}, a

_{2}, …, a

_{p}]

^{T}refer to the eigenvalues and eigenvectors of correlation array {C}, respectively. The jth eigenvector [V

_{j}] = [a

_{1j}, a

_{2j}, …, a

_{pj}]

^{T}meets the condition (a

_{1j})

^{2}+ (a

_{2j})

^{2}+ … + (a

_{pj})

^{2}= 1. The jth principal components [P

_{j}] are formulated as

#### 3.3. Estimation of the Optimum Mix Formulation

_{PVA}). It was found that the combination of A3 (FA = 0.350), B3 (S/B = 0.500), C1 (W/B = 0.2500), and D3 (V

_{PVA}= 0.010) constituted the optimum mix formulation.

_{1j})

^{2}+ (a

_{1j})

^{2}+ … + (a

_{pj})

^{2}= 1, the weighting parameter for the lth response (ω

_{l}) could be expressed by a simple linear equation containing the squares of elements from the top two principal components’ eigenvectors. Thus, the ω

_{l}was formulated as follows:

_{1}and α

_{2}are the coefficients of correction affected by the relative roles of principal components. It should be a good attempt to determine each coefficient using the eigenvalue of the relevant principal component. Since the weights comply with the condition ω

_{1}+ ω

_{2}+ … + ω

_{p}= 1, it can be concluded that α

_{1}+ α

_{2}= 1. Thus, the coefficients of correction were calculated as follows:

_{1}and λ

_{2}are the eigenvalues of the first and second principal components, respectively. Thus, the weighting parameter for the lth response (ω

_{l}) was established as follows:

_{l}

_{1}and a

_{l}

_{2}are the elements from the eigenvectors of the corresponding principal components. The results are tabulated in Table 3.

#### 3.4. Analysis of Variance

_{PVA}were identified as the significant factors, while S/B with an F-value lower than the critical level (3.84) was insignificant. Furthermore, the contribution rates are plotted in Figure 14, implying the relative importance of each mix design factor. The W/B was observed to be the dominant factor governing the principal performance, which accounted for 47.20% of the total contribution. The PVA fiber was indicated to be an effective reinforcement system for the ECC materials, as it contributed up to 33.60%. Moreover, the effect of ground fly ash as a partial substitution for Portland cement cannot be ignored, the contribution rate of which was 14.39%. It can be stated that both PVA fiber and ground fly ash were the indispensable compositions benefiting the ECC’s overall engineering properties.

#### 3.5. Confirmation Experiment

_{25}orthogonal array, the confirmation experiment was carried out to obtain the actual responses of Mix. A3B3C1D3 (FA: 0.350, S/B: 0.500, W/B: 0.2500, and V

_{PVA}: 0.010). The flow expansion test, compression test, flexure test, electrical indication test, and cyclic freeze–thaw test were performed on the ECC specimens prepared following A3B3C1D3. The test results were compared with the estimated value computed by Equation (15) [45].

_{3}, $\overline{B}$

_{3}, $\overline{C}$

_{1}, and $\overline{D}$

_{3}are the average experimental performance characteristic statistics at the optimal levels of mix design factors, and Q

_{E}is the estimated value of the performance characteristic. Assuming the confidence level of 95%, the confidence interval could be calculated by Equation (16) [45].

_{0.05}(1, f

_{e}) is the F-value corresponding to the confidence level of 95%, and f

_{e}refers to the errors’ degrees of freedom; V

_{e}is the variance of errors; S is the number of replications for confirmation experiments, N is the total number of experiments, and T

_{dof}is the total degrees of freedom related to the estimated value. The estimated values and verified results are summarized in Table 5. It can be seen that all of the experimental values were within the estimated ranges.

## 4. Conclusions

- The original five engineering properties, including flow expansion, compressive strength, flexural strength, charge passed, and maximum freeze–thaw cycles, can be integrated into the single principal performance by the PCA without loss of important information. The principal performance embodies the essential integration of the original responses.
- A new approach based on the PCA was devised to help determine the weighting parameters for utility concept. The optimization results obtained from the updated utility concept were consistent with the PCA-based Taguchi method.
- The analyses of each engineering property and the principal performance indicated that PVA fibers and ground fly ash with proper content (V
_{PVA}: 0.010–0.015; FA: 0.350–0.525) can significantly improve the fresh, hardened, and durability properties of ECC materials. Moreover, the analysis of variance points to the considerable contribution of PVA fiber reinforcement (33.60%) to the principal performance. - An optimum ECC mix formulation (FA: 0.350, S/B: 0.500, W/B: 0.2500, and V
_{PVA}: 0.010) is recommended through statistical analysis of the principal performance. This mix formulation provides the most desired balance of flowability, compressive strength, flexural strength, chloride ion penetration resistance, and freeze–thaw resistance, which was verified by the additional experiment. This hybrid method provides a reliable reference for the ECC’s multi-performance-oriented mix design.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 6.**Average signal-to-noise (S/N) ratios of different engineering properties: (

**a**) flow expansion; (

**b**) compressive strength; (

**c**) flexural strength; (

**d**) charge passed; (

**e**) maximum freeze–thaw cycles.

**Figure 7.**Examples of failed engineered cementitious composite (ECC) compression test specimens with different polyvinyl alcohol (PVA) fiber reinforcement conditions: (

**a**) without fiber; (

**b**) 1.0 vol.% PVA fiber.

**Figure 10.**The distribution of ECC mixtures in the two-dimensional space represented by the top two principal components.

**Figure 12.**The dependence of average principal performance statistics on varying factors and levels.

Hydraulic Binders | Chemical Analysis of Basic Oxides (wt. %) | |||||
---|---|---|---|---|---|---|

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

Portland cement | 21.08 | 5.47 | 3.96 | 62.28 | 1.73 | 2.63 |

Ground fly ash | 55.70 | 25.63 | 5.65 | 6.93 | 2.25 | 0.60 |

**Table 2.**The mix proportions of engineered cementitious composites (ECCs) using the L

_{25}orthogonal array. FA—fly ash content; S/B—sand-to-binder ratio; W/B—water-to-binder ratio; V

_{PVA}—volume fraction of polyvinyl alcohol.

Mixture | Labels | Factors & Levels | Superplasticizer (%) | |||
---|---|---|---|---|---|---|

A(FA) | B(S/B) | C(W/B) | D(V_{PVA}) | |||

1 | A1B1C1D1 | 0 | 0.250 | 0.2500 | 0 | 0.82 |

2 | A1B4C3D2 | 0 | 0.625 | 0.3750 | 0.005 | 0.38 |

3 | A1B2C5D3 | 0 | 0.375 | 0.5000 | 0.010 | 0.09 |

4 | A1B5C2D4 | 0 | 0.750 | 0.3125 | 0.015 | 1.07 |

5 | A1B3C4D5 | 0 | 0.500 | 0.4375 | 0.020 | 0.94 |

6 | A2B4C2D1 | 0.175 | 0.625 | 0.3125 | 0 | 0.22 |

7 | A2B2C4D2 | 0.175 | 0.375 | 0.4375 | 0.005 | 0.05 |

8 | A2B5C1D3 | 0.175 | 0.750 | 0.2500 | 0.010 | 1.51 |

9 | A2B3C3D4 | 0.175 | 0.500 | 0.3750 | 0.015 | 0.30 |

10 | A2B1C5D5 | 0.175 | 0.250 | 0.5000 | 0.020 | 0.50 |

11 | A3B2C3D1 | 0.350 | 0.375 | 0.3750 | 0 | 0.63 |

12 | A3B5C5D2 | 0.350 | 0.750 | 0.5000 | 0.005 | 0.06 |

13 | A3B3C2D3 | 0.350 | 0.500 | 0.3125 | 0.010 | 0.48 |

14 | A3B1C4D4 | 0.350 | 0.250 | 0.4375 | 0.015 | 0 |

15 | A3B4C1D5 | 0.350 | 0.625 | 0.2500 | 0.020 | 1.52 |

16 | A4B5C4D1 | 0.525 | 0.750 | 0.4375 | 0 | 0.48 |

17 | A4B3C1D2 | 0.525 | 0.500 | 0.2500 | 0.005 | 0.68 |

18 | A4B1C3D3 | 0.525 | 0.250 | 0.3750 | 0.010 | 0.10 |

19 | A4B4C5D4 | 0.525 | 0.625 | 0.5000 | 0.015 | 0.05 |

20 | A4B2C2D5 | 0.525 | 0.375 | 0.3125 | 0.020 | 0.59 |

21 | A5B3C5D1 | 0.700 | 0.500 | 0.5000 | 0 | 0 |

22 | A5B1C2D2 | 0.700 | 0.250 | 0.3125 | 0.005 | 0.67 |

23 | A5B4C4D3 | 0.700 | 0.625 | 0.4375 | 0.010 | 0.04 |

24 | A5B2C1D4 | 0.700 | 0.375 | 0.2500 | 0.015 | 1.42 |

25 | A5B5C3D5 | 0.700 | 0.750 | 0.3750 | 0.020 | 0.87 |

Response | Weighting Parameter |
---|---|

Flow expansion | 0.203 |

Compressive strength | 0.192 |

Flexural strength | 0.191 |

Charge passed | 0.207 |

Maximum freeze–thaw cycles | 0.207 |

Mix Design Factor | DF | SS | MS | F-Value | Contribution (%) | Significance |
---|---|---|---|---|---|---|

A | 4 | 105.75 | 26.44 | 16.05 | 14.39 | O |

B | 4 | 22.19 | 5.55 | 3.37 | 3.02 | X |

C | 4 | 346.93 | 86.73 | 52.64 | 47.20 | O |

D | 4 | 246.92 | 61.73 | 37.47 | 33.60 | O |

Error | 8 | 13.18 | 1.65 | - | 1.79 | - |

Total | 24 | 734.97 | - | - | 100.00 | - |

Optimum Combination (A3B3C1D3) | Estimated Value | Experimental Value |
---|---|---|

Flow expansion (cm) | 15.84 ± 3.64 | 17.00 |

Compressive strength (MPa) | 63.16 ± 8.51 | 60.50 |

Flexural strength (MPa) | 13.00 ± 1.83 | 12.17 |

Charge passed (C) | 219.43 ± 281.43 | 359.77 |

Maximum freeze–thaw cycles | 414 ± 73.99 | 425 |

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**MDPI and ACS Style**

Zhong, J.; Shi, J.; Shen, J.; Zhou, G.; Wang, Z. Engineering Properties of Engineered Cementitious Composite and Multi-Response Optimization Using PCA-Based Taguchi Method. *Materials* **2019**, *12*, 2402.
https://doi.org/10.3390/ma12152402

**AMA Style**

Zhong J, Shi J, Shen J, Zhou G, Wang Z. Engineering Properties of Engineered Cementitious Composite and Multi-Response Optimization Using PCA-Based Taguchi Method. *Materials*. 2019; 12(15):2402.
https://doi.org/10.3390/ma12152402

**Chicago/Turabian Style**

Zhong, Junfei, Jun Shi, Jiyang Shen, Guangchun Zhou, and Zonglin Wang. 2019. "Engineering Properties of Engineered Cementitious Composite and Multi-Response Optimization Using PCA-Based Taguchi Method" *Materials* 12, no. 15: 2402.
https://doi.org/10.3390/ma12152402