# Computing Models to Predict the Compressive Strength of Engineered Cementitious Composites (ECC) at Various Mix Proportions

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Methodology and Models

#### 3.1. Data Collection

^{3}), (b) fly ash (FA) content (kg/m

^{3}), (c) w/b ratio (%), (d) SP content by kg/m

^{3}, (e) sand (S) content (kg/m

^{3}), (f) maximum size of sand (MSS) (µm), (g) fiber (F) content by weight (kg/m

^{3}), (h) fiber length (FL) (mm), (i) fiber diameter (FD) (µm), and (j) curing period (T). The presented dataset, which contained the 10 independent components listed above, was used to anticipate the CS of ECC created with various combinations using many techniques compared to the observed reported CS (MPa). The idea behind using all the input parameters indicated above is to reduce the number of trial batches in the laboratory to easily optimize the number of ingredients for a targeted CS. The technique employed in this experiment is shown in Figure 1.

#### 3.2. Modeling

#### 3.2.1. Linear Relationship Model (LR)

^{3}); FA represents fly ash content (kg/m

^{3}); w/b represents water-to-binder ratio; MSS stands for the maximum size of sand (µm); S stands for sand content (kg/m

^{3}); SP stands for superplasticizer dosage (kg/m

^{3}); F stands for fiber content (kg/m

^{3}); FL stands for fiber length (mm); and FD stands for fiber diameter (µm). Furthermore, the model parameters are α1, α2, α3, α4, α5, α6, α7, α8, α9 α10, and α11. Since all factors may be changed linearly, Equation (2) can be used to extend Equation (1). While many factors may influence CS and interact with one another, this is not necessarily the case. Consequently, the model should be updated frequently to appropriately predict the compressive strength [69,70].

#### 3.2.2. Nonlinear Model (NLR)

#### 3.2.3. MLR Model

#### 3.2.4. ANN Model

^{2}[76]. The constructed ANN was trained and evaluated for different hidden layers to establish an ideal network topology based on the projected CS of ECCs, including FA with the CS of the actual collected data. To obtain high ANN efficiency, the authors looked at hidden layers, neurons, momentum, learning rate, and iterations. Finally, they observed that the CS of the SCC containing fly ash is best predicted when the ANN has three hidden layers, each with eleven neurons (as shown in Figure 2), 2000 iterations, 0.2 learning rate, and 0.1 momentum, which provided the greatest R

^{2}and the lowest MAE and RMSE (shown in Figure 3). The general equations of the ANN model may be found in Equations (5)–(7) [76,77,78].

#### 3.2.5. M5P-Tree Model (M5P)

^{3}); FA represents fly ash content (kg/m

^{3}); w/b represents water-to-binder ratio; MSS stands for the maximum size of sand (µm); S stands for sand content (kg/m

^{3}); SP stands for superplasticizer dosage (kg/m

^{3}); F stands for fiber content (kg/m

^{3}); FL stands for fiber length (mm); and FD stands for fiber diameter (µm). Furthermore, the model parameters are α1, α2, α3, α4, α5, α6, α7, α8, α9 α10, and α11.

#### 3.3. Assessment Criteria for the Developed Models

_{p}and t

_{p}indicate the expected and actual values of the route pattern, respectively, as shown in the previous formulations. The mean of the actual and projected values is denoted by T′ and y′, respectively. The letters tr signify trained datasets, the letters tst denote tested datasets, and the letter n denotes the number of patterns (collected data) in the linked dataset. When it comes to the SI parameter, when it is more than 0.3, (reasonably) when it is between 0.2 and 0.3, (well) when it is between 0.1 and 0.2, and (excellently) when it is less than 0.1, a model performs (poorly) when it is greater than 0.3 [79,80].

## 4. Results and Discussion

#### 4.1. Statistical Analysis

^{3}to 39 kg/m

^{3}. Portland cement (OPC) Type I was the most used cement for producing ECC mixes.

^{3}to 756 kg/m

^{3}. Based on the past investigations, the SP type was a polycarboxylate-based high-range water-reducing admixture used to achieve the workability properties of ECC mixes.

#### 4.2. Model Outputs

#### 4.2.1. The LR Model

^{2}, RMSE, and MAE assessment parameters are 0.66, 9.32, and 7.76 MPa, respectively. Furthermore, as shown in Section 5, the current model’s OBJ and SI values for the training dataset are 10.34 and 0.197, respectively.

#### 4.2.2. NLR Model

^{2}, RMSE, and MAE is 0.80 MPa, 7.23 MPa, and 5.95 MPa. The OBJ and SI values for the training dataset are 7.74 and 0.154, respectively.

**Figure 9.**(

**a**) Comparison of the CS of ECC mixtures that were tested and the CS that the NLR model predicted; (

**b**): testing datasets.

#### 4.2.3. MLR Model

^{2}, RMSE, and MAE assessment parameters are 0.79, 7.29, and 5.95 MPa, respectively. In addition, the OBJ and SI values for the current model’s training dataset are 7.76 and 0.154, respectively.

#### 4.2.4. ANN Model

^{2}has an assessment parameter of 0.98, RMSE has a value of 4.55, and MAE has a parameter of 3.46. For the training data, the current model’s OBJ and SI values are 4.39 and 0.096, respectively.

#### 4.2.5. M5P Model

## 5. Model Comparisons

^{2}and lower RMSE and MAE values, as shown in Figure 13, Figure 14 and Figure 15 for R

^{2}values, RMSE, and MAE, respectively. Figure 16 shows model CS estimates for ECC mixes with fly ash based on testing datasets. The residual error for all models that use training and testing datasets is also shown in Figure 17. The estimated and forecasted CS scores for the ANN model are similar in Figure 16 and Figure 17, suggesting that the ANN model outperforms other models.

## 6. Sensitivity Analysis

^{2}, RMSE, and MAE, were established individually. The proportion of model parameter contribution is then computed. The sensitivity assessment result is presented in Figure 20. The results suggest that the most crucial variable for CS prediction is curing time.

## 7. Conclusions

- The average percentage of FA used in the manufacturing of ECC mixtures was 754.83 kg/m
^{3}. In addition, FA replacement with cement ranged from 201 to 1150 kg/m^{3}. The findings from numerous experimental studies had a cure duration ranging from 3 to 180 days; - Except the ANN model, the SI values for all models and stages were between 0.1 and 0.2, indicating that all models performed well. The SI values for the ANN model ranged from 0 to 0.1, indicating that it performed well;
- The ANN model’s OBJ value is 76 percent lower than the NLR and MLR models’, 135 percent lower than the LR model and 47 percent lower than the M5P model. This also demonstrates that the ANN model is more accurate and capable of estimating the CS of ECC mixtures, including FA, than the traditional approach;
- Overall, the data and analyses revealed that particular amounts of FA might be used successfully in ECC manufacturing. Furthermore, the models created in this work, particularly the ANN model, may be utilized to easily predict the mix proportions and CS of ECCs, lowering the number of experimental tests and trial batches in the laboratory.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Based on the model’s R

^{2}, MAE, and RMSE performances, choose the best-hidden layer and neurons for an ANN model.

**Figure 5.**Marginal plot for the CS of ECC versus: (

**a**): cement content; (

**b**): fly ash content; (

**c**): w/b; (

**d**): sand maximum size; (

**e**): sand content; (

**f**): Superplasticizer content; (

**g**): fiber content; (

**h**): fiber length; (

**i**): fiber diameter; (

**j**): specimens ages.

**Figure 8.**Comparison of the CS of ECC mixtures that were tested and the CS that the LR model predicted; (

**a**): training datasets; (

**b**): testing datasets.

**Figure 10.**(

**a**) Comparison of the CS of ECC mixtures that were tested and the CS that the MLR model predicted; (

**b**): testing datasets.

**Figure 11.**(

**a**) Comparison of the CS of ECC mixtures that were tested and the CS that the ANN model predicted; (

**b**): testing datasets.

**Figure 12.**(

**a**) Comparison of the CS of ECC mixtures that were tested and the CS that the M5P model predicted; (

**b**): testing datasets.

**Figure 16.**Comparison of model predictions of the CS of ECC mixtures with data from the test datasets.

**Table 1.**The following is a list of the components of ECC mixes that are documented in the literature.

Refer. | Cement Content (kg/m^{3}) | Fly Ash Content (kg/m^{3}) | w/b | Sand | SP Content (kg/m^{3}) | Fiber | Age (Day) | CS (MPa) | |||
---|---|---|---|---|---|---|---|---|---|---|---|

Max. Size (µm) | Content (kg/m3) | Content (kg/m^{3}) | Length (mm) | Diameter(µm) | |||||||

[24] | 313–570 | 684–940 | 0.28–0.32 | 300 | 380–532 | 2.5–10.4 | 17 | 12 | 26 | 28 | 20–45 |

[34] | 412 | 1150 | 0.23 | 250 | 456 | 10.7 | 18 | 10 | 12 | 28 | 45 |

[35] | 1009.16 | 0 | 0.35 | 300 | 757.53 | 7.05 | 17.9 | 10 | 12 | 28 | 45 |

[36] | 222–375 | 825–978 | 0.26 | 200–425 | 432 | 4.8–5.04 | 26 | 12 | 39 | 28 | 27–50 |

[37] | 471.6 | 754.5 | 0.27 | 300 | 444.1 | 10.8 | 26 | 8 | 39 | 28 | 58 |

[38] | 240–545 | 654–960 | 0.25 | 250 | 432 | 4.8–10.9 | 26–32.5 | 12 | 39 | 28 | 19–32 |

[39] | 570 | 684 | 0.3 | 300 | 0.36 | 5.7 | 28.6 | 12 | 39 | 28 | 59.86 |

[40] | 570 | 684 | 0.56 | 250 | 456 | 6.84 | 29 | 8 | 39 | 7 | 13–69 |

[41] | 232 | 1019 | 0.26 | 250 | 450 | 4.3 | 26 | 12 | 39 | 28 | 17 |

[42] | 250–570 | 684–1000 | 0.25 | 250 | 450 | 7.5–17.1 | 26 | 8 | 39 | 28 | 24–47 |

[43] | 570 | 684 | 0.27 | 400 | 455 | 5.1 | 26 | 8 | 39 | 28 | 53.8 |

[44] | 570 | 684 | 0.27 | 250 | 455 | 4.9 | 26 | 6 | 39 | 7–28 | 28–48 |

[45] | 936 | 201 | 0.32 | 250 | 601 | 4.2 | 26 | 8 | 39 | 56 | 54 |

[46] | 393 | 865 | 0.25 | 250 | 457 | 5 | 26 | 12 | 39 | 28 | 41 |

[47] | 393 | 865 | 0.25 | 250 | 457 | 5 | 26 | 12 | 39 | 28 | 40 |

[48] | 392–570 | 684–862 | 0.27 | 400–1000 | 451–689 | 3–5.5 | 26 | 8 | 39 | 7–180 | 28–78 |

[49] | 820 | 205 | 0.37 | 200 | 656 | 3.07–3.58 | 13–39 | 8–12 | 38 | 7 | 47–63 |

[50] | 570 | 684 | 0.3 | 300 | 456 | 5.1 | 28.6 | 12 | 39 | 28 | 59.86 |

[51] | 337–570 | 684–912 | 0.267 | 250 | 454 | 2.5–5 | 16.9 | 12 | 39 | 28 | 47–52 |

[52] | 578 | 694 | 0.25 | 200 | 462 | 7.51 | 26 | 12 | 39 | 28 | 51 |

[53,54] | 570 | 684 | 0.23 | 150 | 454 | 5.3 | 26 | 8 | 40 | 28 | 60 |

[55,56] | 570 | 684 | 0.27 | 200 | 455 | 4.9 | 26 | 8 | 39 | 7–28 | 37–48 |

[57,58] | 386–570 | 684–847 | 0.27 | 200 | 448–455 | 3.7–4.9 | 26 | 8 | 39 | 7–90 | 21–55 |

[59] | 570 | 684 | 0.27 | 200 | 455 | 5.1 | 26 | 8 | 39 | 7–28 | 37.8–53 |

[60,61] | 375–558 | 669–823 | 0.27 | 200 | 435–446 | 2–2.3 | 26 | 8 | 39 | 14–28 | 27–62 |

[62] | 190–571 | 685–1063 | 0.25 | 250 | 456 | 5.1–6.8 | 26 | 8 | 39 | 3–28 | 8–54 |

[63] | 382–636 | 636–890 | 0.25 | 250 | 462 | 16–17.4 | 26 | 8 | 40 | 3–90 | 17–77 |

[64] | 583 | 699.9 | 0.25 | 100 | 465.7 | 7.6 | 20.1 | 12 | 40 | 28 | 39.9 |

[65] | 418–570 | 684–836 | 0.19–0.25 | 600 | 456 | 5.7–7.41 | 26 | 8 | 40 | 28 | 54–58.6 |

[66] | 404–502 | 605–753 | 0.24–0.3 | 212–4750 | 756 | 23 | 19 | 12 | 24 | 28 | 63 |

[67] | 570 | 684 | 0.27 | 200 | 456 | 7.41 | 26 | 8 | 39 | 28–90 | 47.6–57 |

[68] | 395 | 869 | 0.25 | 200 | 459 | 5.1 | 4.55–24 | 12 | 40 | 28 | 39–51 |

Input Variables | Average | Median | St. Div. | Min. | Max. | Variance | Skewness | Kurtosis |
---|---|---|---|---|---|---|---|---|

Cement content (kg/m^{3}) | 466.11 | 412 | 137.08 | 190 | 936 | 18,791.78 | 0.74 | 0.85 |

Fly ash content (kg/m^{3}) | 754.83 | 763.2 | 173.01 | 201 | 1150 | 29,932.73 | −1.45 | 3.27 |

w/b | 0.27 | 0.27 | 0.04 | 0.19 | 0.56 | 0.00 | 4.21 | 24.82 |

Sand max. size (µm) | 520.05 | 250 | 777.63 | 100 | 4750 | 604,707.45 | 4.31 | 19.88 |

Sand content (kg/m^{3}) | 494.64 | 456 | 92.70 | 380 | 756 | 8593.71 | 0.55 | 4.15 |

SP content (kg/m^{3}) | 7.18 | 5.26 | 4.65 | 2 | 23 | 21.60 | 1.38 | 0.72 |

Fiber content (kg/m^{3}) | 24.71 | 26 | 4.01 | 4.55 | 39 | 16.05 | −1.15 | 4.66 |

Fiber length (mm) | 9.16 | 8 | 1.85 | 6 | 12 | 3.41 | 0.86 | −1.15 |

Fiber diameter(µm) | 37.11 | 39 | 5.18 | 12 | 40 | 26.85 | −2.29 | 4.15 |

Age (days) | 40.22 | 28 | 42.63 | 3 | 180 | 1817.72 | 2.17 | 4.30 |

CS (MPa) | 47.00 | 47.6 | 15.78 | 8.2 | 78.56 | 249.15 | −0.15 | −0.74 |

(LM) num: | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|

α1 | +17.3699 | +33.6287 | +84.574 | +75.5592 | +126.5619 | +62.8256 |

α2 | 0.0276 | 0.0103 | 0.0275 | 0.0316 | 0.0314 | 0.0519 |

α3 | - | - | −0.048 | −0.0379 | −0.0664 | −0.0171 |

α4 | +17.9526 | +30.3504 | −88.3962 | −88.3962 | −187.9927 | −108.9859 |

α5 | +0.0012 | +0.0021 | +0.0059 | +0.0061 | +0.0113 | +0.0042 |

α6 | +0.0064 | +0.0219 | - | - | +0.0228 | |

α7 | +0.2525 | +0.4094 | +0.1043 | +0.1043 | −0.154 | +0.3398 |

α8 | - | - | −0.2552 | −0.2552 | −0.4 | −0.115 |

α9 | - | −1.2723 | - | - | - | - |

α10 | - | - | - | - | - | |

α11 | +0.0998 | +0.1302 | +0.1242 | +0.1242 | +0.1011 | +0.1453 |

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## Share and Cite

**MDPI and ACS Style**

Ghafor, K.; Ahmed, H.U.; Faraj, R.H.; Mohammed, A.S.; Kurda, R.; Qadir, W.S.; Mahmood, W.; Abdalla, A.A.
Computing Models to Predict the Compressive Strength of Engineered Cementitious Composites (ECC) at Various Mix Proportions. *Sustainability* **2022**, *14*, 12876.
https://doi.org/10.3390/su141912876

**AMA Style**

Ghafor K, Ahmed HU, Faraj RH, Mohammed AS, Kurda R, Qadir WS, Mahmood W, Abdalla AA.
Computing Models to Predict the Compressive Strength of Engineered Cementitious Composites (ECC) at Various Mix Proportions. *Sustainability*. 2022; 14(19):12876.
https://doi.org/10.3390/su141912876

**Chicago/Turabian Style**

Ghafor, Kawan, Hemn Unis Ahmed, Rabar H. Faraj, Ahmed Salih Mohammed, Rawaz Kurda, Warzer Sarwar Qadir, Wael Mahmood, and Aso A. Abdalla.
2022. "Computing Models to Predict the Compressive Strength of Engineered Cementitious Composites (ECC) at Various Mix Proportions" *Sustainability* 14, no. 19: 12876.
https://doi.org/10.3390/su141912876