# Predicting Compressive and Splitting Tensile Strengths of Silica Fume Concrete Using M5P Model Tree Algorithm

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## Abstract

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## 1. Introduction

_{2}emissions. Approximately 7% of global CO

_{2}emissions emanate from the construction industry [1]. Due to the alarming threat of climate change, sustainable concrete with enhanced mechanical properties has been developed, incorporating many chemical admixtures and pozzolanic materials such as silica fume (SF).

^{2}/kg and an average particle size that is almost 100 times smaller than that of cement particles. Due to the fact of its fineness, it is a highly effective pozzolanic material with a reasonably quick reactivity in addition to its exceptional micro-filling capacity [2]. From small dosages to up to 50%, SF is added to concrete. However, research shows that the most advantageous and useful dosage range is 5–20%. Its predominant finer fraction acts as a pozzolanic material and reacts in the early stages of strength development, yet it may include larger particles that could persist unreactive at later stages [3]. During cement hydration, C

_{3}S and C

_{2}S in cement particles are hydrated and form calcium silicate hydrate (C-S-H) gel, which plays a vital role in the mechanical strength of concrete. Moreover, some amounts of Ca(OH)

_{2}are produced, remain unreactive, and do not contribute significantly to strength enhancement. With the addition of SF, amorphous silica (SiO

_{2}) reacts with the Ca(OH)

_{2}and produces an additional amount of C-S-H gel, which contributes to mechanical strength enhancement, denser microstructure, and more durable concrete [4]. Studies show that the addition of SF significantly decreases the amount of calcium hydroxide at 3 days. According to the literature, regardless of the water-to-cement (w/c) ratio, all of the Ca(OH)

_{2}was used when 16% SF partial replacement for cement was used [5]. Figure 1b depicts that the amount of CH consumed by the 15% and 20% SF dosages was higher compared with the dosage of 5% at 7, 28, and 56 days [6]. Moreover, it was reported that 12% SF and 0.8% nanosilica increased the total heat of hydration by 48.49% compared to ordinary concrete, while the porosity of the concrete decreased by 6.14%, which resulted in a denser microstructure [7]. Due to the presence of these benefits, SF is also used in ultra-high-performance concrete [8]. However, care should be taken while using SF in concrete with air entrainment, because it may increase the dosage of air-entraining admixtures required for certain air content [9].

## 2. Data Collection

## 3. Methodology

#### 3.1. M5P Model Tree Algorithm

#### 3.2. Comparison of the M5P Models with Other Modeling Techniques

## 4. Model Development and Evaluation Criteria

^{2}). For developing the M5P model for STS, all the settings of the software were kept at default. The default settings were selected because they attained the best performance in terms of the high value of R

^{2}and the low value of the root mean square error (RMSE).

^{2}, mean absolute error (MAE), relative squared error (RSE), RMSE, and discrepancy ratio (DR). The mathematical formulations of these statistical metrics are given in Equations (4)–(9) below.

^{2}< 0.7 indicates poor performance [62], while a model with R > 0.8 generally shows a strong positive correlation between the model estimated and experimental results [63]. The RSME, MAE, and RSE capture the accuracy of the proposed model; higher values of these statistical metrics indicate that the model’s predicted results are far from the actual experimental results, while lower values insinuate that the model’s estimated results have acceptable accuracy. When DR = 0, this shows that the actual and estimated results exactly match each other, while negative and positive DR values indicate underestimation and overestimation, respectively [17]. In this study, for both the CS and STS databases, the accuracy was defined by values of DR ranging from −0.1 to 0.1.

## 5. Results and Discussion

#### 5.1. Compressive Strength

^{2}was 0.82, which shows that the M5P model was well trained based on the training set and gave prediction results with high accuracy for new data unfamiliar to the model and thus far unseen in the testing set. Moreover, the high values of R and DR and low values of MAE, RSE, and RMSE for both datasets confirmed that the M5P model predicted the CS of silica fume concrete with high accuracy. One of the advantages of M5P over other machine learning techniques, such as gene expression programming, is that it gives a simple linear mathematical equation for predicting the desired property [17] and is not a mere backbox tool.

^{2}followed by GEP and linear regression analysis, respectively. Although the accuracy of linear regression analysis was lower compared with that of the other modeling techniques, its primary advantage is that it gives one simple mathematical equation for estimating the CS. In the case of GEP, the accuracy was lower compared to that of M5P. M5P provides simple mathematical equations for calculating CS, while GEP often generates complex nonlinear empirical equations, which may be inconvenient to use [17]. The higher performance of M5P compared with the other modeling techniques considered herein is further confirmed in Table 4, which shows that the values of R and DR for M5P were higher compared with the corresponding values for GEP and the linear regression analysis, while the values of RSE, RMSE, and MAE for M5P were lower.

#### 5.2. Splitting Tensile Strength

^{2}were 0.88 and 0.86 for the training and testing datasets, respectively, as shown in Figure 8, which was slightly higher compared with the corresponding values for the M5P model developed for CS. In Figure 8, the slope of the regression line for both datasets was close to 1, showing that the M5P model was well trained and captured the relationship between input and output variables, which allowed for predicting the STS of silica fume concrete with high accuracy. Moreover, the high value of R and low value of RSE for both the training and testing datasets indicate that the difference between the actual and model estimated results were low and that the predicted and estimated values were close to each other.

^{2}= 0.88) compared with that of GEP (R

^{2}= 0.78) and the linear regression analysis (R

^{2}= 0.66). A similar trend was observed for the testing set. The value of the slope of the regression line (0.82 and 0.86 for the training and testing set, respectively) was close to 1, which indicates that the difference between the actual and predicted values was low. The higher performance of M5P over GEP and the linear regression analysis is also displayed in Table 6, which shows that the value of R for M5P was higher for both datasets, while the values of RMSE, RSE, and MAE were lower. Although different statistical metrics show that the performance of GEP was higher compared with that of the linear regression analysis, the value of DR in the testing set for the former was lower compared to the latter. Therefore, it would be better to use a variety of statistical metrics for the comparison of different models instead of relying only on limited metrics.

#### 5.3. Parametric Analysis

^{3}, the CS increased linearly from approximately 54 to 69 MPa. This increase in strength can be attributed to the pozzolanic activity of SF and its capacity for microfilling because of its ultrafine particles, which increase the density of the matrix and the transition zone between the cement paste and aggregate, densifying the microstructure and strengthening the bond between the paste and aggregate [12]. When the SF is added to the concrete, it is claimed that the interfacial transition zone (ITZ) between the paste and aggregates is less porous and has a homogenous microstructure [64]. It was reported that the reduction in ITZ was 25% by adding 10% SF, while the reduction was 65% at 30% SF [65]. It was illustrated that by incorporating 6% and 12% SF, porous, rough, and heterogeneous concrete microstructural characteristics transformed into dense, flat, and homogeneous features, respectively [66]. Table 7 indicates that the use of SF in concrete decreased the porosity, consequently increasing CS. Similar to the present results, several researchers observed an increase in CS with the incorporation of SF [10,30]. However, it was also reported that beyond a certain threshold, a higher SF dosage was not beneficial for CS enhancement. For example, Siddique et al. [12] noted that SF enhanced the CS of concrete; however, at a very high content, it was not effective for an increase in CS, yet it was effective at improving other hardened properties such as the flexural strength. Due to the fact of its large surface area, a higher dosage of SF absorbs more water, and more SP is needed to make the mixture workable, which also increases the cost [10].

## 6. Conclusions

- (1)
- The results of this study show that the application of the M5P technique for the prediction of the CS and STS of concrete made with SF yielded high predictive and generalization capabilities. A comparison of different techniques showed that M5P had superior predictive performance compared with linear regression analysis and gene expression programming for both the CS and STS databases;
- (2)
- In the case of prediction of the CS using M5P, the values of R
^{2}for both the training and testing sets were 0.82, while for the STS, the value of R^{2}was 0.88 for the training set and 0.86 for the testing set. For predicting both the CS and STS of concrete with SF, the accuracy of the prediction techniques for both training and testing sets was as follows: M5P > GEP > linear regression analysis; - (3)
- PA captured a linear correlation between the SF content and both the CS and STS. Both CS and STS increase by increasing the content of SF. For both the CS and STS of concrete with SF, it was observed that both parameters decreased by increasing the w/b ratio. In the case of CS, high early strength gain was observed owing to rapid SF pozzolanic reactions. While at later ages, the strength gain was not significant. For the STS, the strength gain was almost linear in the first 7 days and then increased nonlinearly with age, mostly up to 28 days.

## 7. Future Research

- (1)
- In this study, only individual machine learning (ML) techniques were used for predicting the mechanical properties of concrete with silica fume. It would be beneficial to predict these properties of concrete with silica fume by using the ensemble machine learning technique and comparing it with individual techniques;
- (2)
- In this study, parametric analysis (PA) was conducted and variation in mechanical properties was checked with only silica fume content, w/b ratio, and the age of specimens. In the future, it will be useful to conduct PA using a more accurate ML technique and to explore variations in mechanical properties with cement content, aggregate, and superplasticizer dosages as well. Moreover, sensitivity analysis needs to be investigated;
- (3)
- We predicted only the compressive and splitting tensile strengths of concrete with silica by using ML techniques. Other properties, such as rheology, elastic modulus, flexural strength, and durability characteristics of concrete with silica fume, need to be predicted.

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**The amount of CH produced by (

**a**) OPC and (

**b**) consumed by silica fume at different percentages of cement replacement [6].

**Figure 2.**Histograms of (

**a**) cement; (

**b**) SF; (

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

**d**) FA; (

**e**) CA; (

**f**) SP; (

**g**) days; (

**h**) CS; (

**i**) STS.

**Figure 3.**Illustration of the M5 algorithm: (

**a**) splitting of the input space; (

**b**) building of the tree.

**Figure 6.**Comparison of the linear regression analysis, GEP, and M5P for the prediction of the CS of concrete made with SF: (

**a**) training dataset; (

**b**) testing dataset.

**Figure 9.**Comparison of the linear regression analysis, GEP, and M5P for the prediction of STS of concrete made with SF: (

**a**) training set; (

**b**) testing set.

Compressive Strength Database | ||||||||
---|---|---|---|---|---|---|---|---|

Statistical Indicator | C (kg/m ^{3}) | SF (kg/m ^{3}) | W/B | FA (kg/m^{3}) | CA (kg/m ^{3}) | SP (kg/m ^{3}) | Days | Strength (MPa) |

Minimum | 188 | 0 | 0.14 | 468.98 | 0 | 0 | 1 | 3.57 |

Maximum | 1000 | 250 | 0.83 | 2750 | 1248 | 80 | 400 | 136.8 |

Mean | 422.55 | 39.35 | 0.42 | 806.32 | 969.9 | 8.7 | 53.4 | 53.72 |

Standard error | 4.44 | 1.37 | 0.005 | 10.02 | 11.51 | 0.46 | 3.11 | 0.83 |

Standard deviation | 125.26 | 38.72 | 0.14 | 282.7 | 324.9 | 13.15 | 87.92 | 23.53 |

Kurtosis | 2.54 | 7.27 | 0.6 | 21.15 | 3.15 | 13.75 | 6.53 | −0.178 |

Skewness | 0.99 | 2.13 | 0.92 | 3.85 | −1.97 | 3.51 | 2.65 | 0.325 |

Splitting Tensile Strength Database | ||||||||

Minimum | 197 | 0 | 0.14 | 535 | 0 | 0 | 1 | 0.51 |

Maximum | 800 | 250 | 0.83 | 1315 | 1248 | 80 | 91 | 10 |

Mean | 458.02 | 54.36 | 0.38 | 816.58 | 892.56 | 13.19 | 32.11 | 4.23 |

Standard error | 11.54 | 4.94 | 0.01 | 16.76 | 29.36 | 1.83 | 2.24 | 0.15 |

Standard deviation | 144.07 | 61.65 | 0.14 | 209.34 | 366.71 | 22.83 | 27.95 | 1.87 |

Kurtosis | −0.07 | 2.46 | 1.31 | −0.15 | 1.37 | 3.64 | 0.15 | 0.46 |

Skewness | 0.73 | 1.76 | 0.67 | 0.85 | −1.54 | 2.29 | 1.12 | 0.68 |

Parameters | GEP Model for CS | GEP Model for STS |
---|---|---|

Head size | 10 | 10 |

Chromosome | 30 | 50 |

Genes | 3 | 5 |

Linking function | Addition | Addition |

Number of generations | 50,000 | 50,000 |

Linear Model | a | b | c | d | e | f | g | h |
---|---|---|---|---|---|---|---|---|

LM1 | 78.471 | 0.0055 | −222.5715 | 0.0343 | 0.0077 | 0.021 | 2.6966 | |

LM2 | 61.8093 | 0.1844 | −92.516 | 0.0277 | 0.0303 | 0.021 | 0.0331 | |

LM3 | 87.4672 | −0.0032 | −161.529 | 0.0268 | 0.0134 | 0.021 | 0.0413 | |

LM4 | 165.2335 | −0.0091 | −380.5541 | 0.0226 | 0.0134 | 0.021 | 0.0423 | |

LM5 | 104.29 | 0.0955 | −172.6348 | 0.0266 | 0.0134 | 0.021 | 0.0422 | |

LM6 | 25.74 | −0.003 | −12.1069 | 0.0001 | 0.0005 | 0.7868 | 1.7661 | |

LM7 | 28.5248 | −0.003 | −12.1069 | 0.0001 | 0.0005 | 0.7868 | 1.4339 | |

LM8 | 31.443 | −0.003 | −12.1069 | 0.0001 | 0.0005 | 1.2469 | 1.5649 | |

LM9 | 38.8668 | −0.0022 | −12.1069 | 0.0001 | 0.0005 | 0.4578 | 0.3137 | |

LM10 | 45.222 | −0.0022 | −12.1069 | 0.0001 | 0.0005 | 0.5065 | 0.3137 | |

LM11 | 22.314 | −0.0017 | −18.5849 | 0.0001 | 0.0005 | 0.2503 | 2.1477 | |

LM12 | 46.1883 | −0.0667 | −15.2811 | 0.0163 | 0.0005 | 0.1293 | 0.0216 | |

LM13 | 57.5337 | −0.0667 | −15.2811 | 0.0063 | 0.0005 | 0.1293 | 0.0216 | |

LM14 | 59.0744 | −0.0955 | −15.2811 | −0.0053 | 0.0005 | 0.1293 | 0.0216 | |

LM15 | 54.7424 | −0.1202 | −15.2811 | −0.0053 | 0.0005 | 0.1293 | 0.0216 | |

LM16 | 67.5622 | −0.0577 | −15.2811 | −0.0054 | 0.0005 | 0.1293 | 0.0296 | |

LM17 | 83.8422 | −0.0238 | −62.7051 | −0.0018 | 0.0005 | 0.1293 | 0.0224 | |

LM18 | 75.9732 | −13.91 | −0.0043 | 0.0005 | 0.1795 | 0.0144 | ||

LM19 | 61.0595 | −13.91 | −0.0006 | 0.0005 | 0.1795 | 0.0144 | ||

LM20 | 66.9734 | −13.91 | −0.0014 | 0.0005 | 0.1795 | 0.0144 |

Models for CS | Training Set | Testing Set | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

R | MAE | RSE | RMSE | DR (%) | R | MAE | RSE | RMSE | DR (%) | |

Linear regression analysis | 0.74 | 13.6 | 0.45 | 16.5 | 47 | 0.73 | 16 | 0.47 | 19.6 | 50 |

GEP | 0.86 | 10.3 | 0.26 | 13.35 | 78 | 0.86 | 9.9 | 0.26 | 13.6 | 70 |

M5P | 0.91 | 8.37 | 0.19 | 10.46 | 78.6 | 0.9 | 9 | 0.18 | 12.4 | 75 |

Linear Model | a | b | c | d | e | f | g | h |
---|---|---|---|---|---|---|---|---|

LM1 | 15.27 | −0.012 | 0.003 | −17.43 | 0.0109 | 0.0293 | ||

LM2 | −2.75 | 0.0113 | 0.0112 | −5.02 | 0.0176 | 0.017 | ||

LM3 | −3.877 | 0.0114 | 0.0056 | 2.1 | 0.0011 | −0.0077 | 0.0173 | |

LM4 | 11.53 | −0.0034 | 0.0091 | −15.12 | −0.0006 | −0.083 | 0.0173 |

Models for STS | Training Set | Testing Set | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

R | MAE | RSE | RMSE | DR (%) | R | MAE | RSE | RMSE | DR (%) | |

Linear regression analysis | 0.81 | 1.1 | 0.37 | 1.23 | 46 | 0.83 | 0.84 | 0.32 | 1.1 | 68 |

GEP | 0.88 | 0.71 | 0.22 | 0.9 | 75 | 0.84 | 0.83 | 0.3 | 1.09 | 66 |

M5P | 0.94 | 0.51 | 0.14 | 0.64 | 75.3 | 0.93 | 0.7 | 0.17 | 0.85 | 75 |

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## Share and Cite

**MDPI and ACS Style**

Shah, H.A.; Nehdi, M.L.; Khan, M.I.; Akmal, U.; Alabduljabbar, H.; Mohamed, A.; Sheraz, M.
Predicting Compressive and Splitting Tensile Strengths of Silica Fume Concrete Using M5P Model Tree Algorithm. *Materials* **2022**, *15*, 5436.
https://doi.org/10.3390/ma15155436

**AMA Style**

Shah HA, Nehdi ML, Khan MI, Akmal U, Alabduljabbar H, Mohamed A, Sheraz M.
Predicting Compressive and Splitting Tensile Strengths of Silica Fume Concrete Using M5P Model Tree Algorithm. *Materials*. 2022; 15(15):5436.
https://doi.org/10.3390/ma15155436

**Chicago/Turabian Style**

Shah, Hammad Ahmed, Moncef L. Nehdi, Muhammad Imtiaz Khan, Usman Akmal, Hisham Alabduljabbar, Abdullah Mohamed, and Muhammad Sheraz.
2022. "Predicting Compressive and Splitting Tensile Strengths of Silica Fume Concrete Using M5P Model Tree Algorithm" *Materials* 15, no. 15: 5436.
https://doi.org/10.3390/ma15155436