# Thermal Conductivity of Coconut Shell-Incorporated Concrete: A Systematic Assessment via Theory and Experiment

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^{2}

^{3}

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^{*}

## Abstract

**:**

^{3}and thermal conductivity of 0.5952 W/mK, which was lower than the control specimen (0.79 W/mK). The p-value of the optimum concrete mix was less than 0.0001 and the F-value was over 147.47, indicating the significance of all models. It is asserted that ANN, GEP, and RSM are accurate and reliable, and can further be used to predict a strong structural–thermal correlation with minimal error. In brief, the specimen composed with 53% of CA as a replacement for fine aggregate may be beneficial to develop environmentally amiable green structural concrete.

## 1. Introduction

_{2}emission level [13,14,15]. To surmount this adverse impact related to landfills and ecological pollutions, extensive research has recently been carried out for reusing various kinds of wastes.

_{2}has increased up to 30% of the world’s total. This undesirable impact has prompted researchers to search and develop comfortable and sustainable concrete with low thermal conductivity (TC) using some alternative materials than natural aggregates and ordinary Portland cement (OPC) [17,18,19]. In this regard, the replacement of natural aggregates with waste materials was found to be beneficial in terms of the TC of concrete mixes wherein the composition optimization can play a significant role to achieve the sustainable goal [20,21]. Briefly, both wastes accumulation and energy consumption can remarkably be minimized if the construction industries heavily rely on various agricultural and industrial wastes. Marie [22] assessed the TC of concrete incorporated with both crumb rubber and recycled concrete aggregate as the partial replacements of fine and coarse aggregates, respectively. The results showed a significant reduction in the TC of concrete, specifically when the replaced crumb rubber and recycled concrete aggregate were 10% and 20%, respectively [23], which agreed with the observation of Wang and Du [24].

## 2. Theoretical and Experimental Approaches

#### 2.1. Design of Composite

_{o}), whereas time (d

_{1}) was the second variable. Figure 1 shows three types of FC-CCD including factorial, axial, and central point according to their locations [57]. For example, the square vertices points with a coded value of −1 and +1 are related to factional point. Moreover, the points that are situated at the centre of each face and far from the centre of the square with a distance of $\pm \alpha $ are referred as axial or star points, while the central points are located at the centre of the square with a value of zero. It should be noted that the value of α is always one using FC-CCD. Consequently, the suggested number of experiment tests was 13 using Equation (1) [58], where Z

_{o}and Z were the real value of independent variables at the centre point and real value of independent value, respectively. Here, α and R are the step change and coded value of the independent variable, respectively. The suggested experimental tests were similar to the FC-CCD which enclosed four corner points, four axial points, and one central point. The relationship between both the coded and actual values of the experimental tests was also expressed using Equation (2) [59], where m is the number of central points. Table 1 displays all points including both coded and real values of the required experimental works according to the FC-CCD method.

_{i}is the linear coefficient, β

_{o}is the intercept of the model, and β

_{ii}is the quadratic coefficient; X

_{1}and X

_{2}represents the independent variables (replaced CA and time). The outputs of the quadratic equation (namely response or dependent variables) refer the flexural strength (FS), splitting tensile strength (STS), and compressive strength (CS). In addition, the accuracy of the equation was checked and verified using analysis of variance (ANOVA).

^{2}), predicted R

^{2}, and adjusted R

^{2}were used for the model validation. Particularly, a developed equation can be classified as significant if p-value is below 0.005 and F-value is high [61]. Similarly, the value of adequate precision should be above 4 to indicate an adequate signal [62]. Moreover, a strong correlation between the actual and estimated results can be obtained if R

^{2}is over 0.75 [63]. In addition, a model can be used for further prediction when the differences between the predicted R

^{2}and adjusted R

^{2}is less than 0.2 [64].

_{T}), degree of freedom (DF), and residual sum of square obtained from regression (SS

_{E}) were first calculated in order to determine the indicators for statistical validation [65]. In this study, values of both SS

_{E}and SS

_{T}were obtained using Equations (4) and (5), respectively, where Y

_{A}and Y

_{P}are the corresponding actual and predicted values; $\overline{{Y}_{A}}$ is the average actual value. Value of R

^{2}was estimated using Equation (6).

_{T}) and residual error (DF

_{R}), the adjusted R

^{2}was obtained using Equation (7) [66]. Furthermore, the predicted R

^{2}was determined using Equation (8) [67], where W is the estimated residual sum of square without the i

_{th}. Equation (9) presents the adequate precision (SN) that is essential to assess the signal-to-noise (SNR) ratio [68] wherein σ

^{2}is the residual mean square.

#### 2.2. Materials and Mix Design Preparation

#### 2.3. TC Test

#### 2.4. Prediction Using GEP Model

_{o}) and time (d

_{1}).

^{2}were evaluated following Equations (15) and (16), respectively [84,85,86]. Consequently, the fitness and strength between the actual and predicted results were established.

#### 2.5. Prediction ANN Model

_{j}and w

_{ij}are the corresponding biases of the network and weights for each node. The target date was processed using several activation functions to form a mathematical equation similar to an electrical signal. Thereafter, the mathematical equation was passed to another layer, namely the output layer wherein the mathematical equation was exposed to statistics indicators for the evaluation purpose. Based on the statistics indicators, the mathematical equation was accepted or rejected in the third layer. This process was repeated until it met the requirement of statistics validation methods. The TanH sigmoid function was used as the activation function (Equation (17)). The experimental data (input data) were divided into training (75%) and validation (25%). The number of neurons and hidden layer were three and one, receptively. For the purpose of model verification the values of R

^{2}, root average squared error (RASE) and sum square error (SSE) were calculated using Equations (18) and (19).

## 3. Results and Discussion

#### 3.1. Informational Modeling Using RSM

^{2}was also determined to evaluate the correlation between the actual and estimated data. The value of R

^{2}for the TC and density were 0.9906 and 0.9986, respectively, affirming the achievement of a good fitness and closeness. Similarly, the differences between ${R}_{predicated}^{2}$ and ${R}_{adjusted}^{2}$ was found to be less than 0.2 for both equations. This result confirmed that the model can predict accurately the results with low errors and consistent with the report of Mohammed et al. [89]. Additionally, the value of adjusted R

^{2}was close to R

^{2}, indicating that the variables had no effect on the model performance. The closeness and correlation between the predicted and actual data were also demonstrated using R. According to Carrillo et al. [90], a strong correlation can be obtained when R is greater than 0.8, while the R values in the range of 0.5 and 0.8 signify a moderate correlation. In contrast, the R values less than 0.5 indicate a bad fitness. In the proposed equations, all values of R were greater than 0.995, thus confirming that the fitness between the estimated and actual data was high. The significance of the predicted equations was also proven using adequate precision with value above 41.028. Gong et al. [91] devised a desirable model with adequate precision value over four.

^{3}because beyond 53% the specimen is classified as lightweight concrete. The present results are in good agreement with the reports of Nowak and Rakoczy [93] and Khoshkenari et al. [94], in which the normal (ordinary) concrete displayed the density values in the range of 2240 and 2400 kg/m

^{3}, while the density values for the lightweight concrete are ranged from 1440–1840 kg/m

^{3}. According to Graybeal and Lwin [95], a concrete is biased to be lightweight when its density is lower than 2160 kg/m

^{3}. In accordance to ACI 213R, 2014 [96], the structural lightweight concrete have the density values in the range of 1350 and 1920 kg/m

^{2}. For structural component purpose, the density of lightweight concrete should be within 800 to 2000 kg/m

^{3}according to EN 206-1 [97]. In this present study, the density of concrete incorporated with 53% of CA as the replacement of fine aggregate was 2246 kg/m

^{3}, which indicated that the CA-based concrete belongs to the normal concrete family. Figure 7 presents the variation of density with different replacement percentages of sand by CA.

#### 3.2. Informational Modeling Using GEP

_{o})). Using the Karva language, the structural tree for the TC of concrete was converted into a mathematical equation.

^{2}and R. The achieved values of both R

^{2}and R were greater than 0.93 for training and validation, demonstrating that both results were very close.

#### 3.3. Informational Modeling Using ANN

^{2}value approached to one for both training and validation datasets. Khademi et al. [99] assessed the performance of ANN, ANFIS, and linear regression models in terms of SSE values. The SSE values for ANFIS, linear regression and ANN models were 13.31, 2.199, and 0.8389 for the models, respectively. In this work, the value of SSE was discerned to be lower than 0.005, indicating the accuracy and reliability of an ANN model in predicting the TC of CA-included concrete. Mohamed et al. [100] used the RASE model to determine the accuracy of the predicted equation for the CS of sustainable self-consolidating concrete. The predicted equation yielded a low RASES value of 0.0549. In the current ANN model, the RASE values corresponding to the training and validation datasets were 0.0183 and 0.032, confirming the attainment of minimum error with the ANN model.

#### 3.4. Parametric Analysis

## 4. Conclusions

- The optimum replacement percentage of fine aggregate by CA was 53% which produced a normal concrete with density of 2246 kg/m
^{3}. Beyond this content of CA, the concrete can be defined as lightweight because the density was below 2000 kg/m^{3}. - The TC of concrete containing 53% of CA (0.5903 W/mK) was lower compared to the control concrete (0.76 W/mK), indicating its suitability in the construction sectors.
- Incorporation of CA as partial replacement of fine aggregate (53%) in the proposed concrete can be beneficial for the creation of sustainable green concrete with lower greenhouse gases emission.
- The accuracy of the developed equation obtained from RSM was proven using ANOVA, in which the p-value was less than 0.0001, while the F-value was high (147.47).
- Error statistics parameters also proved the capability of the GEP model to accurately predict the thermal properties of concrete, in which RMSE < 0.038, RRSE < 0.609, RAE < 0.668, and MAE < 0.035 were obtained for both training and validation.
- Correlation and error statistics parameters for the ANN model reaffirmed that the relationship between the predicted and actual results were close, in which R
^{2}> 0.91, while RASE < 0.0183 and SSE < 0.0050 were obtained for all data set.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Hot guarded box setup with the (

**a**) placement of concrete mix inside the hot box and (

**b**) connection with power supply.

**Figure 6.**Interaction between the TC and density with CA content (

**a**) thermal properties (

**b**) density.

**Figure 9.**TC evolution in CA-based concrete predicted via (

**a**) RSM, (

**b**) GEP, and (

**c**) ANN models; (

**d**) relationship between density and k-value of concrete.

Run No. | Coded Value | Real Value | FC-CCD Division | ||
---|---|---|---|---|---|

Replaced CA (%) | Time (Days) | ||||

1 | −1 | −1 | 10 | 7 | Factorial points (2^{n}) |

2 | 1 | −1 | 100 | 7 | |

3 | −1 | 1 | 10 | 28 | |

4 | 1 | 1 | 100 | 28 | |

5 | 1 | 0 | 10 | 17 | Axial points (2 ^{n}) |

6 | −1 | 0 | 100 | 17 | |

7 | 0 | −1 | 55 | 7 | |

8 | 0 | 1 | 55 | 28 | |

9 | 0 | 0 | 55 | 17 | Centre points |

Item | Second Polynomial Equations and Statistical Parameters | |||||
---|---|---|---|---|---|---|

TC | R = 0.995 | R^{2} = 0.9906 | ${R}_{adj}^{2}=$ 0.9839 | ${R}_{predicted}^{2}$ 0.905 | Adeq. Precision 41.028 | RMSE 0.011 |

$TC=0.522-0.15{d}_{0}+0.05{d}_{1}+0.01{d}_{o}{d}_{1}-0.008{d}_{o}^{2}+0.017{d}_{1}^{2}$ | ||||||

Density | R = 0.999 | R^{2} = 0.9986 | ${R}_{adj}^{2}=$ 0.997 | ${R}_{predicted}^{2}$ 0.986 | Adeq. Precision 104.47 | RMSE 6.652 |

$D=1994.2-171.67{d}_{o}+10.83{d}_{1}-2.5{d}_{0}{d}_{1}-20.89{d}_{o}^{2}+235.6{d}_{1}^{2}$ |

Item | TC | Density | ||||
---|---|---|---|---|---|---|

p-Value | F-Value | Sig. | p-Value | F-Value | Sig. | |

Model 1 | <0.0001 | 147.47 | Y | <0.0001 | 994.33 | Y |

d_{o} | <0.0001 | 660.32 | <0.0001 | 2539.3 | ||

d_{1} | <0.0001 | 71.25 | 0.0155 | 10.11 | ||

d_{o}d_{1} | 0.2173 | 1.84 | 0.5679 | 0.359 | ||

${d}_{o}^{2}$ | 0.4017 | 0.796 | 0.0042 | 17.31 | ||

${d}_{1}^{2}$ | 0.0874 | 3.94 | <0.0001 | 2201.8 |

No. of Solution | CA Content (%) | TC (W/mK) | Density (kg/m ^{3}) |
---|---|---|---|

1 | 100 | 0.4376 | 2045 |

2 | 93.1 | 0.4617 | 2077 |

3 | 90.8 | 0.4698 | 2088 |

4 | 82.4 | 0.4991 | 2126 |

5 | 68.11 | 0.5474 | 2188 |

6 | 53 | 0.5952 | 2246 |

7 | 47.6 | 0.6136 | 2268 |

8 | 38.26 | 0.643 | 2303 |

9 | 20.39 | 0.697 | 2362 |

10 | 10 | 0.7271 | 2394 |

Item (W/kM) | Mathematical Equation and Related Statistical Validation Parameters | ||||||
---|---|---|---|---|---|---|---|

TC | Training | RAE = 0.265 | MAE = 0.022 | RMSE = 0.036 | RRSE = 0.334 | R = 0.964 | R^{2} = 0.93 |

Validation | RAE = 0.668 | MAE = 0.035 | RMSE = 0.038 | RRSE = 0.609 | R = 0.973 | R^{2} = 0.946 | |

$TC=\frac{4\sqrt{{d}_{o}}+2{d}_{1}+2{c}_{o}}{{d}_{0}+3{d}_{1}}$ |

Item (W/kM) | Mathematical Equation and Related Statistical Validation Parameters | ||||
---|---|---|---|---|---|

TC_{ANN} | Training | RASE = 0.0183 | SSE = 0.0050 | Mean Abs. Dev. = 0.0142 | R^{2} = 0.952 |

Validation | RASE = 0.0320 | SSE = 0.0051 | Mean Abs. Dev. = 0.0268 | R^{2} = 0.915 | |

$T{C}_{ANN}=0.537-3.56\mathrm{Tan}H\left(0.5\left(-0.066+0.0018{d}_{o}-0.0023{d}_{1}\right)\right)$ |

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## Share and Cite

**MDPI and ACS Style**

Mhaya, A.M.; Shahidan, S.; Algaifi, H.A.; Zuki, S.S.M.; Benjeddou, O.; Ibrahim, M.H.W.; Huseien, G.F.
Thermal Conductivity of Coconut Shell-Incorporated Concrete: A Systematic Assessment via Theory and Experiment. *Sustainability* **2022**, *14*, 16167.
https://doi.org/10.3390/su142316167

**AMA Style**

Mhaya AM, Shahidan S, Algaifi HA, Zuki SSM, Benjeddou O, Ibrahim MHW, Huseien GF.
Thermal Conductivity of Coconut Shell-Incorporated Concrete: A Systematic Assessment via Theory and Experiment. *Sustainability*. 2022; 14(23):16167.
https://doi.org/10.3390/su142316167

**Chicago/Turabian Style**

Mhaya, Akram M., Shahiron Shahidan, Hassan Amer Algaifi, Sharifah Salwa Mohd Zuki, Omrane Benjeddou, Mohd Haziman Wan Ibrahim, and Ghasan Fahim Huseien.
2022. "Thermal Conductivity of Coconut Shell-Incorporated Concrete: A Systematic Assessment via Theory and Experiment" *Sustainability* 14, no. 23: 16167.
https://doi.org/10.3390/su142316167