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

Abstract

To minimize the energy consumption and adverse impact of excessive waste accumulation on the environment, coconut shell (CA) became a potential (partial) replacement agent for fine aggregates in structural concrete production. Thus, systematic experimental and theoretical studies are essential to determine the thermal and structural properties of such concrete containing optimum level of CA. In this view, an artificial neural network (ANN) model, gene expression programming (GEP) model, and response surface method (RS) were used to predict and optimize the desired engineering characteristics of some concrete mixes designed with various levels of CA inclusion. Furthermore, the proposed model’s performance was assessed in terms of different statistical parameters calculated using ANOVA. The results revealed that the proposed concrete mix made using 53% of CA as a partial replacement of fine aggregate achieved an optimum density of 2246 kg/m³ 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

Over the years, the accumulation of excessive waste has generated major environmental concerns. The designs of concrete mixes vary by incorporating these wastes as partial replacements for aggregates and have become a new strategy to obtain green sustainable concrete [1,2,3,4,5,6,7,8]. Generally, the volume of aggregates in concrete mixes can go up to 80% [3,9], a major component of concrete responsible for rapid depletion of natural resources. Therefore, it forced researchers to find some potential replacement of natural aggregates with the waste materials that are almost free of cost and plentiful [10,11,12]. Conversely, the construction rate of cement-based building has rapidly grown across the globe, increasing the consumption of energy, specifically of fossil fuels. At present, a comfortable building consumes a substantial amount of fossil fuels to provide suitable cooling and heating spaces, leading to an ultimate increase in CO₂ 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.

It was acknowledged Martínez-Molina et al. [16] that the building contribution towards greenhouse gase emission involving CO₂ 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].

Selvaranjan et al. [25] proved the ability of rice husk ash (RHA) as a partial replacement of sand to minimize the TC of concrete. Ngohpok et al. [26] also observed that coal bottom ash (CBA) can reduce the TC of concrete by up to 50% due to two reasons. First, the morphology of CBA with lower density compared to natural aggregates was useful. Second, the high porosity of concrete majorly contributed to the reduction in TC. This result was in a good agreement with Yang and Park [27], wherein an inverse relationship between the CBA content and TC was discerned. With the increase in CBA content, the TC of concrete was decreased. The production of concrete with low TC using other waste materials such as recycled glass [28] and recycled plastic [29] were also investigated [30,31,32,33,34]. Coconut shells (CA) were also utilized as the partial replacement of coarse aggregate in concrete to achieve superior performance wherein most of the studies have only experimentally evaluated the effect of CA substitution on the mechanical properties and durability of concrete [35,36,37,38,39,40,41,42]. In fact, the studies on the thermal properties of concrete remain deficient. For instance, Mathew et al. [43] evaluated the thermal diffusivity, specific heat, and TC of concrete incorporated with various amounts of CA as the replacement of coarse aggregate (10 to 40%). The experimental findings showed that the optimum value of CA that met the criteria of TC of concrete was 40%. Meanwhile, many mathematical models were used to predict the possibility of achieving different concrete with lightweights [44], high strengths [45,46,47], foamed [48,49], geopolymer [50,51,52], and others [53,54]. Despite many experimental efforts, no model studies have been made towards the CA contents composition optimization in such concrete and prediction of thermal properties. Indeed, an optimization model is necessary to minimize the number of too many cumbersome experiments and efforts, materials usages, time, and cost. In addition, the optimization model is also useful for determining the optimum value of the affecting parameter(s), analyzing the correlations among various variables, and predicting accurate and reliable data for future sustainable development of such CA-included green concrete.

Based on the abovementioned overview, it was found that the CA was only utilized and experimentally assessed as the partial replacement of coarse aggregate based on the mechanical properties and durability of concrete; very limited experimental studies have evaluated the thermal properties of concrete containing CA as the replacement of coarse aggregate and no theoretical studied have been made to predict and optimize the replaced CA amount in concrete. To fill the existing research gaps, this work made both model and experimental evaluation to predict and optimize the optimum content of CA in concrete as the replacement of fine aggregate based on its thermal properties. Mathematical models such as genetic expression program (GEP) and response surface method (RSM) were used to achieve the goal of this study. First, several experimental tests were conducted based on the suggested design array from the central composite (CCD-RSM) method. Then, the collected data were used to develop mathematical equations using GEP and RSM models. Next, ANOVA was adopted to verify the accuracy and strength of the proposed model prediction. Finally, the optimum content of CA was obtained using the desirability function.

2. Theoretical and Experimental Approaches

2.1. Design of Composite

Currently, design of experiment (DoE) has been recognized as one of the best mathematical approaches that provide both reliable and accurate results with lesser tests. Indeed, DoE intends to minimize the number of experiments and ascertain the optimum value of the affecting parameters, namely optimization through empirical equations. Through the DoE approach, one can effectively and easily analyze the relationship and interaction among different variables [55]. Two major methods that are related to the DoE family are factorial design and response surface method (RSM) wherein the later one includes several techniques such as Box–Behnken and central composite design (CCD) [56]. In this work, a face-centered CCD (FC-CCD) was considered to design the experiments and optimize (in five steps) the thermal properties of concrete incorporated with CA as the replacement of fine aggregate. The first step involved the number of experiments suggested and determination using FC-CCD. It should be noted that FC-CCD was analysed using the Design-Expert software. The second step dealt with the insertion of collected experimental results into the software. Third, a numerical model was constructed using a second-order polynomial equation (quadratic equation). Fourth, the accuracy and performance of the model was verified using ANOVA. Last, the optimum content of CA was obtained using the desirability function.

FC-CCD comprised two independent variables and three levels. The replaced CA was the first independent variable (d_o), whereas time (d₁) 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. Required experimental strategy based on FC-CCD.

Run No.	Coded Value		Real Value		FC-CCD Division
			Replaced CA (%)	Time (Days)
1	−1	−1	10	7	Factorial points (2n)
2	1	−1	100	7
3	−1	1	10	28
4	1	1	100	28
5	1	0	10	17	Axial points (2n)
6	−1	0	100	17
7	0	−1	55	7
8	0	1	55	28
9	0	0	55	17	Centre points

displays all points including both coded and real values of the required experimental works according to the FC-CCD method.

$$Q=2^n+2n+m$$

(1)

$$R=\frac{Z-Z_c}{\alpha }$$

(2)

Equation (3) represents the general form of the second-order polynomial equation used to develop the model [60], where β_i is the linear coefficient, β_o is the intercept of the model, and β_ii is the quadratic coefficient; X₁ and X₂ 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).

$$Y={\beta }_o+{\displaystyle \sum {\beta }_i}{X}_i+{\displaystyle \sum {\beta }_{ii}}{X}_i^2+{\displaystyle \sum {\beta }_{ij}}{X}_i{X}_j$$

(3)

The integrated mathematical and statistical tool ANOVA was used to verify the significance and accuracy of a proposed model. Various statistical indicators such as p-value, F-value, adequate precision, determination coefficient (R²), predicted R², and adjusted R² 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 R² is over 0.75 [63]. In addition, a model can be used for further prediction when the differences between the predicted R² and adjusted R² is less than 0.2 [64].

Diverse parameters including the total sum of square (SS_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 R² was estimated using Equation (6).

$$S{S}_E={{\displaystyle \sum _{i=1}^n\left(Y_P-{\overline{Y}}_A\right)}}^2$$

(4)

$$S{S}_T={{\displaystyle \sum _{i=1}^n\left({\overline{Y}}_A-Y_A\right)}}^2$$

(5)

$$\begin{array}{l}{R}^2=\frac{S{S}_E}{S{S}_T}\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}=\frac{{{\displaystyle \sum _{i=1}^n\left(Y_P-{\overline{Y}}_A\right)}}^2}{{{\displaystyle \sum _{i=1}^n\left({\overline{Y}}_A-Y_A\right)}}^2}\end{array}$$

(6)

After calculating the degree of freedom for both variance of dependent variables (DF_T) and residual error (DF_R), the adjusted R² was obtained using Equation (7) [66]. Furthermore, the predicted R² 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 σ² is the residual mean square.

$$R_{adj}^2=1-\frac{S{S}_R/D{F}_R}{S{S}_T/D{F}_T}$$

(7)

$$R_{pred}^2=1-\frac{W}{S{S}_T}$$

(8)

$$SN=\frac{\max (Y_p)-\min (Y_p)}{\sqrt{\frac{p{\sigma }^2}{n}}}$$

(9)

2.2. Materials and Mix Design Preparation

In this work, the collected CA (from a local supplier in Johor, Malaysia) was thoroughly ground in several steps to avoid gap-grading. First, the CA was crushed into small chips with a size of 20 mm (Figure 2). Next, the CA chips were impact pulverized and sieved to obtain a fine powder of a size less than 600 µm. Yet again, big particles were exposed to the impact pulveriser to obtain particles of suitable size that can pass through a sieve size of 4.75 mm. The crushed granite and natural sand was used as the coarse and fine aggregates, respectively, in accordance to the standard requirement EN 933-1:2012. Normal tap water and OPC were used to achieve the required hydration process. After the collection and preparation of all materials, the department of environment method (British Standard) was used to make a control concrete mix (without CA) having strength target of 30 MPa after 28 days. Based on the obtained results from department of environment method, the involved materials proportions were water (195 L), cement (435 kg), fine aggregate (535 kg), and coarse aggregate (1250 kg). Conversely, a mix design of concrete incorporated with CA as the replacement of sand (from 10% to 100%) was made using the central composite design method (Table 1). A Rheobuild 1100 super-plasticizing admixture (up to 1.2% by cement weight) was considered for achieving a slump range from 100 to 140 mm.

2.3. TC Test

The TC (k) of any material is defined as the proportionality constant between the temperature gradient and heat flux. Herein, k is used as a mathematical indicator of heat transfer inside the concrete that depended on concrete porosity, indicating that more voids and pores inside the concrete matrix may result in lower TC. In addition, various factors can influence the TC of concrete such as the age of concrete, moisture condition, density, and morphology of aggregates used in the mix design composition [69]. Equation (10) yields the heat flow (Q) in one direction, where A was the area exposed to heat, $\partial x$ denoted the concrete thickness, and $\partial T$ was the temperature differences.

$$Q=kA\frac{\partial T}{\partial x}$$

(10)

A concrete block of dimension 200 mm × 200 mm × 100 mm was prepared (Table 1) for the TC test. Following the referred protocol in [70], the k value of concrete was measured using the guarded hot plate method (Figure 3). The test was carried out according to BS EN ISO 8990 (1996) stipulation.

2.4. Prediction Using GEP Model

Due to the lack of mathematical framework in the existing literature, the genetic expression programming (GEP) method was selected to introduce an additional predictive equation. A mathematical framework was essential to estimate the target properties of the concrete with less materials consumption, cost, time, and errors. The results obtained from the GEP model was also used to compare with the one obtained using RSM. The reputation of GEP has currently been grown within the scientific community, specifically among civil engineers. This is mainly due to its capacity to obtain the relationship among various dependent and independent variables in an easy and effective way [71,72,73,74]. In addition, the process of GEP is inspired from biological evolution and human genetics. For quick understanding of the GEP process, both biological evolution and human genetics are briefly explained. In addition, a simple example is provided to describe the process of GEP.

It is known that a child gets 46 chromosomes from their parents [75] wherein each involves a long string of DNA divided into thousands of regions (namely genes) [76]. The gene is also defined as a long sequence from four chemical compounds, namely genetic nucleotides such as Adenine (A), Guanine (G), Thymine (T), and Cytosine (C) as shown in Figure 4a. Therefore, each child has its own gene sequence known as the fingerprint for hereditary information. In other words, each offspring’s gene differs from one another based on the arrangement of the four genetic nucleotides. In addition, the gene is composed of coding and non-coding regions [77]. The coding region is the main sole parameter that gives instructions such as protein production. In contrast, the non-coding gene has no influence on the physical activity of a human. The arrangement of these genetic nucleotides may be exposed to change because of several factors of surrounding environment [78]. This change can occur through crossover, modification, or mutation (Figure 4b).

Mimicking human genetic and biological evolution, concrete properties are considered as a simulated chromosome that carries all the fingerprint information inside the concrete matrix. Moreover, the gene inside the chromosome acts as the predictive equation or solution that represents the behaviour of the concrete through simulated coding gene (+, /, inv, Sqrt and so on) and non-coding gene (the input data). In other words, the concrete properties are investigated using initial equations (simulated genes) including mathematical expressions. Subsequently, the initial mathematical equation is exposed to statistics indicators. If the mathematical equation (simulated genes) does not satisfy the statistics requirement, the mathematical expression will be modified by changing their location or adding an extra mathematical expression. In this present study, the developed equation was intended to investigate and assess the thermal properties of concrete containing CA. Two independent variables were considered, namely CA (d_o) and time (d₁).

The experimental data were divided into training part (85%) and validation part (15%). GeneXpro Tools 5.0 software was used to achieve the study objectives. In addition, various mathematical operations (−, ×, /, +, Sqrt, not, Inv, Aver, and 3Rt) were used to develop the equations. During the training of the GEP model, the predicted equation was subjected to several statistics validation parameters including error statistical indicators as well as correlation statistical indicators until the best solution was obtained. For example, mean root relative squared error (RRSE), relative absolute error (RAE), root mean square error (RMSE), and mean absolute error (MAE) were calculated and evaluated using Equations (11)–(14), respectively [79,80,81,82,83]. These equations were important to assess the error and differences between the actual and predicted results. High value of RRSE, MAE, RMSE, and RAE indicated weak model with much error between the predicted and actual one; however, when the error approached to zero the model was accurate and provided the results effectively. For the statistical validation of various indicators correlation measures including R and R² were evaluated following Equations (15) and (16), respectively [84,85,86]. Consequently, the fitness and strength between the actual and predicted results were established.

$$RRSE=\sqrt{\frac{{\displaystyle \sum _{i=1}^n{(Y_P-Y_A)}^2}}{{\displaystyle \sum _{i=1}^n{(Y_A-\overline{Y_A})}^2}}}$$

(11)

$$RAE=\frac{{\displaystyle \sum _{i=1}^n\left|Y_A-Y_P\right|}}{{\displaystyle \sum _{i=1}^n\left|Y_A-\frac{1}{n}{\displaystyle \sum _{i=1}^n{Y}_A}\right|}}$$

(12)

$$RMSE=\sqrt{\frac{1}{n}{\displaystyle \sum _{i=1}^n{(Y_A-Y_P)}^2}}$$

(13)

$$MAE=\frac{1}{n}{\displaystyle \sum _{i=1}^n\left|Y_A-Y_P\right|}$$

(14)

$$R=\sqrt{1-\frac{{\displaystyle \sum _{i=1}^n{(Y_A-Y_P)}^2}}{{\displaystyle \sum _{i=1}^n(Y_A-\overline{Y_A}}{)}^2}}$$

(15)

$$R^2=1-\frac{{\displaystyle \sum _{i=1}^n{(Y_A-Y_P)}^2}}{{\displaystyle \sum _{i=1}^n(Y_A-\overline{Y_A}}{)}^2}$$

(16)

2.5. Prediction ANN Model

The ANN model being inspired by the biological neurons system was used to develop a predictive equation that can represent the thermal properties of concrete incorporating CA [87,88]. Three steps are necessary to respond to any information via the human brain, specifically inside the billions of connected neurons. First, the external information (input data) is passed to the neuron that is located inside the human brain. Second, the external information is analyzed and processed inside the core of the neuron cell and ultimately generates an electrical signal. Finally, the generated electrical signal is passed to another connected neuron. In addition, the new neuron has the right to accept or reject the generated electrical signal. This is dependent on the value of the electrical signal. Similarly, at least three layers were adopted to develop a simulated ANN model (Figure 5a).

Referring back to the human brain process, the input data of the predictive model were first weighted and summed. Next, the sum of the weighted data were subjected to the mathematical process in the second layer called the hidden layer (Figure 5b). Herein, i and j are the previous and current layers, respectively; n is the nodal values; b_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 R², root average squared error (RASE) and sum square error (SSE) were calculated using Equations (18) and (19).

$$f_{(x)}=\frac{e^{2x}-1}{e^{2x}+1}$$

(17)

$$RASE=\sqrt{\frac{SSE}{n}}$$

(18)

$$SSE={\displaystyle \sum _{i=1}^n{(Y_A-Y_P)}^2}$$

(19)

3. Results and Discussion

3.1. Informational Modeling Using RSM

The thermal properties and density of the proposed CA-incorporated concrete were predicted using second polynomial equations (

Table 2. Validation of the TC and density predicted equations obtained from the RSM model.

Item	Second Polynomial Equations and Statistical Parameters
TC	R = 0.995	R2 = 0.9906	$R_{adj}^2=$ 0.9839	$R_{predicted}^2$ 0.905	Adeq. Precision 41.028	RMSE 0.011
	$TC=0.522-0.15d_0+0.05d_1+0.01d_o{d}_1-0.008d_o^2+0.017d_1^2$
Density	R = 0.999	R2 = 0.9986	$R_{adj}^2=$ 0.997	$R_{predicted}^2$ 0.986	Adeq. Precision 104.47	RMSE 6.652
	$D=1994.2-171.67d_o+10.83d_1-2.5d_0{d}_1-20.89d_o^2+235.6d_1^2$

) that contained two independent variables (CA and time). As such, it could be inferred that the thermal properties and density were dependent on the CA content and time. The performance of theses equations was verified prior to analysis and optimization using ANOVA. The value of RMSE was calculated to assess the accuracy and difference error between the estimated and actual data. The obtained small value of RMSE clearly indicated the model accuracy compared to the actual results. Likewise, the value of R² was also determined to evaluate the correlation between the actual and estimated data. The value of R² 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 R² was close to R², 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.

The applicability of the proposed optimization models was also assessed using F-value and p-value. These statistical parameters were also used to validate the significance of the regression coefficients. In general, the second polynomial equations and their terms can be considered as significant when the p-value was less than 0.005 and F-value was high. The results in

Table 3. F-value and p-value obtained via RSM model for the verification of significance.

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
do	<0.0001	660.32		<0.0001	2539.3
d1	<0.0001	71.25		0.0155	10.11
dod1	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

show that the F-values of TC and density equations were greater than 147.47, while the p-values were less than 0.0001, confirming that the predicted quadratic equations for all data set were significant. This observation was also consistent with other reported studies. For example, by Hou et al. [92] verified the predicted equation of early age CS of magnesium phosphate cement-based material using F-value and p-value. The findings revealed that F-value and p-value were 21.29 and 0.0003, respectively, demonstrating that the model is significant.

The significance of CA on the TC of concrete was also examined and evaluated (Figure 6a). A sharp gradient of CA confirmed its significance to incorporate into the proposed concrete. In particular, TC greatly decreased with the increase in CA content. These results were consistent with those obtained using ANOVA (Table 3), in which the p-value and F-value of CA content were less than 0.0001 and 660.32, respectively. It confirmed that the content of CA in concrete was significant for the TC. In addition, the CA content was also considered as significant for the concrete density attainment at optimum level. The observed negative sharp slope (Figure 6b) in the concrete density with the increase in CA content implied the important role of CA incorporation into the designed mixes. This fact was also in line with the ANOVA results, wherein the p-value was less than 0.0001 and F-value was 994.23.

After the validation of the predicted equations, desirability functions provided by the RSM model were considered to optimize the content of CA in the concrete matrix (Equation (20)). The optimization equation involved two independent variables such as CA and time wherein the main purpose was to examine the optimum value and effect of CA on the TC of concrete. Generally, the TC of concrete increases over time due to the reduction in porosity. The focus was to evaluate the optimal value of CA based on TC after 28 days. According to the solutions of the desirability functions, 70 solutions were obtained for the optimization purpose with a desirability value of one.

Table 4. Selected solutions for the optimization of CA content based on desirability functions.

No. of Solution	CA Content (%)	TC (W/mK)	Density (kg/m3)
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

presents 10 selected solutions wherein the optimal value of CA was 53%. This study mainly determined the structural properties of normal concrete with density of greater than 2240 kg/m³ 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/m³, while the density values for the lightweight concrete are ranged from 1440–1840 kg/m³. According to Graybeal and Lwin [95], a concrete is biased to be lightweight when its density is lower than 2160 kg/m³. In accordance to ACI 213R, 2014 [96], the structural lightweight concrete have the density values in the range of 1350 and 1920 kg/m². For structural component purpose, the density of lightweight concrete should be within 800 to 2000 kg/m³ 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/m³, 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.

$$DR={\left(d_1\times d_2\times d_3\times \hspace{0.17em}\dots \dots \dots d_n\right)}^{(1/n)}$$

(20)

3.2. Informational Modeling Using GEP

Figure 8 shows the structural tree of the proposed equation (solution or chromosome). As mentioned before, another predictive mathematical equation was developed using GEP in order to estimate the evolution of the TC of concrete incorporated with CA as the partial replacement of river sand (fine aggregates). The results clearly shown that the chromosome contained only one mathematical gene, which in turn involved an active coding gene (/, +, Sqrt, Avg., and constants (c_o)). Using the Karva language, the structural tree for the TC of concrete was converted into a mathematical equation.

The adequacy and performance of the predicted mathematical equation was validated using several statistical parameters. From the viewpoint of the error validations parameters, a minimum error was observed using the GEP model. MAE was calculated to assess the accuracy of the model. The value of MAE was lower than 0.02 for the training and validation steps, confirming higher accuracy of the predicted TC results compared to the actual data. This observation strongly supported results obtained using the RAE, RRSE, and RMSE indicators (

Table 5. Validation of the GEP model derived proposed equation.

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	R2 = 0.93
	Validation	RAE = 0.668	MAE = 0.035	RMSE = 0.038	RRSE = 0.609	R = 0.973	R2 = 0.946
	$TC=\frac{4\sqrt{d_o}+2d_1+2c_o}{d_0+3d_1}$

). In particular, RAE values for the training and validation were 0.265 and 0.668, respectively, asserting that the model has a strong ability to predict accurately with minimum error. This result was consistent with the reports of Shah et al. [98]. Meanwhile, Ashrafian, Gandomi, Rezaie-Balf, and Emadi [81] introduced a novel mathematical equation to predict the CS of roller-compacted concrete pavement using GEP and demonstrated its accuracy and performance in terms of several statistical parameters including RMSE and MAE. Based on their findings, the values of RMSE were lower than 82.6 for all dataset, while the MAE values were below 8.28 for both training and validation datasets. However, in the present study, the values of RRSE and RMSE were less than 0.609, indicating that the model was robust and acceptable. On top, the correlation and closeness between the predicted and real results were also evaluated using R² and R. The achieved values of both R² and R were greater than 0.93 for training and validation, demonstrating that both results were very close.

3.3. Informational Modeling Using ANN

A predictive equation of TC for the proposed CA-based concrete was developed using an ANN model.

Table 6. Validation of the ANN model derived proposed equation.

Item (W/kM)	Mathematical Equation and Related Statistical Validation Parameters
TCANN	Training	RASE = 0.0183	SSE = 0.0050	Mean Abs. Dev. = 0.0142	R2 = 0.952
	Validation	RASE = 0.0320	SSE = 0.0051	Mean Abs. Dev. = 0.0268	R2 = 0.915
	$T{C}_{ANN}=0.537-3.56\mathrm{Tan}H\left(0.5\left(-0.066+0.0018d_o-0.0023d_1\right)\right)$

shows the equation of TC and various statistical parameters needed for the validation. The ANN model was robust in estimating the TC values of the CA-based concrete, in which both RASE and SSE were small, while the R² 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

The effects of CA-inclusion on the TC of concrete were evaluated using RSM, GEP, and ANN models and the results are shown in Figure 9. Overall, the TC values of concrete strongly depended on CA contents, displaying a significant decrease in the TC values with the raise of CA levels for all models. For example, the values of TC obtained using the RSM model were 0.727, 0.5903, and 0.4367 W/mK after 28 days when the corresponding CA contents were 10, 55, and 100%. For the control concrete (made without CA), the TC value was 0.76 W/mK. Similarly, the TC value of concrete at 28 days obtained using the ANN model showed approximately 6, 24, and 44% reduction when the corresponding CA replacement percentages were 10, 50, and 100%. For the GEP model, a similar trend was also observed, in which the k-value significantly dropped with the increase in the CA content of up to 100%. This lowering in the k-value was attributed to the increase in porosity inside the concrete matrix. Essentially, higher degree of pores and voids in CA than natural fine aggregates strongly contributed in the reduction in k-value of concrete. Tasdemir et al. [101] concluded that k-value may depend on the porosity of concrete. Briefly, the value of TC for the proposed concrete was decreased with the decrease in density which supported other findings. Figure 6b illustrates the relationship between density and the TC of CA-based concrete. The achieved almost linear correlation was mainly due to the decrease in k-value with the decrease in density, confirming the formation of concrete with low density, a high degree of pores, and voids. It is worth noting that the k-value of air (void spaces) being very small (0.0026 W/mK) can be advantageous towards the enhancement of concrete’s thermal insulation property [102].

4. Conclusions

The uses of CA as green waste materials (especially in the sustainable concrete production) have gained a great reputation and pulled the attention of both environmentalists and scientists. In this perception, the TC of concrete incorporated with CA as partial replacement of fine aggregate was evaluated both experimentally and theoretically using GEP, ANN, and RSM models. Based on the achieved results we conclude the following:

• The optimum replacement percentage of fine aggregate by CA was 53% which produced a normal concrete with density of 2246 kg/m³. Beyond this content of CA, the concrete can be defined as lightweight because the density was below 2000 kg/m³.
• 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 R² > 0.91, while RASE < 0.0183 and SSE < 0.0050 were obtained for all data set.