Evolutionary Algorithm-Based Modeling of Split Tensile Strength of Foundry Sand-Based Concrete

Abstract

Foundry sand (FS) is produced as a waste material by metal casting foundries. It is being utilized as an alternative to fine aggregates for developing sustainable concrete. In this paper, an artificial intelligence technique, i.e., gene expression programming (GEP) has been implemented to empirically formulate prediction models for split tensile strength (ST) of concrete containing FS. For this purpose, an extensive experimental database has been collated from the literature and split up into training, validation, and testing sets for modeling purposes. ST is modeled as a function of water-to-cement ratio, percentage of FS, and FS-to-cement content ratio. The reliability of the proposed expression is validated by conducting several statistical and parametric analyses. The modeling results depicted that the prediction model is robust and accurate with a high generalization capability. The availability of reliable formulation to predict strength properties can promote the utilization of foundry industry waste in the construction sector, promoting green construction and saving time and cost incurred during experimental testing.

1. Introduction

Concrete is at the top of the list for most widely used material in construction and serves as the backbone of the modern construction industry. It is a heterogeneous material containing cement, fine aggregate, coarse aggregate, water, and admixtures as five major constituents. These natural or man-made materials are finite and will eventually diminish over time. Extensive research is being conducted to utilize waste and by-products of different industrial processes in construction to ensure sustainability. For instance, the production of one ton of cement releases approximately an equal amount of carbon into the atmosphere. Similarly, the production of one ton of concrete releases up to 20% (by weight) of greenhouse gases into the atmosphere. This percentage can have a detrimental impact considering the global concrete production of approximately 30 billion tons. Therefore, the application of green concrete is fast gaining attention. Such concrete utilizes alternative materials such as fly ash, silica fume, glass, rubber, etc. as pozzolanic materials and waste sand and clays as alternates to aggregates. It is pertinent to mention that the use of alternative green materials as a replacement for natural fine aggregate will lower the overall cost of production of concrete. Moreover, the benefits in terms of reduced need for landfill sites for the disposal of wastes will be immense [1,2].

Foundry sand (FS) is a silica sand of high quality produced by ferrous and non-ferrous casting industries. These foundries utilize silica sand as a molding material owing to its ability to endure high temperatures. Recent evidence shows the presence of traces of bentonite and kaolinite clay in FS. These clay materials impart binding properties to FS and the resulting mixture is classified as green sand. The primary constituent of green sand is silica sand (more than 80%) followed by natural clay (up to 10%) and small percentages of water and sea coal [3]. In the process of casting, green sand is reused and recycled several times till it is degraded to an extent where it cannot be used any further and is discarded as waste. The discarded sand is called FS. FS comprises about 70% of the total industrial waste and contains silica sand, chemical binder, bentonite clay, catalysts, and traces of metals as its constituents [4]. The increasing demand for metal tools and metallic items in modern society is causing an exponential increase in FS production, which encompasses a huge environmental threat. A study by the American foundry society reveals that 800 million tons of casting is being done annually and for each ton of steel casting, 600 kg of FS is produced as waste material even after reuse. These wastes pose a major threat to the sustainability of landfills. Generally, cement-based stabilization and solidification are being adopted to decontaminate WFS. However, the process is rigorous and time-consuming. Moreover, the presence of certain inorganic contaminants could halt the hydration and hardening process of cement. However, extensive experimental studies have revealed that the leachate obtained from FS-based concrete contains contaminants that are below the allowable limits. Therefore, FS-based concrete satisfies the durability criteria recommended by different standards and is safe to use in concrete using normal cement [4,5].

Extensive research is being conducted to study the use of FS in the construction industry for various applications. In one of the experimental studies, it was revealed that the addition of FS had a positive impact on the strength characteristics of concrete when treated with 5.5% of cement (hydraulic binder) and poses no environmental impact [5]. It should be noted that the utilization of FS in concrete can help reduce the use of natural sand around the world. Using alternative FS can lower the cost of concrete development and will resolve the issue of pollution caused due to disposal of FS after casting of molds to the landfill sites. In another study, experiments were performed by substituting fine aggregates with FS in the concrete mix [6]. It was concluded that 20% addition of FS in the concrete mixture can attain the same strength as the control mix, while the reduction in strength was about 2.1% as FS content was increased. It should be noted that fine aggregates are the key ingredient to ensure sufficient strength is achieved for any type of concrete. The inclusion of materials such as bentonite clay, FS, and silica sand has a different impact on the ST depending on the composition and source. For instance, the fineness modulus of these materials indicates that the size of this alternative material is small as compared to the natural silica sand. Therefore, by replacing natural sand with these materials in the cement matrix, improvement in the ST has been observed. This is because these materials act as a filler and improve the binding characteristics. The binding improves due to the consumption of calcium hydroxide and the production of additional CSH gel that can improve the ST. However, as the content is increased beyond a certain optimum percentage (20% for FS), the overall content of fine particles exceeds in the cement paste. This results in the consumption of additional water due to an increase in the surface area. Thereby, the hydration slows down, and strength decreases as the content is increased.

In recent times, big data and deep learning techniques have been effectively implemented in civil engineering. The recent advancement in artificial intelligence (AI) has rendered new techniques which can assist in modeling complex engineering problems. AI processes are primarily grounded on natural tools which are implemented in genetic algorithms (GA), genetic programming (GP), fuzzy logic, and artificial neural networks (ANNs) [7,8,9,10,11,12,13,14,15]. These methods implement the pattern recognition ability of AI to produce simple models of complex patterns, which are being extensively used in the engineering field. The ANN technique was used to study the strength of concrete by partially substituting cement and sand with rice husk ash and reclaimed asphalt pavement [16]. Similarly, ANN was used to predict ingredients of self-compacting concrete [17]. A model was developed to predict the punching shear strength of a concrete slab using ANN and GP [18]. Behnood et al. [19] have also applied a modified ANN approach to estimate the compressive strength (f_c) of silica fume concrete while Golafshani et al. [20] used the same approach to predict the modulus of elasticity (MOE) of recycled aggregate concrete. The models developed by ANN possess a high coherence, but there are certain limitations of these techniques. For instance, a complex empirical relationship is obtained as output which may be infeasible for practical applications. A graphical user interface can be an effective method to address this issue, as proposed by Behnood et al. [19].

Gene expression programming (GEP), which is an extension of GP, can encode a small program using simple and linear chromosomes of fixed length [21]. The benefit of GEP is that it results in the development of simplified mathematical equations for practical use with higher prediction accuracy. This technique has been used recently to develop prediction models for the mechanical properties of concrete containing RHA, properties of lightweight concrete containing silica fumes, split tensile strength (ST), and effects of cement properties on fc of cement mortar [22,23,24,25,26,27,28]. Moreover, accurate and efficient models are developed for the prediction of the progressive collapse behavior of reinforced concrete structures using GEP [29,30,31].

Previously, experimental techniques were mainly used to determine the effects of FS on the mechanical properties of concrete [32,33,34]. However, AI tools can also be used to offer reliable models to predict these behaviors to save time, cost, and make the use of FS feasible for the construction industry. Literature review shows that only a few modeling studies have been conducted to formulate the splitting strength of FS-based concrete [4,6]. These models are restricted to regression or similar simple techniques developed based on a small database. In one of our recent research projects, empirical models were developed to predict the mechanical properties of CFS using GEP [35]. The models were accurate based on statistical error analysis and parametric study. However, there were certain limitations of that study. For instance, multiple data points had to be excluded from the database to develop accurate models based on a trial-and-error procedure. This procedure limited the range of applicability of the developed models [36]. Similarly, the properties of WFS-based concrete were predicted by using tree structure modeling techniques and ANN [37,38]. However, a parametric study could not be conducted for the developed models due to the linear nature of these modeling techniques, which can be regarded as an effective tool to assess whether the developed models have accurately learned the underlying physical phenomenon.

To address these research gaps, the presented study focuses on developing a refined and accurate model for the prediction of ST of foundry sand-based concrete. For this purpose, an extensive experimental database has been collated from the literature. GEP has been employed and the number of mathematical operators has been increased so that the simplicity of models is not compromised to improve the accuracy, unlike the previously presented models [36]. Moreover, a few additional data points have been included from recently published experimental studies to further enhance the range of application of the models and to ensure an accurate, yet simplified model. Finally, an in-depth parametric study has been conducted to validate the prediction and learning capability of the programming technique and the empirical formulations, respectively. It should be noted that the availability of reliable empirical models would be helpful for the construction industry. For instance, a significant cost is being spent on the experimental work conducted prior to the use of such alternative material for construction purposes in the field. The availability of reliable correlation can assist in predicting the ST of CFS using a simple formulation. These results would in turn benefit the end-users to assess the application of green concrete for the desired purpose. Thereby, it would promote the use of FS as an alternative to natural sand and extend the application of green concrete in the construction sector for structural applications. This can contribute towards sustainability in terms of resources, cost, and time efficiency.

2. Gene Expression Programming

GEP belongs to the family of evolutionary algorithms modified by Ferreira [21]. It adopts parse trees and linear chromosomes of fixed length from the previous variants GP and GA, respectively. Figure 1 represents the sequence of steps performed in the GEP algorithm. The procedure starts with the random creation of fixed-length chromosomes for each individual population [28]. The chromosomes are expressed as ETs and their fitness is assessed. Then, reproduction (which includes replication, genetic modification, and preparation of new chromosomes of the next generation) is applied to the already-evaluated individuals through a fitness function. The whole process is repeated with newly produced individuals till the desired solution is attained. Since the founder individuals are yet to be toughened up by the environment, they are almost always not good solutions.

Through evolution, the best-fit individuals initiate the reproduction process leading to an increase in the number of generations. The reproduction process runs in conjunction with modification based on random selection and fitness. The aforementioned evolution process which includes genome expression, selection, and reproduction continues for a certain pre-specified number of generations until an effective solution is obtained.

3. Research Methodology

3.1. Experimental Database

In this study, data were collected from international peer-reviewed articles related to CFS [34,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60]. The database comprised 137 numbers of 28-day ST results. It has been provided as Supplementary Data in the manuscript. These datasets were randomly divided into three sets, i.e., training set, validating set, and testing set to train, check the generalization capability of the trained model, and assess the performance on unseen data, respectively. The effectiveness of a model is closely related to the distribution of input and output perimeters [18]. The distribution of input and output parameters of datasets is given in

Table 1. Data range for input and output variables.

Parameters	Min	Max
w/c	0.35	0.83
FS%	0	100
FS/C	0	2.22
ST (MPa)	1.45	4.67

. These values are important as the model is trained on these ranges of parameters, and it is viable to implement the proposed model for the presented range of data. The distribution of input and output parameters is given in Figure 2.

3.2. Modeling and Assessment Criteria

The first step in machine learning-based modeling is to finalize the input parameters which can impact ST significantly. Based on the research recommendations, ST of CFS is considered as the function of the following variables in Equation (1). It is important to understand the selection of FS/C as the input parameter. For every type of green concrete, the interaction and bonding between the cement and alternative green material (binder or aggregate) has a significant role in the final strength of the mix. Therefore, in the presented study data have been collated for the FS and cement content, and the ratio of these two parameters has been considered as input for modeling to better correlate the combined impact of these materials on ST.

$$\mathrm{ST}=f\left(\frac{w}{c},FS\%,\frac{FS}{C}\right)$$

(1)

The specific parameters utilized in the GEP algorithm are described in

Table 2. Parameter settings for GEP algorithm for ST model.

Parameter	Settings
General parameters
Chromosomes	300
Genes	4
Head size	8
Linking function
Function set	exp., +, −, ×, ÷
Numerical parameters
Constant per gene	10
Data type	Floating number
Upper bound	10
Lower bound	−10
Genetic parameters
Mutation rate	0.00138
Inversion rate	0.00546
Gene recombination rate	0.00277
Gene transposition rate	0.00277
Two-point recombination rate	0.00277
One-point recombination rate	0.00277
IS transition rate	0.00546
RIS transposition rate	0.00546

. These parameters are finalized after conducting several test runs. A primary indicator of the performance of the empirical modeling is the correlation coefficient (R). A statistical analysis is performed by calculating mean absolute error (MAE), root mean square error (RMSE), relative root mean square error (RRMSE), and relative squared error (RSE) to assess the accuracy. A performance index (ρ) is proposed, which is dependent on R and RRMSE to assess the overall performance of the prediction model [18]. Mathematical formulations of these errors are given in Equations (2)–(7).

$$\mathrm{RMSE}=\sqrt{\frac{{{\displaystyle \sum }}_{i=1}^n{\left(e_i-m_i\right)}^2}{n}}$$

(2)

$$\mathrm{MAE}=\frac{{{\displaystyle \sum }}_{i=1}^n\left|e_i-m_i\right|}{n}$$

(3)

$$\mathrm{RSE}=\frac{{{\displaystyle \sum }}_{i=1}^n{\left(m_i-e_i\right)}^2}{{{\displaystyle \sum }}_{i=1}^n{\left(\overline{e}-e_i\right)}^2}$$

(4)

$$\mathrm{RRMSE}=\frac{1}{\left|\overline{e}\right|}\sqrt{\frac{{{\displaystyle \sum }}_{i=1}^n{\left(e_i-m_i\right)}^2}{n}}$$

(5)

$$R=\frac{{{\displaystyle \sum }}_{i=1}^n\left(e_i-\overline{e}\right)\left(m_i-\overline{m}\right)}{\sqrt{{{\displaystyle \sum }}_{i=1}^n{\left(e_i-\overline{e}\right)}^2{{\displaystyle \sum }}_{i=1}^n{\left(m_i-\overline{m}\right)}^2}}$$

(6)

$$\rho =\frac{\mathrm{RRMSE}}{1+R}$$

(7)

where $n$ is the total number of samples, $e_i$ and $m_i$are the $ith$ model and experimental outputs respectively, and $\overline{m}$ and $\overline{e}$ are the average value of the model and experimental outputs. Model accuracy is directly proportional to R and inversely proportional to RMSE, RRMSE, and MSE values. $\rho$ ranges from 0 to +∞. As the value of $\rho$ approaches 0, the accuracy of the model increases. Similarly, the R-value ranges from 0 to 1, and the value of 0.8 is considered as an indicator of a strong correlation between the inputs and output [61].

4. Results and Discussion

4.1. Formulation of Split Tensile Strength

As stated earlier, the number of genes finalized in the model was four, resulting in four sub-ETs as shown in Figure 3. The linking function in this model is multiplication and ETs contain +, −, ×, ÷, and exp as mathematical operators for simplicity. These ETs were decoded to develop an empirical equation to predict ST of CFS as a function of w/c, FS%, and FS/C as shown by Equation (9). A comparison of predicted and experimental values as shown in Figure 4 shows that predicted values of ST are quite comparable to the experimental results as evidenced by the high slope of regression line 0.987. An ideal line is drawn at 45° for reference and the trend line for predicted values shows much less deviation for this large dataset, which illustrates correct predictions from the proposed model.

$$\mathrm{ST}\left(\mathrm{MPa}\right)=\mathrm{A}\times \mathrm{B}\times \mathrm{C}$$

(8)

where

$$\mathrm{A}=\frac{\mathrm{FS}\%+\frac{\mathrm{FS}}{\mathrm{C}}-\exp \left(\mathrm{FS}\%\right)+0.0743}{{\left(\frac{\mathrm{FS}}{\mathrm{C}}\right)}^2+\frac{\mathrm{FS}}{\mathrm{C}}-6.66}\times \frac{\exp \left(0.581\frac{\mathrm{FS}}{\mathrm{C}}-\mathrm{FS}\%+3.54\right)}{\frac{\mathrm{w}}{\mathrm{c}}+\frac{\mathrm{FS}}{\mathrm{C}}}$$

(9)

$$\mathrm{B}=\exp .\left(\frac{0.00369\frac{\mathrm{w}}{\mathrm{c}}}{\frac{\mathrm{w}}{\mathrm{c}}-11.65\frac{\mathrm{w}}{\mathrm{c}}+4.68}\right)$$

(10)

$$\mathrm{C}=\frac{\mathrm{FS}}{\mathrm{C}}+\exp .\left[\frac{\mathrm{w}}{\mathrm{c}}-\exp .\left\{{\left(\frac{\mathrm{FS}}{\mathrm{C}}\right)}^2+\frac{\mathrm{w}}{\mathrm{c}}\right\}\right]$$

(11)

4.2. Performance Evaluation

Statistical calculations of the proposed model are given in

Table 3. Statistical analysis of the proposed model.

Parameters	Training	Validating	Testing
RMSE (MPa)	0.41	0.40	0.66
MAE (MPa)	0.32	0.40	0.66
RSE	0.48	0.68	2.54
RRMSE	0.13	0.10	0.17
R	0.82	0.99	0.98
$\rho$	0.07	0.05	0.09

. Interpretation of these values indicates that the presented model is well trained and an acceptable correlation exists between the experimental and predicted values. MAE, RMSE, RSE, and RRMSE for the training set of ST are 0.41 MPa, 0.32 MPa, 0.48, and 0.13, respectively. The values for the validating set are 0.40 MPa, 0.40 MPa, 0.68, and 0.10, respectively. Similarly, for the testing set, the values are 0.66 MPa, 0.66 MPa, 2.55, and 0.17, respectively. It can be observed that the R-value is significantly high for the testing and validation set, which shows that the model is highly generalized and applicable to unseen data as well. Moreover, $\rho$ value for each data set is close to zero, which verifies the overall accuracy of the model.

Researchers have suggested the smallest ratio of datasets to the number of inputs should be three for an acceptable model [18,62]. This ratio is 34 for the ST model developed in this study. The absolute error was calculated to further compare the experimental and predicted values as shown in Figure 5. It can be inferred that predicted and experimental data points are in a high correlation with the minimum, maximum, and mean absolute error of 0.37, 0.002, and 1.10 MPa, respectively. It has been observed that 70% of the predicted results have less than 0.5 MPa absolute error.

4.3. Parametric Analysis

In the case of empirical modeling, it is imperative to conduct parametric analysis to assess that a model is universal and not just a correlation among the input and output variables. One of the benefits of the GEP technique is that it captures the underlying physical phenomena of complex engineering problems accurately. It is for this reason that a parametric study has also been presented to show the efficiency of the input parameters in predicting the trends of ST. The input parameters are fixed at the average value and variation in strength property has been observed by varying one variable from its lowest to highest value in the calculated range. The results of the parametric analysis are shown in Figure 6.

From a material engineering viewpoint, it is a fact that increasing the w/c ratio will result in decreased ST [63]. The concept has been validated in the results of the parametric study presented in Figure 6a. Similar behavior was reported in the literature where concrete having w/c = 0.5 showed higher mechanical strength compared to concrete with w/c = 0.5 [64,65].

The effect of FS% on the mechanical properties of CFS depends on the type, amount, and source of the sand. However, a general behavior reported by several experimental studies is that the properties either improve or remain constant at low replacement percentage and continue to decrease as FS% is increased [32,34,41,59]. It is attributed to the fact that FS is finer compared to fine aggregate and result in better densification and formation of the bond [66]. The high reactivity of FS results in the consumption of calcium hydroxide that results in the production of additional calcium silicate hydrate (CSH) gel. The high surface area results in high reactivity, which in turn consumes amorphous silica that produces CSH gel. This is the primary reason for the densification of pore structure that results in an increase in ST as FS is replaced with natural sand in concrete. However, as the percentage increase beyond a certain amount, the surface area increases, and workability is reduced, which affects the binding process negatively [67,68]. It can be noted from Figure 6b that as the FS% is increased, the ST continues to increase and becomes approximately constant at replacement level from 15 to 20% and then shows a decreasing trend, which is aligned with the conclusion from previous research. This percentage (i.e., 20%) can be considered as an optimum amount of FS that can be replaced in concrete. As the content is increased beyond this level, the surface area of FS which is greater than OPC begins to impart a negative impact on the strength. The voids had been filled already and additional FS cannot be utilized for bond formation. It would, therefore, result in the absorption of water added to the matrix. As more water is added into the mix, non-solid content would increase and result in inferior hardened properties and ultimately low ST. For a particular FS%, a decrease in FS/C content will cause an increase in the mechanical properties of concrete. There are two parameters in the ratio, i.e., FS and cement. The role of cement on strength can be elaborated from a material engineering perspective. For instance, as the cement content is increased, the binding properties are improved, and the ST increased. Therefore, for a particular mix, the increase in cement content would lower the FS/C ratio and, therefore, result in improved ST [65]. It is for this reason that at 0.4 FS/C, the value of ST is 3.8 MPa as compared to a value of 2.5 MPa at the ratio of 1.56. Similar behavior has been noted for the developed model as depicted in Figure 6c. The second parameter in the ratio is FS. As elaborated in Section 1, the inclusion of FS at a higher percentage will cause a reduction in strength. The reason is poor dispersion of high surface area particles of FS resulting in entrapped air and dilution impact resulting in low CSH gel and poor bonding characteristics of concrete. Therefore, as the FS content is increased, the FS/C ratio increases and results in a reduction of ST as shown in Figure 6c.

It should be noted that there are several parameters such as coarse aggregate contents, temperature, humidity, the chemical composition of concrete mix components, and the testing environment, which can have an impact on the ST of concrete. However, this data is not available for most of the experimental studies on the topic. For machine learning-based models, it is mandatory to have a large database to ensure the proposed models are accurate and effective in predicting the desired output. Therefore, based on the source research, the factors that had a high impact on the strength have been considered as the inputs. The results are being validated through experimental studies. The above-mentioned factors can be considered in future models provided a large database is available.

5. Conclusions

The gene expression programming (GEP) technique was implemented successfully to develop an empirical expression to predict the split tensile strength of concrete containing foundry sand. A widely dispersed database was collected from the literature. The database was partitioned randomly into training, validating, and testing sets. The comparison of the predicted model and experimental results shows a strong correlation for the three datasets. The model was validated by verifying various statistical benchmarks such as correlation coefficient, root mean square error, root squared error, mean absolute error, and relative root mean square error. Further, parametric analysis was performed, and the model effectively captured the trends of change in ST. The availability of reliable and verified models can enhance the utilization of FS in the construction sector. These models can be effectively used to estimate the tensile strength of foundry sand-based concrete, which is highly desirable for structural applications.