1. Introduction
Coal is considered one of the prevalent sources of energy production worldwide. However, its exploitation and extraction have caused massive waste materials [
1]. Such irresolvable and non-biodegradable waste materials have been used in many different ways yet have never reached an executive phase for diverse reasons [
2]. With continuing improvements of the industry practice, coal extraction from mines has experienced substantial growth in several locations, resulting in the production of colossal amounts of coal waste. To date, more than two million tons of coal waste material are vacated around factories, and this amount is rising rapidly due to the ascending trend of exploitation and exploration. Coal waste materials are often piled in mountainous and sylvan areas, exposed to snow and rainfall, and endangering the surrounding environment and ecosystems. Accordingly, many researchers and engineers have been exploring effective and cost-competitive solutions to this ongoing issue [
3]. Recent investigations suggest that industrial byproducts can improve the durability of concrete and have a low influence on the material properties up to a certain percentage [
4,
5].
The effects of using recycled tires on the properties of concrete and asphalt have been explored in previous studies [
6,
7]. For instance, Aiello and Leuzzi [
8] investigated the effects of using recycled tires in fresh and hardened concrete and showed that using tire rubber partial replacement for natural fine aggregates in concrete at volume percentages of 25, 50, and 75%, the flexural strength degraded by 4.49, 5.81, and 7.3%. They also found that adding 75% by volume of crumb rubber—replacing natural fines in concrete—increased energy absorption. Abousnina et al. [
5] investigated the application of oil-contaminated sand (OCS) in concrete. The mechanical characteristics, strength development, hydration, and microstructure of cement mortar containing oil-contaminated sand were evaluated. Ferdous et al. [
9] proposed three new railway sleeper concepts for a mainline track and investigated their behaviors experimentally and numerically. The structural behavior of the railway sleepers was evaluated experimentally under five-point static bending and was verified via beams on elastic foundation analysis. Moreover, an in-depth investigation of the in-track behavior of sleepers was conducted using finite element simulation. Rahmani et al. [
10] evaluated the behavior of concrete containing Polyethylene Therephthalate (PET) 5, 10, and 15% by volume of sand replacement at a water-to-cement (w/c) ratio of 0.42 and 0.54. Their results indicated that adding 5% PET at a w/c ratio of 0.42 and 0.54 increased the concrete flexural strength by 6.71 and 8.02%, respectively. However, the flexural strength of concrete specimens decreased with increasing PET content, marking 14.7 and 6.25% of flexural strength reduction for concrete containing 15% PET at the examined w/c ratios, respectively. Several other byproducts have been beneficiated in concrete, including mine tailings [
11], glass sludge [
12,
13] coal bottom ash, [
14] waste latex paint, [
15] waste marble, [
16] sugarcane bagasse ash, etc.
Concrete is the most widely used construction material on earth. If considered by country, the cement industry will rank as the third-largest global emitter of carbon dioxide [
17,
18,
19]. Considering the sheer volume of concrete production, it offers a conducive medium for the beneficiation of large amounts of industrial and mining byproducts. Hence, there need for research to explore the effects of recycling industrial and minim byproducts on concrete performance. A key mechanical characteristic of concrete is its flexural strength. While its magnitude depends on the concrete mixture design, its accurate prediction is hampered with several challenges. Thus, determining the flexural strength of concrete has generally been carried out through time-consuming and costly destructive testing. Predictive models for estimating flexural strength have long been of interest to researchers owing to potential time, labor, and cost savings. Accordingly, several researchers have proposed various models for predicting concrete behavior using different mathematical techniques, such as linear and non-linear regression methods [
20,
21,
22].
More recently, data-driven computational intelligence methods, such as machine learning and deep learning have attracted great interest in predicting the engineering properties of cement-based materials. For instance, such techniques have recently been used for mixture optimization [
23] and predicting the carbonation depth in recycled concrete aggregate [
24], shear strength of reinforced concrete shear walls [
25], compressive strength of phase change materials integrated cementitious composites [
26], shear strength and failure mode of SFRC beams [
27], ultra-high-performance concrete compressive [
28], and structural response of RC slabs exposed to blast loading [
29]. Dedicated literature reviews on the use of machine learning in predicting the properties of concrete are readily accessible in the open literature [
30,
31].
The goal of the present study is to develop a suitable and economical solution for beneficiating coal waste in the concrete manufacturing process. Thus, the feasibility of developing a type of concrete incorporating coal waste and having suitable flexural strength was explored. If using coal waste as an additive material in concrete is successful, not only would it mitigate the disposal problem of this waste, but it would also reduce the need for virgin concrete raw materials, thus saving natural resources. Furthermore, to alleviate the need for laborious, costly, and time-consuming trial batches to develop concrete with adequate flexural strength, a hybrid artificial neural network (ANN) coupled with response surface methodology (RSM) was trained and employed to accurately predict the flexural strength of coal waste treated concrete. In addition, the use of coal waste in concrete yields environmental benefits so that the stockpiling of this harmful by-product can be mitigated. Moreover, partial substitution of cement with coal waste can reduce carbon dioxide emissions from cement production and yield economic advantage through reducing the cost of concrete production.
Given that the influential input parameters on flexural strength of such concrete are not available in the existing literature, this study carried out an extensive experimental study and deployed the response surface methodology and variance analysis, for the first time, to extract the important parameters affecting the flexural strength in order to enhance the modeling accuracy. Such a sustainable alternative to conventional destructive testing is presented to predict the flexural strength of concrete. Determining the most suitable model by comparing the traditional neural network and the response surface methodology (RSM)-modified artificial neural network is another novel aspect of this paper. Finally, a model for predicting the flexural strength is proposed using non-linear regression analysis.
Wastes from coal mine extraction have become a paramount challenge in recent years. For each ton of hard coal produced by mining extraction, 400 kg of waste material is generated. The resulting piles of coal refuse typically have momentous negative environmental implications, including the leaching of iron, manganese, and aluminum residues into waterways, along with the possible generation of acid mine drainage. With the ongoing greater international efforts to achieve the United Nations sustainability goals, novel solutions are needed for the management of such colossal volumes of coal waste. The existing practice to manage coal waste includes complex reprocessing for instance using fluidized beds. The present study pioneers a sustainable and simple solution consisting of using coal waste in the form of a powder in concrete mixtures. Considering the sheer volume of concrete produced worldwide, this practice could alleviate the problems of coal waste disposal. It is noteworthy that there is a dearth of research in this area in the open literature. In particular, informational modeling has not been applied to this topic previously.
3. Modeling Approach
Inspired by the process of the biological brain, artificial neural networks (ANN) offer a powerful strategy to process information. The inputs in ANN are past observations that affect the goal function, while the output results in the prediction of the future outcome by considering the weight of each variable and a certain amount accumulated in each neuron. One of the most critical performance functions is the “tangent hyperbolic”. Neurons are the main constituent of the ANN. Generally, ANN models consist of three parts: inner (input) layer, hidden layer(s), and outer layer, as depicted in
Figure 2. Each layer is responsible for receiving data, processing it, and producing an output unit. Each neuron in the inner layer is connected to the neurons in the hidden layer(s). It is noted that there are no connections between the neurons inside each layer. The number of neurons in each layer depends on several factors. For instance, the number of neurons in the inner and outer layers depends on the input and output parameters considered in the modeling process. Conversely, the number of neurons in the hidden layer(s) is determined using different methods based on the problem complexity, and this often consists of a trial and error process [
35]. Using real data, the output of the ANN primarily tends to be the same as the laid goal output, and thus, the ANN learns [
36]. The network is moderated by comparing its output with the goal output until the difference is minimum. Since there is no proven method to determine the number of layers and neurons, choosing the number of layers and neurons in a way that makes the network output meaningful and makes its difference with the output goal is minimum is the most challenging step in predicting a model by ANN method [
35]. In this paper, more than 300 networks were assessed by changing the neurons of each layer to achieve the most suitable network. Given that each assessment was performed four times, a total of 1200 different experiments were conducted to attain the optimum network.
The Feed Forward network used in this research consists of an input layer, one or several hidden layers, and an output layer. Weight is also considered relative to each connection. This algorithm is one of the most widely used for training ANNs, where the gradient descent slope decrease method is used so that errors are directed from the output layer to the input layer, and the weights are distributed in an order that the errors become minimum. Consequently, the training process consists of gradual weight correction to minimize the error functions. This action continues until one of the stopping criteria is not satisfied [
35,
36]. Modeling errors can be calculated by considering the differences between the network output and the actual data through different criteria in the performance evaluation. The criteria used in this research include the Root Mean Square, Random Error (
R2), Mean Squared Error (MSE), Mean Absolute Error (MAE), and Root Mean Square Error (RMSE), as presented in
Table 4. In this Table,
yt signifies the experimental data,
y0 is the value estimated by the ANN after learning, and
n is the entire count of data at each step. MAE, RMSE, and MSE are in the range of [0,+
, with values closer to zero (
R2 closer to 1) imply better model fitness and closer output data to the goal output.
To attain optimal use of coal waste and mixture design, the RSM method was used in this study. In this method, the Central Composite Design (CCD) solution was deployed, in which the number of experiments is decreased dramatically, leading to saving time, material, and cost. It is noted that this method can not only assess the effects of independent parameters, but also their interactions, predict the outcome using variable inputs, determine the optimum values and their location of occurrence, and present multi-replied optimization for the experimental outputs [
37,
38]. In the RSM model, variables and their changing ranges should be first determined. Subsequently, they are categorized, and their front and end are introduced as two levels coded with +1 and −1. The third level that stands between these two levels is called the zero level or the central level. Two other levels with the ranges of (−∞) and (+∞) are added and placed before the −1 and after +1 levels [
39,
40].
In this study, the dependent variables in the normal ANN modeling included the w/c ratio, cement content, volume of gravel, and coal waste percentage. In contrast, the number of dependent variables was increased to 19 in the RSM-modified ANN modeling to increase model accuracy. The additional independent variables comprised the second-grade effects and mutual effects. As mentioned earlier, the most challenging part of teaching the ANN is to determine the number of layers and neurons in each layer. In this study, 70% of the data were randomly provided to the neural network as input data for training purposes, 15% of the data were used for model validation, and 15% were used for model testing. This ratio was determined by trial and error to achieve accuracy and avoid network overfitting.
The number of hidden layers must be set such that (i) the amount of discrepancy between the network output and the actual data is minimized, and (ii) an excessive increase in the number of layers does not cause over-fitting. Since there is no limitation in determining layers and neurons, more than 200 networks were assessed in this paper to look for the optimal maximum number of layers and neurons using different repetitions by changing the numbers of layers and neurons. Thereby, a total of 1000 different networks were evaluated by considering a five times repetition for each network. As a result, the optimum network for the normal neural network was chosen to have two hidden layers, in which ten and eight neurons were presented in the first and second layers, respectively. Likewise, the optimum network for the RSM-modified ANN was selected to have three hidden layers with eight neurons in the first layer, eight neurons in the second layer, and six neurons in the third layer.