Application of Machine Learning to Predict the Mechanical Characteristics of Concrete Containing Recycled Plastic-Based Materials

Abstract

One of the practical ways to overcome the adverse environmental effects of plastic bottle waste is to implement bottles into concrete, one of the most widely used materials in the construction industry. Plastic bottles are mainly made of polyethylene terephthalate (PET) and can be used as a fiber to reinforce concrete. In recent years, PET fiber-reinforced concrete (PFRC) has attracted researcher attention, and several experimental studies have been conducted. This paper aims to present the benefits of using PET fiber as a reinforcing element in concrete using a machine learning approach. By considering the effect of PET fibers in concrete, engineers and stakeholders may be encouraged to further use these recycled materials. The proposed network was successfully able to capture the response of PFRC with high accuracy (mean squared error (MSE) of 7.11 MPa and R coefficient of 98%). The results of the proposed network show that the amount of PET fiber usage in concrete has a significant effect on the compressive strength of PFRC. Moreover, the PFRC’s response considering the variation of mechanical and geometrical properties of PET fiber mainly depends on the fiber’s shape. The most effective shapes of PET fiber are shapes with deformation, followed by embossed and irregular shapes.

1. Introduction

Concrete, as a popular construction material in the building industry, has several drawbacks, such as a low resistance capacity against tension. Reinforcing the concrete overcomes this defect. Using fibers with different materials is one of these reinforcing methods. Typically, fibers can be made using various polymers, glasses, carbons, or other naturally available materials. Concrete-containing fiber-reinforced materials, such as fiber-reinforced concrete (FRC), can offer superior properties compared to plain concrete. The mechanical characteristics of FRC can be identified based on the type and dosage of fiber and cement matrices, and specifically the geometrical and weight/volumetric percentages of the fibers and cementitious material. Moreover, the fibers’ mechanical properties and the available adherence between the cement and fiber matrices can affect the structural resistance of concrete [1,2]. The fibers reduce the possibility of cracking, and consequently increase the energy absorbed in the fracture process. Furthermore, the implementation of fiber in precast concrete has a positive effect on structures [3,4,5]. Several factors, such as length to equivalent diameter of the fiber’s ratio, the number of fibers, and their orientation, shape, and spread within the cement matrix affect fiber’s efficiency in enhancing the mechanical properties of concrete [6,7].

In recent decades, the issue of reusing waste plastics has attracted researcher attention, considering the environmental and economic impacts of the construction industry [8,9]. This plastic waste has the advantage of being available in large quantities at low prices [10,11]. Polyethylene terephthalate (PET) is one of the subcategories of the large polyethylene family, produced worldwide to a great extent due to various advantages, such as a higher resistance, lighter weight, and lower production cost compared to classical plastics [12]. PET is mainly acquired from plastic container bottles that can be used to store water, beverages, and food packages [1]. To reduce water and land pollution, these plastic bottles are required to be properly recycled. Furthermore, recycling PET waste requires special consideration regarding the process of color changes and degradation impurities of the recycled material. Therefore, incremental costs of recycling are predictable [12,13]. Moreover, the recycling rate of PET bottles is lower compared to the disposal rate, which is about 60 million bottles per hour [14,15]. Therefore, the need for efficient and economic solutions regarding the PET bottle waste is inevitable. The use of PET bottles as continuous long strips arranged in grids to reinforce a concrete element can be considered as one of the methods of recycling PET bottles. This requirement of arranging long strips is currently an important obstacle in the discipline of construction materials. In this context, numerous research studies have been conducted. The promising outcomes on improving the mechanical properties of materials encourage further studies to offer novel methods for using these fibers to enhance the structural response of produced concrete mixtures [1,16].

The prime objective of the presented article is to illustrate the benefits of using PET fiber as a reinforcing method in concrete. This approach is implemented by predicting the mechanical properties of concrete including PET fiber, and by adopting an artificial neural network (ANN) technique. As this machine learning approach has a reasonable accuracy, robustness, and time-saving ability, it was used as a method to estimate the mechanical properties of PFRC. It is worth noting that the main objective is the practical application of ANN in determining the required properties for the concrete industry, as well as an accurate prediction of the mechanical properties of PFRC. In this regard, the understanding about PET fiber reinforced concrete (PFRC) will be improved, and consequently will lead to increasing the incorporation of PRFC in construction practice. Moreover, this research identifies the effect of the most important parameters with the significant impact on the mechanical properties of fiber-reinforced concrete. The ANN is a reliable soft computing approach that can address convoluted issues, however, the shortcomings of this approach should be considered in the process of analysis. This study presents a method to assess the concrete’s compressive strength containing PET fiber by adopting neural networks. In order to establish the ANNs, empirical data of an extensive dataset is used. The final outcomes of the conducted simulation by adopting ANN methods are incorporated to evaluate the connection between the different parameters and their effect to accurately estimate the PFRC’s compressive strength.

2. Artificial Neural Network

One of the advantages of neural network applications is the ability to offer user-friendly models with a higher accuracy compared to complex natural systems, which require including large datasets as inputs [17,18]. Neural networks incorporate uncomplicated operating elements with parallel operations which are inspired by the human brain’s functions. The interconnections of components in nature determine the network operations [19,20]. In this context, the components’ relationship in a neural network can be simulated by assigning a weight to each connection in order to identify and adjust the participation values for each connection. Appropriate training and correct adjustments of the neural network will lead to trustworthy outcomes. Minimizing errors in the simulation process is the most critical part of neural network training and can be achieved by adjusting and optimizing the weight values during the learning process through iterative procedures to reduce the error with an acceptable range. During the iterative procedures, the weight values will be initialized and optimized, and the predicted results will be estimated accordingly. Furthermore, the errors corresponding to each iteration will be determined. The higher error values during the initial steps show the random assignments of weight values and can be optimized during the learning procedure. The main concern during the training produce of the neural network is to assign correct weights to reach the minimum errors for all included data. The required weight numbers in the majority of artificial network methods are considerable due to various involved parameters, which complicate finding the correct weight values. Additionally, weight estimation using trial and error is time-consuming and inefficient. The gradient descent method is an efficient approach to detect the least error sets promptly in the network’s training process. The gradient descent method incorporates the error gradient in order to descend the network’s error [21,22]. The calculated error is contingent on the network’s output, which in respect relates to the hidden neurons’ weighted outputs. Therefore, the chain rule of differentiation is applicable from the error to weight of the first layer, $\frac{\partial E}{\partial w_{nm}}$. This approach is defined as backpropagation and was originally introduced by Werbos [23] and was improved by Rumelhart [24]. The backpropagation approach is an algorithm that was developed based on the concept of gradient descent by shifting the network weights against the direction of the performance function slope. Indeed, the “backpropagation” of the network refers to the backward propagation of the error signal. According to the error signal, the hidden units would be capable of determining their error and adjusting the weights [25,26].

The neural network follows the main assumptions as follows:

• Neurons are simple members responsible for processing the data;
• The neurons pass over connection links achievable by signals;
• Specific weight values are assigned to each connection;
• To calculate the outputs, neurons should transmit the input data from the defined activation function;

The neural network can be identified based on the given activation functions, developed architecture, and the assigned algorithm. The objective is to efficiently reduce the number of required experiments in a time-efficient and cost-effective approach [27,28].

2.1. Dataset

A deep and careful survey of the literature was conducted to establish a model based on the machine learning approach to predict the compressive strength of the concrete containing PET fibers. The dataset includes 85 samples with 12 distinguishable features. The collected dataset contains information about water content (W), binder (B), coarse aggregate (G), fine aggregate (S), PET fibers (P), tensile strength of PET fibers (F${}_t$), PET fiber modulus of elasticity (E), PET fiber length (l), PET fiber width (d), unit weight of PET fiber (U), and PET shapes (F). Four different fiber shapes are considered based on the available experimental studies in the literature, namely string shape, irregular shape, deformed shape, and embossed shape (Figure 1). The mold of specimens was also considered, so the compressive strength was converted to a 150 mm cubic standard mold. The PFRC’s 28-day compressive strength is considered as the network’s output. The statistical indices for PFRC are summarized in

Table 1. Statistical parameters for the concrete containing PET fiber dataset.

Attribute	Unit	Min	Max	Average	Standard Deviation
Water	kg/m${}^3$	79.7	225	183.3	38.5
Binder	kg/m${}^3$	290	558	408.3	63
Coarse aggregate	kg/m${}^3$	600	1223	882.6	175.8
Fine aggregate	kg/m${}^3$	677.5	1000	838.3	111.1
PET fiber	kg/m${}^3$	0.64	27	10.1	5.8
Fiber tensile strength	MPa	100	550	188.5	139.5
Fiber modulus of elasticity	MPa	190	12,000	3821	3720.5
Fiber length	mm	10	64	32.2	15.6
Fiber width	mm	0.2	12	1.9	2.1
Fiber unit weight	kg/m${}^3$	1100	1800	1331	215.7
Fiber shape	-	-	-	-	-
28-day compressive strength	MPa	20.9	84.7	45.7	16.3

. The distribution of the features are shown in Figure 2.

2.2. Network Modeling

In general, the modeling procedure can be defined as the procedure of delineating a physical phenomenon using mathematical functions [29,30]. It is critical to optimize the network’s design to provide a lightweight and high-quality product simultaneously [31]. Considering a direct solution is not available for estimating the number of neurons for each layer and the number of hidden layers. These numbers can be estimated using a trial-and-error process. To offer the best possible architecture for the ANN model, numerous structures using different neurons and hidden layer numbers have been analyzed. The findings on the network’s performance indicated that a single hidden layer network including 19 neurons provides the maximum accuracy to predict the PFRC’s compressive strength for 28 days.

In order to maintain the initial database’s relationships, the input features are normalized with a linear approach in a range between 0 and 1 [19]. Training the neural network was fulfilled by adopting the Levenberg–Marquardt (LM) algorithm, since this method has suitable convergence, more precision, and is time-efficient [32,33]. The LM algorithm randomly separated the datasets into three parts: 15% was reserved for validation, 70% was used to train the network, and the remaining percentage was used to test the performance of network. TANSIG (Equation (1)) and PURELIN (Equation (2)) were adopted as the activation functions for the hidden and output layers, respectively. The learning process of the network terminates if the desirable performance can be achieved.

$$y=tansig\left(x\right)=\frac{2}{\left(1+e^{-2x}\right)}-1$$

(1)

$$y=purlin\left(x\right)=x$$

(2)

Network Performance

The concrete’s mechanical characteristics, including PET fibers, can be evaluated after training the neural network. In this regard, the convoluted relationships between the input data and their impact on the reported output can be evaluated. The networks’ performances to determine the concrete’s 28-day compressive strength are presented in Figure 3a. The best validation performance was reported as 0.0042 at the 13th epoch for PFRC’s compressive strength. The estimation quality is the function of R as the coefficient of determination in the network for all the datasets presented in Figure 3b, which illustrates the correlation between the empirical date (target) and the ANN output. The overall response is based on the R value almost equal to 1, verifying that the trained network produced the optimal outcomes. The R value, including all analyzed datasets, is 0.9806, which is reasonable. Moreover, the comparison of the target and output of the proposed network is illustrated in Figure 4. It was observed that a desirable match is achieved between the empirical results and outcomes. This correlation highlights the capability of the proposed network to determine the PFRC’s compressive strength. Having the PFRC’s compressive strength may help engineers and stakeholders better understand the response of concrete-containing PET fibers, and lays the groundwork for further adoption of this clean and environmentally friendly concrete.

The statistical characteristics of the reported errors, such as root mean square error (RMSE), correlation coefficient (R), mean square error (MSE), and mean absolute percentage error (MAPE), were determined for evaluating the concrete’s compressive strength by the ANN model. These errors can be calculated by Equation (3).

Table 2. MSE, RMSE, MAPE, R coefficient for entire data in the network.

Output	Performance of the Network
	MSE	RMSE	MAPE	R
Compressive strength of PFRC	7.11	2.66	2.88	0.9806

offers a comparison regarding these error metrics including all the analyzed datasets incorporated in the network. The zero value shows the best optimization for all statistical parameters (except for R). On the other hand, the one value is the ideal number for R. The RMSE values shows the deviation within the empirical and predicted values. The MAPE values identify the prediction error and the ratio of the error to the empirical value [34]. The correlation coefficient is considered to assess the predictive performance of the model [35]. The statistical characteristics presented in Table 2 show that the predicted concrete’s compressive strength using ANN network is comparable to the empirical values of PFRC tests. Such comparable results highlight the functionality of the adopted ANN model.

$$\begin{array}{c}\hfill RMSE=\sqrt{\frac{\sum {(T-P)}^2}{N}}MSE=\frac{1}{N}\sum {(T-P)}^2\\ \hfill MAPE=\frac{100}{N}\sum \left|\frac{\overline{T}-P}{P}\right|R=\frac{\sum (T-\overline{T})(P-\overline{P})}{\sqrt{\sum {(T-\overline{T})}^2}\sqrt{\sum {(P-\overline{P})}^2}}\end{array}$$

(3)

where T and P are the target and predicted values, and the $\overline{T}$ and $\overline{P}$ parameters are the averages of the target and the predicted values, respectively.

2.3. Analysis of the Network Sensitivity

As mentioned in Section 2, the weight of each neuron shows its significance during the prediction process. The Garson’s factor [36] is adopted to determine the relative significance of the analyzed features in the neural network. The offered equation for a network with a single hidden layer is as follows:

$$Q_{ik}=\frac{{\sum }_{j=1}^L\left(\frac{w_{ij}}{{\sum }_{r=1}^N{w}_{rj}}{v}_{jk}\right)}{{\sum }_{i=1}^N\left({\sum }_{j=1}^L\frac{w_{ij}}{{\sum }_{r=1}^N{w}_{rj}}{v}_{jk}\right)}$$

(4)

where ${\sum }_{r=1}^N{w}_{rj}$ presents the sum of the connection weights between the N input neurons and the hidden neuron j, and $v_{jk}$ is the connection weight between the hidden neuron j and the output neuron k [37]. The outcomes of the sensitivity analysis are presented in Figure 5.

As can be seen, almost all the parameters participated equally in the determined compressive strength of PFRC. To consider the effect of all parameters, no irrelevant or excess features have been chosen. Excessive features do not contribute additional information and may lead to degradation in the learning algorithm’s performance and an increase in the computational cost [17,38]. Nonetheless, the amount of PET fiber plays an important role in the 28-day compressive strength of PFRC. This is in accordance with the experimental results of Barluenga [39], Watts et al. [40], and Tang et al. [41], in which the PET fibers play a positive role in reducing the number and formation of micro-cracks. The lowest importance belongs to the modulus of elasticity of PET fibers. This is in accordance with proven facts and experimental studies. The bond strength of PET fiber is not significant as these fibers are smooth [42]. Therefore, PET fibers will pull out from the concrete matrix before reaching their ultimate strength [43]. In some cases, these fibers fail because of high applied tensile strength [44,45]. This is the reason that the importance of PET fiber tensile strength is higher that the effect of PET fiber modulus of elasticity.

However, as Figure 5 indicates, the other features have an influence on the compressive strength of PFRC as well. These influences are multi-factored, interwoven, and sophisticated, and can be considered only with numerical-based methods, such as machine learning (ML). ML-based methods are able to involve all the features in the final results simultaneously, and provide the outcomes for each feature’s variation. In the upcoming section, the ability of the proposed network in determining unseen data, i.e., the dataset that is not previously fed into the network and that the model has never trained before, will be evaluated.

3. Results

After ensuring the accuracy of the proposed network in estimating the compressive strength of PFRC, a generalization analysis can be performed. Generalization is the capability of the ML-based approaches to treat unseen data which depends directly on the network training. The generalization ability can further demonstrate the achievement of any ML-based method on real world data. In this section, the effect of most important features on the 28-day compressive strength of PFRC is evaluated using unseen data and the generalization ability of the network.

3.1. Effect of Amount of PET Fiber and Its Geometrical Properties

In order to find out the effect of various amounts of PET fibers, along with the impact of geometrical characteristic of PET fibers on the compressive strength of PFRC, the network’s capability in predicting unseen data is utilized. To do so, the other input features are kept constant and the only parameters that vary are fiber content, fiber length, and fiber shape in the PFRC. The assumed mix design for generalization analysis is summarized in

Table 3. Assumed mix design for generalization analysis.

Water (kg/m${}^3$)	Binder (kg/m${}^3$)	Fine Aggregate (kg/m${}^3$)	Coarse Aggregate (kg/m${}^3$)
150	500	900	750

. The results hereafter are reported for the assumed mix design with the water-to-binder ratio of 0.3.

The effect of variation in fiber length and width is shown as the aspect ratio of the fiber, which is the ratio of length over width of the PET fibers. Figure 6 demonstrates the variation of the compressive strength due to changes in the PET content, PET shape, and PET fiber aspect ratios. As can be seen, the effect of an increase in the aspect ratios for all shapes is negative. In other words, increasing the length or reducing the width of the PET fibers results in a reduction of the 28-day compressive strength of PFRC. Furthermore, this negative impact is more dominant in higher amounts of fiber content. This can be attributed to the fact that using PET fiber, especially with a higher content and/or higher aspect ratios, causes flaws between the PET fibers and the concrete mass. This defect in PFRC will make a weak region inside the dense mass of concrete matrix and can be the origin of crack formations during loading. This is in accordance with the experimental results [12,44,45,46,47,48].

By comparing the results of Figure 6, the effect of PET fiber shapes can be determined. String-shape PET has an almost constant compressive strength for a wide range of various aspect ratios. This means that the effect of this PET shape type on increasing the compressive strength of PFRC can be neglected. This may be due to a lower bond strength between the PET fibers and concrete matrix. In this context, Marthong and Sarma have presented the comparable results [49]. However, the other fiber shapes that have a better interaction with the concrete mass have a wider range of higher compressive strength, resulting in a more stable response in the PFRC. In PET fiber shapes, except the string one, the optimum amount of PET fiber usage is lower than 10 to 15 kg/m${}^3$, which roughly equals 0.7 to 1% fiber replacement. The same results were obtained in the experimental studies of Irwan et al. [50], Al-Hadithi and Hilal [51], Pandya and Purohit [52], Borg et al. [44], and Ochi et al. [42].

The effect of PET fiber content is also obvious in Figure 6. As can be seen, an increase in the fiber content results in an adverse effect on the compressive strength of PFRC. This is in accordance with the experimental studies of Gu and Ozbakkalogl [53], Prahallada and Prakash [54], and Nibudey et al. [55]. This may be due to clogging effect of PET fiber in higher dosages. Moreover, it can be argued that the compressive strength of PFRC is under the influence of both fiber content and fiber aspect ratio for any fiber shapes. It means that these two parameters simultaneously affect the 28-day compressive strength of concrete containing PET fibers.

3.2. Effect of the Mechanical Properties of PET Fiber

Since the PET fiber in the concrete matrix acts as a bridge to improve the consistency of the concrete mass, the mechanical properties of these fibers have an essential influence on the compressive strength of PFRC. Therefore, the effect of the mechanical properties of PET fiber in terms of tensile strength (f${}_t$) and modulus of elasticity (E) on the compressive strength of PFRC is discussed. The generalization results are depicted in Figure 7. According to the initial dataset and based on Figure 2h,g, the tensile strength and modulus of elasticity of PET fiber are determined to be in the range of [100, 550] and [200, 12,000], respectively. As can be seen from the results, the PET fiber shapes have an important impact on the compressive strength of PFRC. For fiber with a string shape, the most essential parameter is the PET fiber modulus of elasticity (E), as in a higher E, the compressive strength has its maximum values. This trend is not in accordance with the other fiber shapes, as in other fiber shapes, the maximum compressive strength occurs in higher tensile strengths of PET fibers. This can be attributed to the fact that the string shape fiber has a lower bond strength and the fiber pull out during the loading before they reach maximum tensile strength. However, the lower tensile strength of fiber results in a lower compressive strength in all fiber shapes. For shapes of fiber with higher bond strengths, the tensile strength of PET fibers plays an important role by bridging the concrete mass and limiting crack formation and propagation [56,57,58]. Therefore, according to the results of the ANN model for unseen data, it is strongly recommended to deform the shape of PET fiber into some patterns to enhance its bond strength.

In addition, the higher compressive strength of PFRC is related to PET fibers with deformed shapes. Furthermore, the concrete made with this type of fiber has a wider region of high strength, meaning that the maximum compressive strength occurs for a higher number of specimens. Moreover, the variation of the compressive strength is independent of the modulus of elasticity, which indicates that this type of fiber is cut during loading due to the applied tensile strength. The same experimental results were obtained by Borg et al. [44], showing the slipping of PET fibers with string shapes from the concrete matrix and the suitable bond strength of deformed PET shapes. It can be concluded that the most effective PET fiber shape is deformed, followed by embossed and irregular. This is in accordance with the experimental research of Ochi et al. [42], Kim et al. [59], and Schembri [60]. Furthermore, the deformed PET fiber shape improves the shrinkage behavior of PFRC by limiting micro-crack formation [61,62,63,64].

4. Conclusions

Using waste PET fibers in concrete may reduce the adverse environmental effect of plastic bottle waste. This paper aims to assess the unreported aspects of using PET fibers in the mechanical properties of concrete. This may help engineers and stakeholders understand the effect of PET fibers and increase their implementation to enhance the mechanical properties and structural responses of concrete. Accordingly, an accurate and comprehensive dataset collected from the available literature and an artificial neural network were utilized to perform a generalization analysis. It was shown that the network is able to predict the results with a MSE error of 7.11 MPa and correlation coefficient of 98%. It can be concluded that the results of the proposed network may be used to understand the response of PFRC. Moreover, it was shown that the most important factors on the behavior of PFRC are PET fiber content, fiber aspect ratio, and fiber shape.

Generalization results indicate that an increase in the aspect ratio has an adverse impact on the compressive strength of concrete. This negative impact is more dominant in higher amounts of fiber content, which is due to the formation of weak regions in the concrete mass. Moreover, by comparing the generalized results of the ANN model, it was concluded that PET fiber shapes have an undeniable effect on the compressive strength of PFRC. This effect mainly depends on the bond strength between PET fibers and the concrete matrix. However, the mechanical properties of PET fiber, i.e., the tensile strength and modulus of elasticity of PET fibers, play an important role in the compressive strength of PFRC. It was demonstrated that the tensile strength of PET fibers is dominant in fibers with a higher bond strength, while the modulus of elasticity of PET fiber affects the compressive strength of FRC containing smooth PET fibers.