Predicting the strength properties of slurry infiltrated fibrous concrete using artificial neural network

Abstract

This paper is aimed at adapting Artificial Neural Networks (ANN) to predict the strength properties of SIFCON containing different minerals admixture. The investigations were done on 84 SIFCON mixes, and specimens were cast and tested after 28 days curing. The obtained experimental data are trained using ANN which consists of 4 input parameters like Percentage of fiber (PF), Aspect Ratio (AR), Type of admixture (TA) and Percentage of admixture (PA). The corresponding output parameters are compressive strength, tensile strength and flexural strength. The predicted values obtained using ANN show a good correlation between the experimental data. The performance of the 4-14-3 architecture was better than other architectures. It is concluded that ANN is a highly powerful tool suitable for assessing the strength characteristics of SIFCON.

Keywords

artificial neural networks / root mean square error / SIFCON / silica fume / metakaolin / steel fiber

Introduction

Slurry infiltrated fibrous concrete (SIFCON) is a special type of fiber-reinforced composite material containing 20% of steel fibers [¹–⁴]. The fiber volume in the conventional fiber reinforced concrete (FRC) is limited to about 2%, as its excess can lead to difficulty in mixing and placing of the concrete. Hence, the need to devise a different construction technique for increasing the fiber volume fraction led to the development of SIFCON [⁵,⁶].

The initial step in the preparation of SIFCON, a preplaced fiber concrete, is the placement of fibers in the form of mold. Under light external vibration, fiber placement can be accomplished either by hand or through the use of commercial fiber dispersing units. On completion of fiber placement, the fine-grained cement-based slurry is poured over the pre-packed fiber bed with subsequent infiltration of the slurry aided by external vibration. High water-reducing admixture is used to provide a suitable slurry viscosity while maintaining its low water-cement (W/C) ratio. Then it is followed by the curing of SIFCON as done for other concrete materials [⁶].

It is essential to study the behavior of SIFCON produced with low tensile strength steel wire fibers in compression, tension, and flexure. Besides, the utility of mineral admixture like silica fume and metakaolin in producing SIFCON also needs detailed investigation. The present work, therefore, focuses on determining the methods involved in producing SIFCON using locally available low tensile strength steel wire fibers. Investigating the strength parameters of SIFCON by experimentation is time consuming, expensive and involves sampling problems. Moreover, it is difficult to develop an empirical or analytical model for SIFCON due to the complex multi parametric relationship among the various constituent materials like cement, sand, admixture, fiber, and water. Thus, in the present work, artificial neural networks (ANNs) are used for developing a compact model to predict the strength characteristics of SIFCON.

Artificial neural networks

ANNs have been used in the past for modeling material characteristics. Ghaboussi et al. [⁷] demonstrated the application of ANN for modeling the stress-strain behavior of concrete, and Mukherjee et al. [⁸] presented the ANN model as a technique to enhance the mechanical behavior of metal matrix composites. Chopra et al. [⁹] developed concrete compressive strength prediction models with the help of two emerging data mining techniques, namely, ANNs and Genetic Programming (GP). A comparison of the prediction results obtained using both the models inferred that the ANN model with the training function Levenberg-Marquardt (LM) is the best prediction tool of concrete compressive strength. Numerous other studies have also focused on the use of ANN model in improving the characteristics of concrete and other composite materials [⁸–¹²].

In this paper, an ANN model has been applied to predict the compressive, tensile, and flexural strengths of SIFCON. Since the above strength parameters depend on the percentage of fiber, fiber aspect ratio, type, and percentage of mineral admixture, an experimental investigation has been carried out to determine these strength parameters. Based on the literature, the appropriate ANN models were selected for the analysis of experimental results. These networks were also trained and tested. The numerical comparisons revealed a good agreement between the test and ANN results. The performance of the models used in the application was evaluated by using the root mean square error (RMSE). ANNs operate as a black box and include powerful tools to capture and learn significant structures in data. They are suitable particularly for problems that are too complex to be modeled and solved by classical mathematics and traditional procedures [¹³–¹⁵]. The great majority of civil engineering applications of neural networks are based on the use of back propagation algorithm primarily because of its simplicity [¹⁶]. Training of ANN with a supervised learning algorithm such as back propagation means determining the weights of the links connecting the nodes by using a set of training data [¹⁷,¹⁸].

An error function in the form of the sum of squares of the errors between the actual outputs from the training set and the computed outputs is minimized iteratively. A typical neural network has three layers; the input layer, the hidden layer, and the output layer. Through the training of the samples, back propagation networks attain the induction by adjusting the connecting weights and the thresholds. While training, the back propagation networks store the information between the influence factors and the strength in weight matrix in parallel, and the network gives the corresponding output based upon the input factors during recall [¹⁹–²⁶].

The neural networks based modeling process involves five aspects: (1) data acquisition, analysis, and problem representation; (2) architecture determination; (3) learning process determination; (4) training of the network; and (5) testing of the trained network for generalization evaluation. In the present study, the adequacy of the developed ANN model was evaluated by considering three statistical evaluation criteria. These statistical parameters are coefficient of determination (R²) Eq. (1), Root Mean Squared Error (RMSE) Eq. (2) and Mean Absolute Percentage Errors (MAPE) Eq. (3). Besides, the matching figures were drawn for both training and testing data to see relationship between model and experimental results.

(1)R^{\mathrm{2}}=\mathrm{1}-{\displaystyle \frac{{\mathrm{\Sigma }}_{i=\mathrm{1}}^N{(t_i-a_i)}^{\mathrm{2}}}{{\mathrm{\Sigma }}_{i=i}^N{(t_i-t_{ia})}^{\mathrm{2}}}}

(2)\mathrm{RMSE}=\sqrt{{\displaystyle \frac{\mathrm{1}}{N}}{\displaystyle \sum _{i=\mathrm{1}}^N{(t_i-a_i)}^{\mathrm{2}}}}

(3)\mathrm{MAPE}={\displaystyle \frac{\mathrm{1}}{N}}{\displaystyle \sum _{i=\mathrm{1}}^N|t_i-a_i|\times \mathrm{100}}

Where, N= No. of data sets, t_i= target output, a_i= network output, t_{ia}= average of target output.

In this study, the multilayered feed-forward networks trained with back Levenberg–Marquardt propagation has been used in the strength prediction model, and the sigmoid and purelin activation functions have been used. Fig. 1 shows the methodology of development of the Artificial Neural Network (ANN).

Statement of problem

The strength parameters of SIFCON can be determined by mapping a functional relationship between the strength parameters and the various factors affecting it. This is because the strength parameters are greatly influenced by several other parameters, viz. fiber material, percentage of fiber volume, fiber aspect ratio, etc. Developing empirical or semi-empirical formulae for macro- mechanical modeling of SIFCON is difficult due to the highly nonlinear interaction among the parameters. Furthermore, the degree of non-linearity and the extent of interaction between the constituent parameters are not clearly known. Hence, ANNs have been used to develop the strength prediction model of SIFCON.

Experimental details

Generation of training and testing data sets

In order to develop the prediction model, a comprehensive set of data needs to be generated that can cover various micro-structural parameters influencing the behavior of SIFCON. In this study, the required set of data was achieved by carrying out experiments on 84 different mixes of SIFCON with four different percentages of fibers viz. 6, 8, 10, and 12 and fiber aspect ratios of 40, 50, and 60. The effects of silica fume and metakaolin were studied for three different percentage replacements viz. 10%, 20%, and 30% that were selected in the range of practical interest. For each mix, the effect of fiber percentage, aspect ratio, type and percentage of admixture on the compressive, tensile, and flexural strength properties of the SIFCON was evaluated by conducting the necessary experimental studies. The tests for compressive, tensile, and flexural strength were conducted, and the results are presented in the subsequent sections. The data was later divided randomly into data for training (80% of total data) and data for Testing (rest 20%) the neural networks. A part training and testing data set is presented in Table 1 and Table 2.

Test program

In all the concrete mixes, clean river sand was used in a constant cement-to-sand proportion of 1:1. For comparative analysis, 43 Grade Ordinary Portland Cement from a single batch was also used. The study involved various parameters, i.e.,

(1) Water binder ratio (0.45);

(2) Volume percentage of fibers (6, 8, 10, and 12);

(3) Aspect ratio of fibers (40, 50, and 60);

(4) Dosage of super plasticizer (1.5% by weight of cement);

(5) Replacement of cement by mineral admixtures (10, 20, and 30% by weight of cement). Three varied types of matrices were used in producing SIFCON as per the details given below:

Matrix 1- Cement+ Sand+ Water

Matrix 2- Cement+ Sand+ Silica fume+ Water

Matrix 3- Cement+ Sand+ Metakaolin+ Water

In matrixes 2 and 3, 10%, 20% and 30% of cement were replaced by silica fume and metakaolin, respectively.

Fabrication and Casting

The concrete cubes were cast in steel molds with inner dimensions of 150 × 150 × 150 mm, and the cylinders were cast in steel molds of 150 mm diameter and 300 mm height. The flexural beams were cast in steel molds with inner dimensions of 600 × 150 × 150 mm.

SIFCON is the preplaced fiber concrete with the placement of fibers in the molds. Therefore, in this investigation, fibers were placed in molds manually. Three types of matrices, as explained above, were used for producing slurry with a water-binder ratio of 0.45 along with a high range water-reducing admixture. The prepared slurry was infiltrated individually into the preplaced fibers in the molds.

The vibration was affected for one minute, and it was maintained at a constant for all the specimens. After 24 hours, the molds were removed, and the specimens were kept immersed in a clear water tank for 28 days. The specimens were then removed out and allowed to dry under shade. Three cubes, three cylinders, and three flexural beams were cast for each mix, and the average strengths were considered.

Results

In the present study, it is required to develop a strength prediction model of SIFCON, which can predict the values of compressive, tensile, and flexural strengths for a given input (percentage of fiber, PF; fiber aspect ratio, AR; type of admixture, TA; and percentage of admixture, PA) to the network. Hence, the input vector selected for this model is:

\mathrm{IP}=\{\mathrm{PF,AR,TA,PA}\}

Similarly, the output of the network comprises compressive strength (F_{\mathrm{c}}), tensile strength (F_{\mathrm{t}}), and flexural strength (F_{\mathrm{f}}). Accordingly, the output vector for the neural networks model is selected as:

{\mathrm{OP=}\{F}_{\mathrm{c}}{,F}_{\mathrm{t}}{,F}_{\mathrm{f}}\}

Neural network training could be made more efficient by performing certain reprocessing steps on the network inputs and targets. Network input processing functions transforms inputs into better form for the network use. The normalization process for the raw inputs has great effect on preparing the data to be suitable for the training. Without this normalization, training the neural networks would have been very slow. There are many types of data normalization. It can be used to scale the data in the same range of values for each input feature in order to minimize bias within the neural network for one feature to another. Data normalization can also speed up training time by starting the training process for each feature within the same scale. It is especially useful for modelling application where the inputs are generally on widely different scales. The input and output parameters have been normalized in the range (0, +1) using suitable normalization or scaling factors that are presented in Table 3. The output parameters are presented in Table 4.

Discussion

Development of ANN model

The architecture of an ANN model describes the number of layers in a network, the number of neurons in each layer, activation function of each layer, and how the layers connect to each other. The best architecture of ANN depends on the type of problem to be represented by the network. Selecting the optimal ANN architecture is an open problem for investigation and solely depends on its application domain. The neural network architecture was determined by training and testing the number of networks under varied conditions.

In this study, neural network analysis is performed using MATLAB software on Pentium IV Machine. There is an involvement of large variety back propagation algorithms [²⁷], out of which the following unidirectional multilayer error using back propagation networks were selected. They were: 1) Fletcher – Powell conjugate gradient algorithm (traincgf); 2) Scaled conjugate gradient algorithm (train-scg); 3) Resilient back propagation algorithm (trainrp); and 4) Levenberg – Marquardt algorithm (trainlm).

The above methods were compared by using trail networks consisting of one hidden layer and two hidden layers with different hidden nodes. Currently, there is no accepted systematic method to choose the number of hidden layers and corresponding hidden nodes. With too few nodes, the network may not be powerful enough for a specific learning or training task. Moreover, computation is time consuming due to the large number of nodes and connections [²⁸–³⁴]. Excessive number of hidden layers and nodes may also be used to provide the network with the resources to minimize the input training samples. Such a network tends to perform poorly on new test samples and essentially contradicts with the generalization purpose of neural computing [³⁵–⁴¹] Hush and Home [²⁷] have suggested that the network size should capture the structure of the available data of the underlying problem. The number of hidden nodes should be found by trial and error approach and must be less than the number of training samples in most of the applications.

The ANNs were trained to reduce the error between neural networks output and the target output. As the aim of training was to find a set of connection weights (hidden neurons) that will minimize the MSE in the shortest possible training time, the training process was terminated when any of the following conditions were satisfied.

(1) The maximum number of epochs reached 1000.

(2) The MSE of the training set reached 1×10⁻⁶.

It can be noticed from the Table 5 that network N10, has the best possible architecture. Despite of having same R² value for different architectures, N10 is selected as the final architecture of these networks based on their sum of weights. It was chosen because of the sum of weights of N10 lower than other architectures given in Table 5.

The results in this table show that the average training error decreased with the increase in the number of hidden neurons/nodes. In other words, the neural networks store knowledge in the connection weights or the hidden neurons as a result of which the increasing number of connection weights enable the neural network to learn more.

There is a tradeoff between the reduction in the training error and increase in the number of hidden neurons. It is obvious from Table 5 that each network has been trained with one hidden layer and two hidden layers, which showed a significant difference in terms of accuracy and computational time required for learning.

Various neural networks with the above-mentioned algorithms were trained and tested to find the best one for the task, and the Levenberg – Marquardt network was ultimately chosen after comparing the performance with other algorithms shown in Table 6. The choice of the neural network with Levenberg – Marquardt algorithm is proved to be the right, as evidenced mainly by the calculated low training and testing RMSEs for the network and the low values of relative testing error. The architecture of this network is 4-14-3, i.e., there are 4 neurons in the input layer, 14 in the hidden layer, and 3 in the output layer (Fig. 2). The MAPE and RMSE statistics obtained by comparing Actual and Predicted results by using Eqs. (2) and (3). The ANN models predictions show good agreements as evident of RMSE and MAPE presented in Table 7. Figs. 3(a), 3(b), 3(c) and Figs. 4(a), 4(b), 4(c) show the comparison between the actual and the predicted results for testing and training models with respect compressive strength, tensile strength, flexural strength.

Training of the network

After choosing the network architecture, the training of the network for mapping the relationship between the input and the corresponding output was carried out. The 4-14-3 network trained on a Pentium IV machine using MATLAB software has been presented in Table 8 and Fig. 2. The convergence of the solution is evident from Figs. 5(a) and 5(b).

It can be observed that the MSE values considerably reduced with the increasing the number of training epochs. After 1,000 training epochs, the MSE was recorded to be only 0.00000638. At this stage of training, the network was terminated to avoid its over-training as it may hamper the generalization capabilities of the network. Hence, it can be noted that the network required 1,000 training epochs for satisfactory training.

The learning of the network model (Figs. 6-8) presented only 68 data sets for training and found that the network has learned the strength prediction problem satisfactorily. It can be observed that the ANN model is able to predict the compressive, tensile, and flexural strength satisfactorily for the data in the training set.

Also, the uniqueness of this network is owing to the fact that for brevity and clarity, it was trained using traincfg, trainscg, trainrp, trainlm algorithms. It is seen that trainlm performance is best among other algorithms and has given best possible results for the training network.

Testing of neural network model

Testing of the network included the testing of the ANN model for the parameters that are not used in network training. The network then predicted the strength parameters for 16 new data sets that were not included in the training data set (Figs. 9-11). The predicted values by neural networks model for the new sets of data matched satisfactorily with the results of experiments. Hence, the results proved that the neural network model can be used for strength prediction of SIFCON.

Conclusions

In this study, a neural network based model has been developed for predicting the compressive, tensile and flexural strengths of SIFCON. This network was trained by using total 84 data sets obtained from the experimental results.

Subsequently, the following conclusions are deduced from this study:

• The performance of the 4-14-3 architecture with sigmoid activation function and Levenberg- Marquardt training algorithm was found to be effective and gave best possible results for the training of network.

• The MSE for training set was 0.00000638 for the 68 training data sets and 0.0000278 for the rest 16 testing data sets.

• The ANN model predicts strength parameters of SIFCON with high correlation coefficient of R²=0.996 and the least RMSE value of 0.046 and MAPE value of 0.0348. All the values were very are reliable, accurate to the experimental results.

• The results predicted by ANN model are nearly closer to the experimental studies, Which indicated a good agreement between the test and ANN results. From the results obtained by the ANN, SIFCON can be recognized in terms of strength with an accuracy rate of about 92% from the engineering point of view. Thus, the application of these networks in predicting complicated phenomena is valid and useful.

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