Keywords

1 Introduction

Self-Compacting Concrete (SCC) mixes can be defined as those mixes which, because of their enhanced flow characteristics, can effectively flow even around the congested reinforcement bars, without leaving any voids and get fully compacted by their own weight, without the need for any external compaction efforts.

Presently RC structures are designed and constructed to resist earthquake load also, which further results in an increase in the density of reinforcing bar structural members and especially in locations such as beam-column joints. The current construction industry requires to use of such concrete which has sufficient strength and also be able to fill the most complex shapes and places. Thus SCC, which has high fluidity along with enough viscosity to carry aggregates and prevent segregation, has been developed and increasingly used. Construction methods have also been evolved in response to this with wide use of pump pouring of concrete, improvement in pumping capacity, and non-vibrational construction. These methods also reduce the noise generated due to the extensive use of vibrators for construction purposes.

Mineral additions such as fly ash are a very important element of SCC and its significance has increased in the current concrete scenario, as they enhance the concrete properties, especially with its immunity to aggressive environment and the use of such additives is economical too. Also, by increasing the use of mineral additives we making a move towards sustainable development, decreasing the waste of fly ash, reducing the amount of energy consumed in the production of cement, and ultimately helping the environment by reducing the emission of CO2 [1].

Due to these merits, SCC has gained popularity in the construction industry, but the mix-proportioning and prediction of the workability properties and compressive strength are complex. Various researchers are trying to come up with new and more effective mix proportioning methods which can be used to produce concrete with desired properties [2]. Prediction of properties of SCC, before construction employing artificial intelligence (AI), could help to save cost and time. Thus, by using this method, an initial mix-proportion for desired properties can be obtained, and it will be more effective in optimizing the ingredient proportion from there onwards by various tests.

Various AI methods such as fuzzy logic (FL) system, artificial neural network (ANN) [3], expert systems (ES) along with some other statistical techniques such as least square support vector machine (LSSVM) [4, 5], relevance vector machine (RVM), data envelopment analysis (DEA) [6], etc. are used and popularised by many researchers in the field of civil engineering.

The aim of this study is to propose an ANN model for the prediction of flow properties and compressive strength of SCC.

2 Artificial Neural Network

ANN is a type of artificial intelligence that imitates the way how a human brain works by learning through experiences and utilizing that knowledge in solving future problems. ANN is a nonlinear information processing framework that is built from interconnected computing elements called neurons. Every neuron is linked with the neuron of the next layer by information transmitting channels called connections, and these connections are associated with weights. These weights indicate the influence of each input on the output response. The sum of weighted input signals is then applied with an activation (or transfer) function to obtain the output response This study consists of ANN modeling which consists of three layers (Input layer, Hidden layer, and output layer). First, the network is trained over several iterations with already available datasets, then it can be used for a dataset that the network has never encountered before.

3 Experimental Database

For the development of the ANN model, 138 datasets containing experimental results of various flow and strength tests are collected from published literature [8,9,10,11,12,13,14,15,16,17,18,19,20,21,22]. For the effective modeling of the network, only datasets conforming to EFNARC:2005 [7], are used for training. Furthermore, 16 more datasets are taken from the literature of the already existing model to test and compare the efficiency of the proposed ANN model [6]. Statistics of the datasets are presented in Table 1.

Table 1 Statistics of the database
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4 Parameters Considered for ANN Modeling

For the modeling of the current model contents of Binder (B), Fly ash (F), Water (W), Fine aggregate (FA), Coarse aggregate (CA), and Superplasticizer (SP) are taken as input parameters, and Slump flow diameter (D), L-box ratio (L), V-funnel flow time (V), and Compressive strength (fc) are taken as output parameters. For better performance of the model, all the input parameters are taken in single units i.e., kg/m3. The datasets which differ from this unit system in any literature are converted to kg/m3 before it was included in datasets used for training. For compressive strength, cube strength is used. If in literature cylindrical compressive strength is measured, then it is converted into cube compressive strength based on assumption that the cube compressive strength is 25% greater than the cylindrical compressive strength.

5 ANN Modeling

MATLAB (R2021a-academic use) is used for developing the ANN model for this research. The architecture of the feed-forward neural network is modeled with one single hidden layer. A single hidden layer neural network is capable of approximating continuous function very effectively. Due to this reason, researchers have adapted the use of a single hidden layer in their studies [3]. The number of neurons in the input layer and output layer is 6 and 4 respectively and the number of neurons in the hidden layer is selected by evaluating the performance of the network with a varying number of hidden neurons, i.e., from 1 to 20 neurons. The performance of the network is evaluated using the correlation coefficient (R) for each network. A graph is plotted taking R-value along the Y-axis and the number of hidden neurons along the X-axis Re (Fig. 1).

Fig. 1
A graph shows the architecture of A N N model, between R value and the number of hidden neurons.

Finding best architecture for the ANN model

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The network with 15 neurons showed the best results in comparison to other networks, hence the hidden layer has 15 neurons Re (Fig. 2a). The Levenberg–Marquardt backpropagation algorithm is used for training the network. The activation function used in the hidden layer and output layer is ‘tansig’ and ‘purelin’ respectively. Dataset used is randomly divided into three parts. For training of the network 70%, for testing 15%, and for validation 15% of the data are used.

Fig. 2
A. is the process between input, hidden and output layer. B. is a screenshot of the view for function fitting neural network and its layers.

The architecture of the ANN model

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The architecture of ANN obtained from MATLAB is shown in Fig. 2b.

6 Result and Discussion

Once all the required parameters have been selected, the network is trained by running the MATLAB code. The training continues till the error arising during validation fails to decrease for six iterations or epochs and then validation stops. The maximum number of iterations that can be achieved during the training stage is set to 1000. For our current ANN model, it took 9 iterations or epochs to train the network, and the mean squared error (MSE) for each iteration is shown in Fig. 3. Mean squared error (MSE) is the average squared difference between the output and targets. Lower values are indicative of better results and zero indicates no error. The mean squared error is calculated as per Eq. (1).

Fig. 3
A graph depicts best validation performance is 526.3797 at epoch 3

Performance of network for each iteration

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$$MSE=\frac{1}{n}\sum\nolimits_{i=1}^{n}{\left({O}_{i}-{P}_{i}\right)}^{2}$$
(1)

where \({O}_{i}\) and \({P}_{i}\) are observed and predicted output results respectively.

The performance of the current ANN model is checked by the coefficient of correlation (R) value, during training, testing, validation, and after that for whole datasets. The R-value determines the correlation between the output and targets. An R-value of 1 means a close relationship, and 0 means a random relationship. The R-value is defined as shown in Eq. (2).

$$R=\frac{{\sum }_{i=1}^{n}({O}_{i}-\overline{{O }_{i}})({P}_{i}-\overline{{P }_{i}})}{\sqrt{\sum_{i=1}^{n}{({O}_{i}-\overline{{O }_{i}})}^{2}{({P}_{i}-\overline{{P }_{i}})}^{2}}}$$
(2)

where \(\overline{{O }_{i}}\) and \(\overline{{P }_{i}}\) are the mean observed and predicted output values. The R values and regression graphs are plotted with the help of MATLAB. Results obtained from the experiment show that the model achieved a very good predicting capacity for the given dataset. R values for the training, testing, and validation stage are 0.998, 0.99475, and 0.99807 respectively Re (Fig. 4). And the R-value obtained when the model was tested on the whole dataset is 0.99746 which shows the current model can predict output values very close to experimental results Re (Fig. 5).

Fig. 4
A set of illustrations depicts the R plots for training data, testing data and validation data in A N N model.

a R plot for training data, b R plot for Testing data, c R plot for validation data

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Fig. 5
An illustration shows the R plot for predicted values and actual values for all data in A N N model.

R plot for actual values and predicted values for all data

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7 Comparison with Data Envelopment Analysis (DEA) Model

To validate the actual performance of the proposed ANN model, the network is tested on a dataset that was not used for the training of the network. This dataset is obtained from the literature it is used to check the accuracy of the existing DEA model (Table 2).

Table 2 Comparison between DEA and ANN model with experimental results
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8 Conclusion

  1. 1.

    ANN model is proposed for the prediction of the flow properties and compressive strength of SCCs.

  2. 2.

    The proposed ANN model shows relatively greater accuracy than the already existing DEA model. Hence, the proposed model can be utilized for the prediction of the properties of SCCs.

  3. 3.

    Through the application of ANN time and cost can be saved, which would have been spent on experimental works otherwise.