1 Introduction

Concrete is one of the most widely used construction materials in the world. However, much of the current available knowledge on concrete technology has been mainly generated in the most developed parts of the world [1]. During the last years, special types of concrete like high-performance concrete and self-compacting concrete are commonly used.

Self-compacting concrete (SCC) has emerged in Japan in the late 1980s as a material that can flow under its own weight. This allows the facility of concrete placement without the need of additional mechanical compaction in complicated formwork, congested reinforced structural elements and hard to reach areas [2, 3]. This saves time, reduces overall cost, improves working environment and opens the way for the automation of the concrete construction. SCC is an innovative homogeneous and dense concrete in hardened state, and it has the same engineering properties and durability as traditional vibrated concrete.

Many researchers have set some guidelines for mixture proportioning of SCC, which include reducing the volume ratio of aggregate to cementitious material; increasing the paste volume and water–cement ratio (w/c); carefully controlling the maximum coarse aggregate particle size and total volume; and using various viscosity enhancing admixtures [4]. For SCC, it is generally necessary to use superplasticizers in order to obtain high workability and viscosity-modifying admixture eliminate segregation. Adding chemical admixtures are, however, expensive, and their use may increase the materials cost. Savings in labor cost might offset the increased cost, but the use of mineral additions could increase the slump of the concrete mixture without increasing its cost. These new building materials are known as supplementary cementing materials (SCMs) that are defined as material from the waste stream of a manufacturing process. These include fly ash, silica fume and blast furnace slag or limestone filler. Their use as a partial replacement for Portland cement reduces the amount of cement needed for concrete. This reduces the energy and CO2 impacts of concrete and helps improve the workability and long-term properties of concrete [5].

Fly ash (FA) is the finely divided residue that results from the combustion of ground or powdered coal and that is transported by flue gases from the combustion zone to the particle removal system [6]. Fly ash is an industrial by-product and is considered one of the most widely used in different concrete applications. When FA is used as a mineral admixture in concrete, it improves its strength and durability characteristics at later ages depending on its reactivity, the distribution of particle size and the carbon content. Generally, FA is used as a partial replacement of cement. However, it can also be used as a partial replacement of fine aggregates to achieve different concrete properties. Previous investigations show that the use of FA in SCC reduces the dosage of superplasticizer needed to obtain similar slump flow compared to concrete made with Portland cement only [7]. In addition, the use of FA improves significantly the rheological properties and reduces concrete cracking due to the heat of hydration of cement [8].

A few studies have been carried out on the optimization of the mix proportion by the addition of FA to SCC. It is reported that 30 % of cement replacement optimized percentage of FA in SCC resulted in excellent workability and flowability [9]. However, due to difference in quality and quantity of material constituents and depending on the adopted design specifications, an uncertainty is created in establishing a general relationship between FA and cement ratio, chemical admixtures and w/c ratio. Meanwhile, there is insufficient research on modeling the rheological and mechanical properties of SCC with FA where the most of the researches are based on traditional methods.

For the last two decades, different modeling methods based on artificial intelligence (AI) techniques have become popular like artificial neural networks (ANNs), fuzzy logic (FL) systems, genetic algorithm (GA) and expert system (ES). Those methods have been used by many researchers for a variety of engineering applications [10]. In civil engineering, many researchers proposed models using these techniques for predicting concrete properties [11–13]. For SCC, these techniques are also used by some researchers proposing many predictive models. A fuzzy logic prediction model for fresh and hardened properties of SCC containing fly ash and polypropylene fibers was developed by Gencel et al. [14]. A shrinkage prediction models for SCC based on an independent methodology that combines fuzzy logic and genetic algorithm were developed by Da Silva and Štemberk [15]. An expert system was developed with the goal of classifying the surface finish of SCC precast elements by Da Silva and Štemberk [16]. A fuzzy inference system was built for the specific case of various SCC mixtures subjected to ammonium sulfate attack by Nehdi and Bassuoni [17].

ANNs are based on the principle that a highly interconnected system of simple processing elements can learn the nature of complex interrelationships between independent and dependent variables. Artificial neural networks are one of the most widely used methods for predicting SCC properties. Several investigations were carried out to develop ANN models for predicting rheological and mechanical properties of SCC. Some researchers focused on predicting the SCC compressive strength [18–20], while others used some rheological properties of SCC like setting times and slump flow [21, 22]. The prediction of the SCC performance with fly ash was initially tried using a neural network with single architecture [23, 24].

However, all the previous proposed ANN models for predicting each property separately, none of them considered both of the most important rheological and mechanical properties.

In this context, the main purpose of this study is to develop an ANN model for predicting the most important rheological properties combined with the most important mechanical property (the compressive strength at 28 days) based on mixture proportioning of SCC with fly ash, while maintain the same architecture. The slump flow test, V-funnel time test and the L-box test are used to evaluate the flowability, viscosity, filling ability and the passing ability.

2 Artificial neural networks (ANNs)-based model

Artificial neural networks (ANNs) are computing systems that simulate the biological neural systems of the human brain exhibiting the ability to learn reason and solve problems [25]. They are a family of massively parallel architectures that can be used to solve difficult problems described by a large amount of data via the cooperation of highly interconnected but simple computing elements (Fig. 1). These units are commonly referred to as neurons. Each neuron receives an input signal from the neurons to which it is connected. Each of these connections has numerical weights associated with them. These weights determine the nature and strength of the influence between the interconnected neurons. The signals from each input are then processed through a weighted sum on the inputs. The processed output signal is then transmitted to another neuron via a transfer function. The transfer function adjusts the weighted sum of the inputs so that the output approaches unity when the input gets larger and approaches zero when the input gets smaller.

Fig. 1
figure 1

Architecture used in the neural network model

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Back-propagation is generally known to be the most powerful and widely used supervised learning technique to train a network [26]. To obtain some desired outputs, weights, which represent connection strength between neurons and biases, are adjusted using a number of training inputs and the corresponding target values. The network error, that is the difference between calculated and expected target patterns, is then back-propagated from the output layer to the input layer to update the network weights and biases. The input and output neurons are defined by the problem to be solved, whereas the number of hidden layers and the corresponding number of neurons per layer may be determined by trialing different configurations until reaching the optimum. The network errors that arise during the learning process can be expressed in terms of mean square error (MSE) and are calculated using Eq. (1).

$${\text{MSE}} = \left( {\frac{1}{p}} \right) * \sum\limits_{j} {\left( {t_{j} - o_{j} } \right)^{2} }$$
(1)

In addition, the absolute fraction of variance (R 2) and mean absolute percentage error (MAPE) are calculated using Eqs. (2) and (3), respectively.

$$R^{2} = 1 - \left( {\frac{{\sum\nolimits_{j} {\left( {t_{j} - o_{j} } \right)^{2} } }}{{\sum\nolimits_{j} {\left( {o_{j} } \right)^{2} } }}} \right)$$
(2)
$${\text{MAPE}} = \frac{1}{p}\sum\limits_{j} {\left( {\left| {\frac{{o_{j} - t_{j} }}{{o_{j} }}} \right| * 100} \right)}$$
(3)

where t j is the target value of jth pattern, O j is the output value of jth pattern and P is the number of patterns.

2.1 Data collection

The main purpose of this study is to develop an ANN model to predict rheological and mechanical properties of self-compacting concrete with fly ash. In most previous research, all applications predict one property of concrete through a large number of components. The primary goal in this model is to predict a large number of outputs from a limited number of inputs, the more we can predicted a number of properties of SCC from a limited number of its components as much as possible, the model will be successful and applicable in the field. Sufficient data are collected to build a database consisting a set of data on fly ash SCC mixtures. The data were obtained from different sources and used for training and testing the ANN model. To construct this model, a total number of 114 different experimental data were gathered from the literature (see Appendix for table showing the data source collected for constructing the model) [27–39].

The data used in the proposed neural networks model are arranged in a format of six input parameters that cover the binder content, fly ash percentage, water–binder ratio, fine aggregates, coarse aggregates and superplasticizer. The majority of previous works construct a database from their experimental results, so the results are limited just for their environment, but our database is built from many different sources of data including the literature in different countries; moreover, it can be applied in a wider area. Four outputs parameters are predicted by the ANN model as the slump flow diameter, the L-box ratio, the V-funnel time and the compressive strength at 28 days of SCC. The boundary values for input and output variables used in the multilayer feed-forward neural network model are listed in Table 1. The input parameters are distributed in different ranges in a homogeneous form for training the model as shown in Table 2.

Table 1 Input and output quantities
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Table 2 Distribution of inputs in the data base
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2.2 Training the ANN model

For building and training the neural network model, specialized computer software was used [40]. A MATLAB-based program with a graphical user interface (GUI) was developed to train and test the ANN model. To provide an ANN model with good generalization capability, the data were divided into sets: (91) training and (23) testing patterns (randomly selected 20 % of data as testing set).To avoid over-fitting (over-training), thus enabling a good generalization capability, 11 validation patterns were used to stop earlier the training process.

A multilayer perceptron (MLP) was employed in this research of three layers: an input layer, a hidden layer and an output layer. Each layer consists of a number of neurons. The neurons of the input layer receive information from the outside environment and transmit them to the neurons of the hidden layers without performing any calculations. The hidden layer neurons then process the incoming information and extract useful features to reconstruct the mapping from the input space. The neighboring layers are fully interconnected by weights. Finally, the output layer neurons produce the network predictions to the outside world. There is no general rule for selecting the number of neurons in a hidden layer. The choice of hidden layer size is mainly a problem and to some extent depends on the number and quality of the training pattern. The numbers of neurons in input and output layers are based on the geometry of the problem. Nevertheless, there is no general rule for selection of the number of neurons in a hidden layer. Hence, they are determined by trial-and-error method in this study. It should be noted that it is possible to achieve satisfactory results with different network architectures. This involved the development and testing more than 1000 architectures with various numbers of hidden layers and neurons in hidden layer sizing the back-propagation algorithm. Consequently, the ANN model was selected as having 6 neurons in input layer representing influential parameters (binder content, percentage replacement of fly ash, water-to-binder ratio, fine aggregates, coarse aggregates and superplasticizer), 17 neurons in hidden layer and 4 neurons in output layer (slump flow, V-funnel, L-box ratio, compressive strength at 28 days) as illustrated in Fig. 1.

A tangent sigmoid transfer function was employed as an activation function for all neurons. Weights and biases were randomly initialized. A maximum number of epochs (learning cycles) reached during the training of the network model was 1000. The following values of network training parameters are summarized in Table 3.

Table 3 Parameters used in the neural network model
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Accordingly, a comparison between experimental values and those predicted by the ANN showed a high correlation proving its high accuracy in estimating target value in the training phase as well as in the validation and the testing phase (Fig. 2).

Fig. 2
figure 2

Linear relationship between experimental and predicted properties for SCC. a Slump flow (mm), b, L-box ratio, c V-funnel time (s) and d compressive strength (MPa)

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2.3 Validation of ANN model

The validity of a successfully trained ANN model is determined by its ability to generalize its predictions beyond the training data and to perform well when it is presented with unfamiliar new data within the range of the input parameters used in the training. Therefore, the ability of the proposed ANN model developed to predict the SCC properties of new data obtained by additional results from other researcher’s excluded from the training data must be validated. The more data available, the more reliable a prediction of SCC properties by ANN will be obtained.

The model was presented with a total of 16 unseen records and was required to predict the four SCC properties associated with each set of values within the six influential parameters [41–44]. The comparison between the predicted values by the developed ANN model and the validation new data records is shown in Table 4. In this table, the computed relative error in each prediction as expressed by Eq. 4 is represented correctly.

$$E\left( \% \right) = {\text{ABS}}\left( {\frac{{O_{\exp } - O_{\text{ANN}} }}{{O_{\exp } }}} \right) * 100$$
(4)

where O exp is the experiment output and O ANN is the output obtained by the ANN model.

Table 4 Comparison of ANN-based model with other researcher’s results
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The validation of the ANN model is represented in a total relative error, and it indicates that using the proposed model is possible to accurately predict the slump flow value, the V-funnel time, the L-box ratio and the compressive strength at 28 days of SCC containing different percentages of fly ash.

3 Parametric analysis based on ANN model results

Because of the complexity of the system, it is difficult to identify the change on different output parameters on this model by the change of just one parameter. However, in order to check the capability of the ANN model to capture the sensitivity of SCC mix properties to individual constituents, a parametric analysis was carried out.

3.1 Effect of fly ash content

The simulation results of various fresh properties as slump flow diameter; L-box test [ratio of heights at the two edges of L-box (H 2/H 1)]; V-funnel test (time taken by concrete to flow through V-funnel); and the compressive strength at 28 days with fly ash replacement level (from 0 to 60 %) at various binder contents (350, 450 and 550 kg/m3) are shown in Fig. 3. In this case, a great effect of replacement level of fly ash on the outputs parameters was found. Test results of this analysis indicated that all SCC mixes meet the requirements of allowable slump flow, L-box, V-funnel flow time and compressive strength. This improves concrete performance in both the fresh and hardened state.

Fig. 3
figure 3

Effect of fly ash on properties of SCC. a Slump flow (mm), b L-box ratio, c V-funnel time (s) and d compressive strength at 28 days (MPa)

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The slump flow diameter improves with the increase in fly ash content and decreases with the increase in binder content at any level of fly ash (Fig. 3a). This produces a paste with improved plasticity and more cohesiveness. All the values of the predicted slump flow obtained by the ANN model for all binder content in this analysis are in the range of 640–790 mm which maintains the workability of SCC mixes within the acceptable slump flow range (500–800 mm) [4].

The L-box passing ability of the SCC mixtures with fly ash increased with the increase in fly ash replacement level. All the L-box ratio values converge to some point within 0.7–0.9 at 30 % of fly ash replacement (Fig. 3b). It was also observed that as the replacement percentages of fly ash continue to increase up to 30 %, the L-box ratio was in the range of 0.8–1, the generally recommended values [4].

The V-funnel passing time get reduces as the fly ash percentage increases (Fig. 3c). In this study, the V-funnel flow times predicted values were in the range of 4–13 s, which confirm the adequate V-funnel time for the SCC (<27 s).

The compressive strength at 28 days is found to decrease with the increase in fly ash content and to increase with increasing the binder content (Fig. 3d). This strongly influenced the SCC strength with constant water-to-binder ratio. The decrease in the compressive strength is directly dependent on the amount of cement replacement by the fly ash which agrees with previously published results [42].

3.2 Effect of water–binder ratio

The variation of the slump flow, V-funnel time, L-box ratio and the compressive strength at 28 days with water-to-binder ratio (w/b) for different quantities of fly ash is shown in Fig. 4.

Fig. 4
figure 4

Effect of water–binder ratio on properties of SCC. a Slump flow (mm), b L-box ratio, c V-funnel time (s) and d compressive strength at 28 days (MPa)

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The slump flow diameter values increases with the increase in water–binder ratio and fly ash content (Fig. 4a). It has been also shown that fly ash has the highest potential to be used in SCC. This was especially the case for producing highly workable SCC with high volume of the paste mortar, which often leads to a higher water-to-binder ratio [5].

All the L-box ratio values converge to some point within 0.75–0.95 and increase with increasing the fly ash content for water–binder ratio up to 0.37 (Fig. 4b). This was inverted when using lower percentage of fly ash and water–binder ratio.

The V-funnel passing time get reduce as the fly ash percentage increases from 20 to 60 % (Fig. 4c). Almost the V-funnel time values, which are <6 s, are recommended for concrete to qualify as a SCC.

The combined influences of an increase in fly ash content from 20 to 60 % and water–binder ratio from 0.30 to 0.45 decrease the 28-day compressive strength of SCC (Fig. 4d). This agrees well with previously published results [37].

3.3 Effect of Superplasticizer

Superplasticizer plays a fundamental role to improve the rheological properties of SCC. It is an essential material component that must be used to produce SCC. The variation of the slump flow, V-funnel time, L-box ratio and the compressive strength at 28 days with superplasticizer dosages (from 1 % to 4 %) for different quantities of fly ash is shown in Fig. 5.

Fig. 5
figure 5

Effect of superplasticizer on properties of SCC. a Slump flow (mm), b L-box ratio, c V-funnel time (s) and d compressive strength at 28 days (MPa)

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The slump flow diameter and the L-box ratio are increased with increasing the superplastisizer dosages up to 1 % and fly ash content (Fig. 5a, b). The slump flow seems to be related to the dosage of superplasticizer. The V-funnel flow time decreases with increasing both of the superplastisizer and the fly ash dosages (Fig. 5c). Those results are consistent with the results of other researchers which showed that the superplasticizer improves the flowability of SCC by their liquefying and dispersing actions [45].

The compressive strength at 28 day is seen to decrease with the increase in fly ash content and superplastisizer dosages until it reaches a specific value so that the effect does not appear significantly (Fig. 5d). The superplastisizer can either increase the strength by lowering the quantity of mixing water for a given flowability or reduce both cement and water contents to achieve a given strength and flowability [46]. At given water-to-binder ratio, the use of fly ash in SCC reduces the dosage of superplasticizer needed to obtain similar strength compared to SCC made with Portland cement only [42].

In fact, it is difficult to simplify the interaction of the superplasticizer on SCC mix properties. In addition, there is a correlation between the superplasticizer adsorption on the particles surface, which depend on many parameters (the charge density of the polymers, the zeta potential, pore solution ionic content and strength, cement and cement blending materials chemistry).

4 Conclusion

In this study, artificial neural network is used for predicting different properties of SCC containing volume of fly ash as a cement replacement. For this purpose, a feed-forward neural network comprising of one hidden layer with 17 neurons and a back-propagation training algorithm was used. The study conducted and presented in this paper shows the feasibility of using a simple ANN to predict both rheological and mechanical properties of SCC. It was demonstrated that the developed ANN model was successfully trained and validated. SCC is a complex material, and there is correlation between many factors. ANNs is a highly interconnected system that can learn the nature of complex interrelationships between independent and dependent variables. As a result, the model was able to predict the slump flow, L-box ratio, V-funnel time and compressive strength at 28 days. It was mentioned the capability of model to recognize and evaluate the effect of individual constituents that cover the total binder content, fly ash replacement percentage, water–binder ratio, fine aggregates, coarse aggregates and superplasticizer on the properties of SCC.