Introduction

Over the last two decades, there has been a greater focus on reducing carbon dioxide emissions into the atmosphere on a global level. As a result of the use of mineral additives in cement production and the substitution of cement with additives in concrete mixes, the cement industry contributes for around 5% of all emission sources (Jayant, 2013). Concrete's mechanical characteristics have been influenced by these additives. Compressive strength is one of the most essential mechanical properties of concrete.

In addition, several infrastructures, such as bridges, dams, and building foundations, require high-strength concrete. These infrastructures have massive dimensions, which are accompanied by high temperatures during casting. As a result, the temperature difference between the inside of structural members (at early ages) and the outside environment is large. Thermal cracking can occur as a result of this situation. Reducing the amount of cement used is one option. As a result, using alternative cement additives to minimize the amount of cement in the concrete mixture has become popular (Al-Gburi, 2015; Mustafa, 2018).

The influence of concrete mixture components (cement, sand, and gravel) on the mechanical properties of concrete has been studied extensively (Jayant, 2013; Kaveh & Khalegi, 2000; Mustafa, 2018). Moreover, various research have looked into the effects of additives on concrete characteristics. Some of these additives, such as silica fume and slag, generate higher concrete strength resistance (Bhanjaa & Sengupta, 2005; Bharatkumar et al., 2005; Lam et al., 1998). Some of them, such as fly ash, have had the reverse impact, lowering concrete strength (Atiş, 2005; Babu & Yerramala, 2012; Yazici, 2008; Yazici et al., 2012).

It takes a long time and a lot of money to cast concrete mixes. It is possible that the variables under investigation have several effects. As a result, it is essential to understand which parameter has the greatest impact and concentrate on its consequences. The effect of the specific weight of concrete mixture components and additives has been overlooked in previous investigations. The goal of this research was to determine the impact of cement specific weight, fine and coarse aggregate, and mineral additives on concrete strength.

The specific gravity of a material at a given temperature (23C) is the ratio of the mass of a unit volume of that material to the mass of the same volume of water at the same temperature (ASTM C128-15, 2015). It is a non-dimensional value that is used to determine the material's strength and quality. It is frequently important to determine an aggregate's porosity. Pore size is expressed as a percentage of the total material size divided by the size of the pores. It is impossible to calculate the volume of pores in any material. The specific gravity can be used to determine the relationship between the pores and bulk solids. The volume of the mixture increases when cement is replaced by a mineral additive with a lower density based on mass-to-mass. The specific gravity of mineral additive is lower than that of cement, which must be taken into account while proportioning the mix. If the strength and durability qualities of the concrete are maintained, the addition of cementations may actually result in a reduction in the number of cementations (in terms of mass) per unit volume of concrete. This is significant in terms of making the best use of cementation ingredients in concrete (Jayant, 2013). The efficiency factor for mineral admixture is defined as the quantity of cement in the concrete mixture that can be replaced by one part mineral admixture without affecting the attribute being studied, which is usually compressive strength. In many technical applications, the back-propagation neural network and neural networks with genetic algorithm approach has been applied (Iranmanesh & Kaveh, 1999; Kaveh & Iranmanesh, 1998; Kaveh & Rahimi Bondarabady, 2004; Kaveh and Raiessi Dehkordi, 2003; Kaveh & Servati, 2001; Kaveh et al. 2001a, 2001b; Kaveh et al., 2008; Rofooei et al., 2011).

Aims and purposes

This paper's goals and objectives are to:

  • Clarify and investigate the influence of the most important parameter on concrete compressive strength.

  • Investigate the impact of substituting additives for cement on the compressive strength of concrete.

  • Determine the impact of the concrete mix's specific gravity on concrete strength.

Data preparation for the neural network

To improve the training of the neural network, the data were preprocessed via scaling.

The input and output data were scaled in the intervals 0.1 and 0.9 to avoid the sluggish rate of learning around end points, notably in the output range, due to the sigmoid function's trait of being asymptotic to values 0 and 1. The linear scaling equation is written as follows:

$$p_{{{\text{normlize}}}} = \frac{{(p - p_{\min } )0.8}}{\Delta } + 0.1.$$
(1)

Equation (1) was used in this study for a variable limited to minimum (\(p_{\min }\)) and maximum (\(p_{\max }\)) input values given in Table 4.4, with:

$$\Delta = p_{\max } - p_{\min } .$$
(2)

Any new input data should be scaled before being submitted to the network, and the associated predicted values should be unscaled before being used.

Back-propagation algorithm

The BPNN is trained using the back-propagation algorithm (back-propagation neural network). Using the gradient descent method, this program searches for the smallest error function in weight space. A solution to the learning issue is considered to be a combination of weights that minimizes the error function. Hudson et al. (2021) and Hagan et al., (1996) define the algorithm in the following steps:

  1. 1.

    It calculates the input to the hidden layer once the input vector is supplied to the input layer., \({h}_{j}^{H}\), as:

    $$h_{j}^{H} = \theta_{j} + \mathop \sum \limits_{i = 1}^{{{\text{NI}}}} w_{ji} p_{i} ,$$
    (3)

where pi reflects the value of the input parameter, \(\theta_{j}\) represents the hidden layer's bias function, NI represents the number of neuron in the input layer and wji indicates the difference in weight between the input and hidden layers.

Each neuron in the hidden layer takes its input, passes it through a function, and creates an output, which is determined by

$$Y_{j}^{H} = f(h_{j}^{H} ).$$
(4)

The input to the output layer's neurons, \({h}_{k}^{0}\), is now calculated as

$$h_{k}^{o} = \theta_{k} + \mathop \sum \limits_{j = 1}^{{{\text{NH}}}} w_{kj} Y_{j}^{H} ,$$
(5)

where \(\theta_{k}\) represents the bias function of output layer, wkj represents the weight factor between hidden and output layer, and NH represents the number of neuron in the hidden layer.

The network output, \({y}_{k}\), is then given by:

$$y_{k} = f\left( {h_{k}^{o} } \right),$$
(6)

where f represents the activation function.

Learning an ANN

Previous research (Atiş, 2005; Atan & Awang, 2011; Bhikshma & Florence, 2013; Burden, 2006; Duval & Kadri, 1998; Gesoğlu et al., 2009; Kesharwani et al., 2017; Ren & Wang, 2014; Babu & Yerramala, 2012; Bhanjaa & Sengupta, 2005; Bharatkumar et al., 2005; Lam et al., 1998; Liu, 2010; Özcan et al., 2009; Uygunolu et al., 2012; Yazici, 2008; Yazici et al., 2012) as stated in Table 1, the selection factors were used in the creation of the concrete mixtures. The three hundred and fifteen mixes were sorted into two groups: the artificial neural network ANN was trained using 283 concrete mixtures. The accuracy of the training mixtures was 94%, as shown in Fig. 1a. ANN was put to the test with 32 different concrete compositions. Figures 1 and 2 show that the compressive strength produced from the ANN was 93 percent accurate when compared to earlier experimental research (Fig. 1b). The back-propagation approach is used to train Perceptron Multilayer Networks. The current study uses the multi-layer feed-forward back-propagation technique to create and train the neural network. The sigmoid transform function was also utilized, as explained in Al-Gburi, (2015), Al-Gburi et al., (2012), Yousif and Al-Jurmaa (2010). The ANN model was built with one hidden layer. There were fifteen input parameters and one output parameter in the ANN model. The available data sets were used for the training, testing, and validation processes.

Table 1 List of parameters and their values variation in the experimental work of concrete mixes and parametric study
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Fig. 1
figure 1

a Training ANN model. b Comparison between experimental data and ANN model

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Fig. 2
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Relative importance of mixture components on concrete strength

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Relative importance

Although we can use techniques like multiple regression or discriminant analysis to evaluate neural network prediction or classification success rates, no method that analyzes the relative relevance of the input parameters employed by the network to reach its conclusions has been accepted. One of the most advantages of ANN-based models is that they make sensitivity analysis easier to analyze the relative importance of their input variables (Kim & Ahna, 2009). One of the most interesting properties of ANN-based models is that they make sensitivity analysis of the relative relevance of their input variables more easier (Kim & Ahna, 2009). To determine the most significant input–output relationship that has been manually carried out, sensitivity studies use a "leave one out" technique. It is used to offer information on the relative importance of the input factors in each geometrical dimension's parameter on compressive strength, see (Bharatkumar et al., 2005; Lam et al., 1998; Mustafa, 2018). In this work, the relative importance of the input parameters is determined using the partitioning weights approach established by Garson (1991) and later adapted by Goh (1995). The weights of the connections between ANN layers are used in this method to calculate the maximum change in output caused by changes in specific input variables. To determine the relative importance of the various input parameters, this approach is interested in the connection weight between ANN layers.

The SGC is the most influential factor in the sensitivity to the compressive strength of concrete, according to the findings in the study provided in Table 1. The cement content C and the SGCAgg are followed by an SGFAgg and then the cement content C and the SGCAgg. The rest of the additive factors are in low effect ratios, as indicated in Fig. 2. Concrete strength is influenced mainly by the SGC and aggregates (fine and coarse). As a result, the remaining mineral additions have a minimal effect on compressive strength. Additives can be used to replace high-cost cement without affecting the strength of the concrete.

Results

Effect of specific gravity of cement

As seen in Fig. 3, increasing the cement's specific gravity increased the concrete's compressive strength. Depending on the amount of moisture in the cement, the specific gravity might rise or fall. The greater the specific gravity, the more water is required. It will result in a lower quantity of water in the cement, enhancing the compressive strength. Furthermore, the higher cement concentration resulted in an increase in concrete compression strength, which is consistent with Salem and Pandey's findings (2015).

Fig. 3
figure 3

Variation of the compressive strength with cement content and specific gravity of cement

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Effect of specific gravity of fine aggregate

As illustrated in Fig. 4, increasing the specific gravity of fine particles reduced concrete strength. Maina et al. (2018). discovered the similar perception in behavior. The strength behavior changed as the cement content was increased to over 450 kg/m3. With an increase in the specific weight of fine aggregate, the compressive strength increased.

Fig. 4
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Variation of the compressive strength with cement content and specific gravity of fine aggregate

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Effect of specific gravity of coarse aggregate

The concrete strength is influenced by the specific gravity of coarse material. When the specific gravity of the coarse aggregate was the highest, the compressive strength increased, as shown in Fig. 5. Al-Oraimi et al., 2006; Ryu & Monteiro, 2002 both found the same indication.

Fig. 5
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Variation of the compressive strength with cement content and specific gravity of coarse aggregate

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Effect of silica fume

When silica fume is added to a concrete mix with a little amount of cement, the compressive strength is reduced (by a significant amount). Figure 6 shows how the influence of silica fume changes as the cement content is increased, resulting in increased concrete strength. Atiş (2005), Babu and Yerramala (2012), Tanyildizia and Evik (2010), and Uygunolu et al. (2012) demonstrate the same indication of the impacts of silica fume alone on the concrete mix. The specific gravity of silica, on the other hand, is lower than the specific gravity of cement. As a result, replacing the same amount of cement with the same amount of silica reduces the strength of the concrete. Previous research has concentrated on the effect of varied amounts of silica fume on concrete strength while ignoring the effect of silica fume specific gravity. The specific gravity of silica fume is the most influential, as shown in Figs. 2 and 7. Concrete strength increased as the specific weight of the concrete increased.

Fig. 6
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Variation of the compressive strength with cement content and silica fume

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Fig. 7
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Variation of the compressive strength with cement content and specific gravity of silica fume

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Effect fly ash (FA)

The water–cement ratio of concrete has been reduced as a result of increased FA content less than the reduced amount of cement, resulting in a direct reduction in concrete strength. As the amount of fly ash in the mixture increased, the compressive strength decreased, as seen in Fig. 8. This is comparable to the behavior described in Atiş (2005), Liu (2010), and Siddique (2003). Increasing the specific gravity of fly ash, on the other hand, increased concrete strength, as shown in Fig. 9. This behavior is consistent with the findings of Jayant (2013), Bhanjaa and Sengupta (2005), Yazici (2008) and Atiş (2005).

Fig. 8
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Variation of the compressive strength with cement content and fly ash

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Fig. 9
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Variation of the compressive strength with cement content and specific gravity of fly

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Effect of slag

As seen in Fig. 10, adding more slag to the mix improved the concrete's strength. These findings are consistent with Akcaozoglu and Atis (2011), Bharatkumar et al., (2005). Most standards limit the amount of BFS added to slag cement to 70%, see (Jayant, 2013). Furthermore, increasing the fineness of GGBS might result in higher compressive strength.

Fig. 10
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Variation of the compressive strength with cement content and slag

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Effect of superplasticizer

Increased superplasticizer content resulted in increased concrete strength (see Fig. 11). These findings are consistent with Alsadey (2012) and Dumne (2014).

Fig. 11
figure 11

Variation of the compressive strength with cement content and superplasticizer

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Conclusions

The study demonstrated the feasibility of employing an artificial neural network to investigate the impact of concrete mixture additions on concrete compressive strength. The specific gravity of cement has been shown to be the most important factor in the compressive strength of concrete. Following that, there is a significant variation in the specific gravity of aggregate and sand. The amount of cement used as a variable in compressive strength was next. The specific gravity of the additions exhibited the similar tendency, resulting in increased compressive strength. The artificial neural network's results were found to match the analysis of previous experimental results. As a result, using an artificial neural network to understand the behavior of complicated data without having to do costly practical testing is critical.