1 Introduction

Concrete is a building material obtained as a result of mixing the aggregate, cement, and water that constitute it in certain standards [1, 2]. Basic components utilized in the preparation of concrete are variation sizes of aggregates, cement and water. In addition to these, chemical additives and mineral additives are needed to produce concrete with the required high strength [3,4,5].

Since aggregates form more than 60% of the concrete volume, the physical and mechanical characteristics of the aggregates directly affect the features of the concrete [6, 7]. The effect of the type of aggregate in concrete on the properties of concrete has been studied since ancient times and has been an important research topic. The effect of the aggregate types such as basalt, limestone and sandstone on strength and durability of concrete in the concrete production was investigated [8, 9]. In Alyamac and İnce [10], the hardened concrete characteristics of self-compacting concretes produced utilizing waste marble powder were researched . In Alyamac and Tugrul [11], waste marble powder was used instead of aggregate to produce durable, aesthetic, and eco-friendly concrete. In Hong et al. [12], different types of aggregate were tested to investigate the effects of aggregate content on the strength of concrete. In Tugrul Tunc [13], the strength characteristics of concrete specimens produced using quartzite natural aggregates were determined. In Tugrul Tunc [14], the usability of basalt aggregates of Elazig province in Turkey in concrete production was experimentally investigated. The strength of cementitious composites produced using basalt aggregate has been studied in the previous study [15]. In Chang et al. [16], a series of tests were conducted using different components for the production of ultra-high-strength concrete.

Abrasion resistance of concrete aggregates is an important parameter that should be examined for all structures, especially engineering structures such as roads and airports [17, 18]. Among the tests to determine aggregate abrasion resistance, Los Angeles test is recommended because it is easy to apply [19, 20]. It can be said that the resistance to abrasion increases with decreasing Los Angeles value (LA) [18]. Since concrete strength is directly related to the properties aggregate in content, aggregate abrasion resistance directly affects concrete strength [21,22,23].

According to TS 802 [24], mixing water should be selected as the minimum amount that will provide the workability and durability properties needed in fresh and hardened concrete. One of the most important parameters affecting concrete strength is the water-to-cement ratio (W/C). This ratio is directly related to the strength class of concrete, as it directly affects all properties, especially the strength properties of concrete [25]. In Haddad et al. [26], self-compacting concrete mixes were designed for high water-to-cement ratios (W/C = 0.40 and 0.50) and the strength of the produced concrete specimens was compared. Topcu et al. [27] investigated the effect of different water-to-cement ratios and hyper-plasticizer content on the 28-day compressive strength of concrete. It was determined that concrete strength decreased as the water-to-cement ratio increased. Since aggregate is cheaper than cement, the higher the ratio of aggregate to cement in concrete, the greater the economic gain, provided that concrete is produced to certain required standards. Therefore, choosing the right aggregate is very important in concrete production.

Chemical additives are materials that are added to the concrete in a very small amount compared to the cement content during the mixing process to improve the properties of fresh and hardened concrete [4]. The opposite effects can occur as a result of adding these additives to the mixture more than they should be, and they may not provide any benefit if they are used too little [28]. Among the most commonly used chemical additives, plasticizers, set retardants, set accelerators, air-entraining additives, waterproofing additives, and antifreeze can be shown [29]. In Basyigit and Ozturk [30], the optimum value of setting accelerator admixture in concrete was investigated.

During the production phase of the concrete mix, its design must be done correctly in order to obtain concrete suitable for its purpose. In order to determine the optimum concrete mix designs, statistical/numerical modeling studies should be given importance. In In Açıkgenç et al. [31], self-compacting concretes containing waste marble aggregate were analyzed with artificial neural networks model and concrete design was performed. In Alyamac et al. [32], Response Surface Methodology, a multi-purpose statistical method, was used to produce self-compacting concrete using waste marble instead of aggregate. In Tugrul Tunc [33], the equations that can be safely used for high-performance eco-friendly concretes produced using waste aggregates have been developed. In Tunc and Alyamac [34], the strength properties of a series of concretes produced by utilizing different aggregate types were analyzed both experimentally and by Response Surface Methodology.

It is obvious that the biggest reason for the collapse of approximately 230 thousand buildings in the recent earthquakes of magnitude 7.8 and 7.7 in Turkey is poor-quality concrete. For this reason, it is very important to produce concrete with the desired strength by taking into account the relevant standards and regulations in order to build the structures durable. There are many studies in the literature to investigate the concrete strength. However, there is a lack of experimental and statistical studies on the effect of aggregate type and chemical admixture on concrete strength. Considering the fact that the concrete content and concrete mix ratio should be decided in order to obtain the desired concrete strength and this should be achieved with high accuracy, the present study has a high original value.

The novelty of the present study compared to previous studies is to determine how the constituent materials of concrete such as aggregate type, aggregate abrasion resistance and chemical admixtures change the concrete strength. By utilizing the findings of the present study, which is both an experimental and statistical study, the optimum concrete content and concrete mix design will be made to ensure the production of high-quality concrete in accordance with its purpose. The quality concrete is of great importance for the durability and continuity of structures.

The aim of this study is to determine the optimum concrete mix designs in the production of superplasticizer concrete depending on the tested parameters. It is aimed to predict with high accuracy the compressive strength and splitting tensile strength values, which are the most important hardened concrete properties, without testing by using dimensionless parameters such as Los Angeles abrasion value, water–cement ratio, aggregate–cement ratio and chemical additive ratio with experimental data. Thus, safe, economical, practical and time-saving pre-mix designs will be presented to application engineers and the literature.

2 Materials and Method

2.1 Materials

In the present study, different aggregate types such as basalt, marble, limestone and natural aggregate (stream bed material) extracted from Elazığ province of Turkey were tested. Some of these aggregate types are waste aggregates. These types of aggregates are easy to obtain and cheap. In addition, the grain size curves of the aggregates that are deemed suitable for use in concrete must remain between the A32–B32 standard curves according to TS 802 [24]. In the present experimental study, Dmax = 8 mm was chosen for the aggregates tested. The tested aggregates were firstly sieve-analyzed and made available for use in the relevant concrete production. Saturated surface dry weights and water absorption values of these aggregates were determined in accordance with TS 706 EN 12620+A1 [35] (Table 1). Thus, the necessary information about the physical properties of these aggregates has been provided. In Table 1, basalt aggregates with different properties are symbolized as BS1 and BS2, natural aggregates as NA, waste marble aggregates as WM, and limestone aggregates with different properties as LS1 and LS2.

Table 1 Physical properties of the aggregates
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In the current study, Chryso Fluid Optima 280 SC3 a new-generation polycarboxylate-supported superplasticizer was used in order to ensure processability and prevent decomposition since water–cement ratios are low. The characteristic properties of the related additive provided by the manufacturer are given in Table 2.

Table 2 Characteristics of the chemical additive
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The specific gravity of CEM I 42.5 N Portland cement used in concrete production in the present study is 3.06 g/cm3, and the Blaine specific surface area is 3490 cm2/g. The initial setting time of this cement is 2.6 h, and the final setting time is 3.5 h. In accordance with TS EN 197-1, 1-day, 7-day and 28-day compressive strengths of cement mortar have been determined as 26.7 MPa, 39.4 MPa and 48.5 MPa, respectively [34]. In addition, a liquid-brown-colored, highly water-reducing superplasticizing chemical admixture with a density of 1.075 ± 0.02 g/cm3, pH 4.00 ± 1 and chloride content < 0.1% was used in the experimental studies [4].

2.2 Los Angeles Abrasion Test

Los Angeles abrasion tests were conducted with the present device (Fig. 1a) separately for each aggregate in order to determine the abrasion losses of the aggregates to be utilized in the concrete mixes. For the experimental test, a total of 5000 g aggregate sample, 2500 g of coarse aggregate and 2500 g of medium aggregate, was washed, dried in a drying oven at 110 ± 5 °C and weighed in accordance with the relevant standard [35]. This process was continued until the aggregate sample reached a constant weight. The balls and oven-dried aggregates were left in the drying oven, which was 31–33 revolutions per minute at a constant speed, and the gate was closed and 500 cycles were made. At the end of the test, the balls inside the Los Angeles abrasion test device were carefully cleaned of aggregate particles to avoid experimental errors. The aggregate particles obtained at the end of the experimental test were sieved with a mesh size of 1.6 mm, and the particles remaining on the sieve were weighed (Fig. 1b). After these processes, Eq. (1) was used to calculate the LA abrasion loss value (%) [36]. As a result of Los Angeles abrasion tests performed in accordance with the relevant standard [36] for these six types of aggregates, it was decided that they could be utilized in concrete.

$${\text{LA}} = \left( {{5}000 - m} \right)/{5}0$$
(1)

where LA = Los Angeles abrasion value (%), m = the weight of the material remaining on the 1.6 mm sieve (g).

Fig. 1
figure 1

Los Angeles abrasion test: a test device; b sieving the wearing material

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2.3 Compressive Strength Test and Splitting Tensile Strength Test

The cubic specimens of 150 mm × 150 mm × 150 mm obtained from concrete mixes were subjected to compressive strength test in accordance with TS EN 12390-3 standard [37] at the end of a 28-day curing period. In this experimental test, a concrete test press with a capacity of 2500 kN was used (Fig. 2a). The specimens placed in the device were loaded at a constant speed of 6.8 MPa/s, their fracture loads were determined, and their compressive strength value was calculated using Eq. (2). The view of the specimens after the compressive strength test is given in Fig. 2c,

$$f_{{\text{c}}} = P/A$$
(2)

where fc = compressive strength (MPa), P = the maximum load that causes the specimen to fracture (N), and A = the cross-sectional area of the specimen perpendicular to the load application direction (mm2).

Fig. 2
figure 2

Strength tests for concrete specimens; a compressive strength test, b splitting tensile strength test, c the view of specimens after compressive strength tests, d the view of specimens after splitting tensile strength tests

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In addition, the cubic specimens of 150 mm × 150 mm × 150 mm were subjected to the splitting tensile strength test in accordance with the TS EN 12390-6 standard [38] at the end of the 28-day curing period (Fig. 2b). The specimens placed in the test device were loaded with a constant speed of 1.05 MPa/s, their fracture loads were determined, and the test was conducted. The splitting tensile strength value was calculated using Eq. (3). The view of the specimens after the splitting tensile strength test is shown in Fig. 2d.

$$f_{{\text{t}}} = 2 \cdot P/\pi \cdot D \cdot L$$
(3)

where ft = splitting tensile strength (MPa), P = pressure load causing fracture (N), D = diameter of cubic specimen (mm) and L = length of cubic specimen (mm).

2.4 Statistical Analysis

SPSS is an advanced statistical software program. SPSS can successfully perform statistical studies such as data analysis, data management and data visualization. With this program, statistical modeling and regression analysis based on various data can be performed. Available in different versions, IBM SPSS Statistics 22 program was used in the present study. SPSS includes analytical and research graphics in addition to standard 2D and 3D graphics. It enables the investigation of outliers and data analysis. Different data estimation methods can be tried with SPSS.

In this study, an analysis based on “Nonlinear Estimation” has been made. From the “Data View” tab, after defining the relevant parameters to the program and entering the data, the Analyze → Regression → Nonlinear sequence is applied, respectively. The formulation is created from the “Model Expression” tab by selecting the dependent parameter (fc) and independent parameters (W/C, A/C, CA, LA) from the “Nonlinear Regression” window. After defining the sensitivity ranges of the relevant parameters in the “Parameters” tab, the analysis is performed. The formula that gives the highest determination coefficient (R2) is determined, and the process is ended. In order to determine the most suitable model, many different models have been tested using SPSS in the present study.

3 Experimental Results and Discussion

In this study, firstly, SEM pictures, EDX and FTIR analyses of six types of aggregates to be tested from the relevant region were made and Los Angeles abrasion test was performed separately for these aggregates. A total of 150 concrete cube specimens were prepared with these aggregates. Slump test was performed for fresh concrete properties. After 28 days of curing, 75 specimens were tested for concrete compressive strength and 75 specimens were tested for splitting tensile strength. The effects of the relevant parameters, water–cement ratio (W/C), aggregate–cement ratio (A/C), chemical admixture ratio (CA) and Los Angeles abrasion value (LA), on the strength were discussed both experimentally and statistically by modeling. The comprehensive and detailed flowchart of the study is given in Fig. 3.

Fig. 3
figure 3

Description and flowchart of the present study

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In this study, the effect of aggregate type and chemical admixture used in concrete mixtures on concrete strength was investigated experimentally and statistically by varying the related parameters. By using various aggregate types (such as limestone, basalt and marble), concrete mixes with a chemical additive (CA) for 400 kg/m3 cement content and for W/C = 0.38, 0.40, 0.42 and 0.45 were prepared. A series of trial mixes were produced to determine the optimum proportion of chemical admixture to be included in the concrete. Since the highest strength for superplasticizer concrete was determined for a chemical admixture ratio of 1.2%, this ratio was settled on. Therefore, in the concrete mixes produced, the chemical admixture was added at 0% and 1.2% by weight of cement and tested. In addition, reference concrete mixes with W/C = 0.50, 0.55 and 0.60 with limestone and natural aggregate with a cement content of 300 kg/m3 and 400 kg/m3 were prepared. In this study, a total of 25 concrete mixes were prepared in order to obtain high-strength superplasticizer concrete and to determine the fresh and hardened concrete properties (Table 3).

Table 3 Mix ratios (for 1 kg/m3) and measured strength values of the concrete specimens
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Concrete mixes containing basalt aggregate types are named BS1C and BS2C, concrete mixes containing natural aggregate NAC, concrete mixes containing waste marble aggregate WMC, and concrete mixes containing limestone aggregate types are named LS1C and LS2C in the present study. Saturated surface dry weights of the aggregates were used while preparing concrete mixes. In addition, the slump values representing the fresh concrete properties of the tested concrete specimens are presented in Table 3. Accordingly, it was concluded that the consistency classes of the concrete specimens in question were S3 to S4 and were compatible with their strength values.

The concrete mixes (BS1C, BS2C, NAC, WMC, LS1C, and LS2C) were prepared by using a vertical axis rotating in a mixer with the mix design given in Table 3. In order to determine the mechanical properties of the hardened concrete mixes, 150 concrete specimens of 150 mm × 150 mm × 150 mm were produced. The concrete specimens were placed in a curing pool at 23 ± 2 °C and cured for 28 days. The compressive strength in accordance with TS EN 12390-3 standard [37] for 75 cubic specimens of 150 mm × 150 mm × 150 mm removed from curing, and splitting tensile strength tests in accordance with TS EN 12390-6 standard [38] for 75 specimens of the same dimensions were carried out. The compressive strength and splitting tensile strength values obtained as a result of the tests are given in Table 3 as the arithmetic mean of 3 concrete specimens for each series. The total test series is 25 and 3 for compressive strength and 3 for tensile strength at splitting were produced from each series. A total of 150 specimens, 75 specimens for compressive strength and 75 specimens for splitting tensile strength, were subjected to the experimental test to determine the related strengths.

3.1 SEM Images, EDX Analysis and FTIR Analysis of the Aggregates

In the present study, the microstructural morphology and chemical content of the aggregates tested were investigated. In this context, scanning electron microscopy (SEM) test was performed using the existing energy-dispersive X-ray (EDX) micro-analyzer to examine the microstructure. SEM images and EDX analysis findings are presented in Fig. 4.

Fig. 4
figure 4

SEM images and EDX analysis for the aggregates tested: a basalt; b waste marble; c limestone

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SEM images are selected at × 5000 magnification. When the microstructure of the basalt aggregate tested in the present study is analyzed, a regular settlement with less pore space can be seen. However, it is possible to say from the SEM image that there are too many elements (Fig. 4a). This situation is consistent with the elemental map obtained as a result of EDX analysis given in Fig. 4a. It is seen that elements such as Fe, O, Si and Al are at high levels. The occasional brightness appearance in the SEM image also indicates the presence of these elements, especially the Si element (Fig. 4a). The presence and concentration of elements such as Fe and Si indicate that basalt aggregate can be durable [39,40,41].

When examining the microstructure in the SEM image for the waste marble aggregate tested, the presence of strong bonds draws attention, although small pore spaces were observed (Fig. 4b). According to the elemental structure, the existence of a large number of elements is observed. In EDX analysis, Ca, O, Fe, Al, Si and Mg are the most prominent elements (Fig. 4b). This situation is supported by previous studies [18, 42, 43].

When the microstructure is examined in the SEM image in Fig. 4c for the tested limestone aggregate, it is seen that the pore spaces are excessive. In addition, prominent micro-cracks are noticeable. This indicates that limestone aggregate can be less durable than others. According to the elemental structure, relatively few elements are observed. While Ca, O, C, N and Al elements are observed in EDX analysis, it is seen that the element with the highest value is Ca (Fig. 4c). This is supported for marble aggregate and its derivatives by previous studies [44, 45].

Fourier transform infrared (FTIR) spectroscopy is a technique for obtaining structural, compositional and functional information from the titration of functional groups of the sample macromolecules under investigation. This spectroscopic technique is advantageous compared to other techniques in that it provides fast, sensitive and efficient results in a relatively inexpensive way, without the need for lengthy sample preparation procedures involving the use of additional substances such as staining and labeling, and without damaging the sample. When Fig. 5 is examined, it is seen that there is a fluctuation for all three aggregate types after 1000 wave number. This difference indicates C–O (carbon–oxygen) tension and the formation of oligosaccharides, carbohydrates, etc. FTIR analysis of limestone and marble aggregate shows that they are similar to each other (Fig. 5b, c). Accordingly, it is concluded from the FTIR analysis that basalt aggregate will be more durable (Fig. 5a).

Fig. 5
figure 5

FTIR analysis findings within the scope of microstructural investigation: a basalt aggregate, b limestone aggregate, c waste marble aggregate

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3.2 Variation of Concrete Strength with Water-to-Cement Ratio

As water and cement are effective materials in concrete content, water-to-cement ratio is the main parameter affecting concrete strength. It is known from previous studies [46,47,48] that concrete strength decreases with the increase of water-to-cement ratio. In the present study, the effect of this change on the decreasing trend with the different types of aggregates tested in the concrete content is discussed. Since the properties of the same type of aggregate can differ from each other, it has been observed that its effect on concrete strength is also different. It was determined that the compressive strength values of BS1C specimens produced with a type of basalt aggregate were approximately 23% higher than BS2C specimens produced with another type of basalt aggregate (Fig. 6a). It was determined that the splitting tensile strength values of BS1C specimens were approximately 12% higher than BS2C specimens (Fig. 6b). Similarly, it has been calculated that there are 23% difference for compressive strength and 17% difference for splitting tensile strength between LS1C and LS2C specimens produced with limestone aggregates with different properties.

Fig. 6
figure 6

Variation of strength of the concrete specimens with water-to-cement ratio: a for compressive strength; b for splitting tensile strength

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The highest strength values were obtained for BS1C, and the lowest strength values were obtained for LS2C for the superplasticizer concrete. It is seen that the lowest strength values are obtained from NAC specimens produced with natural aggregates for the concrete without chemical additive. Although the usability of this aggregate type in concrete is economically advantageous, it is not recommended in terms of strength [49, 50]. However, it is seen that the strength values in accordance with the relevant standards [28] are obtained for the concrete produced with this aggregate in the present study. In addition, it is seen that the tendency of the concrete strength to change with water-to-cement ratio is compatible with the literature [48, 51, 52]. It is clearly seen in Fig. 6 how the strength of 6 series of concrete specimens produced according to various aggregate types changes with water-to-cement ratio. The determination coefficients (R2) of the fitting nonlinear curves varying between 0.96 and 1.0 show the reliability of the obtained findings (Fig. 6).

3.3 Variation of Concrete Strength with Aggregate-to-Cement Ratio

Since the most basic material forming the concrete is aggregate, it directly affects the strength of concrete. The effect of the type and property of the aggregate on concrete strength is quite high [53, 54]. As seen in Fig. 6, concrete strength is listed as BS1C, BS2C, LS1C, WMC LS2C and NAC from high to low. Basalt aggregate (BS1) is seen to be the most durable aggregate in terms of concrete strength. This situation is also supported by the literature [14]. Generally, it is seen that the compressive strength and splitting tensile strength increased as the dimensionless aggregate-to-cement ratio (A/C) increased. Although the aggregate-to-cement ratio of three specimens tested for LS2C increased, there is a clear decrease in strength values (Fig. 7a, b). This is because chemical additive is not used for these three specimens. For the LS2C specimens tested, it is seen that the A/C value increased approximately 40%, and the compressive strength decreased approximately 16% (Fig. 7a). Similarly, it is seen that with the increase of A/C value approximately 40%, the splitting tensile strength decreased approximately 27% (Fig. 7b). Thus, the effect of chemical additive on strength is clearly seen. The effect of chemical additive increasing concrete strength is clearly seen. This situation is also supported by the literature [55,56,57].

Fig. 7
figure 7

Variation of strength of the concrete specimens with aggregate-to-cement ratio: a for compressive strength; b for tensile splitting strength

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In Fig. 7, it is seen that the determination coefficients (R2) of the linear curves fitted to each series of test results for the superplasticizer concrete specimens are generally higher than 0.90. An increasing trend is observed for these curves. Concrete specimens without chemical additive tend to increase among themselves. However, the determination coefficients of the fitted curves are relatively lower than the others (Fig. 7a, b). The reason for this is that lower strength values are obtained compared to specimens containing chemical additive with the same properties.

3.4 Variation of Concrete Strength with the Los Angeles Abrasion Value (LA) of the Aggregate

One of the most current tests applied to measure the abrasion resistance of aggregates is the Los Angeles abrasion test. As the Los Angeles abrasion value (LA) determined by this test increases, the abrasion resistance of the aggregate decreases [18, 34]. The LA value of utilized BS1 aggregate type in BS1C specimens, in which the highest strength of superplasticizer concrete was obtained, was measured as 9.2%. The LA value of utilized LS2 aggregate type in LS2C specimens, in which the lowest strength of superplasticizer concrete was obtained, was measured as 46.2%. Thus, this situation indicates that concrete (BS1C) produced with BS1 aggregate type will have high strength, while concrete (LS2C) produced with LS2 aggregate type will have low strength.

It was calculated that the aggregate Los Angeles abrasion value (LA) increased approximately 5 times and the mean compressive strength value decreased approximately 35% among the concrete specimens containing chemical additive, i.e., superplasticizer concrete specimens (Fig. 8a). Similarly, it has been calculated that the aggregate abrasion value increases approximately 5 times and the mean splitting tensile strength value decreases approximately 27% among the superplasticizer concrete specimens (Fig. 8b).

Fig. 8
figure 8

Variation of the strength of the superplasticizer concrete with the aggregate Los Angeles abrasion value: a for mean compressive strength; b for mean splitting tensile strength

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3.5 Comparison of Present Study Findings with Previous Study Findings

From the present experimental study, it was determined that the highest concrete strength values were measured for the BS1C specimens produced with a type of basalt aggregate BS1 and the lowest concrete strength values were measured for the LS2C specimens produced with limestone aggregate type LS2 for the superplasticizer concrete. In Fig. 9, concrete strength values varying with water-to-cement ratio have been presented for both the findings of the present study and the findings of the previous studies. In this context, the concrete strength values have been analyzed and discussed for concrete specimens produced with sandstone [3], for specimens produced with natural aggregate-recycled aggregate [58] and for specimens produced with river sand-crushed aggregate [59].

Fig. 9
figure 9

Comparison of the concrete strength findings obtained from present study and from previous studies

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The strength values of BS1C specimens and LS2C specimens from the present study were compared with the findings of the previous study. When the findings of the present study were analyzed, it was observed that the 28-day compressive strength and 28-day splitting tensile strength generally decreased parabolically with increasing water–cement ratio (Fig. 9a, b). It is thought that the reason for the difference in the strength values for constant water–cement ratio values is the chemical additive used. The reason for the strength values measured for increasing water–cement ratio can also be explained by the use of chemical admixture. In addition, relatively high strength values were obtained even in the samples produced with natural aggregates taken from the river bed. Thus, it is clearly understood that chemical admixture has a very important effect on concrete strength considering its type.

4 Statistical Analysis and Discussion

Within the scope of the present study, it is aimed to estimate the compressive strength and splitting tensile strength of superplasticizer concrete specimens by a nonlinear statistical model developed using IBM SPSS statistics 22 software for statistical data analysis. For this purpose, many different models have been tested. In the analyzes, the experimental results given in Table 3 and the selected effective dimensionless parameters were used. After detailed analysis, the most suitable model was selected and Eqs. (4) and (5) were developed, respectively, in order to calculate the compressive strength and splitting tensile strength of the superplasticizer concrete with high accuracy. There appears to be a fairly good fit between measured fc values and predicted fc values. This is also understood by the fact that the curve fitted to the data almost coincides with the perfect agreement (Fig. 10a). In addition, the determination coefficient R2 = 0.98 indicates the safe usability of the developed Eq. (4), because R2 close to 1.0 means that the developed equation is very close to the truth [60, 61].

Fig. 10
figure 10

a Comparison of the measured and predicted fc values; b Absolute relative deviation (ARD) of predicted fc values

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The data obtained from the experiments were compared with the data obtained from the models in order to verify the accuracy and limitation of the developed models. In order to predict the accuracy of Eqs. (4) and (5), absolute relative deviation ARD (%) calculation has been made by Eq. (6). ARD (%) calculation was performed in accordance with previous studies [32, 34, 62]. In Fig. 10b, it is seen that the absolute relative deviation values for the measured fc values and predicted fc values are mostly scattered around the zero axis. It has been determined that the models developed to calculate compressive strength and splitting tensile strength within the scope of the present study with the area deviation values between −5 and + 5% are determined to be highly accurate.

$$f_{{\text{c}}} = \frac{{\left[ {12.79 \times \left( \frac{W}{C} \right) + 6.753 \times \left( \frac{A}{C} \right) - 23.124 \times \left( {{\text{CA}}} \right) - 0.153 \times \left( {{\text{LA}}} \right)} \right]}}{{\left[ {\left( \frac{W}{C} \right)^{118.848} + \left( \frac{A}{C} \right)^{ - 2.402} + \left( {{\text{CA}}} \right)^{ - 267.944} + \left( {{\text{LA}}} \right)^{ - 0.935} } \right]}}$$
(4)
$$f_{{\text{t}}} = \frac{{\left[ { - 0.148 \times \left( \frac{W}{C} \right) + 0.070 \times \left( \frac{A}{C} \right) + 0.099 \times \left( {{\text{CA}}} \right) - 0.003 \times \left( {{\text{LA}}} \right)} \right]}}{{\left[ {\left( \frac{W}{C} \right)^{24.50} + \left( \frac{A}{C} \right)^{ - 2.052} + \left( {{\text{CA}}} \right)^{ - 141.878} + \left( {LA} \right)^{ - 1.949} } \right]}}$$
(5)

where W/C = dimensionless water-to-cement ratio, A/C = dimensionless aggregate-to-cement ratio, CA = chemical additive ratio used as a percentage of cement, and LA = Los Angeles abrasion value.

$${\text{ARD }}(\% ) = \frac{{{\text{Experimental}} - {\text{Model}}}}{{{\text{Experimental}}}} \times 100$$
(6)

Similarly, it is observed that splitting tensile strength (ft) values calculated with Eq. (5) developed to predict ft values are very close to the measured ft values. There appears to be a fairly good fit between measured ft values and predicted ft values. This is because the curve fitting in the graph almost coincides with the perfect agreement (Fig. 11a). In addition, the determination coefficient R2 = 0.96 indicates the safe usability of the developed Eq. (5).

Fig. 11
figure 11

a Comparison of the measured and predicted ft values; b Absolute relative deviation (ARD) of predicted ft values

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It is seen that absolute relative deviation values for measured ft values and predicted ft values are mostly scattered around the zero axis (Fig. 11b). It has been determined that the model is developed to calculate the splitting tensile strength value of the concrete containing chemical additive within the scope of the present study with the deviation values generally between − 5 and + 5%, because the obtained deviation values are thought to be quite small for the findings obtained with such a statistical model [63, 64].

It is known from the previous study [65] that there is a good match between compressive strength and splitting tensile strength and that both parameters change directly proportional to each other. In Fig. 12, the variation of ft values with fc values is presented for both measured and predicted values. In addition, when both the experimental findings and statistical findings obtained are analyzed, it was observed that fc values varied approximately 7–9 times ft values. This is supported by previous study [66]. The determination coefficient between fc values and ft values for measured values was determined as R2 = 0.89. The determination coefficient between fc values and ft values for predicted values was determined as R2 = 0.86. It is possible to say that there is a good harmony with these determined coefficients.

Fig. 12
figure 12

Relationship between fc values and ft values: a measured values; b predicted values

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5 Conclusions

The main conclusions drawn from present study are presented below:

  • Since it is aimed to build earthquake-resistant structures with the production of superplasticizer concrete, the current study contributed to the quality of life.

  • Since waste aggregates are also recycled in the current study, it is thought that it will have a positive impact in terms of both sustainable environment and energy since it is thought that environmental damage will be reduced. Thus, it is thought that a great contribution will be made in terms of national economic security.

  • By obtaining the desired strength from concrete, it is thought that potential sectoral application areas, global market projections, employment contribution and competitiveness in the relevant market will increase. As can be seen, superplasticizer concretes have a significant superiority in terms of strength.

  • For the production of superplasticizer concrete tested in the present study, new numerical models have been designed to contribute to concrete technology in terms of determining concrete strength and mix design by advancing university–industry cooperation. In this respect, it is considered to be an original study carried out on a systematic basis within the scope of research and development.

  • When the variation of concrete strength values with water-to-cement ratio is examined, it is determined that the determination coefficients (R2) of the fitted nonlinear curves (decreasing parabolic) change between 0.96 and 1.0.

  • It was concluded that the strength values of concrete specimens containing chemical additive increased with a nearly perfect agreement (R2 > 0.90) with the aggregate-to-cement ratio.

  • From the developed equations by SPSS in the present study, a fairly good fit (R2 = 0.98 and R2 = 0.96, respectively) was determined between the measured and predicted values of compressive strength and splitting tensile strength.

  • Absolute relative deviation (ARD) ratios for predicted fc values were determined to generally vary between − 5% and + 5%.

  • Investigation of the change of concrete strength depending on the parameters LA, W/C, A/C, CA adds originality to the study. In addition, it was seen that the method developed using these four parameters gave high accuracy values.

In the present study, with the statistical method developed using experimental findings and concrete strength for different test parameters, it is concluded that it is predicted in a practical, economical and reliable way. Thus, it is aimed to offer pre-concrete mix designs that can be used safely, economically, practically and to save time.

On February 6, 2023, at least 53,537 people in Turkey and at least 8476 people in Syria lost their lives and approximately 230,000 buildings collapsed as a result of the earthquakes of magnitude 7.8 and 7.7 in the region including Elazığ province, where the current study was conducted. This situation shows that more importance should be given to the production of durable and long-lasting concrete in line with the relevant regulations.