## 1 Introduction  
### General Facts on Compressive Strength Estimation  
Concrete is one of the most consumed materials in the construction industry. Apart from durability, consumers normally demand a target strength. The target strength can be achieved in different ways, e.g., by increasing the cement content, incorporating a specific amount of supplementary cementitious materials (SCM), and decreasing the water content or introducing a superplasticizer (Sp). For that purpose, researchers have proposed several formulas to calculate the strength of concrete [1; 2]. Researchers normally focus on the quality of the cement paste to calculate the strength of concrete. However, the strength of concrete not only depends on the strength of the hydrated product and the porosity of the cement paste [3] but also on the properties of the aggregates [4]. Further details regarding the mentioned factors are provided in the following paragraphs. The strength of the hydrated product in the cement paste depends on the chemical and physical properties of cement [5; 6]. The porosity of concrete depends on the air content that is mainly affected by the maximum size of the aggregates, and the particle size distribution in the used materials, mixing procedure, workability, placing, and compaction [4]. The properties of the aggregates directly or indirectly affect the strength of concrete. The influence of the aggregates' properties can be clearly seen in high strength concrete, because failure occurs through the aggregates. For that purpose, a previous study [7] attempted to classify aggregates into four classes (A, B, C, and D) based on their physical properties, mainly by considering their density and water absorption (WA), and mechanical properties (Los Angeles (LA) abrasion) from the results of 116 studies (Table 1). The authors believe the strength of concrete produced with class A (high quality of aggregates) should be higher than that of those with B class, followed by classes C and D.  
In our study, the strength of concrete made with ordinary Portland cement (OPC) and natural aggregates (NA) was calculated using different formulas (Section 1.2) and compared with the actual (experimental) strength. Then, the strength of the NA concrete was classified based on the quality of the aggregates. The first objective of this procedure was to show the importance of the quality of the aggregates rather than their procurement source (e.g., recycled aggregates (RA) versus NA) and confirm the relationship between the strength of concrete and the properties of the aggregates, regardless of the type of virgin aggregates used. Regarding the indirect effects of the aggregates, studies have concluded that the quality of the hydration products affects the bond between the aggregates and cement paste (Interfacial Transition Zone--ITZ) [8]. Therefore, some of the recent investigations (Section 1.2) have considered the cement content and strength class of cement to calculate the strength of concrete. However, other studies [9] that updated the Bolomey formula [10] realized that, for the same quality of cement paste, the compressive strength of concrete made with rolled natural aggregates (NA) differs from that of concrete made with crushed NA, when both come from the same natural sources. This is because the shape of aggregates also affects the ITZ [11]. In fact, for concrete made with crushed aggregates, the effective water/cement ratio (main contributor to the quality of the cement paste and of the ITZ) should be increased in order to obtain the same workability as concrete made with rolled aggregates [12]. However, all the formulas proposed until then to calculate the strength of concrete failed to consider one of the most effective factors that affects the bond between aggregates and cement paste (ITZ), which is the texture of aggregates. The texture of the aggregates depends on the geological nature of the aggregates (e.g., limestone, basalt, sandstone, granite).