## 3 Results
### Effect of the Geological Nature of Natural Aggregates on the Compressive Strength of Concrete  
As mentioned in the literature review, the strength of concrete may be affected by different factors, including the quality of the cement paste. Therefore, the original models ([PERSON], Slater, and ACI) calculated the strength of concrete based on the \(w/c\) (Figure 2). The results showed that the estimated strength of concrete based on the quality of the cement paste is not accurate, and the relationship between the actual and calculated strength in all of the original models was poor (R\({}^{2}\) was \(-0.31\), \(-0.14\) and \(0.15\) in the [PERSON], [PERSON], and ACI models, respectively) when only \(w/c\) was considered to be an influencing factor. This is because the compressive strength of concretes with the same \(w/c\) may vary with cement content [23] and cement class [24], which respectively influence the aggregate: cement volume ratio and void index and the quality of the hydration product. The other reason is that the original formulas ignore the quality (e.g., geological nature) of the aggregates. Thus, the relationship between the calculated and actual strength of concrete mixes improved when the original formulas also considered the geological nature of the aggregates (R\({}^{2}\) was \(-\)0.23, 0.03, \(-\)0.58, \(-\)0.05, 0.52 and 0.46 with [PERSON]'s model, and 0.27, 0.20, \(-\)0.57, 0.20, 0.85 and 0 with [PERSON]'s model, and 0.25, 0.40, \(-\)0.03, 0.23, 0.81, 0.84 with the ACI model when the aggregates were classified as basalt, granite, limestone, NA (geological nature not given), quartz, and sandstone, respectively. The negative R\({}^{2}\) is due to the fact that the linear trendline was set to intercept the origin of the axes [130,131]). This behaviour is further discussed in the next paragraphs. Furthermore, for the 95% confidence intervals (red dashed lines in each graph), there is a big scatter between \(w/c\) and compressive strength of concrete, and the lower and upper \(k\) (\(f_{\rm cm,\ calculated}/f_{\rm cm,\ experimental}\)) values in all original models were 0.67 \(\pm\) 0.02 and 1.67 \(\pm\) 0.01, respectively. As mentioned previously, the calculated strength based only on the \(w/c\) independently of the cement content and its properties, is not reliable. Therefore, this study essentially focused on the modified models ([PERSON] and Feret) rather than the original models ([PERSON], [PERSON], and ACI). Figure 1: Relationship between the compressive strength “\(f_{\rm cm}\), cylinder 150 mm x 300 mm length” and \(w/c\) ratio of concrete. Figure 3a,b show the relationship between the experimental and calculated compressive strength obtained according to the [PERSON] and [PERSON] models, respectively. Relative to the original models (R\({}^{2}\) was up 0.15) that only considered the \(w/c\) as a main factor, the relationship between the calculated and actual compressive strength significantly improved (R\({}^{2}\approx 0.50\)), as seen in Figure 3a. This is due to the additional factors considered in [PERSON]'s model, namely the strength class of cement and the way that aggregates are produced (Table 2). However, this model neglected the effect of the cement content (volume of aggregates to cement ratio) which significantly affects the results due to its influence on the strength of concrete (for the same \(w/c\), the strength may vary with the cement content [23]). As shown in Figure 3b, by using [PERSON]'s model, the relationship between the calculated and experimental strength of concrete significantly improved (R\({}^{2}\approx 0.60\)) relative to the original models. This is because of the factors considered in the model, namely, the cement strength and content. However, this model neglected the aggregates' production methods. Figure 2: Relationship between the actual and calculated compressive strength of concrete mixes made with NA sourced from different geological natures. The strength values were calculated according to the (**a**) Abrams, (**b**) Slater and (**c**) ACI formulas.