## 2 Methodology  
Three original models ([PERSON], [PERSON] and ACI) (Table 2) and two modified models ([PERSON] and Feret) (Tables 2 and 3) were used to estimate the compressive strength at 28 days of concrete made with ordinary Portland cement (OPC) and NA. The mentioned formulas were applied to 206 concrete mixes (206 concrete mixes \(\times\) minimum 3 samples = 618 concrete samples) made with 100% NA sourced from 84 studies (Table 4). After that, the results were classified based on the aggregates' classes (Table 1) proposed by [PERSON] et al. [7]. Then, the geological nature of the aggregates (e.g., limestone, basalt, granite, sandstone) was considered to analyse the results. Additionally, for each analysis (by considering the aggregates' quality or geological nature), different studies (Table 4) were considered based on the supplementary information given in the publication. For example, the studies that did not provide the geological nature of the aggregates (Table 4--5 th row) were still considered in the analysis of the effect of the quality of the aggregates on the compressive strength of concrete when their WAs and densities were provided. In the first stage of this analysis, all the concrete mixes used were made with NA and OPC (without any SCM). In the second stage, some examples (Table 4) containing 100% coarse RA were studied. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **Formula a,b** & **Notes/Limitations** \\ \hline [PERSON] & \(f\)**cm = \(\frac{A}{\mathbf{g}^{m/c}}\)** & The constants A and B are 96 MPa and 7, respectively. The \(w/c\) ratio should be between 0.3 and 1.2 \\ \hline [PERSON] & \(f\)**cm = 0.007**\(\cdot\left(\mathbf{2700}\cdot\frac{C}{w}-\mathbf{760}\right)\)** & This formula can be used only for mixes without Sp \\ \hline American Concrete Institute & & The \(w/c\) ratio and cement content of the concrete \\ Manual of Concrete Practice (ACI2000-I) & \(f\)**cm = 117.07**\(\cdot\)\(e^{-2.872\cdot w/c}\)** & respectively. The equation was adapted from the results of the table given in the specification with R\({}^{2}\) = 0.996 \\ \hline [PERSON] & \(f\)**cm = \(A\mathbf{1}\cdot\left(\frac{1}{w/c}-\mathbf{0.5}\right)\)** if \(w/c\)\(>\) 0.4 & The constants (A1 and A2) depend on the way aggregates are produced and on the strength class of cement (Table 3) \\ \hline Feret & \(f\)**cm = \(k\cdot\left(\frac{p}{p+1}\right)^{2}\)** & The constant, \(k\) depends on the strength class of cement. It is 265–290 and 315–350 for cement class CEM I 32.5 and 42.5, respectively; \(p\) is the absolute volume of cement paste and I is the volume index (air and water contents) \\ \hline \hline \end{tabular}  
* \(c\) and \(w\) are the cement and water contents, respectively. In other words, \(w/c\) is the water to cement ratio; b\(f_{\text{cm}}\) is the average compressive strength of the concrete in cylinders (150 mm diameter \(\times\) 300 mm length) at 28 days (MPa).  
\end{table} 
Table 2: Formulas to calculate the compressive strength of concrete. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**References***} & \multicolumn{6}{c}{**Aggregates**} & \multicolumn{4}{c}{**Crossment**} & \multicolumn{4}{c}{**Mis Composition**} & \multicolumn{2}{c}{**Strength**} \\ \cline{2-13}  & **Caelogical** & **Physical** & **Open-Droid Periodic** & **Proceeding** & **Max. Aggregate** & **  
It is well known that the shapes and sizes of the concrete samples (e.g., cube or cylinder) affect the results. Therefore, this study took into account these two factors, and the experimental results (non-standard cylinder sizes) were converted to be equivalent to those of a cylinder with a 150 mm diameter \(\times\) 300 mm length (\(f_{\text{cm, cube 100 mm}}\to f_{\text{cm, cube 150 mm}}\to f_{\text{cm, cylinder 150 }\times 300}\gets f_{\text{cm, cylinder 100 }\times 200}\)) in order to compare them with the calculated strength.