## 1 Introduction
### Background of the Compressive Strength Estimation Models  
[PERSON] [1] is considered one of the pioneers in devising a formula to calculate the strength of concrete based on the volume of aggregates to the cement ratio and the void index. He was followed by [PERSON] [2] who calculated the strength of concrete by taking into account the \(w/c\) ratio. A study of [PERSON] [17] simplified [PERSON]'s formula [18] and reported that the strength of concrete linearly changes with the \(w/c\) ratio. Similarly to [PERSON]'s formula, ACI 2000-I [19] calculated the strength of concrete by considering the effect of the \(w/c\) ratio. [PERSON] and [PERSON] [3] concluded that the porosity of the cement paste affects the strength of concrete. Thus, they developed the [PERSON]'s formula by considering another factor, namely, the \"gel (volume of hydration products) to space (capillary porosity)\" ratio. Then, [PERSON] [20] added another factor (degree of hydration) to the [PERSON] and [PERSON]'s formula. Regarding the porosity of the cement paste, [PERSON] [21] introduced the influence of air content into [PERSON]'s formula. Thirteen years afterwards, the same researcher [22] worked on [PERSON]'s formula and added the effects of cement's hardening rate and the air content. Since the compressive strength of concrete with the same \(w/c\) may vary with its cement content, [PERSON] [23] then added another factor (cement content) to [PERSON]'s formula. However, the number of concrete samples considered to calibrate these factors and the new model were not significant compared to the previous model. Furthermore, [PERSON] [13] updated [PERSON]'s formula by considering the maximum paste thickness, the maximum size of the aggregates, the aggregates' packing density, the content of pozzolanic binders and a few types of aggregates. However, [PERSON] did not consider the properties of cement, and the number of concrete samples used to calculate the factors was not significant. A recent study [15] proposed an innovative way to calculate the strength of concrete mixes using the M5P model tree algorithm by taking into account the results of nine publications. However, the cement class (e.g., CEM I 35.5 or 42.5) and quality of the aggregates were not considered as main factors in the model. According to the parameters considered in each of the models suggested by the above researchers, two common facts can be seen. First, some of the formulas calculate the strength of concrete by only taking into account the \(w/c\) ratio. However, it is well known that the strength of two concrete mixes with the same \(w/c\) may not be equal when their cement contents are different [23]. Therefore, the volume of aggregates to cement ratio and void index (water and air), which depend on the maximum size of the aggregates and the water content, should be considered. Secondly, most formulas fail to consider the strength class of cement. For example, the strength of concrete mixes made with the same cement content is not similar when different cement classes (e.g., CEM I 32.5 or 42.5) are used [24]. The majority of current formulas follow those of [PERSON] [1] and [PERSON] [2]. In the past decades, a few researchers have attempted to update the mentioned formulas, but their results are still not reliable, since they only considered a few case studies (concrete samples) to calibrate the correction factors. However, Sika-comp recently released a new software (SIKA-mix design) to design concrete mixes by using [PERSON]'s [25] method and calculate the strength of concrete by updating [PERSON]'s [1] formula. Thus, the new Feret-based formula depends on the ratio of the volume of aggregates to cement, the void index, the strength class of cement (cement class), and the maximum size of aggregates. In addition, a study [9] proposed a modification of [PERSON]'s [10] formula by taking into account the \(w/c\) ratio, the strength class of cement and the aggregates' production method (e.g., crushed or natural).