## 4 Conclusions  
In this study, the correlation between the properties of four materials, namely quartz, marble, quartzite and metasandstone, and breakage rate parameters have been established. The properties of the materials that were taken into account were P-wave velocity, Schmidt rebound values, uniaxial compressive strength and tangent modulus of elasticity. The breakage rate parameters that were determined through batch grinding experiments were breakage rate \(S_{i}\), parameter \(\alpha_{T}\), parameter \(\alpha\), maximum breakage rate \(S_{m}\) and optimum particle size \(x_{m}\). The results can be summarized as follows:  
Breakage rate \(S_{i}\) or parameter \(\alpha_{T}\) increase with decreasing uniaxial compressive strength (_UCS_) and tangent modulus of elasticity (\(E_{t}\)). Therefore, it is deduced that as the strength or stiffness of a material is reduced this will be ground faster in a mill. Similar results can be obtained from the P-wave velocity (\(V_{p}\)) and Schmidt rebound values (\(R_{L}\)), which are widely considered for the indirect estimation of material's hardness and strength. The properties of the tested materials can be used for an accurate prediction of \(S_{i}\) or \(\alpha_{T}\) of the ground materials since the obtained correlation coefficients are high. Parameter \(\alpha\) which is constant for the same material and independent of grinding conditions is well correlated with \(V_{p}\), \(R_{L}\) and \(E_{t}\) when inverse exponential functions are used. However, the results showed that \(\alpha\) has a moderate correlation with _UCS_ (R\({}^{2}\) = 0.67) and therefore the results of the functions derived are not very reliable. Maximum breakage rate \(S_{m}\) is strongly correlated with \(R_{L}\) and _UCS_ using inverse functions and therefore either \(R_{L}\) or _UCS_ values can be used to predict the maximum breakage rate of each tested material during grinding. However, the prediction of \(S_{m}\) from \(V_{p}\) or \(E_{t}\) is not fully reliable due to the moderate correlations between these parameters. As far as optimum size \(x_{m}\) is concerned, the results showed that optimum size \(x_{m}\) increases with decreasing P-wave velocity, Schmidt rebound value, uniaxial compressive strength and tangent modulus of elasticity. However, marble seems to deviate from this tendency and further research is required, by considering its properties and other aspects including the presence of twinning planes and the production of ultra-fine material during grinding, to elucidate its behavior. It is mentioned that the behavior of mixed materials and the effect of each material type on the overall breakage rate is now under investigation. **Acknowledgments:** The authors would like to thank the anonymous reviewers of this article for their constructive comments and recommendations. The authors also gratefully acknowledge [PERSON], Mining Engineer, Faculty of Rock Mechanics Laboratory, Technical University of Crete, for performing the UCS tests. **Author Contributions:** [PERSON] conceived, designed and performed the experiments, analyzed the data and wrote the paper; [PERSON] critically reviewed the experimental design, the analysis of the results and wrote the paper. **Conflicts of Interest:** The authors declare no conflict of interest. **Nomenclature**  
\(D\): internal diameter of the mill (m)  
\(d\): ball diameter (mm)  
\(E_{t}\): tangent modulus of elasticity (GPa)  
\(f_{c}\): powder filling volume (%)  
\(f\): ball filling volume (%)  
\(i\): size class index  
\(N\): rotational speed (rpm)  
\(Q_{i}\): correction factor (\(\cdot\))  
\(R_{L}\): Schmidt hammer rebound value (\(\cdot\))  
\(R^{2}\): correlation coefficient (\(\cdot\))  
\(S_{i}\): breakage rate (min\({}^{-1}\))  
\(S_{m}\): maximum breakage rate (min\({}^{-1}\))  
\(t\): grinding time (min)