## 2 Materials and Methods
In total, depending on the number of the specimens used, 40 rebound values for each specimen and 240 or 280 for each material were recorded. The rebound values given in this study for each material are the average of all recorded values. After the execution of non-destructive tests, the cylindrical specimens were used for the determination of their uniaxial compressive strength (_UCS_) and tangent modulus of elasticity (\(E_{t}\)). The uniaxial compression tests were performed using a 1600 KN hydraulic device, manufactured by MTS (Mechanical Testing System) corporation (Kalamazoo, MI, USA). According to the procedure, the cylindrical specimens were subjected to a load acting on both ends (Figure 5a), using a loading rate 0.01 mm/s under displacement control mode; the failure of specimens occurred in less than 5 min. The peak stress value and the tangent modulus of elasticity of each specimen were calculated from the complete stress-strain curve (Figure 5b). Figure 1: Core specimens of (**a**) marble and (**b**) metasandstone. Figure 2: P-wave velocity test for (**a**) marble and (**b**) metasandstone. Figure 4: The Schmidt hammer rebound test. Figure 5: (**a**) Cylindrical specimen subjected to loading; (**b**) Stress-strain curve for the determination of _UCS_ and _E_\({}_{t}\). Figure 3: Straight parallel lines drawn along the longitudinal axis of each specimen. For the determination of the breakage rate parameters, experiments were performed in a laboratory-scale ball mill with a volume of 5423 cm\({}^{3}\) (Table 2) operating at a constant speed of \(N=66\) rpm (1.1 Hz), which is 70% of its critical speed. The core samples as well as other materials with the same properties (porosity, density, mineralogy etc.) were crushed and prepared for the grinding tests. The mill charge consisted of 25.4 mm (1 inch) stainless steel balls with density \(\rho_{b}=7.85\) g/cm\({}^{3}\). The parameters \(J\) (ball filling volume) and \(f_{c}\) (material filling volume), were calculated from Equations (4) and (5), respectively. \[J=\left(\frac{Volume\ of\ solid\ balls}{mill\ volume}\right)\cdot\frac{1}{1-\epsilon} \tag{4}\]  
\[f_{c}=\left(\frac{Volume\ of\ solid\ material}{mill\ volume}\right)\cdot\frac{1}{1-\epsilon} \tag{5}\]  
where, \(\epsilon\) is the bed porosity of balls and material (assumed to be 40%) [15]. The material filling volume \(f_{c}\) was kept constant at 4%, corresponding to 345.0 g, 351.5 g, 342.5 g and 273.3 g of quartz, marble, quartzite and metasandstone, respectively. The fraction of the space between the balls at rest that is filled with material (interstitial filling, \(U\)) was calculated from Equation (6); in this study, \(U\) was kept constant at 0.5. \[U=\frac{f_{c}}{0.4\cdot J} \tag{6}\]  
Four mono-size fractions of each material (\(-3.35+2.36\) mm), (\(-1.7+1.18\) mm), (\(-0.850+0.600\) mm) and (\(-0.425+0.300\) mm) were ground in a laboratory ball mill for various grinding times \(t\) (0.5, 1, 2, 4 min). The products obtained after each grinding time \(t\) were wet sieved using a series of screens with a ratio of \(\sqrt{2}\) for the determination of particle size distribution. It should be noted that fresh feed was used in each test and the mill was loaded using successive layers of balls and feed [50].