## 3 Numerical Simulation Process
### REV Calculations  
The REV concept was used in this study in order to observe the effects of sample size and particle size as well as to obtain the microscopic properties representing the homogeneous physical behavior of the model at macro scale. In this study, REV was achieved by obtaining the minimum size of the sample above which the sample diameter does not affect the mechanical behavior of the material; at coefficient of variation to be less than 5% for the average value of five consecutively larger samples. The coefficient of variation (CoV) is defined as the ratio of standard deviation to the mean values of the measured parameter under consideration. Since rock is a natural and not man-made material, the value of CoV for a rock property is generally used as less than 5% for REV studies [21; 22; 23; 24], as the scatter in testing results or CoV of UCS, point load index and Brazilian tests was recorded as far greater than 5% after testing of many types of rock specimens [25; 26; 27; 28; 29; 30]. In order to achieve REV, the initial sample of 30 cm diameter was generated and the macroscopic parameters of the sample i.e., UCS, Young's modulus (E) and Poisson's ratio (\(\upsilon\)), were obtained by performing UCS tests for all rock types in PFC\({}^{\text{2D}}\) code. The microscopic parameters were sequentially calibrated so that the required macroscopic parameters could be achieved. Brazilian tensile strength (BTS) tests and compressive strength tests at confining pressures of 5, 10, 15 and 20 MPa were performed for all rock types using 30 cm diameter sample and the results were recorded. More samples were generated by increasing the sample diameter by 5 cm at a time and UCS, BTS and compression tests were performed for each increased sample diameter until the CoV of all the macroscopic parameters (UCS, E, \(\upsilon\), BTS and compressive strengths at various confining pressures) for five consecutively larger samples was obtained to be less than 5%. Every time diameter of the sample was increased, the calibration of microscopic parameters had to be performed in UCS tests so that the required UCS, E, and \(\upsilon\) for the increased sample size could be achieved. For REV calculations, all the microscopic parameters given in Table 4 needed not to be  
Figure 4: Scatter in material properties with respect to the sample size, illustrating representative elementary volume (REV) based on coefficient of variation (CoV). changed and only four microscopic parameters namely; particle-particle contact [PERSON]'s modulus (\(E_{c}\)), [PERSON]'s modulus of parallel bond (\(\bar{E}_{c}\)), parallel bond normal and shear strength (\(\overline{\sigma}_{c}\) and \(\overline{\tau}_{c}\)) were carefully calibrated in UCS tests each time the sample diameter was increased. In the calibration process, the values of particle-particle contact [PERSON]'s modulus (\(E_{c}\)) were kept equal to the values of [PERSON]'s modulus of parallel bond (\(\bar{E}_{c}\)), whereas, the values of parallel bond normal strength (\(\overline{\sigma}_{c}\)) were kept equal to the values of parallel bond shear strength (\(\overline{\tau}_{c}\)). The compression test results for low modulus ratio, average modulus ratio, and high modulus ratio are presented in Figures 5-7, respectively. The BTS test results for low modulus ratio, average modulus ratio, and high modulus ratio are presented in Figures 8-10, respectively. For each case of intact rock strength (UCS), according to their modulus ratio, the compression tests as well as BTS tests were performed simultaneously by increasing the sample diameter by 5 cm at a time until REV was achieved for both compression and BTS tests. The microscopic parameters, obtained after calibration by performing UCS tests and REV calculations for BTS and compression tests, change with the increase in sample diameter. The values obtained for both compression and BTS tests were then recorded and were used to calculate CoV in each case for a set of five consecutively larger samples.