## 3 Numerical Simulation Process
### REV Application in PFC\({}^{2d}\)  
When a rock engineering project is started, compression tests need to be conducted for the determination of strength parameters of the in-situ rock. The results of the conducted tests provide the measured values that are observed to be widely spread. Different properties of the rock material are usually obtained over a wider range of domain. The spread of these values depend on the natural inhomogeneity and the presence of pre-existing discontinuities in the rock material. In order to cater for this observation, a domain of rock material is needed to be tested for which this spread of measured strength properties does not significantly affect. The basic concept of Representative Elementary Volume (REV) was introduced in 1972 [12] and it is defined as the minimum size or volume of the sampling domain above which the characteristic properties of the material remain basically constant. In other words, for any given material, REV is basically that volume of the material that is able to contain sufficient number of discontinuities or inhomogeneities so that when the tests are conducted repeatedly on the material, the average value is reasonably consistent with the test results [13] and the scatter in the values is minimum (Figure 4). This concept has been used for obtaining REV of permeability, porosity and various petrophysical properties of rock [14; 15; 16] as well as for investigation of REV for fractured and jointed rock mass [17; 18; 19; 20]. In order to use particle mechanics approach in PFC modeling for rock mechanics applications and failure mechanisms, three main issues need to be considered. Firstly, the microscopic parameters such as particle stiffness and friction coefficient needs to be decided because they cannot be directly measured through physical experiments in laboratory. The other two issues are the selection of model size and particle size in compression tests for reliable simulations. The microscopic parameters needed to simulate the actual macroscopic behavior of rock can be obtained by repetitive numerical simulations to calibrate the microscopic parameters in the particle model until the desired macroscopic properties like UCS, Young's modulus and Poisson's ratio are achieved. These microscopic properties for a given particle size to diameter ratio obtained by this process are unique for reproducing the above mentioned macroscopic properties typically needed as the mechanical parameters of rock. The effects of model size and particle size of the bonded particle model (BPM) in PFC\({}^{2D}\) on the mechanical behavior is \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Microscopic Parameter**} & \multicolumn{3}{c}{**Values Obtained by UCS Test**} \\ \cline{2-4}  & **Soft Rock** & **Normal Rock** & **Hard Rock** \\ \hline Particle density (kg/cm\({}^{3}\)) & 2630 & 2630 & 2630 \\ Minimum particle radius, \(R_{min}\) (mm) & 3 & 3 & 3 \\ Particle size ratio, \(R_{max}/R_{min}\) & 1.66 & 1.66 & 1.66 \\ Initial sample height (mm) & 600 & 600 & 600 \\ Initial sample width (mm) & 300 & 300 & 300 \\ Particle-particle contact Young’s modulus, \(E_{c}\) (GPa) & & —REV dependent— & \\ Particle stiffness ratio, \(\{\mu_{i}/k_{i}\}\) & 2 & 2 & 2 \\ Young’s modulus of parallel bond, \(E_{c}\) (GPa) & & —REV dependent— & \\ Parallel bond stiffness ratio, \(\lambda\) & 2 & 2 & 2 \\ Particle friction coefficient, \(\mu\) & 0.5 & 0.5 & 0.5 \\ Parallel bond normal strength, mean, \(\overline{\sigma}_{c}\) (MPa) & —REV dependent— & \\ Parallel bond normal strength, std. dev, \(\overline{\sigma}_{c}\) (MPa) & 5 & 10 & 10 \\ Parallel bond shear strength, mean, \(\overline{\tau}_{c}\) (MPa) & —REV dependent— & \\ Parallel bond shear strength, std. dev, \(\overline{\tau}_{c}\) (MPa) & 5 & 10 & 10 \\ \hline \hline \end{tabular}  
* REV, Representative Elementary Volume.  
\end{table} 
Table 4: Microscopic parameters obtained by calibration after unconfined compressive strength (UCS) tests 1.  
interrelated.