# A Novel Method of Calibrating Micro-Scale Parameters of PFC Model and Experimental Validation
## 2 Microscopic and Macroscopic Parameters of PFC Model
### Measurement of Macroscopic Mechanical Parameters  
The macroscopic parameters of the parallel-bond model for uniaxial compression simulation include uniaxial compressive strength, Young's modulus, and Poisson's ratio. Since the PFC model used for rock fracture analysis is two dimensional, three prismatic sandstone specimens (length \(\times\) width \(\times\) height = 100 mm \(\times\) 25 mm \(\times\) 150 mm) were first made and tested in uniaxial compression. According to the stress-strain curves, the average values of the uniaxial compressive strength and Young's modulus were 102.61 MPa and 20.78 GPa, respectively. Due to the difficulty in measuring the Poisson's ratio of the prismatic specimens, three other cylindrical specimens with a diameter of 50 mm and a height 100 mm were further prepared for uniaxial compression tests, which were conducted by MTS (Mechanical Testing & Simulation) 815 rock mechanics testing machine. The Poisson's ratio, calculated from the axial strain and hoop strain measured by the axial and hoop strain extensometers, was 0.258.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Item** & **FISH Name** & **Meaning** & **Unit** & **Remarks** \\ \hline \multirow{6}{*}{Particle-based parameters} & \multirow{2}{*}{et2\_radius\_ratio} & Ratio of largest-to-smallest & \multirow{2}{*}{/} & Reflecting rock \\  & & ball radii, \(R_{\text{max}}\)/\(R_{\text{min}}\) & & heterogeneity (default 1.66). \\ \cline{2-4}  & \multirow{2}{*}{md\_dens} & Particle density, \(\rho\) & kg/m\({}^{3}\) & 2925 \\ \cline{2-4}  & & Smallest particle radius in & \multirow{2}{*}{mm} & \multirow{2}{*}{0.4} \\  & & sample, \(R_{\text{min}}\) & & \\ \cline{2-4}  & \multirow{2}{*}{md\_Ec} & [PERSON]’s modulus at each & \multirow{2}{*}{GPa} & Reflecting rock \\  & & particle–particle contact, \(E_{\text{c}}\) & & elastic modulus. \\ \cline{2-4}  & & & & Reflecting rock \\ \cline{2-4}  & \multirow{2}{*}{md\_knowerks} & Ratio of particle normal to & \multirow{2}{*}{/} & Reflecting rock \\  & & shear stiffness, \(k_{\text{n}}\)/\(k_{\text{s}}\) & & Poisson’s ratio. \\ \cline{2-4}  & \multirow{2}{*}{md\_fric} & \multirow{2}{*}{Particle friction coefficient, \(\mu\)} & \multirow{2}{*}{/} & Reflecting the slope of \\  & & & & stress–strain curve after the \\  & & & & peak, 0.6. \\ \hline \multirow{6}{*}{Parallel-bond parameters} & \multirow{2}{*}{pb\_radmult} & Parallel-bond radius & \multirow{2}{*}{/} & Default 1.66. \\  & & multiplier & & \\ \cline{2-4}  & \multirow{2}{*}{pb\_Ec} & [PERSON]’s modulus of each & \multirow{2}{*}{GPa} & Reflecting rock \\  & & parallel bond, \(\overline{E}_{c}\) & & elastic modulus. \\ \cline{2-4}  & \multirow{2}{*}{pb\_knowerks} & Ratio of parallel-bond & \multirow{2}{*}{/} & Reflecting rock \\  & & normal to shear stiffness, & & [PERSON]’s ratio \\ \cline{2-4}  & \multirow{2}{*}{pb\_sn\_mean} & Mean value of normal & \multirow{2}{*}{MPa} & Reflecting rock strength. \\  & & strength, \(\sigma_{c}\) & & \\ \cline{2-4}  & \multirow{2}{*}{pb\_sn\_sdev} & Mean value of shear & \multirow{2}{*}{MPa} & Reflecting rock strength. \\  & & strength, \(\tau_{c}\) & & \\ \cline{2-4}  & \multirow{2}{*}{pb\_ss\_mean} & Standard deviation of & \multirow{2}{*}{MPa} & Reflecting rock strength. \\  & & normal strength, \(\overline{\sigma}_{c}\) & & \\ \cline{2-4}  & \multirow{2}{*}{pb\_ss\_sdev} & Standard deviation of shear & \multirow{2}{*}{MPa} & Reflecting rock strength. \\  & & strength, \(\overline{\tau}_{c}\) & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Main microscopic parameters of parallel-bond model.