# A Novel Method of Calibrating Micro-Scale Parameters of PFC Model and Experimental Validation
## 5 Application of Calibrated Model to Rock Fracture and Experimental Validation  
### Stress-Strain Curves  
In rock mechanics and rock engineering, a good many of rock disasters like rock burst, water gushing-out, surrounding rock instability happen frequently in underground excavation at great depth [40; 41; 42; 43; 44; 45]. Thus, it is critical to examine the failure process of opening under compressive stress. On the other hand, the accuracy of the micro-scale parameters can be verified. Hence, we adopted the calibrated PFC model to simulate the fracturing behavior around circular, square, and D-shaped openings in prismatic samples (length \(\times\) thickness \(\times\) width = 100 mm \(\times\) 25 mm \(\times\) 150 mm) subjected to uniaxial compression. After that, the numerical results were compared with the experimental results. In the laboratory tests, the selected rock material was still the red sandstone which came from Shandong province of China. A total of nine specimens were made, including three specimens with a circular opening (radius = 10 mm, marked as SC), three specimens with a square opening (length \(\times\) width = 17.72 mm \(\times\) 17.72 mm, marked as SS), and three specimens with a D-shaped opening (length \(\times\) width = 16.59 mm \(\times\) 22.11 mm, marked as SD) (Figure 10). To better understand the impact of the opening shape on fracturing response, the cross-sectional areas of the three openings excavated by high-pressure water \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**Parameters of Particle**} & \multicolumn{2}{c}{**Parameters of Parallel-Bond**} \\ \hline Ratio of & & [PERSON]’s modulus of each & \\ largest-to-smallest ball & \(1.6\) & & parallel bond, \(\overline{E}_{c}\) & 19.46 GPa \\ radii, \(R_{\text{max}}/R_{\text{min}}\) & & & \\ \hline Smallest particle radius & & & \\ in sample, \(R_{\text{min}}\) & & & \\ \hline Particle density, \(\rho\) & 2925 kg/m\({}^{3}\) & & \\ \hline [PERSON]’s modulus at each & & & \\ particle–particle contact, & 19.46 GPa & & \\ \(E_{\text{c}}\) & & & \\ \hline Ratio of particle normal & & & \\ to shear stiffness, \(k_{\text{n}}/k_{\text{s}}\) & & & \\ \hline Particle friction & 0.10 & & \\ coefficient, \(\mu\) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Main micro-scale parameters of parallel-bond model for rock model. Figure 9: Comparison between experimental and numerical stress–strain curves. cutter were designed to be equal. Further on, the aforementioned three intact samples, which were named IS, served as a reference. Uniaxial compression experiments were conducted on these three types of prehled samples under the same loading conditions as the above intact sandstone samples. Correspondingly, three models of the same size and type as the sandstone samples with an opening were created and numerically loaded in uniaxial compression. The achieved curves of axial stress versus axial strain of these models are plotted in Figure 11. It can be seen that the axial strain of the intact model grows linearly as the axial stress increases firstly. When the axial stress approaches the peak, the curve of the intact model becomes concave down. This means that the plastic deformation starts to occur. In regard to the curves of the models with an opening, a noticeable fluctuation appears before the peak, which is induced by the sudden appearance of the cracks near the openings. Figure 11 also demonstrates the development of the number of the micro-scale cracks in the models during the numerical loading simulation. When the axial strain is very small, the number of the micro-scale cracks is limited. It is because there are a few cracks in the first two loading stages, i.e., initial pores and fissures compaction stage and linear elastic stage. Once the plastic deformation stage is reached, the micro-cracks begin to initiate and propagate drastically.