# 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
### Crack Development around Openings  
By using the calibrated PFC model, the simulated failure processes of the above three kinds of models containing an opening in uniaxial loading are shown in Figure 12. As the calculation step rises, four different types of cracks are observed in the vicinity of the openings. In terms of the model with a circular opening, no cracks are found near the opening in the elastic deformation stage. When the number of calculation steps is \(1.06\times 10^{5}\), two cracks \(1^{\mathrm{a}}\) and \(1^{\mathrm{b}}\) propagating in the vertical direction are observed symmetrically at the top and bottom of the opening. After that, two exfoliation cracks \(2^{\mathrm{a}}\) and \(2^{\mathrm{b}}\) caused by spalling failure are formed on the left and right sidewalls of the opening, respectively. When the number of steps reaches \(1.17\times 10^{5}\), it is seen that two cracks \(3^{\mathrm{a}}\) and \(3^{\mathrm{b}}\) occur on the upper-right and lower-left corners of the opening, respectively. They propagate rapidly parallel to the direction of loading until they get connected with the opening. With the further increase of the calculation step, two shear cracks \(4^{\mathrm{a}}\) and \(4^{\mathrm{b}}\) appear in turn on one diagonal of the model. If the shear cracks extend to the opening, the model fails immediately. Since the cracks 1 and 3 are both induced by concentrated tensile stress, we hereby define them as initial-tensile cracks and secondary-tensile cracks, respectively. With regard to the exfoliation crack 2, they are caused by the concentrated compressive stress. In contrast, the shear cracks are attributed to the high shear stress along the diagonal, which is formed by the coupling of end friction and applied load. Similarly, Figure 12 also illustrates the fracture responses of the SS and SD models under uniaxial loads. The crack development process is almost the same as that of the model SC, i.e., the initial-tensile crack initiates first from the roof and floor of the opening, and stop growing when the secondary-tensile crack begins to appear. Second, exfoliation crack resulted from compressive stress concentration starts to peel from the sidewall of the opening. During the period, the secondary-tensile crack originates from the corners of the opening, and then rapidly develops towards the opening. Further on, shear crack occurs along one diagonal and eventually get coalesced with the opening. To conclude, the shear failure of the model is caused by the coalescence of the shear crack and the \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Mechanical Property** & **Model IS** & **Model SC** & **Model SS** & **Model SD** \\ \hline \(\sigma_{\mathrm{b}}\)/MPa & 102.86 & 75.91 & 69.98 & 81.12 \\ E/GPa & 22.02 & 19.75 & 19.90 & 20.07 \\ \(\epsilon_{\mathrm{p}}\)/\%\({}_{\infty}\) & 4.44 & 3.60 & 3.59 & 3.73 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Mechanical parameters of models under uniaxial compression. Figure 11: Curves of axial stress versus axial strain by numerical method. spalling fracture zone. By contrast, the two categories of tensile cracks do not dominate the final failure of the model. Currently, it is widely recognized that DIC (Digital Image Correlation) measurement is an advanced and promising optical test method [46]. Thus, it is extensively employed in rock mechanics experiment in recent years. Generally, the visually displayed strain localization areas by DIC technique represent the cracks formed on the speckle surface of the prismatic specimen. For details of the principle and adopted experimental apparatus, please refer to References [47; 48]. Based on the DIC results [48], the crack evolution of the real rock samples with an opening subjected to uniaxial compression is sketched in Figure 13. It can be clearly seen that four identical sorts of cracks also appear around the opening in the specimen during uniaxial loading tests.