# Study on Dynamic Loading Characteristics of Rock Containing Holes
## 4 Simulation Results and Analysis
### Failure Behaviours of Specimens with Holes  
After the experiments, the failure modes of specimens with holes under different strain rate conditions showed consistent characteristics. To understand the differences in failure modes between single-hole and double-hole rock specimens, two specific experimental configurations (6 mm hole, 2 \(\times\) 6 mm holes) were selected for an in-depth analysis of the rocks' evolving failure modes. Tables 3 and 4 (a-c) depict the patterns of fractures, failure morphology, and force chain distribution for both hole configurations under the same impact scenarios. In these illustrations, green represents tensile stress, blue signifies compressive stress, and the thickness of the force chain indicates the magnitude of internal force within the specimen. Section 3.2 elaborates on confirming the dynamic equilibrium of the SHPB model, identifying four critical time points on the stress-damage time curve to mark different stages from the onset of loading to the complete breakdown of the specimens, focusing on conditions at points T\({}_{\text{D}}\), T\({}_{\text{S}}\), T\({}_{\text{P}}\), and T\({}_{\text{W}}\). Tables 3 and 4 (d) also present the failure modes observed in laboratory experiments, \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \(\mathbf{T_{d}}\) & \(\mathbf{T_{s}}\) & \(\mathbf{T_{p}}\) & \(\mathbf{T_{w}}\) \\ \hline \hline (a) & (b) & (c) & (d) & (e) \\ \hline \hline (b) & (d) & (e) & (f) & (f) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Progressive failure modes of double-hole specimens: (a) crack distribution; (b) fragmentation distribution; (c) force chain pattern; (d) laboratory experiment image. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \(\mathbf{T_{d}}\) & \(\mathbf{T_{s}}\) & \(\mathbf{T_{p}}\) & \(\mathbf{T_{w}}\) \\ \hline (c) & (d) & (e) & (f) & (f) \\ \hline \hline (d) & (e) & (f) & (f) & (f) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._In Table 3, point T\({}_{\text{d}}\) signifies the commencement of degradation for the single-hole specimen, highlighted by the appearance of initial microcracks, with the specimen displaying its first minor crack and minimal overall damage. The force chain distribution remains even, and tensile cracks begin to form at the hole's axial apex, following the direction of the stress wave, attributable to tensile stress. On the other hand, a concentration of compressive stress is noted at the hole's crest, perpendicular to the stress wave's direction, consistent with observations from studies on vertical stress field distribution. As the specimen is subjected to stress up to point T\({}_{\text{s}}\), it enters the yield phase, characterized by a notable escalation in the number of cracks, especially around the hole's axial and radial apexes. Axial compressive deformation in the specimen leads to the emergence of minor end-face cracks. The stress concentration at the hole's vertical apex shifts, with the force chain in the stressed region moving to the crack initiation area, thus aiding crack extension. Moreover, the force chain distribution begins to display irregularity, becoming more pronounced in the crack initiation zone. Upon reaching peak stress (point T\({}_{\text{p}}\)), cracks stemming from the hole converge with end-face cracks, creating macroscopic X-shaped fractures. Nevertheless, the specimen remains in one piece. The once even force chain distribution now changes, causing detachment of debris. In regions of intersecting cracks, force chains intensify and cluster around the new cracks. Finally, at point T\({}_{\text{w}}\), the drilling hole is thoroughly fragmented and deformed, with macroscopic X-shaped cracks fully matured, segmenting the specimen into four separate sections. Consequently, force chains are now concentrated within these four large fragments, signifying the specimen's inability to sustain load. In Table 4, point T\({}_{\text{d}}\) marks the initial phase for the double-hole specimen, where the ends reach dynamic stress equilibrium with no evident damage.