## 3 Discrete Element Analysis
### Comparison of Results by Numerical Modelling and Laboratory Tests  
In this study, numerical specimens with \(H\) = 0.3 were selected for both UCTs and direct tensile tests. These results were then compared with those obtained from laboratory UCTs.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Specimen No.** & **A** & **B** & **C** & **D** & **E** & **F** & **G** \\ \hline \(H\) & 0.1 & 0.2 & 0.3 & 0.4 & 0.5 & 0.6 & 0.7 \\ \hline Total number of particles & 10,131 & 19,101 & 28,075 & 37,065 & 46,064 & 55,035 & 64,027 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Number of particles in the numerical specimen.  
Figure 4: Numerical model with different RFCAs.  
Figure 3: Numerical modelling.  
Parameter calibration was conducted, and a parallel bonding model was chosen to simulate the bonding force generated by the hydration reaction between gypsum and water.  
According to studies by [PERSON] et al. [11], the internal friction angle of similar materials simulating Class IV surrounding rocks is estimated to range from 25\({}^{\circ}\) to 40\({}^{\circ}\). Therefore, a value of 30\({}^{\circ}\) was selected as the internal friction angle of similar materials. The parallel bonding component influences the sample under both tension and compression, while the linear contact component acts solely under compression and has no effect under tension. Therefore, during mesoscopic parameter calibration, a direct tensile test was first simulated for the numerical specimen. The parallel modulus of adhesion was calibrated based on the elastic modulus obtained from the laboratory test. The linear contact modulus was then calibrated by simulating the UCT. Finally, mesoscopic parameters such as cohesion and tensile stress of the numerical specimen were calibrated, in accordance with the stress-strain curve of the laboratory test. The specific values are tabulated in Table 3.  
Figure 5 shows a comparison between the simulated results and the experimental results of UCTs. To facilitate comparison with laboratory test results, Figure 5a displays a comparison between the numerical simulation and laboratory test results for peak stress, while Figure 5b presents a comparison for the elastic modulus. By comparing these figures, it can be observed that the peak stress and elastic modulus of the numerical specimen closely match the laboratory test results. This outcome validates the feasibility of this simulation and the rationality of calibrating micro-scale parameters, allowing for further analysis of the simulation results of the triaxial compression tests.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter Type** & **Mesoscopic Parameters** & **Numerical Value** \\ \hline \multirow{6}{*}{Basic particle parameters} & Fine aggregate particle size (mm) & 0.24–0.27 \\ \cline{2-3}  & Coarse aggregate particle size (mm) & 1.8–2.7 \\ \cline{2-3}  & Particle surface density \(\rho\) (g/m\({}^{2}\)) & 2.5 \\ \cline{2-3}  & Linear contact modulus \(E\) (MPa) & 75 \\ \cline{2-3}  & Particle normal/shear stiffness (\(k_{n}/k\)) & 1.2 \\ \hline \multirow{6}{*}{Parallel bonding parameters} & Parallel-bond modulus \(E\) (MPa) & 296 \\ \cline{2-3}  & Parallel-bond normal/shear stiffness (\(k_{n}/k_{s}\)) & 1.2 \\ \cline{2-3}  & Tensile strength (MPa) & 0.3 \\ \cline{1-1} \cline{2-3}  & Cohesion (MPa) & 1.5 \\ \cline{1-1} \cline{2-3}  & Internal friction angle (\({}^{\circ}\)) & 30 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Mesoscopic parameters of numerical specimens.