# Numerical Modeling of Engineering-Scale Jointed Coal Mass and Confining Pressure Effect
## 3 Model Construction of Engineering-Scale Jointed Coal Mass
### Construction of Coal Mass Matrix Model and Calibration of Laboratory-Scale Parameters  
(1) Calibration of laboratory-scale model parameters  
After obtaining a jointed coal mass model without assigned parameters, this section continues to calibrate the laboratory-scale model parameters. The calibration was carried out by matching the uniaxial compression tests with numerical simulations. The specimen was a standard cylindrical specimen with a diameter of 50 mm and a height of 100 mm, which sampled from an intact and unjointed coal block. It was demonstrated that the mechanical behaviors of the model tended to be consistent when the ratio of the particle radius to the minimum size of the model was less than 1/20 [40]. In this paper, the minimum particle radius was taken as 0.3 mm, and the ratio of the radius of the largest particle to that of the smallest particle was taken as 1.66 in agreement with [PERSON] [39], which could better simulate the uniaxial compression mechanical properties. The particle porosity was set to 0.1, and the loading velocity of the upper and lower walls was 0.5 m/s. The number of particles in the established model totaled 8753. Based on the calibration of the initial laboratory-scale parameters (as shown in Table 1), the numerical simulation results were used to match the laboratory test results by a trial-and-error method. The comparison of the calibrated uniaxial compression numerical simulation results with the experimental results is illustrated in Figure 2.  
Comparison of the numerical simulation results with the laboratory test results indicated that the errors of the elastic modulus and the uniaxial compressive strength were within 2%, as presented in Table 2. The loading curve obtained from the numerical simulations tends to shift to the left compared to the experimental curve. The reason is that the coal specimen undergoes initial compression as the stress increases, which is not evident \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**Simulation Parameters**} & **Unit** & **Magnitude** \\ \hline \multirow{4}{*}{Particle properties} & Density & kg/m\({}^{3}\) & 1340 \\  & Minimum particle radius & mm & 0.3 \\  & Maximum particle radius & mm & 0.3 \\  & Porosity & / & 0.1 \\  & Damping ratio & / & 0.7 \\  & Contact friction coefficient & / & 0.5 \\ \hline \multirow{4}{*}{Linear parallel bond model parameters} & Contact Young’s modulus & GPa & 2.15 \\  & Ratio of normal to tangential stiffness (/) & / & 2.16 \\ \cline{1-1}  & Tensile strength & MPa & 14.25 \\ \cline{1-1}  & Cohesion & MPa & 9.76 \\ \cline{1-1}  & Friction angle & \({}^{\circ}\) & 27 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 1: Construction of numerical model under the uncalibrated parameters. in the numerical simulations. In addition, the various failure modes of the coal samples are reflected in the numerical models, as shown in Figure 2, which indicated that the calibrated model parameters could be used in the follow-up studies on the mechanical behaviors of coal. (2) Engineering-scale model construction based on step-by-step matching method  
The parameters of the laboratory-scale models cannot be directly applied to the numerical models at the engineering scale. A series of studies had been conducted on the critical size in the discrete elemental modeling of engineered rock masses, which was usually in the range of 1-4 m [41; 42; 43; 44]. The larger the model size, the longer the computation time and the lower the efficiency. Under comprehensive consideration, 1.25 m \(\times\) 2.5 m was chosen as the critical size of the coal mass model for this study. A total of 88 million particles were needed to construct the engineering-scale coal mass model with a particle radius of 0.3 mm, which was extremely computationally intensive and inefficient. To address this problem, this paper adopted a step-by-step matching method from the experiment scale to the engineering scale to carry out model calibration.