## 3 Comparison Study on Experimental and Numerical Results
### Numerical Modeling  
In this paper, a 100 mm \(\times\) 50 mm rectangular rock model is built with PFC2D. The mechanical model should be established first; thereafter, the thermodynamic model would be built on the basis of the mechanical model. When the model is running, applying axial loading leads to a change in stress distribution in the model. The stress change will induce a change in temperature distribution caused by the thermoelastic effect, friction effect, damping effect, and heat conduction effect as described in Section 2. In the meantime, the change in temperature will also have an influence on the stress distribution in the model. The calculation process of this thermo-mechanical coupling model is demonstrated in Figure 3.  
A flowchart for the work process in this study is shown in Figure 4. This process includes several main steps, as follows:  
1. Building the particle flow model and calibrating the mechanical parameters according to the mechanical behaviors (macro mechanical properties) in the laboratory compression test results;
2. Calibrating the thermal parameters according to the temperature variations (macro thermal properties) in the laboratory compression test results;
3. Conducting a series of numerical experiments and sensitive analyses considering different factors for the further mechanism studies. Figure 3: Calculation process of the thermo-mechanical coupling model. Figure 2: Infrared radiation image of a marble specimen subjected to uniaxial compression experiment at different stress levels (**a**) 0.1 \(\sigma_{\text{c}}\); (**b**) 0.4 \(\sigma_{\text{c}}\); (**c**) 0.8 \(\sigma_{\text{c}}\); (**d**) \(\sigma_{\text{c}}\); (**e**) 0.1 \(\sigma_{\text{c}}\)[52]. According to the flowchart in Figure 4, the mechanical model is built first with a linear, parallel bond model between particles. The calibrated parameters of the model are listed in Table 1. The numerical uniaxial compression experiment shows that this model has similar stress-strain behavior to the laboratory experimental result (Figure 1). The calculated UCS is 125 MPa, and the elastic modulus is 22.8 GPa, which are also very close to the laboratory experiment results. The thermodynamic model is built by implanting the thermodynamic calculation scheme into the above-mentioned mechanical model [53], and three steps are required as follows:  
1. Giving the basic thermal parameters. The basic thermal parameters are given as shown in Table 2.
2. Distributing the thermal contact model. The thermal pipe contact model is distributed between particles and has two modifiable parameters: the thermal expansion coeffi \begin{table}
\begin{tabular}{c c c} \hline \hline
**Microparameter** & **Definition** & **Value** \\ \hline \(E^{\star}\) (GPa) & Effective modulus & 7 \\ \(\mu\) & Friction coefficient & 0.8 \\ \(\beta_{n}\) & Normal critical damping ratio & 0.5 \\ \(\beta_{5}\) & Shear critical damping ratio & 0.0 \\ \(\overline{E}^{\star}\) (GPa) & Bond effective modulus & 17 \\ \(k^{\star}\) & Normal-to-shear stiffness ratio & 1.5 \\ \(\overline{\sigma}_{c,ave}\) (MPa) & The average of tensile strength & 51 \\ \(\sigma_{c,ave}\) (MPa) & The variance of tensile strength & 10 \\ \(\overline{\varepsilon}_{ave}\) (MPa) & The average of cohesion & 110 \\ \(\overline{\varepsilon}_{ave}\) (MPa) & The variance of cohesion & 20 \\ \(\overline{\varphi}_{ave}\) (\({}^{\circ}\)) & The average of friction angle & 30 \\ \(\varphi_{ave}\) (\({}^{\circ}\)) & The variance of friction angle & 10 \\ \(R_{max}/R_{min}\) & Particle size ratio & 1.6 \\ \(R_{ave}\) (mm) & The average of particle size & 0.5 \\ \(\rho\) (kg/m\({}^{3}\)) & Density & 2620 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Microparameters of the contact bond model and parallel bond model. Figure 4: Flowchart for the work process. cient, \(\alpha\), and the thermal resistance, \(\eta\).