# The Bolt Anchorage Performance of Fractured Rock under a Freeze-Thaw Cycle Load
## 3 Numerical Simulation Parameters  
This study employs the coupled approach of PFC3D-FLAC3D to simulate the uniaxial compression test characteristics of rock-like specimens under anchoring and fracture conditions. The geometric parameters of the model are set in proportion to the experimental setup. The discrete element method is employed to construct models for rock-like materials, with the main material adopting a parallel bonded constitutive model and prefabricated fractures utilising a smooth joint constitutive model. The linear parallel bond model, as an application of a linear model, is suitable for contact situations such as ball-ball and ball-facet interactions. This model includes the finite mechanical behaviour between contacts and can simulate the mechanical properties of various materials like cementitious materials. The existence of parallel bonding does not inhibit sliding between contact surfaces. Additionally, parallel bonding functions to transmit forces and moments, effectively connecting and influencing the interactions between two contacting bodies. The material calibration parameters for various components of the numerical simulation are defined as follows in Tables 2-4.  
Currently, there is no dedicated constitutive model for metallic materials in FLAC. To describe this process more accurately, this section adopts a strain softening/hardening model to simulate the behaviour of anchors under tension. This model is based on the Mohr-Coulomb model and is characterised by strain softening or hardening behaviour after yielding, as shown in Figure 3. After plastic yield, cohesion, frictional resistance, and tensile strength undergo softening or hardening phases. This hardening and softening behaviour can be flexibly controlled using piecewise linear functions based on plastic strain. By defining the yield point and parameters of the post-yield hardening phase of anchor  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Particle Parameters** & **Value** & **Bonding Parameters** & **Value** \\ \hline Minimum particle radius (mm) & 0.8 & Parallel cohesive modulus of elasticity/GPa & 1.2 \\ Maximum particle radius (mm) & 1.28 & Normal-to-shear stiffness ratio & 1.5 \\ Particle density (kg/m)\({}^{3}\) & 2700 & Internal friction angle/\({}^{\circ}\) & 30 \\ Normal/tangential critical damping & 0.2 & Tensile strength/MPa & 8 \\ Max. bonding distance (mm) & 0.08 & Cohesive force/MPa & 9.6 \\  & & Linear modulus of elasticity/GPa & 0.8 \\  & & Linear coefficient of friction & 0.5 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Mechanical parameters.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Particle Parameters** & **Value** & **Bonding Parameters** & **Value** \\ \hline Minimum particle radius (mm) & 0.8 & Parallel cohesive modulus of elasticity/GPa & 4 \\ Maximum particle radius (mm) & 1.28 & Normal-to-shear stiffness ratio & 1.5 \\ Particle density (kg/m)\({}^{3}\) & 2700 & Internal friction angle/\({}^{\circ}\) & 35 \\ Normal/tangential critical damping & 0.2 & Tensile strength/MPa & 13 \\ Max. bonding distance (mm) & 0.08 & Cohesive force/MPa & 15.6 \\  & & Linear modulus of elasticity/GPa & 2 \\  & & Linear coefficient of friction & 0.5 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameters of sandstone-like materials.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Geometrical Parameters** & **Value** & **Bonding Parameters** & **Value** \\ \hline Thickness of contact area (mm) & 5.5 & Normal stiffness & 0.4 \\ Length of structural surface (mm) & 50 & Tangential stiffness & 0.4 \\ Width of structural surface (mm) & 30 & Friction coefficient & 0.1 \\ Undulation angle/\({}^{\circ}\) & 0 & Tensile strength/MPa & 0 \\  & & Cohesive force/MPa & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Prefabricated structural surface parameters.  
materials, a simplified anchor model has been constructed to better simulate its mechanical performance in practical engineering applications. The specific parameters for the anchor are detailed in Table 5.