## 4 Simulation Realization of Rock Bolt Pile Unit  
### Numerical Model of Roadway with Layered Composite Roof  
In FLAC\({}^{\text{3D}}\), the cable unit is generally used to simulate rock bolts, but the cable unit can only bear axial loads and cannot reflect shear loads, while the shear resistance of rock bolts has a great influence on the support effect. In order to better simulate the comprehensive effect of the tensile and shear resistance of rock bolts, the pile unit is selected: The pile unit combines the beam element and the anchor cable element. Besides being able to bear the axial pulling load, it also has the ability to resist bending and shear; The pile unit can also calculate the stress softening between the pile and the grid and the rupture of the pile, thereby simulating the rupture of the rock bolt and the decoupling of the anchorage interface. The use of the pile unit can better simulate the mechanical behaviors, such as tension, bending, shear, fracture, and anchor failure of the rock bolt. In this paper, the HBRB500 high-strength rock bolt with a diameter of 22 mm is uniformly used for simulation. The drilling diameter is 30 mm. The parameters of the rock bolt and the anchoring agent are listed in Table 2.  
In the pile unit, \"cs-scoh\" refers to the peak bond force, which determines when the bonding interface decouples and detaches from the anchor; \"cs-sk\" refers to the bond stiffness, which determines the resistance-increasing speed of the anchorage body; cs-scoh and cs-sk jointly determine the mechanical properties of the anchorage body and have a very significant influence on the support effect. To provide a basis for determining cs-scoh and cs-sk of the numerical rock bolt, a pull-out test was carried out in the laboratory. A steel pipe with a length of 125 mm and an inner diameter of 30 mm was used to simulate the drilling hole, and a left-handed high-strength threaded steel with a diameter of 22 mm was selected for the rock bolt. After repeated tests, when the anchorage section length was 125 mm, the average maximum pull-out force was 140 kN, and the corresponding average displacement was 13 mm. Calculate cs-scoh = 1.12 \(\times\) 10\({}^{6}\) N/m. Considering that the on-site rock bolts are anchored in the coal and rock mass, the peak strength of the bonding interface should be lower than the laboratory test results. [PERSON] et al. [27] took advantage of the repeatability and scalability of numerical simulation calculations and proposed calibrating the mechanical parameters of the coal and rock mass through the repetitive trial-and-error method. In this paper, the above method was adopted to obtain cs-scoh = 4.37 \(\times\) 10\({}^{5}\) N/m, cs-sk = cs-scoh/13 mm = 3.3 \(\times\) 10\({}^{7}\) N/m. The parameters of pile Units are shown in Table 3.  
Figure 8: Schematic Diagram of Numerical Model.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Elastic** & **Poisson’s** & **Cross-** & **Sectional** & **Perimeter/m** & **Yield** & **Moment of** & **Moment of** & **Polar** & **Bond Force** & **Bond Stiffness** \\
**Modulus/Pa** & **Ratio** & **Area/m\({}^{2}\)** & **Perimeter/m** & **Force/N** & **Inertia \(I_{\text{s}}\)/m\({}^{4}\)** & **Inertia \(I_{\text{s}}\)/m\({}^{4}\)** & **of Inertia/m\({}^{4}\)** & **of Inertia/m\({}^{4}\)** & **(cs-scoh)/(N/m\({}^{3}\))** \\ \hline
200 \(\times\) 10\({}^{9}\) & 0.25 & 3.8 \(\times\) 10\({}^{-4}\) & 0.094 & 2.47 \(\times\) 10\({}^{5}\) & 1.15 \(\times\) 10\({}^{-8}\) & 1.15 \(\times\) 10\({}^{-8}\) & 2.3 \(\times\) 10\({}^{-8}\) & 4.37 \(\times\) 10\({}^{5}\) & 3.3 \(\times\) 10\({}^{7}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Parameters of Pile Units.