## 2 Methods  
This study focuses on the reinforcement performance of full-grouting rock bolts under the uniaxial loading environment. Therefore, the traditional PO method was used. Specifically, a rock bolt was installed in a rock block and a low PO rate was applied on the external end of the rock bolt. This test was continued until the rock bolt anchorage system failed. During the whole test process, the PO force and displacement were recorded to indicate the reinforcement performance of rock bolts. In this study, the numerical software FLAC3D 6.0 was used. The reason to use this program is that it is an advanced commercial program. Previous research indicated that this program is robust in modelling kinds of mining engineering issues [22]. More importantly, in FLAC3D 6.0, various structure elements are embedded. Therefore, users can adopt those structure elements to model rock reinforcement bolts. When using the FLAC3D 6.0, a numerical PO scenario was created, as shown in Figure 1. It is basically composed of three parts: the rock bolt, the grout column and the surrounding rock. The rock bolt can be divided into two parts: the free length and the EL. The free length is only 0.1 m. The purpose of this free length is to simulate the protruding section of rock bolts in experimental PO tests. Below the free length, it is the EL. More importantly, the EL can be adjusted by users. Since the numerical software has the convenience of creating numerical blocks, the EL can be easily increased or decreased by users. In this study, the EL was changed between 0.5 m and 3 m.  
To model the PO influence, a low PO rate of \(5\times 10^{-7}\) m/s was applied at the external end of the rock bolt. Moreover, this low PO rate was fixed during the whole PO process. In this study, two kinds of rock bolts were used. One was metal rock bolts and the other was FRP rock bolts. The basic information of those two rock bolts is tabulated in Table 1. Basic information of tested rock bolts. The modified pile elements can simulate tensile rupture of rock bolts. It indicates that after the tensile force in the rock bolt reaches 220 kN and the corresponding tensile strain in the bolt reaches \(1\times 10^{-4}\), tensile rupture of the rock bolt will occur. As for the surface between rock bolts and grout, an elastic debonding law was used to model it. It is defined that before the shear slip of the surface between rock bolts and grout reaches 1 mm, the bonding stress at the surface increases linearly to the strength of 2 MPa. After that, the bonding stress at the surface declines directly to the residual strength of 1 MPa. Since then, the bonding stress of the surface between rock bolts and grout remains constant. The rock bolt is installed in a numerical rock block. The rock block had an elastic modulus (EM) of 25 GPa and Poisson's ratio of 0.25. It is admitted that in reality, the rock is an elastoplastic material. Therefore, the rock may generate plastic deformation. Then, in rock mechanics, the elastoplastic models are always used to simulate the rock mass, such as the Mohr-Coulomb model or the strain-softening model. However, in this study, attention is concentrated on the bonding failure of rock bolts. Therefore, no failure of the rock mass occurs. Then, an elastic model is used to simulate the numerical rock block. Moreover, \begin{table}
\begin{tabular}{c c c} \hline \hline
**No.** & **1** & **2** \\ \hline Rock bolt type & Metal rock bolt & FRP rock bolt \\ Elastic modulus (GPa) & 220 & 50 \\ Rock bolt diameter (mm) & 22 & 22 \\ Rock bolt perimeter (mm) & 69.1 & 69.1 \\ Cross-sectional area of rock bolts (mm\({}^{2}\)) & 380.1 & 380.1 \\ Tensile rupture force (kN) & 220 & 220 \\ Tensile failure strain & \(1\times 10^{-4}\) & \(1\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Basic information of tested rock bolts. Figure 1: The PO protocol for rock bolt testing. when using the elastoplastic models, more input parameters are needed. This decreases the practicability of this numerical calculation.