## 5 Simulation Calculation Model of Grouting
### Analysis of Influencing Factors of Slurry Diffusion Radius  
This experiment primarily investigates the slurry diffusion of self-drilling anchors during the drilling and grouting process in sandy pebble strata, with the grouting effect preliminarily assessed through the slurry diffusion radius. The slurry diffusion radius is typically influenced by factors such as the grouting process and stratum conditions. To account for the construction conditions of various factors in real-world scenarios and to facilitate precise control and implementation in particle flow software, this study selected three relatively significant and controllable factors: grouting pressure (\(p\)), drilling speed (\(s\)), and slurry viscosity (\(\mu\)). Under a confining pressure of 1 MPa, the simulation scheme \begin{table}
\begin{tabular}{c c c c c c} \hline
**Maximum Radius** & **Maximum and Minimum** & **Stiffness** & **Friction** & **Porosity** & **Normal Bonding** & **Tangential Bond** \\
**(Rmax)/cm** & **Radius Ratio (Rmax/Rmin)** & **Ratio (k)** & **Factor (f)** & **(n)** & **Strength/N** & **Strength/N** \\ \hline
4 & 2 & 4 & 0.25 & 0.2 & \(3\times 10^{4}\) & \(3\times 10^{4}\) \\ \hline \end{tabular}
\end{table} 
Table 10: Basic parameters of particles. Figure 8: Numerical simulation diagram of grouting in sandy pebble stratum. included grouting pressures of 0.2 MPa, 0.3 MPa, and 0.4 MPa. Considering the drilling efficiency of self-drilling anchor equipment during construction, drilling speeds of 0.2 m/min, 0.3 m/min, and 0.4 m/min were selected. In accordance with the Technical Specification for Building Foundation Pit Support (JGJ120-2012), the water-cement ratio for cement slurry in engineering construction ranges from 0.5 to 0.55. However, based on actual construction and site conditions, the water-cement ratio typically ranges from 0.7 to 1. Therefore, slurry viscosities of 83.3 mPa*s, 138.9 mPa*s, and 416.6 mPa*s were chosen. By generating a Scalar to represent pore pressure, the program identifies the abscissa values of the Scalar at the farthest left and right points at the final time step, and the average of these values is taken as the slurry diffusion radius. This simulation employs an orthogonal test design, comprising a total of nine groups. Assuming no interaction between the factors, the three selected factors-grouting pressure, drilling speed, and slurry viscosity--were arranged according to a three-level, three-factor orthogonal analysis table, denoted as L9(3\({}^{3}\)). The factors were labeled in the order of \"Grouting pressure-Drilling speed-Slurry viscosity\". The orthogonal test design and corresponding calculation results are presented in Table 11.  
It can be seen from the relevant research results [13], the slurry diffusion range has a power function relationship with grouting pressure, grouting time and slurry viscosity. In this simulation process, the grouting time can be expressed by the drilling speed, so it is assumed to obey the function equation:  
\[R=Ap^{B}s^{C}\mu^{D} \tag{8}\]  
In the above equation, \(R\) is the grouting diffusion radius, m; \(p\) is grouting pressure, MPa; \(s\) is drilling rate, m/min; \(\mu\) is slurry viscosity, mPa*s; \(A\), \(B\), \(C\), \(D\) is undetermined coefficients. The equation is a nonlinear equation, which can be transformed into a linear equation after taking logarithms on both sides. The experimental data are analyzed by multiple linear regression method, and the constant \(A\) and partial regression coefficients \(B\), \(C\) and \(D\) can be obtained. However, the partial regression coefficient is affected by the corresponding factor units and values, and cannot directly reflect the relative importance of the independent variables. Therefore, the regression coefficient \(\beta i\) is often obtained after standardization. The greater the absolute value of \(\beta i\), the greater the influence of this factor on the grouting diffusion radius.