## 4 Results Analysis
### Comparison and Analysis of Experimental and Theoretical Results  
As shown in Table 4, the table provides the experimental diffusion radii for the four test sets compared with the theoretical diffusion radii calculated using Equations (16) and (18). When measuring the actual grouting body, multiple measurements of the horizontal diffusion radius were taken, and the average value was considered in this study. Figure 8 presents a comparison between the experimental values and the theoretical results of [PERSON] fluid diffusion, taking into account different particle size distributions.  
Figure 6: Schematic diagram of sensing electrode placement.  
Figure 7: Working 1 slurry body versus apparent resistivity diagram.  
From Table 4 and Figure 8, it can be observed that the theoretical diffusion radius of [PERSON] fluid in porous media with different particle size distributions is lower than that in porous media with the same particle size distribution. Additionally, the theoretical diffusion radius of [PERSON] fluid slurry in porous media with different particle size distributions is closer to the experimental measurements in the laboratory. Therefore, studying the infiltration grouting mechanism of [PERSON] fluid slurry in porous media with different particle size distributions is more practically significant for grouting in media composed of varying particle sizes.  
Analysis of Table 4 and Figure 8 reveals that there is a certain deviation between the theoretical values and experimental values of the diffusion radius of Bingham fluid in porous media with different particle size distributions. Several main reasons contribute to this deviation. (1) Equation (16) takes into account the influence of porous media with different particle size distributions on the diffusion behavior of Bingham fluid. However, the factors affecting the diffusion behavior of infiltration grouting are multifaceted. Factors such as the diffusion path of the slurry, which can be tortuous and meandering, can impact the slurry diffusion radius [19]. Additionally, the influence of gravity on slurry diffusion behavior should not be overlooked. Moreover, the time-varying parameters and viscosity of the slurry can change over time and thus affect its diffusion behavior. Furthermore, when the slurry flows through pore channels in porous media, particle precipitation can occur as particles block relatively smaller channels, resulting in seepage effects that also affect the slurry's diffusion behavior. (2) The theoretical assumption assumes that porous media are isotropic and homogeneous. However, in the laboratory setting, gravel and pebble materials do not perfectly conform to this idealized notion. In the derivation of the formulas, the structural characteristics and arrangement of particles within the gravel and pebble materials were not considered, and these characteristics can indeed influence the infiltration and diffusion behavior of Bingham fluid in practice.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Working Condition**} & \multicolumn{3}{c}{**Theoretical Value/cm**} \\ \cline{2-4}  & **Considering Different** & **Not Considering Different** & **Experimental Value/cm** \\  & **Particle Size Distributions** & **Particle Size Distributions** & **Experimental Value/cm** \\ \hline
1 & 12.95 & 18.71 & 8.65 \\
2 & 15.12 & 27.39 & 10.24 \\
3 & 13.52 & 24.85 & 9.56 \\
4 & 15.75 & 29.25 & 11.32 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Experimental values and theoretical calculations for the two different models.  
Figure 8: Comparison analysis of experimental and theoretical models.