## 3 Analysis of Test Results
### Slurry Diffusion Radius Time Profile Analysis  
The time-course variation curves of the diffusion radius in the x+, x\(-\), y+, and y\(-\) directions of grouting materials with different water-cement ratios were obtained by statistical analysis of the data for diffusion radius R, as illustrated in Figure 5.  
As shown in Figure 5, the diffusion radius time-course curve indicates that during the 0 to 5 s period, both the diffusion radius R and the grouting time t exhibit nonlinear growth across the x+, x\(-\), and y+ directions, with a particularly noticeable increase in the diffusion radius. From 5 s to 10 s, R and t display linear growth, signaling a transition phase. In the 10 s to 25 s period, the slurry diffusion radius changes more slowly, following a linear growth pattern, especially notable with a water-cement ratio of 0.5 and a viscosity of 33.6 mPa-s. Throughout the 5 s to 25 s period, a linear growth trend is observed. In the y\(-\) direction, the diffusion radius and grouting time show nonlinear growth during the 0 to 10 s period, with extended nonlinear growth in the x+, x\(-\), and y+ directions. From  
Figure 4: Slurry diffusion patterns in different water–cement ratios: (**a**) \(\xi=0.5\) viscosity 33.6 mPa-s; (**b**) \(\xi=0.6\) viscosity 20.2 mPa-s; (**c**) \(\xi=0.7\) viscosity 6.3 mPa-s; (**d**) \(\xi=0.8\) viscosity 3.2 mPa-s; (**e**) \(\xi=0.9\) viscosity 2.5 mPa-s; (**f**) \(\xi=1.0\) viscosity 1.8 mPa-s.  
10 s to 25 s, the slurry diffusion radius increases linearly with time due to the combined effects of viscosity and gravity. The diffusion radius of the slurry consistently increases over time in each direction for any given water-cement ratio, as illustrated by the diffusion radius time-course curve. This trend is uniformly observed across different water-cement ratios. The curve's growth pattern remains consistent for slurries with varying water-cement ratios in the x+, x\(-\), and y+ directions. Initially, the diffusion radius grows rapidly, quickly reaching a certain linear growth rate. Within the first 5 s, the diffusion radius increases by more than half of its total value. Following this, the growth rate begins to decelerate. During the 5 s to 15 s interval, while time progresses, the diffusion radius continues to expand, though at a markedly slower rate compared to the initial phase. This slower growth phase can be identified as a transitional stage. Between 15 s and 25 s, the curve representing the slurry diffusion radius begins to level off, signaling that the average diffusion distance across all water-cement ratios is approaching a certain percentage of the total diffusion distance. Specifically, the diffusion radius in the x+ direction reaches 4%, in the x\(-\) direction, 9.0%, and in the y+ direction, 7.7%. As the viscosity of the slurry increases and the pressure decreases, diffusion starts to encounter resistance, indicated by the presence of a diffusion radius limit. In the x-direction, the first 5 s demonstrate continued rapid growth, accounting for 48.7% of the total diffusion distance. The slurry's self-weight provides a steady driving force, which allows the average diffusion distance during the 15 s to 25 s interval to constitute 18.6% of the total. Consequently, it is anticipated that diffusion in the x\(-\) direction will persist even after reaching the limiting values observed in the other three directions. Figure 5: Time history curves of diffusion radius in different water–cement ratio: (**a**) x+ direction; (**b**) x\(-\) direction; (**c**) y+ direction; (**d**) y\(-\) direction. In the x+, x\(-\), and y\(-\) directions, following an extended period of grouting, the radius of diffusion demonstrates an increase in proportion to the water-cement ratio; in the x+ direction, the radius of diffusion correlates with the water-cement ratio of 0.8, 0.7, 0.6, 0.9, 1.0, and 0.5 in ascending order, which demonstrates that the diffusion in the direction opposite to gravity is not positively correlated with the water-cement ratio.