## 3 Results and Discussion
### Analysis of Dynamic Deformation Characteristics of Transparent Sand Particles in Grouting Process  
Transparent sand grouting tests were conducted with three water-cement ratios (\(w/c\) = 0.8, 1.0, 1.2). To maintain consistency in the experimental sand parameters, the sand filling height was set at 300 mm, and the natural consolidation time was standardized to 24 h. The laser was directed from top to bottom to avoid the influence of the model bucket on laser penetration and to minimize the occlusion of the laser beam by the grout, primarily focusing on monitoring the vertical displacement of the sand layer. To obtain the dynamic deformation characteristics during the grouting process in transparent sand, different \(w/c\) of grout were selected at four time points (0.25 t, 0.50 t, 0.75 t, t) based on grouting time (t), and the uplift displacements (\(v\)) of sand at three heights (burial depth \(h\)) from the ground surface (0.15 m, 0.10 m, 0.05 m) were analyzed. At each height, 18 data points were extracted along the horizontal direction at equal intervals. The dynamic deformation characteristics of transparent sand during the grouting process can be obtained, as depicted in Figures 7-9. According to the test results, the vertical displacement of transparent sand increases progressively with the grouting process. For \(w/c=1.0\), during the later stages of grouting (\(k=\) t), the vertical displacement of sand layers at different depths exhibits a similar distribution trend along the horizontal direction. Due to the lower concentration of grout with the \(w/c=1.2\), the vertical displacement values of the sand at the same height along the horizontal direction during grouting are similar, indicating an overall uplift phenomenon of the transparent sand. The grout with \(w/c=1.2\) exhibits an overall \"inverted cone\" diffusion pattern, but there are significant differences in the direction of grout diffusion during this process, resulting in a \"ripple\" effect on the particle displacement of the overlying transparent sand throughout the grouting process. Further analysis reveals the impact patterns of different water-cement ratio grouts on the displacement of transparent sand at various burial depths. As illustrated in Figure 7, at a burial depth of \(h=0.15\) m, during the initial stages of grouting, the effect of the grout on the sand is minimal, resulting in relatively small displacement of the sand. Specifically, the uplift displacement for grouts with water-cement ratios of 0.8 and 1.2 is similar, while that for \(w/c=1.0\) is relatively larger (k = 0.25 t). When the grouting process reaches  
Figure 8: Dynamic deformation characteristics of transparent sand at \(h=0.10\) m. (a) \(k=0.25\) t; (b) \(k=0.50\) t; (c) \(k=0.75\) t; (d) \(k=\) t.  
\(k=0.50\) t, the vertical displacement of the transparent sand significantly increases. All three water-cement ratio grouts exhibit a typical displacement pattern of \"higher in the middle and lower on both sides\", indicating that the grout primarily uplifts the central portion of the transparent sand at this stage. At \(k=0.75\) t, the grout-induced uplift displacement for \(w/c=0.8\) and \(1.2\) still follows the pattern of \"higher in the middle and lower on both sides\" along the horizontal direction, but with increased displacement. However, for \(w/c=1.0\), it exhibits a \"lower in the middle and higher on both sides\" pattern, indicating the initiation of \"sheet-like\" fracturing diffusion of the grout (Figure 7b,c). At the end of grouting (Figure 7d), the grout with \(w/c=1.2\) does not experience significant horizontal loss, resulting in the highest uplift displacement. In contrast, the grout with \(w/c=1.0\) tends to develop towards the left laser plane, leading to a gradual decrease in uplift displacement within the \(-0.1\) to \(-0.02\) m range.