## 4 Conclusions  
Through the self-developed three-dimensional grouting model experimental device, non-constant-pressure grouting diffusion model experiments were conducted to study the spatiotemporal development characteristics of grout diffusion in both common sand and transparent sand. Based on the visualization properties of transparent sand, the time-varying characteristics and interrelationships among grouting pressure, grout diffusion, and surface uplift displacement during non-constant-pressure grouting were analyzed. The conclusions are as follows:  
1. During non-steady-pressure grouting, at lower grouting pressures, grout primarily permeates through the sand, resulting in the formation of spherical grout bodies. As the grouting pressure increases, the compaction effect of the grout in the sand gradually becomes dominant, compacting the surrounding soil. With a continued increase in grouting pressure, the sand undergoes splitting, and the grout rapidly fills the cracks. During the initial stages of fracturing, there is permeation and compaction around the cracks. As the grouting pressure continues to increase, the pressure within the cracks gradually rises, promoting crack propagation. Additionally, as the grouting pressure increases, the grout pockets expand, leading to the formation of new cracks. 2. When compaction is predominant, the grouting pressure curve exhibits a smooth characteristic, whereas during low-pressure permeation, the grouting pressure curve is non-smooth. A sharp decrease in grouting pressure occurs when grouting fracturing happens, followed by an increase in grouting pressure that exceeds the rate of decrease. Each segment has distinct features in terms of its starting and ending points on the graph, showing a concave tip on the pressure curve. 3. The changes in surface displacement induced by grouting also exhibit noticeable characteristics. The curves of grouting pressure and surface displacement show good consistency with grouting time, displaying a gradual increase followed by rapid growth. The characteristics of surface uplift displacement curves are generally consistent, all undergoing three developmental stages: a slow increase stage, an accelerated increase stage, and a stable increase stage. The diffusion mode and direction of grout have a direct impact on the deformation characteristics of the overlying sand. 4. The uplift displacement curve exhibits a characteristic \"step-like\" growth pattern, with an increase in speed after each step, indicating distinct stage-wise features in the surface displacement curve with increasing grouting time. Visualized grouting experiments reflect good consistency in the effects of grouting pressure, grout diffusion, and their corresponding uplift displacement. For the grout with \(w/c\) = 0.8, the deformation overall shows a symmetrical distribution pattern of \"higher in the middle, lower on the sides\". The distribution of vertical displacement along the horizontal direction for \(w/c\) = 0.8 and 1.2 tends to become horizontal with decreasing depth. The diffusion direction of the grout with \(w/c\) = 1.0 varies, leading to a fluctuating dynamic deformation pattern resembling \"ripples\" in the transparent sand. In the future, we aim to achieve three-dimensional visualization of large-scale transparent soil and simultaneously capture multidirectional displacements. This will allow us to investigate the spatiotemporal correlation characteristics between grout diffusion and uplift deformation. Conceptualization, H.-X.H. and C.D. ; methodology, W.C.; formal analysis, Y.-F.L. ; writing--original draft preparation, W.C. and C.D. ; writing--review and editing, W.C. and C.D. ; supervision, H.-X.H. and C.D. ; funding acquisition, H.-X.H. and C.D. All authors have read and agreed to the published version of the manuscript.