## 1 Introduction
[18] conducted in situ grouting experiments using the hole-sealing grouting method to study the diffusion characteristics of expansive polymer grouting materials in sand, gravel, and sand-gravel mixtures. [PERSON] et al. [19] investigated the diffusion patterns of grout in silt after exposure to different levels of vacuum. [PERSON] et al. [20] conducted chemical grouting experiments in saturated sand to study the diffusion patterns of chemical grout in water-saturated loose sand layers. [PERSON] et al. [21] investigated the diffusion patterns of grout in sand through laboratory grouting model experiments, analyzing the diffusion behavior of cement grout in sand under different water-cement ratios, grouting pressures, grouting volumes, and soil conditions. [PERSON] et al. [22] and [PERSON] et al. [23; 24] conducted grouting model experiments on loose sand layers to investigate the diffusion patterns of grout. The aforementioned research and practices on grouting in sand layers are of significant importance. However, current studies mostly focus on the diffusion of grout in sand and its reinforcement effects. Moreover, previous studies have mainly relied on methods such as bulk excavation, core drilling, or cross-section cutting to investigate the grouting diffusion mechanisms and patterns. There has been a lack of attention to the temporal variations in grouting pressure, grout diffusion, and surface displacement during the grouting process. Grouting is a concealed engineering construction, making it difficult to directly observe the diffusion of grout. Achieving stable pressure grouting in engineering practice is often challenging, especially in the context of grouting lift correction projects. Due to variations in the geological conditions and the objects targeted for lifting, it is difficult to determine the exact pressure required for lift grouting to prevent secondary damage to the lifted structures [25]. Therefore, non-steady pressure grouting is employed in most practices. The actual determination of grouting pressure and the termination of grouting are based on the deformation and displacement measurements of the lifted structures. In this study, non-steady pressure grouting was utilized, with the grouting pressure gradually increasing over time. A self-developed three-dimensional grouting model test apparatus was utilized for grouting experiments. The study combined transparent sand with particle image velocimetry (PIV) technology to investigate the influence of grout diffusion on the displacement characteristics of sand particles. The diffusion patterns and distribution characteristics of cement grout in ordinary sand and transparent sand were studied. The visualization grouting model apparatus was employed to directly observe the diffusion patterns and distribution characteristics of cement grout in transparent sand during the grouting process, thereby validating the diffusion characteristics of grout in ordinary sand. Based on the visualization characteristics of transparent sand, the study analyzed the temporal variations in grouting pressure, grout diffusion, and surface uplift displacement under non-steady pressure grouting. It investigated the interactions between grouting pressure, grout diffusion, and surface displacement. Utilizing model experiments to study the diffusion patterns of grout and the temporal variations in surface displacement can provide scientific basis for grouting process design and control of grouting uplift effects.