Diffusion of polymer permeation grouting in water-rich sand layers: Mathematical model and experimental validation

Water-rich sand layers are frequently encountered as adverse geological conditions during underground construction. Polymer slurry grouting has been widely recognized as an effective technique for reducing permeability and enhancing the stability of such strata. In this study, a mathematical model is established to describe the diffusion behavior of polymer slurry in porous media under dynamic water conditions and is further validated through laboratory experiments. The theoretical formulation of the slurry permeation process is developed based on Darcy’s law, the Hagen–Poiseuille flow principle, and the physicochemical characteristics of the slurry. The derivation primarily focuses on analyzing the dynamic response of the slurry under the influence of water flow, considering the effects of flow velocity, grouting pressure, and sand-layer porosity on diffusion behavior. To verify the proposed model, a visualized grouting simulation system was designed to observe the diffusion process of polymer slurry in water-rich sand layers. The results demonstrate that slurry diffusion is significantly affected by grouting pressure, porosity, and water flow velocity. The observed staged diffusion characteristics, dynamic evolution patterns, and directional effects are in good agreement with theoretical predictions. Furthermore, the average relative deviations between the theoretical and experimental results for diffusion pressure and diffusion distance are both less than 25%, confirming the reliability of the proposed model. Additionally, this study identifies distinct differences in slurry diffusion between porous and void media. In porous media, slurry propagation encounters greater hydraulic resistance, leading to rapid pressure attenuation and a limited diffusion range. Conversely, diffusion in void media occurs more smoothly due to the continuous cavity structure, resulting in slower pressure decay and a substantially larger diffusion radius. These findings elucidate the mechanisms governing slurry diffusion under dynamic water conditions and provide a theoretical basis for optimizing grouting parameters and improving construction efficiency in water-bearing strata.