Grouting mechanism of quick-setting slurry in fracture with random fracture opening considering time–space characteristics of viscosity

The coupling effect between the spatial variability of slurry diffusion and the time-varying viscosity of quick-setting slurry is the time–space characteristics of slurry viscosity (TSCSV). The TSCSV is the governing factor for the complex and uncontrollable flow of slurry in fractures. In this regard, the flow pattern of quick-setting slurry is considered as a Bingham fluid with viscosity spatiotemporal characteristics. Using the fractal function with random parameters (W-M function), a single fracture with random fracture opening (RFO) is drawn, and a theoretical model on grouting diffusion in fractures is established considering the TSCSV. The RFO is corrected for head loss, and the spatiotemporal distribution equation of the RFO grouting pressure is derived. The relationship between grouting pressure, grouting time, and slurry diffusion distance is obtained. Additionally, the effects of the RFO, the fractal dimension of the fracture curve, the horizontal movement distance of the lower end face of the fracture, and the effects of viscosity and grouting rate on the viscosity and grouting pressure in the slurry diffusion space are discussed. Finally, by predefining the spatial distribution function of slurry viscosity for a single fracture in the numerical calculation model, a numerical simulation of random fracture distribution grouting considering viscosity spatiotemporal characteristics is achieved. The rationality of the model is validated through a comparison of theoretical analysis and numerical simulation, providing reference for the determination of grouting parameters in practical grouting projects.