Abstract: Water inrush disasters frequently occur during tunnel and underground engineering construction.Grouting is one of the most effective measures for preventing and controlling such disasters.The diffusion and migration of slurry significantly influence the success of disaster control engineering design and construction.Due to the concealed and complex nature of the injected media,the diffusion process of slurry in rock masses cannot be directly observed.Numerical simulation methods for grouting can visually demonstrate the diffusion process,gradually becoming a critical tool in grouting mechanism research.This paper first introduces commonly used numerical methods for grouting simulation,then reviews recent research advancements in two areas:grouting simulation in fractures and conduits and grouting simulation in porous media.Finally,it predicts and discusses the future development trends of grouting simulation methods.The authors’ proposed slurry property characterization model and a series of grouting simulation methods address two key issues in current numerical simulations:representing the spatiotemporal variability of slurry viscosity and characterizing slurry-water interactions.Future research priorities include establishing high-precision models for multi-physical field coupling during the entire grouting process,coordinating the relationship between numerical simulation accuracy and computational scale,and developing grouting simulation methods for engineering-scale applications.Research on grouting numerical simulation methods is crucial for advancing underground engineering grouting design from “experience-driven” to “quantitatively guided” approaches.