# Discrete Element Analysis of Grouting Reinforcement and Slurry Diffusion in Overburden Strata
## 1 Introduction  
Grouting is an efficient, convenient, and flexible anti-seepage treatment technique for overburden strata. The core principle is to inject slurry into the overburden under grouting pressure, forming a continuous solidified vein, thereby effectively reducing seepage pressure or flow beneath structures [1]. However, the concealed nature of grouting, coupled with the loose structure and heterogeneous particle size of the grouted medium, poses significant challenges to studying slurry diffusion mechanisms in overburden, resulting in a reliance on empirical knowledge during construction. Therefore, research on visualization and numerical simulation of the grouting process holds both theoretical value and practical significance for guiding overburden grouting in hydropower projects. Numerical simulation methods offer distinct advantages in addressing complex engineering problems, owing to their intuitive and detailed nature. They not only provide solutions to grouting challenges but also dynamically visualize both global and local diffusion patterns during the grouting process [2]. Various numerical simulation techniques--including the finite element method [3], extended finite element method [4], boundary element method [5], and composite element method [6]--have been employed for detailed analyses and engineering applications related to grouting diffusion. Regarding the theory of cement slurry diffusion, [PERSON] and [PERSON] [7], [PERSON] et al. [8], and [PERSON] et al. [9] derived diffusion formulas based on porous media theory and validated the accuracy of cement slurry diffusion models. In research on grouting construction strategies, [PERSON] et al. [10] developed a refined 3D geological model integrating various geological data and proposed a three-dimensional mathematical model for Bingham fluid turbulence during grouting. [PERSON] et al. [11] simulated grouting in porous media under sequential porosity conditions and analyzed the diffusion behavior of cement slurry. Although continuum-based numerical simulation of grouting has achieved notable success, traditional approaches to overburden grouting and anti-seepage reinforcement primarily emphasize macroscopic project safety and stability, often neglecting the particle-scale heterogeneity of overburden and cementitious media [12]. This idealization frequently leads to discrepancies between simulation outcomes and real-world performance. In addition, constitutive models based on continuum mechanics typically capture only specific aspects of soil behavior and have limited applicability. Their formulations are often dominated by mathematical assumptions rather than physical principles, which makes it difficult to accurately account for the interaction processes between slurry and soil. As a result, certain micro-scale reinforcement mechanisms cannot be effectively revealed. To more accurately capture the heterogeneous structure of the overburden and visualize the slurry diffusion process, the discrete element method (DEM) combined with random generation techniques offers an effective approach for studying grouting in heterogeneous geotechnical media. [PERSON] [13] investigated the effects of cofferdam grouting on the excavation of water-rich tunnels using the particle flow-based DEM, and analyzed how grouting pressure and hole arrangement affect slurry seepage patterns. [PERSON] et al. [14] examined grouting in fractured surrounding rock using a DEM-based model, finding that crack dilatancy induced by deviatoric stress widens fracture openings, thereby altering slurry diffusion behavior. However, existing DEM-based grouting studies often simplify formations to uniform particle sizes and simulate slurry vein expansion via hydraulic fracturing, neglecting the pronounced particulate characteristics of both overburden and cement slurry. [PERSON] [15] developed a discrete element grouting model using PFC's Fish scripting language and employed a servo mechanism to apply grouting pressure, thereby simulating the grouting process.