# Discrete Element Analysis of Grouting Reinforcement and Slurry Diffusion in Overburden Strata
## 5 Conclusions
Error analysis indicated that the modified equations improved the goodness of fit by 34% to 39% compared to classical models (Maag formula and cylindrical diffusion formula). These equations are expected to offer valuable reference for the study of grout diffusion mechanisms and the design of grouting schemes in similar overburden conditions. Compared with continuum-based methods, the discrete element method (DEM), despite its limitations in computational efficiency, offers significant advantages in modeling granular media. DEM provides a more realistic representation of the internal particle structure of the overburden layer, enabling the simulation of particle flowability, non-uniform contact, and interpenetration between soil particles, as well as between soil and slurry. With the development of grouting technology and numerical calculation theory, using discrete element numerical simulation to visualize the grouting diffusion process is of great significance for in-depth understanding of the grouting mechanism of overburden. There are still some problems in the research process of this paper. Due to the limitation of computer efficiency, considering that the wide particle size distribution coefficient (\(\rm{D_{max}/D_{min}}\)) will lead to the generation of a large number of calculated particles, the filling medium of this study is the overburden particles with a grading range of 0.1-5 mm; In addition, due to the small size and large number of cement slurry particles, as well as the complexity of particle dynamic process, the simulation of cement particles has become an important factor restricting the calculation efficiency and calculation scale. Therefore, how to simplify the model, improve the calculation efficiency, and shorten the calculation time are the keys to further optimize the numerical simulation of grouting. Although this method can only carry out small-scale slurry diffusion research, it provides a way to study the mesoscopic diffusion mechanism of overburden grouting. Although the current coarse-graining methods can reduce the number of particles by several orders of magnitude--significantly lowering memory requirements for storing particle information (such as positions, velocities, and contact forces) and contact pair data--and increase computational speed by tens to hundreds of times, they inherently possess certain limitations. Coarse graining drastically decreases the number of contact pairs and simplifies the complexity of contact geometries, thereby reducing the computational burden of contact detection and force calculation. However, this simplification results in the complete loss of microscale dynamic details, including micro-sliding and micro-rotation between particles, the microscopic force chain network structure, and local porosity distribution. Moreover, coarse-grained models require complex calibration procedures, such as simulating standard tests or matching macroscopic responses to determine appropriate parameters, with multiple parameter sets often yielding similar macroscopic behaviors. Additionally, the surfaces of coarse-grained particles are typically too smooth to accurately represent the surface roughness and frictional characteristics of real particle aggregates. Their rotational behavior--particularly rolling resistance--is also challenging to model accurately, as it involves complex coupling effects between sliding and rotation of multiple fine particles. Therefore, current coarse-graining approaches fundamentally serve as a trade-off between computational efficiency and simulation accuracy. Further research could investigate the grouting behavior of slurries with varying viscosities. Additionally, future studies may incorporate analyses of the effects of particle shape on grouting performance. Conceptualization, P.G. and W.Z. ; methodology, P.G. and Y.M. ; formal analysis, P.G. and W.Z. ; Investigation, P.G. ; writing--review and editing, W.Z. and H.G. ; supervision, P.G., W.Z., and Y.M. ; project administration, P.G. and W.Z. ; funding acquisition, W.Z.