# A State-of-the-Art Review on the Study of the Diffusion Mechanism of Fissure Grouting
## 4 Research Status of the Numerical Simulation of Fissure Grouting in Rock Masses
### Progress in Numerical Simulation Methods for the Study of Slurry Diffusion in Fissure Media  
Numerical simulation is an important method for studying the diffusion law of grouting in fissured rock masses. Compared with theoretical research, numerical simulation does not rely heavily on assumptions and can continuously and dynamically obtain numerical solutions for the diffusion process of grout under complex conditions, with a wide range of applicability. For model experiments, numerical simulation can adjust various parameters in a model using programming or computer software, thus simulating grouting models under various working conditions without being limited by model size, flow field disturbances, personal safety, or measurement accuracy, which makes the research process more convenient and economical. These are of great significance for a correct understanding of the diffusion behavior of grout in fissures. At present, many scholars have conducted a large amount of work in this area.  
[PERSON] et al. [71] constructed height regression models for 33 water-conducting fissure zones using the PSO-SVR particle swarm-support vector machine, quantitatively evaluated the prediction accuracy of the water-conducting model, and then predicted water-conducting fissure zones for three mines. [PERSON] et al. [72] used the finite element method to numerically simulate grouting in micro-fissured rock masses. They solved partial differential equations to simulate multi-physics field interactions. The calculation model included a single horizontal fissure within the surrounding rock masses, as shown in Figure 2. Their study focused on the diffusion process of grouting in micro-fissured rock masses, considering the fluid-solid coupling effect. In addition, they also investigated the impact of fissure aperture and the elastic modulus of rock masses on the grouting diffusion process. [PERSON] et al. [73] used finite element software to simulate the two-phase fluid seepage of underground fluids in fissures within porous media. They established a relationship between flow velocity and permeability pressure differences. In numerical simulations using the finite element method, fissures can be simulated using line segments or surface elements to predict the deformation and changes in a fissure during the grouting process. In addition, the effects of seepage and consolidation during the grouting process on the mechanical behavior of rock masses can also be considered to predict and evaluate the stability of a rock mass after grouting. The advantages of the finite element method are that it can handle complex geometric and boundary conditions and that it considers the nonlinear and deformation characteristics of materials. However, the finite element method also has drawbacks, such as a high computational cost and a long computation time.  
[PERSON] et al. [74] used the lattice Boltzmann method to simulate the evolution process of velocity and the concentration field, considering the dissolution effect on the fissure surface, and established a rough rock fissure seepage-dissolution coupling model. They discussed the effects of different fractal dimensions of the surface of a fissure, two dimensionless variables: Pe (characterizing the relative size of convection and diffusion) and Da (characterizing the relative relationship between reaction rate and diffusion), and other factors on the mechanism of rough fissure seepage-dissolution coupling. [PERSON] et al. [75; 76] introduced the basic assumptions of the Hele-Shaw model and transformed the three-dimensional problem of fluid flow in a plane fissure into a two-dimensional problem about the fissure aperture, thus establishing a quasi-three-dimensional method for high polymer grouting in plane fissures. They effectively simulated the diffusion process of high-polymer slurry in fissures, greatly reduced the model size, and saved computation time.