## 3 Establishment of a Grouting Pipeline Blockage Model  
### Establishment of Gangue Pipeline Blockage Form  
The length of the pipeline in the grout filling system varies, and during numerical simulations, a buffer zone is commonly included to ensure adequate grout flow. In the experiment, an extra horizontal section of 3 m to 5 m is chosen as the buffer zone. In this study, a 5 m long straight pipe is selected as the buffer zone. Based on the field conditions, this study simulates a 21 m long horizontal straight pipe and a 90\({}^{\circ}\) elbow with a 2 m bending radius, using 16 Mn wear-resistant seamless steel pipes. And based on the process of blockage formation in the on-site grouting pipeline, blockages can be classified into attachment-type blockages (A-blockage), deposition-type blockages (B-blockage), and composite blockages (C-blockage), as shown in Figure 4[17]. Furthermore, according to the cause and nature of the blockage, they can be categorized into partial blockages and complete blockages. Partial blockages can be further divided into single blockages and multiple blockages[18].  
Figure 4: Schematic diagram of slurry pipeline blockage types.  
In actual grouting pipeline blockages, most blockages are partial rather than complete. The shape and distribution of the blocking material are irregular and unpredictable. In this study, the simulations focus on three specific types of blockages: attachment-type, deposition-type, and composite blockages. To preserve the integrity of characteristic parameters and minimize the complexity of subsequent model calculations, the irregular shape of the blocking material within the pipeline is simplified and approximated to a regular shape, as shown in Figure 5.  
In the Figure 5, S0 represents the cross-sectional area of the grout pipeline, in square meters (m\({}^{2}\)); S2 represents the cross-sectional area of the pipeline segment affected by blockage, also in square meters (m\({}^{2}\)); L\({}_{1}\) is the distance from the start of the pipeline to the beginning of the blocked section, in meters (m); L\({}_{2}\) is the length of the blocked segment in the pipeline, in meters (m); and L is the total simulated length of the grout pipeline, in meters (m).  
To thoroughly investigate the flow characteristics of the grout in the injection pipeline, a 1:1 scale three-dimensional model of the grout pipeline and blockage scenario was established using ANSYS. The three-dimensional physical model of the grout pipeline, with different blockage locations and degrees of blockage, is established as shown in Figure 6. The cross-sectional view of the pipeline is shown in Figure 7. The experiment primarily utilizes SolidWorks to create the 3D geometric model, with the fluid inside the pipe being filled using the Volume Extraction command. The ANSYS-mess module is then employed to generate the mesh for the fluid inside the pipeline, ensuring accurate simulation of the fluid flow. Due to the relatively simple pipeline structure, the mesh generation prioritizes the use of hexahedral elements for accuracy and computational efficiency. In areas with irregular shapes, such as blockage locations, tetrahedral elements are used. This choice is made because hexahedral meshes offer better quality, faster convergence, and lower computational costs, while tetrahedral meshes are more adaptable, efficiently filling complex geometric shapes. Additionally, mesh refinement is applied near the pipe wall, the blockage region, and the inlet and outlet areas. The use of hexahedral meshes yielded good results, with the total number of mesh elements ranging from 1.29 million to 1.4 million. Finally, mesh quality was evaluated using the Skewness criterion, which indicated that the element quality was classified as excellent and good.  
Figure 5: Regular non-completely clogged-pipe microelements.