# Ballast Flow Characteristics of Discharging Pipeline in Shield Slurry System
## 6 Conclusions  
The ballast carrying capacity and movement state in the slurry system was studied based on a two-way coupling of the discrete phase model, and the conclusions are as follows:  
(1) A hydraulic lifting numerical model of a four-meter-long vertical pipeline was built with the spherical ballast group with particle size between 10 and 40 mm as the research object. The accuracy of the numerical model was verified by comparing the distribution state and suspension speed of ballast, and the difference between experimental and simulation data was within 8%. (2) Increases in the slurry flow rate and ballast volumetric concentration improve the ballast mass flow rate \(K_{m}\) in each pipeline and reduce the detained mass percentage \(R_{m}\) in the horizontal pipeline, to effectively improve the carrying capacity of the pipeline. With increasing slurry flow rate, the maximum increase in \(K_{m}\) was 120%, and 322% when the ballast volumetric concentration increased. The effect of the ballast volumetric concentration on the mass flow rate is stronger than that of the slurry flow rate. With increasing slurry flow rate, the maximum decrease of \(R_{m}\) was 87.5%, whereas the maximum decrease of \(R_{m}\) was 47.3% with the increase in the ballast volumetric concentration. The slurry flow rate has a stronger effect on the \(R_{m}\) than ballast volumetric concentration. Increases in ballast size have no effect on the \(K_{m}\) of each pipeline section, but they can significantly increase the \(R_{m}\) of the horizontal pipeline section with a maximum increase of 97.2%. Therefore, increasing the ballast size is likely to cause a risk of the ballast retention and blockage in the horizontal pipeline. (3) The slurry flow rate and the ballast size are the main factors affecting the ballast motion state. Increasing the slurry flow rate changes the ballast movement state to suspension in inclined pipelines, decreases the ballast accumulation area in horizontal pipelines, and aggregates the ballast in the vertical pipelines toward the central area. Increasing the ballast size changes the ballast motion state to bottom movement in the inclined pipeline, and it increases the ballast accumulation area in the horizontal pipeline, which has little effect on the diffusion degree and ballast movement state in the vertical pipeline. The increase in the ballast volumetric concentration has little effect on the ballast motion state in each pipeline. It can significantly increase the ballast diffusion area in the inclined and vertical pipelines, and increase the ballast accumulation area in the horizontal pipeline. (4) We found that the variation in the wall thickness in various regions of the inclined section and the horizontal section was mainly concentrated in the bottom of the pipeline by measuring the wall thickness of each pipeline in the field. The maximum wear rate of the inclined pipeline was 54.2%, whereas that of the horizontal pipeline was 68.6%. The horizontal pipeline wall thickness was basically unchanged along the length direction. The areas where wall thickness varied at V\({}_{1}\) of the vertical pipeline were mainly located on the flushing side, and the maximum wear rate was 66.5%. The inner wall of the vertical pipe at V\({}_{2}\) and V\({}_{3}\) did not wear, and the maximum wear rate was only 4.2%. The wall thickness variation curve and the ballast distribution area in the simulation condition were mutually proved. [PERSON] and G.Z. is responsible for the frame design of the paper and guide the writing of the paper. [PERSON] performed experiments and numerical studies on analytical objects and write the paper. [PERSON] is responsible for the model setup and helps analyze the data. [PERSON] and P.C. provide on-site construction data and assists in the survey.