# Ballast Flow Characteristics of Discharging Pipeline in Shield Slurry System
## 1 Introduction  
As large-scale underground tunneling equipment, the slurry shield machine has been widely used in cross-river tunnels, water projects, and urban rail transit engineering [1; 2; 3]. The shield slurry system is key to ensuring the stability of the excavating face and the degree of ballast transportation, and the system is mainly composed of a feeding line section and a discharging line section, as shown in Figure 1. Each pipeline section is equipped with a flow meter, density meter, pressure gauge, and pump. The fresh slurry passes through the feeding line section to the cutter head excavation area through pump P1.1, and pumps P2.1, P2.2, and P2.3 absorb the ballast mixture from the cutter head face area and then carry it to the slurry recycling station via the discharging line section. The ability of the slurry system to carry the ballast mixture impacts the shield excavation and its working efficiency. Inadequate ballast carrying capacity can lead to serious engineering accidents, such as pipeline stagnation, blockage, and excavation chamber blockage. The discharging pipeline section is composed of horizontal, inclined, and vertical pipelines. The total length of the pipeline can reach several kilometers and the ballast flow characteristics differ in different sections. The ballast size of an individual particle differs onthe millimeter-scale to 400-600 mm, which occurs in the Lanzhou gravel stratum in China. As such, exploring the ballast carrying performance and the flow characteristics in the slurry system under complex geological conditions is required. Many scholars conducted experiments and simulation studies on the particle motion in the pipeline system. [PERSON] et al. [4], [PERSON] et al. [5], [PERSON] et al. [6], and [PERSON] et al. [7] established a pipeline circulation experiment system, with a tube diameter of 40-150 mm and extension distance of 5-25 m, and discussed the critical slip velocity of 5-85 mm spherical particle in the pipeline, the particle motion state, and the pressure loss characteristics. So far, no experimental platform has been formed to the shield slurry system, and the experimental results of the published studies have varied. The rules that were obtained by the experiments were often limited and needed to be modified. The particle moving velocity, distribution state, pressure scatter, flow rate, and other information in the pipeline system have been determined while using high-speed cameras, flow meters, pressure gauges, and other methods [8; 9; 10]. During the experimental process, purchasing the monitoring equipment is often necessary for obtaining particle movement information. The experiment is expensive, the monitored pipe has a simple structure, and the conveying medium in the pipeline is water, which is quite different from the actual flowing medium. Others established the numerical transportation model for particle sizes between 0.1 mm and 20 mm in the pipeline system based on fluid dynamics, coupled with the discrete element methods, and quantitatively extracted the data, such as particle velocity, distribution region, solid phase volume fraction, and pressure loss of the pipeline [11; 12; 13; 14; 15]. The melting phenomenon of ice slurry in the pipe, the mixing effect of solid particles in the viscous liquid, the mechanism of jigging separation of mineral particles, and the cleaning process of non-spherical solid particles in the well hole with the help of a numerical simulation have been investigated [16; 17; 18; 19]. By comparison, the numerical method has unique advantages in some respects, such as model accuracy, applicability, completeness, and cost, hence it is suitable for researching particle transportation in a complex pipeline structure.