applied sciences Article Ballast Flow Characteristics of Discharging Pipeline in Shield Slurry System Yang Wang 1,2 , Yimin Xia 1,2,*, Xuemeng Xiao 1,2, Huiwang Xu 3, Peng Chen 3 and Guiying Zeng 1,2 1 School of Mechanical and Electrical Engineering, Central South University, Changsha 410083, China; [email protected] (Y.W.); [email protected] (X.X.); [email protected] (G.Z.) 2 State Key Laboratory of High-Performance Complex Manufacturing, Central South University, Changsha 410083, China 3 China Railway 14th Construction Bureau Co. Ltd., Jinan 250014, China; [email protected] (H.X.); [email protected] (P.C.) * Correspondence: [email protected]; Tel.: +86-0731-88876926 Received: 19 October 2019; Accepted: 6 December 2019; Published: 10 December 2019 Abstract: We adopted two-way coupling of discrete and finite elements to examine the non-spherical ballast flow characteristics in a slurry pipe system during a shield project. In the study, we considered the slurry rheological property and the flake shape of the ballast. A ballast size between 17 and 32 mm under different slurry flow rates and ballast volumetric concentration conditions was investigated for determining the law through which the mass flow rate, detained mass percentage, and ballast distribution state are influenced. The results indicate that increasing slurry flow rate and the ballast volumetric concentration increase the mass flow rate; the influence of the latter is stronger. Increases in both in the slurry flow rate and the ballast volumetric concentration can reduce the detained mass percentage in the slurry discharging pipeline, whereas increasing the ballast size has the opposite effect. The increase in both the slurry flow rate and the ballast size changes the ballast motion state. Experiments verified the numerical lifting model of the ballast in the vertical pipeline. The measurements of the actual pipeline wall thickness verified that the simulation results regarding the ballast distribution were accurate. Keywords: slurry shield; slurry system; ballast; mass flow rate; detained mass percentage; distribution state 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 [1–3]. 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 Figure1. 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 on Appl. Sci. 2019, 9, 5402; doi:10.3390/app9245402 www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, 5402 2 of 20 Appl. Sci. 2019, 9, 5402 2 of 20 the 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 gravel stratum in China. As such, exploring the ballast carrying performance and the flow complex geological conditions is required. characteristics in the slurry system under complex geological conditions is required. Figure 1. WorkingWorking principle diagram of a shield slurry system. P, pump. Many scholars conducted experiments and simulation studies on the particle motion in the pipeline system.system. Li-an etet al.al. [[4],4], VanVan WijkWijk et et al. al. [ 5[5],], Zouaoui Zouaoui et et al. al. [ 6[6],], and and Ravelet Ravelet et et al. al. [7 [7]] established established a pipelinea pipeline circulation circulation experiment experiment system, system, with with a tubea tube diameter diameter of of 40–150 40–150 mm mm and and extension extension distance distance of 5–25of 5–25 m, andm, and discussed discussed the criticalthe critical slip velocityslip velocity of 5–85 of mm5–85 spherical mm spherical particle particle in the pipeline,in the pipeline, the particle the motionparticle state,motion and state, the pressureand the pressure loss characteristics. loss characteri So far,stics. no So experimental far, no experimental platform hasplatform been formed has been to theformed shield to slurrythe shield system, slurry and system, the experimental and the experime resultsntal of theresults published of the published studies have studies varied. have The varied. rules thatThe rules were that obtained were byobtained the experiments by the experiments were often we limitedre often and limited needed and to needed be modified. to be modified. 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