2018 International Conference on Advanced Chemical Engineering and Environmental Sustainability (ICACEES 2018) ISBN: 978-1-60595-571-1
Research on the Distribution Model of the
Slurry Pressure in the Shield Tunnel
Yanbin Fu and Yong Yang
ABSTRACT
This paper focuses on the distribution model of the slurry pressure in the shield tunnel when grouting simultaneously. The theoretical derivation of the slurry pressure distribution model is carried out respectively according with Bingham flow model. The theoretical formula of the slurry pressure in the cross section of the shield tail is established. The relationship between slurry viscosity coefficient and the time and the relationship between the slurry pressure and slurry viscosity coefficient are analyzed. On this basis, the law that the slurry pressure changes with time and the distribution of the slurry pressure along the longitudinal di rection of the tunnel are summarized. Furthermore, monitoring on the spot proved the rationality of the above theoretical derivation. The results of this paper can provide great reference and guiding significance for the simultaneous grouting of the shield tunnel.1
INTRODUCTION
The grouting slurry pressure distribution of the shield tunnel and the grouting effect are directly related to the work of the segments, the bolts and settlement deformation of the surrounding soil. Thus it will affect the safety of the shield tunnel structure. Therefore, the distribution of the grouting slurry pressure and the effect of slurry pressure on the segments are always being focused on by the engineering and the academe. Grouting was adopted as an important measure for ground treatment to deal with the unfavorable geological conditions [1]. From the experimental results, the main influencing parameters on the dewatering behavior and on the development of the
1Yanbin Fu, Yong Yang, College of Civil Engineering, Shenzhen University, Guangdong, China.
513 required shear strength could be defined [2]. There was a discovery that focusing on the stress and volume change of the tail void grout with time, the simulation results were evaluated with respect to the deformation and stress state of the ground [3].The optimal thickness of reinforcement cycle and permeability can be adopted as 8 m and 1/100 of the surrounding rock permeability in the curtain grouting reinforcement cycle in the case of Yonglian Tunnel [4]. As the soil pressure increases, a gentle increase bending moment and eccentricity was observed. And changes in soil pressure have little effect on internal forces of thrust force and the distribution of internal forces [5]. In summary, many experts and scholars have launched a series of studies on the distribution model of slurry in shield construction and the way of improving the effects of grouting. However, there are few studies on the distribution model of slurry pressure in the tail gap, which have not yet reached a conclusion. Therefore, based on the existing research results, considering the relationship between the slurry pressure and time, the circumferential and longitudinal distribution of the slurry pressure under different fluids are derived.
DERIVATING THE CIRCUMFERENTIALDISTRIBUTION MODEL OF THE GROUTING SLURRY PRESSURE
The Circumferential Filling Mechanism of the Slurry in the Shield Tail Void
For the annular section, the slurry fills in void under the pressure from the grouting hole. The slurry flowing process is shown in Figure 1. In order to simplify the process of the theoretical calculation, the slurry filling is considered as two independent stages, that’s circumferential filling and longitudinal filling.
y
K P+dP τ B 1 B2 R P d G A1 A3 α
α A2
x
Figure 1. Slurry flows in the grouting ring. Figure 2.The analysis on the fluid force.
514 Take theπ/4grouting hole for example when the slurry flows upward. We take a micro-unit out of the fluid to analyze the stress. And we assume that the shear stress is on the front and rear sides, as Figure 2 shows. According to the balance among the fluid forces, we can obtain:
dP d cos( ) (1) R d 2 r
In the formula, Pis the grouting slurry pressure; Ris the mean radius of the grouting ring;αis the angle between the micro-body and the x-axis; γis the gravity of the slurry; τ is the shear stress; ris the radius of the micro-unit.
The Slurry is the Bingham fluid
The shear stress fits the condition:
0 ()/t du dr (2)
In the formula, τ0is the initial shear stress; μ(t) is the viscosity coefficient. Due to the existence of the nuclear height of the Bingham fluid, it exists:
dP ( cos ) r (3) 0 Rd p
dP cos du rr Rd p ()r r r (4) dr()() t t p 0
In the formula, rp is the nuclear radius; r0is the fluid radius. According to the boundary condition, the flow can be expressed as:
dP 3 3 2 2d ( cos ) (rpp 2 r00 3 r r ) Q 2= r d u Rd (5) 0 3
Referring to the several formulas above, α is replaced by π/2-θ and we can obtain:
3(t) QR PP0 3 3 2 ( ) R (sin cos ) (0 /4) (6) (rpp 2 r00 3 r r ) d 4 4
Similarly, we can obtain the expressions of the slurry pressure at the 3π/4 grouting hole. The results are summarized in TABLEΙ.
515 TABLE Ι. THE CALCULATION FORMULAS OF THE SYNCHRONOUS GROUTING PRESSURE DISTRIBUTION FOR THE BINGHAM FLUID.
The The Range of Grouting The Calculation Expressions θ Hole
3 QR (t) /4 PP0 3 3 2 ( ) R (sin cos ) (0 ) (rpp 2 r00 3 r r ) d 44
3' QR 3 (t) 3 / 4 PP 0 3 3 2 ( ) R (sin cos ) (0 ) (rpp 2 r00 3 r r ) d 44
DERIVATION OF THE LONGITUDINAL DISTRIBUTION MODEL OF THE GROUTING SLURRY PRESSURE
The Time-dependent Law of the Slurry Viscosity Coefficient and the Slurry Pressure
Through fitting a large number of experimental data, it is summed up that the slurry viscosity coefficient is exponentially related to time as follows:
()t AeBt (7)
Referring to the existing indoor experimental data under the different water- cement ratios [6], and we can make the Figure 3 about the viscosity coefficient varying with time as follows.
Figure 3.The slurry viscosity coefficient curve.Figure4.The slurry pressure dissipation.
516 Analyze Figure3, and we can discover that the viscosity coefficient changes gently in 90min under the same water-cement ratio. There are few relative changes of the viscosity coefficient under different water-cement ratios. As time goes by, the slurry viscosity coefficient increases rapidly. Based on Bingham fluid, the initial condition is determined: the grouting pressure is 200kPa and the time-dependent function of the viscosity coefficient is μ(t)=12.33e0.018t. Then fixing on the π/4grouting hole, we make the figure 4 about the slurry pressure dissipation with time. Clearly, in the initial stage of grouting, the slurry pressure dissipates slightly. It is considered that the value is equal to the initial pressure value of the grouting hole. As time goes by, the pressure dissipation rate continues increasing. The slurry pressure dissipated more quickly and the pressure dissipated into 0kPa about 250 minutes later. The law can be concluded that the backfill slurry pressure decreases exponentially with time along the longitudinal direction of the tunnel.
PROJECT EXAMPLE VERIFICATION
Project Overview
This passage studies the shield tunnel interval between Chegongmiao Station and Nonglin Station, which belongs to the ShenZhen Metro Line7. The outside diameter of the segment ring is 6.0m and inside diameter is 5.4m. Every segment is 0.3m thick, 1.5m wide, and every ring is composed of 6 prefabricated segments.
The Analysis on Monitoring Results of the Slurry Pressure at the 753th Ring
The monitoring slurry pressure of the segments is carefully analyzed at the 753th ring on the right line of Line 7. The results are shown in figure 5.
Figure 5.The distribution model of the slurry pressure at the 753th ring.
517 When the shield drives to the 755th ring, the monitored 753th ring is completely out of the shield hull and the soil pressure release out of the shield. At this time, the shield is simultaneously grouting, and eventually soil and grouting slurry are mixed into cement-soil. It can be seen that the slurry pressure on the outer side of the duct piece ring trends to increase gradually from top to bottom. The slurry pressure of the nethermost segment is the largest which equals self-stress of the water on the753th ring plus self-stress of the duct pieces of the single ring.
CONCLUSIONS
Based on the field monitoring data and comparative analysis, the formulas of the Bingham fluid is close to the actual situation. There is little difference between the monitoring slurry pressure and the calculated slurry pressure. Therefore, it is verified that the slurry pressure distribution model derived from Bingham fluid theory is reasonable. The slurry viscosity coefficient is exponentially related to time from the experimental data. According to the theoretical calculation formula of the slurry pressure distribution, it is concluded that the slurry pressure is linearly dependent on the viscosity coefficient. So it can be concluded that the slurry pressure dissipation decreases exponentially with viscosity coefficient. The pressure dissipation process can be divided into two stages. In the initial stage of grouting, the slurry pressure changes slightly with time in 90min. In the stage when the pressure dissipates quickly, the viscosity coefficient increases by a substantial margin and the slurry pressure decreases quickly.
REFERENCES
1. Zhang, D., Fang, Q., & Lou, H.2014. “Grouting techniques for the unfavourable geological conditions of xiang’an subsea tunnel in china,” Journal of Rock Mechanics and Geotechnical Engineering,6(5), 438-446. 2. Youn, B. Y., & Breitenbücher, R.2014. “Influencing parameters of the grout mix on the properties of annular gap grouts in mechanized tunnelling,” Tunnelling and Underground Space Technology incorporating Trenchless Technology Research,43, 290-299. 3. Oh, J. Y., & Ziegler, M., 2014. “Investigation on influence of tail void grouting on the surface settlements during shield tunnelling using a stress-pore pressure coupled analysis,” KSCE Journal of Civil Engineering,18(3), 803-811. 4. Zhang, Q., Li, P., Wang, G., Li, S., Zhang, X., & Zhang, Q., et al.2015. “Parameters optimization of curtain grouting reinforcement cycle in yonglian tunnel and its application,” Mathematical Problems in Engineering,2015(12), 1-15. 5. Fang, Y., Wang, H., Guo, J., Chen, Z., & Wu, C.2016. “Study on the mechanical behavior and the model test of segmental linings for the shield tunnel undercrossing the yellow river,” Procedia Engineering,166, 19-31. 6. Wen-Jun, R. 2005. “Research on diffusion of grouting and basic properties of grouts,” Chinese Journal of Geotechnical Engineering,27(1).
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