# Optimisation of Synchronous Grouting Mix Ratio for Shield Tunnels
## 3 Results and Discussion
### Uniform Test
#### 3.2.2 Effect of Slurry Rheology on Bleeding and Segregation Rates  
The slurry bleeding rate was selected to explore the influence of rheology on the bleeding phenomenon, and a three-dimensional scatter plot of the yield shear stress, viscosity coefficient, and bleeding rate was generated. As shown in Figure 4, the synchronous grouting slurry of a shield tunnel with a low yield shear stress and viscosity coefficient is more likely to cause bleeding. However, a synchronous grouting slurry with a high yield shear stress and high viscosity coefficient is less likely to bleed. According to the mechanic analysis of aggregate particles in the suspension state, when slurry aggregate particles are in the suspension state and the settling velocity is 0 m/s, the formula of medium resistance subjected to the slurry is \(F=\pi^{2}a^{2}\tau_{0}/4\); that is, the greater the yield shear stress of the slurry, and the greater the medium resistance it can provide [56]. The high viscosity coefficient provides greater internal friction force within the slurry [47]. Studies have shown that the slurry viscosity coefficient is positively correlated with consistency [57], and at this time, the slurry has a low moisture content [58], thus making it less prone to bleeding. When the yield shear stress \(\tau_{0}\) of the synchronous grouting slurry is 15 Pa \(\leq\tau_{0}\) < 20 Pa and the viscosity coefficient \(K\) is 0 Pa\(\cdot\)s \(\leq K\) < 400 \(\times\) 10\({}^{-4}\) Pa\(\cdot\)s, the bleeding rate is zero, and the slurry did not bleed. When the yield shear stress \(\tau_{0}\) is 5 Pa \(\leq\tau_{0}\) < 17.5 Pa and the viscosity coefficient \(K\) is 0 Pa\(\cdot\)s \(\leq K\) < 600 \(\times\) 10\({}^{-4}\) Pa\(\cdot\)s, the bleeding rate is  
Figure 4: A 3D scatter plot of yield shear stress, viscosity coefficient, and bleeding rate. controlled in the range of 0.5275-1.055%. When the yield shear stress \(\tau_{0}\) is 0 Pa \(\leq\tau_{0}\) < 5 Pa and the viscosity coefficient \(K\) is 200 \(\times\) 10\({}^{-4}\) Pa\(\cdot\)s \(\leq\)\(K\) < 400 \(\times\) 10\({}^{-4}\) Pa\(\cdot\)s, the bleeding rate is controlled in the range of 1.846-2.11%. Considering the segregation rate to explore the influence of rheology on the segregation phenomenon, a three-dimensional scatter plot of the yield shear stress, viscosity coefficient, and segregation rate was generated. As shown in Figure 5, the synchronous grouting slurry of a shield tunnel with a low yield shear stress and high viscosity coefficient is more likely to produce segregation, whereas synchronous grouting slurry with a high yield shear stress and low viscosity coefficient is less likely to produce segregation. The segregation of mortar depends on the stress state of the mortar aggregate; that is, the segregation of mortar is determined by its viscous resistance [59]. According to the mechanical analysis of suspended aggregate particles [56], it can be seen that when the yield shear stress of the slurry is higher, the viscous resistance of the aggregates in the slurry is also higher, the acceleration of aggregate sedimentation decreases [60], and the slurry is less likely to segregate at this time [59]. When the yield shear stress \(\tau_{0}\) of the synchronous grouting slurry is 5 Pa \(\leq\tau_{0}\) < 20 Pa and the viscosity coefficient \(K\) is 0 Pa\(\cdot\)s \(\leq\)\(K\) < 200 \(\times\) 10\({}^{-4}\) Pa\(\cdot\)s, the segregation rate is less than 0.075%, and the slurry does not segregate. When the yield shear stress \(\tau_{0}\) is 2.5 Pa \(\leq\tau_{0}\) < 15 Pa and the viscosity coefficient \(K\) is 200 \(\times\) 10\({}^{-4}\) Pa\(\cdot\)s \(\leq\)\(K\) < 400 \(\times\) 10\({}^{-4}\) Pa\(\cdot\)s, the segregation rate is controlled within the range of 0.075-2.05%. When the yield shear stress \(\tau_{0}\) is 10 Pa \(\leq\tau_{0}\) < 20 Pa and the viscosity coefficient \(K\) is 400 \(\times\) 10\({}^{-4}\) Pa\(\cdot\)s \(\leq\)\(K\) < 1000 \(\times\) 10\({}^{-4}\) Pa\(\cdot\)s, the segregation rate can be controlled in the range of 2.05-9.95%.