# Optimisation of Synchronous Grouting Mix Ratio for Shield Tunnels
## 5 Conclusions  
This paper investigates the effects of the dosages of water reducer and latex powder on the fluidity, segregation rate, and bleeding rate of mortar. It reveals the degree of influence of five mixed proportion factors on the rheological parameters of mortar, as well as the impact of rheological parameters on the segregation rate and bleeding rate of mortar. Finally, the mortar mix proportion is optimised under specific constraints and validated through experimentation. The conclusions are as follows:  
1. As the water-reducing agent dosage increased, the fluidity of the synchronous grouting slurry increased, and the segregation rate first decreased and then increased. When the water-reducing agent dosage was 0.73, the slurry segregation rate was the lowest, and as the latex powder dosage increased, the slurry fluidity first increased and then decreased. The slurry segregation rate was lowest when the latex powder dosage was 0.37. 2. The rheological behaviour of the synchronous grouting slurry conformed to the H-B model. When the shear rate was lower than 10 s\({}^{-1}\), the yield shear stress of the slurry decreased, and the viscosity decreased rapidly as the shear rate increased. When the shear rate was 10 s\({}^{-1}\), the shear stress increased linearly as the shear rate increased, and the viscosity was stable. The fitting results indicate that the regression model is highly accurate. 3. After conducting a multiple linear regression analysis, it was found that the bentonite -water ratio has the greatest impact on the rheological properties of the grouting slurry. 4. Slurries with a high a yield shear stress and viscosity coefficient were unlikely to bleed, and slurries with a high yield shear stress and low viscosity coefficient were unlikely to segregate. When the yield shear stress \(\tau_{0}\) of the slurry was 15 Pa \(\leq\tau_{0}\) < 20 Pa and the viscosity coefficient \(K\) was 0 Pa\(\cdot\)s \(\leq K\) < 400 \(\times\) 10\({}^{-4}\) Pa\(\cdot\)s, the slurry bleeding rate was zero and no bleeding occurred. When the yield shear stress \(\tau_{0}\) was 5 Pa \(\leq\tau_{0}\) < 20 Pa and the viscosity coefficient \(K\) was 0 Pa\(\cdot\)s \(\leq K\) < 200 \(\times\) 10\({}^{-4}\) Pa\(\cdot\)s, the segregation rate was less than 0.075% and no segregation occurred. 5. Through the multi-objective programming optimisation method and MATLAB optimisation toolbox, a mix ratio that meets the required specifications was obtained. The optimised slurry fluidity, 3 h bleeding rate, 24 h bleeding rate, segregation rate, setting time, and 28 d compressive strength were 257.5 mm, 0.71%, 0.36%, 3.1%, 6.7 h, and 2.61 MPa, respectively, which meet the requirements of synchronous grouting slurry for shield tunnels. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Cement** & **FLYASH** & **Sand** & **Bentonite** & **Water** & **Water Reducing Agent** & **Late Powder** \\ \hline
**[kg/m\({}^{3}\)]** & **[kg/m\({}^{3}\)]** & **[kg/m\({}^{3}\)]** & **[kg/m\({}^{3}\)]** & **[kg/m\({}^{3}\)]** & **[kg/m\({}^{3}\)]** & **[kg/m\({}^{3}\)]** \\ \hline
143.490 & 407.510 & 874.610 & 74.390 & 413.250 & 1.653 & 0.276 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Mixture ratio of high-performance grouting slurry behind shield tunnel wall. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Fluidity** & **3 h Bleeding Rate** & **24 h Bleeding Rate** & **Segregation Rate** & **Setting Time** & **28 d Strength** \\ \hline
**[mm]** & **[\%]** & **[\%]** & **[\%]** & **[h]** & **[MPa]** \\ \hline
257.50 & 0.71 & 0.36 & 3.1 & 6.70 & 2.61 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Verification of test results. * 6 The optimised grouting slurry meets the requirements for the synchronous grouting slurry in shield tunnels, effectively preventing soil disturbance and deformation in the surrounding areas of underground construction sites. However, in addition to optimising the slurry properties, improving construction techniques can also enhance the quality of shield tunnel construction.