# Optimisation of Synchronous Grouting Mix Ratio for Shield Tunnels
## 1 Introduction  
To alleviate urban traffic, it is necessary to further develop and utilise underground spaces. Shield tunnel construction is a core technology in the development of urban underground public spaces. During the shield construction process, to prevent soil disturbance or deformation in the surrounding area of the construction site [1], the waterproof and anti-seepage performance of the segment lining structure must be enhanced. This requires shield synchronous grouting to be poured between the surrounding rock and tunnel lining [2, 3, 4]. In actual projects, grouting slurry is usually required to have good fluidity and stability to avoid problems such as segregation, stratification, and bleeding. Therefore, the relationship between the grout components and physical properties has been studied worldwide. Additionally, the flow and deformation properties of grout have been studied based on the rheology theory, and the relationship between material characteristic parameters and engineering properties has been established [5, 6, 7]. Research on slurry mix ratios has mainly focused on the influence of slurry components and their contents on slurry properties. By studying the effects of the dosage of bentonite, water-reducing agents, and fly ash [8, 9, 10] on the volume shrinkage deformation [8, 10], time loss of fluidity [9], bleeding rate, setting time [10], mechanical properties [11], and the water retention rate of slurry [12], it was found that as the cement dosage increases, the slurrysetting time and bleeding rate decrease, and the compressive strength increases. As the fly ash dosage increases, the slurry workability improves. As the bentonite dosage increases, the water retention and slurry viscosity increase. Based on these findings, the proportion of slurry components was optimised, and an admixture suitable for synchronous grouting slurry was developed [13]. In addition, by using styrene-acrylic emulsion, pure acrylic emulsion, and emulsified asphalt [14] to modify the synchronous grouting fluid, the effects of these three components on the performance of mortar were analysed in detail and it was found that for highly permeable aquifers, turbidity and system pH must also be considered [15]. Several related studies have been conducted on the rheological properties of slurries, and the addition of rice husk ash has been shown to affect the rheological properties of mortar. As the amount of rice husk ash increases, the yield stress and plastic viscosity of repair mortar increase. Rice husk ash does not change the rheological type of cement slurries [16]. The addition of a thickener reduces mortar fluidity but increases the yield stress and plastic viscosity [17; 18]. Although anionic viscosity modifiers can increase the yield stress of slurries, the improvement effect weakens as the dosage increases, and a super absorbent resin viscosity regulator can increase the yield stress and plastic viscosity of slurries [18]. Shear-resistant synchronous grouting mortar differs from conventional grout because its properties are similar to toothpaste and retain high fluidity after a long interval [19]. Studies on the rheological properties of slurries have been performed using numerical simulations. [PERSON] et al. [20] used numerical simulation methods to simulate the rheology of granular materials in the Navier-Stokes solver program. [PERSON] [21] used the plastic analysis method to calculate the critical yield stress and performed a bounded analysis on it. [PERSON] [22] used the generalised moving object method to simulate the movement and static segregation of coarse aggregates and studied the effects of mortar yield stress and viscosity on the movement process of aggregates. [PERSON] et al. [17] established a method that considered flocculation, hydration, and particle aggregation. The novel yield stress evolution model was jointly affected by the interaction between the cement paste and the three factors.