# Spatial Variability of Grouting Layer of Shield Tunnel and Its Effect on Ground Settlement
## 2 Spatial Variability of Grouting Layers  
The shield tunneling method allows excavation while preventing tunnel collapse by assembling steel or concrete segmental blocks in a ring conformation to create a tunnel structure. In order to permit the advance of the shield machine and assemble the segments under the protection of the shield, the excavation diameter is usually larger than the external diameter of the segmental lining, thus a gap exists between the excavation boundary and segmental linings. The purpose of backfill grout injection is to immediately fill voids left by the shield machine body between the tunnel wall and the segmented blocks, preventing subsidence of surrounding ground and adjacent structures. Nevertheless, the distribution of the backfill-grouting cannot be uniformly distributed around segmental linings. As shown in Figure 1, the grouting layer in reality has spatial variability due to the geological randomness and mortar arbitrary flowing. Although the injected grouting is enough to fill the voids, a settlement can immediately occur after the passing of the shield tail. The settlement patterns and amount are considered to be closely related to the spatial variability of grouting layers [21]. The distribution of the grouting layer can be obtained by two methods, ground penetrating radar (GPR) and large visualized model test. GPR is a rapid nondestructive method that can recognize the interfaces of different objects. This method has been widely applied in the detection of tunnel defects to evaluate the quality of backfill-grouting layers [22; 23]. The visualized model test is another method which can directly observe the characteristics of grouting layers, and many relevant studies can be found in the literature [24]. Based on previous studies, the statistical characteristics obtained from some monitoring results of the grouting layers are listed in Table 1. The obtained results indicate that the backfill-grouting layers have significant variability. The coefficient of variation (COV) ranges from 0.1 to 0.4. Figure 2 presents the distribution of a grouting-layer thickness; the data are collected from a monitoring section reported by [PERSON] et al. [24]. To further test the normality hypotheses, the Anderson-Darling test within the Matlab was used. The Anderson-Darling test results indicate that the thickness of the grouting layer can be successfully fitted by the normal distribution, passing the test at 5% significance level. It has been found that most of the ground settlement occurs at the passing of the shield tail. The distribution of the backfill-grouting layer greatly affects the convergence patterns along the excavation surface of tunnels. As shown in Figure 3, the displacement convergence patterns can be concluded as three types based on different grouting-layer distribution. In Type I, a uniform convergence pattern corresponds to a uniform distribution of the grouting layer. In Type II, the maximum convergence pattern corresponds to as that most of the grouting fluid flows to the bottom of the tunnel. The distribution of the grouting layer can be simplified as a tangent circle outside the tunnel circle. In Type III, the spatial variability convergence pattern corresponds to a grouting layer with random defects. The first two types have been widely used to estimate ground displacement and can be found in many studies [25; 26]. However, the ground movement caused by the defective grouting layer is rarely discussed. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Source.** & **Mean** & **Span** & **COV** & **Test Method** \\ \hline [PERSON] et al. (2016) [23] & 300 mm & 220 mm–380 mm & 0.1–0.20 & Ground penetrating radar (GPR) \\ [PERSON] et al. (2019) [24] & 169 mm & 105 mm–240 mm & 0.15–0.40 & Large visualized model test \\ \hline \hline \end{tabular} Note: COV refers to the coefficient of variation.  
\end{table} 
Table 1: Statistic parameters of grouting-layer thickness. Figure 1: Schematic diagram of backfill-grouting-layer distribution.