# Spatial Variability of Grouting Layer of Shield Tunnel and Its Effect on Ground Settlement
## 5 Engineering Applications  
The construction of a tunnel needs to strictly control the ground-surface settlement, especially in urban metro projects. The above study shows that when the spatial variability of the grouting layer has a significant impact on the ground settlement, which cannot be ignored in the tunneling process. It emphasized the importance of the investigation of the grouting layer quality. The construction safety may not be guaranteed by the amount of the grouting injection volume. Additionally, the spatial variability of soil mechanics parameters is a secondary factor affecting the ground settlement. A detailed site characterization before the tunnel construction should be conducted to obtain enough information for reducing uncertainties in soil parameters.  
In the design phase, a \"characteristic value\" is often used to account for the variability of materials [38]. Eurocode 7 recommends that the \"characteristic value of a geotechnical parameter shall be selected as a cautious estimate of the value affecting the occurrence of the limit state\" [38]. In the case of this study, it means selecting the 95% fractile as the \"characteristic value\". Engineers can optimize the construction plan according to the predicted \"characteristic ground-surface settlement\".  
Figure 10: Effect of the grouting-layer parameters on settlement. (a) Grouting-layer thickness; (b) COV(\(t\)).  
Figure 9: Effect of the soil SOFs on settlement. (a) \(s_{\text{2}}\); (b) \(s_{\text{h}}\).  
Generally speaking, there are two methods for predicting the maximum ground settlement \(s_{max}\) under the random field: (a) The theoretical formula derived from the classification of probability distribution; (b) The prediction curve based on the statistical value of numeric simulation. In this study, the first method is used to provide a practical and realistic approach for maximum settlement estimation.  
According to the normal probability distribution function, the maximum ground settlement \(s_{max}\) of 95% confidence degree can be obtained,  
\[s_{\text{max}}=\mu+1.65\sigma \tag{5}\]  
where \(\mu\) is the mean value of a specific random case, \(\sigma\) is the standard deviation of a specific random case.  
The definition of \(COV(t)\) is shown as below,  
\[\text{COV}(t)=\frac{\sigma_{t}}{\mu_{t}} \tag{6}\]  
where \(\mu_{t}\) is the mean value of grouting-layer thickness, \(\sigma_{t}\) is the standard deviation of grouting-layer thickness.  
The theoretical formula for calculating the \(s_{max}\) can be obtained by combining Equations (5) and (6),  
\[s_{\text{max}}=\mu_{t}(1.65\times\text{COV}(t)+1) \tag{7}\]  
In practice, the mean value of the grouting-layer thickness can be easily obtained using the injected grouting volume. Thus, engineers can use this approach to evaluate the maximum settlement once the grouting distribution is determined.  
The characteristic value of the numeric simulations is selected as the 95% fractile of the overall simulations to draw the numeric simulation curve. Figure 11 shows the comparison between the maximum settlement obtained from the theoretical prediction approach and numeric simulations. It can be seen from this figure that the maximum settlement increase with the increasing COV of grouting-layer thickness. The slope of the predicted curve based on numeric simulation is smaller than the one based on the theoretical formula, whereas small discrepancy is noted with the increase of the COV of grouting layer. The predicted settlement is a little larger than the numeric results, indicating a conservative estimation of the surface settlement. The discrepancy is around 10% when the COV of grouting layer reaches 0.4, which can be accepted in the engineering practice.  
Figure 11: Predicted curve for ground-surface settlement.