## 2 Deformation Allowance of Loess Tunnel and Statistical Monitoring Samples
### Setting of Deformation Allowance  
Figure 3a,b shows the spatial position of the reserved deformation amount in the tunnel and the stress on the tunnel from different angles. Figure 3c represents the tunnel shield machine, and Figure 3d represents the stress on the tunnel support and the deformation trend of the surrounding rock and tunnel face during the forward excavation process of the shield machine. The deformation of surrounding rock refers to the shrinkage deformation of surrounding rock towards the tunnel direction due to the loss of restraint after tunnel excavation. The surrounding rock deformation is crown settlement and surrounding convergence in the monitoring items. Generally, the total deformation of surrounding rock after excavation \(\mu\) includes advanced deformation before tunnel excavation \(\mu_{\text{f}}\). Deformation from the excavation of the tunnel face to the beginning of measurement work \(\mu_{\text{i}}\) and accumulated deformation obtained during measurement \(\mu_{\text{m}}\), as shown in Figure 3. The most reliable and available is the deformation monitoring in part 3[27; 28; 29]. The deformation allowance setting includes \(\mu_{\text{m}}\) and \(\mu_{\text{i}}\) two parts; when the surrounding rock deformation is stable, it just reaches the position of the design contour line, so the secondary lining construction can not only save materials, but also ensure the lining quality [30; 31; 32].  
Figure 2: Unreasonable design of deformation allowance.  
Considering the current support conditions and construction technology, the initial support will be applied after tunnel excavation. Due to the inherent characteristics of the surrounding rock, the tunnel is designed to accommodate displacement during operation. The cumulative displacement during initial support and subsequent stability represents the initial tunnel support deformation. Excavation span, tunnel support form, construction technology, surrounding rock properties, construction methods, and other factors impact the initial tunnel support deformation [33].  
The reasonableness of the deformation allowance directly impacts the project's economy and safety. The analysis of loess tunnel deformation and deformation allowances relies on field measurement data. By examining the variations in the surrounding rock's grade, we are able to identify the deformation patterns and establish a range of appropriate deformation allowances. Based on varying rock levels, we can refer to specific guarantee rates (the percentage of the number of sections with initial support deformation less than the given value in the total number of statistical sections) to better align the deformation allowance with the project's actual conditions. Furthermore, due to the complex interaction between tunnel support and the loess strata, as well as the various uncertain factors influencing the deformation of the initial support, the field-measured data may exhibit some degree of variability. To ensure that the deformation allowance aligns with site conditions, it is suitable to utilize a range value associated with a specific guarantee rate. When the corresponding guarantee rate of a given deformation allowance is greater than 80%, the deformation allowance is considered appropriate.