# Stability Analysis of the Longitudinal Slope Linear Shield Tunnel Excavation Face
## 2 Materials and Methods for Longitudinal Slope Shield Tunneling
### Transparent Soil Model Test for Longitudinal Slope Shield Tunneling
#### 2.1.2 Test Equipment  
The core components of the test system include (1) the model box system and (2) the optical observation and post-processing system. The test setup is illustrated in Figure 1. The model box system consists of a model box, a platform, and a shield model. The model box has overall dimensions of 300 mm (length) \(\times\) 240 mm (width) \(\times\) 400 mm (height) and is constructed from 5 mm thick acrylic glass. A hole is reserved on the central axis of the front face of the model box, positioned 160 mm above the bottom. A four-hole flange is used to secure the model shield, allowing the metal pusher to move freely forward and backward through the center of the isolation plate. The tunnel is externally connected to the platform's power equipment, with a lubricating oil seal ensuring proper sealing during the slow advancement of the pusher. The platform serves to secure both the model box and the power unit. The power equipment consists of a turbine reducer driven by a servo-motor, providing stable propulsion at different speed levels with a displacement accuracy of 0.1 mm. The shield model features a nested two-layer casing design, where the inner tube represents the shield tunnel lining and the outer tube represents the shield machine shell. The outer diameter of the inner tube is 65 mm, while that of the outer tube is 75 mm. In the experiment, the backward movement of the inner tube is used to simulate the active failure of the soil at the excavation face. The puller provides horizontal backward displacement, and with the restriction of the outer tube and the design of the slide rail, the inner tube can be restricted to carry out the ideal up and down displacement, and finally realize the inclined displacement with a specific slope; the schematic diagram of the shield model is shown in Figure 2. To facilitate a clearer analysis of the excavation face stability under different slope conditions, the slopes were set to \(i=-15\%\), 0%, and 15%. Here, \(i\) represents the longitudinal slope gradient of the tunnel excavation face, where \(i>0\) denotes an upward (elevated) slope and \(i<0\) denotes a downward (pitched) slope. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Material Type** &
\begin{tabular}{c} **Density** \\ **\(\gamma\) (g/cm\({}^{3}\))** \\ \end{tabular} & **Friction Angle \(\varphi\) (\({}^{\circ}\))** & **Cohesive Force c (kPa)** \\ \hline Transparent soil & 1.8 & 20 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Physical properties of the transparent soil material. The optical observation and post-processing system consists of a laser emitter, a CCD industrial camera, and the Particle Image Velocimetry (PIV) software MicroVec V3. A speckle field is generated by irradiating the transparent soil with the laser beam emitted from the laser emitter. The CCD industrial camera continuously captures the speckle field images during the test to monitor soil displacement. Figure 1: Schematic diagram of the model test. Figure 2: Schematic diagram of the shield machine model. A CCD camera (model: ICL-B2520M-SC000) was used in this experiment for image acquisition. The camera features a resolution of 2448 \(\times\) 2050 pixels and a maximum frame rate of 16 frames per second (fps), and is equipped with a lens with a focal length of 25 mm and a maximum aperture of f/1.4. The laser emitter used in this experiment was a model EPS32-3W, as shown in Figure 1. It emits a laser beam with a wavelength of 535 nm. The laser features a spectral linewidth of less than 0.1 nm, and the thickness of the laser sheet generated for the test ranged from 0.5 mm to 1 mm. MicroVec V3 software was employed to perform post-processing on the speckle images. The system captures particle images at two time steps (t\({}_{0}\) and t\({}_{0}\) + \(\Delta\)t) and performs cross-correlation analysis to calculate the average displacement of particles within predefined subregions of the images. This enables the derivation of the 2D displacement field of the soil in the observed section.