## 2 Similar Model Test Design
### Test Equipment  
During the similar model scaling tests conducted in the shield tunneling chamber, the primary components utilized are the loading equipment system, sample molds, and monitoring equipment. The loading equipment system is a comprehensive setup that encompasses a loading frame, a sophisticated control system, an actuating system, and a data-monitoring system. These elements work in tandem to provide precise control and data collection throughout the testing process. The sample molds play a crucial role in the preparation of scaled models. They consist of a model box specifically designed for crafting scaled-down samples that mimic the actual tunnel environment. Additionally, a tunnel model is included to simulate the shield driving and lining processes, thereby replicating the conditions encountered during real-world tunnel construction. The data-monitoring system is an integral part of the testing setup. It is tasked with diligently monitoring the stress changes and distribution patterns in the strata located above the tunnel face, particularly in the area directly ahead of the shield tunneling process. Furthermore, this system also tracks the surface deformation processes occurring in the strata on the sides of the scaled test model. Through this comprehensive monitoring, valuable insights into the mechanical behavior of the tunnel and surrounding strata are obtained, facilitating a deeper understanding of the tunneling dynamics. The details are as follows:  
1. Loading device  
The testing apparatus employed is a large-scale dynamic and static coupling loading system designed for assessing slope stability. This advanced system comprises several key components: a return reaction frame serving as the main engine, an electro-hydraulic servo loading system, an electrical driving system, a measurement control system, and a computer control and data-processing system. This integrated system is capable of simultaneously applying dynamic and static loads in both vertical and horizontal directions. This dual-loading capability allows for an in-depth investigation into the mechanical behavior of large-scale soil samples under \begin{table}
\begin{tabular}{l l l} \hline \hline
**Physical Quantity** & **Symbol** & **Similarity Ratio** \\ \hline Geometric dimension & \(C_{L}\) & 20 \\ Density & \(C_{\rho}\) & 1 \\ Elasticity modulus & \(C_{E}\) & 1 \\ Strain & \(C_{e}\) & 1 \\ Stress & \(C_{\sigma}\) & 1 \\ Displacement & \(C_{A}\) & 20 \\ Velocity & \(C_{\tau}\) & 1 \\ Accelerated velocity & \(C_{a}\) & 0.05 \\ Time & \(C_{t}\) & 20 \\ Frequency & \(C_{f}\) & 0.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Similarity relationship between engineering prototype and indoor similar model. the complex interplay of dynamic and static forces. A schematic representation of the equipment is presented in Figure 1.  
During the testing procedure, the meticulously prepared sample is positioned on a trolley. The electrical driving system then precisely maneuvers the trolley to the optimal loading location. The electro-hydraulic servo loading system takes over, expertly controlling the horizontal and vertical servo actuators to impart predetermined loads onto the sample. Throughout the test, the measurement control system, in conjunction with the computer control and data-processing system, diligently records and stores the horizontal and vertical displacements of the sample model within the control computer. This comprehensive data capture ensures a thorough analysis of the sample's response to the applied loads. The back reaction frame type adopts the form of a reflexive integrated host frame, uses the whole cast frame structure, and forms a closed stress frame. The frame structure is stable and rigid, which can ensure the safety and stability of the test process. The frame size (length \(\times\) width \(\times\) height) of the host frame is (2800-3200) \(\times\) (800-1000) \(\times\) (2900-3200) mm.