## 3 Experimental Apparatus  
### Preparation and Procedure  
Physical model tests are laboratory simulations of the geomechanical problems at a proportionally reduced scale, which are often employed to clarify critical mechanisms, and are an instrument for validation or calibration of numerical models [34; 35]. The theory and techniques for statical and geomechanical models were methodically developed by [PERSON] [34; 36]; thereafter, they have been employed in a variety of engineering practices for stability evaluation [35; 36]. Similarity theory imposes a set of similarity requirements on physical models in regard to the geometry, physical-mechanical properties, boundary conditions, and initial states. These similarity requirements can be derived from the force equilibrium equations, geometric equations, Hooke's law and boundary conditions according to the elastic-plasticity theory and dimensional analysis [34; 37]. Some similarity coefficients, that are defined as the ratios of prototype to model parameters, must be constants. These parameters are geometry, stress, strain, displacement, modulus, Poisson's ratio, cohesion, etc. [34; 37].  
In the physical model tests, the geometry and unit weight of soils are taken as control physical quantities based on the similarity theory. Thereafter, a 1/20 model scale of the geometry, elastic modulus (\(E\)) and cohesion (\(c\)), and a 1/1 model scale of the internal friction angle (\(\varphi\)), bulk density (\(\gamma\)) and Poisson's ratio (\(\mu\)) were determined for the experimental tests. The model box size is 4000 mm \(\times\) 1500 mm \(\times\) 2000 mm (length \(\times\) width \(\times\) height), as shown in Figure 3. The foundation pit's support scheme in the model test is the same as the aforementioned engineering prototype. The model tunnels are made of gypsum mixed with water, and the diaphragm walls are simulated with organic glass. The elastic modulus of the tunnel liner and diaphragm wall in the prototypes were 34.5 GPa and 28 GPa, respectively. The elastic modulus of the model tunnel is 1.725 GPa, while that of the model diaphragm wall is 1.4 GPa. Both of these values comply with the mechanical similarity constant. The model tunnels have a thickness of 15 mm, an outer diameter of 300 mm, an inner diameter of 270 mm, and a length of 1500 mm; the model diaphragm wall has a thickness of 40 mm, a height of 400 mm, a width of 1000 mm, and a length of 1750 mm. The model tunnels and the diaphragm wall were preburied into the soils before the excavation of the foundation pit. The steel supports are simulated by using the thin steel pipes, which are installed in the holes reserved for the connection during the excavation. The photos descripting the experiments are illustrated in Figure 4.  
Figure 3: Layout and geometry of the model.  
The existing tunnels are mainly located in three soil layers, namely, backfilling, silt and silty clay. Turnnels and the foundation pit were both built above the water table line. Therefore, soil-like materials were prepared in a dry condition, and the groundwater is not considered. The mechanical similarities of soils are employed for realization of the similar materials in physical model tests. The soil-like materials were made with four materials: barite powder (BP), bentonite (BT), gypsum (GP) and lime (LM), of which gypsum and lime were used as the binder. The soil-like material compositions and formulations are shown in Table 1, where the symbols \(p\) and \(m\) represent prototype and model parameters, respectively.