## 2 Indoor Test  
### Similar Materials Test  
The similarity test is a widely used research method that is based on the similarity theorem. This theorem uses a certain similarity ratio to the original rock produced in the field to conduct a series of indoor tests. The data recorded by the test are then used to deduce the field situation and solve any engineering problems that may arise during the actual project. To accurately reflect the deformation characteristics and effects of the surrounding rock and support during tunnel excavation, it is important to establish a clear relationship between the simulation prototype and the test model. The First Similarity Theorem explains the nature of similar phenomena, which refers to a group of phenomena sharing identical equations and criteria. When determining similar phenomena, two conditions must be satisfied: firstly, the ratios of corresponding physical quantities in similar phenomena should remain constant, encompassing geometric, kinematic, dynamic, and other factors; secondly, similar phenomena can be described by the same fundamental equations, meaning both the prototype and the model must adhere to the basic equations of elasticity theory: equilibrium equations, geometric equations, and boundary conditions. The Second Similarity Theorem leverages the relationships among physical quantities to express the intrinsic relationships of physical processes or phenomena. If a physical process or phenomenon cannot be described by equations, but a certain physical quantity has a decisive impact on the research subject, similarity criteria can be determined through dimensional analysis. The Third Similarity Theorem, also known as the Existence of Similarity Theorem, posits that for phenomena of the same kind, if they satisfy the condition that the numerical values of their similarity criteria for single-valued quantities are equal, then these phenomena are considered to be mutually similar. The physical parameters of the specimens involved in this test contain compressive strength (\(\sigma\)), material strain (\(\varepsilon\)), angle of internal friction (\(\varphi\)), [PERSON]'s ratio (\(\mu\)), unit weight (\(\gamma\)), model test displacement (\(\chi\)), elasticity modulus (\(E\)), model dimensions (\(L\)) and cohesive (\(c\)). Based on the similarity triple theorem [25; 26], it can be seen that the relationship equation between different variables is as shown in Equation (1). \[f(\sigma,\varepsilon,\varphi,\mu,\gamma,\chi,E,L,c)=0 \tag{1}\]  
Calculations are available based on the method of quantitative analysis:  
\[F\bigg{(}\sigma,\varepsilon,\varphi,\frac{\gamma L}{\sigma},\frac{\chi}{L}, \frac{E}{\sigma},\frac{\chi}{\sigma},\frac{c}{\sigma}\bigg{)}=0 \tag{2}\]  
The derivation of the similarity ratio relationship for each physical quantity yields:  
\[\left\{ \begin{array}{c}C_{\varepsilon}=1\\ C_{\varphi}=1\\ C_{\gamma}C_{L}=C_{\sigma}\\ C_{\chi}=C_{L}\\ C_{E}=C_{\sigma}\\ C_{c}=C_{\sigma}\end{array} \right. \tag{3}\]  
In Formula (3), \(C_{\varepsilon}\), \(C_{\varphi}\), \(C_{\gamma}\), \(C_{L}\), \(C_{\chi}\), \(C_{E}\) and \(C_{c}\) are similar ratios of \(\sigma\), \(\varepsilon\), \(\varphi\), \(\mu\), \(\gamma\), \(\chi\), \(E\), \(L\) and \(c\). Meanwhile, this paper focuses on the Tianhe Road station, which has an overburden depth of approximately 19 m. The main body of the station is 16 m deep, with a cross-section width of 27.7 m on both sides. The dimensions of the model box used for the test were 1.8 m in height, 1.8 m in length, and 1.0 m in width. The mechanical parameters of the specimen included compressive strength, weight, and modulus of elasticity. Using the similarity triple theorem, the geometric similarity ratio of the test was calculated to be 35. The formula is shown in Equation (4). \[C_{L}=L_{H}/L_{M}=1/35 \tag{4}\]  
where \(C_{L}\) is the geometric similarity ratio. \(L_{H}\) is the model geometry. \(L_{M}\) is the prototype geometry.