## 2 Similarity Theory of Fluid-Solid Coupling  
A rock mass is composed of a rock block and a structural plane; in most cases, the rock block also contains small and dense fissures, and the structural plane is composed of fissures, joints, fault strata, unconformity, and foliated surface. When the distribution of these structural planes is relatively uniform, the seepage flow of the rock mass depends on the fissures, and the rock block is relatively impermeable, the rock mass with fissures is regarded as an equivalent continuous medium from a macroscopic point of view. Therefore, the seepage flow of the rock mass can be regarded as an equivalent continuum seepage flow; the permeability coefficient tensor is used to describe the permeability of the rock mass; the stress in the rock mass is regarded as equivalent stress; and the stress tensor is used to describe the stress in the rock mass. [PERSON] [12] and [PERSON] [13] analyzed an equivalent continuous medium model for coupling the seepage and stress fields in rock masses.  
According to the similarity principle of physical similarity model testing [14], it is required that the geometric dimensions, boundary conditions, loads, bulk density, strength, deformation characteristics, and hydraulic characteristics of the similar materials of the model follow certain similarity laws. [PERSON] [11] conducted a theoretical analysis of the mathematical model of solid-fluid coupling in homogeneous continuous media. Firstly, the basic mathematical model of the solid-fluid coupling of an equivalent homogeneous continuum was adopted:  
(1) Seepage equation:  
\[K_{x}\frac{\partial^{2}p}{\partial^{2}x}+K_{y}\frac{\partial^{2}p}{\partial^{ 2}y}+K_{z}\frac{\partial^{2}p}{\partial^{2}z}=S\frac{\partial p}{\partial t} +\frac{\partial e}{\partial t}+W \tag{1}\]  
(2) Equilibrium equation:  
\[\sigma_{ijj}+X_{j}=\rho\frac{\partial^{2}u_{i}}{\partial t^{2}} \tag{2}\](3) Effective stress equation:  
\[\sigma_{ij}=\overline{\sigma_{ij}}+\alpha\delta p \tag{3}\]  
The above three equations are the basic solid-fluid coupling equations for homogeneous continuous media, where  
\(Kx\), \(Ky\), and \(Kz\) are the permeability coefficients in the three coordinate directions, with \(Kx=Ky=Kz\); \(P\) is the water pressure; \(s\) is the water storage coefficient; \(e\) is the volume strain; \(W\) is the source-sink term; \(\sigma_{ij}\) is the total stress tensor; \(\overline{\sigma_{ij}}\) is the effective stress tensor; \(X_{j}\) is the volume force; \(\rho\) is the density; \(\alpha\) is the effective stress coefficient of Biot; and \(\delta\) is the Kronecker sign.  
From the equilibrium Equation (2), combined with its geometric equation, 15 basic physical equations are obtained to eliminate the stress and deformation components of the aforementioned equation containing only the displacement component:  
\[\left\{\begin{array}{l}G\
abla^{2}u+(\lambda+G)\frac{\partial c}{\partial x} +X=\rho\frac{\partial^{2}u}{\partial x^{2}}\\ G\
abla^{2}  
From the similarity of the stress, we obtained \(C_{\sigma}=C_{\gamma}C_{l}\). At the same time, when the equivalent pore pressure coefficient is equal to 1, \(C_{p}=C_{\gamma}C_{l}\), that is, the water pressure is similar;  
From the similarity of the source and sink terms, we obtained \(C_{w}=\frac{1}{\sqrt{C_{l}}}\);  
From the similarity of the storage coefficient, we obtained \(C_{S}=\frac{1}{C_{\gamma}\sqrt{C_{l}}}\);  
From the similarity of the permeability coefficient, we obtained \(C_{K}=\frac{\sqrt{C_{l}}}{C_{\gamma}}\).