## 3 Test Results and Analysis
### Sergage Model Building Scheme  
To investigate the fluid flow characteristics of weakly cemented sandstone under various confining pressures, pore pressures, and deviatoric stresses, numerical simulations were performed using the UDEC 7.0 software, and the physical mechanical parameters obtained from laboratory tests were incorporated into the model.  
The numerical simulations utilized the steady-state flow method provided by the software. Pressure differentials were applied at the upper and lower boundaries of the rock sample, while monitoring the average flow rate, Q.  
The numerical simulation model employed displacement loading with a velocity of 0.1 mm/s. The bottom boundary was fixed in the y-direction, and the left and right boundaries were impermeable, while the top and bottom boundaries were permeable. Different pore pressure differentials, confining pressures, and deviatoric stress conditions for weakly cemented sandstone were recorded by altering the top boundary pore pressure, As shown in Figure 5.  
The initial parameters of the model are shown in Table 3, with some mechanical parameters already optimized based on previous research [32].  
experiments being valid only when flow reaches a steady state. In physical experiments, the steady state of flow conditions is determined based on the equilibrium of pore pressure at the top and bottom of the rock specimen, ensuring that no changes occur. Additionally, the flow rates at the top and bottom of the specimen should be equal, meaning that the inflow equals the outflow. At this point, flow conditions have reached equilibrium, allowing for accurate permeability calculations [33; 34; 35; 36; 37].  
In numerical simulations, it is possible to monitor pore pressure, flow velocity, and other data using code inputs to assess whether flow has reached a steady state [29]. The simulation in this experiment focuses on changes in permeability in the final equilibrium state and does not provide a detailed study of permeability throughout the entire loading process.  
[PERSON]'s law is used to calculate liquid permeability, and the formula is as follows:  
\[k=\frac{\mu LQ}{\Delta PA} \tag{7}\]  
where \(K\) is permeability; \(\mu\) is the dynamic viscosity coefficient of the liquid, taking \(\mu=1.005\times 10^{-3}\) Pa\(\cdot\)s; \(L\) is the height of the rock 0.1 m; \(Q\) is the flow rate of fluid through the rock per unit time; \(A\) is the cross-sectional area of the rock; and \(\Delta P\) is the difference in pore-pressure at both ends of the rock.  
In UDEC, the model block is impervious to water, and fluid can only migrate in the joint, as shown in Figure 6. The inter-plane fluid flow in the model is calculated by the following formula:  
\[Q=-\frac{\Delta PK_{j}\mu}{L} \tag{8}\]  
\(kj\) is the permeability factor of the joint, the theoretical value is \(1/12\)\(\mu\). \(\mu\) is the fluid viscosity coefficient = 83.3. a is the joint aperture \(a=a0+un\); \(a0\) is the joint aperture under no pressure; \(un\) is the normal displacement between the joints. \(L\) is the length of the joint between regions; \(\Delta P\) is the difference in pore-pressure at both ends of the rock.