# Experimental Study on Permeability Evolution of Sandstone during Triaxial Compression Damage
## 3 Analysis of Test Results
### Permeability Characteristics
#### 3.3.1 Relationship between Permeability and Axial Stress-Strain
With the initial loading of deviatoric stress, the combined effect of confining pressure and deviatoric stress leads to further closure of pores and micro-fractures within the rock. As new fluid flow pathways have yet to establish, a gradual decrease in permeability ensues until the point of minimum permeability \(K_{min}\) becomes evident. 2. During the linear elastic deformation stage, the sandstone approaches an elastic behaviour, where the fracture aperture remains approximately unchanged or slightly decreases. Fluid flow channels remain relatively constant or narrow in width, leading to a near-constant or slightly reduced permeability. 3. In the phase of stable crack propagation, the newly formed fractures within the sandstone have minimal aperture and connectivity. The rock undergoes a shift from volume compression to volume expansion. This phase corresponds to the maximum volumetric compression point permeability \(K_{c}\), where the inhibitory effect of confining pressure weakens and permeability gradually increases. 4. During the phase characterized by unstable crack propagation, the interconnection of internal fractures intensifies, thereby leading to a substantial augmentation in the count of fluid flow pathways and the rapid escalation of permeability. The permeability \(K\)s is observed at the peak stress point. Upon complete failure of the sandstone, macroscopic interconnected fractures form, leading to shear failure along these interconnected fractures, resulting in the maximum permeability \(K_{max}\). To comprehensively dissect the permeability evolution pattern within sandstone, this study proceeds to delve into the analysis of permeability at distinct stress thresholds, as delineated in Table 5. The permeability associated with the closure stress of rock fractures, denoted as \(K_{cc}\), and the permeability corresponding to the initiation of fracturing stress, \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Seepage Pressure/MPa** & **Confining Pressure/MPa** & \(\mathbf{K_{a}}\) & \(\mathbf{K_{min}}\) & \(\mathbf{K_{c}}\) & \(\mathbf{K_{x}}\) & \(\mathbf{K_{x}}\) & \(\mathbf{K_{x}}\) & \(\mathbf{K_{max}}\) \\ \hline \multirow{2}{*}{2} & 5 & 1.37 & 0.48 & 12.3 & 17.3 & 23.5 & 28.8 \\  & 10 & 1.21 & 0.79 & 1.89 & 3.75 & 5.27 & 13.8 \\ \hline \multirow{2}{*}{2} & & 1.27 & 0.43 & 1.79 & 3.36 & 3.68 & 8.26 \\  & 15 & 2.03 & 1.37 & 2.67 & 5.56 & 5.83 & 9.46 \\ \cline{1-1}  & & 3.52 & 2.56 & 4.03 & 11.1 & 16.6 & 27.1 \\ \hline \multirow{2}{*}{2} & 20 & 1.20 & 0.77 & 1.43 & 3.09 & 2.32 & 3.23 \\ \end{tabular}
\end{table} 
Table 4: Six key permeability values of sandstone during the whole stress–strain process under different conditions. Figure 11: Relationship between sandstone permeability and axial stress–strain under different working conditions. denoted as \(K_{ci}\), are analysed in depth. Combining Tables 4 and 5 reveals that the difference between \(K_{cc}\) and the minimum permeability \(K_{min}\) for different conditions is negligible. During the micro-fracture closure and linear elastic deformation phases, the permeability \(K_{cc}\) can be considered as equivalent to the minimum permeability \(K_{min}\). The permeability \(K_{cl}\), associated with the initial state of rock fracturing, is lower than the value of \(K_{c}\) due to the relatively underdeveloped nature of fluid flow pathways.