# 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  
During the triaxial compression process, permeability is closely associated with various deformation stages within the rock sample, such as initiation, propagation, and connection of internal fractures. To further investigate the evolution of the axial stress-strain-permeability response under the coupling of fluid flow and stress, this investigation undertakes an exhaustive analysis of the axial strain, volumetric strain, and permeability reactions exhibited throughout the complete deformation progression of sandstone under varying conditions. The distinctive correlation between permeability and axial stress-strain is visually represented in Figure 10.  
Figure 10: Typical relationship curve between permeability and axial stress–strain. Figure 9: The strength characteristics of sandstone under different conditions. Within the permeability evolution curve of sandstone, six critical permeability values are identified: (1) initial permeability under static hydrostatic pressure (\(k_{0}\)); (2) minimum permeability (\(k_{min}\)); (3) permeability at the maximum volumetric compression point (\(k_{c}\)); (4) permeability at the zero volumetric strain point (\(k_{z}\)); (5) permeability at the peak stress point (\(k\)s); (6) maximum permeability (\(k_{max}\)). In accordance with the insights gleaned from Figure 11 and Table 4, a discernible trend emerges in permeability evolution during the deformation phases of sandstone specimens under diverse conditions. This trend unfolds in four distinctive stages: gradual decrease, steady development, gradual increase, and rapid growth. These stages showcase a marked correspondence with the micro-fracture closure phase, linear elastic deformation phase, fracture development and propagation phase, and post-peak strain and failure phase, as discerned from the corresponding sandstone deviatoric stress-axial strain curves. For instance, in the case of a pore pressure of 2 MPa and a confining pressure of 10 MPa, the permeability of the sandstone sample gradually decreases from the initial permeability \(K_{0}\) of 1.21 \(\times\) 10\({}^{-17}\) m\({}^{2}\) to the minimum permeability \(K_{min}\) of 0.79 \(\times\) 10\({}^{-17}\) m\({}^{2}\), then stabilizes and gradually increases to a \(Kc\) of 1.89 \(\times\) 10\({}^{-17}\) m\({}^{2}\), and finally rapidly increases to a \(K\)s of 5.27 \(\times\) 10\({}^{-17}\) m\({}^{2}\), reaching the maximum permeability \(K_{max}\) of 13.8 \(\times\) 10\({}^{-17}\) m\({}^{2}\) at the post-peak stage. Comparing \(K_{max}\) and \(K_{min}\), there is a two-order-of-magnitude difference, and, compared with \(K_{0}\), there is a one-order-of-magnitude difference. This effect becomes more pronounced with lower confining pressures under the same pore pressure, for instance, at a pore pressure of 2 MPa and confining pressures of 15 MPa, the initial permeability \(K_{0}\) significantly increases compared with the state with a confining pressure of 10 MPa, primarily due to variations in the degree of development of inherent microcracks within the rock. Prior to the commencement of deviatoric stress loading, elevated confining pressures result in a reduction of the initial permeability, denoted as K0. Notably, the permeability of sandstone is predominantly influenced by the confining pressure, which corresponds to the disparity between the actual confining pressure and the pore pressure. As the confining pressure increases, the radial inhibitory effect on the rock sample intensifies, leading to densification of inherent micro-fractures within the sandstone, resulting in reduced openness of these fractures. This phenomenon induces a constriction and diminishment of fluid flow pathways, consequently yielding a gradual decline in permeability. The connection between fracture advancement and permeability across distinct loading stages can be delineated as follows:  
1.