# Experimental Study on Permeability Evolution of Sandstone during Triaxial Compression Damage
## 3 Analysis of Test Results  
### Stress-Strain Curve and Damage Characterization  
The whole stress-strain behaviour of sandstone is the basis for studying its mechanical deformation characteristics, which show different physical significances in different yield stages. Figure 4 depicts the whole set of stress-strain curves of sandstone specimens under hydromechanical conditions. Observing Figure 4a-f, a distinct brittle behaviour is evident in the sandstone samples. As the confining pressure increases, a transition from brittle failure to ductile failure is discernible in the sandstone. This effect becomes notably pronounced, particularly under high confining pressures, accompanied by a noteworthy augmentation in the failure strength. At low confining pressures, the compression degree of fissures within the sandstone remains minimal. At this time, the crack tip area easily receives a high concentration of stress, which leads to the rapid development of cracks, and the sandstone is easily destroyed. Under elevated confining pressures, a substantial closure of micro-cracks is observed, the crack propagation is difficult, and the failure strength is larger. Under water-saturated conditions, the peak strength is reduced due to the weakening of water. According to the crack volumetric strain method [23; 24], the correlation between volume strain (\(\varepsilon_{\
u}\)) and axial strain (\(\varepsilon_{1}\)) can been examined, along with the relationship between crack strain (\(\varepsilon_{cv}\)) and axial strain (\(\varepsilon_{1}\)). The precise values of volume strain (\(\varepsilon_{v}\)) and crack strain (\(\varepsilon_{cv}\)) can be computed using the following equations:  
\[\varepsilon_{v}=\varepsilon_{1}+2\varepsilon_{3} \tag{2}\]  
\[\varepsilon_{cv}=\varepsilon_{v}-\frac{(1-2\mu)(\sigma_{1}-\sigma_{3})}{E} \tag{3}\]  
where \(\varepsilon_{1}\), \(\varepsilon_{3}\), and \(\varepsilon_{cv}\) represent axial strain, circumferential strain, and elastic volume strain, respectively; \(\sigma_{1}\) and \(\sigma_{3}\) correspond to major and minor principal stress, respectively. Additionally, \(E\) and \(\mu\) denote the elastic modulus and Poisson's ratio, respectively. The technique employed for determining the fracture closure stress of the rock involved the utilization of the axial strain difference approach. This method identifies the stress level at which the primary microfractures within the specimen achieve complete closure. The methodology is described by the following equations:  
\[\Delta\varepsilon_{1}=\varepsilon_{1}-\frac{\varepsilon_{cd}}{\sigma_{cd}}( \sigma_{1}-\sigma_{3}) \tag{4}\]  
where \(\Delta\varepsilon_{1}\) represents the axial strain difference and \(\varepsilon_{cd}\) is the axial strain associated with the threshold of crack damage stress \(\sigma_{cd}\). \begin{table}
\begin{tabular}{c c} \hline
**Seepage Pressure/MPa** & **Confining Pressure/MPa** \\ \hline
2 & \(5,10,15,20\) \\
4 & \(15\) \\
8 & \(15\) \\ \hline \end{tabular}
\end{table} 
Table 2: Test programme. According to different stress thresholds, the full stress-strain curve of sandstone can be segmented into five distinct stages as follows:  
Figure 4: Stress–strain curves of sandstone during the whole process of deformation. Stage I (microcrack closure stage): The internal primary pores and microcracks are closed in a compression manner, which is mainly the deformation of the weakest portion of the rock's internal bearing capacity, and the deviatoric stress-axial strain curve at this stage has no obvious upward-concave characteristics. The relationship between deviatoric stress and axial strain appears as an approximately linear trend, characterized by an upper limit stress value which corresponds to the rock's crack closure stress \(\sigma_{cc}\). 2. Stage II (linear elastic deformation stage): As deviatoric stress progressively escalates, the primary pores and microcracks within the rock continue to close and compact.