# Experimental Study on the Pre-Peak Mechanical and Seepage Characteristics of Granite
## 3 Analysis of Test Results  
### Mechanical Characteristics  
#### 3.1.1 Pre-Peak Progressive Failure Analysis  
In the loading process, the rocks showed different mechanical characteristics at different stress stages. According to the deformation of the rocks and the development of cracks, the concept of a stress threshold was introduced to characterize the stress-strain process of the rocks before the peak into a gradual failure process and to analyze the change rule of the rock stress threshold, which is of great significance for monitoring the stability of the surrounding rock in seabed bedrock mining. The characteristic thresholds in the pre-peak stress-strain process contain a crack closure threshold \(\sigma_{cc}\), crack initiation threshold \(\sigma_{ci}\), crack damage threshold \(\sigma_{cd}\), and peak strength \(\sigma_{p}\)[28,29]. The pre-peak stress-strain process in rocks can be divided into four stages based on the stress threshold: (1) the crack closure stage (OA), (2) the linear elasticity stage (AB), (3) the stable crack expansion stage (BC), and (4) the unstable crack expansion stage (CD), as shown in Figure 4.  
A lot of research has been conducted on the determination of stress thresholds. [PERSON] et al. [30] used acoustic emission techniques to identify the crack initiation strength (\(\sigma_{ci}\)) and crack damage strength (\(\sigma_{cd}\)) and found that the number of acoustic emission events captured starts to increase when the stress reaches \(\sigma_{ci}\). However, determining other stress thresholds is more ambiguous due to noise in the acquisition environment. By observing the stress-volumetric strain curve, it was determined that the turning point of the curve is the crack damage strength \(\sigma_{cd}\). This method can determine the \(\sigma_{cd}\) more intuitively, but it cannot accurately identify the \(\sigma_{ci}\)[31]. Therefore, the crack initiation strength (\(\sigma_{ci}\)) is determined with the help of the crack volumetric strain, and the relevant formulation is given as follows:  
\[ \begin{array}{c}\varepsilon_{v}=\varepsilon_{1}+2\varepsilon_{3}\\ \varepsilon_{cv}=\varepsilon_{v}-\frac{(1-2\mu)(\sigma_{1}-\sigma_{3})}{ \varepsilon}\end{array}  \tag{2}\]  
Figure 3: Flow chart of granite conventional triaxial test. where \(\varepsilon_{1}\), \(\varepsilon_{3}\), \(\varepsilon_{v}\), and \(\varepsilon_{cv}\) are the axial strain, radial strain, volumetric strain, and crack volumetric strain, respectively, where E and \(\mu\) are the modulus of elasticity and Poisson's ratio, respectively. Considering that rock samples have greater randomness during the transition from the crack closure stage to the elasticity stage, there will be a significant error if the stress-strain curve is used to determine the crack closure strength [11]. Therefore, the axial strain difference curve was used to determine the crack closure strength, as shown in Figure 5, and its calculation formula [11] is as follows:  
\[\Delta\varepsilon_{1}=\varepsilon_{1}-\frac{\sigma_{1}-\sigma_{3}}{\sigma_{cd} }\varepsilon_{cd} \tag{3}\]  
where \(\Delta\varepsilon_{1}\) and \(\varepsilon_{cd}\) are the axial strain difference and the axial strain corresponding to the crack damage strength (\(\sigma_{cd}\)). Figure 4: Schematic diagram of progressive failure process in rocks. Figure 5: Determination of axial strain difference using stress–strain curve. According to the axial strain difference calculated using the above formulation, the axial strain difference-stress curve can be plotted, as shown in Figure 6. The stress value corresponding to the peak of the curve is the crack closure strength (\(\sigma_{ci}\)). Stress-volumetric strain curves, the crack volumetric strain, the axial strain difference, and stress-strain curves were used to determine the crack damage strength (\(\sigma_{cd}\)), crack initiation strength (\(\sigma_{ci}\)), crack closure strength (\(\sigma_{cc}\)), and peak strength (\(\sigma_{p}\)), respectively, of the rock during progressive rock failure under different confining pressures.