# Percolation Threshold of Red-Bed Soft Rock during Damage and Destruction
## 3 Results and Discussion
### Percolation Test Results of Compression Damage of Red-Bed Soft Rock  
#### 3.2.1 AE Test Results under Uniaxial Compression  
Damage to the rock sample after compression is shown in Figure 5b. By extracting the ringing count in the AE of rock samples, the relationships between strain, ringing count, accumulative ringing count and stress were obtained, as shown in Figure 7. According to the ringing count curves in Figure 7a1-a3, there are almost no AE events in silty mudstone at the initial stage of the test, and only a small amount of AE events were scattered. With increasing strain, the number of AE events gradually increases. After a peak number of AE events, their number begins to decrease. Therefore, the damage characteristics of silty mudstone can be summarized into the following five stages:  
1. Initial stage of damage: this stage roughly includes the compaction stage and the early elastic stage of the rock sample. At this stage, the amount of AE is zero or small, indicating that no damage or minor damage has occurred to the sample. The initial microfracture in the rock sample is squeezed by external force and closes gradually. Most of the energy exerted on the rock sample by external forces is converted into elastic potential energy, which is stored in the rock sample. Only a small amount of energy cannot be converted effectively and causes a small amount of damage, so most damage to the rock sample at this point is initial damage. The measured porosity value of soft rock is 0.084 and the permeability value of soft rock is 1.02 \(\times\) 10\({}^{-9}\) m/s. Figure 6: The fixed point of renormalization transformation in soft rock failure. 2. Stable development of damage stage: this stage includes the middle and later stages of the elastic stage. During this period, the amount of AE increases and is relatively stable, indicating that under external force, the internal damage of the rock sample begins to occur and new microfractures appear. With the stable increase in microfractures, damage also develops steadily. 3. Sharp damage stage: this stage includes the yield stage. During this stage, the amount of AE increases rapidly, and the rise of the cumulative number curve of ringing count accelerates. This acceleration indicates that under the action of external force and the addition of new microfractures in the rock, the microfractures are partially connecting to form macroscopic fractures. However, the macroscopic fractures have yet to connect. Figure 7: Relationships between AE (damage) characteristics and stress–strain curves of rock samples. (**a1**) Accumulative ringing count (No. 1 rock sample); (**a2**) Accumulative ringing count (No. 2 rock sample); (**a3**) Accumulative ringing count (No. 3 rock sample); (**b1**) Stress (No. 1 rock sample); (**b2**) Stress (No. 2 rock sample); (**b3**) Stress (No. 3 rock sample). 4. Peak of damage stage: this stage includes the stress softening stage. During this period, the number of AE reaches a peak, and the cumulative number curve for the ringing count rises in an almost straight line. This result indicates that under the action of external forces, more microfractures are formed in the rock, these microfractures are connecting to form macrofractures, and the macrofractures are also connecting with each other. This then leads to a sharp decline in the strength of the rock, and eventually its damage. Percolation then occurs. 5. Residual damage stage: this stage includes the post-destruction stage. At this stage, the AE ringing count will gradually fall, showing that some residual energy continues to cause fracture to the rock sample after its destruction, although this fracture is small. The three rock samples can be divided into two types, according to the relation between stress, ringing count and strain in Figure 7b1-b3. First, when the rock sample reaches peak stress, the stress-strain curve drops rapidly, such as that seen for the No. 3 rock sample. The second type of rock sample did not show rapid decline in the stress-strain curve after reaching peak value.