# Percolation Threshold of Red-Bed Soft Rock during Damage and Destruction
## 2 Research Contents and Methods  
### Renormalization Model of Percolation Threshold of Red-Bed Soft Rock Damage and Destruction  
Renormalization models are based on self-similarity. Similar skeleton particles and the filler between skeleton particles can be found in the rock from microscopic, mesoscopic and macroscopic levels. Brittle rocks with higher strength generally have stronger fillings between skeletons. In a renormalized group model, the filler can be considered part of the skeleton, so the model can be constructed in the form shown in Figure 1a. In Figure 1a, the small cube with scale 1 is a basic unit, and four units of scale 1, forms a basic unit of scale 2. In scale 3, the four basic units of scale 2 constitute a basic unit of scale 3. When a scale 1 unit is damaged in some way and satisfies the transformation criterion for destruction, it is also damaged under observation in scale 2, as shown in Figure 1b (white blocks are non-damaged and black blocks are damaged). The elements that cannot reach the transformation criterion for destruction are not destroyed under observation in scale 2, as shown in Figure 1c.  
Compared with brittle rocks, the cementie strength between the skeleton particles of red-bed soft rocks is low, so the cementie member and the skeleton particles should be considered separately in the renormalization group model. Take silty mudstone, a type of red-bed soft rock, as an example: its microstructure is shown in Figure 2a. Silty particles (spherical in the figure) and clay minerals (rod-shaped in the figure) are seen in the microstructure. Silty particles act as the framework while the clay minerals act as the cementing substance in the structure. Due to the special structure of soft rock, renormalized model units can be established, as shown in Figure 2b. The skeleton particles are connected by a cementing substance, and the strength of the skeleton particles is higher than that of the cementing substance. In the process of change at each level of scale, the material acting as skeleton and the cementing substance can always be found in red-bed soft rock. The failure of the basic unit at the higher levels of the scale only affects the cementation component of the basic unit at the current scale.  
same. When the soft rock is damaged, the microscopic cementation component damages and accumulates to cause mesoscopic cementite damage, and the mesoscopic cementation component damages and accumulates to form macroscopic damage.  
To simplify the calculation, the following assumptions were made of the renormalization model of soft rock: (1) the renormalized model is isotropic, (2) at the same scale, the failure probability of the cementing component is equal.  
The rules of renormalization transformation can be determined according to the failure of rocks under load compression, as shown in Figure 3.  
The transformation rules are as follows: (1) the cementation component of each basic unit can be divided into three groups as shown in Figure 3a; (2) each group has four cementation components and when three of these components are damaged, the group is deemed to be damaged; (3) when one group of cementation components in a basic unit is damaged, that unit is deemed to be damaged, as shown in Figure 3b,c.