# Percolation Threshold of Red-Bed Soft Rock during Damage and Destruction
## 2 Research Contents and Methods
### Numerical Simulation of Percolation in Compression Test of Red-Bed Soft Rock  
In this section, the uniaxial compression test is numerically simulated from aspects of the stress-strain curve, the damage characteristics and the percolation threshold, and by using real fracture process analysis (RFPA) based on the finite element principle. The characteristics of the simulation process include: (1) the heterogeneity of rock and randomness of damage distribution were considered and calculated by a statistical method; (2) it was assumed that the elastic modulus and compressive strength of the rock conformed with a certain statistical law, such as the Weibull distribution, and the elastic modulus and compressive strength were randomly selected for each unit according to the selected distribution in order to simulate the fracture process of the rock; (3) it was assumed that the number of units damaged is in direct proportion to the amount of AE, and the AE energy is in direct proportion to the compressive strength of the failure unit. In the process of rock failure, AE data will be generated when the unit is constantly destroyed. The simulation method meets the requirements of the model for damage for calculating the percolation threshold in Section 2.2.  
The numerical simulation of the uniaxial compression percolation test of red-bed soft rock was carried out according to the following requirements. The model adopted a 50 mm \(\times\) 100 mm model consistent with an experimental situation, the elastic modulus and compressive strength of experimental rock samples, a displacement loading control method, with a speed of 0.04 mm/s. The numerical simulation was carried out using the Mohr-Coulomb strength criterion and 20,000 computing units.  
Based on numerical simulation results of uniaxial compression, the percolation characteristics of red-bed soft rock under triaxial compression were further studied by numerical simulation compression test, and the factors affecting the percolation threshold were analyzed. The numerical simulation included two parts: conventional numerical simulation of triaxial compression and numerical simulation of triaxial compression under water-stress coupling.  
First, based on the conventional triaxial compression test, the experimental stress-strain curve of the rock sample was taken as the numerical simulation object, and numerical simulation was judged to be consistent with the compression test by realizing the coincidence of the stress-strain curve in the numerical test and the stress-strain curve in the compression test. Based on this, the AE data from the numerical simulation was obtained in order to calculate the percolation threshold under numerical simulated conditions. In the conventional triaxial compression test, the rock sample is separated from water, but a characteristic of red-bed soft rock is that it will disintegrate and its strength will decrease rapidly when it meets with water. The conventional triaxial compression test alone will therefore not adequately capture the percolation of red-bed soft rock.  
Instead, it is necessary to consider the triaxial compression test under the action of water-stress coupling in order to better describe the percolation characteristics of red-bed soft rock. In the triaxial compression test under the action of water-stress coupling, silty mudstone samples were filled with water for 48 h and then directly inserted into the pressure chamber with water as the confining pressure for the loading test. The 48 h saturation and confining pressure environment formed the water-stress coupling condition. Under this condition, the stress-strain curve obtained is the water-stress coupling stress-strain curve.