# Percolation Threshold of Red-Bed Soft Rock during Damage and Destruction
###### Abstract
However, theoretical and experimental research on the percolation phenomenon and percolation threshold has been insufficient, especially in relation to soft rocks. The study of percolation theory with regard to rock damage has typically taken two approaches: one is to study percolation phenomenon by calculating the percolation threshold; the other is to study the percolation characteristics of physical quantities of rocks [1,16, 17, 18]. The percolation threshold for rock damage can be calculated by the theoretical method. Among these methods, the renormalization group method is an effective method that has clear physical meaning, and can be used not only to calculate the theoretical percolation threshold but also to analyze the nature of its destruction. Therefore, this method is widely used [19, 20, 21, 22, 23, 24]. Percolation characteristics can be studied through the characteristics of energy damage. The process of rock damage and destruction is monitored in experiments that study changes in external radiant energy during the whole process of destruction. It is generally believed that energy which radiates from inside the rock can represent the damage to the rock. When percolation occurs during rock damage, the radiative energy apparently increases [25, 26, 27, 28, 29, 30, 31, 32, 33]. However, existing research and percolation models have mainly focused on brittle rocks, which often differ in their properties from red-bed soft rocks. Furthermore, the experimental determination of percolation thresholds has yet to mature, and the factors that influence the percolation threshold of rocks require further study. At the same time, the effective application of percolation theory to rock damage should be based on two aspects, namely, the constitutive and the quantitative description of the damage process. Most damage constitutive studies combine different assumptions to construct different damage constitutive structures, so as to obtain the damage evolution model [34, 35, 36, 37, 38, 39, 40]. In quantitative descriptive research of damage in rocks, various techniques are used, but there is no unified method for describing damage [41, 42, 43, 44, 45, 46, 47]. An effective quantitative method for describing damage in the percolation of red-bed soft rock is urgently needed. In conclusion, while there have been some achievements in the study of percolation and rock damage, some problems remain: (1) research into rock percolation has been insufficient and research into damage criticality based on the rock percolation needs to be built; (2) most studies of percolation phenomena and models have been based on brittle rocks, but few studies have been undertaken on the percolation of soft rocks; (3) effective quantitative description methods of the damage process need to be studied under laboratory compression test conditions. To address the above problems, this paper employs the renormalization group theory to study the percolation of red-bed soft rock, including the method of calculating its theoretical percolation threshold. The constitutive model of percolation damage of red-bed soft rock is derived and, combined with the indoor uniaxial compression acoustic emission (AE) test, the percolation phenomenon in soft rock is studied and its threshold calculated [23]. The percolation phenomenon and threshold under different stress conditions--such as uniaxial compression, conventional triaxial compression and water-stress coupling triaxial compression--are studied by numerical simulation. The influences of confining pressure, water and other factors affecting the percolation threshold are analyzed. Effective quantitative description of damage was carried out in the experiment. Combined with theory and simulation, the critical failure conditions and the percolation characteristics of red-bed soft rock under different states are obtained. At the same time, the relationship between the percolation and soft rock failure is obtained, which can generate new directions for studying the instability and failure of red-bed soft rock.