# Percolation Threshold of Red-Bed Soft Rock during Damage and Destruction
###### Abstract  
The critical damage point of the red-bed soft rock percolation phenomenon can be described as the percolation threshold. At present, there are insufficient theoretical and experimental studies on the percolation phenomenon and threshold of red-bed soft rock. In combination with theoretical analysis, compression experiment and numerical simulation, the percolation threshold and destruction of red-bed soft rock are studied in this paper. The theoretical percolation threshold of red-bed soft rock was obtained by constructing a renormalization group model of soft rock. Based on damage mechanics theory, rock damage characterization and strain equivalent hypothesis, a constitutive model of red-bed soft rock percolation damage was obtained. The percolation threshold of red-bed soft rock was determined by compression test and a damage constitutive model, which verified the rationality of the theoretical percolation threshold, and we numerically simulated the percolation of red-bed soft rock under triaxial compression. The results showed that the percolation threshold increases as the confining pressure rises, but decreases significantly with the action of water. In this study, the critical failure conditions and percolation characteristics of red-bed soft rock under different conditions were obtained. The relationship between percolation and soft rock failure was revealed, providing a new direction for studying the unstable failure of red-bed soft rock. red-bed soft rock; percolation; renormalization group; constitutive model of damage; threshold value +
Footnote †: journal: Medical  
Red beds, widely distributed from the early Proterozoic to the Neogene, are particularly notable for their red color. Red beds are also widely distributed in space and have been found on seven continents and in four oceans [3,4]. Red-bed soft rock is widely distributed and relatively complete, hard and good in its mechanical properties when under natural conditions (relative to the excavation environment) [5,6]. However, in an engineering excavation, the red-bed soft rock rapidly expands, disintegrates and softens in a short time after coming into contact with water, and its mechanical properties are greatly reduced, which leads to engineering disasters. When red-bed soft rock meets water, it forms a complex three-directional stress state under the action of water-stress coupling. In a short time, the rock rapidly expands, softens, disintegrates, and internal damage develops continuously until, finally, the rock suddenly breaks. This is typical of the percolation phenomenon, and the critical point of damage of red-bed soft rock can be described as the percolation threshold. Red-bed soft rock is a common type of soft rock with special properties in engineering construction [5, 6, 7, 8]. After project excavation, the red-bed soft rock, under the action of water and water-stress coupling, will form the complex state of three-directional stress. Under the action of these forces, damage will start gradually from the inside of the rock before developing and expanding. When the damage reaches a certain critical value, a large number of cracks will occur and the rock will gradually reach a state of unstable failure [9, 10, 11]. When the amount of damage is less than the critical threshold, the soft rock is in a stable state. When the amount of damage reaches the critical threshold, its state changes and leads to destruction. From the perspective of percolation, the sudden change in mechanical properties is a percolation phenomenon [12, 13, 14, 15]. According to percolation theory, the critical point of damage and destruction of red-bed soft rock can be described as the percolation threshold. Under different stress states, red-bed soft rock has different percolation characteristics and percolation thresholds. Therefore, the influence of different stress states on percolation should be taken into account when studying the percolation of red-bed soft rock during its damage and destruction.