# Analysis of Damage and Permeability Evolution of Sandstone under Compression Deformation
## 1 Introduction  
The construction and excavation of underground engineering often cause the redistribution of stresses in the surrounding rock, and the resulting new cracks and damage deformation have adverse effects on the safety and stability of the engineering facilities [1; 2; 3]. Moreover, stress-induced damage further leads to an increase in permeability and causes leakage accidents, such as natural gas and nuclear waste leakage in underground chambers due to the damage and cracking of surrounding rock, mine cavern collapse, tunnel lining cracking, and water leakage caused by excavation disturbance [4; 5]. The interaction of seepage and damage is actually a fluid-solid coupling effect. Stress-induced damage and deformation lead to changes in the pore and crack structure of the rock, and the resulting fluid flow (seepage field) reacts on the stress field, affecting the volume deformation and crack growth, forming a full coupling. One can see that safety accidents in underground engineering are usually not caused by a single factor but are the result of multi-factor coupling. The deformation and permeability characteristics of rocks or rock formations become complicated under the strong influence of a fluid-solid coupling effect. Laboratory test results and engineering practice indicate that the seepage and mechanical parameters of rock are not constant [6; 7; 8; 9] but are a function of stress or stress-induced deformation, which poses a significant obstacle to analyzing and predicting the flow behavior of fluids in rocks and the deformation behavior of rocks. However, this work has to be conducted because the characteristics of rock permeability and damage evolution widely exist in underground engineering, such as underground energy storage, unconventional petroleum and gas extraction, nuclear waste disposal, carbon dioxide geological storage, and underground chamber excavation. As a geotechnical material, the crack closure, growth, and propagation in rocks under mechanical loading make a relationship and interaction between seepage and damage. This is best evidenced by the hydraulic fracturing of rocks, and the permeability changes dramatically due to damage in fracturing rocks (also known as the permeability surge phenomenon) [10; 11; 12]. In fact, whether to consider the flow-solid coupling effect has a huge impact on the flow behavior of fluids and the deformation behavior of rocks. Many scholars have established the relationship between permeability and effective stress based on triaxial compression tests, including logarithmic functions and exponential functions [13; 14; 15]. These prediction models can well describe the change in permeability during the rock compaction stage but cannot explain the drastic change in permeability in the stage of rock dilatancy. This is because the influence of damage on permeability evolution cannot be ignored, and it is as important as effective stress. Another major problem is to characterize the damage behavior of rocks, which depends on the research tools and methods. At present, studies on rock damage characteristics mainly focus on theoretical analysis based on continuum mechanics, experimental analysis based on acoustic emission tests, and mesoscopic damage analysis based on statistical physics [7; 16; 17; 18]. Revealing the characteristics of permeability and damage evolution in rocks is the key to accurately describing the fluid flow behavior and rock deformation behavior. The permeability and damage evolution of rocks is not a single problem of mechanics or seepage but the result of the interaction between the stress field and flow field [19; 20; 21]. Given the complexity of the problem, one of the most effective study methods is numerical simulation. But there is a prerequisite; that is, it is necessary to establish a relationship model that can describe the evolution of rock damage and permeability. [PERSON] et al.