## 4 Discussion  
(1) The results of this study elucidate several key aspects of the damage evolution process in layered rocks. Firstly, the damage variables defined based on transverse wave velocity effectively reflect the damage evolution process of layered rock. This finding is particularly important as it underscores the sensitivity of transverse waves to internal changes within the rock structure, which is crucial for understanding damage mechanisms. Moreover, the influence of confining pressure on the damage evolution process is significant. As confining pressure increases, the damage variable-strain curve shifts to the right, indicating that higher pressures lead to greater initial damage. This relationship highlights the necessity of considering confining pressure in the analysis of rock stability and integrity. Additionally, the inclination angle of the slab plays a critical role in the damage evolution process. Under the same confining pressure, samples with inclination angles of 45\({}^{\circ}\) and 60\({}^{\circ}\) exhibit a higher susceptibility to damage. Interestingly, the initial damage shows a tendency to increase and then decrease, suggesting a complex interaction between the rock's structural characteristics and the applied stress conditions. These findings are consistent with previous research that has explored the relationship between rock properties and damage evolution [27]. By integrating these insights, this study contributes to a deeper understanding of the damage evolution characteristics of layered rocks, which is essential for engineering safety assessments and the design of rock structures. (2) Layered rocks have a layered structure and distinct layers that give rise to anisotropic properties. This anisotropy greatly affects the way in which ultrasonic waves propagate through the rock and the response of the rock to the pressure of the surrounding rock. The angle of tilt between the layers and the direction of ultrasonic propagation play a crucial role in determining the behavior of ultrasonic waves in layered rock. If the ultrasonic wavespropagate parallel to the plane, they may encounter less resistance and higher velocities due to the orientation of the mineral grains. Conversely, when ultrasonic waves propagate at an angle to the facies, interaction with the layered structure results in an increased scattering and attenuation of the ultrasonic waves. Furthermore, for layered rock, longitudinal and transverse waves are not equally sensitive to level changes. The relationship between longitudinal wave velocity and rock damage characteristics has been extensively studied. Longitudinal wave velocity in a free state reflects rock deformation characteristics and fracture state. However, after fracture closure, the influence of longitudinal waves diminishes significantly. This study, in contrast, finds that transverse waves are more sensitive to these changes [27]. Unlike existing studies on ultrasonic wave velocity [28; 29; 30; 31; 32], this paper focuses on the characteristics of ultrasonic waves during damage evolution under various conditions. It defines damage variables and initial damage using ultrasonic transverse wave velocity. Additionally, it analyzes the influence of confining pressure and laminar inclination on the damage evolution of layered rocks. (3) This study's results indicate that confining pressure and laminar inclination angle significantly affect the damage evolution process. This effect is likely related to the generation, propagation, and closure of microfractures within the rock. Although transverse wave velocity, which is more sensitive to the internal state of the rock, is used to define initial damage and damage variables, it cannot accurately reflect changes in the fine structure of layered rock from a macroscopic perspective. To bridge this gap, appropriate initial damage and damage variables from fine damage mechanics can be introduced.