## 5 Conclusions  
In this paper, we conducted a synchronous and isotropic stress wave velocity test experiment to investigate the behavior of slate under loading conditions. By analyzing the changes in wave velocity and the characteristics of the stress-strain curve during the loading process, we defined the crack closure wave velocity as the wave velocity of the rock in an undamaged state. This allowed us to quantitatively characterize the initial damage of the rock. Furthermore, we revealed the damage reduction pattern during the crack compaction stage of the loading process. Our study also addressed the challenge of obtaining the wave velocity of the rock in an undamaged state, which is crucial for determining the damage variable based on wave velocity. The research results indicate the following:  
(1) Confining pressure and laminar inclination angle significantly influence the damage evolution process of layered rocks. As confining pressure increases, the damage variable-strain curve shifts to the right. This shift makes the slow-rising stage of damage more pronounced and increases the initial damage. Specimens inclined at 45\({}^{\circ}\) and 60\({}^{\circ}\) are particularly susceptible to damage. Under the same confining pressure, the initial damage tends to increase and then decrease, peaking at a 60\({}^{\circ}\) inclination. This finding demonstrates that the inclination angle of the laminae significantly affects the initial damage of the rock. Additionally, initial damage, as defined by ultrasonic wave velocity, effectively reflects the degree of damage development in the rock. (2) To accurately describe the evolution process between damage variables and strain during the loading of laminar rock, a segmented damage evolution equation characterized by wave velocity was established. Initially, an inverse proportional function was employed to characterize the strain before crack closure. Subsequently, a logistic function was utilized to represent the curve from crack strain to peak strain. These functions collectively provide a more comprehensive depiction of the relationship between damage variables and strain throughout the loading process. (3) While this study provides valuable insights, several limitations should be acknowledged. The experiments were conducted on a limited number of samples, which may not fully capture the variability present in natural rock formations. To enhance the generalizability of the results, future studies should consider larger sample sizes and include more highly stratified rocks. Additionally, the tests were performed under controlled laboratory conditions, which may not accurately replicate the complex environmental factors encountered in the field. For instance, the evolution law of the damage variable could be altered under the influence of complex lateral pressure, potentially shifting the damage initiation threshold to higher stress values. Moreover, the interaction between lateral pressure and other factors such as temperature, loading rate, and water content was not investigated. Future research should aim to incorporate field studies or employ more sophisticated laboratory setups that better simulate real-world conditions. (4) Future studies should compare the effects of longitudinal and transverse wave velocities on damage evolution in layered rocks to achieve a more comprehensive understanding of how different types of waves interact with rock structures. Additionally, it is crucial to conduct field studies to validate laboratory results within natural environments. Such field studies could involve the in situ monitoring of the damage evolution of layered rocks, thereby providing valuable insights into how environmental factors influence the damage process. By integrating laboratory findings with field observations, researchers can develop a more holistic view of the mechanisms driving damage in layered rock formations. Conceptualization, J.L. and G.L. ; Methodology, G.L. ; Formal analysis, S.X. and G.L. ; Resources, G.L. ; Writing--original draft, J.L. and S.X.