A Study on the Damage Evolution Law of Layered Rocks Based on Ultrasonic Waves Considering Initial Damage

The damage evolution process of layered rock is influenced by its fine structure, lamination direction, and confining pressure, exhibiting significant anisotropic characteristics. This study focuses on shale as the research object, employing indoor tests and theoretical analysis to define damage variables and initial damage based on ultrasonic wave velocity. This research investigates the damage evolution law of layered rock under varying confining pressures and dip angles. The findings reveal that damage variables defined using transverse wave velocity effectively reflect the damage evolution process. Additionally, confining pressure significantly affects damage evolution, with increasing pressure causing a rightward shift in the damage variable–strain curve and an increase in initial damage. The slab inclination angle also influences damage evolution; samples with 45° and 60° inclinations are more susceptible to damage, with initial damage showing a trend of increasing and then decreasing. To accurately describe the relationship between damage variables and strain during the loading process, this paper establishes a segmented damage evolution equation characterized by wave velocity. Initially, an inverse proportional function is employed to characterize the strain before crack closure. Subsequently, a logistic function represents the curve from crack strain to peak strain. This combined approach provides a comprehensive depiction of the damage evolution. This study underscores the importance of considering confining pressure and laminar inclination in the analysis of rock stability and integrity. These results provide critical insights into the damage evolution characteristics of layered rocks, offering valuable references for engineering safety assessments.