Stress and Load Path Dependent Static and Dynamic Moduli and Ultrasonic Velocities in Granite

ABSTRACT: We performed a study of ultrasonic velocity as a function of stress and stress path using axial and radial ultrasonic P and S-waves. Young's modulus and Poisson's ratio are calculated using these velocities along axial and radial directions. Static elastic moduli are also measured along the same stress and stress path protocol. Effects of pre-existing microcracks in the sample are hypothesized via directional observations of velocity changes as a function of differential stress and mean stress. Dynamic Young's modulus is observed to increase primarily as a function of mean stress, whereas static Young's modulus is mainly dependent on differential stress. Since the dynamic moduli are reliant on the accuracy of manually picked arrival times, a comparison is made between the manual picks and automated picked arrival times using AIC, STA/LTA, and CUSUM methods. The agreement between manual and automated picks is highest for P-wave arrivals found through AIC, and more varied for S-wave arrivals overall. 1 INTRODUCTION Experimental damage mechanics provides an excellent lens for which to view the evolution of rock physical property behavior. The ability to set user-defined testing environments creates a wide variety of stress states rock samples can be subjected to. Ultrasonic velocities and strain recorded in situ can be used to measure the dynamic and static elastic properties of a material under stress (Knippel et al. (2023b)). The state of stress and stress path contribute to the magnitude and behavior of these elastic properties (Tutuncu et al. (1998a); Tutuncu et al. (1998b)). The co-evolution of stress-strain relationships and ultrasonic velocities is well-known to be influenced by the presence and accumulation of microcracks within a sample (Zoback and Byerlee (1975)). The presence of microcracks changes the intrinsic material properties that govern elasticity and compliance at the continuum scale. Cracks experiencing a positive volumetric change under stress increase pore space within the rock, decreasing acoustic wave speed which is used to calculate dynamic elastic moduli. Permeability can also be affected by the presence of microcracks, as tensile microcracks with positive volumetric change could coalesce and provide additional pathways for fluid movement (Hampton et al. (2019); Kluge et al. (2021)).