This study analytically investigates the influence of microdefects on the effective velocity of stress waves in deep macrojointed rock masses subjected to geostatic stress. A time-domain analytical approach based on the characteristic-line method was developed to theoretically investigate stress wave propagation. The method transforms the governing equations into compatibility equations along specific characteristic-line. The effective velocity is determined as the ratio of the propagation distance to the time difference between the peak arrivals of the incident and transmitted waves. The influence of geostatic stress on the effective velocity of stress waves is systematically examined. A comparison is conducted between cases accounting for and ignoring microdefects. The critical geostatic stress is introduced to discriminate microdefect effects on the effective velocity of the stress wave. The results indicate that when the geostatic stress is small, the effective velocity accounting for microdefects is smaller than that obtained by ignoring microdefects due to enhanced scattering and energy dissipation. However, when the geostatic stress is larger, the effective velocity accounting for microdefects exceeds that obtained by ignoring microdefects. This is due to compression-induced microdefect closure and increased stiffness, resulting in a larger effective velocity. Therefore, a critical geostatic stress is identified at which the effective velocities accounting for and ignoring microdefects are equal. Above the critical geostatic stress, the effect of microdefects transitions from reducing wave velocity to enhancing it. The critical geostatic stress is strongly dependent on propagation distance and incident wave frequency, while its dependence on incident wave amplitude is negligible.
Wang et al. (Tue,) studied this question.