Energy Budget of Brittle Fracturing in Granite Under Stress Relaxation and Creep

Creep and relaxation are the two major time-dependent fracturing processes in rocks. While a considerable amount of research has been done in understanding these two mechanisms, critical gaps remain regarding how different energy components evolve during time-dependent fracturing processes in rocks. In this study, a series of relaxation and creep experiments were conducted on prismatic Barre granite specimens in the laboratory to estimate the energy budget of brittle fracturing in granite. For the input energy, the work done by the machine (W) is calculated and for the output energy the radiated seismic energy (\({E}_{R})\), released in the form of acoustic emissions (AEs), is calculated as the only measurable output energy component in the conducted experiments. The low-frequency plateau (\({\Omega }_{0})\) and corner frequency (\({f}_{0})\) for each AE waveform was estimated by fitting the observed AE spectra with the theoretical spectra using the Omega model. These parameters were used to estimate the seismic moments (\({M}_{0})\) based on the radiation pattern for the double couple (shear) and non-double-couple (non-shear) events. The range of \({f}_{0}\) and \({M}_{0}\) varied from 150 to 750 kHz and 10⁻⁴ to 10⁻¹ N m, respectively. Moment magnitude (\({M}_{w})\) varied in a wider range from − 9 to − 6 in creep and − 8.5 to − 7 in relaxation. Stress drops (\(\Delta \sigma )\) and source radius (\(r)\) were estimated for the AEs using Brune’s model. The results report on three primary observations: (1) the effects of different source mechanisms on the estimated source parameters showed that \({M}_{0}\) and \(\Delta \sigma\) were higher for DC events as compared to NDC in both relaxation and creep. (2) The radiation efficiency in the case of creep is 70% higher as compared to relaxation and, (3) the stress drop estimated in relaxation and creep demonstrated a breakdown in scaling with the seismic moment.