Fractal dimension of rock fractures and acoustic-emission energy for damage prediction

Microscopic fracture evolution and macroscopic energy release were linked in weakly metamorphosed slate and metasandstone under triaxial confinement. Specimens were tested at 5 MPa, 15 MPa, 20 MPa and 25 MPa with synchronous acoustic-emission (AE) monitoring. Scanning electron microscopy images obtained before and after failure were processed using a validated fracture-extraction workflow, and the fractal-dimension difference (ΔDf) quantified changes in fracture-network complexity. AE-energy and pressure variables were integrated into a hybrid Bayesian non-linear regression–Gaussian process regression model. Retrospective threshold analysis showed that the anomalous cumulative AE energy at 20 MPa reflected numerous low-amplitude hits, few high-energy events and loading/contact disturbances; these data were excluded from model fitting. Both lithologies had positive ΔDf at 5 MPa and 15 MPa, whereas negative ΔDf at 25 MPa coincided with fracture closure, delayed failure and lower AE peak energy. The energy-peak and pressure ratios captured the non-linear dependence of ΔDf on energy release and confinement. The hybrid model outperformed the individual models (R2 = 0.826). ΔDf links microscopic fracture evolution to macroscopic AE response and supports pressure-dependent damage prediction within the tested range.