Fractal structure of the time distribution of microfracturing in rocks

Using acoustic emission data obtained from laboratory double torsion tests, we have analysed the fractal nature of a series of 29 granite microfractur ing processes in time. The data represent a wide variety of timescales, str ess environments (increasing load with a constant displacement rate, relaxa tion, creep), soaking conditions [air, water, dodecyl trimethyl ammonium br omide (DTAB), polyethelene oxide (PEO)], and material anisotropy. We find t hat the time distribution of rock microfracturing displays fractal and mult ifractal properties. In some cases, it has a single fractal or a multifract al structure. In other cases, it changes from a single fractal structure in to a multifractal structure as the system evolves dynamically. We suggest t hat the heterogeneity of the rock, the distribution of joints or weak plane s, the stress level, and the nature of the microfracturing mechanism lead t o these multifractal properties. Whatever the fractal structure of the syst em, a lower fractal dimension is generally produced at near-failure of the rock due to an increased clustering. This result concerning the fractal-dim ension decrease is consistent with the conclusion drawn from the spatial di stribution of rock microfracturing. Therefore, from the vantage point of ob servation of the time distribution of rock microfracturing, the decrease of the fractal dimension has a potential use as a rock failure predictor.