Using acousticemission data obtained from laboratory bouble torsion tests, we have analysed the fractal natureof aseries of 29 granited microfracturing processes in time. The data represent a wide variety of timescales, stress environments (increasing load with a constant displacement rate, relaxation, creep), soaking nditions [air, water, dodecyl trimethyl ammonium bormide (DTAB), poylethelene oxide (PEO)], and materialanisotroy. We fine that the timedistribution of rock microfraturing displays fractal and multifractal properties, In some cases, it hasasinglefractal of a multifractal structure. In other casese, it changes form a single fractal structure into a multifractal structure as the system eveoles dynamically. We suggest that the heterogeneity ofthe rock, the distribution of jojints of weak planes, the stress level, and the nature of the microfracturing mechanism lead to these multifractal properties. Whatever the fractal structure of the system, al lowerfractal dimentsion is generally produced at near-failure of the rockduee to an increased clusteing. This resultconcerning the fractal-dimension decrease is consistent with the conclusion drawn from the spatialdistribution of rock microfracturing. Thererore, from the vantage oint of observation of thime distribution of rock microfracturing, the decrease of the fractal dimension has a potential use as a rock failure predictor.