Power-law singularity as a possible catastrophe warning observed in rock experiments

The question which type of signals can be determinately related to catastrophic rupture in heterogeneous brittle media still remains open. Here we report a specific precursor of catastrophic rupture, i.e. a power-law singularity of responses, based on rock experiments. Our experimental observations show that the singularity with power exponent −β, where β=0.51±0.10 (mean±s.d.), appears ahead of catastrophic rupture in some rocks, and the singularity does not appear at all for gradual failure. It is indicated that the power-law singularity can emerge well only close to catastrophic rupture and thus it could serve as a specific warning for catastrophic rupture. To address the potential forewarning of imminent catastrophic rupture, a fitting process based on the data before catastrophic rupture was developed to determine the two unknowns related to the occurrence, catastrophe point UF and the power exponent −βu. It is demonstrated that the power-law singularity appears only in the vicinity of catastrophe, and that the power-law singularity does not occur for gradual failure.