Power law singularity of catastrophic rupture in heterogeneous media

Catastrophic rupture in heterogeneous media, such as earthquake in crust, has long been a topic of scientific and societal importance. However, there has been no reliable approach to its prediction. Recently, our experimental study of rocks unveiled a power law singularity ahead of catastrophic rupture, namely the response of the rock specimen R (the ratio of the increments of sample deformation u and controlling crosshead displacement U) can be expressed as R∼(1−U/UF)−β with β=0.51±0.10 (mean±s.d.) ahead of the catastrophic rupture UF. Numerical simulations also demonstrate the power law singularity ahead of catastrophic rupture. Theoretical analysis gives the power law singularity with the critical exponent β=1/2. In addition, other tests with cement specimens showing gradual failure without catastrophic rupture do not demonstrate such a singularity.