Macroscopic crack propagation in brittle heterogeneous materials analyzed in Natural Time

Here, we analyze in natural time $\chi$, the slow propagation of a macroscopic crack in brittle heterogeneous materials through sudden jumps and energy release events which are power law distributed with universal exponents. This macroscopic crack growth is currently believed to exhibit similar characteristics with the seismicity associated with earthquakes. Considering that the crack front is self affine and exhibits Family-Vicsek universal scaling, we show that the variance $\kappa_1 (\equiv\langle \chi^2\rangle -\langle \chi \rangle^2)$ of natural time is equal to 0.0686, which almost coincides with the value $\kappa_1\approx 0.07$ obtained from the seismicity preceding major earthquakes. This sheds light on the determination of the occurrence time of an impending mainshock.