Abstract
The isothermal depolarization current relaxation in uniaxial compressed rocks follows a generalized exponential function which explicitly introduces hierarchically constrained dynamics and macroscopic interactions. The interactions are associated with the non-extensive entropy parameter q and exhibits a behavior indicating a scaling with normalized uniaxial stress Σ=σ/σY, where σY is the yield stress where deviation from the elastic region starts in a stress-strain curve. Combining ideas of Levy and Tsallis statistics we argue the remarkable result that a Levy-walk–type mechanism can organize the geometry of the heterogeneous system to criticality. The stress-dependent q-estimation leads to the conclusion that fracturing is a subextensive process with strong interaction.
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