Tectonic Critical Phenomena with Dilatancy in Analogue Models

Abstract

The dilatancy of soil and rock eludes continuum mechanics, thermodynamics and materials science as it is localized in fractal patterns of shear bands (faults) and/or cracks. As far as shear bands dominate it is captured by a driven succession of saddle points of the specific elastic energy, which are equivalent to a Mohr-Coulomb condition with effective stress, growing friction and waning cohesion. A driven dilatation turns into a spontaneous contraction when the energy reaches a tipping point with regard to the pore volume, then the pore water pressure grows and the stress deviator drops. The implied state variables and rates are defined as quasi-local and -momentary by means of fractional derivatives. Energy-based constitutive equations include a relation of stress and dilatancy with maximal dissipation, while rockburst with dominant cracks is excluded by a criterion. Successions of driven dilatation and spontaneous contraction imply seismogenic mechanical chain reactions, which are enhanced by seismic waves and spreading of pore water. Such mechanisms are observed in sandbox and cell tests, which serve as analogue models beyond usual similarity rules. The scale-independence of features thus. obtained is validated in the companion paper on lithosphere sections.