Viscoelastic behaviour and temporal fractal properties of lherzolite and marble: Possible extrapolation from experimental results to the geological time-scale

The viscoelastic relaxation behaviour of lherzolite and marble and their temporal fractal properties are studied. Based on the high-temperature viscoelastic behaviour for these rock types derived from the time-temperature superposition principle, the relaxation function for the viscoelastic behaviour of lherzolite and marble can be expressed as a flow law from a power-law function of temperature-reduced time given by normalizing the various temperature behaviours, with a non-integer exponent. The relaxation function is thus time-scale invariant, i.e. there is a temporal fractal property to the temperature-reduced time. Their rheological behaviour over geological time-scales at low temperature can be extrapolated from the experimental high-temperature behaviour based on the temporal fractal property. Our derived flow law satisfies not only transient behaviour but also steady-state behaviour.