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Viscoelastic behaviour and temporal fractal properties of lherzolite and marble: possible extrapolation from experimental results to the geological time‐scale
Author(s) -
Kawada Yusuke,
Nagahama Hiroyuki
Publication year - 2004
Publication title -
terra nova
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.353
H-Index - 89
eISSN - 1365-3121
pISSN - 0954-4879
DOI - 10.1111/j.1365-3121.2004.00540.x
Subject(s) - viscoelasticity , rheology , fractal , extrapolation , power law , time–temperature superposition , geology , exponent , superposition principle , relaxation (psychology) , power function , thermodynamics , mineralogy , statistical physics , mechanics , physics , mathematics , mathematical analysis , psychology , social psychology , linguistics , statistics , philosophy
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.