Constitutive Equations, Rheological Behavior, and Viscosity of Rocks

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48 Scopus citations


This chapter reviews micromechanical mechanisms of deformation and the associated constitutive equations as applied to describing the rheological behavior of rocks and compares predictions based on laboratory-derived flow laws with the viscosity structure of Earth's upper mantle determined from geophysical observations. First, the essential roles of lattice defects - point defects (e.g., vacancies), dislocations, and grain-grain interfaces (e.g., grain boundaries) - in permitting individual grains and collections of grains to deform without fracturing in response to an applied differential stress are examined. Second, the flow laws resulting from the diffusion of ions, movement of dislocations, and sliding on grain-grain interfaces are analyzed. In this context, both high-temperature dislocation creep and low-temperature dislocation plasticity are included, and the effects of water, melt, and crystallographic texture on rock viscosity are considered. Finally, extrapolations of experimentally determined flow laws are compared to global average values of mantle viscosity obtained from analyses of glacial isostatic adjustment in response to the retreat of continental ice sheets and to the regional viscosity structure of the western United States determined from analyses of filling and drying of lakes and crustal deformation following earthquakes. For olivine-rich rocks with a water concentration of ∼1000H/106Si, laboratory-derived flow laws yield a viscosity of 1020-1021Pas in good agreement with global average values of viscosity. Experimentally determined flow laws predict a lower value for mantle viscosity of 1018-1019Pas, similar to that reported for the western United States, provided that rocks are water-saturated as has been proposed for this region in association with rehydration of the upper mantle due to the long history of flat-slab subduction of the Farallon Plate.

Original languageEnglish (US)
Title of host publicationMineral Physics
PublisherElsevier Inc.
Number of pages32
ISBN (Electronic)9780444538031
ISBN (Print)9780444538024
StatePublished - Jan 1 2015


  • Constitutive equations
  • Crystallographic fabric
  • Deformation
  • Dislocations
  • Flow laws
  • Grain boundaries
  • Mechanisms of deformation
  • Partially molten rocks
  • Point defects
  • Rheological properties
  • Strain rate
  • Strength
  • Upper mantle viscosity profile
  • Viscosity
  • Viscous anisotropy
  • Water weakening


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