A Possible Use of Structure Factors in Constitutive Equations for Rocks

Abstract

During deformation, a rock changes in internal structure; it becomes a new material with new properties. It cannot effectively be described as a material whose properties are strain dependent or as a material whose properties are stress dependent; rather, a rock at one moment is a member of a suite of materials that can be changed one into another by deformation. Each member of the suite has its own structure and its own mechanical properties—the properties of the members of the suite are structure dependent.

Behavior that is structure dependent cannot well be represented by conventional spring and dashpot models, but can be reproduced in an emulsion model with surface energy. Inspection of such a model suggests that the form γ = Aτ^B can be replaced by the form γ = (SF)τ^B where SF is a structure factor. If this change is made, tertiary creep leading to rupture can be embraced under the same formula as secondary or steady-state creep. In addition, primary or transient creep will be seen as partly a nonrecoverable change of structure and only partly as a damped recoverable change. It seems that the inclusion of structure factors could make the constitutive equations for rocks correspond more closely to the phenomena they attempt to describe.