Flow laws of multiphase materials and rocks from end-member flow laws

Rheological properties of polyphase rocks play an important role in the dynamics of the lithosphere and asthenosphere. However, flow laws for large portions of the polyphase rocks in the Earth's crust and mantle have not been well determined. An analysis based on the theory of mixtures has been made to calculate the general flow laws of coarse (≥5 μm), nearly equant-grained (aspect-ratio ≤3), and massive polyphase rocks and materials for which only the flow laws and volume fractions of the constituents are taken into consideration in the modeling of the bulk rheology and effects of microstructure could be ignored. The theoretical analysis is based on three assumptions: (1) the polyphase composite and the monophase aggregates of its constituents obey the same kind of flow laws (linear, power or exponential), (2) there is no change in the operative deformation mechanism of each phase when it is in the composite as compared to when it is in a monophase aggregate, and (3) neither chemical (metamorphic) reactions take place among the constituent phases nor eutectic melting occurs due to the phase mixing. The proposed iterative process allows to predict, to the first approximation, the flow laws for a large number of polyphase rocks in terms of the experimentally determined flow laws of a relatively small number of monomineralic aggregates. Applications of this approach to typical polyphase rocks such as granite, diorite, diabase, aplite and websterite as well as to synthetic two-phase materials such as forsterite–enstatite mixtures and water ice–ammonia dehydrate aggregates yield quite accurate approximations to the experimental values.