The Minimized Power Geometric model: An analytical mixing model for calculating polyphase rock viscosities consistent with experimental data

Abstract

Here we introduce the Minimized Power Geometric (MPG) model which predicts the viscosity of any polyphase rocks deformed during ductile flow. The volumetric fractions and power law parameters of the constituting phases are the only model inputs required. The model is based on a minimization of the mechanical power dissipated in the rock during deformation. In contrast to existing mixing models based on minimization, we use the Lagrange multipliers method and constraints of strain rate and stress geometric averaging. This allows us to determine analytical expressions for the polyphase rock viscosity, its power law parameters, and the partitioning of strain rate and stress between the phases. The power law bulk behavior is a consequence of our model and not an assumption. Comparison of model results with 15 published experimental data sets on two-phase aggregates shows that the MPG model reproduces accurately both experimental viscosities and creep parameters, even where large viscosity contrasts are present. In detail, the ratio between experimental and MPG-predicted viscosities averages 1.6. Deviations from the experimental values are likely to be due to microstructural processes (strain localization and coeval other deformation mechanisms) that are neglected by the model. Existing models that are not based on geometric averaging show a poorer fit with the experimental data. As long as the limitations of the mixing models are kept in mind, the MPG model offers great potential for applications in structural geology and numerical modeling.

Compositional dependence of lower crustal viscosity

“…Using the mineral proportions calculated from Perple_X, we use the mixing model of Huet et al . [] to calculate aggregate viscosity of the mineral assemblage assuming deformation occurs via dislocation creep of all phases. Huet et al .…”

“…Huet et al . [] defines the effective aggregate viscosity as where ϕ i and n i are the volume percentage and stress exponent of phase i , respectively, and the parameter a is defined for each phase as a i = ∏ i ≠ j ( n j + 1). This method assumes a large enough scale that the rock can be considered homogeneous and isotropic.…”

The effect of bimineralic composition on extensional processes at lithospheric scale

“…Experimental and theoretical studies of polymineralic rocks show that their bulk strength also depends on the proportion, shape, distribution, and strength ratio of the minerals [Gerbi et al, 2010;Handy, 1990Handy, , 1994Handy et al, 1999;Huet et al, 2014;Jordan, 1988;Tullis et al, 1991]. To address this problem, some lithospheric scale models use a laboratory-determined flow law for polymineralic rock like granite, diabase, or gabbro [Lavier and Manatschal, 2006;Van Wijk and Blackman, 2005].…”

“…To address this problem, some lithospheric scale models use a laboratory-determined flow law for polymineralic rock like granite, diabase, or gabbro [Lavier and Manatschal, 2006;Van Wijk and Blackman, 2005]. For these studies, a bulk strength envelope for the polymineralic aggregate is estimated by an average flow law taking into account the different proportions of the different phases [Gerbi et al, 2010;Handy, 1994;Handy et al, 1999;Huet et al, 2014;Tullis et al, 1991]. These studies, however, do not take into consideration the interaction between the different phases and imply, as for monomineralic assemblages, that deformation mechanisms are either brittle (elastoplatic) or ductile (viscous).…”

New parametric implementation of metamorphic reactions limited by water content, impact on exhumation along detachment faults

“…Accounting for the fact that retrograde metamorphic changes do not affect the bulk of the exhumed material but only the shear zone accommodating their exhumation, some authors (e.g., Huet et al, 2011a) have proposed not to account for thermo-dynamic reactions when modeling the exhumation of high-grade metamorphic rocks. While minimizing the error on buoyancy, this approach tends to misestimate the viscous strength of the retromorphosed shear zones (Gueydan et al, 2003;Huet et al, 2014).…”