A NEW ANALYTICAL MODEL TO PREDICT STRENGTH CHANGES DUE TO METAMORPHIC REACTIONS

Metamorphic reactions are most often considered as a passive record of the changes in pressure, temperature and fluid conditions that rocks experience. As such, they provide major constraints on the tectonic evolution of the crust and mantle. However, natural examples of strain localization in ductile shear zones show that metamorphism can modify the strength of rocks by reaction softening processes. Hence, metamorphic reactions also have an active role in tectonics by inducing softening and, probably, hardening as well. Quantifying the mechanical effect of metamorphic reactions is, therefore, a crucial task for determining the strength distribution and evolution in the lithosphere.

Experimentally determined flow laws of rheologically important monophase aggregates (quartz, feldspar, olivine, …) and polyphase rocks (granite, gabbro, eclogite, …) have been published by many authors. These provide good constraints on lithology-controlled lithospheric strength variations. However, since the whole range of mineralogical and chemical rock compositions cannot be experimentally tested, variations in reaction-controlled rock strength cannot be systematically and fully characterized. Theoretical models are, therefore, essential for estimating the strength of polyphase metamorphic rocks. Unfortunately, the existing models cannot be easily applied to natural rocks since they only provide upper and lower strength bounds and/or do not work with more than two phases and/or do not handle non-linear flow laws.

Here we present a new theoretical model that can be applied to any number of non-linear phases. The derivation is analytical and is based on the Least Action Principle applied to the power dissipated in a polyphase rock during deformation. It provides closed-form equations for calculating the bulk viscosity, bulk flow law and stress/strain-rate partitioning, based on the phase fractions and flow laws. The model shows a very good fit to both laboratory and numerical data sets from the literature. It is, hence, easy to use and provides accurate strength estimates. Finally, we will use it to predict the strength changes that accompany the main metamorphic reactions.