Flow in rocks modelled as multiphase continua: application to polymineralic rocks

The notion of a multiphase continuum is applied to the problem of determining the flow properties of two-phase rocks. The assumptions made include (i) that both the bulk rock and the constituent phases have a linear viscous rheology, (ii) that the phases are uniformly mixed and distributed in the rocks, and (iii) that no segregation occurs during the deformation. A theoretical analysis is made assuming the additive relationships for the linear momentum, the stresses and the entropy production rates. Two possible relationships between the normalized bulk rock viscosity (the ratio of bulk rock viscosity to the viscosity of the less viscous phase) and the volume fraction of the constituent phase are derived. The first relationship is linear (mode 1 behaviour), while the second is non-linear (mode 2 behaviour). In mode 2 behaviour, the normalized bulk rock viscosity decreases at first rapidly and then less so as the volume fraction of the less viscous phase increases from zero. The rate of the initial rapid decrease in viscosity is in proportion to the viscosity contrast between two phases and in inverse proportion to the density contrast. The mode 2 behaviour shows good agreement with published deformation experiments of synthetic two-phase rocks. The bulk rock deformation rate can be related to those of the constituent phases. In mode 1 behaviour there is no deformation rate partitioning. In contrast, in mode 2 behaviour the ratio of the deformation rate partition coefficients of the less viscous phase to that of the more viscous phase is equal to the ratio of the inverse viscosity contrast to the density contrast. This relationship corresponds to the rule of strain refraction derived for multilayer systems. Mode 2 behaviour can be further subdivided into two regimes: one where the viscosity contrast is greater than the density contrast (mode 2a), and a second where the opposite is true (mode 2b). In mode 2a behaviour more strain is partitioned into the less viscous phase; while, in mode 2b behaviour more strain is partitioned into the more viscous phase.