A granular flow theory for the deformation of partially molten rock

A model is developed for deformation of partially molten rock in which the primary mechanism is the relative movement of grains and the strain rate is controlled by the rate at which the interferences to this movement are accommodated by local melting. It is concluded that, in multicomponent rocks with moderate melt fractions where this model is applicable, the strain rate is generally determined by the rate of diffusion of the grain components in the melt, with linear dependence on deviatoric stress, quadratic dependence on melt fraction, and inverse quadratic dependence on grain size. Where melt is free to escape, the strain rate is somewhat higher than for a closed system but the melt escape rate is more strongly dependent on the pressure differential between grains and melt (effective pressure) than on the applied principal stress difference. Unless the stress difference is large compared with the effective pressure, any substantial increase in rate of melt release due to deformation would have to come from other factors such as increase in permeability due to microfracturing.