On the rheologically critical melt fraction

With increasing melt fraction (φ), the strength of partially molten granite decreases from a value characteristic of solid, competent rock to a value nearly equal to that of the melt. Previously published mechanical and microstructural data indicate that deformation in partially molten rocks often involves brittle processes. Thus, the pressure in the melt is expected to be important in determining strength. When the volume changes during deformation, strength and fluid flow will be coupled by such parameters as permeability (k), storage capacity per unit volume or storativity (βs), melt compressibility (βf), grain size (d), fluid viscosity (η), and strain rate (ϵ̇). Experiments on brittle rock at low temperatures show that the strain rate at which the internal fluid pressure can be maintained constant is approximately proportional to k/(ηβs). An evaluation of published experimental data suggests that this relation also holds for partially molten granites, indicating that the strength of these rocks depends on their transport properties. Since the permeability is related to φ, below a critical melt fraction (φrcmf), the melt pressure will change if deformation is not iso-volumetric. By assuming a power-law relationship between k and φ, we estimate thatφrcmf∝(ϵ̇ηβf/dm)1/(n−1)where m and n relate permeability to grain size and φ, respectively.