Melt segregation under compaction and shear channeling: Application to granitic magma segregation in a continental crust

[1] We present a model of melt segregation in a mush submitted to both compaction and shear. It applies to a granitic melt imbedded within a partially molten continental crust, able to sustain large stress values. The mathematical derivation starts with the equations for melt and plastic flow in a mush. They are manipulated to obtain equations for the mean flow field and for the separation velocity. Assuming that the mean flow field is simple shear, a specific set of equations for the melt flow in a shear field is obtained. After simplifying the equations, they finally reduce to two systems of coupled equations. One is the well-known equation for compaction. The other is new and describes melt channelling during shear in a mush with a constant viscosity plastic matrix. Three free parameters are observed. One is the usual compaction length, and the other two are functions of the stress and strain amplitude during shear. Compaction instabilities lead to the development of spherical pockets rich in melt while shear channelling instability segregates melt in parallel veins. The size of the pockets and the distance between veins remain close to the compaction length. Actually, the viscosity ratio between the matrix and its melt controls the compaction length L, which is found metric or submetric. The two types of instability segregate melt. However, the compaction process is generally so sluggish that it cannot compete with the channelling one. The channelling time is controlled by the amount of intergranular melt present in the system and of the amplitude of the shear stresses. During each channelling cycle, lasting for about 30 to 300 kyr, the intergranular melt is completely squeezed out from the volume in between veins. As melting progresses, the successive batches of melt, as well as the residual solid matrix, are increasingly more dehydrated. As a result, both phases progressively stiffen without changing their viscosity contrast and the associated compaction length. The segregation process stops when the dehydration process clamps the deformation of the solid matrix.