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

1 DTP - Dynamique terrestre et planétaire 2 G2R - Géologie et gestion des ressources minérales et énergétiques

Abstract : 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 rheology of the melt and of the matrix constitute the external constraints. Time and length considerations also provide a posteriori constraints on the results. 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 driven mechanisms are observed. One leads to the usual compaction length, and the two others 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. The two types of instability segregate melt. But the compaction process is generally so sluggish that it cannot compete with the channelling one. The shape of the initial porosity perturbation has little influence on the final amplitude and wavelength of the generated structures. Scaling the equations provides insight on the dependence of the solutions on the initial parameters. In fact, few parameters control the system. The viscosity ratio between the matrix and its melt controls the compaction length, i.e. the distance that separates the main veins of segregated melts. During channelling the inter-granular 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 with the advancing melting and dehydration process clamps the deformation of the solid matrix. The shear channelling time is controlled by the amount of inter-granular melt present in the system. Our model is surprisingly constrained to a narrow window of the parameters. This suggests that the compaction length L is metric or sub-metric, as is the distance between veins. Bursts of magma develop which lead to a segregation of a small amount of melt about 5% during a channelling cycle. Each cycle lasts for about 30 ka to 300 ka. Those cycles are driven by the melting resulting from the heating due to diffusion of a deep heat source. The heat source must be located at some distance about 10 km from the melting zone, so segregation has time to develop as melting progresses. Few cycles may develop, but they restrict the amount of melt to about 20 % in total to be extracted from the matrix.

Keywords : melt extraction partial melting granites instabilities

Author: Michel Rabinowicz - Jean-Louis Vigneresse -

Source: https://hal.archives-ouvertes.fr/