Quantitative analysis and scaling of sheared granitic magmas

Abstract

We present a quantitative treatment of the macroscopic behaviour of a sheared granitic magma using Biot's theory [Biot, 1941] and a shear‐dilatancy sensitive material model for the solids. The calculations are relevant to a magma in the solidosity range 0.55–0.7. The resulting excess pore pressure distribution is a function of the position and the time. Results are presented in graphical form. A scaling emerges that enables the results to be presented in non‐dimensional form. A sensitivity study is carried out of the parameters describing the rheology of the solid matrix (including permeability features). The model enables the estimate of pressure and flow rates, thus opening a way of understanding the features in the granite crystal mush that are caused by upflowing magma. At high strain rates (10−10S−1) flow rates due to shear far exceed melt movement due to buoyancy effects.

Shear-induced material transfer across the core-mantle boundary aided by the post-perovskite phase transition

“…Details of the model, including full analytical solutions to the governing differential equations, are given in Koenders and Petford (2000) and Petford and Koenders (2003) and not repeated in detail here. A key feature of this analysis is the coupling of pure shearing stress to volumetric strain, so that the modified Biot equation captures many important parameters relevant to deforming porous layers including the average melt displacement, melt (fluid) pressure, permeability and the set temperature corresponding to a pressure of 136 GPa, calculated using a molecular dynamics ab-initio approach (Stackhouse et al, 2005).…”

“…1) is now considered (the short time solution is given in Koenders and Petford, 2000). The outcome is…”

“…The macroscopic part of the problem has been modelled successfully in recent large scale numerical simulations of whole mantle flow (Kellogg et al, 1999;McNamara et al, 2002), and the deformation effects arising from this are summarised elegantly by Karato (1998). Our approach combines a microscale, sheardilatancy sensitive material deformation model for the solid component of D idealised to a set of constant moduli to simplify the analytical solutions (Koenders and Petford, 2000), coupled to the macroscale dynamics. A comparable microscale formalism for two-phase flow with Maxwellian viscoelastic rheology in the upper mantle has been devel- Kellogg et al (1999), and Karato (1998).…”

Deformation-induced mechanical instabilities at the core-mantle boundary

“…Garnero, 2000). An important feature of the model is that from the perspective of strain rate-sensitive media, upwelling velocities velocity scales linearly with the rate of deformation (see Koenders and Petford, 2000;Petford and Koenders, 2003;Petford et al, 2005a), thus overcoming textural problems relating to percolation of Fe-rich melts through a silicate matrix constrained by high dihedral angles (e.g. Bruhn et al, 2000;Rushmer et al, 2000).…”

“…Although Biot's theory describes well the mechanical behaviour of porous media under compaction, it does not take into account the coupling between volume strain and shear stress that in granular materials results in dilatancy. Koenders and Petford (2000) and Petford and Koenders (2003) give a modified form of Eq. (1) that takes into account the effects of coupled shear strain and volume stress.…”