We present a model for flow and seepage in a deforming, shear-dilatant sensitive porous layer that enables estimates of the excess pore fluid pressures and flow rates in both the melt and solid phase to be captured simultaneously as a function of stress rate. Calculations are relevant to crystallizing magma in the solidosity range 0.5-0.8 (50-20 per cent melt), corresponding to a dense region within the solidification front of a crystallizing magma chamber. Composition is expressed only through the viscosity of the fluid phase, making the model generally applicable to a wide range of magma types. A natural scaling emerges that allows results to be presented in non-dimensional form. We show that all length-scales can be expressed as fractions of the layer height H, timescales as fractions of H2(nβ′θ + 1)/(θk) and pressures as fractions of Rco H2/(θk). Taking as an example the permeability k in the mush of the order of magnitude 10-15 m2 Pa-1 s-1, a layer thickness of tens of metres and a mush strength (θ) in the range 108-1012 Pa, an estimate of the consolidation time for near-incompressible fluids is of the order of 105-109 s. Using mush permeability as a proxy, we show that the greatest maximum excess pore pressures develop consistently in rhyolitic (high-viscosity) magmas at high rates of shear (c0 > 10-1 Pa s-1), implying that during deformation, the mechanical behaviour of basaltic and rhyolitic magmas will differ. Transport parameters of the granular framework including tortuosity and the ratio of grain size to layer thickness (a/H) will also exert a strong effect on the mechanical behaviour of the layer at a given rate of strain. For dilatant materials under shear, flow of melt into the granular layer is implied. Reduction in excess pore pressure sucks melt into the solidification front at a velocity proportional to the strain rate. For tectonic rates (generally 10-14 s-1), melt upwelling (or downwelling, if the layer is on the floor of the chamber) is of the order of cm yr-1. At higher rates of loading comparable with emplacement of some magmatic intrusions (∼10-10 s-1), melt velocities may exceed effects due to instabilities resulting from local changes in density and composition. Such a flow carries particulates with it, and we speculate that these may become trapped in the granular layer depending on their sizes. If on further solidification the segregated grain size distribution of the particulates is frozen in the granular layer, structure formation including layering and grading may result. Finally, as the process settles down to a steady state, the pressure does not continue to decrease. We find no evidence for critical rheological thresholds, and the process is stable until so much shear has been applied that the granular medium fails, but there is no hydraulic failure.
- Granular flow
- Porous media