Shear-induced pressure changes and seepage phenomena in a deforming porous layer - I

Abstract

S U M M A R YWe 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 H 2 (nβ θ + 1)/(θ k) and pressures as fractions of Rċ 0 H 2 /(θ k). Taking as an example the permeability k in the mush of the order of magnitude 10 −15 m 2 Pa −1 s −1 , a layer thickness of tens of metres and a mush strength (θ ) in the range 10 8 -10 12 Pa, an estimate of the consolidation time for near-incompressible fluids is of the order of 10 5 -10 9 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 (ċ 0 > 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.

Deformation-induced mechanical instabilities at the core-mantle boundary

“…But the observation that migration of FeS melt upwards in the experimental charge (i.e. against gravity) suggests that transient granular dilatancy and associated pressure gradients driven by shear, as predicted in theoretical models of Petford and Koenders (2003), lends further support to the basic physics underlying the microscopic regime (Fig. 9).…”

“…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).…”

“…(1) that takes into account the effects of coupled shear strain and volume stress. The reader is referred to Petford and Koenders (2003) and Petford (2005, 2007) for a full treatment of the mathematical details of granular aggregates deforming under pure and simple shear that includes also the effects of rate-dependency. The basic model is incremental, and by assigning fixed material properties for the permeability and stiffness of the solid phase, Eq.…”

“…The model put forward is described in detail in Petford and Koenders (2003) but summarised here for completeness. The total stress is σ ij = σ' ij Ϫ pδ ij where p is the excess pore pressure and σ' is the skeletal stress (Terzaghi, 1943).…”

“…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.…”