Granular dilatancy of deforming, partially molten rock

When a confined packing of sand grains is sheared, the shear strain generates a compressive normal stress [1].  If the sand is unconfined, the shear leads to a volume expansion of the pore space between grains, low fluid pressure, and imbibition of fluid [1]. This physics is known as dilatancy [2].   We hypothesise that dilatancy occurs within a deforming, basalt-saturated aggregate of olivine grains. We extend a theory for the dynamics of partially molten rock [3,4] to describe this.  We analyse the theory in the geometry of laboratory experiments and show that the dilatancy hypothesis can explain a variety of robust, non-trivial features of experiments. These include the angle of melt bands and the inward melt segregation in torsional and Poiseuille flows [5,6].

One mechanism by which partially molten rock can deform is grain-boundary sliding with geometric incompatibility between grains accommodated by mass diffusion. Dilatancy would also accommodate granular incompatibility.  The balance of diffusive and dilatant accommodation of compatibility might depend on the ratio of shear stress to confining stress.  Rock sheared by a larger stress would strain faster and potentially undergo more dilatant accommodation.  Moreover, shear strain could be associated with an anisotropy in the generated normal stress.  At smaller melt fractions, partially molten rock might create greater dilatancy stress, but would also have a smaller resistance to (de)compaction.  Our theory addresses these issues.

A theory of anisotropic viscosity [7,8] has previously been proposed to explain the features of deformation experiments on olivine aggregates. We compare and contrast its physical basis and predictions with those of dilatancy.

[1] Guazzelli, and Pouliquen, Rheology of dense granular suspensions, J Fluid Mech, 2018.

[2] Reynolds, LVII. On the dilatancy of media composed of rigid particles in contact. With experimental illustrations. The London, Edinburgh, and Dublin Phil Mag and J Sci, 1885.

[3] McKenzie, The generation and compaction of partially molten rock, J Pet, 1984.

[4] Katz, The Dynamics of Partially Molten Rock, Princeton University Press, 2022.

[5] King, Zimmerman, & Kohlstedt. Stress-driven melt segregation in partially molten olivine-rich rocks deformed in torsion. J Petrology, 2010.

[6] Quintanilla-Terminel, Dillman, Pec, Diedrich, & Kohlstedt. Radial melt segregation during extrusion of partially molten rocks. Geochem. Geophys. Geosys., 2019.

[7] Takei & Holtzman.  Viscous constitutive relations of solid–liquid composites in terms of grain boundary contiguity: 1. Grain boundary diffusion control model. JGR: Solid Earth, 2009.

[8] Takei & Katz. Consequences of viscous anisotropy in a deforming, two-phase aggregate. Part 1. Governing equations and linearized analysis. J Fluid Mech, 2013.