Granular dilatancy of deforming, partially molten rock

<p>When a confined packing of sand grains is sheared, the shear strain generates a compressive normal stress [1].&#160; 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]. &#160; 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.&#160; 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].</p> <p>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.&#160; The balance of diffusive and dilatant accommodation of compatibility might depend on the ratio of shear stress to confining stress.&#160; Rock sheared by a larger stress would strain faster and potentially undergo more dilatant accommodation.&#160; Moreover, shear strain could be associated with an anisotropy in the generated normal stress.&#160; At smaller melt fractions, partially molten rock might create greater dilatancy stress, but would also have a smaller resistance to (de)compaction.&#160; Our theory addresses these issues.</p> <p>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.</p> <p>[1] Guazzelli, and Pouliquen, Rheology of dense granular suspensions, J Fluid Mech, 2018.</p> <p>[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.</p> <p>[3] McKenzie, The generation and compaction of partially molten rock, J Pet, 1984.</p> <p>[4] Katz, The Dynamics of Partially Molten Rock, Princeton University Press, 2022.</p> <p>[5] King, Zimmerman, & Kohlstedt. Stress-driven melt segregation in partially molten olivine-rich rocks deformed in torsion. J Petrology, 2010.</p> <p>[6] Quintanilla-Terminel, Dillman, Pec, Diedrich, & Kohlstedt. Radial melt segregation during extrusion of partially molten rocks. Geochem. Geophys. Geosys., 2019.</p> <p>[7] Takei & Holtzman.&#160; Viscous constitutive relations of solid&#8211;liquid composites in terms of grain boundary contiguity: 1. Grain boundary diffusion control model. JGR: Solid Earth, 2009.</p> <p>[8] Takei & Katz. Consequences of viscous anisotropy in a deforming, two-phase aggregate. Part 1. Governing equations and linearized analysis. J Fluid Mech, 2013.</p>