Scale-Dependent Brittle-Ductile Rheology: Insights from Laboratory Experiments.

The lithosphere appears as an heterogeneous system on a large range of length-scales, from the grain size to faults, dikes and sills sizes. These heterogeneities in material properties (composition, density, rheology) will result in a complex "effective" rheological behaviour of the lithosphere. But an important question is the scale on which this rheology will remain valid. We therefore present here an experimental study using mixtures of aqueous superabsorbent polymers where we systematically investigate the influence of the heterogeneities size on the effective rheology and its domain of validity. In water, these polymer powder grains swell up to 200 times and form gel grains whose size can be controlled by controlling the size of the initial powder. The rheology of this system is expected to combine viscous, elastic and plastic aspects, and can be characterized using the free-fall of spheres of different diameters (between 3 and 30 mm-diameter) and densities. As the typical size of the gel grains was varied between 1 and 8 mm, there is a range where it becomes comparable to the size of the falling spheres.

We therefore observe three different regimes. (1) A steady-state motion with a constant terminal velocity, as in Newtonian fluids, is reached only for high density contrast between sphere and fluid and for spheres that are large enough compared with gel grain sizes. (2) A no-motion regime appears when spheres are not buoyant enough to overcome the yield stress of the fluid. (3) In between, a "stick-slip" regime develops where spheres have an irregular vertical motion and horizontal oscillations. The two first regimes are typical of a visco-elasto-plastic fluid, with a yield stress that depends on the size of the gel, but also on the size of the intruder. The third regime directly comes from the interaction between the sphere and the gel scales. This could explain observations on the settling of crystals and nodules in a magma, as well as the upwelling of magma bodies in an heterogeneous lithosphere.