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Classical scaling relationships for rheological quantities such as the$\mu(J)$-rheology have become increasingly popular for closures of two-phaseflow modeling. However, these frameworks have been derived for monodisperseparticles. We aim to extend these considerations to sediment transport modelingby using a more realistic sediment composition. We investigate the rheologicalbehavior of sheared sediment beds composed of polydisperse spherical particlesin a laminar Couette-type shear flow. The sediment beds consist of particleswith a diameter size ratio of up to ten, which corresponds to grains rangingfrom fine to coarse sand. The data was generated using fully coupled, grainresolved direct numerical simulations using a combined lattice Boltzmann -discrete element method. These highly-resolved data yield detaileddepth-resolved profiles of the relevant physical quantities that determine therheology, i.e., the local shear rate of the fluid, particle volume fraction,total shear, and granular pressure. A comparison against experimental datashows excellent agreement for the monodisperse case. We improve upon theparameterization of the $\mu(J)$-rheology by expressing its empirically derivedparameters as a function of the maximum particle volume fraction. Furthermore,we extend these considerations by exploring the creeping regime for viscousnumbers much lower than used by previous studies to calibrate thesecorrelations. Considering the low viscous numbers of our data, we found thatthe friction coefficient governing the quasi-static state in the creepingregime tends to a finite value for vanishing shear, which decreases thecritical friction coefficient by a factor of three for all cases investigated.

Rheology of mobile sediment beds in laminar shear flow: effects of creep and polydispersity