Viscoplastic modeling of granular column collapse with pressure-dependent rheology

Abstract

International audienceA mechanical and numerical model of dry granular flows is proposed that quantitatively reproduce laboratory experiments of granular column collapse over inclined planes. The rheological parameters are directly derived from the experiments.The so-called \mu(I) rheology is reformulated in the framework of Drucker-Prager plasticity with the yield stress and viscosity \eta(||D||,p) depending on both the pressure p and the norm of the strain rate tensor ||D||. The granular domain, velocities, stress deviator and pressure fields are calculated using a finite element method based on an iterative decomposition-coordination formulation coupled with the augmented Lagrangian method. 2-D simulations using this model well reproduce the dynamics and deposits of collapsing granular columns. The flow is essentially located in a surface layer behind the front, whereas it is distributed over the whole depth near the front where basal sliding occurs. The computed runout distances and slopes of the deposits agree very well with the values found in the experiments. Using an easily calculated order of magnitude approximation of the mean viscosity during the flow (\eta = 1 Pa s here), we show that a Drucker-Prager rheology with a constant viscosity gives results very similar to the \mu(I) rheology and agrees with experimental height profiles, while significantly reducing the computational cost. Within the range of viscosities 0.1 < \eta < 1 Pa s, the dynamics and deposits are very similar. The observed slumping behavior therefore appears to be mainly due to the flow/no-flow criterion and to the associated strain-independent part of the "flowing constitutive relation" (i.e. related to plastic effects). However, the results are very different when an unrealistically large value of viscosity (10 Pa s) is used

An analytic approach for the evolution of the static/flowing interface in viscoplastic granular flows

“…Furthermore, this continuum approach is in good agreement with discrete element simulations of granular column collapse [37]. Reference [32] showed that using a constant viscosity gives very similar results to using the µ(I) rheology for granular column collapses of small aspect ratios over horizontal and inclined planes. In all these regimes, the basic ingredients, required to reproduce dry granular flows at the "large scale" from the destabilization phase to the arrest phase, seem to be present in the proposed viscoplastic rheologies.…”

“…The so-called µ(I) rheology, where I is the inertial number, involves a viscosity that depends on the pressure and the strain rate experienced by the granular material. It enables to quantitatively reproduce granular column collapse over horizontal and inclined slopes and granular flow experiments over erodible substrate [35,32]. Furthermore, this continuum approach is in good agreement with discrete element simulations of granular column collapse [37].…”

“…At the "large scale" (i.e. the scale of the flow), this transition has been described by introducing a Drucker-Prager [35,37,18,32] or a Coulomb [19] yield stress or by describing explicitly the transition from the flowing to the static states through an order parameter that varies continuously between these two states [4,5,42].…”

Effective friction of granular flows made of non-spherical particles

“…More generally, this approach has been successfully applied in different geometries [2,3], e.g. silo discharge [11], granular chute flows [12][13][14][15] and granular column collapse [16,17], as well as to describe dynamic compressibility effects associated with spontaneous oscillatory motion [18,19]. Interestingly, experiments and numerical simulations have recently provided evidence for limie-mail: somfai.ellak@wigner.mta.hu tations of the μ(I)-rheology, when some non-local effects come into play (see e.g.…”

Augmented Lagrangian Methods for Numerical Solutions to Higher Order Differential Equations

“…with various boundary values [7], mechanics [7] [8] [9], medical imaging and computational biology [10], geophysics [11], ontology regarding big data representation and storage [12], and elastica theory [13], to name just a few.…”