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摘要
This work examines the bulk internal friction coefficient, mu, and effective wall friction coefficient, mu(w), for finite number of nearly identical dry glass spheres in avalanche down a narrow inclined reservoir of smooth frictional bed using a validated discrete element scheme. Instantaneous deviatoric strain rate tensor (gamma) over dot(d)(ij) and stress tensor tau(ij) are computed locally to evaluate a three-dimensional constitutive model developed based on the rheology of steady homogeneous surface flows. On one side, the algebraic mu - I relation conforms to conventional relation for glass beads, mu = 0.34 + 0.31/(1 + 0.15/I) (Jop et al. in J. Fluid Mech. 541: 167-192, 2005, Midi in Eur. Phys. J. E 14:341-365, 2004, Jop in Comptes Rendus Phys. 16: 62-72, 2015), when the inertial number I > I-c = 2 x 10(-2). The assumption of collinear tau(ij) and (gamma) over dot(d)(ij), however, does not hold and such misalignment agrees to the findings in non-uniform inhomogeneous flows (Cortet et al. in Europhys. Lett. 88(1): 14001, 2009). Below I-c, we observe a decaying mu - I as found in slowly deforming rheology tests and a simplified model is developed in view of shear-induced dilatation upon yielding. Non-constant effective wall friction coefficient is measured to grow in time and with I towards the sphere-wall sliding friction coefficient in the contact model while preserving the depth-weakening feature as in confined steady surface flows (Richard et al. in Phys. Rev. Lett. 101: 248002, 2008, Brodu et al. in Phys. Rev. E 87: 022202, 2013). The fact that rotation at one sphere center can divert surface relative velocity across the contact area to render lower sliding friction is considered to develop a model describing how mu(w) drops with the ratio between rotation-induced velocity and sliding velocity, Omega. The simulation data compares fairly well to the predicted monotonic decay of mu(w) with Omega.
- 出版日期2016-11
