Dynamics of submerged gravitational granular flows
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Debris flows are complex, natural phenomena, characterized by a mixture of poorly sorted sediments and water driven by gravity. To investigate the basic physics of debris flows, it is very useful to analyze the flow of a mixture of identical, spherical particles saturated by water and driven by gravity down a steep channel in steady flow condition. The flow presents three regions: an external one, near to the free surface, dominated by nearly instantaneous contacts among the particles (collisional regime), an internal region dominated by prolonged contacts among the particles (frictional regime) and a static bed in which the particles are immobile. Armanini et al. (2009) analysed the stratification of rheological mechanisms inside the flow, focusing on the coexistence of frictional and collisional regimes, on the stress transmission inside the flow and on particles kinematics. In particular, it was observed that debris flows may show locally a typical intermittence of the flow regime, switching alternatively from frictional to collisional. In general, the tensor of the granular phase can be assumed to be the composition of two tensors: one, Tijgocoll, representative of the stresses exchanged with a collisional mechanism and one, Tijg-fir, representative of the stresses expressed by a frictional mechanism. While the rheology of the collisional layers is well described by the dense gas analogy (kinetic theory), a persuasive theoretical description of the frictional regime does not yet exist. A Coulombian scheme is often assumed, but this hypothesis is rather limitative because it requires a constant concentration or a distribution of particles concentration known a priori. An interesting scheme of this kind was recently proposed by GDR-Midi (2004), but this model does not contain a suitable formulation for the granular pressure (equation of state of the mixture). Following Armanini (2010), we propose a reinterpretation of the model, as weighted average of a pure Coulombian stress (dependent on the static friction angle at the static bed level) and of a dynamic stress, represented by a dynamic friction angle. Besides, a state relation is introduced for the granular pressure and the dynamic friction angle is derived from the kinetic theory. The proposed relations are finally compared with the experimental data. © 2013 Taylor & Francis Group, London.