A two-layer depth-averaged approach to describe the regime stratification in collapses of dry granular columns

Abstract

The dynamics of dry granular flows is still insufficiently understood. Several depth-averaged approaches, where the flow motion is described through hydrodynamic-like models with suitable resistance laws, have been proposed in the last decades to describe the propagation of avalanches and debris flows. Yet, some important features of the granular flow dynamics cannot be well delivered. For example, it is very challenging to capture the progressive deposition process, observed in collapses and dam-break flows over rough beds, where an upper surface flow is found to coexist with a lower creeping flow. The experimental observations of such flows suggest the existence of a flow regime stratification caused by different momentum transfer mechanisms. In this work, we propose a two-layer depth-averaged model, aiming at describing such a stratification regime inside the flowing granular mass. The model equations are derived for both two-dimensional plane and axi-symmetric flows. Mass and momentum balances of each layer are considered separately, so that different constitutive laws are introduced. The proposed model is equipped with a closure equation accounting for the mass flux at the interface between the layers. Numerical results are compared with experimental data of axi-symmetric granular collapses to validate the proposed approach. The model delivers sound agreement with experimental data when the initial aspect ratios are small. In case of large initial aspect ratios, it yields a significant improvement in predicting the final shape of deposit and also the run-out distances. Further comparisons with different numerical models show that the two-layer approach is capable of correctly describing the main features of the final deposit also in the case of two-dimensional granular collapses.