Orateur
Description
Predictive modeling of large-scale geophysical mass movements, such as rock avalanches and pyroclastic currents, heavily relies on depth-averaged continuum equations. To account for basal dissipation, these models necessitate closures in the form of a basal friction coefficient, $\mu$, which encompasses the complex interplay of local multiphysics and multiphase dissipation mechanisms. In order to match runout distances and flow velocities, this coefficient is often empirically calibrated. To date, there is no consensus in the literature on a universal friction law that remains valid across a wide range of configurations, and standard granular rheologies (such as $\mu(I)$) show limits on steeper or smoother topographies where the flow significantly accelerates. Additionally, the values tuned in geophysical models are often much lower than those measured locally at the basal interface.
To bridge the gap between local interfacial rheology and macroscopic models, we employ DEM simulations to investigate granular flows over a smooth incline in a geometrical configuration resembling a laboratory-scale experimental facility. Unlike typical numerical setups that rely on streamwise periodicity to enforce steady-uniform regimes, our configuration retains the full streamwise extent of the flow by incorporating an inlet silo discharge and an outlet chute. This complete resolution of the flow along the incline provides a robust basis for developing an inverse method approach: by formulating a complete set of depth-averaged integral conservation laws, we evaluate all macroscopic terms directly from our depth-integrated DEM measurements. Extracting the effective basal friction in this manner allows us to systematically test how different macroscopic assumptions dictate the required $\mu$ closure.
Based on this analysis, we propose a new compressible depth-averaged framework. We show that this compressible formulation remains remarkably consistent with the friction obtained from local stress ratios at the bottom across a wide range of flow regimes, whereas standard incompressible frameworks yield anomalously low effective friction as the flow accelerates and dilates. This comparison questions the standard choice of depth-averaged models in highly inertial contexts and could help explain the persistent gap between the artificially low friction values tuned in large-scale geophysical models and actual local measurements.
Applying this inverse framework across diverse configurations, we introduce a modified Froude number yielding a robust macroscopic $\mu(Fr)$ law. However, while well-defined for any given setup, this description unfolds into a family of distinct curves depending on the microscopic interparticle and bottom friction coefficients. Seeking a more universal scaling, we perform a DEM-based parametric study to unpack the underlying physics. By analyzing the basal sliding-to-rolling ratio ($S$) alongside the basal volume fraction ($\phi_b$), we reveal a global transition from dense, rolling-dominated states at low inertia to highly agitated, sliding-dominated regimes, highlighting that granular flows adapt to boundary constraints by adjusting their internal structure---specifically via local dilation and near-wall rotation---to minimize global dissipation.