The rheophysical approach in the study of natural gravity-driven flows
Abstract: Natural gravity-driven flows are frequent phenomena in the Alps. Typical examples include snow avalanches, debris flows, rock avalanches, and so on. These flows of bulk materials threaten man's activities and life and consequently the rising demand for higher safety measures has given impetus to the development of models for predetermining the flow features and the probability of their occurrence. A key point in the development of these models is the (bulk) constitutive equation. Most current models speculate the form of the constitutive equations; the parameters involved in the resulting equations of motion are then adjusted from field data. However, this does not provide evidence that the assumed constitutive equation is appropriate. Another approach is to directly derive the constitutive equation (or, more precisely, some rheological properties) from field data similarly to what is done in fluid rheometry. Exemplifying this approach with real snow avalanches, we show that the deduced rheological properties cannot properly be interpreted. Notably, we provide evidence that the Coulomb frictional model is a suitable model for describing the motion of snow avalanches, but the status of the friction coefficient is unclear: is it a genuine friction parameter or does it reflect a complex combination of various processus (including bulk deformation, slipping, mass variation, etc)?
This problem is quite general in continuum mechanics: do we understand the physics behind the constitutive equation? Is the constitutive equation a black-box model mimicking bulk behaviour? To gain insight into this issue, the rheophysical approach is helpful: its objective is not only to determine the constitutive equation but also to explain and interpret its origin from physical considerations on the particle scale. The bulk stress tensor is introduced as the average of local stresses. We present an application of this approach in the case of dry granular flows, which can be seen as the simplest representation of natural gravity-driven flows on the laboratory scale. Experiments reveal complicated rheological properties that can be better understand from a microstructural viewpoint. Notably we propose a model for determining the constitutive equation for the frictional-collisional regime, based on the notion of percolating networks of particles in close contact.