Non-equilibrium vs. classical approaches for 2D erosive and sediment-laden models

Sergio Martínez-Aranda

Erosive and sediment-laden surface flows are among the most challenging gravity-driven geophysical processes and many recent studies are focused on improving their mathematical an numerical modelling. From the physical point of view, in Earth surface flows, sediment transport can occur under a steady equilibrium state or, contrarily, under transient non-equilibrium conditions, regardless of the transport mechanism considered, i.e. bedload or suspended load. The classical equilibrium approach considers that the actual solid rate is the capacity of the flow to carry solid weight and hence only depending on instantaneous local flow features. This capacity solid rate can be estimated using different empirical closure relations measured in laboratory and found in literature, and probably is the most widespread approach because of its symplicity. Contrarily, in sediment transport models based on the non-equilibrium assumption, the actual transport rates must be computed through the advection of the solid particles in the flow layer and the mass exchange with the underlying static riverbed, and usually it does not agree with the local load capacity of the flow. Extremely transient flows, such as dam collapses, erosive dike breach or rapid fully saturated landslides, are systems which always change in space and time, hence absolute equilibrium states in the coupled fluid/solid transport rarely exist. Intuitively, assuming non-equilibrium conditions in transient flows should allow to estimate correctly the solid transport rates and the bed level evolution. However, non-equilibirum hypothesis involves a high uncertainty in the estimation of the parameters associated to entrainment/deposition rates and the advective transport rate. Furthermore, considering the unbalanced movement of the transported solid particles respect to the water phase may lead to the appearance of shear-induced pore fluid pressures during the movement of dense-packed sediment-laden flows. To get insight into this topic, novel 2D Finite Volume models for solid transport based on the non-capacity approach have been developed along the last 5 years. These models include the analysis of the mechanical interaction between moving water phase and sediment particles at a grain scale, and propose new generalized mathematical formulaitons for bed material exchage and solid transport rates for highly transient processes. The non-equilibrum models have been tested against laboratory dateset and recent field-scale events, offering promising results regarding the need and the applicability of the non-equilibrium hypothesis.