Numerical modelling of debris surges based on shallow-water and homogeneous material approximations

Abstract

The objective of this contribution is to analyse the formation of debris waves in natural channels. Numerical simulations are carried out with a 1D code based on shallow-water equations and on the weighted averaged flux method. The numerical code represents the incised channel geometry with a power-law relation between local width and flow depth and accounts for all source terms in the momentum equation. The debris mixture is treated as a homogeneous fluid over a fixed bottom, whose rheological behaviour alternatively follows Herschel-Bulkley, Bingham or generalised visco-plastic models. The code is applied to real debris flow events that consisted of a single wave and multiple surges, in particular in the Illgraben catchment (Switzerland) and in the Cortina d'Ampezzo area (Dolomites). Numerical results are presented and compared with available flow depth registrations. A statistical analysis of debris waves shows that a good representation of wave statistics can be obtained with a proper calibration of rheological parameters.Wave propagation in time along the channel is investigated to verify if overtaking phenomena like in water roll waves do develop. Finally, an original interpretation for the formation of finite amplitude waves in a transient unstable flow is provided, based both on field data and numerical simulations.

Keywords:

• Debris
• wave
• shallow-water
• rheology
• instability
• overtaking