Instability and surge development in debris flows

Abstract

Debris flows are often described as a succession of surges, which are characterized by enhanced peak depth and velocity and therefore by a tremendous increase of their destructive power. For given characteristics of the base flow, if the channel is sufficiently long to allow an appreciable wave development, the linear stability analysis in shallow streams is shown to provide a reasonable prediction of the critical flow condition and of the instability growth rate. The one‐dimensional (1‐D) theory, however, does not allow the determination of the wave period of the fastest growing perturbations. Debris waves most frequently develop following a mechanism similar to water roll waves: Instabilities grow up becoming clearly distinguishable waves, and then waves overtake one another with increasing wave period and amplitude. The typical hydrograph of a multiple‐peak event is shown to be composed of a first surge, which is usually characterized by the highest depth, the longest duration, the greatest erosive power, and the most symmetrical shape, and of secondary waves that burst on the flow tail in the recession phase. The characteristics of the first surge can be explained by two different mechanisms. All waves that rise up near the flood crest run faster than this first surge and coalesce into it, causing its high depth and great volume. Moreover, segregation during the flow induces the concentration of boulders at the fronts, contributing to its depth enhancement, erosive power, and symmetrical shape. When a debris surge impacts a structure, the force pattern can be interpreted as the superposition of the reflection of the bouldery front and the formation of a vertical muddy jet due to the impact of the front wedge. Wave reflection can be described by a 1‐D mass and momentum balance across the front, whereas the pressure impulse, due to the incompressibility of the interstitial fluid, can be analyzed through inviscid formulations validated for the representation of tsunami forces.