Debris-flow Run-up on Vertical Barriers and Adverse Slopes.

Abstract:

Run-up of debris flows against obstacles in their paths is a complex process that involves abrupt flow deceleration and redirection, and it thereby provides a stringent test of physically based debris-flow models. We have investigated run-up dynamics by using large-scale laboratory experiments, simple analytical models, and a depth-integrated numerical model (D-Claw). Our findings indicate that run-up behavior (and the relationship between run-up height, $H$, and incoming flow speed, $u_0$, and depth, $h_0$) varies significantly as the steepness of the obstacle varies, and also varies in response to wave interactions during the unsteady run-up process. Run-up against vertical walls that are normal to the incoming flow path is dominated by development of a shock, or jump in flow height, associated with an abrupt deceleration of the flow speed from $u_0$ to 0. With some incoming flow conditions, $H$ can greatly exceed $u_0^2/2g$, the value predicted by a point-mass run-up model (where $g$ is the gravitational acceleration). As the angle of inclination of the run-up obstacle decreases, the character of the run-up process changes to one dominated by a sustained, smooth flux of mass and momentum from the flow body into the flow head. Reduced energy dissipation in the absence of a shock can result in higher run-up. An obstacle inclination angle of about 20 to 30 degrees generally allows the highest run-up, although the optimal slope angle depends on a variety of factors such as debris liquefaction and a resultant reduction in friction. Our comparisons of model predictions and experimental data lead us to conclude that analytical models of shocks and momentum fluxes provide guidance for conceptualizing the run-up process, but fail to account for some of the dynamics involved. In contrast, D-Claw predictions of run-up are accurate and illustrate the dependence of run-up height on nuances in flow dynamics and obstacle geometry.