Spillage Over an Inclined Embankment

Abstract

Accidental release of liquid from a storage tank, and the subsequent spillage over the surrounding embankment is considered. The present analysis is based on two simplifying assumptions: (1) The supercritical flow over the inclined embankment can be considered quasi‐steady, and thus treated by a classical model for gradually varied flow in open‐channels; (2) it is assumed that the overflow quenches when the level in the reservoir has reached a certain critical limit, so that the remaining liquid in the tank will be trapped by the dike. An analytical solution for the spill fraction is derived, showing that the spill fraction is a decreasing function of the ratio of the dike height to the initial tank level. The spill fraction is furthermore found to depend on a critical Froude number, the slope of the embankment, and a Chezy coefficient. The latter quantity, which accounts for ground friction and turbulence, is the only empirical parameter in the analysis. Predictions based on this simple model compare favorably with experimental observations from model inclines.