RESPONSES OF BED SLOPE RATIO TO BED-LOAD FORMULAS IN OPEN CHANNELS WITH ABRUPTLY WIDENING/NARROWING APPROACHES

Abstract

 Present study examines responses of the longitudinal bed profiles to bed shear stress changes and associated changes of the bed load transport rates which are caused in straight open channels with different flow widths where the channel is connected by an abruptly widened approach or a narrowed one. To investigate the response of bed slope ratio to the change of bed-load transport rate, we employ two bed load formulas for discussions; one is the bed- load formula characterized by τ_∗^3/2 with τ_∗c, and the other is the bed load formula expressed by τ_∗^5/2. Besides, to see role of the bed load formula explicitly in the regime relation, the regime formulas for describing the bed slope ratio, specific bed elevation etc. were obtained, assuming that an equilibrium sediment transportation accomplished. The regime formula shows that the bed slope ratio, i₂/i₁ increases monotonically with the increase of the flow width ratio when τ_∗^5/2 type of the bed load formula is employed in the regime equation, where suffixes 1 and 2 show the quantities upstream and downstream. However, the regime formula shows that the bed slope ratio depends on the bed shear stress change when τ_∗^3/2 type bed load formula is employed. The present study topics are classic, and not new, but it is very important to study the response of the longitudinal bed profile to the bed load transport rate to look for a suitable form of the bed load equation.