In an open channel with a mobile bed, intense transport of bed load is associated with high-concentrated sediment-laden flow over a plane surface of the eroded bed due to high bed shear. Typically, the flow exhibits a layered internal structure in which virtually all sediment grains are transported through a collisional layer above the bed. Our investigation focuses on steady uniform turbulent open-channel flow with a developed collisional transport layer and combines modelling and experiment to relate integral quantities, as the discharge of solids, discharge of mixture, and flow depth with the longitudinal slope of the bed and the internal structure of the flow above the bed. A transport model is presented which considers flow with the internal structure described by linear vertical distributions of granular velocity and concentration across the collisional layer. The model employs constitutive relations based on the classical kinetic theory of granular flows selected by our previous experimental testing as appropriate for the flow and transport conditions under consideration. For given slope and depth of the flow, the model predicts the total discharge and the discharge of sediment. The model also predicts the layered structure of the flow, giving the thickness of the dense layer, collisional layer, and water layer. Model predictions are compared with results of intense bed-load experiment carried out for lightweight sediment in our laboratory tilting flume.
Collisional interactions in a sheared granular body are typical for intense bed load transport and they significantly affect behavior of flow carrying bed load grains. Collisional mechanisms are poorly understood and modelling approaches seldom accurately describe reality. One of the used approaches is the kinetic theory of granular flows. It offers constitutive relations for local shear-induced collision-based granular quantities – normal stress, shear stress and fluctuation energy – and relates them with local grain concentration and velocity. Depth distributions of the local granular quantities produced by these constitutive relations have not been sufficiently verified by experiment for the condition of intense bed load transport in open channels and pressurized pipes. In this paper, results from a tilting-flume facility including measured velocity distribution and deduced concentration distribution (approximated as linear profiles) are used to calculate distributions of the collision-based quantities by the constitutive relations and hence to test the ability of the kinetic-theory constitutive relations to predict conditions observed in these collision-dominated flows. This test indicates that the constitutive relations can be successfully applied to model the local collisional transport of solids at positions where the local concentration is not lower than approximately 0.18 and not higher than approximately 0.47.
The paper describes results of validation of authors' recently proposed formulae for sediment transport and bed friction in the upper plane bed regime using laboratory experiments in a pressurized pipe. Flows of mixture of water and fine to medium ballotini (d50 = 0.18 mm) were observed in a rectangular pipe (51 x 51 mm) with a deposit at the bottom of the pipe. A comparison of test results with transport-formula predictions shows a satisfactory match confirming a good prediction ability of the proposed transport formula at high bed shear. A prediction ability of the friction formulae appears to be less convincing but still reasonable. A joint use of the formulae for transport and friction predicts the delivered concentration of transported sediment within the accuracy range of ± 40 per cent for flows in which transported sediments strongly affect the bed friction, i.e. for flows with delivered concentration of sediment higher than say 3 per cent.
Intense collisional transport of bimodal sediment mixture in open-channel turbulent flow with water as carrying liquid is studied. The study focusses on steep inclined flows transporting solids of spherical shape and differing in either size or mass. A process of vertical sorting (segregation) of the two different solids fractions during the transport is analyzed and modelled. A segregation model is presented which is based on the kinetic theory of granular flows and builds on the Larcher-Jenkins segregation model for dry bimodal mixtures. Main modifications of the original model are the carrying medium (water instead of air) and a presence of a non-uniform distribution of sediment across the flow depth. Testing of the modified model reveals that the model is applicable to flow inclination slopes from 20 to 30 degrees approximately, making it appropriate for debris flow conditions. Changing the slope outside the specified range leads to numerical instability of the solution. A use of the bimodal mixture model is restricted to the grain size ratio 1.4 and no restriction is found for the grain mass ratio in a realistic range applicable to natural conditions. The model reveals trends in the vertical sorting under variable conditions showing that the sorting is more intense if flow is steeper and/or the difference in size or mass is bigger between the two sediment fractions in a bimodal mixture.