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 friction conditions at the top of a mobile bed are discussed for flows in the upper-plane-bed regime, i.e. for the flows with values of the bed Shields parameter larger than approximately 0.6. A special attention is devoted to flows of the bed Shields parameter bigger than 2. Experimental data for flows at high bed shear are collected from literature and new data are added from own measurements of flows of a 1.36-mm sand slurry in the 100-mm pipe loop of the Institute of Hydrodynamics. The database represents flows of very different solids and covers friction conditions within a broad range of Shields parameters up to the maximum value of about 23. The paper analyses the data in order to evaluate a relationship among the equivalent roughness of the top of the bed and other relevant parameters. A semi-empirical formula is proposed that relates the equivalent roughness to the bed Shields parameter, the ratio of flow velocity and particle settling velocity, and the ratio of flow hydraulic radius and particle diameter. The formula is applicable primarily to flows of combined load (contact- and suspended loads together). and Příspěvek se zabývá mechanismem tření na povrchu erodovatelného dna za podmínek horního režimu pohybu splavenin nad plochým dnem, to jest při hodnotách Shieldsova parametru větších než přibližně 0,6. Zvláštní pozornost je věnována proudění při Shieldsově parametru větším než 2. Z literatury byla sebrána experimentální data pro proudění za vysokých smykových napětí, ke kterým byla přidána nová data z vlastních měření s pískem velikosti středního zrna 1,36 mm v potrubí průměru 100 mm trubního okruhu Ústavu pro hydrodynamiku AV ČR. Databáze obsahuje výsledky měření pro částice různých vlastností v širokém rozsahu hodnot Shieldsova parametru až do hodnoty okolo 23. Příspěvek analyzuje data za účelem stanovení závislosti hydraulické drsnosti povrchu sedliny na ostatních parametrech proudění. Je navržen semiempirický vztah, který předpokládá závislost hydraulické drsnosti na Shieldsově parametru, poměru rychlosti proudění k usazovací rychlosti částic a poměru hydraulického poloměru průtočného profilu k velikosti částic. Tento vztah se doporučuje především pro proudění nesoucí jak dnové splaveniny, tak suspendované částice.
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.