· · · Institutional Repository

A bed-load sediment transport formula has ben devlopd for every fraction of the sediment mixture. All existing bed-load formula have been reanalysed on their application for this purpose (Kalinske, Einstein, Meyer-Peter and Muller) as well as adaptations by different other authors

An experimental study was carried out in the framework of a research project concerning the development of a mathematical model for morphological computations in rivers in case of non-uniform sediment. The study consists of a series of laboratory experiments in a straight flume under steady, uniform (equilibrium) conditions with a restriction to bed-load transport and dune regime. The flume was fed upstream by different mixtures of two very narrow sieved size fractions. During one experiment the total amount and composition of the input mixture, the water discharge and the downstream water level were kept constant. When equilibrium was reached besides regular registrations of water and bed level the dunes were extensively sampled. The latter occurred in such a way that vertical probability distributions of the size fractions could be determined. The main results of the experiments are: (i) Vertical sorting of the size fractions occurred in all experiments: at the steep lee side of the dunes the coarse size fraction is generally deposited at a lower level than the fine size fraction. Differences in volume concentration per size fraction until 30% occur between upper and lower layers. (ii) A transition layer was found which is generally below the propagating dunes; it has a relatively coarse composition (vertical sorting:) and has a thickness of 0.1 - 0.5 H (H = average dune height). Exchange of size fractions between this layer and the upper bed layer occurs at a time scale much larger than the dune period. (iii) Because of the phenomena described above several assumptions in a mathematical model for non-uniform sediment (Ribberink, 1980) concerning the transport layer and the deposition/erosion of size fractions to/from non-moving bed are generally not fulfilled. (iv) Data are obtained for the verification and development of semi empirical components in the mathematical model (i.e. transportformula per size fraction, predictors for dune height and bed roughness).The theory of Egiazaroff (1965) concerning the critical bed shear stress per size fraction seems to be useful in a bed-load formula per size fraction of the type of Meyer-Peter & Mueller (1948). (v) A bed sampling technique was developed and suggestions are made concerning the conditions of a non -equilibrium experiment which has the aim to verify the above-mentioned mathematical model for non-uniform sediment.

The problem of aggradation in a river due to overloading is tackled with a mathematical model consisting of a set of one-dimensional (in space) basic equations in which the water motion is assumed to be quasi-steady and the sediment transport is determined by local conditions. Analytical solutions are presented of a linearized simple-wave model, parabolic model and the more general hyperbolic model. For large disturbances in the sediment transport the linearization is not allowed and an adapted solution of the hyperbolic model is obtained. Numerical computations with the complete set of basic equations learn that this solution yields better results for large disturbances but also for small disturbances. A validity diagram is presented for the different analytical models using only one dimensionless time parameter. An attempt is made to verify the analytical models with experiments of Soni et al (1980).