Predicting entrainment of mixed size sediment grains by probabilistic methods
The bedload transport of mixed size sediment is an important process in river engineering. Bedload transport controls channel stability and has a significant bearing on the hydraulic roughness of the channel. The prediction of bedload transport traditionally relies upon defining some critical value of fluid force above which particles of a particular diameter are assumed to be put into transport. The suggestion here is that the transport of bed material is size dependent with large grains being more difficult to remove from the bed surface than small grains and that all grains of the same size start to move under identical conditions. While it is relatively straightforward to assess the forces required to engender transport in a bed of uniform size grains, it is not so simple where there are a number of different grain sizes present. Multitudinous experimental studies have revealed that where there are a number of grain sizes present, large grains tend to become mobilised under lower fluid forces and small grains mobilised under higher fluid forces than those required for beds of uniform material. These results led to the development of so-called hiding functions which are used to model the variation of particle mobility with its relative size within the mixture. These functions derive their name from the tendency of large grains to shelter smaller grains from the action of the flow. Determining the relative mobility of each fraction in a mixture under given hydraulic conditions is the key to predicting how the composition of the bed load will relate to that of the bed surface material. Experiments were carried out in a rectangular, glass sided channel, in a sediment recirculation mode, under varying hydraulic conditions with a set of six different sediment mixtures. Laser Doppler Anemometry (LDA) was used to attain instantaneous velocity measurements at a number of locations in the flow. A Laser Displacement Meter was used to measure the detailed topography of small sections of the bed surface. Novel analysis techniques facilitated the determination of the grain size distribution of the bed surface by a grid-by-number method. The minimum force required to entrain each grain could also be estimated by a grain pivoting analysis. This information represents the resistance of the bed grains to erosion by flowing water. With the critical conditions for the bed grains known, it is possible to estimate the proportion of each fraction entrained from the bed surface under given hydraulic conditions. To estimate the bedload composition it is first necessary to scale by the proportion each size comprises on the bed surface and then, by a function of grain diameter to account for size dependency of travel velocity. For mean hydraulic conditions the proportion of the bed mobilised can be simply determined by inspection of a cumulative distribution of critical conditions. In reality, although it may be possible to entrain some grains at the mean velocity/shear stress, the majority of transport may be anticipated to occur during high magnitude events. Turbulence may be incorporated by adopting a probabilistic approach to the prediction of grain entrainment. By considering the joint probability distribution of bed shear stress and critical shear stress, one may attain the probability of grain entrainment. Comparison of the probability of erosion of each fraction facilitates a prediction of the bedload composition. Results show that the probabilistic approach provides a significant improvement over deterministic methods for the prediction of bedload composition.