Application of sediment transport formulae to sand-dike breach erosion

The Technical Advisory Committee on Water Defences in the Netherlands has decided to develop a mathematical model for breach erosion in dunes and dikes, with which it will be possible to predict the growth of the breach and the discharge rate through the breach in case of a dike-burst. An essential part of such a mathematical model is the description of the entrainment of the sediment (sand or clay) and its transport through the breach. The process of breach erosion, especially in the first phases, is characterized by relatively steep slopes and large flow velocities. None of the existing sediment transport formulae has been derived and tested for these circumstances. This report presents the results of an investigation into the applicability of sediment transport formulae to sand-dike breach erosion. In view of the steep slopes and the large flow velocities, the following sediment transport conceptions have been included in the study: formulae for sand-water mixture flows: Wilson (1966), Wilson (1987), Mastbergen and Winterwerp (1987); formulae for sediment transport in flows on relatively steep slopes: Mizuyama (1977), Smart and Jaeggi (1983), Bathurst et al. (1987), Takahashi (1987), Rickenmann (1991); formulae for river regimes which have been tested for (relatively) large flow velocities (large shear stress velocities): Engelund and Hansen (1967), Van Rijn (1984a, 1984c); energetics-based sediment transport conceptions: Bagnold (1963, 1966), Yang (1979), Bagnold-Bailard, see Bailard (1981), Bagnold-Visser, see Visser (1988), these last two formulae are modifications of the original conception of Bagnold (1963, 1966); formulae for debris flows: Takahashi (1978, 1980, 1987, 1991). These sediment transport formulae, combined with Galappatti's model (1983) for the pickup of sediment, are compared with the data of two laboratory experiments (Schelde Flume experiments, see Steetzel and Visser, 1992a, 1992b) and the data of a field experiment (Zwin'89 experiment, see Visser et al., 1990). Experimental sediment transport rates have been determined as volumes of sand eroded over a certain period of time. All tests concern super-critical flow (Froude number Fr > 1, i.e. here 2.8<5 Fr<5 4.1), large values for Shields' mobility parameter (10 < theta < 100) and high concentrations (depth-averaged values rising up to about 0.25 by volume). Most of the tested sediment transport formulae predict sand transport rates being much larger than the observed quantities. Only the Bagnold-Visser formula, see Visser (1988), predicts sand transport rates within a factor two of the experimental values. With the formulation of Van Rijn (1984a, 1984c) this is possible within about a factor three. All other formulae give larger deviations from the experimental data. These conclusions hold for the three initial phases of the process of breach erosion, when the flow is supercritical, and confirm the good results obtained up to now with the BagnoldVisser formula, see Visser (1988, 1994). Once more it should be emphasized that this formula has not been derived for a situation where the rate of sand entrainment is so large as in the first three phases of the breach erosion process (this applies to both the energeticsbased method and the semi-empirical determination of the efficiency factor). The relatively large entrainment of sediment causes a relatively large increase of both the flow rate and the sediment concentration of the sand-water mixture along the inner slope (so that the effect of 'hindered entrainment' is possibly not negligible). Further study is necessary to establish the effects of the large rate of sediment entrainment on the breach erosion process. For the time being it is recommended to apply the formula of Bagnold-Visser in a mathematical breach growth model for the description of the first phases (i.e. as long as the flow is supercritical) of the breach erosion process. The present study does not recommend a formula for the important later phases of breach growth (when the flows becomes subcritical), in which most of the breach erosion takes place and in which also the dimensions of the ultimate breach are determined. Probably the data of the recent Zwin'94 field experiment (see Visser et al, 1995) will allow such a recommendation in the near future. For the present the conclusion of Voogt et al. (1991) is still valid, i.e. that the formulae of Engelund and Hansen (1967) and in particular Van Rijn (1984a, 1984c) can also be applied for relatively large current velocities in subcritical flow.