Interaction of side weir overflow with bed-load transport and bed morphology in a channel

Side weirs, also known as a lateral weirs, and overflow dams are free overflow regulation and diversion devices commonly encountered in hydraulic engineering. They are set into the side of a channel or river allowing to spill a part of the discharge over their crest when the surface of the flow in the main-channel exceeds a certain level. The lateral loss of water is reducing the sediment transport capacity in the main-channel yielding to aggradation and the formation of a local sediment deposit in the downstream weir alignment. The reduced cross section generates backwater effects and additional contraction and expansion losses. As a consequence, the head over the side weir rises and the side overflow discharge as well. The design discharge to be diverted over the weir is increased by this flow-sediment transport interaction. Since the interaction of side overflow with bed-load and bed morphology in a channel has not been studied so far, systematic tests have been performed. Three test series and one reference experiment without side weir have been carried out in a 20.00 m long, 1.50 m wide and 1.20 m high rectangular flume. The first test series consisted of a 3.00 m long side weir, the second one had a 6.00 m long weir and the third series was characterised by two weirs of 2.50 m length each. The approach discharge varied between 0.098 m3/s ≤ Q1 ≤ 0.222 m3/s. The overall flow regime has been subcritical. The average initial bottom slope was 0.21 %. The mobile bed was characterized by a median particle size of d50 = 0.72 mm. During the experiments the water surface, the 2D-velocity field, the side overflow discharge and sediment supply were measured. The final bed morphology has been recorded by means of digital photogrammetry. Based on the systematic experimental flume study a one- and a two-dimensional empirical model for the prediction of the mobile bed evolution near the side weir have been developed. The models allow a simple and straightforward estimation of the interaction of a side overflow with bed-load transport and bed morphology in engineering practice. The 1D-model represents the overall mobile bed evolution in the weir reach. The model takes into account a deposit being uniform over the channel width. The height of the deposit only varies in longitudinal direction. In addition to the 1D-approach the 2D-model incorporates the variation of the deposit over the channel width. For the parameterisation of the two models a Maxwell-type distribution function is applied. Input parameters for both models such as the location and height of the maximum bed elevation and a shape factor are expressed in terms of non-dimensional geometric channel and side weir variables as well as hydraulic parameters and bed load transport relations. For the 2D-approach an additional relationship considering the spanwise variation is developed. To implement the models in numerical flow simulations expressions for the location of the empirical deposit relative to the side weir are established. Regarding the impact of the deposit on the intensity of side overflow it has been found out that the spilled discharge might increase by a factor of up to ≈ 3 compared to fixed plane bed conditions. In this context about 25 % of the total increase are attributed to effects of form roughness and about 75 % to bed aggradation phenomena. In this regard the height of the deposit represents the most important parameter. The location of the deposit with respect to the position of the side weir has a smaller influence, whereas the downstream shape of the deposit is of minor importance. To test the prediction accuracy of the models they have been implemented into 1D-flow calculations. The predicted side overflow was about 85 % for the 1D-model and about 91 % for the 2D-model. The difference is mainly caused due to the implementation of the spanwise variation in the 2D-model. Besides the two models a simple relationship for direct estimation of side overflow discharge in presence of bed-load transport has been established. The empirical models have been applied in a case study on the Rhone river upstream of Lake Geneva in Switzerland. In the case of a flat bed without deposit a protection for a flood event with a hundred year return period persists. Taking into account the mobile bed evolution a protection even for an extreme flood might be obtained. This presumes a sufficiently large storage volume of the retention bassin. The skewed deposit induces the formation of an oscillatory erosion gutter downstream of the weir. For the description of the sine-generated evolution of the thalweg indicative expressions are proposed. In order to test the capability of a numerical tool to reproduce the bed aggradation phenomena observed in the experiments, 1D-numerical simulations with bed-load transport have been performed (DUPIRO). From these computations it can be concluded that the most experimental phenomena are captured with reasonable accuracy.