A Master of Science thesis in Civil Engineering by Mahsa Hashemi entitled, “Stage-discharge relationship in two-stage channels”, submitted in July 2019. Thesis advisor is Dr. Serter Atabay. Soft and hard copy available.
Predicting the stage-discharge relationship in a flood event is an important concern. Once the flow exceeds the bank level in a two-stage channel, there is a momentum transfer that occurs at the interface between the main channel and its floodplain, which makes the problem more complicated. Several methods predict the stage-discharge relationship in two-stage channels; single-channel method (SCM), divided channel method (DCM), coherence method (COHM), weighted divided channel method (WDCM) and exchange discharge model (EDM). For analysis, all these methods were applied to the 18 m flume data collected in a symmetric smooth compound channel and the four cases of the symmetric rough compound channel. The SCM overestimated the stage for a given flow, whereas the DCM underestimated it. Although the WDCM is simple to use, it neglects the momentum transfer while calculating the stage-discharge, and it requires defining an appropriate weighing factor ξ to determine the stage-discharge relationship. On the other hand, the COHM and the EDM consider the momentum transfer; hence, showed better stage-discharge results. However, both COHM and EDM are very complex to use. Therefore, the aim of this study was to develop a simple method that can predict the stage-discharge relationship in symmetric compound channels accurately during flood events. In this study, the new method is proposed by improving the WDCM, and it is called improved weighted divided channel method (IWDCM), which includes the apparent shear force (ASF), wetted perimeters and B/b ratio. It was concluded that IWDCM is limited to all rigid symmetric compound channels with B/b ratios greater than or equal to 3. The IWDCM for smooth, symmetric compound channel led to percentage errors of 5.59%, 6.01% and 4.91% for total, main channel and floodplain discharges, respectively. On the other hand, for the rough symmetric compound channel, the results showed 1.85%, 7.74%, 10.75%, and 5.91% for total discharges for cases 1, 2, 3, and 4 respectively. Lastly, the IWDCM was applied to two datasets for validation purposes, and similar results were obtained. Therefore, the IWDCM can be used to predict the stage-discharge relationship in compound channels during flood events.