Validation of River Bank Profiles in Sand-Bed Rivers

1. Researchers have suggested different equations for river bank profile, such as trigonometric, parabolic, exponential equations, etc [1]. In this research, a laboratory study has been conducted in a straight reach of sand-bed river in order to validate ten types of river bank profile equations. For this purpose, several stable channel geometry and especially experimental observations for channel bank shapes were compared with theoretical bank profiles and then the mean standard error of each equation was calculated and according to the results the closer ones were identified. 2. Experimental study:This research concerns a carefully controlled set of experiments, to study in detail on river bank profiles in sand-bed channels. All the experiments were carried out in the Water Research Institute (WRI) in Tehran, Iran. The flume in which the experiments were carried out is 12 x 0.75 x 0.6 meters as shown in Fig. 1. The side walls of the flume are made of glass, which allows the convenience of visual observations. Water is circulated by a pump, and the discharge is measured with a triangular weir equipped at the upper tank. An adjustable tailgate controls the flow depth at the downstream end, so as not to yield the drawdown backwater. Two samples of well-graded sands with median diameter, D50, of 1.2 and 1.6 mm, and the gradation coefficient, less than 1.3 were used, because for these sizes ripples or dunes were not produced [2]. The initial cross sections for both types of sand were semi-trapezoidal and modeled by steel templates. Only one side bank was made mobile to exclude the tendency toward meanders [2, 3]. The dimensions of the semi-trapezoid were computed using the Lacey, Julien and Wargadalam, Arbelaez et al. and Meija regime equations [4]. Finally, for D50=1.2 mm, the initial semi-trapezoidal section was made with a lateral slope of 30°, and 17-cm bottom width, 32-cm top width, and 8-cm depth. For this type of sand, the amounts of constant discharge were 11.09, 12.07 and 12.88 l/s throughout the runs. In the same way, for D50=1.6 mm, the initial semi-trapezoidal section was made with a lateral slope of 30°, and 22-cm bottom width, 41-cm top width, and 11-cm depth. For this type of sand, the constant discharge rates were set 14.17, 16 and 17.96 l/s throughout the runs. For each experiment, the flume was filled by the uniform sand. Then, a channel was carved along the left side of the flume with the help of mentioned steel former fixed on a carriage. The modeled channel (carved channel) filled slowly with still water before the start of experiments. Then the tailgate was opened and the water was re-circulated. The desired discharge was kept constant until a stable channel section was reached. In other words, the experiment was continued until a dynamically stable state had been achieved. The duration of the experiments was such that the channel would establish a regime was often lasted about 5 hours. In this research equilibrium was considered to exist when changes in channel shape (width and depth) were less than 4% and the longitudinal profile of the water surface was regular and nearly constant [2, 3].Finally, the elevations of free surface and channel geometry were measured by a point gage at four sections in the 4.5-m, 5.5-m, 6.5-m and 7.5-m section from the entrance which were named section A, B, C and D. 3. In order to validate ten types of river bank profile in comparison with experimental observations for sand-bed channel tests, the mean cross sections’ shape for channel banks according to the experimental results in section A, B, C and D were determined and with the other theoretical bank profiles were drown as Figs. 2 and 3. At the next step, mean standard error of each profile equation was calculated and the results are presented in Table 1.Table 1. MSE of river bank profiles in comparison with experimental dataSand size Type of river bank profile D50=1.6 mm D50=1.2 mm 6.3100 8.3914 (1951) Cosines of Glover & Florey2.5137 3.0459 (1978)Cosines of Parker 5.8349 9.7468 (1963) Sinus of Stebbings0.7343 0.9897 (1998) Parabolic of Cao & Knight0.0421 0.0507 (1981)Exponential of Ikeda 0.0499 0.0512 (1990) Exponential of Diplas0.0532 0.0177 (1998a)Hyperbolic of Babaeyan-Koopaei and Valentine 0.1043 0.1800 (1998b)Hyperbolic of Babaeyan-Koopaei and Valentine 0.5989 0.4378 (1992)Fifth-Degree Polynomial of Diplas and Vigilar 0.1205 0.762 (1998)Third-Degree Polynomial of Diplas and Vigilar 4. The results of this research indicate that stable river bank profile can not be introduced agreeably via trigonometric equations corresponding to stable condition and non-cohesive materials. In this manner, the hyperbolic and exponential equations have less diversion in comparison with others while trigonometric equations present the most diversion in comparison with observed data. In other words, it seems that the models which consider the Reynolds-stresses resulting from turbulent momentum transfer have more accuracy in comparison with the other ones.