BED LEVEL VARIATION IN ALLUVIAL STREAMS

Abstract

Addition of clear water flow to a stream originally in equilibrium causes degradation of the bed and banks. Similarly, withdrawal of clear water flow from a stream in equilibrium results in aggradation. These processes continue for sometime until a new equilibrium is reached. In the present study, these problems of aggradation and degradation respectively due to withdrawal and addition of clear water from/to an alluvial stream of constant width and in equilibrium have been investigated. The equations which govern the flow in an alluvial stream are : continuity equations for water and sediment, resistance relationship, sediment transport equation and equation of motion for water, combining these equations and making certain assumptions,de Vries (69) has proposed the following parabolic model for bed level variation : 2 et = Ko "JS (1) Here 2 is the depth of deposition (or erosion) above (or below) the original bed level, t is the time, K is the theoretical o aggradation (or degradation) coefficient and x is the distance measured in the downstream direction. For the boundary conditions of the problem of aggradation due to overloading at a constant rate, Mehta (43) obtained the following solution for Eq.(1). and 2_ Z VKt o •v = 1.128 b G (iii) r) V n erfc 77 AG K (1-X) o 3 S (l-\) o where r) = 2 VKt o (2) (3) (4) (5) Here Z is the maximum depth of deposition at x=0, S is the o o original bed slope, G is the equilibrium sediment transport rate, b is the exponent in the sediment transport relation (G=aU ), AG is the rate of excess sediment load and \ is the porosity of the sediment. The cases of aggradation and degradation due to withdrawal and addition of flow have been converted into the cases of aggradation due to excess sediment load and degradation due to deficient sediment load respectively to enable the use of the above solution to the present case. The equation for the rate of overloading/underloading AG/G.may be obtained as : AG G. JJtl b/3 m b/3 (6) Where q and q are the initial and changed water discharge rates respectively, G is the sediment transport capacity of the flow corresponding to q.. (iv) Experiments were carried out by simulating the conditions of aggradation and degradation on account of withdrawal and addition of flow respectively in two titling flumes, one 0.75 m wide and 16m long and the other 0.20 m wide and 30 m long. Three nearly uniform materials of sizes 2.37 mm, 1.18 mm and 0.71 mm (and relative density = 2.65) were used as bed material in these experiments. Uniform flow condition was first established in the flume for a particular discharge and equilibrium mean sediment transport rate was determined. The discharge was then varied in very short time and in one step keeping the rate of sediment injection the same as that during uniform flow. The bed and water surface profiles were recorded at regular intervals of time. The changed discharge in aggradation experiments ranged from 0.21 to 0.75 times the initial discharge while in degradation experiments it varied from 1.27 to 4.55 times the initial discharge. The data collected by Soni (57) and Mehta (43) on aggradation due to overloading have also been used in the analysis. The experimental data did not show good agreement with the results from the parabolic model of de Vries (when the theoretical expression for KQwas used) and it was observed that the data exhibited significant departure from the theoretical curve represented by Mehta's solution (43). The analysis of data revealed that the parabolic model with a modified aggradation/degradation coefficient K predicts the transient bed profiles satisfactorily. It was found that the modified aggradation (or degradation) coefficient K is a function of the (v) rate of overloading/underloading ,AG/Ge and time t. Using principles of dimensional analysis, a relation for K /K in o terms of Ut/Rfa and AG/G was developed. Here U, R e • -, ..b velocity and hydraulic radius respectively under equilibriu flow condition. The modified aggradation coefficient K enabl satisfactory prediction of bed profiles in aggradation for the entire range of „ f=_^_lvaiues and in degradation for r> < 0.4. For 7) > 0.4, it was observed that the data depart considerably from Eq. (2) in case of degradation. For such r) values the following empirical equation predicts the bed profiles satisfactorily. = 0.5 e"0'7^ are m es (7) The experimental data have been analysed to obtain the following equation for the maximum depth of deposition or erosion. V G t e c -„ .-0.34 Ut -0.097 Cl {S0} (-R-) (8) The coefficient C^n Eq. (8) is obtained as a function of the rate of overloading or underloading, AG/Gg. Equations (2) to (8) along with the graphical relations for K and C enable computation of temporal and spatial changes in bed levels under aggrading or degrading flows. Sediment transport rates under non-equilibrium conditions have been computed using the measured bed profiles and the continuity equation for sediment. The data of Soni (57) and Mehta (43) as well as those of the present study on the (vi) variation of sediment transport rate during aggradation and degradation were first used to check some of the existing non-equilibrium sediment transport relationships and the agreement of experimental data with these relationships was found to be not satisfactory. The modified form of non-equilibrium sediment transport relationship of Rahuel et al. (52) proposed by Ranga Raju et al.(55) viz. -(-€-) -Ki -£• e 1 h (9) shows some promise. (Here K is the loading coefficient and h is the local flow depth). The analysis revealed that the loading coefficient K. is a function of U/U where U is the 1 o local mean flow velocity and U is the mean flow velocity under o uniform flow conditions. However, the accuracy of this predictor for K needs to be improved if Eq.(9) alongwith this predictor is to be used for morphological calculati