STUDY OF AGGRADATION IN ALLUVIAL STREAMS

Abstract

The equilibrium condition of an alluvial stream of constant width is disturbed by change in any one or more of the following variables; sediment load, discharge, slope and characteristics of sediment. Aggradation in an alluvial stream can occur if sediment load is increa sed over and above its carrying capacity, due to with drawal of clear water, or due to sudden reduction in slope. In the present study the problem of aggradation due to increase in sediment load over the carrying capacity of an alluvial channel carrying constant water discharge has been investigated experimentally and numerically. The supply of sediment is assumed to be continuous and at a constant rate. The transient condition of an alluvial stream can be described by the equations, viz., continuity equations for water and sediment, resistance relationship, sediment transport equation and equation of motion for water flow. Combining these equations, and making certain assumptions de-Vries has proposed two models viz. (a) parabolic and (b) hyperbolic type, and Cunge has suggested a numerical model for describing the transient phenomenon. These are represented as under; Parabolic: |-| =K§-| (l) 8 x Ill Hyperbolic: |f . Kif} ♦ f |f& (2) Cunge Model: ^Ay^BjAZ^CJAy^+DjAZ^+H.^ 0 and ALiVyi+B^Zi+C^Ayi+1+D'AZi+1+H2= 0 (3) where Z is the depth of deposition above original bed level, t is the time, K is the aggradation coefficient, x is the distance measured in the downstream direction, c is the celerity of the bed wave, A! , Ej etc. are functions of depth of water and bed elevation at known time t at sections, i and i+l,A.y is the change in the water surface elevation in the time At and AZ is the change in bed elevation in time At. Here the sub script refers to the distance. By solving Eq. 1 for the boundary condition of the present problem the following expressions are obtained: and Z o 2 Z —1 - = e i -t\Y% erfc^ (4) _°_ = i is —£±£—T (5) iv in which r^= x/2{K t (6) where ZQ is the maximum depth of deposition at x = 0, AG is the rate of excess sediment load, /\ is the porosity of sand mass. Using the finite difference method Eq. 2 has been solved by using the double sweep method. This method was also used for the solution of Eq. 3. The experiments were conducted in a 0.20 m wide and 30 m long recirculatory tilting flume of rectangular cross-section, using nearly uniform sediments of 0.50 mm and 0.71 mm diameter. After the establishment of uniform flow, the excess sediment was added continuously at a constant rate at the upstream end of the flume. The bed and water surface profiles downstream of the section of sediment injection were recorded at certain intervals of time. The aided sediment load was varied from 0.5 Ge to 16.0 Gg, where GQ is equilibrium sediment transport rate. The data collected by Soni using 0.32 mm sand have been used in the analysis. The experimental results are compared with the results of mathematical models described above. The experimental data did not show good agreement with the results from any of the three models mentioned earlier. Analysis of data also revealed that the parabolic model with a modified aggradation coefficient predicts the transient bed profiles satisfactorily. The modified aggradation coefficient was seen to be a function of the slope, equilibrium transport rate and the rate of over loading. Experimental, data show agreement with the following equation for the maximum depth of deposition ZQ/fKt . 1.25AG/((1 -/\)K) (7) The experimental data have also been used to test the accuracy of some of the existing relations for sediment transport and channel resistance under uniform and non uniform flow conditions.