SCOUR AROUND BENDS IN ALLUVIAL CHANNELS

Abstract

This thesis presents a study of shear distribution in rectangular rigid boundary open channel bends and the scour pattern in rectangular open channel bends with rigid side walls and mobile bed. The forced vortex conditions were assumed to prevail at the exit section. The constant involved in the assumr-d mean velocity distribution was evaluated on the basis of continuity equation with the assumption that entire super elevation dies 1 out at exit section. Further it is assumed that a mean velocity relationship as suggested by Keulegan is valid for bend flow, It is then showed, that ^r (hr- (p+'f jlP - where Lf is the bed shear at a distance T and Z is tnc average shear in the straight approach channel, b is the channel width/0 the centre line radius of bond and p is the index in forced vortex law, Eqn. (i> can be used for finding the sheadistribution in a radial direction at the exit section. It is assumed that for the equilibrium condition the intensity of bed material load transport at all points at the exit section is equal to the average rate of bed material transpo; before entrance to the bend. Further assuming the discharge inten sity to remain constant at a distance r before and after the scour, and the velocity distribution in a vertical to follow power law, the following relationship has been obtained. [-y } ry* l- f v&J in which K<l —-. (/. ^"Q ^ //,\/^j,. A &s read frou Shields curve, and I — f_ V (ii) The parameter ( Dr ) can b, f3& from Eq. (ii) for the known values of K«, FVD D/d, (Wb) and p , for different values of ( r/rc ). On the basis of orders of magnitude of various terms, it is shown that the second term on right hand side can be noglect.d without loss of much accuracy. This staple, the rplptionshlp for Dr/D considerably. bpertohtl vera conducted in a 0.6 . wide open channel bend With rigid vertical walls to determine, (i) Shear distribution, in a rigid boundary bend with a bed roughened with sand 0.2 mm, 0.5 mm and 0.7 mm median diameter. The local shears were measured with the help of a Preston- tube calibrated for the grain roughnesses used in the bend', (ii) ' Scour pattern with mobile bed open channel bend with varying values of rc/b and 8 was obtained. The bed materials used were sands of 0.2 mm, 0.5 mm and 0,7 mm ' median diameter and 0.3* mm diameter coal. Atotal ^ number of 114 runs were conducted.. . Scour data for 34 channel bends were also collected.' The range of variables covered in laboratory and field data as follows ^wntorv Data ?ieId Data rc/b - 1.5 to 6.0 / 2.79 to 365 Q = 30° to 150° -, 37° t0 142° F = 0.16 to 0.72 .11 to °-78 The data on field channel bends as observed by Khalid along with those collected in the present study and Einstein and Harder were utilised to determine the index power f as a function of Reynolds number and rc/b . The maximum shear was seen to occur near the exit towards the outside. Analysis of data revealed that the (JL}^ varied with Reynolds number, b/D and rc/b for a given contra! angle Q .The shear distribution as determined ta Eq.(i) was compared and reasons given fordM ^ It was found that the parameter G? —^ , (yj • ( ^) can take into amount the sediment and flow characteristics whore v, = fall velocity of bed material <? = mass density of the fluid f = unit weight of the fluid It has been shown that, on the basis of laboratory and field data, maximum scour depth D1 is given by 1 Di/D • • —i = f2( rc/>) (iii) * ,125 0.42- 2 b Iffy d The curve shows a promising trend and could be used to find the maximum scour for a given channel bend. Since D-^d was found to vary with g , the values of Dwn as obtained from mathematical analysis were multiplied by q0.4 ^ so aS to account for the effect of central angle of the bend. The bed profile at the exit section for the experi mental runs and the prototype were thus calculated . The predic ted profiles compared fairly well with the observed ones both on the model and the prototype. The maximum scour as computed ranged within 30 percent of the observed one.