K. G. Ranga Raju

Scour around spur dikes and bridge abutments

Realistic estimation of scour depth around spur dikes and bridge abutments in alluvial rivers is important for safe and economic design of their foundations. Procedures have been developed by previous investigators for determination of design scour depth in steady flows at abutments and spur dikes by making use of the design discharge. However, the time required by the design discharge to scour to its full potential is generally much larger than the time for which it runs. Therefore, computations on temporal variation of scour depth are also important for design purposes. Scour processes at bridge piers, abutments and spur dikes have been found to be similar except that the boundary layer effect induced by the channel wall upstream of the abutment or spur dike causes less scour around these as compared to the case of piers. In the present study, therefore, the concept of an analogous pier is developed. The analogous pier would have the same equilibrium scour depth as the given abutment or spur dike under similar hydraulic conditions. The parameters relating to drag due to flow around abutment/ spur dike and bridge pier have been found to be useful in establishing a relationship for the diameter of the analogous pier. The temporal variation of scour depth and the equilibrium scour depth at the spur dike and the abutment are then computed using pier scour equations with size of the analogous pier being taken as the pier diameter. Results obtained are verified using laboratory data of several investigators for both clear-water and live-bed scour conditions.

Resistance Of Two Dimensional Triangular Roughness

Measurements of shear and pressure distribution on smooth and sand coated two-dimensional triangular elements, simulating ripples and dunes, have been reported. Relations have been derived for the local and average skin shear coefficients in terms of the geometry of the elements and the flow Reynolds number. The local pressure coefficient and the form drag coefficient have been related to the relative roughness and the geometry of the elements. Analysis of the data has shown that the grain resistance of undulated beds calculated by the existing methods is generally greater than the measured average grain resistance of the bad. A large amount of alluvial channel data show agreement with the relation for form drag of the two-dimensional triangular roughness.

Influence of cohesion on scour around bridge piers

Experimental results on temporal variation of scour around circular bridge piers founded in cohesionless and cohesive sediments under steady clear water flows are reported. The difference between scour patterns in cohesionless and cohesive sediments is brought out. Considering the horse shoe vortex to be the prime agent causing scour, a procedure is developed for computing the temporal variation of scour depth in cohesive sediments. Empirical relationships have also been obtained for maximum scour depth around bridge piers in cohesive sediments.

Live-bed scour around cylindrical bridge piers

Considering the primary vortex in front of the pier to be the prime agent causing scour at bridge piers, a scheme has been proposed for computation of the temporal variation of scour depth during live-bed condition. An equation has also been developed for the computation of maximum scour depth around circular bridge piers in uniform sediments during live-bed condition. The equation follows logically from the scheme proposed for the computation of the temporal variation of scour. The effect of unsteadiness of flow on scour depth has been also studied.

Fractionwise calculation of bed load transport

Extensive experiments conducted by the writers on fractional bed load transport rates are reported. These data as well as those available from other sources, covering wide range of flow conditions and sediment nonuniformity, have been analysed. Firstly, the semi-theoretical model proposed by Misri et al. (1984) is modified to evolve a method of bed load calculation and finally an empirical relationship is proposed incorporating the several parameters influencing the bed load transport of nonuniform sediments.

Critical tractive stress of nonuniform sediments

Experiments on initiation of motion and rate of bed load transport of different fractions in case of nonuniform sediments are reported. Analysis of these data as well as those from earlier studies by other investigators has shown some limitations of the available relationships for critical tractive stress (CTS) of sediment mixtures. Further analysis of the data has resulted in a new relationship for CTS in terms of the size of the particular fraction in question (di ), the geometric mean size (dg ) and the geometric standard deviation (σ g ) of the mixture. An empirical relationship has been obtained for the critical tractive stress of the size d σ defined as dg σg.

Design of settling basins

Experiments have been carried out in the laboratory concerning the efficiency of settling basins. The data indicate that the existing methods of their design are not satisfactory. Analysis of all t...

RATIONAL ASSESSMENT OF BLOCKAGE EFFECT IN CHANNEL FLOW PAST SMOOTH CIRCULAR CYLINDERS

Experiments concerning the drag force on circular cylinders placed in an open channel with a smooth boundary are reported. The studies were carried out under subcritical flow conditions using 31 mm...

GEOMETRY OF RIPPLES AND DUNES IN ALLUVIAL CHANNELS

The geometrical characteristics of bed forms have a significant effect on the hydraulic roughness of alluvial channels. Knowledge of the size of ripples and dunes would make a rational approach to the resistance problem possible. In this paper a semi-theoretical approach to the problem of prediction of bed form geometry is proposed. The study is restricted to ripples and dunes but practically all available data have been used in arriving at dimensionless relations for the height and length of these undulations.

Finite difference scheme for longitudinal dispersion in open channels

The available analytical and numerical solutions of the equation for longitudinal dispersion in open channels are limited to uniform flows. Presented in this paper is a solution technique based on combined operator approach where advection and diffusion processes of longitudinal dispersion equation are treated concurrently in non-uniform flows. A variable size spatial grid based finite difference solution of the advection process has been obtained by developing a variable spatial grid so that the root of the trajectory of the concentration characteristic passes through the computational nodes. For solution of the diffusion process, Crank-Nicholson scheme has been used. To eliminate the possibility of numerical oscillations, weighting coefficient has been introduced to the pollutant concentration in the time stepping. Proof-of-the-concept tests have been made using the existing numerical and analytical solutions as the basis. The model has been extended by incorporating in it the one-dimensional grid searc...