Journal of Hydraulic Engineering

A theoretical model to predict the velocity distribution for sediment‐laden flow is developed by means of a new mixing‐length concept. The solution is obtained as a function of the vertical sediment concentration. The von Kármán coefficient is independent on suspended load and equal to 0.4. The model is applicable to an alluvial‐bed condition as well as a flat‐bed condition. The possibility of adapting the model to clear‐water flow is also discussed. For clear‐water flow, the velocity equation consists of a logarithmic term and power‐series terms that explain the wake effect. The theoretical velocity distribution for sediment‐laden flow departs from the logarithmic law in the outer layer. The magnitude of the departure is larger with the increase in the sediment load. The numerical calculation is carried out and its prediction is compared to five independent sets of experimental data previously obtained. The theoretical result shows good agreement in the whole flow layer with these experimental results.

A one‐dimensional numerical model of sediment routing is derived to simulate erosion, transport, and deposition of individual size‐density fractions in the bed material within a relatively straight, nonbifurcating alluvial channel. The reach of interest is subdivided into a number of longitudinal elements of varying width‐averaged properties. During each time step, flow depths and velocities in each element are determined from the gradually varied flow equation using the standard step method for backwater calculations. The bedload transport rate of each size fraction is calculated from a modified Bagnold equation implementing a novel approach that takes into consideration the effects of turbulent fluctuations in the bed shear stress. Critical shear stresses for entrainment of particles from the mixed bed are determined using relationships that treat grain protrusion and hiding. The transport of particles in suspension is modeled using a convection‐diffusion sediment continuity equation, either explicitly solved by the Rouse equation or implicitly solved using a finite difference scheme. Changing vertical geometry is handled using coordinate stretching. The velocity profile in the vertical is calculated at each point using the von Karman‐Prandtl logarithmic velocity distribution, and vertical sediment diffusivities for the suspended sediment are computed assuming a parabolic distribution for diffusion of fluid momentum. Interaction of the transported load and the bed is calculated by a bed‐continuity equation solved for each size‐density fraction in an active layer. Bed composition and elevation are monitored through time, so that simulations produce complete stratigraphic sequences of sediment. The advantages of this model over previous models are a treatment of turbulent fluctuations of bed shear stress, minimization of calibration factors, and explicit consideration of multiple grain densities.

A one‐dimensional numerical model of heterogeneous size‐density sediment transport has been developed to simulate the movement of graded sediments in natural and laboratory flow reaches. Predicted temporal and spatial variations in bed and armor‐layer grain size distributions, eroded grain size distribution, eroded thicknesses, and total bedload transport rates compare quite favorably to observed variations in flumes, the San Luis canal, Colorado, and the East Fork River, Wyoming, for a large variety of flow scales and flow conditions. The main advantages of this model over others is the high degree of accuracy of model results obtained using only bed and flow variables as input, the treatment of turbulent fluctuations of bed shear stress, the minimization of calibration factors, and the explicit treatment of multiple grain densities. In addition, only the active layer thickness must be calibrated.

A laboratory study was conducted to investigate the effects of footing location on the depth of scour. None of the existing pier‐scour equations have provisions for accounting for nonuniform pier configurations; rather they have a single characteristic pier dimension. This study was aimed at evaluating various techniques for characterizing the effective dimensions for a pier/footing combination when both are exposed to the flow field. The following three techniques were considered in the analysis: (f) Use of the footing width as the characteristic dimension when the footing occupies more than 10% of the flow depth; otherwise, use of the pier width (10% depth switch); (2) use of a weighted pier width (weighted width technique); and (3) use of the dominant pier/footing component by making two computations with appropriate flow parameters and selecting the larger value (dominant component technique). The first technique was the Federal Highway Administration (FHWA) recommended procedure prior to this study, but both of the other techniques gave better results in this study. The third technique has subsequently been adopted for FHWA's Hydraulic Engineering Circular No. 18 (HEC‐18) on bridge scour. The second technique, however, is a simpler technique and is as accurate.

Rehabilitation of existing dams in a cost‐effective manner with due regard to hydrologic safety requires a rational method to determine the design‐basis flood (DBF). Four methods are presented to determine the DBF based on economic considerations alone. These include the expected damage, indemnification cost with and without price escalation, and modified expected damage approaches. The expected damage approach is presented to provide a basis for comparison with other approaches. One of the indemnification‐cost approaches includes no price escalation and the other provides for escalation of dollar‐denominated damages attributable to dam failure that is likely to occur in the future. The modified expected damage approach considers probabilities of flood damages during the life of the rehabilitated dam, rather than the absolute probabilities. In most cases, however, consideration of nondollar‐denominated consequences of rehabilitation are equally or more important. An approach based on a combination of the delphi and fuzzy‐set methods is presented to evaluate rehabilitation alternatives with different DBFs and select the most cost‐effective and acceptable DBF, based on both economic and nondollar‐denominated factors.

A numerical model is developed to compute the time variation of leachate flow in landfills. The two‐dimensional moisture‐transport equation, along with the boundary conditions, is solved using an implicit finite difference scheme in a vertical plane. The time‐varying boundary conditions include computation for runoff, evapotranspiration, and infiltration in an unsteady state condition. The leachate accretion is obtained from the time history of moisture content. The downward leachate accretion helps develop the leachate mound at the bottom of the landfill. Solution of the saturated leachate flow equation with respect to the bottom of the landfill establishes lateral flows toward the perimeter or collection system at the landfill. Also, vertical flow through the bottom clay layer is computed using Darcy's law. The model is applied to a landfill section in New York to demonstrate the simulation of runoff, moisture content, recharge, as well as lateral and vertical flows for the field conditions in a landfill.

A rainfall intensity‐duration‐frequency relationship is needed for planning and design of water resources projects. Little information is available about rainfall intensities, in particular for short durations. Data from 80 rain‐gage stations in India were analyzed. Making use of the assumption that general properties of the convective cells that are associated with short‐period (i.e. less than 24 hr) rainfalls are similar in different hydrologic regions, a general relationship for rainfall intensity, duration, and frequency was developed. The correctness of form of the developed relationship was ascertained through its comparison with existing equations and the use of data from different hydrological regions. The relationship proposed herein is found to produce more realistic results for Indian conditions than the ones in vogue. The applicability of this relationship to the data from other countries was checked with the limited data available. The proposed relationship may be used in India for design practices.

Many open‐channel flow problems may be modeled as depth‐averaged flows. Petrov‐Galerkin finite element methods, in which up‐wind weighted test functions are used to introduce selective numerical dissipation, have been used successfully for modeling open‐channel flow problems. The underlying consistency and generality of the finite element method is attractive because separate computational algorithms for subcritical and supercritical flow are not required and algorithm extension to the two‐dimensional depth‐averaged flow equations is straightforward. Here, a reconsideration of the fundamental role of the characteristics in the determination of the up‐wind weighting and the use of the conservation form of the governing equations, leads to a new Petrov‐Galerkin scheme entitled the characteristic dissipative Galerkin method. A linear stability analysis illustrates the selective damping of short wavelengths and excellent phase accuracy achieved by this scheme, as well as its insensitivity to parameter variation. Numerical tests are also presented to illustrate the rugged performance of the scheme. This method could be extended to other hyperbolic systems such as: two‐dimensional flows, multilayer fluids, or sediment‐transport problems.