Journal of Hydraulic Engineering

On the basis of a field study of a piedmont braided reach of the gravel-bed Laba River, in the northern Caucasus, Russia, an undistorted 1:50 scale mobile bed hydraulic model was constructed in an outdoor experimental plot of the State Hydrological Institute, St. Petersburg, Russia. Channel and hydraulic regimes of the Laba River were studied in this model. Attention was paid to the regime of bed load transport and its relation to the hydraulic characteristics of the flow. The same problems were investigated in an 100 m long, 1 m wide flume with glass walls also located at the State Hydrological Institute, and in an 18 m long, 2.46 m wide steel tilting flume at HR Wallingford Ltd., U.K. Quantitative characteristics of bed load transport were obtained from the laboratory experiments and compared with the field data. Proximity of the field and scaled up laboratory data demonstrates that the processes of bed load transport of gravel-bed rivers can be faithfully reproduced in small-scale models and flumes.

Total bed-material load computations for nonuniform sediment mixtures were evaluated for the commonly used Engelund and Hansen, Ackers and White, and Yang transport formulas. The results of sediment transport computations indicate considerable scatter is in bed-material load transport relations for nonuniform sediment mixtures. The analysis demonstrates that a single fixed size, such as D₃₅ or D₅₀, cannot reflect the presence of various size fractions on the transport of nonuniform sediment mixtures. A size gradation compensation factor incorporates the effect that the size distribution has on the transport of sediment mixtures. The size gradation compensation factor, K_g, which is a function of the geometric standard deviation, σ_g, of the bed material and the flow conditions, in conjunction with the D₅₀ of the bed material yields an equivalent representative diameter, D_e. By including D_e in the Engelund and Hansen, Ackers and White, and Yang formulas, the agreement between computed and measured bed-material concentrations was improved significantly. These results for 118 sets of laboratory and field data were further verified by the use of Colorado State University (CSU) experimental data that include three different σ_g values for the same median sediment size.

Contrary to general statements in the literature, the investigations reported in this paper show that semicoupled models are not necessarily unstable and give results comparable to those of coupled models. For this purpose, a two-dimensional model is developed to calculate bed variations in alluvial channels. Vertically averaged Navier-Stokes equations in transformed coordinates are numerically solved in conjunction with the sediment transport equation for the bed load. These equations are solved simultaneously in a fully coupled model and separately in a semicoupled model using the Beam and Warming alternating-direction implicit scheme. Both models are applied to predict bed-level changes due to sediment overloading and sediment shut-off. The computed results compare satisfactorily with the experimental results obtained in a laboratory flume. The results obtained by the semicoupled model are relatively close to that of the fully coupled model. Because the former algorithm permits any sediment formula and armoring effect to be easily incorporated, the semicoupled model appears to be more attractive for general applications to real-life systems than the coupled model.

The Prandtl-von Karman mixing length concept for clear-water flows is generalized for sediment-laden flows. The new model is applied for the analysis of dilute equilibrium sediment-laden flows down an inclined flat bed composed of mobile suspendable sediment particles. The derivation and the features of the modified formulation are discussed in detail. The model incorporates the effect of density stratification and accounts for the presence of a solid phase in the flow. Computational results are compared with experimental data. The model successfully explains the observed characteristics of these flows.

This paper describes a mathematical model leading to experimental analysis to estimate the hydraulic forces on a prototype edge-hinged panel (wicket gate) in gradually varied flow. The two-dimensional potential theory of hydrodynamics is used to model the effect of the mean water flow approaching a gate aperture controlled by a hydraulic wicket in a locks-and-dam system. The mean pressure against a typical wicket partially blocking the aperture is then modeled using conformal mapping. The elastic reaction at the supporting shaft of the gate is derived from equilibrium considerations. The effect of the fluctuations of the pressure field about the mean is obtained through an application of the theory of stationary random processes. The total design reaction at the shaft of the wicket is cast in a first-order second-moment format. The theoretical model is compared to experiments on a 1/25-scale physical model. The application of the model in hydraulic design of wicket gates is illustrated by means of a practical example.

Shear stress distribution around vertical wall abutments is studied experimentally, and maximum shear stresses that occur at the upstream corner of vertical wall abutments are determined. Shear stress distributions are presented for Froude numbers ranging from 0.30 to 0.90 and for protrusion ratios (ratio of protrusion length perpendicular to direction of flow to total channel width) of 0.1, 0.2, and 0.3. Shear stress at the nose region of an abutment can be expressed as the sum of stresses due to contraction and the abutment structure alone. An expression for the nose shear amplification factor, Λ_nose, defined as the ratio of the bottom shear stress at the nose region to the approach flow shear stress, is derived. This amplification is due to the contraction and to the presence of a protrusion. In the computation of total shear stresses due to vertical wall abutments, expressions for the shear stress amplification at short contracted reaches, Λ_cont, and amplification due to abutment structure alone, ${\Lambda }_{\mathrm{nose}}^{\prime }$, are presented. Shear stresses around vertical wall abutments are amplified up to a factor of 10 and velocities are increased by up to 50% depending upon flow conditions and abutment protrusion ratios. Results are compared with previous experimental and numerical studies for shear stress distribution around groins and spur dikes. Local scour is mainly caused by increased flow velocity and shear intensity. By quantifying the shear amplification and by identifying regions of shear concentration, the method developed in this paper can be used to determine sediment sizes needed to protect structures against local scour.

This paper presents an efficient solution algorithm for one-dimensional unsteady flow routing through a dendritic channel network system. The finite element method is used to solve the Saint Venant equations in all branches of the network simultaneously. The maximum active memory required is only 2N× 2N, where N= number of branches in the network. Importantly, the algorithm does not require any special node numbering schemes, and the nodes or elements can be numbered independently for each branch. The algorithm is also suitable for programming using a parallel processing computer. The solution technique can also be extended to finite difference methods.

The study of flow through media consisting of large-sized grains is important in a number of civil engineering applications. Employing the square root of permeability as the characteristic length in defining friction factor and Reynolds number, theoretical curves, relating friction factor and Reynolds number—similar to the Moody diagram used in pipe flow to estimate the friction factor—have been developed using the ratio of characteristic length d and square root of permeability $\mathit{k}$ as the third parameter. The existing experimental data on flow through porous media have been sorted based on the $\mathit{d}\mathit{k}$ ratio and are used to verify the theory developed. The agreement is good. From the set of theoretical curves so obtained, the Reynolds number at which the friction factor–Reynolds number relationship deviates from Darcy's law and the Reynolds number at which turbulent flow is fully established are identified. Empirical equations for these Reynolds numbers in terms of media parameters have been obtained. The factor affecting linear parameter a and nonlinear parameter b have been brought out. The empirical power law applicable for high Reynolds number flows is given a theoretical justification.

This study presents an analytical approach for solving both the upstream-to-downstream depth ratio, $\overline{Y}$, and the energy loss through junctions of equal-width subcritical flows over horizontal beds, based on three experimental test setups with junction angles, θ being 30°, 45°, and 60°. Under a known discharge ratio, $\overline{Q}$, between upstream and downstream of main channel and a known downstream boundary condition, $\overline{Y}$ is computed using a third-degree polynomial function. $\overline{Y}$ is found to increase with increasing θ and with increasing F_rd. The energy loss coefficient, K_e, through the junction is expressed as a function of $\overline{Q}$, downstream Froude number, F_rd, and $\overline{Y}$. For F_rd< (4$\overline{Y}$⁶+ 2)^1/2− 2$\overline{Y}$³, it is found that K_e increases with increasing θ and F_rd. The results of the analytical approach are found to be in fairly good agreement with the experimental values and the values obtained by other studies. The polynomial function is further transformed to an approximation equation allowing $\overline{Y}$($\overline{Q}$−Δ$\overline{Q}$) to be computed by $\overline{Y}$($\overline{Q}$). Finally, an equation relating the increment of the water depth and the discharge at the upstream and downstream of junction is proposed to serve as an interior boundary condition for one-dimensional numerical simulation.

The flow upstream of a free overfall from smooth circular channels is theoretically analyzed to calculate the end-depth ratio (EDR), applying the momentum equation based on the Boussinesq approximation. The present approach eliminates the need for an empirical pressure coefficient. In subcritical approaching flows, the EDR is related to the critical depth, which occurs upstream of the end section, and the value of EDR is found to be around 0.75 for a critical depth-diameter ratio up to 0.82. On the other hand, in supercritical approaching flows, the end depth is expressed as a function of the streamwise slope of the channel using the Manning formula. Simple methods are presented to estimate the discharge from the end depth in subcritical and supercritical approaching flows. A relationship of discharge to the end depth and the channel characteristics parameter is also proposed. Streamline curvature at the free surface is used to compute the flow profiles upstream of a free overfall. This paper also presents a theoretical model to analyze the free overfall from horizontally laid rough circular channels with the aid of an autorecursive search scheme.

To predict debris flow characteristics it is necessary to determine the rheological properties of these mixtures. It is suggested that such a mixture can be obtained by adding successively to clear water, coarser particles derived from a sample of the debris flow material. At each addition different suspensions are obtained that can be considered as progressively coarser interstitial fluids of the complete mixture. These suspensions are easier to test and their rheological properties can thus be determined. The behavior of the complete material can then be inferred from these results. This procedure has been adopted for a debris flow which occurred on Moscardo Torrent (Friuli Region, Northeastern Italy) in 1995. A wide range of rheometrical techniques have been used to determine the rheological characteristics, such as laboratory rheometer, inclined plane test, large-scale rheometer, and field tests. The rheological parameters and behavior type of the complete material have been inferred from the yield stress-solid fraction curve and from the flow curve evolution. The behavior has been found to be mainly viscoplastic and representable by a Herschel-Bulkley model.

In this paper the velocity calculation in rivers has been obtained on the basis of a sediment transport formula. This paper develops a methodology for evaluation of the velocity of flow in alluvial channels and rivers based on the analytical solution presented in a previous article. The present study investigates the application of a sediment transport equation for calculating alluvial channel velocities with or without particles in motion and calculating river velocities. The velocity predicted is based on the depth of flow, slope, and a critical particle diameter. The procedure can be applied in sand and gravel bed rivers. Limitations are found in high-velocity, fine-sand rivers where plane beds or antidunes are formed.