Journal of Hydraulic Engineering

The main objective of this paper is to develop a new unbiased plotting‐position formula for the Pearson type‐III (P3) distribution. The probabilityweighted moment (PWM) method is used to estimate the exact plotting positions. It is shown that the estimation of plotting positions for the P3 distribution using the PWM technique has several advantages over both the direct numerical integration method and the Monte Carlo simulation procedure. For the convenience of practical application, a simple formula representing a very good approximation of the exact plotting positions is proposed. It is found that the suggested formula gives a better agreement with the exact plotting positions than several existing formulas. Further, the proposed formula is more flexible, because it can take explicitly into account the skewness coefficient of the underlying distribution. It can be concluded that the plotting formula developed in this study is the most appropriate for the P3 distribution and for both small and large samples. Finally, the development of probability papers for the P3 distribution for various skewness values is presented. Results of a numerical example have demonstrated the advantages related to the use of these special probability papers in engineering practice.

Equilibrium sediment transport experiments were made in two flumes, one with a 6‐m long by 0.15‐m wide channel and the other with an 11‐m long and either 0.74‐ or 0.53‐m wide channel. The sediment (0.1 to 32 mm, $D_{50}=3.03\mathrm{mm}$) was fed at the upstream end of the channel and was trapped in the sump at the downstream end. For the runs of this study the bed‐surface grain size became finer and the sediment transport rate increased as the total bed shear stress decreased slightly and then increased. This decrease in bed shear stress was probably caused by the varying coarseness of the bed surface. In the runs with higher transport rates the bed surface was finer, so bed shear stresses were lower. The difference in friction factors (determined from the Moody diagram for rough turbulent flow) for $D_{65}$ of the bed surface sediment and $D_{65}$ of the original sediment mix (or of the sediment in transport) was used to represent the extra friction factor due to roughness changes. Subtracting this quantity from the bed friction factor allowed the calculation of an effective shear stress available for sediment transport. The relation of sediment transport rate and bed‐surface grain size to shear stress was improved by using the effective shear stress rather than the total shear stress.

An equation for bank erosion, and thus channel migration rate, is derived theoretically from the equation of sediment continuity. The relation so derived lends credence to the hypothesis that bank erosion is proportional to a nearbank “excess” velocity, defined to be the difference between near‐bank and centerline depth‐averaged streamwise flow velocity. The theory also leads to the definition of a coefficient of bank erosion of a general nature. Based on data for channel shift for several Japanese rivers, it could be concluded that the universal erosion coefficient decreases as the index (number of blows) of the standard penetration test, as applied to the river bank, increases. Two trends appear, however, depending on whether or not bank texture is sandy or clayey.

Potential errors in calculated vertical suspended sediment concentration profiles in river flows carrying mixed sediments are investigated. These profiles are usually obtained through application of a standard ‘diffusion‐dispersion’ model; however, such models are normally formulated on the basis of a unique grain size for the sediment. Accordingly, in the case of sediment mixtures, the grain size distribution is usually divided into several size ranges (‘fractions’), which are then characterized by their respective geometric means. Numerical errors induced through this procedure are quantified in a parametric study. While depthaveraged concentrations can be over‐esimated by a factor of 1.2 when the concentration gradient is weak, they can be under‐estimated by a factor of 15 when the gradient is large. Estimates are found to be particularly sensitive when the chosen reference level is small and the fraction width is large. Fall velocity coefficients are introduced to correct the discrepancy between the actual representative fall velocity of a fraction and that of the geometric mean size of the fraction.

The turbulence structure of open channel flow is measured and analyzed systematically in this study. The turbulence characteristics measured in clear water flow are essentially consistent with existing data. Compared with that of a clear water flow, turbulence intensity of a sediment‐laden flow is weaker, its turbulence frequency is smaller, and the longitudinal sizes of turbulence eddies are larger. On the other hand, the distribution of probability density and the autocorrelation coefficients of fluctuating velocity are similar to that of a clear water flow. These results show that the fundamental turbulence structure of a sedimentladen Newtonian flow remains unchanged.

A theory has been developed to explain the generation of dunes and ripples on an erodible bed in open channel flow. The flow is conceived as a stratified flow both with respect to the velocity distribution and the density distribution of the sediment‐fluid mixture. The free internal waves that may occur in such a flow are assumed to be the triggering mechanism for the generation of dunes and ripples on an initially flat bottom. The effectiveness of the theory is demonstrated by comparing the calculated free waves with the peaks in the bed‐wave spectrum as measured at small times after starting the flow in a channel with an initially flat bed. The theory shows that dunes are generated by internal waves corresponding with the steady free‐surface waves. Ripples are due to free internal waves that only occur in flows with sediment transport. The theory has been demonstrated for bedload transport. However, an extension to any other transport mode is straightforward.

Laboratory models made of sand, water, and small amounts of cement (“weak mortar”) are shown to be practical, inexpensive alternatives to standard porous media models made from sand epoxy resins, glass geads, or sand only. By varying proportions of the weak mortar mix, one can fashion complex layered models with hydraulic conductivities ranging from 1.4 × 10 ^-8 m/s to 3.7 × 10 ^-4 m/s. Dispersion tests using Rhodamine dye were performed on a 2.4 m × 1.14 m × 0.15 m rectangular weak mortar model; the results compared favorably with the analytical predictions, with longitudinal dispersivities on the order of 10 cm. Anticipated applications of weak mortar models are for verification of mathematical models, hydraulic scaled models and laboratory demonstrations.

Analysis demonstrates, and experiments confirm that the frictional behavior of mobile beds at high shear stress is inherently different from either of the two classical cases—smooth wall and rough wall. For those two cases, the characteristic lengths for friction are based on viscosity and grain size, respectively. For the new mobile-bed friction relation this length varies with the thickness of the shear layer occupied by the moving bed-load particles. This thickness is itself directly related to shear stress, giving rise to the prediction that at high shear stress (Shields ordinate greater than unity) the effective roughness ratio (effective roughness/particle diameter) should be approximately five times the Shields ordinate. The high-shear-stress experimental results show a variation in accord with the prediction.