Journal of Hydraulic Engineering

Our infrastructure is aging. There are many bridges over water in this country, and these aging bridges are now showing signs of weakening due to scour around the pier foundations. In response, engineers are being required to design “safe” bridge piers such that the pier foundations will not be undermined by local scour. In this paper, the problem of relating the risk of bridge failure to the estimated maximum local scour depth is examined. Since safety factors are commonly used to incorporate uncertainties into design, the relationship between the risk of failure and safety factors is examined. A best‐fit pier scour model, rather than a conservative model, is used to develop a probabilistic approach to pier scour engineering. An example is provided to demonstrate the probabilistic approach. The level of risk for a bridge pier design is provided by the development of safety factors that are a direct reflection of the desired or allowable level of risk.

The addition of a dissipation step to the widely used McCormack numerical scheme is proposed for solving one‐dimensional open‐channel flow equations. The extra step is devised according to the theory of total variation diminishing (TVD) schemes that are capable of capturing sharp discontinuities without generating the spurious oscillations that more classical methods do. At the same time, the extra step does not introduce any additional difficulty for the treatment of the source terms of the equations. Results from several computations are presented and comparison with the analytical solution for some test problems is shown. The overall performance of the method can be considered very good, and it allows for accurate open‐channel flow computations involving hydraulic jumps and bores.

A finite element (FE) model is used to study tides and hurricane storm surge in the Gulf of Mexico in the region ranging from the Mississippi Sound to the northwest coast of Florida. Issues that are emphasized include the use of large domains, the importance of a high degree of grid resolution in coastal regions of interest, the use of meshes with highly varying nodal densities to minimize the size of the discrete problem, and the use of the generalized wave‐continuity equation (GWCE) for FE‐based solutions to the shallow‐water equations. The computations presented are unprecedented in their scope, level of localized detail, and degree of grid‐size variability. The GWCE‐based FE model leads to very accurate and efficient flow solutions.

A mathematical model for predicting the velocity field and suspended solids transport in secondary rectangular settling tanks is presented. The model is applied to investigate the effects of density stratification on the hydrodynamics in the settling tank, such as the behavior of the bottom current and surface return flow and solids concentration distribution. The model can be used to simulate the so‐called density waterfall phenomenon at the front end of the settling tank. With the application of a double exponential relationship to describe the settling process of suspended solids with nonuniform particle sizes, the simulations of the solids concentration distribution in the low‐concentration environment can be significantly improved. By comparing the predictions with field measurements, this model is verified and generally good agreement is obtained.

The complex nature of low‐flow mixing in natural channels has been investigated using both laboratory experiments and the numerical solution of a proposed mathematical model that is based on a set of mass balance equations describing the mixing and mass exchange mechanisms. Laboratory experiments, which involved collection of channel geometry, hydraulic, and dye dispersion test data, were conducted in a model of four pool‐and‐riffle sequences in a 49‐m (161‐ft) long tilting flume. The experimental results show that flow over the model pool‐riffle sequences is highly nonuniform. Concentration‐time curves are significantly skewed with long tails. Comparison between measured and predicted concentration‐time curves shows good agreement in the general shape, peak concentration, and time to peak. The proposed model shows significant improvement over the conventional one‐dimensional dispersion model in predicting natural mixing process in open channels under low‐flow conditions through pools and riffles.

The Agricultural Research Service's (ARS) low‐drop structure was developed to provide grade control for streams in northern Mississippi. Since development, the U.S. Army Corps of Engineers has broadened application of the structure to include energy dissipation. Although the ARS structure is an effective means of stabilizing a stream channel, it is vulnerable during construction, requires refinement to be an effective energy dissipator, and is hydraulically submerged at moderate discharges. A model study was conducted to evaluate the performance of the ARS structure for high submergence conditions, to determine if the baffle plate could be replaced by H‐piles, to evaluate the basin effectiveness by reducing the depth, and to evaluate the structure during flow frequency events greater than 10 years. Test parameters included the discharges ranging from 2,200 cu ft/sec $(62.3m^3/s)$ to 6,800 cu ft/sec $(192.6m^3/s)$ and 0.5, 1.0, 1.25, 1.50, and 1.75 submergence levels. The study results indicated that the basin baffle can be replaced by two rows of H‐piles (seven H‐piles) without a reduction in basin efficiency while improving overall basin flow conditions. It was determined that the riprap becomes unstable using current design procedures. Also, a coefficient‐of‐discharge relationship was developed. Further, the stilling‐basin depth can be reduced by approximately 3.0 ft (0.91 m) without loss of basin effectiveness.

A methodology is developed for evaluation of bed-load transport based on the analytical solution presented in a previous publication. The present-day knowledge of this subject is such that it required empirical determined coefficients to evaluate bed-load transport. The equation proposed here does not have a coefficient; therefore, it has been used to calculate Meyer-Peter and Muller's coefficient as well as Smart's, Shields' and Bagnold's bed-load coefficients. The application of the proposed equation is investigated under different kinds of conditions and it has been tested satisfactorily. The close agreement between predicted and measured values allow for several different transport equations to be compared to each other by defining coefficients. These comparisons suggest why some transport relations work better in some instances than in others.

Goodwin Creek is a steep (bed slope of study reach = 0.003) gravel-bed stream in the bluff-line hills east of the Mississippi River floodplain in the north-central part of the state of Mississippi. Records of the flow for a nine-year period and 488 bed-load transport samples collected during a four-year period allow a comparison between weighted and nonweighted calculations of the size distribution of the bed load. The mean size distribution of the bed load on Goodwin Creek was calculated using the size distribution of the bed load weighted by transport rate and flow frequency. The size of the bed load was found to be slightly finer ($D_{50}$ = 6.8 mm) than the bed subsurface ($D_{50}$ = 8.3 mm) during the nine-year period. The weighting technique greatly reduced the bias (nonweighted $D_{50}$ = 3.16 mm) in the calculation of the mean size distribution.