Journal of Hydraulic Engineering

This paper reports the double-averaged (in space and in time) hydrodynamic equations for mobile-boundary conditions that are derived based on the refined double-averaging theorems, modified Reynolds decomposition, and improved definitions of the spatial and time bed porosities. The obtained double-averaged conservation equations provide a mathematical framework for studying mobile-boundary flows such as gravel bed rivers during flood events or flows over vegetated beds. These equations will help in designing measurement campaigns for obtaining mobile bed data and their interpretation and parameterization, eventually leading to improved and more robust predictive models.

Piers with back-to-back stems or columns and piers for which part of the foundation becomes exposed as a result of the development of scour over large periods of time or because of severe flood events are fairly common at bridge waterways. The present paper uses eddy-resolving numerical simulations to study flow and turbulence structure at piers of complex shape and/or with multiple components. In particular, the study considers cases with one and two back-to-back pier columns for which the section of the main column is neither circular nor rectangular. In addition to a design case for which the foundation of each pier column is submerged, the study analyzes a case when scour exposes part of the foundation of the main column. The results show that the shape and size of the pier column have a significant effect on the spatial and temporal distributions of the bed friction velocity induced by the horseshoe vortex system. The large-scale shedding behind the main column greatly influences flow structure and increases bed friction velocity around the downstream column for piers with two back-to-back columns that are aligned with the incoming flow direction. The present study shows that the presence of large-scale unsteady coherent structures in the vicinity of the bed around piers of complex shapes results in very complex distributions of the bed friction velocity and in large-scale temporal oscillations of the bed friction velocity. The results of eddy-resolving simulations strongly suggest the need to account for the effect of these large-scale oscillations around the mean value when bed friction velocity distributions are used to estimate the flux of entrained sediment in movable bed simulations that do not resolve the large-scale turbulent flow structures.

To prevent damages due to transported wooden debris during a flood, the debris is often retained in defined zones upstream of populated areas using a debris rack. Because thorough numerical modeling of the debris accumulation process is still challenging given the randomness of debris accumulation and the interaction between sediment and wooden debris, one main tool to study debris retention structures involves small-scale modeling. The main purpose of this experimental study is to analyze various aspects regarding the modeling of wooden debris and to provide information on reducing the laboratory effort. The focus is on the various factors influencing the accumulation process and the backwater rise and whether or not it is important to model them properly in small scale. The results indicate a significant effect of the approach-flow Froude number on the debris accumulation process, whereas the debris properties have only a minor effect on the resulting backwater rise so that effects of debris mixture are negligible.

A simplified physically based model has been developed to simulate the breaching processes of homogenous and composite earthen embankments owing to overtopping and piping. The breach caused by overtopping flow is approximated as a flat broad-crested weir with a trapezoidal cross section, downstream connected with a vertical drop (headcut) and a straight slope for cohesive and noncohesive homogeneous embankments, respectively. For a composite dam with a clay core, the downstream becomes two straight slopes after the core is exposed. The breach by piping is assumed to be a flat pipe with rectangular cross section until the pipe top collapses and overtopping takes place. Sediment transport and morphology changes on the breach top flat section and downstream slopes and inside the pipe are calculated using a nonequilibrium total-load sediment transport model, whereas the time-averaged headcut migration rate is determined using an empirical formula. Stabilities of the side slope, pipe top, headcut, and clay core are analyzed by comparing the driving and resistance forces. The breach side slope is set as the average of the steepest stable slope and its corresponding failure plane angle. The model is able to handle dam and levee breaching by adopting various routing algorithms for headwater and tailwater levels and allowing embankment base erosion. It has been tested using 50 sets of data from laboratory experiments and field case studies. The calculated peak breach discharges, breach widths, and breach characteristic times agree generally well with the measured data.

Experimental research was undertaken to investigate the changes in spatial turbulence intensity in a compound channel and the influence of rigid, emergent floodplain vegetation on turbulence intensity. Five tests for two various roughness values of floodplains were realized. In the first series of experiments (three tests), the surface of the main channel bed was smooth and made of concrete, whereas the floodplains and sloping banks were covered by cement mortar composed of terrazzo. In the second set of experiments (two tests), emergent vegetation (trees) on the floodplains, modeled by aluminum pipes, was added. Instantaneous velocities were measured with the use of a three-component acoustic Doppler velocity meter. The influence of floodplain trees, on the distributions of relative turbulence intensity ($u^{\prime }/U$, $v^{\prime }/U$, $w\prime /U$) in the main channel and on the floodplains was presented. It was found that the longitudinal ($u^{\prime }/U$) and transverse ($v^{\prime }/U$) turbulence values decreased from the bottom upward to the floodplain elevation ($z/h=0.56$) in the main channel but remained constant above the floodplain level. Vertical relative turbulence intensity ($w^{\prime }/U$) increased going up from the bottom until $z/h=0.15$, decreased until about $z/h=0.7$, and then increased again upward to the water surface. Trees on the floodplains resulted in changes in vertical distributions of the relative turbulence intensities in all three directions on the floodplains and over the bottom of the main channel. In the main channel bed of the compound channel with emergent vegetation (trees) on the floodplains, the values of longitudinal and transverse relative turbulence intensities decreased from the bottom upward to a depth of $z/h=0.35$, and then these values increased upward to the water surface. Vertical relative turbulence intensity increased with the distance from the bottom until $z/h=0.15$, decreased until $z/h=0.4$ and then increased again upward to the water surface. The distributions of relative turbulence intensities were described with regression equations.

In recent years, sand-filled geotextile bags (geobags) have become a popular means of long-term riverbank protection. However, the associated failure mechanisms of geobag revetments are still not well understood. Three interactions influence geobag performance, namely, geobag–geobag, geobag–water flow, and geobag–water flow–riverbank interactions. To enhance the fundamental understanding of the performance of geobags in a revetment, a laboratory experimental program has been undertaken using both a fixed bed and a mobile sediment bed. In the experimental study, 600 bags were used to construct geobag revetments, and failure modes were observed for these two bed configurations. In general, there were some common trends for both bed configurations (i.e., uplifting, turbulent bursting–induced flow through the revetment voids, overtopping, pulling out, and/or internal sliding), but in the mobile bed case, toe scouring had a significant negative influence on geobag performance. To extend the laboratory measured hydraulic parameters, the conveyance estimation system (CES) was used. A CES model was validated against fixed-bed experimental observations, and the validated model was then used to predict mobile-bed formations. The CES bed predictions were used to produce a failure diagram under geobag–water flow interactions and classification of bed formation under geobag–water flow–riverbank interactions. It is concluded that the CES can be a useful and computationally efficient tool for the prediction of hydraulic parameters and bed formations. In the next phase of the research, observations from the experimental program will be used to validate a discrete element model of a geobag revetment, which will be used to help develop much-needed geobag revetment design guidance.

An intensive study including laboratory experiments and use of a computer software on geobag revetment performance was reported in the companion paper. To represent the failure initiation, a set of quasi-physical model runs was carried out and the conveyance estimation system (CES) computer software was employed to predict active shear stress on geobags and mobile sand bed formation. The CES could predict the depth-averaged velocities in the laboratory measurements with reasonable accuracy. This paper reports the second part of the study, dealing with the discrete element modeling (DEM) simulation. The CES results were used for preparing a mapped velocity field for a coupled DEM simulation of geobag revetment failure. The validated DEM model could identify well the critical bag location in varying water depths and with varying bed formations. Toe scour, one of the major instability factors in revetments, and its influence on bottommost layer of the bags were also reasonably represented in this DEM model. It is envisaged that the use of a DEM model will provide more details on geobag revetment performance in riverbanks.

Culvert performance curves relate the flow through a culvert to the headwater and tailwater elevations. These curves are calculated differently by the USGS and Federal Highway Administration (FHWA), leading to the possibility of significant discrepancies in predicted culvert performance under some flow conditions. The FHWA methodology generally leads to conservative culvert designs relative to designs based on the USGS equations, and the degree of conservatism is the focus of this paper. The largest discrepancies in estimated headwater elevations for given flow rates occur under high-headwater and low-tailwater conditions, and these discrepancies are due in large part to the uncertainty in whether Type 5 or 6 flow will exist. The results of this paper show that for horizontal culverts with square-edge entrances and smooth surfaces the overestimation in the headwater depth can range from 9–45% for headwater depths in the range of 1.5–3 culvert diameters, with lesser overestimations of 7–30% in cases of rounded entrances. The amount of overestimation will be less for high-roughness culverts. In cases for which the culvert is not horizontal, the overestimation, if any, will depend on the slope of the culvert, length-to-diameter ratio, and roughness.

The importance of fuse plugs for spillways along embankments and levees has become very important in flood management. The present case study summarizes a series of laboratory tests conducted at the Laboratory of Hydraulics, Hydrology, and Glaciology, ETH Zurich, to examine the feasibility of a fuse plug spillway along the River Aare at the Hagneck Canal. This fuse plug will prevent uncontrolled overtopping of the existing levees for extreme flood scenarios and discharge the surplus water into a destined flood plain. The fuse plug is 300 m long and 1.2 m high, and should provide a spillway discharge of approximately $300{\mathrm{m}}^3/\mathrm{s}$. Two fuse plug designs were tested at both laboratory and prototype scales and analyzed in detail regarding the breach development. Design A, with an inclined clay core, was successfully adopted from a previous study. Design B consisted of a nearly homogenous sand body. Both designs are sufficiently impermeable to prevent seepage failure for water levels below the trigger water level. Both designs erode rapidly once they are overtopped. The fuse plug with the inclined clay core erodes progressively due to undercutting and collapse of the core; the homogenous sand body breaches continuously. The fuse plug Design B with homogeneous sand body was finally chosen for the Hagneck Canal spillway, primarily because of its simple structure and ease in constructional effort.

Free jets are important flow phenomena from outflow structures of dams and reservoirs. The basic case of jet flow originates from a free overfall with upstream critical flow conditions and a fully ventilated nappe. In this paper, a two-dimensional potential flow model has been developed. Semiinverse mapping of the Laplace equation has been employed in conjunction with an analytical solution of the Boussinesq equations to initiate iterations for locating the free streamlines under atmospheric pressure. A systematic iteration method is proposed using the squaring technique for solving the Laplacian field, a computation of the free streamlines using the curvilinear formulation of velocity at boundary streamlines in the energy equation, and an iteration of the position of the terminal jet section versus the brink section conditions. The model permits a convergent numerical solution, which was verified against experimental data, thereby indicating that the proposed ideal fluid flow model can be applied to predict the shape of free jets by simple computations.

Using riprap stones is a common method to prevent scouring around bridge piers. Many parameters affect stable riprap size. In the present work, stability of riprap stones around rectangular bridge piers are studied experimentally under clear-water conditions. Round-nose rectangular piers with three different aspect ratios of 3, 5, and 7 were tested. Furthermore, each pier was tested aligned with the flow and skewed at 5, 10, and 20° to the flow. Failure of the riprap layer occurred either because of high shear forces at the upstream face of the pier or under a combination of forces attributable to wake vortices and shear stresses downstream of the pier. Analysis of experimental data showed that relative flow depth, relative stone size, and effective pier width are the important factors affecting the stability of the riprap layer. At different stone sizes and pier skew angles, the region at which the riprap layer fails varies. Based on more than 140 sets of experiments, a design equation is presented for stable riprap size.