Journal of Hydraulic Engineering

Experiments on scour at bridge piers were carried out in a sediment recirculating flume with a bed of polystyrene particles. The focus of the research reported in this paper was given to live-bed experiments. All experiments were run until equilibrium conditions with flow velocities $u$ ranging from 0.8–8.5 times the critical velocity for the incipient motion of sediment particles $u_c$. Maximum scour depth was continuously measured with an endoscopic camera from inside the pier, which was constructed by a plexiglass cylinder. Bed load transport with dunes was identified as the main transport mode for $1<u/u_c<4$. For ratios of $u/u_c\ge 4$ entrainment into suspension without development of bedforms dominated. Results show that scour rapidly reach equilibrium in the bed of polystyrene pellets. In the clear-water experiments equilibrium scour depth remained constant in time. In the bed load region the fluctuation of scour depth corresponded to the dune migration through the scour hole, while in the suspended load region the fluctuation of scour depth was negligible and was superposed by general erosion. For both clear-water and live-bed conditions maximum equilibrium scour depth continuously increased with flow intensity $u/u_c$. Maximum scour depth was in accordance with a logarithmic curve and reached values up to 3.3 times the pier diameter for $u/u_c=8.5$. Extrapolation of the obtained results for an estimation of equilibrium scour depth in a lifelike worst-case scenario is discussed.

Detailed $K$-factors measured for a symmetrical nonreducing steel cross junction were published in this journal in 2010. This article describes a variable $K$-factor model for cross junctions that can take advantage of the published data and be incorporated into most existing hydraulic simulation software. The raw data are transformed and represented with bicubic spline surfaces. Newton’s method is used to solve the system of equations resulting from linearization of the equations. Despite the variable junction $K$-factors, solutions converge quadratically or nearly so. For each iteration step, flow patterns must be detected, cross legs identified, and $K$-factors updated. Inherent complexity of flow through cross junctions creates challenges: $K$-factor surfaces have steep gradients and the values are often negative, branches with laminar flow occur alongside branches with turbulent flow, and flow stoppage is recurrent. In addition to comparing solutions based on constant and variable $K$-factors, intriguing flow phenomena are highlighted and suggested as research topics. An important application of the methods presented in this article is validation of hydraulic simulation software.

Two separate large eddy simulations (LES) are carried out to investigate the effects of accurate computation of the curvilinear water-surface deformation of the flow through a bridge contraction. One LES employs the rigid-lid boundary condition at the water surface, while the other uses a highly accurate level-set method (LSM), which allows the water surface to adjust itself freely in response to the flow. The simulation with the LSM is validated with data from complementary physical model tests under analogous geometrical and flow conditions. Streamwise velocity, bed-shear stress and second-order turbulence statistics obtained from both simulations are compared, and it is shown that the turbulence structure of this flow is influenced strongly by the water-surface deformation. While bed-shear stresses and first-order statistics are very similar for both cases, the instantaneous turbulence structure and consequently, the second-order statistics, are distinctly different. The correct prediction of the water-surface deformation of such flows is deemed important for the accuracy of their simulation.

Sediment particles smaller than 64 μm, with a noncohesive base mineral, are referred to as silt. The settling velocity of suspended sediment decreases with increasing concentration due to hindered settling effects. Compared with clay and sand, hindered settling of silt is poorly documented and understood. A formulation is proposed for the hindered settling of silt-water mixtures, derived from physical reasoning. The effect of silt on the mixture’s viscosity is addressed in particular. The formulation compares favorably with laboratory experiments on the settling of silt-sized sediment. This study shows that effective settling velocities can be derived from a single concentration time series measured within the settling mixture, provided that the sediment is initially homogeneously distributed.

Hydraulic investigations of three hydraulic model studies on side channels are presented. These include the side channels of the Trängslet Dam, Sweden, the Kárahnjúkar Dam, Iceland, and the Lyssbach diversion tunnel, Switzerland, of which the former two have a trapezoidal cross section and the latter has a rectangular cross section. The observed flow patterns are described, with particular attention on the single- and two-vortex spiral flow patterns, the formation of a tornado vortex, and air entrainment. The measured streamwise free-surface profiles are compared with one-dimensional computations on the basis of the standard spatially varied flow equation. Although a good agreement results in general, deviations are primarily explained by local perturbations. The measured cross-sectional free-surface profiles indicate an increase in the flow depth along the side walls compared with the computed flow depth at the impact point of lateral inflow. For the side-channel design, safety provisions should therefore be considered. Side channels with geometrical complexities and a high hazard potential should be investigated in detailed hydraulic model tests, whereas the remainder essentially follows computations on the basis of the preceding procedure.

Liu’s theory of 1957 to estimate the point of incipient motion, derived assuming a flat bed slope and uniform flow, states that for large particles the movability number (defined as the ratio of the shear velocity to the settling velocity), is constant. Data collected from 12 undistorted and unscaled laboratory tests was used to investigate the applicability of the theory on steep riprap slopes. The tests indicate that the dimensionless movability number (MN) is constant for large particle Reynold numbers. For design purposes, the recommended movability number which emerged from this study is 0.18, provided that the steep bed slope is taken into account, the energy slope is considered in MN, and that the theoretical settling velocity is calculated using an accurate drag coefficient and the $d_{90}$ sieve size of the riprap.