Equilibrium Scour Condition Research Articles

Numerical Analysis of Flow Structure Evolution during Scour Hole Development: A Case Study of a Pile-Supported Pier with Partially Buried Pile Cap

This study numerically investigates a pile-supported pier, which comprises a column with a partially buried pile cap and a group of piles, recognizing that partially buried pile caps lead to the highest scour depth. Most research has focused on equilibrium scour conditions in laboratory settings, overlooking the detailed dynamics of horseshoe vortices around pile groups. This study aims to clarify the flow structure and vortex dynamics at a pile-supported pier during local scour hole development stages using an in-house developed numerical model. The model’s accuracy is validated against flat-channel and compound pier reference cases. For the pile-supported pier, fixed bed geometry was used in flow simulations at selected scouring stages. Results show significant changes in flow structure and vortex formation with scour hole time development, particularly as the bed surface moves away from the pile cap. The study reveals variations in vortex size, number, and positioning, alongside turbulent kinetic energy and Reynolds shear stress distributions over time. High positive Reynolds shear stress near the bed during intermediate scouring stages highlights the complex interactions within the flow field. This research provides the first detailed visualization of flow structure evolution within a scour hole at a pile-supported pier.

Development of scour around a circular pier and its modelling using genetic algorithm

AbstractThis paper deals with generalized scour estimation to investigate maximum scour depth at equilibrium scour condition using experimental data obtained from experiments conducted by the authors along with data of previous researchers. Three hundred experimental data were used to derive the generalized clear water scour relationship around circular a bridge pier by using genetic algorithm (GA) and multiple linear regression (MLR) techniques. The GA-based maximum scour depth relationship showed more precise results than MLR. In addition, the present GA and MLR relationships were compared with some equations developed by earlier researchers. Graphically and statistically, it was observed that the GA and MLR relationships provide better agreement with experimental data as compared to earlier relationships. The present study highlights that the GA approach could be effectively used for estimation of maximum scour depth prediction around the bridge pier.

Effect of abutment aspect ratio on clear‐water scour in floodplains

AbstractScour around abutments is recognized as one of the main reasons of bridge foundations failure. This paper presents the experimental results of the effects of abutment width and length on the scour development up to its equilibrium condition around 45° wing‐wall setback abutments in a compound channel. The developing scour hole characteristics are tested for three different lengths and widths at different time intervals until its equilibrium scour conditions. The findings showed that the abutment width has a profound effect on the characteristics of the scour hole, contradicting the results of previous studies. Generally, an increase in the relative abutment width leads to a reduction in the scour depth and width. However, the scour length, area, and volume initially increase with an increase in the relative abutment width, Lc/yf, from 1.33 to 10.67, where Lc is the abutment width and yf is the floodplain flow depth, and then these characteristics decrease significantly with a much wider abutment, Lc/yf, from 10.67 to 21.33. Overall, the effects of the abutment width on abutment scour should be accounted. To this end, empirical equations are proposed to predict the scour hole characteristics. Scour data from previous studies are also used to compare with the proposed equations.

Maximum scour depth around bridge pier in gravel bed streams

Precise prediction of scour near the circular uniform pier may lead to the economic design of piers and avoid disastrous instances. Present study mainly deals with cohesionless sediment with gravel particles. Authors checked the three latest bridge pier scour models in this study. Three new relationships are proposed by authors for computing maximum scour depth, maximum scoured length and maximum effected scoured width in cohesionless sediment at equilibrium scour condition. Maximum scour depth equation is validated by the available literature data, and this relationship is applicable for both gravel as well as the sand bed. Graphically and statistically the new maximum scour depth relationship gives better agreements between observed and computed values of maximum scour depth. Relationships for maximum scoured length and maximum effected scoured width are only applicable for gravel and coarse sand bed and also gives better agreement with computed values.

On the flow and coherent structures generated by a circular array of rigid emerged cylinders placed in an open channel with flat and deformed bed

The flow and the turbulence structure generated by a circular porous cylinder of diameter $D$ containing solid cylinders of diameter $d$ placed in an open channel of depth $h\approx 0.5D$ are investigated using eddy-resolving simulations which resolve the wakes past the individual solid cylinders in the array. The solid cylinders extend from the bed through the water surface. This geometrical set-up is directly relevant to understand the physics of flow past an emerged patch of aquatic vegetation developing in a river channel or over its floodplain. Simulations are conducted with different solid volume fractions (SVFs) of the porous cylinder ($0.034<\text{SVF}<0.23$), relative diameters of the solid cylinders ($d/D=0.03$ and 0.06) and with flat and equilibrium scour bathymetry corresponding to the start and respectively the end of the erosion and deposition process. Comparison with the limiting case of a solid cylinder ($\text{SVF}=1$) is also discussed. The bed shear stress distributions and the turbulent flow fields are used to explain the sediment erosion mechanisms inside and around the porous cylinder. Simulations of the flat-bed cases reveal that for sufficiently large SVF values ($\text{SVF}>0.2$), necklace vortices form around the upstream face of the cylinder, the downflow penetrates partially inside the porous cylinder and a region of strong flow acceleration forms on the sides of the porous cylinder. These flow features are used to explain the development of scour around high-SVF porous cylinders. The effects of the SVF and $d/D$ on generating ‘corridors’ of strong flow acceleration in between the solid cylinders and energetic eddies in the wake of these cylinders are discussed, as these flow features control the amplification of the bed shear stress inside the porous cylinder. Simulations results are also used to quantify the time-averaged drag forces on the cylinders in the array, to identify the regions where these forces are comparable to those induced on an isolated cylinder and the percentage of cylinders in the array subject to relatively large mean drag forces. A logarithmic decrease of the mean time-averaged streamwise drag coefficient of the solid cylinders, $\overline{C}_{d}$, with increasing non-dimensional frontal area per unit volume of the porous cylinder, $aD$, is observed. Behind the cylinder, the eddies shed in the separated shear layers (SSLs) of the porous cylinder, and, for sufficiently large SVFs, the von Kármán wake billows are the main coherent structures responsible for the amplification of the bed shear stress and sediment entrainment. This paper also analyses the vertical non-uniformity of the mean flow and turbulent kinetic energy, and discusses how the SVF and bathymetry affect the spatial extent of the wake region (e.g. length of the SSLs and steady wake, total wake length) and other relevant variables (e.g. strength of the bleeding flow, dominant wake frequencies, turbulence amplification in the near wake). For the relatively shallow flow conditions ($D/h\approx 2.0$) considered, the simulation results show that the antisymmetric (von Kármán) shedding of wake billows behind the porous cylinder is greatly weakened once equilibrium scour conditions are approached. Comparison with data from laboratory experiments and from 3-D and 2-D simulations conducted for long porous cylinders (no bed) is also discussed.

Splitter plate as a flow-altering pier scour countermeasure

Results of an experimental study on the countermeasure of scour depth at circular piers are presented. Experiments were conducted for pier scour with and without a splitter plate under a steady, uniform clear-water flow condition. The results of pier scour without splitter plate were used as a reference. Different combinations of lengths and thicknesses of splitter plates were tested attaching each of them to a pier at the upstream vertical plane of symmetry. Two different median sediment sizes (d 50 = 0.96 and 1.8 mm) were considered as bed sediment. The experimental results show that the scour depth consistently decreases with an increase in splitter plate length, while the scour depth remains independent of splitter plate thickness. In addition, temporal evolution of scour depth at piers with and without a splitter plate is observed. The best combination is found to be with a splitter plate thickness of b/5 and a length of 2b. Here, b denotes the pier diameter. An empirical formula for the estimation of equilibrium scour depth at piers with splitter plates is obtained from a multiple linear regression analysis of the experimental data. The flow fields for various combinations of circular piers with and without splitter plate including plain bed and equilibrium scour conditions were measured by using an acoustic Doppler velocimeter. The turbulent flow fields for various configurations are investigated by plotting the velocity vectors and the turbulent kinetic energy contours on vertical and horizontal planes. The splitter plate attached to the pier deflects the approach flow and thus weakens the strength of the downflow and the horseshoe vortex, being instrumental in reducing the equilibrium scour depth at piers. The proposed method of pier scour countermeasure is easy to install and cost effective as well.

Approximate methodology to account for effects of coherent structures on sediment entrainment in RANS simulations with a movable bed and applications to pier scour

Movable-bed Reynolds-Averaged Navier–Stokes (RANS) simulations of local scour around bridge piers and abutments without ad hoc corrections tend to underestimate scour. This is generally attributed to the inability of RANS to accurately capture the unsteady dynamics of the large-scale coherent structures forming in the bed vicinity. Moreover, the characteristics of these coherent structures and their erosive capacity are expected to change as the bed evolves toward equilibrium. In the present study, Detached Eddy Simulations (DES) of flow past circular and rectangular piers are performed with bathymetry corresponding to different stages of the scour process between initial (flat-bed) conditions and equilibrium scour conditions to better understand how the coherent structures drive scour around the pier at different stages of the scouring process and to assess the capabilities of RANS to predict the flow and the turbulence statistics. Using these results, a new methodology is proposed to account for the effects of large-scale coherent structures on sediment entrainment that is directly applicable to RANS simulations with movable bed. The main idea is to improve the predictions of the local flux of sediment entrained from the bed by considering the effect of bed friction velocity fluctuations induced by the coherent structures situated near the bed, a critical effect that is generally neglected in RANS simulations. The new methodology is based on augmenting the bed friction velocity available from the time-accurate RANS calculation by a term that is proportional to the standard deviation of the bed friction velocity. This term is estimated from the turbulent kinetic energy field predicted by RANS. The model has one free parameter. Its value is calculated such that for fixed bed simulations the total entrainment flux predicted by the time-accurate RANS matches the value predicted by DES. Based on simulations conducted for flow past circular and rectangular piers, the value of the free parameter was estimated to be between 1.5 and 4, with lower values recommended to be used for cases when the time-accurate RANS simulation captures the large-scale vortex shedding behind the pier. Movable bed simulations performed using the augmented bed friction velocity model are shown to predict much more accurately the maximum scour depth around circular and rectangular piers compared to the corresponding simulations where the entrainment flux was calculated only based on the local value of the bed friction velocity calculated from the RANS velocity field.

Effects of Jet Flipping on Local Scour Downstream of a Sluice Gate

This study shows that a jet-flipping phenomenon may occur during the scouring process downstream of a sluice gate. The flipping consists of a digging and a filling phase. The former scoured the bed, and the latter refilled the scour hole. The process is cyclical, the phases changed intermittently, and no equilibrium scour condition was reached. The scour depth during digging reached a high of 60% more than the filling phase. Moreover, the scour is more severe with jet flipping compared to no-jet-flip conditions. Generally, the maximum scour depth for the digging and filling phases increases with the increase in the tailwater depth and densimetric Froude number but decreases as the apron length increases. The jet-flipping frequencies increase with the increase in the densimetric Froude number and apron length but decrease as the tailwater elevation increases. The Coandă effect is the most significant factor that triggers the jet-flipping phenomenon. A review of relevant data from previous studies showed that the scouring duration tested for many cases was not long enough to observe the jet-flipping phenomenon. Prediction equations are proposed for the maximum scour depth at the end of the digging and filling phases and for the frequencies of jet flipping. A threshold diagram to predict the occurrence of jet flipping is also presented and could be applied in design to avoid the undesirable phenomenon in local scour below a sluice gate.

Flow Field Upstream of an Orifice under Fixed Bed and Equilibrium Scour Conditions

AbstractFlow behavior upstream of a circular orifice with the invert at the bed level (initially) is investigated under fixed bed and equilibrium scour (mobile bed) conditions. The experiments are performed under three different constant heads and sediment sizes. Longitudinal and vertical components of velocity are measured in the vertical and horizontal planes passing through the center of the orifice. The velocity decay upstream of the orifice (along the centerline of the orifice) is slower for the fixed bed case than for the unbounded orifice. Under equilibrium scour condition, the velocity decay transitions from the velocity profile for the unbounded orifice to the fixed bed condition. The longitudinal velocity profiles in the horizontal plane at different locations upstream of the orifice are found to be similar for both fixed and mobile bed cases. The longitudinal velocity profiles in the vertical plane are also found to be similar for each case. The maximum velocity is found to occur below the cent...

Flow and Turbulence Structure around Abutments with Sloped Sidewalls

AbstractResults of eddy-resolving numerical simulations are used to investigate flow and turbulence structure around an isolated abutment with sloped sidewalls at conditions corresponding to the start (flatbed) and the end (equilibrium bathymetry) of the scour process. Besides cases where the abutment is not protected against scour using riprap, the paper considers cases where a riprap apron of constant width is present around the base of the abutment at the start of the scour process. The paper also discusses the effect of large-scale turbulence (e.g., horseshoe vortex system, eddies shed in the separated shear layer, vortices forming in the recirculation regions) on sediment entrainment and transport. Using information about the position and coherence of the large-scale turbulent structures present in the vicinity of the bed surface, the paper discusses some of the reasons for the very different bed scour patterns observed at equilibrium scour conditions for cases without and with a riprap apron. The ef...

Scour upstream of a circular orifice under constant head

The transport mechanism as well as the extent and the shape of the scour upstream of a circular orifice is investigated under steady flow conditions for different sediment sizes and heads on the orifice. The main mechanism of sediment transport is found to be vortex-related, appearing randomly within the scour hole. The scour length, maximum scour width, and maximum scour depth are evaluated for various sediment sizes and under different heads on the orifice. The non-dimensional scour depth profiles along the orifice centreline are found to be similar. The non-dimensional scour depth profiles across the width of the scour hole at various locations upstream of the orifice are found to be similar as well. The flow characteristics related to the scaled centreline longitudinal velocity and the scaled position of the maximum longitudinal velocity are found to approach those for the unbounded orifice at the equilibrium scour condition.

Flow and turbulence structure around a spur dike in a channel with a large scour hole

The flow and turbulence structure around a vertical‐wall spur dike that extends over the whole depth of a straight channel are investigated using detached eddy simulation (DES). The channel Reynolds number in DES and the corresponding experiment is ReD = 2.4 × 105, which is typical of applications in small rivers and outside the range where well‐resolved large eddy simulation (LES) can be conducted. The bathymetry at equilibrium scour conditions is obtained from a loose bed experiment. This paper discusses the main mechanisms which drive the growth of the scour hole upstream and downstream from the spur dike during the later stages of the scour process, and how these mechanisms change between the initial (flat bed conditions) and later stages of the scour process. Scale effects are investigated by comparing simulation results at ReD = 2.4 × 105 with those from simulations performed at a much lower Reynolds number, ReD = 18,000. Results show that while the structure of the horseshoe vortex (HV) system changes with respect to the case in which the bed is flat, the main necklace vortex of the HV system is still subject to large‐scale aperiodic oscillations, similar to the ones observed in flows past in‐stream bluff‐body obstacles mounted on a flat surface. Present results show that the amplification of the horizontal vorticity within the lower part of the separated shear layer (SSL) and the associated formation of streaks of high‐bed shear stress below the region where the SSL eddies are convected in the near‐bed region is a general feature of high‐Reynolds‐number flow past a vertical‐wall spur dike placed in a loose‐bed channel at all stages of the scour process.

Anomalous Contraction Scour? Vertical-Contraction Case

Clear-water scour due to a short vertical (pressure flow) contraction was investigated in a laboratory channel. Two approach velocities were studied for a (nominally) single configuration of depth and degree of contraction, with experiments conducted for various durations up to a maximum of 48 h, and the evolution of the scour hole over time monitored. The location of maximum scour in both cases was observed to occur downstream of the contraction, with maximum scour depths substantially in excess of values predicted by published models, even though equilibrium scour conditions were not reached.

Coherent Structures in the Flow Field around a Circular Cylinder with Scour Hole

Large-eddy simulation (LES) and laboratory-flume visualizations were used to investigate coherent structures present in the flow field around a circular cylinder located in a scour hole. The bathymetry corresponds to equilibrium scour conditions and is fixed in LES. The flow parameters in the simulation correspond to the experimental conditions in which the approach flow is fully turbulent. Detailed consideration is given to the interaction of the horseshoe vortex (HV) system within the scour hole with the detached shear layers formed from the cylinder, and the near bed turbulence. It is found that the overall structure of the HV system varies considerably in space and time, though a large, relatively stable, primary necklace vortex is present at practically all times inside the scour hole. The simulation captures the presence of bimodal chaotic oscillations inside the HV system, as well as the sharp increase in the resolved turbulent kinetic energy levels and pressure fluctuations reported in prior experimental investigations. High levels of the mean bed shear stress are observed beneath the primary necklace vortex, especially over the region where the bimodal oscillations are strong, as well as beneath the small junction vortex at the base of the cylinder. It is also found that the detachment and advection of patches of vorticity from the downstream part of the legs of the necklace vortices can induce large instantaneous bed shear stress values. When the critical bed shear stress value for sediment entrainment on a flat surface is adjusted for bed slope effects, the LES simulation correctly predicts that the distribution of the mean bed shear stress is consistent with equilibrium scour conditions.

Effect of grain size on local channel scour below a sluice gate

In this study, the effect of grain size on the dynamics of local scour processes is discussed in the context of the erosion that takes place downstream from a submerged sluice gate. Four gradations of non-cohesive bed material were used to study the scour process for various tailwater depth and flow rate conditions. The sand gradations included three sizes of uniformly graded sand and a fourth size, which was obtained by mixing the three uniform sands in equal proportions by weight. A total of 36 tests was carried out, each for a period of 24 h. An equilibrium scour condition was not attained over this time period for any of the tests, although a sense of similarity in the bed profiles is observed in the region close to the sluice gate. The present results indicate that the depth and the area of scour are highly dependent on the bed grain size, both increasing as the grain size is reduced. As well, it was found that the tests with a mixed (i.e., graded) sand bed resulted in less scour relative to those in which a uniformly graded sand of similar grain size was used. Moreover, the maximum scour depth increases with increases in the discharge and the tailwater depth. Finally, it was found that the location of the point of maximum scour depth, as measured from the upstream end of the erodible sand bed, moved downstream with an increase in either the discharge or tailwater depth and upstream with an increase in the grain size.Key words: grain size, grain size distribution, local scour, scour dynamics, sluice gate, tailwater depth, video image data acquisition.

TIME-VARIATION OF SCOUR IN THE VICINITY OF CIRCULAR PIERS.

A theoretical model is presented to estimate the time-variation of scour depth in an evolving scour hole at circular piers under clear-water and live-bed scour conditions with uniform and non-uniform sediments. The procedure developed for computing the time-variation of scour depth was based on the concept of the conservation of the mass of sediment, considering the horseshoe vortex system to be the main agent of scouring and assuming a layer-by-layer scouring process. The present model corresponds closely with the experimental data of time-variation of scour depth under clear-water and live-bed scour conditions with uniform and non-uniform sediments reported by various investigators. Computation is extended up to the equilibrium scour condition and the corresponding design formula for estimation of maximum scour depth is also proposed for given flow, sediment and pier conditions. The computed values of maximum scour depth showed adequate and safe estimation for bridge pier foundations.

Three-Dimensional Simulation of Scour-Inducing Flow at Bridge Piers

Presently available formulas for estimating the maximum depth of scour near bridge piers often lead to unreliable results. A fully three-dimensional hydrodynamic model is therefore used in this study to simulate the flow occurring at the base of a cylindrical bridge pier within a scour hole. The results of the numerical simulation are compared with laboratory observations by Melville and Raudkivi (1977). Quantitative and qualitative agreement between the studies is quite good. Discrepancies between the results of the two studies are of an order that may be attributed to choices in numerical model parameters. The simulations may be supplemented by Lagrangian particle-tracking to estimate the depth of the equilibrium scour condition.