Maximum Equilibrium Scour Depth Research Articles

Scouring around bridge pier: A comprehensive analysis of scour depth predictive equations for clear-water and live-bed scouring conditions

Abstract The failure of bridges, attributed to bridge pier scouring, poses a significant challenge in ensuring safe and cost-effective design. Numerous laboratory and field experiments have been conducted to comprehend the mechanisms and predict the maximum equilibrium scour depth around bridge piers. Over the last eight decades, various empirical methods have been developed, with different authors incorporating diverse influencing parameters that significantly impact the estimation of equilibrium scour depth around bridge piers. This paper aims to consolidate: (1) available experimental and field data sets on different types of bridge pier scouring, (2) the influence of flow and roughness parameters on both clear water scouring (CWS) and live bed scouring (LBS), and (3) existing empirical equations suitable for computing equilibrium scour depth around a bridge pier under CWS and LBS conditions. The presented research encompasses over 80 experimental/field data sets and more than 60 scour-predicting equations developed for CWS and LBS conditions in the past eight decades. Based on the performance of different empirical models in predicting scour depth ratio, suitable models are recommended for CWS and LBS conditions.

Formation of a scour funnel upstream of an orifice affected by a bottom-mounted cylinder

A scour funnel before a bottom orifice on a dam is able to help intaking water with low sediment concentration and thus protect the water turbine. Appropriate placement of pier-like structures in front of a bottom orifice may increase the size of a scour funnel. This work experimentally investigates the formation and development of a scour funnel upstream of a bottom orifice affected by a bottom-mounted cylinder. It is found that the cylinder blocks the flow so as to reduce the flow rate by as much as 8.27%. Nevertheless, the sizes of equilibrium scour funnel generally increase due to the use of a cylinder; for instance, the equilibrium scour depth may increase by as much as 36.1%. The enlargement of scour funnel is closely related to the motion of large-scale turbulent vortices caused by the cylinder. We found that the turbulent kinetic energy around the cylinder is significantly increased due to the presence of a cylinder with a maximum relative increase in 192.5%. The placement of a cylinder leads to a drastical increment of sediment erosion rate. For cases with a cylinder, it may take only 1.1% of the time (for the first time) to reach the same level of equilibrium scour depth in a same case without a cylinder. Therefore, by appropriately placing a cylinder before a bottom orifice, it is possible to achieve a larger-sized scour funnel in a very shorter time with smaller abandoned water. A formula is established to calculate the maximum equilibrium scour depth.

Development of a Framework for Cost–Benefit Analysis of I-Head and T-Head Groynes Based on Scour and Turbulent Flow Characteristics

River bank protection is a vital component of sustainable development. This study investigates and compares the scour and flow features around two different types of groynes, an unsubmerged I-head groyne (IHG) and T-head groyne (THG), to provide insights into their performance and efficiency in river reaches. Experiments were conducted to examine the scouring pattern, mean and turbulent flow characteristics including 3D mean flow velocity distribution, Reynolds stresses, turbulent kinetic energy, and bed shear stress near the bed region around the groynes under similar flow conditions. The results indicated that THG had a maximum equilibrium scour depth over three-fold greater than IHG. For both the IHG and THG cases, it was observed that there is a direct correlation between the location of maximum negative vertical velocity and its magnitude to the region of maximum local scour and its depth. All the stresses of high magnitude are found along the propagation of the detached shear layer profile, which turns back sharply downstream towards the bank containing the IHG while remaining mostly away from the bank in the case of THG. The effective bank protection length was estimated to be two-fold the groyne length in the case of IHG and three-fold the groyne transverse length in the case of THG. Cost–benefit analysis of the two groyne types shows IHG as the more cost-efficient groyne with respect to bank protection lengths. This study provides valuable insights for developing design methodologies aimed at promoting the wider utilization of different head-shape groynes in river reaches and aids in selecting appropriate groyne head configurations that align with specific field requirements.

Physically based formula for the maximum scour depth induced by a propeller jet

In the last two decades, many studies have been dedicated to the employment of predictive formulas able to assess the maximum scour depth produced by propeller jets. Owing to the complexity of the phenomenon, most of the literature formulas were built on empirical arguments, making them susceptible to scale issues and not fully coherent with the physics underpinning the scouring problem. Recent studies exploited the phenomenological theory of turbulence and the paradigms of sediment incipient-motion theory to derive a predictive formula of the maximum equilibrium scour depth in different cases: scour produced by jet, scour at bridge piers, and scour downstream of hydrokinetic turbines. In the present study, using the same considerations of the aforementioned works, we propose a new model that allows the derivation of a predictive physically based formula that includes all the relevant parameters controlling the scouring process induced by the propeller rotation. The theory is validated at the laboratory scale with experimental published data: a good agreement between theoretical predictions and literature data is shown. The proposed design formula clearly indicates that, when tested against experimental data, it leads to lower scattering levels than those obtained with empirical literature formulas.

The Effect of Rough Rigid Apron on Scour Downstream of Sluice Gates

Presented in this paper is an experimental study on scour downstream of rough and smooth stiff aprons under the influence of wall jets. The effect of various parameters on asymptotic scour depth is studied. The analysis of data reveals that maximum scour depth reduces with increasing sediment size, sluice opening, and apron length. It is directly proportional to densimetric Froude number. Maximum equilibrium scour depth initially decreases with increasing tailwater level (up to a minimum), but thereafter an increase is observed. The effect of roughness of stiff apron on scour is studied and quantification of decline in maximum scour depth due to roughness is carried out. Scour profiles and their temporal variation are also studied. A regression-based equation to predict equilibrium scour depth under smooth and rough apron is proposed, which conforms to experimental data. Based on the conclusions of this study, it is recommended to use roughness over the surface of stiff apron to confine scour under-wall jets.

A comparative study on equilibrium scour volume around circular cylinders in clay–sand mixed cohesive beds, at near threshold velocity of sand – an experimental approach

Abstract Local scour around a bridge pier is a complex phenomenon resulting from the interaction of the three-dimensional turbulent flow field around hydraulic structures. An accurate estimation of scour depth below the stream-bed is important during design since it determines the foundation levels and the expansion of the bridge foundation structures. The present study reveals the results of flume experiments on equilibrium scour depth and scour volumes around circular bridge pier models in clay–sand sediment mixtures. The scouring process in a cohesive sediment mixture is a complex interaction between clay–sand network structure and bed shear stresses. The bed shear stress reduces inside the scour hole as scour depth increases, and this is related to the different modes of scouring in clay–sand mixtures. An exponential equation for the non-dimensional scour volume is proposed considering all the experimental runs to get a specific understanding of the surrounding volume of scour hole from maximum equilibrium scour depth in a clay–sand mixed cohesive bed, when the approach flow velocity is near to the critical velocity for mixed sand. The proposed equations are validated using the pre-existing data from the literature dealing with experimental investigations on bridge scour using clay–sand mixed cohesive sediment and show good agreement with observed data.

Experimental study on wave- and current-induced scour around an anti-deposition permeable breakwater

Local scour around structures is a hot topic in ocean engineering research. In this study, a physical model is developed to simulate wave- and current-induced scour around a novel anti-deposition permeable breakwater. The scour process is monitored by applying acoustic Doppler velocimetry (ADV) at 32 points that are uniformly arranged along the front and back sides of the model. The scour topography and scour depth are investigated in detail under various wave and current conditions. The experimental results indicate that the maximum scour depth and scour range increase with increasing wave height and period of the incident wave, water depth, or water velocity. The combined wave–current condition results in a larger scour range and longer equilibrium scour time than the wave- or current-only condition. The results further indicate that the lower board that is set for sediment trapping serves to protect the sediment around the pile, that the maximum equilibrium scour depth is smaller than that without the lower board, and that the scour pit is farther away from the model in the presence of the lower board.

Secondary Currents with Scour Hole at Grade Control Structures

Most studies on local scouring at grade control structures have principally focused on the analysis of the primary flow field, predicting the equilibrium scour depth. Despite the numerous studies on scouring processes, secondary currents were not often considered. Based on comprehensive measurements of flow velocities in clear water scours downstream of a grade control structure in a channel with non-cohesive sediments, in this study, we attempted to investigate the generation and turbulence properties of secondary currents across a scour hole at equilibrium condition. The flow velocity distributions through the cross-sectional planes at the downstream location of the maximum equilibrium scour depth clearly show the development of secondary current cells. The secondary currents form a sort of helical-like motion, occurring in both halves of the cross-section in an axisymmetric fashion. A detailed analysis of the turbulence intensities and Reynolds shear stresses was carried out and compared with previous studies. The results highlight considerable spatial heterogeneities of flow turbulence. The anisotropy term of normal stresses dominates the secondary shear stress, giving the impression of its crucial role in generating secondary flow motion across the scour hole. The anisotropy term shows maximum values near both the scour mouth and the scour bed, caused, respectively, by the grade control structure and the sediment ridge formation, which play fundamental roles in maintaining and enhancing the secondary flow motion.

Pier scours in fine-grained non-cohesive sediment and downstream siltation, an experimental approach

ABSTRACT Scour is a natural phenomenon involving the removal of bed sediments by the perturbation of flow field with the erection of hydraulic structures such as guide bank, abutments and bridge piers. Removal of sediment at the base of the pier due to scouring not only undermines its foundation support considerably but also leads to deposition and siltation downstream due to lower flow velocities. This deforms the river bed configuration and thereby flow kinematics. While there have been numerous studies of scouring in gravel and sand beds, there are few studies involving fine sand to silt beds. In the present flume-based study, an attempt was made to study the effect of pier size, shape and flow velocity on scouring process, scour depth for piers in fine sand to silt bed. Results reveal that scouring process significantly differs for different pier shapes and sizes. Equilibrium scour depth and downstream bed deformations show considerable correlation with turbulent flow characteristics. Empirical equations have been proposed to predict the maximum equilibrium scour depth. Outcomes of the investigation support and assist engineering practices related to site-specific, cost-effective designs of bridge pier foundations and the consequence on streambed modifications at the lower reach of rivers.

Pier Scour Prediction in Non-Uniform Gravel Beds

Pier scour has been extensively studied in laboratory experiments. However, scour depth relationships based on data at the laboratory scale often yield unacceptable results when extended to field conditions. In this study, non-uniform gravel bed laboratory and field datasets with gravel of median size ranging from 2.7 to 14.25 mm were considered to predict the maximum equilibrium scour depth at cylindrical piers. Specifically, a total of 217 datasets were collected: 132 from literature sources and 85 in this study using new experiments at the laboratory scale, which constitute a novel contribution provided by this paper. From the analysis of data, it was observed that Melville and Coleman’s equation performs well in the case of laboratory datasets, while it tends to overestimate field measurements. Guo’s and Kim et al.’s relationships showed good agreements only for laboratory datasets with finer non-uniform sediments: deviations in predicting the maximum scour depth with non-uniform gravel beds were found to be significantly greater than those for non-uniform sand and fine gravel beds. Consequently, new K-factors for the Melville and Coleman’s equation were proposed in this study for non-uniform gravel-bed streams using a curve-fitting method. The results revealed good agreements between observations and predictions, where this might be an attractive advancement in overcoming scale effects. Moreover, a sensitivity analysis was performed to identify the most sensitive K-factors.

Hydrodynamic Structure with Scour Hole Downstream of Bed Sills

Experimental turbulence measurements of scour hole downstream of bed sills in alluvial channels with non-cohesive sediments are investigated. Using an Acoustic Doppler Velocimeter (ADV), the flow velocity-field within the equilibrium scour hole was comprehensively measured. In this study, we especially focus on the flow hydrodynamic structure in the scour hole at equilibrium. In addition to the flow velocity distribution in the equilibrium scour hole, the turbulence intensities, the Reynolds shear stresses, the turbulent kinetic energy, and the turbulent length scales are analyzed. Since the prediction of equilibrium scour features is always very uncertain, in this study and based on laboratory turbulence measurements, we apply the phenomenological theory of turbulence to predict the maximum equilibrium scour depth. With this approach, we obtain a new scaling of the maximum scour depth at equilibrium, which is validated using experimental data, satisfying the validity of a spectral exponent equal to −5/3. The proposed scaling shows a quite reasonable accuracy in predicting the equilibrium scour depth in different hydraulic structures.

Experimental study on scour around a composite bucket foundation due to waves and current

Local scour around foundations is a hot research topic in ocean engineering, especially for shallow composite bucket foundations. In this study, a physical model was developed for the scour induced by waves and current around a composite bucket foundation. Foundation models with scales of 1:40 and 1:60 were placed in a flume, and the scour process was monitored at eight points arranged evenly and symmetrically along the model circumference. The scoured topography was investigated in detail under different wave and current conditions, and the maximum equilibrium scour depths were compared. The experimental results showed that the combined wave–current condition induced a greater scour range than the wave-only or current-only condition, but it did not necessarily induce a greater equilibrium scour depth than the current-only condition. In contrast to the current-induced scour, the combined wave–current and wave-only conditions induced obvious scour pits in the front of and close to the foundation. The effects of dimensionless parameters such as the Keulegan–Carpenter number (KC), ratio of velocities (Ucw) and Froude number (Fra) on the maximum equilibrium scour depth were considered.

Local Scour of Armor Layer Processes around the Circular Pier in Non-Uniform Gravel Bed

Flume experiments have been carried out under clear water scour conditions to analyze the maximum equilibrium scour depth and scour processes in armored streambeds. A total of 85 experiments have been carried out using different diameters of circular piers and non-uniform gravels. A graphical approach for dimensionless scour depth in equilibrium condition around the circular pier in armored streambeds has been developed. As per this curve, the maximum dimensionless scour depth variation with dimensionless armor particle size depends on the densimetric particle Froude number (Frd50), and the decreasing rate of dimensionless scour depth decreases with the value of Frd50.

Scour around Spur Dike in Sand–Gravel Mixture Bed

Scour is the main cause of failure for spur dike. The accurate prediction of scour around spur dike is essential to design a spur dike. The present study focuses on the maximum scour depth in equilibrium condition and parameters, which influence it in a sand–gravel mixture bed. Outcomes of the present experimental study showed that the non-dimensional maximum equilibrium scour depth increases with critical velocity ratio (U/Uca), water depth-armour particle ratio (h/da), Froude number for sediment mixture (Frsm), water depth-spur dike length ratio (h/l), and decreases with increase in armour particle-spur dike length ratio (da/l). The maximum scour depth is proportional to dimensionless parameters of U/Uca, h/da, Frsm, h/l, but the scour depth is inverse proportional to da/l. Scour around spur dike in a sand–gravel mixture is mainly influenced by the property of the sediment mixture. The scour increases with decrease in non-uniformity of the sediment mixture. A non-linear empirical equation is proposed to estimate the maximum scour depth at an upstream nose of rectangular spur dike with a maximum error of 15%. The sensitivity analysis indicates that the maximum non-dimensional equilibrium scour depth depends on Frsm, followed by the secondary sensible parameters da/l, h/l, and h/da.

Flume study on contraction scour in clay–sand mixed cohesive bed

Flow constriction, whether man-made or natural, occurs whenever there is a significant reduction of the width of natural flow and hence the induced beds shear stress increases considerably and consequently the bed sediment within the contraction get scoured. The problem is often idealized as a rectangular long contraction consisting of a contracted zone, length of which is greater than the transverse width of the flow. From the literature survey, it is revealed that several empirical models were proposed to compute the maximum equilibrium scour depth at contraction. In almost all the reported investigations, bed sediment used were non-cohesive sand, except one or two where bed sediment was made up of clay and completely cohesive in nature. In the present investigation, an attempt has been made to study the scour in long contraction for the sediment comprises the mixture of clay and fine sand with varying proportions. A total of 30 experimental runs in laboratory flume on clay–sand mixed cohesive sediment were carried out to study the effect of varying clay fraction, approach flow velocity and contraction ratio, on maximum equilibrium scour depth and its location within long contraction.

Pier scour within long contraction in cohesive sediment bed

In the present study, an attempt has been made to study the bridge pier scour embedded long contraction for the bed sediment prepared by a mixture of clay and fine sand with varying proportions having a specific range of antecedent moisture content. Results particularly focused on the clay–sand mixed cohesive bed at varying clay fractions of the sediment bed, approach flow velocity, contraction ratio and different pier shapes, on maximum equilibrium scour depth for pier scour within long contraction. Further, regression based equations for the estimation of non-dimensional maximum scour depth for piers within long contraction in clay–sand mixed cohesive bed embedded were proposed.

Scour at wind turbine tripod foundation under steady flow

Results of a physical modelling study of clear-water scour at a tripod obstacle in uniform bed sediment under steady flow conditions are presented. 4 flow depths, 2 flow velocities and 3 angles of attack were considered. Maximum scour depth increased with increase in flow depth or velocity. For deep flows and high flow rate, the maximum value of the ratio of the equilibrium scour depth to the diameter of the tripod’s leg was 3.5, which is significantly greater than values of 1.3 or 2.5 suggested by guidelines for offshore wind turbine monopiles design. This ratio may be even larger because of the increased shear stress when waves are superimposed on current. All maximum equilibrium scour depths occurred at the upstream surface of a tripod leg despite the centre pile having a larger diameter. The alignment angle had a small effect on scour depth. But it is notable that there is an increase in scour development depth at 60° alignment angle. Equations are suggested for estimating the clear-water scour depth at wind turbine tripod foundations.

Scour in the transition from super- to subcritical flow without a hydraulic jump

Local scour in the transition from super- to sub-critical flow without a hydraulic jump is investigated based on model experimentation. Supercritical flow was enforced by a box-culvert, passed a curved bed, and then flowed over the sediment bed. The scour processes and the initiation of sediment motion are discussed. Attempts are also made to explain similarities among scour processes and profiles. The temporal development of the maximum scour depth is evaluated. Results indicate that the maximum equilibrium scour depth and scour hole geometry in the transition from super- to sub-critical flow without a hydraulic jump significantly depend on the upstream supercritical approach flow, and the densimetric Froude numbers. Scour profiles were also compared with those resulting from equivalent hydraulic jumps, indicating that the geometrical characteristics of the scour holes are significantly smaller than those of the corresponding hydraulic jumps. Finally, relationships characterizing the equilibrium scour hole geometry are derived based on the experimental results.

The influence of upstream slope on the local scour at drop structure

The drop structure will fail as a result of local scoring downstream. This paper discusses the influence of a drop structures’ upstream slope to local scour. Empirical equations of the scour hole were developed by laboratory experiment, theoretical assumptions, and regression analysis. These equations include the maximum scour depth and length during the scouring period, the maximum equilibrium scour depth and length, and the unit width scour rate. The four channel slopes (0%, 2%, 4%, and 6%) before the drop structure has been included in the analysis. A series of laboratory experiments were conducted to obtain 48 groups of experiments and 419 scour hole profiles during the scouring period. The material used in the scour section is uniform non-cohesive and with a median diameter of d50 = 0.5 mm. The results have been used to develop empirical equations via regression analysis to determine the coefficients of theoretical equations. The high correlation coefficient indicates that the equations developed in this study are suitable for verifying the characteristics of a scour hole at drop structure in the sloped channel. The semi-empirical equation is more accurate than the empirical equation. Compared to a horizontal channel, a sloped channel tends to cause a greater equilibrium maximum scour length, shorter equilibrium maximum scour depth, and faster unit-wide scour rate.

Scour around vertical piles due to random waves alone and random waves plus currents on mild slopes

This paper provides a practical stochastic method by which the maximum equilibrium scour depth around a vertical pile exposed to random waves plus a current on mild slopes can be derived. The approach is based on assuming the waves to be a stationary narrow-band random process, adopting the Battjes and Groenendijk (2000) wave height distribution for mild slopes including the effect of breaking waves, and using the empirical formulas for the scour depth on the horizontal seabed by Sumer and Freds e (2002). The present approach is valid for wave-dominant flow conditions. Results for random waves alone and random wave plus currents have been presented and discussed by varying the seabed slope and water depth. An approximate method is also proposed, and comparisons are made with the present stochastic method. For random waves alone it appears that the approximate method can replace the stochastic method, whereas the stochastic method is required for random waves plus currents. Tentative approaches to related random wave-induced scour cases on mild slopes are also suggested.