Equilibrium Scour Depth Research Articles

Influence of Cumulative Effective Stream Power on Scour Depth Prediction Around Bridge Piers in Cohesive Bed Sediments

Streambed scour in cohesive sediment is complex because erosion processes depend on the physical, geochemical, and biological properties of the sediment. The scouring processes can also be characterized as a slow fatigue phenomenon. Therefore, repetitive hydraulic loadings from multiple stormflow events are likely necessary for equilibrium scour depths to develop in cohesive sediment compared with non-cohesive sediment. Cumulative effective stream power, which is a surrogate measure of effective stream power duration, showed a significant relation with scour development and propagation in cohesive sediments around bridge piers, where results from this study identified a statistically significant correlation between cumulative effective stream power and the observed scour depths around different bridge piers ( R2 = 0.56, p < 0.001). However, some localized and site-specific variations were observed. It was also observed that scour depth development in cohesive soil appeared to be dependent on effective shear duration, rather than the number of flow events above erosion threshold values. In addition, the relationship between an erodibility index ( K) and critical stream power showed a significant statistical correlation ( R2 = 0.61, p = 0.017). Results from this study deviated from the Annandale empirical relationship for sediments when K < 0.1. This finding supports that site-specific critical stream power should be measured using an empirical relationship for cohesive bed sediments to predict scour depths.

Theoretical approach for the equilibrium scour depth underneath a partially submerged bridge deck

The destructive implication of pressure-flow scour during flood events is a critical issue for researchers throughout the world. The current paper presents two models to estimate the pressure-flow scour depth underneath a partially submerged bridge deck in the equilibrium phase based on the jet flow theory. An estimate of the submergence distance of the jet flow under the bridge deck is the base point of the first model. The second model uses the phenomenological theory of turbulence where the tangential component of jet velocity is scaled to the velocity of the eddy formed under the bridge deck. This theory has already been used by researchers to estimate the scour depth of the jet flow. Dimensionless parameters are constructed in the theoretical framework of both models. The angle and velocity of the combined jet under the bridge deck and the effective depth underneath the bridge deck have been obtained using the relations presented in the previous research. The application of the presented models is limited to cases where the relative opening height of the bridge deck is greater than 0.25. The derived equations of the current study are calibrated based on the data with sufficient time durations. The results show that both models predict fairly well the maximum pressure-flow scour depth. The values of Nash–Sutcliffe efficiency and relative root mean square errors of the second model predictions are more appropriate, compared to the estimates of the first model and estimates obtained by equations presented in the previous studies.

Experimental study on silty seabed scour around the single pile induced by the current

In this study, the effects of the current velocity, water content, consolidation strength, and soil particle size on the silty seabed scour around the single pile are studied through flume tests. The liquid limit and plastic limit of the silt are determined through water content tests to calculate the plasticity index. The shear strength and density of the soil were determined through direct shear tests and ring knife methods, respectively. The experimental results indicate that the ultimate equilibrium scour depth of the single pile on silty seabed does not increase or decrease with the increase of water content, but as the water content increases to a certain value, it begins to decrease. The consolidated silty seabed has a substantially smaller scour depth than unconsolidated seabed, and the greater the consolidation strength, the smaller the scour depth, and the more time is needed to achieve scouring equilibrium. The water content and consolidation strength both have an impact on the shape and radius of the scour hole. At high flow rates, the time for the silty seabed to reach the ultimate equilibrium scour depth is greatly shortened. When the flow rate is high, the time history curves of different water contents become more similar. Based on the experimental results, a prediction formula for the scour depth of the silty seabed considering the characteristics of fluid and soil is established. The error of the new formula is less than 20%, which can provide reference for pile scour protection on the silty seabed.

Clear-water scour at monopile foundations subjected to cyclic lateral loads in different directions

Monopile foundations have been widely used to support offshore wind turbines in shallow waters. Current-induced local scour at monopile foundations, as a universal problem threatening the structure safety and the operational efficiency of the turbines, has been extensively studied in recent decades by flume experiments and numerical models. Recent studies reported that the scour process around monopile foundations is affected by cyclic lateral loads induced by waves, currents, and winds. However, the scour mechanism around monopile foundations subjected to cyclic lateral loads in different directions remains unclear, necessitating further investigation. This paper presents an experimental study investigating the clear-water scour characteristics around monopile foundations under cyclic lateral loads applied parallel and perpendicular to the flow direction at a relatively low flow intensity. The experimental results reveal that when the amplitudes of the cyclic lateral loads exceed 4% of the monopile diameter at the monopile’s top, the equilibrium scour depths at monopile foundations subjected to cyclic lateral loads perpendicular to the flow direction are generally larger than those under cyclic lateral loads parallel to the flow direction. Sour holes extent more significantly in the direction of cyclic lateral loads rather than the unload direction, and the slope angles in the load directions are gentler than those in the unload directions. Furthermore, based on the experimental data, an empirical equation is proposed to predict the current-induced equilibrium scour depth at cyclically vibrating monopile foundations in different directions.

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.

Numerical Simulations of Scour around Vertical Wall Abutments with Varying Aspect Ratios under Combined Waves and Current Flows

The present study employs numerical simulations to investigate vertical wall abutment scour with different aspect ratios (B/L, where B is the abutment length in the flow direction, and L is the abutment length transverse to the flow direction) under the combined effect of waves and current. The numerical model solves the Reynolds-averaged Navier–Stokes (RANS) equations and incorporates the Exner formulation to account for bed-level changes. The utilization of the Level Set Method (LSM) in the present numerical model enhances the accurate tracking of free surface and sediment bed. The numerical model validation was performed using a truncated numerical wave tank. The validated model was utilized to examine scour around vertical wall abutments with varying aspect ratios under different wave-current flows. The highest and lowest abutment scour depths were observed for aspect ratios of 0.5 and 2, respectively, in both steady current and the combined effects of waves and current. The vertical wall abutment of aspect ratio 0.5 had a maximum normalized equilibrium scour depth (S/B, where S is equilibrium scour depth), primarily attributed to a sharp edge, leading to increased turbulence and forming a strong primary vortex. The results suggest that the increase in the aspect ratio of the vertical wall abutment decreases the normalized equilibrium scour depth (S/B). According to the authors’ knowledge, this study is the first of its kind that utilizes a three-dimensional, semi-coupled model to examine combined wave- and current-flow-induced scour at vertical wall abutments with varying aspect ratios.

Numerical investigation of local scour around twin piles under steady current using CFD-DEM coupling method

In recent years, the local scour has developed into a major threat to the safety of offshore group piles. The numerical simulation methods are useful tools in investigating the key mechanisms behind local scour. However, conventional simulation methods often neglect the microscopic sediment behavior, thus impeding a more profound understanding of the scour mechanism. In this research, the CFD-DEM method was applied to investigate the local scour around twin piles. And the coarse grain method and porous media model were incorporated to enhance simulation efficiency. The CFD-DEM model was constructed and validated using experimental data. Based on the validated model, a series of local scour simulations around twin piles were conducted under different arrangements. The time-development curves of scour depth were analyzed, and the variation of the equilibrium scour depth with pile spacing exhibits good agreement with the dates from previous studies. Based on the simulation results, the flow field, scour pit morphology, sediment flux, and microscopic behavior of sediment around twin piles were analyzed under different arrangements, and four key mechanisms of twin piles' local scour were observed and analyzed during this process.

Numerical Simulation of Local Scour Around a Square Artificial Reef

Abstract Artificial reefs (ARs) are one of the key anthropogenic constructs used to restore offshore fishery resources and recover the ecological environment. However, many ARs lose their stability and function due to scour. To ensure the functional effect of ARs, it is of great significance to study the factors causing AR instability, such as burying caused by scour under different flow conditions. In present study, a three-dimensional numerical model is established in FLOW-3D to study the local scour characteristics around an AR in steady currents. Reynolds-averaged Navier–Stokes (RANS) equations, closed with the renormalization group (RNG) k–ɛ turbulence model, are established to simulate a stable flow field around one AR. The simulation results are compared with previous experimental results, exhibiting good agreement. The effects of the opening number and the incident angles of ARs on the scour characteristics, equilibrium scour depth, and maximum scour volume were also investigated. The results indicate that the scour depth and scour volume decreased as the opening number increased. Furthermore, empirical equations are proposed herein based on the numerical results derived for the effects of the AR opening number on the equilibrium scour depth and maximum scour volume. A change in the incident angle affected the bed shear stress at the most-upstream corner of the AR. The greater the bed shear stress was, the more intense the scour was. In this study, we provide theoretical support and practical guidance for the optimized engineering design and construction of ARs.

FAILURE OF SEAWALLS DUE TO TSUNAMI-INDUCED SCOUR

The Indian Ocean tsunami in 2004 and the Tohoku tsunami in 2011 have shown that tsunami-induced scour is one of the primary reasons for the failure of coastal defence structures (Bricker et al., 2012; Jayaratne et al., 2016). In a coastal structure, scour can occur when the plunging jet impacts the landward toe of the structure, resulting in digging a hole around the foundation which eventually may destabilize the structure. This can be exacerbated by rapid drawdown induced liquefaction during the receding wave, and can lead to the failure of the structure. Therefore, accurate prediction of local and plunging scour is very vital in order to ensure the safety of the coastal structures under such conditions. Data we have at present are based on final or equilibrium scour depths, not the maximum scour depths. Survey teams measure scour profile once the extreme event is over. However, the trough or scour hole made can be partly filled by sediment transport from upstream (in the live bed case) or from sediment suspended within the scour hole that settles after the flow slows down. Thus, the scour depth survey teams measure are less than the actual maximum depths. Therefore, a novel experimental and numerical study is proposed to tackle this problem with the funding of the Royal Society, UK.

Estimation and interpretation of equilibrium scour depth around circular bridge piers by using optimized XGBoost and SHAP

Most bridge failures result from scouring around bridge piers, resulting in economic losses and risks to public safety. The conventional equations for predicting the depth of scour at bridge piers have several limitations: (1) They mainly use regression-based techniques that cannot robustly capture the nonlinear relationship between the scour depth and its effective variables; (2) they are applicable only to a narrow range of variability of data; and (3) they are typically calibrated using laboratory data rather than field measurements and thus cannot simulate the prototype environment. To overcome these limitations, in this study, three novel hybrid machine learning methods: particle swarm optimization - extreme gradient boosting (PSO – XGBoost), red fox optimization - XGBoost (RFO – XGBoost), and relativistic particle swarm optimization - XGBoost (RPSO – XGBoost) are applied to estimate the scour depth around circular bridge piers, and their effectiveness is validated using three statistical metrics, i.e. the mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R2). RPSO – XGBoost generates the best results for both dimensional and dimensionless data. Moreover, the proposed approaches outperform the state-of-the-art techniques. The SHapley Additive exPlanations (SHAP) method is used to assess the relative significance of the contributing factors for predicting the scour depth.

Identify most promising temporal scour depth formula for circular piers proposed over last six decades

Temporal scour depth (dst) measurement at bridge piers is a significant issue for application engineers because accurate prediction is required for real-time monitoring. Although several formulas were employed, definitive study is still needed to determine which formula predicts most accurately. Therefore, here, a comparative analysis of dst prediction formulas, at circular piers in clearwater conditions, is performed using laboratory datasets for evolution over 57-years based on seven parameters: sediment coarseness, flow shallowness, constriction ratio, threshold-Froude number, sediment uniformity, relative density, time. Goal is also to select best option that will provide more useful compromise solution concept rather than examining ideal solutions based on inconsistencies. Therefore, useful statistical influence factors are used to perform 11 literature formulas with a newly derived formula in relation to their fitting coefficients. Weightage of each influencing factor is calculated using equal weightage and CRITIC methods. Ranking of each formula is determined using compromise programming. Overall study reveals that NCHRP (2011) formula is still most useful to determine dst if equilibrium scour depth (dse) and equilibrium time (te) are known. Melville and Chiew's (1999) formula is very close to NCHRP (2011). But without presuming dse and te, the newly proposed formula most accurately predicts the dst.

Experimental and numerical modelling of scour at vertical wall abutment under combined wave-current flow in low KC regime

The present study investigates the scour at vertical-wall abutments under a strong current-dominated combined wave-current and current-only environment using experiments and computational fluid dynamics (CFD) modeling. The CFD modelling is performed using an open-source three-phase numerical model (REEF3D), which solves Reynolds-Averaged Navier Stokes (RANS) equations with k-ω turbulence closure. The CFD model is first validated using the experiments and then used for further investigation. The Exner equation was used to compute alterations in bed elevation, while the Level-Set method recorded the free surface and bed topography in a realistic manner. The experimental findings demonstrate that the initial phase of scour development is more rapid under combined wave-current flow, but the equilibrium scour depth is higher in current-only conditions. The increase in Keulegan Carpenter (KC) number increases the scour depth at vertical-wall abutments for a specific relative flow velocity (Ucw). In contrast, a mild increase in vertical-wall abutment scour depth is observed with an increase in Ucw. To the best of the authors’ knowledge, the present work is the first of a kind of experimental and three-dimensional CFD study that estimates abutment scour under strong current-dominated combined wave-current flow.

Large-scale experimental study on scour around offshore monopile under combined wave and current condition

This work conducts large scale (1:13) experiments to study local scour around a monopile under combined irregular wave and current condition. The Keulegan–Carpenter (KC) numbers range from 1.1 to 6.73, and the relative current strength parameter Ucw numbers range from 0.17 to 0.77. The large-scale experiment indicates the 3D shape of scour holes is always an inverted cone under wave-current condition which has nothing to do with wave irregularity and Ucw. The changes of maximum scour location are associated with KC and Ucw numbers. The location of maximum scour depth is shifted from upstream to downstream of the monopile with large KC number under current-dominated condition. The characteristic scour timescale is closely related to KC, Ucw and Shields parameter θw when Ucw<0.3 and may be only related to θw when Ucw>0.7. The equilibrium scour depth is a function of vortex scale parameter referring to KC and Ucw numbers. A change in the definition of KC can improve the accuracy of existing formula under large-scale experimental condition, and scour volume formulae are further proposed from the relation with maximum scour depth. Finally, a scour volume formula of KC and Ucw numbers is suggested to estimate the protection material amount around monopile.

Effects of sediment supply on scour at submerged grade control structures

Grade control structures (GCSs) are common river training structures constructed to prevent riverbed degradation. Existing scour predictors for GCSs are based on flume experiments with either no sediment supply or equilibrium sediment transport conditions, the quantitative impacts of sediment supply on the scour at submerged GCSs are still unclear. The present study reports a series of flume experiments to investigate the effects of sediment supply on scour at submerged GCSs. The experimental results show that, compared with the equilibrium sediment transport condition, a decrease of upstream sediment supply rate can reduce the upstream scour depth (down to zero), increase the downstream scour depth (maximumly by 2.3 times) and change the scour process at a submerged GCS. If the sediment supply rate is close to the sediment transport capacity of the flow, the downstream scour depth first increases rapidly and then oscillates obviously around an equilibrium value (i.e. quasi-live-bed scour). If the sediment supply rate is close to zero, the downstream scour depth oscillates initially, then increases monotonically with time towards an equilibrium value (i.e. quasi-clear-water scour). Based on the experimental data and theoretical analysis, the quantitative impacts of sediment supply rate on the equilibrium scour depth at submerged GCSs are evaluated; and calculation methods considering the sediment supply are proposed for estimating the equilibrium scour depth at submerged GCSs.

Scaling laws for two- and three-dimensional wall jet scour based on the phenomenological theory of turbulence

The scour induced by wall jets may cause serious bed erosion and thus damage to hydraulic structures. Previous studies are largely empirical, providing only correlations of experimental data. At present, it is not clear what difference exists in the physical mechanisms of two-dimensional (2D) and three-dimensional (3D) wall jet scour. This study first summarizes previous efforts for predicting wall jet scour depths. Then, a scaling analysis is presented for investigating scour depths by applying the phenomenological theory of turbulence. It is shown that for wall jet cases, the dimensionless equilibrium scour depth can generally be expressed as a power function of the densimetric Froude number and relative roughness height, with the power index depending on jet configurations. The predictions of scour depth using the resulting formulas agree well with published data. The present analysis provides new insights into the understanding of the underlying physical mechanisms of wall jet scour as well as the difference between 2D and 3D configurations.

Riverbed Morphologies Induced by Local Scour Processes at Single Spur Dike and Spur Dikes in Cascade

Spur dikes are elongated structures extending from banks into rivers that mitigate erosion by forcing the flow away from the bank. The research on grouped spur dikes is insufficient in comparison with those on isolated spur dikes. Most of the studies focus on the maximum scour depth, omitting the bed morphological changes induced by local scour processes. Moreover, as yet, there is no established procedure for predicting the scour depth around spur dikes. This study aims to provide insights into the temporal and spatial morphological patterns around a single spur dike and spur dikes in cascade (three, five, and seven, consecutively). Experiments (of up to 318 h) were performed on a rectangular straight channel with dimensions of 20 m (length) × 1.0 m (width) × 1.0 m (depth). Nearly uniform sand with median grain size of 1.7 mm and sediment gradation of 1.5 was used for the mobile bed. The spacing between the elements for the spur dikes in cascade was 3b, where b is the spur dike width. All runs were conducted under a clear-water regime and steady flow conditions. Some limitations of the formulas for the equilibrium scour depth at the first spur dike reported in the literature were emphasised, with underestimations up to 160% and overestimations up to 200% at the earlier scour stages. The temporal evolution of the scour depth at the first spur dike was satisfactorily predicted with a correlation coefficient of 0.91. The scour processes at the other spur dikes were delayed and started at a dimensionless time greater than approximately 103. However, the scour rates increased to a high degree, with the scour depths tending to match those at the first spur dike.

A Study on Local Scour of Large-Diameter Monopile under Combined Waves and Current

The complex-load environment of offshore monopile foundations makes the combination of waves and current, and the variation in water depth, important factors for local scour. A flume test model of flow–pile–soil coupling for large-diameter monopile foundations is established, which comprehensively considers the combined reciprocating action of wave/current and the influence of tide depth. The precision of the experiment is ensured by the extension method of series models. The results show that the local scour caused by tides and the wave–current combination is obviously different from the unidirectional wave–current combination. The equilibrium scour depth obtained by the test is found to have some deviation from the predicted scour-depth equation. The maximum scour depth decreased with the increase in water depth within the range of 3 to 6 times the pile diameter. The bed shear-stress equation was generally consistent with the scouring-depth rule measured by the model, which can be considered to evaluate the rationality of the test results.

Semi-theoretical prediction for equilibrium scour depth of a mono-pile supported tidal stream turbine

Local scour around the mono-pile foundation of a tidal stream turbine is an essential issue regarding its structural safety and stability. A semi-theoretical framework for equilibrium scour depth prediction of the mono-pile foundation is proposed with consideration of effects from the rotating rotor. The equivalent mean velocity is obtained by fitting to the accelerated flow beneath the turbine rotor and used to derive the scour depth prediction equation based on the phenomenological theory of turbulence. Both clear-water and live-bed conditions are considered. Results show that the acceleration effect from the turbine rotor turns more pronounced with increasing thrust coefficient and tip clearance. Such acceleration generally leads to an increased scour depth around the mono-pile foundation, reaching the maximum scour depth when the equivalent mean velocity is equal to the critical velocity of sediment entrainment. In addition, a reduction factor of 0.74 is obtained for the bi-directional flow condition. Overall, the proposed prediction framework agrees with the experimental data in the literature with acceptable accuracy, although it could be improved with more data available in the future.

Scour at River-Crossing Cylindrical Structures in Degrading Channels

Channel degradation can expose river-crossing cylindrical structures (e.g., pipelines, canals, and tunnels) that are completely buried in the riverbed, altering their surrounding flow patterns to cause scour that threatens their structural safety. This paper reports a case study of scour at a river-crossing canal in a degrading river. Based on the historical topography and hydrological data, the cause, development process, and performance of countermeasures for scour at the river-crossing canal were analyzed, and recommendations for scour protection are proposed. The findings from 53 experiments of the scour at a river-crossing cylindrical structure in a degrading channel are presented. The experimental results indicate that there are three scour development modes at a river-crossing cylindrical structure in a degrading channel: (1) the exposure of the buried cylindrical structures induces downstream scour, with no tunnel erosion (i.e., scour below the bottom of the cylindrical structure) occurring at the cylindrical structure, (2) the riverbed degradation downstream of the cylindrical structure increases the water head over the cylindrical structure and seepage below the cylindrical structure, inducing tunnel erosion at the cylindrical structure, and (3) tunnel erosion is induced when a large-scale bedform trough approaches the cylindrical structure. Based on the experimental data, the critical conditions of each scour development mode were determined. The effects of the flow intensity, dimensionless water depth, and bed material roughness on the equilibrium scour depth were analyzed, and predictors for estimating the equilibrium scour depth at a river-crossing cylindrical structure in a degrading channel are proposed.