Approach Flow Depth Research Articles

Forecasting of time-dependent scour depth based on bagging and boosting machine learning approaches

ABSTRACT Forecasting the time-dependent scour depth (dst) is very important for the protection of bridge structures. Since scour is the result of a complicated interaction between structure, sediment, and flow velocity, empirical equations cannot guarantee an advanced accuracy, although they would preserve the merit of being straightforward and physically inspiring. In this article, we propose three ensemble machine learning methods to forecast the time-dependent scour depth at piers: extreme gradient boosting regressor (XGBR), random forest regressor (RFR), and extra trees regressor (ETR). These models predict the scour depth at a given time, dst, based on the following main variables: the median grain size, d50, the sediment gradation, σg, the approach flow velocity, U, the approach flow depth y, the pier diameter Dp, and the time t. A total of 555 data points from different studies have been taken for this research work. The results indicate that all the proposed models precisely estimate the time-dependent scour depth. However, the XGBR method performs better than the other methods with R = 0.97, NSE = 0.93, AI = 0.98, and CRMSE = 0.09 at the testing stage. Sensitivity analysis exhibits that the time-dependent scour depth is highly influenced by the time scale.

The universal two-fifths law of pier scour

Understanding scour at bridge piers is crucial for safeguarding public safety, ensuring infrastructure resilience, and planning effective maintenance. Despite over six decades of extensive studies aiming to develop predictive formulas for the equilibrium scour depth at bridge piers, more than 20 000 highway bridges in the United States have been spotted “scour critical.” The traditional reliance on existing empirical formulas has posed a severe challenge for researchers, hindering to achieve a unified relation for the equilibrium scour depth from a fundamental scientific tenet. This perspective article presents a breakthrough—a universal law governing the equilibrium scour depth at a circular pier embedded in a sediment bed, specifically in clear-water scour condition. Derived from a phenomenological model, the universal law reveals that the equilibrium scour depth to pier diameter ratio obeys a consistent two-fifths scaling law with the introduction of a newly coined pier-scour number. This number accounts for all the key parameters involved in a local scour phenomenon, including the approach mean flow velocity, threshold shear velocity for sediment grain motion, approach flow depth, pier diameter, and sediment grain size. Importantly, the scaling law contains an additional term involving the drag coefficient raised to the power of 2/5, addressing the impact of the pier shape on the equilibrium scour depth. The derived universal law undergoes the validation through an extensive dataset of experimental measurements on circular pier scour.

Prediction of scour depth around bridge abutments using ensemble machine learning models

Abutments are the structures that support the ends of a bridge deck. Scouring of streambed is a significant problem and ultimately results in the failure of the bridge when the abutments are exposed to flowing water over the long term. Abutment scour is influenced by the type of abutment, shape, and size of the abutments. In the current study, machine learning (ML) models have been utilized for predicting the scour depth around abutments making use of experimental data. The scour depth was modeled around three types of abutments: a vertical wall, a semicircular wall, and a 45° wing wall. Five input parameters, namely, the length of the abutment (L), breadth of the abutment (B), sediment size (d50), approaching flow depth (h) and average approaching flow velocity (U), were used in this study. For predicting the abutment scour depth, ML models such as Adaptive Neuro-Fuzzy Inference System (ANFIS), Gradient Tree Boosting (GTB), Group Method of Data Handling (GMDH), and Multivariate Adaptive Regression Splines (MARS) were applied. Statistical metrics such as Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Relative RMSE (RRMSE), Normalized Nash–Sutcliffe Efficiency (NNSE), Kling-Gupta Efficiency (KGE), and Willmott Index (WI) have been employed to evaluate the performance of each model. It was found that the GTB model provided relatively accurate predictions of the scour depth around the semicircular and 45° wing wall abutments with good metrics. Similarly, the MARS model outperformed all other models in terms of predicting vertical wall abutment scour depth.

Pressure-Flow Scour under a Bridge Deck in Clear Water Conditions

The issues of scouring around a bridge have become prominent in recent research mainly due to recurrent extreme weather events. Thus, designing a bridge with the appropriate protection measures is essential to safeguard it against failure, which may take place due to scouring from high flows resulting from extreme weather events. Bridges may become partially or entirely submerged during extreme weather events such as large floods and are subject to pressure-flow scour, a condition where the flow is directed downward and under the bridge deck, creating an increase in flow velocity and a corresponding increase in bed scour. This study aims to explore the pressure-flow scour depth under a bridge deck without piers in the presence of two vertical wall abutments under clear water experiments. Sixty-six tests were conducted involving the approach flow depth, bed material size, contraction length, contraction width, and bridge opening for both pressure and free surface flow conditions. An empirical equation was deduced to determine the maximum scour depth, which could be applied as a preliminary design for bridges under pressure-flow conditions. The experimental data were used to determine the performance of the earlier models of pressure-flow scour. The results revealed that for pressure-flow conditions, the maximum scour depth increased by a factor between 2.15 and 9.81 times the maximum scour depth under free surface flow conditions. With same flow depth, when the relative bridge length was increased from 5 to 7.5 and 7.5 to 10, the maximum scour depth decreased by up to about 7.4% and 2.3%, respectively. When the relative bridge width was decreased from 5.5 to 5.2 and 5.2 to 4.4, the maximum scour depth increased by up to about 45.6% and 81.2%, respectively.

Developing meta-heuristic optimization based ensemble machine learning algorithms for hydraulic efficiency assessment of storm water grate inlets

ABSTRACT This research explored the performance comparison of machine learning algorithms, i.e. random forest (RF) and Adaboost, each coupled with the genetic algorithm (GA) and particle swarm optimization (PSO), in intercepted discharge calculations. Thus, six different storm water grate inlets were evaluated through laboratory experiments, and the acquired data was used to construct the integrated prediction framework. Consequently, the RF-based models outperformed the models constructed with Adaboost. Overall, the PSO-RF was found as the best strategy with Nash-Sutcliffe Efficiency index and determination coefficient values of 0.8896 and 0.8990, respectively. In addition, the game-theoretical SHAP analysis demonstrated that the approach flow depth is the most influential variable for hydraulic efficiency evaluations, followed by the grate inlet width and transversal slope of the road. This study further concluded that the lower the grate inlet width, the lower the intercepted discharge capacity, while the increase in transversal slope results in an increase in hydraulic efficiency.

Numerical simulation of hydraulic characteristics of an upstream wing submerged T-shaped groyne

Groynes can prevent erosion of banks. In this study, an upstream wing submerged T-shaped groyne (ST) was proposed. The hydraulic characteristics and the bed elevation of the proposed groyne were compared with those of a T-shaped groyne. Under the consideration of the flow field measurements of a 60° bend movable bed experiment, a digital terrain after the bed development was obtained, using laser scanning technology. The flow field numerical simulation was performed with this digital terrain as the boundary. The results demonstrated that in comparison with the T-shaped groyne, the depth-averaged velocity of ST near the groyne head decreased by 14%, the length of the back-flow zone behind the ST was shortened by about 36%, and the streamlines near the wing of the groyne were smoother. Additionally, the scour depth in the range of the groyne increased by about 0.2 times the approaching flow depth H.

Performance and Design of a Stepped Spillway Aerator

Stepped spillways are frequently limited to specific discharges under around 30 m2/s due to concerns about potential cavitation damages. A small air concentration can prevent such damages and the design of bottom aerators is well established for smooth chutes. The purpose of this study is to systematically investigate the performance of a deflector aerator at the beginning of stepped chutes. Six parameters (chute angle, step height, approach flow depth, approach flow Froude number, deflector angle and deflector height) are varied in a physical model. The spatial air concentration distribution downstream of the aerator, the cavity sub-pressure, water discharge and air discharges are measured. The results describe the commonly used air entrainment coefficient, the jet length, as well as the average and bottom air concentration development to design an aerator. The lowest bottom air concentration measured in all tests is higher than the air concentration recommended in literature to protect against cavitation damages. And, unlike smooth chutes, there appears to be no significant air detrainment downstream of the jet impact. One deflector aerator seems therefore sufficient to provide protection of a stepped spillway.

Mathematical simulation of air-water flow along Ski Jump Jet

AbstractIn the present study, using a quasi 3D analytical simulation, air concentration distribution in ski jump generated jet is calculated. A numerical simulation is also performed to verify the results of the analytical model in parallel with the available experimental and other analytical data. By solving continuity and momentum equations in the case of air-water flow for three different cases, it was confirmed that the air concentrations along the ski jet are uniquely linked to the relative black water core length. Results showed that the black water core length is also influenced by the approach flow depth, Froude number, geometrical parameters of ski jump and the chute bottom angle. Finally, an analytical equation is proposed to predict the air concentration distribution along the ski jump jet regarding different hydraulic and geometric parameters. By calculating the velocity profiles along the jet, it showed that increasing the air concentration reduces the jet velocity profile.

Experimental investigation of flow characteristics over asymmetric Joukowsky hydrofoil weirs for free and submerged flow

Weirs are one of the most common hydraulic structures used to regulate the upstream approach flow depth and measure the flow discharge. The hydrofoil weirs are a type of short-crested weirs that are designed based on the airfoil theory. These weirs have some merits compared to other types, such as a higher discharge coefficient, more stability, better submergence limiting condition, and lower fluctuations of the pressure and the free-surface profile. In the present study, experimental models of hydrofoil weirs with different relative eccentricities, cambers, angles of attack, and upstream slope angles are applied to investigate their hydraulic characteristics under free and submerged flow conditions. The longitudinal profiles of static pressure over different hydrofoil weirs are compared to circular-crested and ogee weirs. The results indicate that the maximum bed negative pressure belongs to the circular-crested weir, and the lowest bed pressure over the hydrofoil and ogee weirs are approximately the same. Applying a hydrofoil weir with an appropriate curvature and angle of attack instead of a circular-crested weir not only increases the structural weir height as well as the upstream water depth but also results in the lowest values of bed negative pressure, thereby reduces the potential of cavitation over the weir body, being safer hydraulic structures. The results also show that the discharge coefficient of hydrofoil weirs is greater than that of the broad- and short-crested weirs for the upstream approach flow depth relative to the weir crest to weir length h1/L > 0.12 and is greater than that of the ogee weirs for 0.35 < h1/L < 0.45. Furthermore, the derived relationships for the discharge coefficient, threshold submergence, and the discharge reduction factor due to submergence accurately predict the hydraulic characteristics of hydrofoil weirs compared to the available developed empirical relationships for these weirs and can be used efficiently for design purposes.

Effect of various flow, sediment and geometrical parameters on partially or fully submerged deck scour

The effect of various parameters of flow, sediment and geometric features of the bridge on the depth and shape of the scour hole occurred underneath a bridge deck model without a pier was investigated by a series of experiments conducted in a flume under partially and fully submerged flow and clear water conditions. The experiments were performed with factors such as approach flow depth, discharge, sediment size, degree of submergence, girder location and depth. A total of 112 experiments were conducted for both partially and fully submerged flow conditions. The experimental data showed that the partially submerged flow increased the maximum depth of scour hole and affected the shape of the scour hole more when compared to the fully submerged flow. It was also noted that parameters that directly affected flow structure in the bridge opening such as girder height might significantly increase the maximum depth of scour hole. Effect of the distance between a single girder and the bridge edge was also tested by using three different girder location and it was found that as the distance increased, the depth of the scour hole decreased and the location of the maximum scour depth moved with the girder to where the contraction in the flow area occurred.

Flow through side-combined structure in a channel bend under subcritical flow regime

ABSTRACT In this paper, the effects of the nondimensional parameters influencing the discharge coefficient of a side-combined structure located in a channel bend were studied using 288 experimental data. Experiments were conducted in a rectangular recirculating U-shaped channel (0.6 m width and 0.7 m height) for different discharges and depths of flow in the channel. The effects of approach Froude number Fr , the ratio of the gate height to gate opening d/a, the ratio of the approach flow depth to gate opening h 1/a, and angle of the bend curvature α on the discharge coefficient under subcritical flow conditions are investigated. It was found that the flow diversion by a side-combined structure leads to a reverse flow, two separation zones, and a stagnation zone in the main channel. The specific energy remains constant along with the side-combined structure. It was found that the discharge coefficient is a decreasing function of Fr and d/a. Moreover, the discharge coefficient increases by increasing h 1/a. By changing the location of the side-combined structure along the channel bend, the discharge coefficient reduces from upstream, reach to a minimum value at α= 90ᵒ, and increase further downstream. The discharge coefficient of a side-combined structure is maximums when it is located at section 115° of the bend. New equations for the discharge coefficient of a side-combined structure under subcritical flow conditions were obtained.

Length Parameter for Scaling Abutment Scour Depth

Flow constriction caused by bridge abutment increases bed shear stress and thus enhances local scour. For scaling the maximum scour depth at the abutment, either abutment length or flow depth has been empirically used in previous studies. By performing a step-by-step analysis, this study proposes a new length scale, which is able to represent combined effects of abutment length, approach flow depth and channel width. Physically, the new length scale describes the maximum possible dimension of the associated vortex system (or large-scale turbulence). Six series of data compiled from the published literature were used in the analysis. The results indicate that the new length scale helps improve the agreement of predictions with the experimental data.

Experimental assessment and prediction of temporal scour depth around a spur dike

Spur dikes are river training structures that have been extensively used worldwide for towards enhancing flood control and the stability of embankments and riverbanks. However, scour around spur dikes can be a major problem affecting their stability and hydraulic performance. The precise computation of temporal scour depth at spur dikes is very important for the design of economical and safe spur dikes. This study focuses on experimentally assessing the temporal variation of scour depth around a vertical wall spur dike and identifying the parameters, which mostly influence spur dike performance for a channel bed surface comprised of sand-gravel mixtures. In the current study, the authors did physical experiments in a flume based study to obtain new data, aimed at deriving a new predictive model for spur dike scour and comparing its performance to others found in the literature. It was found that the dimensionless temporal scour depth variation increases with an increase in (i) the threshold velocity ratio, (ii) the densimetric Froude number of the bed surface sediment mixture, (iii) the flow shallowness (defined as the ratio of the approach flow depth, y, to the spur dike’s transverse length, l), and (iv) the flow depth-particle size ratio. It is also concluded that the temporal scour depth variation in the sediment mixture is influenced by the non-uniformity of sediment and decreases with an increase in the non-uniformity of the sediment mixture. A new mathematical model is derived for the estimation of temporal scour depths in sand-gravel sediment mixtures. The proposed equation has been calibrated and validated with the experimental data, demonstrating a good predictive capacity for the estimation of temporal scour depth evolution.

Prediction of local scour around bridge piers: artificial-intelligence-based modeling versus conventional regression methods

This paper presents the use of two artificial intelligence modeling methods, namely genetic programming (GP) and adaptive neuro-fuzzy inference system (ANFIS), to predict pier scour depth based on clear water conditions of 320 data sets of laboratory and field data measurements. The scour depth was modeled as a function of five main dimensionless parameters: pier width, approaching flow depth, Froude number, standard deviation of grain size distribution, and channel open ratio. A functional relationship was established using the trained GP model, and its performance was verified by comparing the results with those obtained by the ANFIS model and seven conventional regression-based formulas. Numerical tests indicated that the GP model yielded much superior agreement than the ANFIS model or any other empirical equation. The advantage of the GP model was confirmed by applying the derived GP equation to predict the scour depth around the piers of Imbaba Bridge, Egypt.

Experimental investigation of the effect of skew angle on partially or fully submerged deck scour

This paper presents the results of an experimental study investigating the effect of skew angle on clear-water contraction scour under a bridge deck at partially and fully submerged flow conditions. Two bridge deck models without a pier, one of which was located perpendicular to the flow while the other one was located with skewness of 15°, were used in the study. Forty experiments were performed for each deck model, 24 of which were under partially submerged and 16 were under fully submerged flow conditions. Analysis of the experimental data showed that as the discharge and approach flow depth increased, the maximum scour hole depth under the skewed deck model increased up to 25%–66% for fully submerged flow and 17%–57% for partially submerged flow conditions. Furthermore, the effect of skew angle significantly enlarged the width of the scour hole as you move along the skewed deck.

Experimental study of the local scouring around sloped piers and its estimation using statistical tools

Local scouring around sloped bridge piers in steady currents was studied both experimentally and mathematically. The effects of different inclination angles, flow intensities, flow depths, and pier size on local scouring were investigated. The experimental results show that the scouring depth increases with an increase in the values of discharge and pier width. The scouring depth for the sloped piers is smaller than the vertical piers one and the maximum scouring depth continuously decreases as the pier inclination angle increases. Prediction of the scouring depth around bridge piers using analytical models can be utilized in the feasibility studies of different models, and evaluations of the parametric analytical. Therefore, it was tried to model the scouring depth as a function of Froude number, flow intensity, and relative roughness parameters using non-dimensional analysis. The regression analysis based models were introduced to determine the scouring depth at upstream side of the pier using experimental tests data. Step-wise linear regression showed that the value of relative scouring depth has considerably good correlation only with two non-dimensionless parameters of inclination angle and normalized approaching flow depth. In this regard, some linear and nonlinear regression tools were utilized to establish functional relationships between these variables. Statistical indices and residual analyses of the models revealed the suitability of the models. Comparison of the experimental and predicted value of relative scouring depth illustrates that the suggested models can reasonably predict this parameter.

Pressure flow and weir scour beneath a bridge deck

In this study, a series of experiments in a flume was conducted to investigate the maximum scour hole depth that occurred due to the vertical contraction of the flow underneath a bridge deck model without a pier. The bridge model was tested under pressurized and weir type of flows governed by clear water conditions. Various parameters of flow, sediment, and geometric features of the bridge, such as approach flow depth, discharge, sediment size, girder depth and degree of submergence were varied to investigate their effects on the maximum depth of scour hole. A total of 102 experiments were conducted and two empirical equations were developed separately for pressure and weir flow types with the use of experimental data. Effects of the aforementioned parameters on the scour hole were also analyzed and discussed.

Live-Bed Scour at Wide and Long-Skewed Bridge Piers in Comparatively Shallow Water

An investigation of the characteristics of live-bed scour at circular and skewed rectangular (slab) piers in comparatively shallow flows is presented. The 110 experiments were undertaken in a 2.4-m flume using two circular piers and a slab (long) pier. Based on flow shallowness, that is, the ratio of approaching flow depth (y0) to pier diameter (D), the new data span the wide-pier (y0/D<0.2) and transition-pier (0.2≤y0/D<1.4) scour ranges. The Sheppard-Melville (S-M) method shows better performance than the other existing predictors and is more readily modified. Modification to the equation for the flow shallowness factor in the S-M method is proposed, based on both the data from the present study and those from literature. The results show the considerable influence of flow shallowness ratio on scour depth at piers in comparatively shallow water, and that, even for non–ripple-forming sediment, the scour depth at the live-bed peak may still exceed that at the clear-water threshold. The modified predictor provides better accuracy than the original Sheppard-Melville method for piers with y0/D<1, and no significant underestimation of the maximum scour depth is observed.

Effect of Debris on the Local Scour at Bridge Piers

Scour is one of the most recurrent causes of failure of bridge structures in alluvial rivers. There is a variety of formulas for the assessment of bridge scour characteristics and for the design of suitable protection. Nevertheless, current approaches neglect the effect of debris carried by natural streams during floods, even when the accumulation of debris can extremely amplify the action of scouring processes. Until now, very limited efforts have been conducted to systematically investigate these effects. The present study focuses on the effect of debris on the maximum clear-water scour depth at cylindrical piers inserted in uniform, fully-developed turbulent flows in wide rectangular channels with flatbed composed of uniform, non-ripple forming sand. For these purposes, an experimental campaign was carried out by performing 17 long-duration (td = 7 days) experiments. The experimental tests were performed in the hydraulic structures channel at the University of Beira Interior. The channel was 0.83 m wide, 12.0 m long and 1.0 m deep. In the central reach of the flume, a 3.0 m long and 0.30 m deep recess exists where scour is free to develop. The experiments were carried out with a cylindrical pier with 0.05 m diameter and two boxes, each with debris of different dimensions, either of triangular or rectangular shape. The tests were carried out with constant approach flow depth, d = 0.15 m, and average approach flow velocity, U, approximately equal to the average approach flow velocity for the threshold condition of sediment entrainment, Uc ~ 0.31 m/s. For this velocity, the scour depth can be expected to be maximal. The experiments will give a special focus to the development of scour hole as the accumulated debris increase. Moreover, the experimental results will be compared with a reference experimental run without debris, so that the increments on scour depth due to the single debris clusters of different characteristics will be obtained and discussed. The following conclusions were obtained: i) The shape and position of the debris accumulation have a strong influence on the final scour depth. Debris placed on the bottom, upstream of the bridge pier, with a triangular shape, does not induce any increase in scour depths, the values are practically the same as the one obtained for the reference pier (without debris); ii) The method suggested by [3], as modified by [6], performed well, replicating the main trends observed in the experiments; and the influence of the relative submerged ratio of the debris on the scour depth, followed the trend observed previously by [8], with an increasing scour depth up to a critical value of the ratio, and then decreasing scour for ratios higher than this critical value.

Hydrodynamic Flow Patterns Around Three Inline Eccentrically Arranged Circular Piers

An experiment was conducted under clear-water equilibrium scour state to measure flow formations and characteristics using a velocimeter, in local-scour holes around three identical circular-type piers arranged inline and eccentrically in staggered manner. Two inline piers were positioned towards flow, and eccentric one was placed in middle region of two inline piers. The flume experiment was done for an approach flow depth 0.125 m on uniform bed of sand particles having 0.825 mm median diameter. The hydrodynamic consequences of three-pier arrangement on scour were investigated here. The contour profiles and subsequent distributions of time-independent velocities, turbulence kinetic energy and intensities are well addressed for different vertical azimuthal planes \(0^{\circ }\), \(\pm 45^{\circ }\) and \(\pm 90^{\circ }\) around the piers. Velocity vectors derived from velocity profiles are also utilized to explain further flow attributes. Vorticity and all circulation values for horseshoe vortices, developed at upstream zone of each pier, are determined. The three-pier combination and their interferences caused by them play a key function in the enhancement of greater scour depth near the eccentric-middle pier and more shifting of sand towards the side wall. Flow formations and characteristics of such horseshoe vortices, responsible for above-noted phenomena, are explained here in detail. Vortices strengths for eccentric-middle and inline-rear piers are found greatest and lowest, respectively, compared with strength of inline-front pier.