Live-bed Conditions Research Articles

Critical revision of check dams hydraulic design criteria

This paper addresses the problem of sizing the spillway of a closed check dam. Check dams are structures designed to control the solid transport and morphology of mountain streams. Paradoxically, however, their spillways are typically sized in clear-water conditions. The paper first analyses the behaviour of a check dam under clear water and then under live-bed conditions which is by far the most frequent operating condition. The theoretical approach is based on the conservation equations of solid mass, total mass, momentum and energy of the flow. The results of the theory are then compared with the results of some experiments in a laboratory channel equipped with a closed circuit for solid and liquid flow rates. The comparison between experiments and theory shows the validity of the approach. As expected, in some conditions that are far from rare, the design made in the clear-water condition is not safe.

Numerical investigation of the scour around a diamond- and square-shaped pile in a narrow channel

In this paper, a numerical investigation is conducted to study the scour dynamics around vertical square- and diamond-shaped piles in clear-water and live-bed conditions. The focus is particularly on cases involving narrow channels, aiming to examine the differences compared to more extensively studied scenarios, such as wide channels with circular piles. This work employs a Large Eddy Simulation (LES) model to simulate the turbulent flows around the structures. The hydrodynamic model is based on the Navier–Stokes equations in σ-coordinate, and the bed evolution is simulated by solving the Exner-Polya equation. The governing equations are solved using a second-order unstructured finite-volume method. The model is initially validated through a comparison with experimental data and numerical results found in the literature. Subsequently, it is applied to conduct a comprehensive study, enhancing our understanding of the various conditions influencing the scour process. The results indicate that the shape of the piles has different effects on the scour depth under clear-water and live-bed conditions. In live-bed conditions, the simulations reveal a deeper scour around the square-shaped pile compared to the diamond-shaped pile at the equilibrium stage. Conversely, an opposite behavior is observed in clear-water conditions, with a deeper scour around the diamond pile. Moreover, this behavior is consistent across both narrow and wide channels. It is discovered that, in clear-water conditions, the evolution of the scour in a narrow channel reaches equilibrium faster than in a wide channel, leading to a deeper equilibrium scour hole in the wide channel scenario.

Time development of live-bed scour around an offshore-wind monopile under large current–wave ratio

Scour around a circular monopile in coastal regions has been investigated extensively over the past decades, but the time development of scour depth around an offshore-wind monopile under large current–wave ratio still lacks a predictive model. By considering the conservation of sand volume and adopting the conventional exponential law for temporal variation, a semi-empirical model, which has three parameters, i.e., an equilibrium scour depth, a shape coefficient and a scour characteristic time scale, is developed for predicting the time development of scour depth around a monopile under live-bed conditions of combined wave–current flows. A series of laboratory experiments was conducted in current-only and wave–current flows to obtain data for model calibration and validation. Experimental results indicate that adding weak waves on current accelerates scour development, which is successfully captured by the proposed model through using the far-field bottom shear stress as a key model input. The overall model inaccuracy is within 25%, and the model’s applicability is further confirmed by field measurements from an offshore wind farm in east China. This model can help to determine the timing of installing scour protection around offshore monopiles, especially for the circumstances with very strong local sediment transport (live-bed).

Spatio-temporal analysis of scour around complex offshore foundations under clear water and live bed conditions

This study investigates scour around offshore wind foundations, focusing on two complex structures with varying degrees of flow blockage: a novel hybrid gravity-based jacket (structure “A") and a conventional four-legged jacket (structure “B"). As offshore structures like jackets become more prevalent, mainly due to their structural stability and growth of offshore wind energy in general, understanding scouring phenomena around complex structures is crucial. Laboratory tests under steady flow clear-water and live-bed conditions, with measurements of 3D laser scans for test durations of 15, 90, and 420 min were conducted. In addition the scour development over time was measured and analyzed with eight echo sounders. The findings confirm that scouring around complex structures displays significant variability in dependency of the structure type, making standardization a challenging task. However, some common trends can be derived. Under live-bed conditions, both types of structures exhibit global erosion, regardless of the complexity or flow obstruction of the structure. The spatial erosion depth, relative to the footprint, is markedly higher (2.5 times) for the gravity-based structure as opposed to the jacket structure. In clear-water conditions, no global scour was observed for both structures and a very similar spatial erosion depth was reached after 420 min.

Evaluation of collar efficiency to prevent scouring around cylindrical bridge piers under live bed condition

The present study was carried out to experimentally investigate the effect of single and double collar on development of local scouring around cylindrical bridge piers under live-bed condition. The single collar with diameter of 3 times the pier diameter placed on the streambed level and double collars one on the streambed level and one on a lower elevation were used. Tests were conducted with different flow intensities equal to 1.4, 2.0, 2.4, 2.8 and 4.0 where flow intensity is defined as the ratio of bed shear velocity to shear velocity of bed material at threshold of motion. One experiment was also carried out with flow intensity of 4.7 at which dunes were washed out and transition flow regime prevailed. The duration of the experiments was long enough to assure complete dune formations and multiple traverses of dunes through the pier location. Results showed that the scour depth fluctuated between a maximum and a minimum value due to the bed features migration. A graph was developed to show the efficiency of single and double collars at different positions and under different flow intensities. With two collars in place, the mean and maximum scour depths at the highest flow intensity, reduced by about 53% and 35% respectively. Efficiency of collar was better in lower flow intensities. Finally, based on the present results, a design table is presented for the elevation of the lower collar based on the flow intensity.

Numerical Study of the Flow and Blockage Ratio of Cylindrical Pier Local Scour

A three-dimensional large eddy simulation model is used to simulate the turbulent flow dynamics around a circular pier in live-bed and clear-water scour conditions. The Navier–Stokes equations are transformed into a σ-coordinate system and solved using a second-order unstructured triangular finite-volume method. We simulate the bed evolution by solving the Exner-Polya equation assisted by a sand-slide model as a correction method. The bedload transport rate is based on the model of Engelund and Fredsœ. The model was validated for live-bed conditions in a wide channel and clear-water conditions in a narrow channel against the experimental data found in the literature. The in-house model NSMP3D can successfully produce both the live-bed and clear-water scouring throughout a stable long-term simulation. The flow model was used to study the effects of the blockage ratio in the flow near the pier in clear-water conditions, particularly the contraction effect at the zone where the scour hole starts to form. The scour depth in the clear water simulations is generally deeper than the live-bed simulations. In clear-water, the results show that the present model is able to qualitatively and quantitatively capture the hydrodynamic and morphodynamic processes near the bed. In comparison to the wide channel situation, the simulations indicate that the scour rate is faster in the narrow channel case.

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.

Experimental investigation of flow pattern over a fully developed bed at a 60° river confluence in large floods

River confluences have a complex flow and sedimentation pattern that have vital influences on the hydraulic and bed morphology of river reach and the surrounding area. Confluences can be observed in waterways with various situations such as live bed conditions. This condition is a hydro-morphological situation with a high densimetric Froude number, i.e., bed load transport is supplied from upstream. According to the literature review, most of the experimental studies investigate the flow pattern on the flatbed and not on the developed riverbed, or/and in the low densimetric Froude number, or/and without supplying the sediment from upstream. Therefore, in the present study for the quantification of the flow pattern under these conditions, each developed bed was fixed with the cement blanket method in the laboratory. Then, the 3D velocity was measured at specific points at the confluence. The current study was designed to understand the flow pattern corresponding to the river bed behavior in the case of large floods. It is expected that the morphological features downstream of the confluence have a different pattern than the ones in the condition described in other literature. Thus, this paper describes briefly what are the different bed features and investigates the corresponding flow pattern. The results of the flow pattern on the developed bed show that all zones at the river confluence can be observed except the point bar due to the approximate equality of the mean longitudinal velocity of the separation zone and the main channel upstream of the confluence. Moreover, results show that by increasing the bedload ratio (sediment discharge to water discharge of the main channel of upstream of the confluence) from 0 to 3 × 10−4, flow deflection to the outer bank of the channel decreased down to 45%, the stagnation equivalent area decreased down to 2.5 times, and bed shear stress decreased down to 40%. Hence, the momentum of lateral flow decreased with increasing bedload. Besides, the recovery zone occurred at a longer distance after the confluence compared to the case without bedload. Hence, the location of the maximum velocity zone, vortices, and secondary flows changed downstream of the confluence, by changing the bed load value.

Numerical simulation of early stages of scour around a submarine pipeline using a two-phase flow model

Current-induced scour around a submarine pipeline during onset and tunnel erosion are investigated in both clear-water and live-bed regimes using an Eulerian–Eulerian two-phase model for sediment transport. The Hybrid Fictitious Domain-Immersed Boundary (HFD-IB) method is adopted to simulate the pipeline structure. The model is validated against two published experimental data: (1) flow past a pipeline near a rigid bed and (2) scour around a pipeline over a sand-bed, showing favorable results for the flow and scour patterns around the pipe. The driving mechanisms of the onset and tunnel erosion are investigated by examining the detailed fluid–sediment interactions around the pipe in both regimes. The driving mechanisms for the onset and tunnel erosion are found similar in both regimes, except their time and magnitude scales. The onset is triggered by the piping mechanism induced by the upstream–downstream pressure gradient beneath the pipe. Meanwhile, the jet flow is the driving mechanism for the tunnel erosion. The simulated live-bed condition shows a higher upstream–downstream pressure gradient beneath the pipe, faster piping mechanism, more intense jet flow velocity and sediment flux compared to the clear-water condition. The model well capture these underlying mechanisms, suggesting its promising capability as a predictive tool for scouring.

Experimental study on time factor of scour around pile groups

Pile groups are widely used in hydraulic and ocean engineering. They may suffer serious threats from long time scour process during constructions and operations. Time factor is crucial to predict this long duration process. However, mostly previous studies on time factor are proposed for single pile and pipeline, limiting the application effectiveness in pile groups. Previous researches focus on scour under threshold velocity intensity and cannot be directly applied in live bed condition. To expand the velocity intensity, flume experiments are conducted with uniform quartz sand in clear water and live bed condition. With selected experimental data from literatures and data of present work, an improved time factor taking velocity intensity and equivalent width of pile groups into consideration is proposed and verified, proving that this new time factor can make a reliable prediction of scour process and equilibrium scour depth with short duration for both single pile and pile groups. Another time factor with three exponential functions is also proposed for interpolating, which produce good performance from literatures. All experimental data mentioned above shows that the former optimized method is a reasonable predictor of scour depth around pile groups and the later method is applicable to interpolating.

Estimating the equilibrium scour depth around two side-by-side piers with different spacing ratios in live-bed conditions

The aim of this research was to numerically investigate the flow behaviour and evolution of the local scour around a group of two side-by-side piers in live-bed conditions. A coupled hydro-morphodynamic model was developed in OpenFOAM®. The hydrodynamic part of the model solved the unsteady Reynolds Averaged Navier-Stokes equations. The morphodynamic part of the model entailed solving both bedload and suspended load sediment transport. The model validation was performed for the available experimental data in the literature. The modelling for the pier groups was carried out with three different spacing ratios of G/D = 1, 2, and 3, where G represents the distance between the piers and D is the pier diameter. The results presented detailed information regarding the flow field and scour hole progression adjacent to two side-by-side piers. The dimensionless equilibrium scour hole depths of 1.74, 1.38 and 1.29 were predicted for the pier groups with G/D = 1, 2, and 3, respectively. The results showed an inverse correlation between the spacing ratio and the scour hole depth adjacent to the piers. The results were generalised, and an equation was obtained for the prediction of the equilibrium scour hole depth as a function of the spacing ratio.

Experimental Study on Aspect Ratio and Velocity Intensity of Scour Around Submerged Pile Groups

Submerged pile groups are important components of complex piers in hydraulic engineering and are analogs for a range of subsea structures. These may sustain severe damages from local scour. The velocity intensity (U / Uc, the ratio of critical velocity to mean velocity) and aspect ratio (H / Dp, the ratio of pile height to pile diameter) are critical variables in this scour process. However, previous studies on scour around submerged pile groups were conducted in clear-water conditions (U / Uc < 1). In addition, many research studies are being conducted in shallow water flow conditions, which cannot eliminate the effect of the water depth on the scour process. Thus, these research studies cannot directly be applied to live-bed scour around submerged structures. To expand the velocity intensity and aspect ratio of scour around submerged pile groups, flume experiments were conducted with uniform quartz sand in both clear-water and live-bed conditions. Pile groups with different heights are adopted as experimental models. An improved time factor for both clear-water and live-bed scour around submerged structures is determined with the present experiments to extrapolate the scour depth of the present work to the equilibrium scour depth. This new time factor is then tested with experimental data from the literature. The tests demonstrate that this new time factor can reliably predict the scour process and equilibrium scour depth for submerged structures. Empirical relationships to demonstrate the effects of the studied variables including the equilibrium scour depth, scour area, and scour volume are presented. Different methods to predict the effects of the velocity intensity and aspect ratio on the scour depth are compared based on the present work. Furthermore, a correction coefficient is proposed to illustrate the effect of aspect ratio on scour depth. Then, equations of scour area and volume are derived according to the present experiments.

An Innovative Eco-friendly Method for Scour Protection around Monopile Foundation

Local scour around the monopile foundation will undermine the stability of the wind turbine. As an environmentally friendly technology, microbial induced carbonate precipitation (MICP) was used as an innovative method for scour protection around monopile in this paper. A series of scour tests were carried out in the large section flume. The development of the scour around monopile was captured, and the protective effects of MICP and riprap were analysed. Results show that MICP is an eco-friendly technology to resist the local scour around monopile. The maximum scour depth (Send/Dp) is reduced by 84% after 2-times treatments, and the scour hole does not appear after 4-times treatments. The quantitative relationships between protective strength ratio and maximum scour depth, CaCO3 content are preliminarily proposed, and the 2% CaCO3 content is sufficient to resist scour under the live-bed condition (0.3m/s) in this study. Spherical crystals play roles in increasing the cohesion between the sands and coating the particles. The formed inverted cone-shape cementation can resist the downflow, horseshoe vortex and lee-wake vortex. It is necessary to consider the balance of MICP protection times and edge scour.

Experimental investigation of 90° intake flow patterns with and without submerged vanes under sediment feeding conditions

In this study, two experiments were conducted in a 90° water intake to study 3D flow patterns and sediment distribution using submerged vanes under sediment feeding and live-bed conditions. One column three vanes were installed at a 20° angle maintaining for a water discharge ratio of qr ≈ 0.1. Three-dimensional mean and turbulent velocity components of flow in a 90° channel intake were measured using acoustic Doppler velocimetry (ADV). Flow characteristics of the intake structure area with no vanes were compared with these conditions. Results showed that three vanes with a single column reduced the amount of sediment by 20% during intake diversion. In the downstream corner of the intake, high velocities were measured where scouring occurred. The vanes affected the intensity of secondary flow, turbulence energy, flow separation, and moved sediment deposition downstream of the main channel.

Investigation of the flow behaviour and local scour around single square-shaped cylinders at different positions in live-bed

Scour around non-circular cylinders has seldom been studied before. This paper aims to numerically investigate the flow behaviour and evolution of local scour around two single square-shaped piers with 90° (square pier) and 45° (diamond pier) orientation angles to the flow under steady-current and live-bed conditions. For this purpose, a coupled approach between a hydrodynamic and a morphodynamic model is developed and validated against flow and scour experimental data sets. Hydrodynamic model simulations reveal the formation of strong horseshoe vortices (HSVs) upstream of the square pier compared to the diamond pier. The scour simulation results show a faster rate of increase in the scour depth around the square pier, which leads to a deeper equilibrium scour hole. The model gives values of normalized quasi-equilibrium scour depths of Seq/wp = 1.94 and 1.00 for the square and diamond piers, respectively, where Seq is the quasi-equilibrium scour depth, and wp is the pier's projected width under steady current flow and live-bed conditions. It is discovered that the impact of other factors, such as bed material gradation, Froude number, Shields Parameter, as well as flow depth, can be as important as the shape factor in the study of equilibrium scour depth in live-bed conditions.

Scour protections of collar around a monopile foundation in steady current

An experimental study on scour protection around a monopile foundation in steady current was carried out with the adoption of collar base and collar column. Through the analysis of scouring features, the effectiveness of the collar base and collar column on the local scour was quantified. The parameters of flow conditions (θs/θcr), diameter (Dp/D), and thickness (hs/D), together with the initial buried depth (xb/D) for the collar base and collar column were investigated. For the collar base, the increase in thickness would effectively prevent the local scour beneath the base and lead to a decrease in the critical value of Dp/D. The influence of the diameter Dp/D can be ascribed to the fact that the collar base can take over the seabed region that the horseshoe vortex governs and further reduce the sediment transport at the junction. As for the collar column, the existence of the initial buried depth xb/D would provide space for the local scour to develop. At a large value of initial buried depth, the diameter Dp/D is no longer the main physical parameter. The effectiveness of the collar base and collar column is independent of the flow intensity in live-bed conditions.

Prediction of submarine pipeline equilibrium scour depth based on machine learning applications considering the flow incident angle

Scouring below submarine pipelines, due to fluid, structure and soil material interaction, is a complex phenomenon involving numerous effective parameters. In this research, machine learning methods, such as the GA-BP (Genetic Algorithm based Back Propagation) neural network, RBF (Radial Basis Function) and SVM (Support Vector Machine) are presented and prediction models are built for forecasting pipeline equilibrium scour depth. The results of the prediction models are compared with observed data, which shows that the GA-BP model provides the best predictive performance for scour depth exhibiting highest correlation coefficient and lowest Root Mean Square Error as compared with RBF, SVM in live-bed conditions. Results of the sensitivity analysis indicate that Froude number (Fr) is the most effective parameter for predicting the scouring depth below the pipeline. With the increase of flow incident angle, its influence on the predicted scour depth results becomes more obvious.

Effect of a Submerged Vane-Field on the Flow Pattern of a Movable Bed Channel with a 90° Lateral Diversion

This laboratory study focused on the effect of a submerged vane-field on the flow pattern and bed morphology near and inside the entrance reach of a movable bed 90° lateral diversion. The system was modelled under live bed conditions for a water discharge ratio of ≈0.2. Two experiments were run until bed equilibrium was reached: with and without a vane-field installed close to the diversion entrance to control the transfer of sediments into the diversion channel. The equilibrium bed morphology and the associated 3D flow field were measured in great detail. The bed load diverted into the diversion was reduced by approximately one quarter due to the action of the vane-field. The vanes prevented the formation of the diversion vortex in the main channel, upstream of the diversion’s entrance, thus contributing to that decrease. They also created a main channel vortex that started at the most upstream vanes and further decreased the amount of bed load entering the diversion. The flow separation zone inside the diversion was larger with vanes, but conveyance was balanced through a slightly deeper scour trench therein. The flow structures described were confirmed through the measurements of the turbulent kinetic energy.

Estimating Pier Scour Depth: Comparison of Empirical Formulations with ANNs, GMDH, MARS, and Kriging

Scouring, occurring when the water flow erodes the bed materials around the bridge pier structure, is a serious safety assessment problem for which there are many equations and models in the literature to estimate the approximate scour depth. This research is aimed to study how surrogate models estimate the scour depth around circular piers and compare the results with those of the empirical formulations. To this end, the pier scour depth was estimated in non-cohesive soils based on a subcritical flow and live bed conditions using the artificial neural networks (ANN), group method of data handling (GMDH), multivariate adaptive regression splines (MARS) and Gaussian process models (Kriging). A database containing 246 lab data gathered from various studies was formed and the data were divided into three random parts: 1) training, 2) validation and 3) testing to build the surrogate models. The statistical error criteria such as the coefficient of determination (R2), root mean squared error (RMSE), mean absolute percentage error (MAPE) and absolute maximum percentage error (MPE) of the surrogate models were then found and compared with those of the popular empirical formulations. Results revealed that the surrogate models’ test data estimations were more accurate than those of the empirical equations; Kriging has had better estimations than other models. In addition, sensitivity analyses of all surrogate models showed that the pier width’s dimensionless expression (b/y) had a greater effect on estimating the normalized scour depth (Ds/y).

A novel CFD-DEM upscaling method for prediction of scour under live-bed conditions

Despite intensive research efforts, the accurate modelling and prediction of bridge pier scour is an outstanding challenge due to the complexities arising from the detailed interactions between granular and fluid mechanics in the riverbed. Pier scour predictions based on empirical formulas are used in conventional bridge design codes which fail to realistically account for these interactions, and thus fail to facilitate pier design optimization. A critical step towards optimal pier design is an improved physical understanding of detailed mechanisms of the scour process and the development of appropriate modelling techniques to resolve these mechanisms in engineering applications. In this study, a combination of computational fluid dynamics (CFD) and discrete element modelling (DEM) is used to improve physical understanding of the scour process, including detailed interactions between river hydrodynamics, transport of suspended particles, and granular mechanics of the riverbed. As CFD-DEM models of turbulent hydrodynamics coupled with densely packed granular assemblies are computationally expensive, it is currently not feasible to accurately model scour in macroscopic engineering applications. To address this problem, we propose a novel upscaling methodology based on highly-resolved microscale simulations that significantly reduces the computational overhead, facilitating macroscopic prediction of scour under live-bed conditions. Predictions of scour initiation, rate and extent from these microscale simulations have been validated against previously published experimental data. Results indicate that the microscale model is reasonably capable of predicting the scour initiation as well as the equilibrium scour depth. This upscaling model provides a viable methodology for the macroscopic prediction of scour in engineering applications with modest computational resources.