Numerical simulation of the effect of downstream material on scouring-sediment profile of combined spillway-gate

Scouring is a phenomenon that occurs due to the flow of a fluid, particularly water, at the contact boundaries with other objects in hydraulic structures. The cause of this phenomenon is the creation of a vacuum at the contact boundaries of two environments due to a change in fluid velocity (Yang et al. 2023; Abbaszadeh et al. 2024; Süme et al. 2024). The fluid at these boundaries is influenced by the roughness and shape of roughness elements and the flow path. In hydraulic structures, this phenomenon can significantly damage the stability and durability of the structure, as water can erode the soil at the base and around the foundations of hydraulic structures or wash away the walls and banks, carrying them downstream (Hassanzadeh et al. 2019). When the bed consists of fine-grained cohesive particles, using criteria based on non-cohesive sediments overestimates the dimensions of the local scour hole, leading to high costs. Among common flow-controlling structures are gates, which come in various shapes and functionalities and spillways which are structures designed to transfer excess water and floods from the upstream of a dam or reservoir to the downstream. Combining spillways and gate structures can address the major issues of sediment deposition behind spillways and the accumulation of sediment and waste behind gates (Abbaszadeh et al. 2023). Moreover, they reduce the scour depth downstream of the structure. In a combined spillway-gate structure, new hydraulic conditions prevail, different from those of each structure alone. Due to the jet flow passing over or under the structure, a scour hole may form, potentially compromising the structure's stability. Therefore, determining the characteristics of scour holes has gained attention among hydraulic flow researchers. The importance of studying the scour phenomenon becomes evident when the scour depth is significant enough to reach the foundations of riverine structures, threatening their stability or causing destruction.

One of the earliest and most comprehensive laboratory studies on scouring at spillways and gates was conducted by Chabert & Engeldinger (1956). Their results indicated that the maximum scour occurs between a mobile bed and clear water. Breusers et al. (1977) conducted experiments on a single cylindrical base diameter and one type of sediment under various hydraulic conditions (flow depth and depth-averaged flow velocity) to achieve both clear water and mobile bed regimes. They introduced scour depth as a function of time, base diameter, depth-averaged velocity, and upstream depth. If the shear stress of the water flow through the channel exceeds the critical threshold for particle movement, numerous factors can then influence downstream scour, including sediment size and gradation, tailwater depth, particle Froude number, and structure geometry. Local scour is a phenomenon that occurs due to the interaction between water flow and soil in rivers, streams, and downstream of hydraulic structures (Breusers & Raudkivi 1991). This type of study is particularly crucial during floods when the simultaneous operation of dam gates and spillways is inevitable (Chang & Davis 1998).

Chiew (1992) found that the scour depth reaches equilibrium when the hole depth changes by 1 mm over 8 h. Abdou (1994) conducted extensive laboratory research to investigate the effect of bed materials on local scour depth under clear water conditions, concluding that the coarse fraction size of the material has the greatest impact on scour depth. The coarse fraction size of sediment plays a significant role in determining scour depth primarily due to an armoring effect, which occurs when larger particles accumulate on the surface, protecting the finer sediment layers beneath. This armoring layer increases the resistance to erosion, as the larger particles are heavier and require higher shear stresses to be displaced. Graf & Istiarto (2002) examined flow patterns around a gate upstream and downstream of a cylindrical base and vertically within the hole using an acoustic-Doppler velocity profiler (ADVP) device. They found that the shear stress inside the hole decreases compared with outside, but the turbulent kinetic energy upstream of the base is very strong, and this turbulent kinetic energy remains powerful in the downstream wake region.

Dey & Raikar (2007) studied the development of horseshoe vortices in the scour hole of a base. Their results showed that the maximum down flow occurs 2 cm upstream of the base at a depth of 0.09 m in the hole, with a velocity of 0.6 that of the flow velocity. As the Reynolds number increases, the development of the horseshoe vortex within the hole becomes more pronounced, and the upstream shear stress distribution becomes greater than or equal to the critical shear stress. Dehghani et al. (2010) conducted laboratory investigations of the scour hole downstream of a combined structure, examining various conditions such as weirs, gates, and their combinations. Saneie et al. (2014) simulated the concurrent flow from a trapezoidal combined weir-gate model at the end of an open channel with a circular cross-section using the FLOW-3D software. Their results showed that the software accurately estimates the water surface profile in the absence of surface tension effects. The application of a clay and montmorillonite nanoclay mixture has a significant impact on controlling scouring. It can be highly beneficial in cases such as rivers where bed protection using concrete is not feasible (Daneshfaraz et al. 2023).

Recently, various AI solution methods have been deployed to address these hydraulic issues. Li & Yang (2022) considered suspended sediment load (SSL) to be crucial for dams. Due to the complexity and stochastic nature of sedimentation, they highlighted that predicting SSL presents various challenges, with conventional methods offering limited accuracy in result analysis. Therefore, they developed a machine learning (ML) model by integrating seasonal adjustment (SA) and Bayesian optimization (BOP) to predict sediment load. Kumar et al. (2023) modeled scour depth using particle swarm optimization (PSO), M5 Tree, and hybrid artificial neural network (ANN) techniques. Their results indicated that the proposed M5 Tree model predicted scour depth more accurately than empirical approaches. Guguloth & Pandey (2023) analyzed extensive data on static and dynamic scour depths under short and long impinging jets. They evaluated previously proposed static and dynamic scour depth equations using graphical and statistical tools. Their findings showed that the equations proposed by Amin et al. (2021) better predicted scour depth for short impinging jets compared with other equations. Eini et al. (2023) estimated and interpreted the equilibrium scour depth around circular bridge piers using eXtreme Gradient Boosting (XGBoost) optimization and SHapley Additive exPlanations (SHAP) analysis. They highlighted the limitations of regression models in predicting scour depth. Their results demonstrated that the relativistic particle swarm optimization (RPSO)-XGBoost method provides favorable outcomes for both dimensional and dimensionless data. Baranwal & Das (2024) examined the impact of flow parameters and roughness on clear-water and live-bed scour by integrating existing experimental and field datasets on various types of bridge pier scour. They also evaluated existing empirical equations suitable for calculating equilibrium scour depth around bridge piers.

Gates and weirs are extensively used for flow control, regulation, and bed stabilization in open channels. The jet flow passing over or under these structures can create downstream scour holes, potentially reducing the stability of the structures. A combined spillway-gate model can address some of the shortcomings of using weirs and gates separately by allowing floating materials (such as wood and ice) to pass over the structure and settleable materials (such as sediments) to pass underneath. In a combined spillway-gate structure, new hydraulic conditions prevail, differing from those of each structure when used independently. A review of previous research indicates that no studies have been conducted to quantify the scour and sediment deposition downstream of a combined spillway-gate structure. Therefore, the present study numerically examines the flow profile, scour, and sediment deposition downstream of a combined spillway-gate structure under various sediment gradations in both free and submerged flow conditions using the volume of fluid (VOF) method. This study aims to mitigate the problems and deficiencies associated with spillways and gates by leveraging the advantages of both structures in a combined use.

In the above equations, B_i represents the body force in the i direction, μ is the dynamic viscosity of the fluid, ρ is the density of water, x_i,j, and k are the spatial coordinates in the i, j, and k directions, respectively, and δ_ij is the Kronecker delta, which is 1 if i = j and 0 otherwise (Daneshfaraz et al. 2022).

Boundary conditions are defined on all exterior surfaces of the solution domain. A pressure boundary condition is used for the channel inlet, with the fluid elevation set to 0.7 m within the software. An outflow condition is defined at the channel outlet, allowing the flow characteristics reaching this boundary to exit the solution mesh unchanged with zero second derivatives in all transported variables. A wall boundary condition is applied to the channel walls and bottom, while symmetry conditions are set for the top boundary. Initially, the pressure distribution is applied hydrostatically. To reduce simulation time, a fluid region is defined behind the spillway-gate (Norouzi et al. 2023). For submerged flow conditions, a fluid region is also defined downstream of the structure. The initial flow depth under submerged flow conditions downstream is 0.1 m. In addition, a fluid region is defined for the sediment area to ensure that the sediments are within the fluid. In this study, simulations were conducted using the following turbulence models: k-ε, k-ω, large eddy simulation (LES), and re-normalization group (RNG). Based on the results from simulations and previous research, the RNG turbulence model was selected for simulating the models (Table 1; Figure 4).

Table 1

Comparison of turbulence model results at cross-section (y) for X = 1.8 m with a grain diameter of 0.0008 m

Model .	.	.	.
RNG	5.84	0.024	0.874
k-ε	8.25	0.048	0.741
k-ω	7.14	0.038	0.748
LES	28.48	0.118	0.428

Model .	.	.	.
RNG	5.84	0.024	0.874
k-ε	8.25	0.048	0.741
k-ω	7.14	0.038	0.748
LES	28.48	0.118	0.428

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In this study, turbulence models such as k-ε, k-ω, LES, and RNG were evaluated to select the most suitable model simulation. Figure 4 illustrates the variation in scour across different turbulence models. As observed, the erosion patterns in the RNG, k-ε, and k-ω turbulence models exhibit similar trends, although there are variations in sediment deposition. The scour and sedimentation patterns in the LES turbulence model show distinct results compared with the other turbulence models. This discrepancy is attributed to the LES model's application in simulations with significant water surface fluctuations and large vortices, which may not be well-suited for scour simulations. Based on the evaluation, the RNG turbulence model was selected for simulating the remaining models in the present study. The results presented in Table 1 demonstrate that the RNG turbulence model exhibits higher accuracy and lower error compared with k-ε, -ω, and LES turbulence models. Therefore, the reasons for choosing this model include its reliability in addressing various issues, high accuracy of results in Table 1, accurate solution of equations, high precision in detailing flow characteristics, and previous studies such as those by McCoy et al. (2008), Dodaro et al. (2016), Calomino et al. (2018), Tafarojnoruz & Lauria (2020), Zaffar et al. (2023), and Tabassum et al. (2024).

In performance evaluation metrics such as mean absolute percentage error (MAPE) and root mean square error (RMSE), values closer to zero indicate higher model accuracy. A lower MAPE signifies minimal percentage error in predictions, while a lower RMSE reflects reduced differences between observed and predicted values, highlighting better precision. For the Kling–Gupta efficiency (KGE) index, values closer to one indicate higher accuracy. The KGE index is a composite metric that considers correlation, bias, and variability to provide a comprehensive measure of model performance. Based on the KGE results, performance can be categorized as very good (0.7 < KGE < 1), good (0.6 < KGE < 0.7), satisfactory (0.5 < KGE ≤ 0.6), acceptable (0.4 < KGE ≤ 0.5), or unsatisfactory (KGE ≤ 0.4).

A comparison between submerged and free flow conditions reveals a reduction in scour at a given time in the submerged state compared with the free flow condition. In the free flow scenario, the flow passing over the spillway and under the sluice gates encounters a mobile bed area, which leads to scour and erosion, and this effect increases over time. In contrast, under submerged conditions, the flow passing over the spillway and through the sluice gates encounters a downstream submerged flow. This submerged flow acts as a barrier, reducing the velocity of the flow over the spillway and gates, which in turn decreases the velocity of the flow impacting the moving bed. The submerged flow downstream absorbs the flow from the structure, reducing the energy of the flow in the area before the moving bed. This reduction in scour is more pronounced in the initial seconds, and increases as the water exits the downstream area. However, even in the later seconds, the scour is still less than in the free flow condition. Therefore, the presence of fluid flow downstream plays a significant role in reducing scour.

The simulations were designed to compare scouring and sediment deposition characteristics under free flow and submerged flow conditions. To evaluate the significance of the differences between these two scenarios, we considered several specific criteria and metrics.

Scour depth: The maximum depth of the eroded bed was measured at different cross-sectional points (y = 0.1 m, y = 0.5 m, and y = 0.9 m) along the downstream channel. This provided a direct comparison of the erosion extent under varying flow conditions.

Scour length: The length of the scour hole downstream of the structure was also assessed. This metric helped quantify the extent of bed erosion influenced by different flow regimes.

The thickness of deposited sediment downstream of the scour hole was analyzed. This parameter was crucial for understanding how different particle sizes behave under free and submerged flows, particularly in terms of their transport and settling characteristics.

The kinetic energy and momentum of the flow were examined to assess their impact on sediment transport. In free flow conditions, the absence of a downstream water cushion increases the energy impacting the bed, leading to more pronounced scouring. Conversely, in submerged conditions, the reduced flow velocity and energy due to the existing downstream water body mitigated the scouring effect.

The insights gained from this study could inform several design improvements and operational guidelines for hydraulic structures, specifically:

Optimized material selection: By understanding the effect of particle size on scouring, engineers can select or modify downstream materials to control sediment deposition. For instance, using a mix of larger particles in areas prone to high scouring could help reduce erosion and enhance stability.

Structural adjustments: The study's findings on particle size effects suggest that incorporating adjustable features, such as variable gate openings, can help manage flow velocities and reduce downstream scouring, particularly in free flow conditions where fine particles accumulate.

Flow regulation strategies: In submerged conditions, where sediment thickness is less variable, controlling downstream flow rates could further stabilize sediment deposition patterns. These findings could guide operational protocols to adjust flow rates during varying flow conditions, reducing maintenance needs, and extending the structure's lifespan.

Enhanced design for sediment management: Finally, insights into the scouring patterns from different sediment sizes provide a basis for designing enhanced sediment management systems, such as integrating sediment traps or scour protection mats in areas with finer particles to reduce erosion impacts.

To enhance the practical application of the findings from this study, we can delve into several critical areas that would bolster the utilization of these results in real-world scenarios. This discussion aims to highlight how the insights gained from the analysis can be transformed into actionable strategies for engineers, policymakers, and environmental managers involved in the design and maintenance of hydraulic structures. Here are several key points to consider:

The study's findings on the impact of sediment size and flow conditions on scour depth provide a scientific basis for developing comprehensive design guidelines. Engineers can utilize the results to select appropriate sediment sizes and configurations for various hydraulic structures, such as bridges and spillways. By incorporating specific recommendations based on sediment diameter and flow conditions, practitioners can optimize the design of structures to minimize scour and its associated risks.

The research highlights the dynamic nature of sediment behavior under varying flow conditions. This knowledge can inform adaptive management strategies that are responsive to changes in environmental conditions, such as increased rainfall or altered river flow patterns due to climate change. By understanding how different sediment sizes behave in submerged versus free flow conditions, stakeholders can develop flexible management practices that can be adjusted as conditions evolve, thereby ensuring the long-term stability of hydraulic infrastructures.

The study emphasizes the importance of understanding scour dynamics over time. To further strengthen the practical applications, implementing real-time monitoring systems that track scour depths and sediment movements can provide valuable data. By utilizing sensors and automated data collection methods, practitioners can continuously assess the effectiveness of scour mitigation strategies and make data-driven decisions. This real-time feedback loop can enhance the accuracy of predictions and the effectiveness of interventions.

The findings can serve as a foundation for improving existing predictive models of scour and sediment transport. By integrating the study's results into computational fluid dynamics (CFD) models, researchers and engineers can enhance the predictive accuracy regarding scour in different sediment and flow conditions. Improved models can better inform design decisions and optimize maintenance schedules for hydraulic structures, thereby reducing the likelihood of failure and costly repairs.

The insights derived from this study can inform public policy decisions related to infrastructure investment and maintenance priorities. Policymakers can utilize the findings to allocate resources effectively, focusing on regions or structures at higher risk of scour and erosion. By aligning funding and regulatory frameworks with scientific insights, governments can enhance the resilience of infrastructure and protect public safety.

Understanding sediment dynamics and scour patterns is crucial for balancing engineering needs with ecological considerations. By collaborating with environmental agencies, engineers can develop solutions that address both sediment management and habitat preservation. For instance, the study's results can guide the design of eco-friendly scour protection methods that enhance biodiversity while safeguarding hydraulic structures from erosion.

Finally, the findings can be integrated into educational programs for civil engineering and environmental science students. By using the study as a case example, educators can highlight the importance of sediment dynamics in hydraulic engineering and environmental management. This can cultivate a new generation of professionals who are equipped with the knowledge to tackle complex challenges related to scour and sediment management.

By focusing on design guidelines, adaptive management strategies, real-time monitoring, predictive modeling, public policy implications, environmental collaboration, and educational integration, we can ensure that the insights gained from this research translate into effective solutions for scour management. This holistic approach not only enhances the resilience of hydraulic infrastructures but also fosters sustainable practices that benefit both human and ecological systems.

Furthermore, based on the findings of this study, we recommend the following considerations and modifications for hydraulic structures focusing on spillway-gate systems.

To enhance the stability of spillway structures, we recommend designing a protective downstream bed layer using coarse materials. This layer can serve as an armoring surface, reducing the depth of scour and preventing undermining of the structure.

The study suggests that scouring is highly influenced by flow velocity and sediment size. For better control, we recommend implementing adjustable gates or sluice gates that can dynamically control flow rates, reducing the impact of high-velocity flows on the downstream area. This approach can help minimize erosive forces and manage sediment transport more effectively.

To further protect against scouring, incorporating energy dissipation structures such as stilling basins, stepped spillways, or baffle blocks can help reduce the energy of the flow before it impacts the downstream bed. These features can decrease the flow velocity, limit the extent of scour, and protect the structural foundations.

By applying these recommendations, engineers can enhance the resilience of spillway-gate structures, reduce maintenance needs, and increase their overall performance in handling sediment transport and scouring issues.

In this study, numerical simulations of scour and sediment deposition downstream of a spillway-gate structure were conducted. The study examined the impact of sediment parameters on the scour profile for different particle sizes (0.0008, 0.0014, and 0.001 m) under both free and submerged flow conditions. The results indicated that in larger mesh sizes, the lower quality of the shape and the increased flow passing underneath the sluice gate and over the spillway at a constant depth resulted in higher scour and, consequently, greater sediment deposition downstream of the scour area. The study evaluated turbulence models k-ε, k-ω, LES, and RNG, with the RNG model selected for further simulations. The results showed that the greatest sediment deposition was associated with the smallest particle diameter. This is attributed to the smaller curvature of particles with smaller diameters, which are more uniformly and tightly packed. In contrast, larger particles create voids between them, reducing friction and increasing the threshold for movement, leading to increased scour and decreased sediment thickness. In submerged flow conditions, the variations in scour across different sediment sizes were minor, and the results were similar. This is due to the immersion of particles in the fluid, which alters particle characteristics, including cohesion. Under submerged conditions, sediment deposition decreased with increasing particle diameter downstream of the scour area. The findings demonstrate a reduction in scour in submerged conditions compared with free flow conditions over the same period.

While this study provides valuable insights into the dynamics of scour and sediment behavior, several limitations must be acknowledged. First, the research primarily focuses on specific sediment sizes and flow conditions, future research should explore a broader spectrum of sediment characteristics and varying hydraulic conditions to enhance the robustness of the findings. Proposed improvements include integrating advanced computational models that account for additional variables, such as sediment composition and environmental influences. Future directions should prioritize the development of comprehensive predictive tools that incorporate the findings from this study, facilitating more effective scour management strategies and enhancing the design of hydraulic structures in diverse settings. Overall, a multidisciplinary approach that combines experimental, computational, and field studies will strengthen the applicability of the research outcomes in practical engineering contexts.

Based on the above explanations, the following aspects are recommended for further investigation.

Future studies should explore a broader range of sediment types, including cohesive sediments (like clay and silt) and mixed sediment beds. Investigating the influence of sediment cohesion on scouring patterns will provide a more comprehensive understanding of sediment dynamics in diverse hydraulic environments.

The current study focused on specific flow conditions (free and submerged flow). Further research should investigate the effects of unsteady flow conditions, such as varying discharge rates during flood events, which can significantly alter scouring and sediment deposition behavior.

Future research could explore the impact of different spillway and gate designs, such as stepped spillways, baffle blocks, or varying gate openings, on scouring patterns. Understanding how these structural features influence sediment transport can help optimize designs to minimize scouring and enhance sediment management.

By addressing these areas, future studies can build on our findings and contribute to a more detailed understanding of the complex dynamics involved in scouring and sediment deposition, ultimately leading to improved designs and mitigation strategies for hydraulic structures.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.