Due to the frequent threat of floods to structures and engineering construction in rivers, in order to study the impact characteristics of river hydrodynamics on structures under excessive flow during floods, this study takes Jiefang Bridge as an example and uses the fluid volume two-phase flow model (VOF) in computational fluid dynamics (CFD), combined with advanced geometric reconstruction techniques such as iso Advector method, to simulate the dynamic changes of gas-liquid interface in the river. On the premise of guaranteeing the independence of the grid, the high precision structure grid is used for numerical simulation. The results indicate that when a flood contacts a bridge, the force on the bridge rapidly increases and fluctuates, reaching a significant peak of over 6,000,000 N. Bridge piers have a significant hindering effect on floods, and their impact gradually expands over time. Vorticity and turbulence energy analysis indicate the presence of strong flow disturbances around the bridge pier. In addition, the characteristics of the contact surface between water flow and bridges also significantly affect the stress and flow characteristics of bridges. Especially at a 45° angle of attack, the force on the bridge decreases, but the wake velocity increases.

  • The law of bridge stress and water erosion under the influence of flow field in flood process is clarified.

  • This paper presents the dynamic response model of bridge structure under flood condition and the optimization measures of reducing force.

Climate change often leads to extreme rainfall, greatly increasing the probability of excessive floods in rivers (Merz et al. 2021). Many important structures in rivers, especially aged or poorly designed bridges, embankments, and other buildings, exhibit vulnerability in the face of extreme floods, often leading to safety issues for life and property. Therefore, it is imperative to have a deeper understanding of their bridge dynamic response under flood conditions and the complex water flow patterns around them. Studying the interaction between river structures and flood flow, as well as the complex flow patterns around them, is of great significance for accurately assessing the stress on structures. The damage of floods to buildings mainly stems from their strong impact force. When a significant water level difference generates high water pressure, these forces are converted into strong water flow, which directly impacts the structure and causes damage or tilting deformation. Given the severity of flood-induced structural damage, scholars worldwide have devoted considerable research efforts to uncover the underlying scientific principles. By constructing mathematical models, conducting physical model experiments, and leveraging advanced numerical simulation techniques, they have continually explored the mechanisms of flood–structure interactions and the intricate flow field variations around structures. These studies have not only enhanced our understanding of flood damage mechanisms but also provided invaluable theoretical foundations and technical support for improving the flood resistance of structures.

Many scholars at home and abroad have conducted relevant research on the structural changes caused by excessive water flow in rivers (Kyriakopoulos et al. 2022; Abdulkathum et al. 2023). Ling et al. studied the evolution of dam-break floods and their impact on structural pressure. It was found that when the flood first contacts the structure, there is a significant instantaneous impact pressure, which may reach 1.5–3.0 times the maximum pressure after the initial impact. This instantaneous impact pressure is directly proportional to the initial water depth of the reservoir (Peng et al. 2021). In this study, three-dimensional numerical simulations were performed for three typical laboratory experiments, focusing on hydrodynamic effects. Two turbulence closure models based on Reynolds-averaged Navier–Stokes (RANS) kε and large eddy simulation were selected. The volume of fluid (VOF) method was employed to track the free surface. The numerical model provided satisfactory results for water depth and hydrodynamic load variations over time, which were in good agreement with experimental data. The study revealed that the time-varying behavior of impact forces is significantly influenced by the upstream initial depth, with the maximum impact force exhibiting a quadratic relationship with the initial depth (Peng et al. 2023). Postacchini et al. conducted experimental tests by replicating a 1:10 scale masonry compartment, and the effect of water flow impacting the structure was obtained by moving the structure through still water. Pressure sensors were used to record the fluid-induced pressures on the four walls of the structure. Their findings indicated that the overpressure acting on the structure depends on the different flow characteristics of the front, side, and rear walls (Anfuso et al. 2021; Brocchini et al. 2022). Muñoz et al. proposed a three-dimensional non-hydrostatic RANS model using the VOF method to simulate dam-break flows. They introduced a method for recalibrating two-dimensional models to improve consistency with three-dimensional model predictions. Simulation results also showed that strong three-dimensional effects occur in regions with high river curvature, near sudden contractions, and obstacles (Munoz & Constantinescu 2020). Hien's research demonstrated that the numerical values of impact forces on obstacles from dam-break flows are more realistic in three-dimensional solutions from VOF simulations compared to two-dimensional solutions from shallow water equations. This highlights the importance of considering three-dimensional effects in simulating flood flows (Hien & Van Chien 2021). Nan et al. developed a coupled method based on the VOF method and structural dynamics to gain insights into the structural dynamic responses of bridges. Their results showed that the water flow velocity near the bridge rapidly decreased from 6 to 1 m/s, leading to bridge damage and structural deformation (Nan et al. 2023).

In summary, significant progress has been made in the numerical study of flood–structure interaction through model experiments and commercial software, providing guidance for designing structures to resist floods. However, in practical engineering cases and full-scale flood scenarios, especially under the complex hydraulic characteristics around bridge piers, there are still shortcomings in the in-depth exploration of bridge dynamic response and flow field dynamics. Recognizing this limitation, the present study builds upon the foundations of previous research by innovatively employing the OpenFOAM platform integrated with the isoAdvector method for capturing two-phase flow interfaces (Díaz-Ojeda et al. 2019; Darwish & Moukalled 2021). This approach aims to achieve precise simulation of water surface variations during flow processes, a technological breakthrough that enables more accurate capture of the nuanced details of water–structure interactions during floods. Furthermore, to enhance computational accuracy and stability, this study utilizes the snappyHexMesh tool to generate high-precision structural meshes, ensuring high resolution and reliability in the numerical simulation process. This method not only optimizes computational efficiency but also significantly improves the fidelity of simulation results to actual physical phenomena. Focusing on river velocity variations and hydraulic evolution processes under flood conditions, this research conducts detailed numerical simulations and analyses. The ultimate goal is to provide scientific evidence and practical guidance for the design, reinforcement, and optimization of river structures (such as bridges) in flood prevention efforts.

This section delves into the specifics of the numerical methods employed in our flood research. The open-source, two-phase incompressible flow solver ‘interFoam’ is adopted to simulate the flow characteristics during flood events within river channels. All descriptions in this section are based on the interFoam solver and the modifications made to enhance interface capturing. The interFoam solver utilizes the finite volume discretization method to solve the governing equations of two-phase flow (Schmitt et al. 2020).

The finite volume method, implemented in interFoam, divides the computational domain into a series of control volumes, each representing a finite volume of fluid. Conservation laws, such as the mass and momentum conservation principles, are then applied to each control volume to derive the discrete equations. This approach ensures that the numerical solution accurately reflects the physical behavior of the fluid system, especially crucial in capturing the complex interactions between water and river structures during flood events. Moreover, to improve the accuracy of interface capturing between the water and air phases, specific modifications and enhancements have been integrated into the interFoam solver. These advancements, including the adoption of the isoAdvector method for tracking two-phase flow interfaces, enable a more precise simulation of subtle variations in the water surface and the intricate hydraulic characteristics around bridge piers and other river structures.

Governing equations in the interFoam solver

In the presence of gravity and source terms, the momentum and continuity equations in the interFoam solver can be formulated by analogy with the single-phase NS equations. The solver employs either the VOF method or the level-set method to track the interface between the two phases, while utilizing a pressure-based solver (such as the Pressure Implicit with Splitting of Operator (PISO) algorithm) to handle the momentum and continuity equations of the fluid (Cerne et al. 2001; Wu et al. 2014; Yu et al. 2020). The momentum equation for two-phase flow, as implemented in interFoam, can be expressed as follows in Equation (1).
(1)
where ρ is the fluid density, κ is a function of the phase fractions in the VOF or the level-set method, U is the fluid velocity vector, prgh is the pressure field, τ is the shear stress of the fluid, and h represents the position vector of the centroid of the grid cell.

In the interFoam solver, the spatial domain is discretized into a series of control volumes (i.e., grid cells), where the physical quantities (such as velocity, pressure, and volume fractions) are represented by their averaged values within each cell. By integrating the governing flow equations over these control volumes, a set of discrete algebraic equations is derived. These discrete equations are then solved iteratively using solution algorithms such as SIMPLE or PISO (Marsooli & Wu 2014). The SIMPLE and PISO algorithms are designed to handle the coupling between pressure and velocity fields in fluid dynamics problems. They iteratively update the pressure and velocity fields to satisfy the continuity equation and the momentum equations simultaneously. In the context of interFoam, these algorithms enable the solver to accurately capture the intricate fluid dynamics, including the interactions between the water and air phases, the effects of gravity, and any additional source terms. By discretizing the spatial domain into control volumes and applying the integral form of the flow equations, interFoam transforms the continuous fluid dynamics problem into a tractable set of discrete equations. The subsequent iterative solution process, facilitated by algorithms like SIMPLE or PISO, ensures that the numerical solution converges to a physically meaningful and accurate representation of the two-phase flow phenomenon.

The VOF method

The core concept of the VOF method lies in the introduction of a fluid volume function α, which represents the phase fraction of the fluid within a given computational cell. In a two-phase (gas–liquid) system within a specific grid cell, if the cell is entirely filled with fluid, then α = 1; conversely, if the cell is completely occupied by gas, then α = 0. When α takes a value between 0 and 1, it indicates that the cell contains a mixture of gas and liquid. The phase volume fraction can be mathematically expressed as shown in Equation (2).
(2)

This phase volume fraction α serves as a crucial indicator for tracking the interface between the two phases. In the VOF method, the continuity and momentum equations are solved over the entire domain, taking into account the effects of varying α values within each cell. This allows for the accurate simulation of the dynamic behavior of the fluid interface, including its deformation, breakup, and coalescence, which are essential features in two-phase flow phenomena.

Given the density and viscosity appearing in the continuity and momentum equations, these properties can be expressed as weighted averages based on the phase volume fraction α mentioned previously, resulting in Equation (3). The weighted averages account for the varying presence of the gas and liquid phases within each computational cell.

Specifically, for properties like density (ρ) and viscosity (μ) in a two-phase system, the effective values used in the governing equations are calculated as a function of the phase volume fraction alpha. If ρw and μw represent the density and viscosity of the fluid phase, respectively, and ρa and μa correspond to those of the gas phase, the effective density ρ and viscosity μ for a given cell can be expressed as weighted averages according to Equation (3).
(3)

ρw represents the density of the liquid phase, ρa represents the density of the gas phase, and μw and μa denote their respective viscosities. These weighted averages ensure that the governing equations accurately capture the influence of the varying phase distributions within the computational domain. By incorporating the phase volume fraction α into the calculations of density and viscosity, the VOF method enables the simulation of complex multiphase flow systems with realistic phase interactions and dynamic behaviors.

According to the principle of mass conservation, the increase in the amount of a particular phase within a grid cell is equal to the mass of that phase flowing into the cell. This concept, when applied to the phase volume fraction α, leads to the formulation of a phase equation, which can be expressed as Equation (4). In this context, the phase equation encapsulates the dynamics of the interface between the two phases, ensuring that the overall mass of each phase within the computational domain remains consistent.
(4)
is a manually added compressible term with a computational domain of 0 in the pure phase (non-interface). Uc is the speed that needs to be modeled. It should be compressed in the normal direction of the interface instead of tangential; otherwise, it will cause false diffusion. It can be specifically expressed as Equation (5).
(5)

Among them, c is the manually set compression factor. When c = 0, there is no compression effect. The larger the value of c, the more pronounced the compression effect.

isoAdvector method for geometric reconstruction

After discretizing the phase equation using the finite volume method, a numerically solvable equation is obtained, which is typically represented as Equation (6). This equation controls the temporal and spatial evolution of phase volume fractions αp (such as liquid or gas volume fractions) and is the cornerstone of simulating two-phase flow behavior.
(6)
In the equation, Vp is the grid volume, and ΔVf (tt) is the volume of phase 1 flowing on each surface of the grid. The expression for ΔVf(tt) is given by Equation (7)
(7)
However, simply discretizing the phase equation is not sufficient to accurately capture the dynamics of the interface between two phases, especially under complex interface geometries or severe flow conditions, as shown in Figure 1(a). In order to improve the accuracy of interface capture, the isoAdvector method was introduced as a geometric reconstruction technique, as shown in Figure 1(b).
Figure 1

Comparison of mesh processing between VOF and the isoadvisor interface.

Figure 1

Comparison of mesh processing between VOF and the isoadvisor interface.

Close modal

The traditional algebraic reconstruction method simplifies the processing of ΔVf(t,Δt) to αfϕΔt, where ϕ represents the grid surface flux. Subsequently, the volume fraction αf is estimated at the center of the grid surface using certain methods, which can be considered relatively rough. In contrast, the equal advection method adopts a more refined and precise processing flow. This improved method not only explains the complex fluid dynamics on the grid interface but also strives to capture the subtle differences in volume fraction evolution with higher accuracy.

  • 1. Assuming that uf remains unchanged from t to t + Δt, this is consistent with algebraic reconstruction.

  • 2. Processing αfSf as the area occupied by phase 1, represented by Af(tt), where Af is a function of time.

  • 3. Finding the expression for Af(tt) and integrating it over t to t+ Δt. Processing ΔVf(t,Δt) as Equation (8) in isoAdvector.
    (8)

isoAdvector has processed the integration of ΔVf(tt) in more detail, resulting in higher accuracy. The main steps of using isoAdvector to solve the VOF phase equation can be described as follows.

The main steps of the VOF phase equation can be expressed as follows.

  • 1. Initializing ΔVf(tt) = Ufαf,upwindSfΔt can meet the calculation requirements for grids that are completely within phase 1 or phase 2. However, it needs to be recalculated for grids at the junction of the two phases.

  • 2. By limiting the Coulomb number Co of the interface, the interface can move no more than one grid at a time (0.5 grids are more suitable), and only the flow on the surface of the grid on the interface needs to be calculated to update the next time step. This part is actually necessary and needs to be carefully combined with the isoobserver algorithm to understand that such limitations actually reduce the discussion of many additional situations (Marsooli & Wu 2014; Wu et al. 2014; Bagherzadeh Azar & Sari 2023).

  • 3. For the mesh on the interface surface (0 < α < 1), reconstructing the interface (more accurately, the isosurface) and calculating the ΔVf(tt) of the interface mesh.

  • 4. Updating αp (t + Δt).

  • 5. Correcting the cases where αp (t + Δt) < 0 and αp (t + Δt) > 1.

For the interface between the gas and liquid phases, the surface normal direction is further realized through a continuous surface tension model, as shown in Figure 2(a). At a given point, the normal vector is denoted as ∇α, which is a continuous function that equals zero within the regions of fluid 1 and fluid 2, and takes non-zero values exclusively at the free liquid surface, as illustrated in Figure 2(b).
(9)
wherein, the vector n, directed from the liquid toward the gas, can be expressed as Equation (9). Furthermore, surface tension is incorporated into the source term of the momentum equation for computation. The overall computational flow of the isoAdvector–VOF method is illustrated in Figure 3.
Figure 2

Normal vector variation of surface tension. (1) Change of the free liquid surface (2) volume fraction of the gas-liquid phase in the grid.

Figure 2

Normal vector variation of surface tension. (1) Change of the free liquid surface (2) volume fraction of the gas-liquid phase in the grid.

Close modal
Figure 3

Calculation process of the isoadvisor–VOF method.

Figure 3

Calculation process of the isoadvisor–VOF method.

Close modal
During flood events, as the water velocity and depth in the river channel rapidly increase, the flow field surrounding bridges undergoes significant changes. These changes directly intensify the impact force of the flood on the bridge, significantly elevating the risk of structural damage or even collapse of the bridge. Refer to Figure 4 for a depiction of changes in water surface velocity during river flood processes.
Figure 4

River flow velocity.

Figure 4

River flow velocity.

Close modal
To accurately assess the impact of floods on bridge safety, we conducted full-scale modeling and simulation analyses (Bagherzadeh Azar & Sari 2023), comprehensively covering the entire computational domain geometry as illustrated in Figure 5(a). This approach enables a deep understanding of the mechanical effects during flooding processes and their potential threats to bridge structures.
Figure 5

Calculation domain size and surrounding flow field mesh of the bridge. (a) Calculate the size of the domain, (b) Calculate mesh size of the domain.

Figure 5

Calculation domain size and surrounding flow field mesh of the bridge. (a) Calculate the size of the domain, (b) Calculate mesh size of the domain.

Close modal

In computational fluid dynamics (CFD) calculations, the quality of the mesh had a significant impact on the computational results. To address this, we employed snappyHexMesh to generate high-precision structured meshes. Within the framework of these high-precision meshes, we utilized a feature-boundary adaptation method to refine the meshes specifically at the boundaries. Initially, a structured mesh with a grid size of 3 m was created for the background grid. However, to capture more detailed flow characteristics, we refined the mesh to a grid size of 1.5 m, as illustrated in Figure 5(b). Local refinement was then applied at the interfaces between the bridge and the flow field to achieve even finer structured meshes in these critical areas. To further assess the impact of mesh density on computational accuracy, we conducted an additional refinement of the background grid from 1.5 to 1 m. Upon comparing the flow information at specific monitoring points within the flow field before and after this mesh densification, we found that the changes were minimal, with errors remaining within 2% for all monitored parameters. This result indicated that the 1.5-m background grid met the criteria for mesh independence, meaning that further increases in mesh density to 1 m would not significantly alter the computational results. Therefore, we concluded that the 1.5-m background grid was sufficient to ensure computational accuracy while maintaining efficient resource utilization.

The computational domain measures 240 m in length and 210 m in width. According to field measurements, the bridge width is approximately 210 m, ensuring that the dimensions of the numerical simulation's computational domain are consistent with the actual measurements. When the size of the computational domain is determined, selecting the fluid properties becomes vital. Based on previous research (Wu et al. 2014; Wang et al. 2020), we have selected the flow parameters for the gas–liquid two-phase system within the VOF model. The parameters for the gas–liquid two-phase system are detailed in Table 1. 

Table 1

Fluid parameters (Nan et al. 2024)

ParameterDensity (kg/m3)Viscosity (m2/s)
Air 1.48 × 10−5 
Water 998 1 × 10−6 
ParameterDensity (kg/m3)Viscosity (m2/s)
Air 1.48 × 10−5 
Water 998 1 × 10−6 

After establishing the fluid properties, it is necessary to set the water velocity at the boundaries of the computational domain model. According to field measurements, the maximum river flow velocity under normal conditions is 15 m/s, whereas, during floods, the internal river velocity surges. To allow for natural development and achieve an internal velocity of 15 m/s, we set the boundary velocity at 2 m/s. The relatively shallow water depth within the river channel can be simplified for the flood process, with the water depth gradually increasing over time as the flood progresses. This entire process – establishing the computational domain, setting fluid properties, and configuring boundary conditions – constitutes the CFD approach to solving river flow problems. Assuming the grid meets the necessary requirements, the simulation is carried out using the interFoam solver within the OpenFOAM code.

Through a comprehensive analysis of the flood flow process, we gain profound insights into the complex characteristics of water flow and its intricate interaction mechanisms with the bridge structure of the Liberation Bridge. This process not only reveals the dynamic evolution of hydrodynamics as the flood flows past the bridge at different time points but also provides a visual representation of how the flow state varies with time and the structural features of the bridge, as illustrated in Figure 6.
Figure 6

Variation of water surface velocity during the flood process.

Figure 6

Variation of water surface velocity during the flood process.

Close modal
By observing the changes in the liquid surface at different time points, we can clearly discern the significant impact of the bridge structure on the flow field. Around the bridge, due to the obstruction of the bridge piers, the water flow velocity decreases significantly, leading to an elevation of the water surface around the piers and the formation of localized water stagnation. As time progresses, the water depth within the river channel gradually increases, and the influence range of the bridge piers on the flood flow also exhibits an expanding trend. This phenomenon is intuitively reflected in the top-down view of the river flow velocity variation as it passes through the bridge, as shown in Figure 7. Furthermore, the streamline diagram in Figure 8 further validates the profound influence of the bridge structure on the flow characteristics during the flood process.
Figure 7

Changes in the flow velocity of flood after passing through bridge piers.

Figure 7

Changes in the flow velocity of flood after passing through bridge piers.

Close modal
Figure 8

Changes in streamlines of floods passing through bridges.

Figure 8

Changes in streamlines of floods passing through bridges.

Close modal

Figure 7 illustrates the significant and progressively widening impact of the bridge piers on the adjacent water flow over time. The underlying cause of this phenomenon is the ‘velocity retardation effect’ triggered by the presence of bridge piers, which causes the water flow to slow down as it passes by. In accordance with Bernoulli's principle, when the flow velocity decreases, the water pressure in the vicinity correspondingly increases, resulting in the water body spreading outward. The most evident consequence is the noticeable elevation of the water surface both upstream and downstream of the bridge piers, creating the so-called backwater effect. The streamline alterations shown in Figure 8 further support this observation, with the flow velocity significantly decreasing in proximity to the bridge piers and the streamline patterns exhibiting vortex-like distortions.

To gain a more intuitive grasp of this dynamic process, a thorough analysis is undertaken utilizing Figure 9, which depicts the fluctuations in river water surface elevation. This figure illustrates the water surface heights at the central cross-section of the river channel at various time points. It becomes apparent that, as time progresses, the water surface heights in the vicinity of the bridge piers gradually increase, with the affected zone expanding outwards. This variation not only confirms the accuracy of the velocity retardation effect and Bernoulli's principle but also visually underscores the substantial influence of the bridge piers on the river's flow field. Figure 10 shows the changes of the liquid level at different times in multiple dimensions from the front view and top view.
Figure 9

Changes in water surface height at different times in the river channel.

Figure 9

Changes in water surface height at different times in the river channel.

Close modal
Figure 10

Changes in water surface elevation near bridges during the flood process.

Figure 10

Changes in water surface elevation near bridges during the flood process.

Close modal
By observing the fluctuations in water surface heights in the vicinity of the bridge piers at various time points, we can distinctly discern that during the time frame spanning from 42 to 62 s, there is a significant increase in water levels across multiple cross-sections surrounding the bridge piers. The alterations in water surface elevations at these distinct cross-sections are depicted in Figure 11(a).
Figure 11

Changes in the elevation of the water surface position on different monitoring sections. (a) Sectional liquid level height at bridge pier (b) Sectional liquid level height between two piers.

Figure 11

Changes in the elevation of the water surface position on different monitoring sections. (a) Sectional liquid level height at bridge pier (b) Sectional liquid level height between two piers.

Close modal

The trends presented in the data in Figure 11(b) clearly demonstrate that the presence of bridge piers has a significant impact on the flow and water levels of the surrounding water bodies, creating a unique hydrological environment. Firstly, the water level at the location of the bridge piers gradually rises from a low of −20 m to stabilize at −15 m, marking a significant change of 5 m. This reflects the phenomenon of local backwater at the water level caused by the obstruction of the flow due to bridge piers. This backwater not only highlights the direct blocking effect of the bridge piers on the flow but also reveals the intricate flow patterns and vortex structures generated around the piers, which further influence the distribution of water levels.

At the intermediate interface between two bridge piers, the water level rise is even more pronounced, lifting from the same starting point of −20 to −16.9 m, which is 3.1 m higher than the water level directly influenced by the piers. This difference indicates that within the narrow channel formed by the two bridge piers, the flow velocity increases. According to Bernoulli's principle, the increase in velocity leads to a decrease in static water pressure, creating a stronger pressure difference between the banks and the space between the piers. This pushes the water body toward the center of the channel, further elevating the water level.

Further observation of the numerical value of velocity variations reveals that near the bridge piers in Figure 12, the flow velocity decreases significantly. This is due to the obstruction of the piers, causing a sharp change in flow direction and converting kinetic energy into rotational energy of vortices, which results in a slowdown in flow speed. In contrast, the flow velocity within the narrow channel between the two bridge piers increases significantly to compensate for the reduced flow rate due to the narrowing of the channel. This change not only intensifies the water level rise but also enhances the scouring effect of the flow on the bridge pier foundations and the riverbed bottom, putting greater demands on the stability of the bridge.
Figure 12

Changes in flow velocity within the river channel.

Figure 12

Changes in flow velocity within the river channel.

Close modal

Additionally, Figure 12 depicts the variation in flow velocity across a mid-section of the river channel. By comparing the flow velocity data at different locations and times, it becomes evident that the flow velocity significantly decreases both upstream and downstream of the bridge piers, while the areas farther away from the piers gradually restore to normal flow velocities. This notable difference in flow velocity further corroborates the retarding effect of the bridge piers on water flow speeds and the resulting phenomenon of water level elevation.

This phenomenon also indicates that when the water surface reaches the bridge piers, the flow encounters significant resistance, leading to a reduction in flow velocity. According to Newton's third law of motion, the attenuation of the flow is a result of the reaction force exerted by the bridge piers, suggesting that the greater the flow velocity attenuation, the stronger the force acting on the bridge. Here, we gain further insights into the force exerted by the water flow on the bridge, as illustrated in Figure 13.
Figure 13

Changes in water flow force at different times.

Figure 13

Changes in water flow force at different times.

Close modal
The curve depicting the force experienced by the bridge during the flow process reveals that at the initial moment, when the flood has not yet reached the bridge, the force is relatively small. As the flood arrives at the bridge piers, it exerts a force on the structure and continues to fluctuate for some time. After the water level stabilizes at an elevated position, the peak value of this flood force can exceed 6,000,000 N. This force poses a significant threat to bridges and other structures, potentially causing substantial impact damage to the structures. We can gain a deeper understanding of the interaction between water flow and structures during flooding by examining the turbulent flow characteristics around the bridge piers, as illustrated in Figures 14 and 15.
Figure 14

Changes in turbulent energy of floods at different times.

Figure 14

Changes in turbulent energy of floods at different times.

Close modal
Figure 15

Vorticity of floods at different times.

Figure 15

Vorticity of floods at different times.

Close modal
The dynamic variations in the vorticity contour and turbulent kinetic energy (TKE) contour clearly reveal the complex flow field characteristics after floodwater flows past the bridge piers. As the water flow encounters the obstruction of the bridge piers and bypasses them, both vorticity and TKE significantly intensify, visually demonstrating the reshaping effect of the bridge piers on the flow structure. Over time, these intensified vortices and turbulent energy not only increase in strength but also gradually diffuse to broader river domains, expanding their influence areas. Further observation of the vorticity and TKE variation curves along the river channel (as shown in Figure 16) reveals definitive trends in these physical quantities along the flow direction. The vorticity curve exhibits fluctuations as the water flow approaches the bridge piers, followed by a sharp increase after bypassing them and then a gradual decay while maintaining a relatively high level in areas farther away from the piers, indicating the persistent influence of the vortices. The TKE curve, on the other hand, more intuitively reflects the process of energy conversion and dissipation, with a sharp accumulation near the bridge piers and subsequent gradual dissipation over a longer river distance, yet its influence can still be detected further downstream.
Figure 16

Changes in vorticity and turbulence energy along the entire river channel.

Figure 16

Changes in vorticity and turbulence energy along the entire river channel.

Close modal

Through a detailed analysis of the vorticity and TKE variation curves at different time instances in Figure 16, we can clearly observe the growth trends of these two physical quantities within the entire river channel over time. Notably, at the bridge piers, both vorticity and TKE reach their peak values, highlighting the significant impact of the piers on the hydrodynamic characteristics of the flow. In summary, when floods surge, bridges and their surrounding areas exhibit pronounced dynamic responses. Specifically, as the water flow encounters obstructions near the bridge piers, its velocity sharply decreases, leading to a dramatic increase in the impact force borne by the piers. This extreme force poses a high risk of damage or destruction to the bridge structure. Throughout the flood flow process, as the flood impacts the bridge, the force experienced by the bridge undergoes intense fluctuations and ultimately reaches a peak state, where the bridge's stability is at its lowest and the risk of damage significantly increases. Notably, even after the peak state, the force on the bridge remains at a relatively high level, further exacerbating the potential for damage. Concurrently, as the water flow approaches and bypasses the bridge piers, not only does its velocity undergo significant changes, but it also triggers a sharp increase in vorticity and TKE. These vortices and turbulent energy, after reaching their maximum values at the piers, gradually diffuse into the surrounding water areas, affecting a broader region. The above research results all indicate that bridges significantly affect water flow and exacerbate turbulence.

On this basis, further discussion is conducted on how to reduce the interaction between bridges and water flow, thereby maintaining the stability of bridges during flood processes. To illustrate how to reduce the interaction between water flow and the bridge pier, especially in terms of the forces acting on the bridge pier and the influence on the flow velocity, we will set different contact angles between the water flow and the bridge pier, as shown in Figures 17 and 18.

In Figure 17 (a) and (b), it can be seen that the water flow is influenced by the structure when passing through the 45° contact surface and the planar contact surface, and there is a significant difference in velocity at the tail of the structure. This indicates that when the water flow comes into contact with the plane of the bridge pier, the obstruction effect on the water flow and the disturbance of the flow field are stronger compared to when the angle of attack is 45°. Based on Figure 18(a), it can be observed that the reduction in flow velocity caused by a 45° angle of attack contact is much smaller than that caused by a flat bridge pier. Although the velocity at the tail of the bridge pier with a 45° contact surface gradually decreases over time, its velocity is still much higher than that of the plane contact. At 2 s, the velocity of 1.58 m/s is greater than that of the plane structure at 0.47 m/s, and at 8 s, the velocity of 0.59 m/s is greater than that of the plane at 0.05 m/s. Furthermore, it was demonstrated that the force exerted on the contact surface of the bridge pier is smaller when in contact at a 45° angle of attack, as shown in Figure 18(b). Throughout the entire flow process, it is evident that the force exerted during contact at a 45° angle of attack is smaller than that exerted during plane contact. This provides guidance for further optimizing or enhancing the stability of bridge piers.
Figure 17

The influence of different bridge pier structures on flow. (a) Flow field of planar bridge pier (b) 45° angle bridge pier.

Figure 17

The influence of different bridge pier structures on flow. (a) Flow field of planar bridge pier (b) 45° angle bridge pier.

Close modal
Figure 18

Force and surrounding flow velocity changes of two contact surface designs.

Figure 18

Force and surrounding flow velocity changes of two contact surface designs.

Close modal

This study simulates the interaction between water flow and bridge structures during flood processes, as well as their impact on bridge performance. By monitoring key parameters such as flow velocity changes, water surface elevation fluctuations, vorticity enhancement, and turbulent energy evolution, the complex hydraulic characteristics and structural stress states of the river channel during flood processes were comprehensively revealed, as well as the influence of the interaction between water flow and bridge pier contact surfaces. Based on the above analysis, the following primary conclusions are drawn:

  • (1) Structures, particularly bridge piers, are subjected to significant dynamic impacts during riverine floods. As floodwaters flow past these structures, their stress states fluctuate continuously and reach peak forces exceeding 6,000,000 N at specific moments. This sustained high-intensity force poses a severe threat to the stability of structures, highly likely leading to damage or other adverse situations.

  • (2) When floodwaters traverse structures, the flow velocity undergoes marked attenuation, whereas vorticity and TKE exhibit significant increases. Over time, the influence range gradually expands, indicating that the obstruction effect of bridge piers on flood flows is not only prominent but also persistent. The enhancement of vortices and turbulence further intensifies the scouring and erosion of structures by water flows, elevating the risk of structural failure.

  • (3) By adjusting the contact between the water flow and the bridge pier, the force exerted by the water flow on the bridge can be reduced, and the impact of the bridge on the water flow can be minimized.

Thank you to Professors Xiaoyu Liu and Chao Yuan for their assistance during the paper revision period. We would like to express our gratitude.

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

The authors declare there is no conflict.

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