https://orcid.org/0000-0001-7068-8291
ABSTRACT
Local scours around the bridge pier are a common phenomenon in the mobile riverbed, leading to a substantial risk of bridge failures. In this study, the primary objective is to present a protective collar of pile foundations on the basis of flow structure and riverbed erosion. For this purpose, model experiment cooperating with numerical simulations under sandy water conditions was applied to investigate the changes in scour patterns around the rectangular pile cap, and the influence of flow velocity and riverbed height on the scour area and depth was analyzed under conditions without protective measures. On this basis, a horseshoe-shaped collar defined by the elliptical equation was proposed to mitigate the scour on the riverbed. The results show that the scour patterns calculated by computational fluid dynamics are similar to those with experimental methods, the maximum relative deviation of the scour area and depth are 9.16 and 23.94%, respectively. The simulation method can evaluate the rationality of anti-scouring collar designs. The comparison of topography indicates that scour around the foundation is effectively mitigated with a protective collar; the maximum scour area decreased by 64.85-85.52% for different conditions. The scour depth was significantly reduced, with a minimum reduction of 66.67%.
HIGHLIGHTS
Numerical simulation is used to investigate local scours around rectangular pile caps.
The area and depth of the scour pit increase with the increasing riverbed height.
A horseshoe-shaped collar defined by the elliptical equation was designed.
Elliptical scour areas appear at the rear of the collar.
The collar decreases local scours effectively.
INTRODUCTION
Bridge piers in the river can induce flow diversion around their vicinity, elevate flow velocity, and result in the formation of a complex flow structure characterized by vortex formation. For sandy riverbeds, the vortex proximate to the sand bed surface vigorously scours both the upstream side of the bridge piers and the surrounding sediments, inducing rapid sediment transfer around the bridge piers, which leads to the decrease in elevation of the riverbed around the piers. Wardhana & Hadipriono (2003) conducted a study in the United States on the causes of 503 bridge structural failures between 1989 and 2000. Their findings revealed that over 50% of these failures were attributed to scouring. Diaz et al. (2009) investigated the causes of 63 bridge collapses in Colombia between 1986 and 2001, and found that 24% of them were caused by erosion. It is clear that local scours around bridge piers represents a critical phenomenon pervasive in sandy riverbeds, posing a substantial risk of bridge failures.
The main reason of local scouring around bridge piers is the change in flow field, which is caused by encounters presented by the piers, i.e. any alteration in the shape or arrangement of the piers will lead to changes in the flow structure and scour. Many research works on the flow structure and scour patterns around bridge piers focuses on cylindrical piers (Luo et al. 2022; Raeisi & Ghomeshi 2022; Zhang et al. 2023), at present, many new pier designs have emerged with economic development and technological advancements (Aghaee & Hakimzadeh 2015; Farooq & Ghumman 2019; Vijayasree et al. 2019), among which rectangular piers are the most common. Compared to cylindrical piers, studies on the flow characteristics and scouring features around rectangular piers are scarce. Previously, scholars believed that the flow structure around rectangular piers was similar to that of cylindrical piers. However, Tseng et al. (2000) found that rectangular piers have a larger surface, which generate downwash flow intensity acutely, resulting in larger horseshoe vortices and wake vortices. Diab et al. (2010) measured the flow field around rectangular piers under clear-water scouring conditions, and analyzed their flow characteristics and scouring features. Izadinia et al. (2013) determined the Reynolds shear stress and turbulent structure around the bridge pier, and analyzed the contribution of these two factors to sediment transport in the scouring process. Thanh et al. (2014) found that the maximum scour depth around rectangular piers occurs at the corners of the pier's front end through physical model experiments.
Local scouring around bridge piers is a major factor contributing to bridge damage. Therefore, it is of great significance to adopt cost-effective protective measures to protect the sandy riverbed and ensure the safe and stable operation of the bridge. The results from the present investigation suggest that the protective measures including rock dumping, enlarged pier foundations, sacrificial piles, pier slots, and gabion protection can effectively reduce scour and erosion around piers in the short term (Tafarojnoruz et al. 2010; Wang et al. 2017; Singh et al. 2019; Bestawy et al. 2020), while these methods are prone to damage over time, leading to high maintenance costs. In order to solve these issues, researchers proposed anti-scouring collars. These collars are installed on the piers to block the descending flow in front of the piers and preventing the formation of horseshoe vortices. In general, the geometric shape, installation height, and size of these collars can affect characteristics of scouring and deposition (Ghorbani & Kells 2008). Zarrati et al. (2004) demonstrated that the protection efficiency cannot be improved when the collars settled below the riverbed level, for the sediment above the collars is quickly eroded, increasing the scour pit depth. They (Zarrati et al. 2006) also found that the collars should cover the scour area, and the protective performance can be improved using anti-scouring collars combining with rock dumping. Beheshti & Ataie-Ashtiani (2009) carried out an experimental study on the three-dimensional turbulent flow field around a complex bridge pier located on a rough fixed bed. The velocity components on different planes were measured, and the results showed that the approaching boundary layer at the upstream of the pile cap separates and forms different flow directions. The interaction between the contracted upward flow on the pile cap and the downward flow in front of the column produces a strong downward flow along the side of the pile cap. The flow at the rear of the pile cap is complex with various characteristics and vortices, and these are the main factors that lead to the entrainment of riverbed sediments. Memar et al. (2009) focused on the impact of the size and position of collars on the scour depth around two tandem bridge piers under clear-water conditions, it shows that placing the collars on the riverbed surface minimizes scouring around the piers; moreover, the flow velocity affects the scour of the piers significantly. Under the steady clear-water condition, Ataie-Ashtiani et al. (2010) conducted experimental research on the local scour depth of complex piers, involving a variety of configurations. The position of the pile cap affects the scour depth. The maximum scour depth occurs when the pile cap is undercut. There is no general formula for determining the elevation at which the pile cap is undercut. When the elevation of the pile cap is close to the bed surface, the impact is significant. When the pile cap is located at the bed, the scour process is complex and its horizontal extension affects the relevant scour conditions. Jahangirzadeh et al. (2014) conducted a series of experiments to study the influence of geometric shape on controlling horseshoe vortices and scour depth, the results shows that rectangular collars perform better than circular collars. The research also presented the most economical size of the collars. Wang et al. (2019) found that collars with an outer diameter three times that of the pier can reduce scour depth by more than half, and the device should be installed below the typical scouring elevation of the riverbed. Pandey et al. (2020) conducted flume experiments under clear-water scour conditions to study the impact of collars with different diameters and heights on scour depth, the results indicate that the protective efficiency of the collars increases with diameter but decreases with mounting height. To date, many researches have made significant progress in protecting bridge piers from local scour, however, the protective effectiveness is influenced by factors such as water flow conditions, riverbed characteristics, pier types, and the protection methods. Previous studies mainly focused on the pier shafts, with less attention given to the pile foundations and caps. Kassem et al. (2023) conducted experiments on clear-water scour to investigate the effects of circular and hexagonal collars on the scour holes around cylindrical bridge piers. The results indicate that collars can alter the scour characteristics by shifting the location of the maximum scour depth and reducing the volume and dimensions of the scour hole. Among the two types, the hexagonal collar showed superior performance, with the average scour depth reduction being 8% higher than that of the circular collar. Using circular and hexagonal collars reduced the maximum scour depth by approximately 57 and 60%. Gupta et al. (2023) employed both experimental and numerical simulation methods to examine the impact of four different airfoil-shaped collar diameters on bridge pier scour. The experiments revealed that when the collar diameter was 2, 2.5, and 3 times the pier diameter, the maximum scour reduction rates were 86, 100, and 100%. Numerical simulations corroborated the experimental results, showing that collars facilitated smoother flow separation, reduced the intensity of the horseshoe and wake vortices, and yielded an error of only 11% when compared to the experimental data. Bharadwaj et al. (2024) conducted experiments under non-uniform sand bed conditions to explore the protective effects of circular, octagonal collars, and sacrificial piles. The results demonstrated that octagonal and circular collars, with a width of two times the pier diameter and placed at bed level, achieved maximum scour reduction rates of 78.33 and 75%. As the installation height of the collars increased and their width decreased, the protection efficiency of both the octagonal and circular collars diminished. The combination of octagonal collars and sacrificial piles arranged transversely achieved a maximum scour reduction rate of 86.67%.
Considering many bridge piers are equipped with pile foundations and rectangular pile caps to ensure stability, it is important to study the impact of rectangular caps on flow structure and riverbed erosion. In this research, the scour characteristics around rectangular caps under various riverbed heights and flow velocities were examined using model testing and numerical simulation, a horseshoe-shaped protective collar of pile foundations was proposed to reduce the scour area and pit depth, and the effectiveness of the protective measure was also analyzed.
MATERIALS AND METHODS
Experimental setup
Experimental setup parameter
| Experimental setup | Material | Parameter |
|---|---|---|
| Channel | Glass | Length × width × height: 15 m × 0.5 m × 0.5 m |
| Water tank | / | Length × width × height: 3 m × 0.5 m × 1.5 m |
| Sand mixing pool | / | Length × width × height: 4 m × 2 m × 1.5 m |
| Piers | White resin | Rectangular pier shaft: Bc = 20.0 mm, Lc = 57.0 mm; Rectangular pile cap: Bpc = 58.0 mm, Lpc = 93.0 mm, Hpc = 23.0 mm; Cylindrical pile: D = 13.4 mm, Sn = 34.0 mm, Sm = 34.5 mm |
| Sand in the flow | / | Density: 2,650 kg·m−3; Sediment content in flow: 2.7 kg/m3 Water temperature: about 20 °C |
| Experimental setup | Material | Parameter |
|---|---|---|
| Channel | Glass | Length × width × height: 15 m × 0.5 m × 0.5 m |
| Water tank | / | Length × width × height: 3 m × 0.5 m × 1.5 m |
| Sand mixing pool | / | Length × width × height: 4 m × 2 m × 1.5 m |
| Piers | White resin | Rectangular pier shaft: Bc = 20.0 mm, Lc = 57.0 mm; Rectangular pile cap: Bpc = 58.0 mm, Lpc = 93.0 mm, Hpc = 23.0 mm; Cylindrical pile: D = 13.4 mm, Sn = 34.0 mm, Sm = 34.5 mm |
| Sand in the flow | / | Density: 2,650 kg·m−3; Sediment content in flow: 2.7 kg/m3 Water temperature: about 20 °C |
Experimental devices.
Grain composition.
Geometry of pier.
In order to reveal the scour characteristic of the riverbed around the pier, the experiments of two riverbed heights cooperating with five flow velocities were carried out. The experimental factors and levels are shown in Table 2.
Experimental factors and levels
| Factors | Levels | ||||
|---|---|---|---|---|---|
| Riverbed height (m) | 0.06 | 0.07 | |||
| Flow velocities (m/s) | 0.20 | 0.25 | 0.30 | 0.35 | 0.40 |
| Factors | Levels | ||||
|---|---|---|---|---|---|
| Riverbed height (m) | 0.06 | 0.07 | |||
| Flow velocities (m/s) | 0.20 | 0.25 | 0.30 | 0.35 | 0.40 |
Note: 0.06 m riverbed height is flush with down surface level of the rectangular pile cap, 0.07 m is at two-thirds of the height from the surface of the rectangular pile cap.
Numerical simulation
is the velocity of the large-scale turbulence; 
is the pressure of the large-scale turbulence; 
is the dynamic viscosity of the fluid. In this study, the Smagorinsky subgrid-scale model is used for modeling. In the Cartesian coordinate system, 
and 
represent the spatial coordinate components; t denotes time; 
represents the filtered velocity component product averaged over time; 
represent the filtered velocity components, where i, j = 1,2,3 correspond to the three directions in the Cartesian coordinate system.
is the subgrid-scale turbulent kinetic energy; 
is the subgrid-scale eddy viscosity, where 
; 
is the Smagorinsky constant, 0.16; 
is the velocity deformation tensor. 
denotes the subgrid-scale stress; 
is the Kronecker delta; 
represents the magnitude of the strain rate tensor; 
denotes the filtering scale.
Boundary conditions.
Mesh size independence verification
Mesh independence analysis was performed under the condition of a riverbed elevation of 0.06 m and a flow velocity of 0.4 m/s, as shown in Table 3. The mesh independence was validated by calculating the average error between the maximum scour area and depth obtained from the numerical simulation and those from the model experiment. The results show that when the mesh size is reduced to 0.005 m, the average error stabilizes and remains <5%. As the mesh size reduced to 0.004 m, the average error decreases by 0.1%. Considering both computational efficiency and the number of mesh elements, a mesh size of 0.005 m is selected as the optimal mesh size for this numerical simulation.
Analysis of mesh size independence
| Mesh size/m | Mesh count | Maximum scour area /m2 | Maximum scour depth /m | Maximum scour area /m2 | Maximum scour depth /m | Average error /% |
|---|---|---|---|---|---|---|
| 0.007 | 684,455 | 0.0228 | 0.048 | 0.0196 | 0.046 | 10.4 |
| 0.006 | 1,046,527 | 0.021 | 0.046 | 7.3 | ||
| 0.005 | 1,798,267 | 0.0186 | 0.044 | 4.7 | ||
| 0.004 | 3,446,279 | 0.0186 | 0.044 | 4.6 |
| Mesh size/m | Mesh count | Maximum scour area /m2 | Maximum scour depth /m | Maximum scour area /m2 | Maximum scour depth /m | Average error /% |
|---|---|---|---|---|---|---|
| 0.007 | 684,455 | 0.0228 | 0.048 | 0.0196 | 0.046 | 10.4 |
| 0.006 | 1,046,527 | 0.021 | 0.046 | 7.3 | ||
| 0.005 | 1,798,267 | 0.0186 | 0.044 | 4.7 | ||
| 0.004 | 3,446,279 | 0.0186 | 0.044 | 4.6 |
COMPARISON OF EXPERIMENTAL AND SIMULATED RESULTS
Here, Ade is the dimensionless maximum scour area; As is the maximum scour area; Apc is the vertical projection area of the pile cap; Hde is the dimensionless maximum scouring depth. Hs is the maximum scour depth; Hpc is the pile cap thickness.
Scour patterns
Comparison of simulated and experimental results of scour patterns for 0.4 m/s velocity: (a) 0.06 m riverbed height and (b) 0.07 m river bed height.
Comparison of simulated and experimental results of scour patterns for 0.4 m/s velocity: (a) 0.06 m riverbed height and (b) 0.07 m river bed height.
The scour pattern around the rectangular pile cap typically exhibits the following specific characteristics: upstream of the rectangular pile cap, the presence of the pier causes flow deflection, resulting in a ‘flow bifurcation’ phenomenon in the flow field. On both sides of the pier, the local flow velocity increases, leading to the formation of intense turbulence. This turbulence not only affects the hydrodynamic conditions around the pier but also exerts significant influence on the pier foundation. Particularly, due to the drastic change in local flow velocity on the pier's surfaces, high shear stresses may be generated, increasing the risk of riverbed scour. Downstream of the pier, although the flow velocity is generally lower, vortex formation leads to localized deceleration, creating a recirculation zone. The vortices behind the pier cause flow instability, further exacerbating local scour. Also, scour typically occurs upstream of the pier, especially in the flow diversion areas near the pier's front edge and on both sides. The deflection and acceleration of flow result in the formation of strong turbulence and low-pressure zones, which can easily lead to sediment erosion. The recirculation zone downstream also serves as another critical region for scour, especially in areas with reverse flow and low flow velocity, where scour holes are more likely to form. In addition, under the action of the flow, scour holes typically appear downstream or on the sides of the pier, manifesting as localized depressions. As the flow continues, the scour depth progressively increases, particularly in the vortex area downstream of the pier. The morphology of the scour hole gradually stabilizes over time, and once it reaches a certain stable depth.
Scour area
Scour areas for different riverbed heights: (a) riverbed height: 0.06 m and (b) riverbed height: 0.07 m.
Scour areas for different riverbed heights: (a) riverbed height: 0.06 m and (b) riverbed height: 0.07 m.
Scour depth
Scour depths for different riverbed heights: (1) riverbed height: 0.06 m and (2) riverbed height: 0.07 m.
Scour depths for different riverbed heights: (1) riverbed height: 0.06 m and (2) riverbed height: 0.07 m.
PROTECTION MEASURE
Structure of a horseshoe-shaped collar.
Topography
Table 4 depicts the scour topography with and without collar at a sediment height of 0.07 m under different flow velocities. It shows that as the velocity increases, the scour extends to both sides of the foundation, enlarging the scoured area. With further velocity increases, a continuous scour area forms around the foundation, and the sediment deposition behind it also increases. After installing the collar, scour around the foundation is effectively mitigated with various flow velocities. At higher flow velocities, elliptical scour areas appear at the rear of the collar, and the area increases with the flow velocity. However, these scour areas have minimal impact on the structural stability of the bridge piers.
Comparison of scour topography with and without collar
 |
| |
Remission of sour area
Decreasing ratio of the scour area.
Decrease ratio of sour depth
Decreasing ratio of the scour depth.
DISCUSSION
Based on the engineering context of the Huanghe Grand Bridge on the Puyang to Hubei Yangxin Expressway, this study investigates the variation of scour patterns around rectangular pile cap foundations. The riverbed elevation under unprotected conditions presents a horseshoe-shaped scour, the scour pattern is familiar with the results presented by Khan et al. (2017). According to the results of scour pattern, a horseshoe-shaped collar protection measures was presented, the horseshoe-shaped collars investigated in this study achieved a maximum scour depth reduction of 64.85–88.52% for rectangular pile cap piers, which is higher than 79% obtained by Jahangirzadeh et al. (2014). The scour depth was reduced, with a minimum reduction of 66.67% in this research, and the value is higher than that obtained by Zarrati et al. (2006), where scour depth reduced by 50% at upstream piers and 60% at downstream piers. In addition, comparing with other protective measures, such as rock dumping, enlarged pier foundations, sacrificial piles, pier slots and gabion protection, collars are positioned based on the pile cap location, offering an advantage of easy installation and low maintenance costs. However, with the changes of flow intensity and scour severity over time, the collar may provide some relief in the short term, but it alters the flow pattern around the pier, causing the flow to form a special flow field beneath the collar, the drawbacks associated with using a collar is obvious. In order to decrease adverse effects, the connecting format of piers and collar can be changed from rigid connection to flexible connection, the collar will descend under the force of gravity as the erosion below the collar occurs.
Additionally, the geometric parameter (e.g., collar thickness, width, and height) of the collar can be further optimized to maximize its protective performance under complex flow conditions. In addition, this paper concentrates on the anti-erosion characteristic of the anti-scouring collar using an acceleration test, and the experiments of long-term effectiveness of the collar under unsteady flow conditions will be performed in subsequent research. Also, the installation of horseshoe-shaped collar protection measures can impact on flow conditions and sediment transport dynamics locally, however, the effect of horseshoe-shaped collars on surrounding ecosystem and sediment transport dynamics has not been considered in this paper, and potential environmental impacts such as the community structure of plants, fish, and microorganisms can be studied during actual construction.
CONCLUSION
In this study, the experiment method cooperating with numerical simulation was employed to investigate the impact of water flows on the local scouring of rectangular bridge piers, and anti-scouring measures were proposed. The conclusions are as follows:
(1) The results of the numerical simulations are in good agreement with the experimental results, the simulation method can be applied to study sediment scour and evaluate the rationality of anti-scouring collar design around the piers.
(2) When water flow impacts the bridge pier foundation, it disperses to both sides, forming lateral vortices. These vortices entrain sediment from both sides of the foundation, creating an inverted conical scouring pit near the bridge pier. The area and depth of the scour pit increase with the height of the riverbed.
(3) Based on the shape of the scouring pit, a horseshoe-shaped riverbed protective collar was proposed. This device effectively decreases the scour area and depth. With the installation of the protective collar, the scouring area can be reduced by 64.9–85.5%, and the scouring depth can be decreased by 66.67–88.89%.
(4) The experiments were conducted under steady flow conditions using an acceleration test, long-term effectiveness of the collar under unsteady flow conditions should be studied in subsequent research works.
ACKNOWLEDGEMENTS
I would like to show my deepest gratitude to the editors and reviewers.
FUNDING
This research was supported by The Scientific and Technological Research Program of Henan Province (No. 242102321001), Qian Kehe Zhicheng [2023] (Yiban 206), Qian Kehe Zhicheng [2024] (Yiban 130), for which the authors are grateful.
DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.
CONFLICT OF INTEREST
The authors declare there is no conflict.
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