SURVEYING THREE-DIMENSIONAL PERSPECTIVES OF THE FLOW STRUCTURE AROUND THE BRIDGE PILE DEPENDING ON THE VEGETATION PATTERN DISTRIBUTION

. Modeling techniques have enabled us to understand how to protect vital infrastructures using nature-based solutions. In this research, we demonstrated that by selecting a specific vegetation pattern distribution upstream of the pile as a nature-based solution, we could reduce the amount of scouring around the bridge piles. This is essential to avoid the negative impacts that occur after landslides, flash floods


Introduction
Scouring transfers materials from the bed and riverbanks around the bridge piles, abutments, and other hydraulic structures by the water flow (Shahriar et al., 2021).It is important to note that three primary sources of scour contribute to the final results, which are: (i) long-term aggradation and degradation, (ii) contraction scour, and (iii) local scour.Long-term aggradation involves the deposition of material eroded from the upstream of the bridge.In contrast, degradation is scouring that occurs due to a deficit in sediment supply from upstream over relatively long reaches, as appearing in clear-water conditions (Arneson et al., 2012).Several studies in the United States have reported extensive irreparable damages caused by bridge failure due to scour and state that scour around foundation structures is a leading cause of bridge collapse (Briaud et al. 2005).The defeat due to erosion and irreparable damages is not only an issue in the United States but globally.Considering the future scenarios where climate change could incorporate a concentration of extreme precipitation events after long periods of droughts, extreme weather conditions, and efficient solutions becoming indispensable (Clarke et al., 2022).The potential economic, financial, and human life lost due to scour-induced failures signifies the importance of identifying the principal causes of scour and taking necessary mitigation actions before damage is incurred (Short et al., 2016).
Many empirical models have been developed to estimate the equilibrium scour depth in bridge piers (Vonkeman and Basson, 2019).The development of these models includes experimental and field data or both, ultimately leading to the creation of mathematical and numerical models (Shahriar et al., PAPER ACCEPTED.PREPRINT VERSION 2021).However, scouring around the piers is a complex process influenced by many factors that are not considered when developing empirical models (Ettema et al., 1998).Also, under the same hydraulic and geometric conditions, different models give significantly different scour estimates.In the design step, using a model that gives non-conservative results may lead to bridge failure, while choosing a very conservative model would lead to an unfavorable economic effect (Beg and Beg, 2013).This issue highlights the necessity of investigating the flow structure around the bridge foundation in different laboratory conditions and understanding and documenting foundation scouring estimation models after a comprehensive understanding of the flow structure.
In general, two approaches have been proposed to prevent the scouring of bridge piers.First, strengthening the bed, and second, changing the flow pattern to reduce the strength of the eddies created around the pile (Zaid et al., 2019).To date, many results have been reported on the interaction between flow and vegetation in channels.For example, the effects of patched vegetation on river morphology, sediment transport, and hydro-environmental sequences have been demonstrated to be very efficient (Caroppi et al., 2019;Afzalimehr et al., 2021).Using vegetation as a nature-based solution would allow protecting rivers, controlling erosion, and trapping sediments (Rossi et al., 2018).Vegetation in rivers and floodplains increases resistance, decreases flow capacity, and changes sediment transport and sedimentation (Mohammadzade et al., 2015).The interaction between flow and vegetation is a complex process, and research in this field has led to essential simplifications in practical applications (Tempest et al., 2015).Investigation of the flow velocity and turbulence intensity distribution around the bridge pile when vegetation is present in the scouring area could provide helpful information.It is well-known that vegetation absorbs significant momentum (Huai et al., 2019), thereby changing the shear stress distribution structure, but this condition has yet to be examined around bridges.
According to past research (Miyab et al., 2022), it can be predicted that the presence of vegetation upstream of the bridge pile can be an effective solution in reducing the amount of scouring.However, investigating the flow structure around the bridge pile is still unknown and has outstanding potential.Supposing the presence of vegetation can be a factor in protecting the bridge piles against the scouring phenomenon.In that case, it will be valuable to analyze its interaction with the flow around the bridge foundations based on studying turbulent flow components.In addition to being simple and costeffective, the vegetation solution does not add to the construction costs.Although the studies conducted on the scouring of bridge foundations are extensive, they have yet to provide a single solution to reduce scouring for different hydraulic conditions, which indicates a weakness in understanding the structure and behavior of the flow around the bridge foundation.Also, most of the methods used in the studies are not environmentally friendly.Therefore, in the current research, the vegetation cover upstream at different spatial patterns will be evaluated as an effective solution to change the flow structure to reduce the eddies created around the bridge pile.This research desires to recognize the coherent flows formed around the bridge pile in the presence and absence of vegetation through quadrant and octant analysis.Furthermore, the amount of Reynolds shear stress and scour profile formed around the bridge support are investigated when vegetation is located upstream of the bridge pile.This research aims to investigate the effect of different vegetation patterns upstream of bridge piles on flow structure, coherent flows, Reynolds shear stress, and scour profile.Specifically, it will compare the flow velocity and turbulence intensity distribution around bridge piles with and without vegetation and analyze the effect of different vegetation patterns on bursting events and scour depth.We consider this research significant in terms of multidisciplinarity due to its diverse applications within control measures related to physical geography, forestry, civil, and terrain engineering studies.Vegetation cover is a simple, cost-effective, and environmentally friendly solution to reduce the loss of money invested in vital infrastructures.This study allows us to understand the flow structure around bridge piles with vegetation, which could be essential for designing effective protection measures for land management plans from the catchment to the regional scales.

Experimental channel
This study was conducted in a flume with a length of 15 meters, a width of 90 cm, and a height of 60 cm, featuring a maximum flow rate of 50 liters per second, located in the hydraulic laboratory of Isfahan University of Technology.The flume had a plexiglass bottom and sidewalls, presenting a rectangular cross-section.The water level was regulated by a sliding gate downstream of the flume.To mitigate turbulence in the flow, there was a flow-calming chamber in the inlet tank constructed with perforated bricks and honeycomb.A digital flow meter measured the flow rate of the inlet stream.Throughout the channel, excluding one meter at the beginning and end, a Teflon platform was installed, standing 20 cm high.A layer of sediments, composed of bed material, was affixed to the platforms to adjust the roughness coefficient.In each series of experiments, a one-meter distance between two platforms was filled with sifted sand, and its surface was smoothed entirely using a trowel and a leveler.Figure 1a shows the schematic view of the experimental channel.

Depth and velocity meters
A limnimeter with an accuracy of 1 mm was used to measure the scour hole profile.This limnimeter was placed on a frame with four support points on the upper edge of the channel.Two parallel bars were attached to the frame body for its transverse movement.In this way, the limnimeter could move in two directions perpendicular to each other and easily measure the scour profile (Kabiri et al., 2022).Velocity measurement was conducted at different points using the new generation ADV threedimensional velocity meter manufactured by Nortek, Norway.Due to the cable structure of this device, it was possible to measure the velocity from different angles.The manufacturer calibrated this device, PAPER ACCEPTED.PREPRINT VERSION and it remains unchanged as long as the device is not physically damaged.This device can assess the characteristics of turbulence.One of the merits of this device is its ability to collect data with high frequency and measure far from the desired surface, minimizing the difference caused by the presence of the measuring device in the flow.Measurements in the ADV device are based on a physical phenomenon called the Doppler effect.
The number of raw data recorded by the device depends on the frequency set for the device and the measurement time.In this project, ADV was set to 200 Hz and 2 minutes, resulting in the average velocity of a point among 120 × 200 = 24,000 points.Additional data collection and filtering software used were Vectrino+, WinADV, and Excel.To filter the data for each point among the 24,000 collected velocities, inappropriate data (correlation < 70 and SNR < 15 or SNR < 5) were removed, and based on other data, the average speed was obtained (Nortek, 2004).

The bed material size and pile diameter
In this study, following Chiew and Melville (1987), the diameter of the pile was chosen to be 5 cm (symbol D).The distance between the axis of the pile and the wall was suitable because of the channel width.The bridge pile was installed at a distance of 1062 cm from the channel's beginning.According to Raudkivi and Ettema (1983), to achieve the maximum scouring depth, the formation of ripples should be prevented.For this purpose, the average size of sediment particles should be greater than 0.7 mm.Chiew and Melville (1987) acknowledged that when the ratio of the pile diameter to the average size of the particles is greater than 50, the effect of the particle size on the scour depth can be ignored.In this research, sand particles with a diameter greater than 0.7 mm will be selected.The characteristics of the bed material are as follows (Pope, 2000): ) 0.5  (1) ) (2) Where d 50 represents the average size of sediment particles, Cu is the uniformity coefficient, Dg means the geometric mean size,  corresponds to the standard geometric deviation and Gr registers the grading factor.According to the uniformity coefficient of Cu and d50, the type of sand bed material was uniform (McGlinchey, 2009).Table 1 shows the geometric characteristics of sediment particles.The thickness of the bed was determined according to the maximum scour depth.For this purpose, an estimate of the maximum scour depth was first obtained.Laursen (1963) presented the relationship based on the pile diameter to calculate the maximum scour depth.dsm = 1.05D 0.75  (5) Where D is the pile diameter in meters and dsm is the maximum scour depth in meters.Therefore, with the help of the above relationship and the chosen diameter of 5 cm for the pile, the maximum scouring depth of 11 cm was obtained, so the height of the substrate particles chose 20 cm to ensure accuracy.

Experimental setup
Two types of dense artificial grass vegetation with a height of two centimeters (10 % of the flow depth) were located upstream of the bridge pile.The vegetation used width is once 90 cm, i.e., the entire width of the stream (Vo), and once 10 cm of the stream width (Vp) in the central axis of the channel.The vegetation cover was placed 30 cm above the bridge pile.Figure 1b shows the distribution of overall vegetation upstream of the bridge pile, Figure 1c shows the distribution of patch vegetation upstream of the bridge pile and Figure 1d shows the density of used vegetation.A single pile with a 5 cm diameter was placed perpendicular to the bed in the flow direction to conduct the experiments.The shields diagram was used to determine the appropriate hydraulic conditions for maximum scour (Cao et al., 2006).An average flow rate of 0.036 m 3 /s and a depth of 20 cm were established for the channel's sand bed.At the experiment's end, the scour hole dimensions were measured.Eventually, several velocity profiles were taken using ADV upstream and downstream of the bridge pile.

Reynolds shear stress (RSS)
Reynolds shear stress (RSS) is a measure of the friction between layers of a fluid due to turbulent flow.It is a key factor in sediment transport and other physical processes.RSS is caused by the uneven motion of fluid particles in turbulent flow.When fluid particles collide with each other, they transfer momentum from one particle to another.This transfer of momentum creates friction between the layers of fluid.RSS is important in physical geography and civil and terrain engineering studies because it plays a role in various physical processes, such as sediment transport, erosion, and deposition.For example, RSS can erode riverbanks and transport sediment downstream.It can also cause the deposition of sediment in floodplains and estuaries.RSS is also crucial for understanding river flow and other fluid dynamics.Turbulent currents account for a significant part of river flows.In this flow type, fluid particles deviate from their original path and move irregularly.In this case, in addition to the fluid's inherent viscosity, the dispersed movements of particles also contribute to flow resistance, and a feature called eddy viscosity is introduced to express it (Pickering et al., 2021).
Turbulent flow characteristics play a significant role in the sediment transport process, including diffusion, erosion, sedimentation, and flow resistance.In turbulent flow, the generation and destruction of small and large eddies cause fluctuations in flow parameters.In this flow, instantaneous parameters such as velocity can be expressed as follows: Where  �, ̅ and  � are the time average of the velocity components in x, y and z directions and u′, v′ and w′ are the fluctuation values of velocity.
Reynolds shear stress is calculated from the following equation:

Quadrant analysis
Turbulent flow in open channels is not a completely random process.However, some continuous temporal and spatial patterns can be identified in them.These patterns are known as coherent structures in turbulent flow.They significantly affect the distribution of shear stress in open channel processes.As a result, coherent structures play an essential role in the erosion and sedimentation of the bed, the phenomena of mixing, nutrient distribution in the river, and aquatic plant implantation.Coherent structure in flow refers to a three-dimensional region of the flow in which at least one of the main PAPER ACCEPTED.PREPRINT VERSION variables of the flow (for example, velocity, temperature, and density components) shows a significant correlation with itself and with another variable in a range of time and space.This temporal and spatial spectrum is much larger than the flow's most minor local temporal and spatial scales (Cellino and Lemmin, 1999).
Turbulence has a significant inherent complexity, leading to various interpretations of its nature.The quadrant analysis method is used to study the presence of coherent structures in flow fields and their contribution to the total shear stress.The quadrant analysis method involves studying the relationship between the velocity fluctuations in the flow direction (u') and perpendicular to the flow (w').For this, u' and w' are plotted against each other, forming a quadrant plane in the trigonometric coordinate system, as indicated in Table 2.This plane represents a bursting cycle (Carino and Brodkey, 1969;Lu and Willmarth, 1973;Willmarth and Lu, 1972), including the four events.The occurrence probability of event k is calculated as the normalized occurrence frequency, fk, for a particular class of events related to different classes of events (Termini, 2015): Primary research to understand the turbulent structure of coherent flows in channel walls and beds dates back to the last 30 years (Corino and Brodkey, 1969;Kline et al., 1967;Kim et al., 1971;Grass 1971;Afzalimehr and Anctil, 2000).Some researchers interpreted this coherent structure as periodically organized events in the time domain that manifest their impact in the Reynolds shear stress time series (Carino and Brodkey, 1969;Lu and Willmarth, 1973).The first event (Q1) involves the occurrence of high-velocity fluid movement from the bed to the water surface, the second event (Q2) is characterized by low-velocity fluid movement to the water surface, the third event (Q3) involves lowvelocity fluid movement toward the bed, and the fourth (Q4) event shows high-velocity fluid movement towards the bed.The cycle that includes these four events is referred to as bursting events (Kabiri et al., 2022).It is important to note that ejection and sweep events generate turbulent energy, and outward and inward interactions are associated with energy dissipation.Additionally, ejection and sweep are often linked to the removal and transfer of sediments (Pope, 2000;Vijayasree et al., 2020).Sweep events are associated with the initiation of bed load movement, while ejections are responsible for lifting and carrying the bed load (Sterk et al., 1998).The investigation of the flow downstream of the submerged vegetation patch by Mayaud et al. (2016) demonstrated high frequencies of Q2 (ejection) and Q4 (sweep) events in the crest of the vegetation patch (Mayaud et al., 2016).In contrast, it is reported that the dominance of outward and inward interactions in the shear layer is induced by the flow passing above the vegetation patch, which is a notable characteristic of the flow in the downstream region of a submerged vegetation patch in a more distant region (Kazem et al., 2021a;Przyborowski et al., 2019;Keshavarzi et al., 2014).

Octant analysis
As mentioned, quadrant analysis is based on the analysis of the probability distribution of the two longitudinal (u') and vertical components (v') of the velocity fluctuation.However, in rivers and natural channels, the flow structure is coherently structured in three dimensions, especially where an obstacle is placed in the flow path.The velocity in the lateral direction cannot be neglected, as it can induce significant secondary circulation (Keshavarzi et al., 2014).Additionally, two-dimensional analysis cannot define sediment entrainment as a three-dimensional phenomenon (Ortiz et al., 2013;Zong and Nepf, 2010).In general, eight burst event classes in 3D octant analysis are defined based on the sign of velocity fluctuations, as outlined in Table 3.The symbols used in this research are inspired by the work of Keshavarzi et al. (2014) and Kazem et al. (2021b).Keshavarzi (2014) stated that the deviations of group events are towards the internal direction or the central line (internal events), while the deviations of group B events are away from the central line and towards the channel walls (external events) (Keshavarzi et al., 2014).This study considers three categories of results for octant analysis: (1) the probability of occurrence of bursting events (Op), (2) the attack angle of bursting events, and (3) the stability of each event (St).Calculating the probability of occurrence of events is similar to the quadrant analysis approach.It is equal to the frequency of occurrence (fk) for a specific event class relative to different events (Bento et al., 2021).Octant analysis is a method for classifying bursts of turbulence in three dimensions, offering more detail than quadrant analysis, which only considers two dimensions.Turbulent bursts are sudden, localized increases in turbulence intensity and play a crucial role in sediment transport and other physical processes.The probability of occurrence of a burst is the fraction of time that the burst occurs at a given point in the flow field.The attack angle of a burst is the angle between the mean flow direction and the direction of the burst.The stability of a burst is a measure of how long the burst lasts.Table 3 displays the eight bursting event classes in 3D octant analysis based on the sign of velocity fluctuations.In this table, the symbol N is used for velocity fluctuations with a negative value, and P is used for positive velocity fluctuations in the class name column.The first letter represents u', the second letter represents v', and the third letter represents w'.The force applied to sediment particles in the bed strongly depends on the angle of inclination of the three-dimensional flow velocity fluctuations (ϴi).Understanding the attack angle of bursting events helps comprehend the entrainment sediment process (Breusers et al., 1977;Bridge and Bennett 1992;Esfahani and Keshavarzi, 2011;Esfahani and Keshavarzi, 2013;Bernard and Handler, 1990).The attack angle is calculated as follows:

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Three-dimensional perspectives of the flow structure around bridge pile Esfahani andKeshavarzi (2013, 2021) and Liu and Bai (2013) employed the aforementioned technique to comprehend the bursting process in a meandering channel (Liu and Bai, 2013;Carnacina et al., 2019;Guan et al., 2019).They recognized that this technique offers greater clarity in understanding coherent flow structures and their impact on sediment entrainment in meanders.Keshavarzi (2014) delved into the coherent structures around the bridge pile (Keshavarzi et al., 2014).Their findings indicated that near the bed, internal ejection and external sweep events play a role in the scouring mechanism around the single bridge pile.Using this technique, Kazem et al. (2021b) examined the eddy structures in a channel with patched vegetation (i.e., artificial bars).They observed that in a channel with a small width of vegetation patch, the flow passing through the vegetation (x direction) and the side flow around the vegetation patch significantly influence the formation of flow structures outside the vegetation (Kazem et al., 2021b).MATLAB programming software was employed for quadrant and octant analysis, and subsequent results were analyzed.

Scouring contour map
Figure 2 (2a-2c) displays contour maps of scouring profiles for single piles without vegetation, with overall vegetation, and with patch vegetation, respectively.In all figures, the X-axis represents the distance from the beginning of the channel, and the flow direction is from left to right.Scouring depths are 6.5 cm in the free-vegetation case, 4.7 cm in the overall vegetation case (Vo-case), and 4.1 cm in the patchy vegetation case (Vp-case).According to the results of this research, the highest amount of scouring occurred in the free-vegetation case.Patched vegetation could reduce the scour depth by 36%.Additionally, vegetation decreased the longitudinal and transverse expansion of the scouring hole.PAPER ACCEPTED.PREPRINT VERSION

Reynolds shear stress
Figure 3 illustrates the distribution of Reynolds stress (RSS).The horizontal axis (x) indicates the distance from the beginning of the channel in centimeters, and the vertical axis (z) indicates the height from the bed represented in centimeters too.Given that RSS is proportional to the flow's capacity to transport sediments and reflects the exchange of turbulent motion between fluid layers, it is understandable that such capacity increases with the enlargement of the scour hole (Bernard Handler, 1990;Carnacina et al., 2019).In all cases upstream of the pile, the region with the maximum RSS developed upstream of the scour hole.This is where the maximum flow power for scouring (area of large value enlarged) was established, aligning with the findings of Bento et al. (2021) and Guan et al. (2019).The maximum RSS occurs upstream of the pile where the maximum positive and negative velocity values occur, indicating that the velocity in this region can be highly unstable.
The presence of vegetation decreased the negative values of shear stress and reduced the intensity of RSS upstream of the pile.Downstream of the bridge pile, the negative values of shear stress increased, especially at the point closest to the pile, where these negative values are higher in the Vocase.In the Vo-case, the highest shear stress values downstream of the pile occurred where the accumulation of sediments was observed.

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Three-dimensional perspectives of the flow structure around the bridge pile

Quadrant analysis
Figure 4 the occurrence probability of quadrant classes.The location of the bridge pile is from x=1059.5 cm to x=1064.5 cm.The results demonstrated that in the upstream of the pile in the free-vegetation case, the sweep near the bed and the inward in the middle part of the flow depth were the dominant events, both of which increased as they approached the pile.The presence of vegetation caused a significant increase in the probability of ejection events at points very close to the bed and near the water surface and the sweep events at mid-depth points and near the bed.Kabiri (2022) also observed an increase in the probability of ejection and sweep in the presence of vegetation, which can be caused by a decrease in momentum of the water flow.In the free-vegetation case, the possibility of ejection and outward events is dominant downstream of the pile.In the presence of vegetation, the probability of an outward event increased in the middle flow depth range and was closer to the bed.Also, the ejection increased in the Vo-case near the water surface and in the Vp-case in the mid-depth of flow.In the upstream of the pile, the zone of ejection events in the Vp-case is closer to the water level than Vo-case, which is in accordance with Kazem et al.'s results (2021b).Downstream of the pile in the Vp-case, the ejection and sweep events are closer to the water surface and the outward and inward are closer to the bed.Also, the possibility of outward and inward occurrences has increased.The horizontal axes show x(cm), and the vertical axes show z(cm).PAPER ACCEPTED.PREPRINT VERSION

Octant analysis
Figure 5 the results of the Op (probability of occurrence) of a sample of octant analysis events in the free-vegetation case, along with the St values for these events.The numbers inside the graphs indicate the angle of each event in radians.For better analysis, the flow depth was divided into three parts: the first zone, z<5 cm (with two sub-zones, z<0 cm and 0<z<5 cm), the second zone, with 5 cm<z<10 cm, and the third zone with z>10 cm.In the free-vegetation case upstream of the pile: in the first zone of A's class, internal and outward occurrences (in sub-zone z<0) have a 33% Op and St of 57, and the angle of attack is close to 1 radian.In class B, external inward occurrences (in sub-zone 0<z<5) with 42% Op and 45 St are the most dominant phenomena, followed by internal ejection with 31% Op and St of 49.In terms of stability, the events of internal outward, internal ejection, and external sweep near the bed have the highest values, consistent with the results of Keshavarzi et al. (2014).

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In classes and B of the second zone, the Op of events was between 18 and 26 % (26% belonging to internal sweep), showing no dominant event.However, in terms of stability, internal ejection with 46 and internal sweep events with 45.3 was the most stable.In the third zone, the Op varied between 15 and 24% (24 % belonging to internal ejection), and the St varied between 30 and 40%.Sediment scoured from the upstream accumulated behind the pile, creating a mound of sediment that caused Zone 1 to be absent.In the second zone downstream of the pile, external ejection is dominant, with a 30% Op and St of 58 near the mound of sediments.Also, above that, internal outward is the most dominant event with a 47% Op and St of 50.In the third zone near the water surface, internal inward, with a 47% Op and St of 50, and external ejection, with a 43% Op and St of 47, are the dominant events near the second zone.Angles of attack downstream of the pile are reduced compared to the upstream.
Figure 6 shows the results of the Op of octant analysis event sample, and the St's value of each octant event of Group B in the free-vegetation case.The numbers written inside the graphs show the angle of each event in radians.In the Vo-case at the pile upstream: in z>0 cm, the dominant events are external ejection with a 60 % Op and 57 % St and external inward with a 52 % Op and 55 of St, and in z<0 cm internal outward with 41 % Op and St 57 is dominant.In the second zone, the Op of events varied between 19 and 35 percent.In terms of stability, external outward with an Op of 35 % and St of 57, followed by external sweep with an Op of 34 % and St of 55, were the most dominant events.In the third zone, the external sweep is with an Op of 52 % and St of 61, and in the second place is external ejection with an Op of 30 % and St of 41.

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Downstream of the pile in the zone, external ejection was the most dominant event with Op of 63 % and St of 45 %, followed by internal outward with a 33 % Op and St of 56 %.In the second zone, internal outward with an Op of 31 %, St of 52 % after that, internal ejection with an Op of 29 %, and St of 41 % are the dominant events.In the third zone, the range of Op was observed between 13 and 20 percent, showing no dominant phenomenon in this zone.In terms of St, external sweep had the highest stability, i.e., 42. Figure 7 shows the events of octant analysis: (a) the Op results; (b) the St in Vo-case.Upstream of the bridge pile in the Vp-case: in the first zone, internal outward with a 61% % Op and 42 St, external sweep with a 39% % Op and 42 St, and internal ejection with 36% % Op and 65 St were the most dominant events.In the second zone, external sweep with Op of 45% % and S St t of 59, internal ejection with a probability of 36% % and stability of 65% %, and external outward with an Op of 35% % and St of 57% were the dominant events.In the third zone, the external sweep was dominant with an Op of 52% % and St of 62 events.

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Three-dimensional perspectives of the flow structure around the bridge pile Downstream of bridge pile in the Vp-case: in the first zone, internal outward with 47 % Op and 52 St and internal ejection with 37 % Op and 50 St were the most dominant events.In the second zone, internal inward with Op of 37 % and St of 50 and internal outward with Op of 31 % and St of 51 were the dominant phenomena.In the third zone, the Op was between 9 and 26 percent, which internal outward having the most dominance with a 26 % Op and 61 St.In terms of stability, internal inward has a St of 60 with an Op of 18. Figure 7 schematically shows the bridge's pile, which phenomenon prevails in each zone.

Conclusions
This study highlights the substantial impact of vegetation on scour rate, Reynolds stress, and coherent flow structure around bridge piles.The presence of vegetation results in a remarkable 36% reduction in scour depth and induces changes in the distribution of Reynolds stress.The maximum Reynolds stress region shifts upstream of the pile, leading to a decrease in negative shear stress upstream and an increase downstream.Quadrant analysis illustrates that vegetation promotes the occurrence of ejection and sweep events, while octant analysis indicates the dominance of internal outward events within the scour hole.In the free-vegetation case, near the bed, the eddies move toward the walls, but as one moves away from the bed, the eddies shift toward the central axis.The overall vegetation redirects the flow towards the walls in the base area, reducing scouring.Stability and event probability increase with the presence of vegetation.Overall vegetation transforms internal events into external ones in front of the pile.However, in the case of patched vegetation, both internal and external events are observed.With a potential 36% reduction in scour depth, vegetation can play a crucial role in mitigating flood risk and stabilizing bridge structures.Future research should delve into quantifying the effects of various vegetation patterns and densities on flow characteristics and scour development.The findings hold substantial implications for flood risk management.Vegetation emerges as a key player in reducing flow velocity and scour depth, thereby enhancing flood resilience and decreasing the risk of bridge failure due to erosion.Engineers can leverage this information to inform the design and maintenance of structures in flood-prone areas, considering vegetation management strategies to bolster flood resilience.

Figure 1
Figure 1.a) The schematic view of the experimental, b) the distribution of overall vegetation upstream of the bridge pile, c) the distribution of patch vegetation upstream of the bridge pile and figure d) the density of used vegetation channel.

Figure 2 .
Figure 2. Contour map of scour profile for single pile a) in without vegetation case, b) in the presence of overall vegetation case and c) in the presence of patched vegetation case.

Figure 3 .
Figure 3. Reynolds shear stress distribution profile for single pile a) in without vegetation case, b) in the presence of overall vegetation case and c) in the presence of patched vegetation case.

Figure 4 .
Figure 4. Probability of occurrence of quadrant classes profile for single pile a) in without vegetation case, b) in the presence of overall vegetation case and c) in the presence of patched vegetation case.

Figure 5 .
Figure 5.The sample of A group event of octant analysis: a) the Op results; b) the St in free-vegetation case.

Figure 6 .
Figure 6.The sample of B group events of octant analysis: a) the Op results; b) the St in free vegetation case.

Figure 7 .
Figure 7. Schematic diagram of dominant phenomena upstream and downstream of the bridge pile a) in without vegetation case, b) in the presence of overall vegetation case and c) in the presence of patched vegetation case.

Table 1 .
Geometric characteristics of sediment particles used in this research.

Table 2 .
A quadrant plane in the trigonometric coordinate system.

Table 3 .
Eight bursting event classes in 3D octant analysis based on the sign of velocity fluctuations.