Efficacy of the Combined Use of Bed Sill and Sacrificial Piles to Control Local Scour around Circular Bridge Piers

,


Introduction
Estimation of scour around a pier is one of the most important and challenging issues in hydraulic engineering.Te bridge pier, as a barrier against the stream fow, causes the fow separation.Due to this separation, the stream fow, as a result of passing over the sides of bridge piers, causes local scouring around the pier [1].Local scouring has been reported as the main cause of the failure and instability of many bridges [2][3][4][5].Terefore, investigation of the scour phenomenon and the ways to control it seems to be necessary for the safer design of bridges.Te main mechanisms of local scour include downfow, horseshoe vortex, and wake vortices.To control the negative efects of these factors on local scouring, two methods of bed armoring countermeasures and fow-altering methods have been proposed in the literature [6][7][8][9].In this study, two countermeasures (bed sill and sacrifcial piles) of the fow-altering methods were combined and evaluated.

Combinations of Scouring Countermeasures in Previous
Literature.Te bed sill is placed as a barrier against sediment transport downstream of the pier to prevent the scour development and reduce the erosive force of wake vortices.Sacrifcial piles are piles serving as a protection factor in the upstream of the pier; they themselves are exposed to scour to protect the bridge pier against local scour.In the past, these countermeasures have been used individually, for example, Grimaldi et al. [10] and Tafarojnoruz et al. [8] for bed sill and Melville and Hadfeld [6] and Haque et al. [11] for sacrifcial piles.
Te combined countermeasures have been investigated in the previous studies [12,13].However, among the combinations of countermeasures that have been implemented, the inappropriate combination of two countermeasures, rather than each countermeasure, may not have a signifcant efect on reducing scour depth.Table 1 presents a summary of the results of some past studies in relation to the combination of countermeasures.In this table, the term r de (%) is defned as the percentage reduction of the pier scour depth.Tree modes could be distinguished for the combination of two countermeasures, as compared to each alone.Te combination of two countermeasures may not be efective at all, be less effective, or be quite efective.A combination is quite efective when the efciency of the combined countermeasures is almost close to the sum of the efciency of each individual countermeasure and/or even greater than their sum.For example, the combination of sacrifcial piles and collar [13] is not efective at all; meanwhile, the combination of slot and bed sill [10] is less efective, and that of cable and collar [7] can be quite efective (according to Table 1).Te conducted investigations show that the combination of countermeasures is of great importance in reducing scour depth.According to Table 1, most of the combined countermeasures are quite efective, but the combination of some countermeasures is not efcient.Terefore, one should be very careful when choosing them..To the authors' knowledge, a combination of BSSP has not been studied for reducing local scour at bridge piers.In this paper, we present the results of an experimental study.
Investigations showed that the combination of sacrifcial piles with countermeasures such as collars, pier slots, and cable was not efective in reducing the local scour (Table 1).Te literature results are not strictly comparable, for example, in order to establish if sacrifcial piles have a greater efciency when combined with other countermeasures.Te efciency of sacrifcial piles can decrease in oblique fow [6,26,27].Experiments conducted by Melville and Hadfeld [6] and Chiew and Lim [26] revealed that sacrifcial piles lose their efectiveness to a large extent under high fow velocities, i.e., for U > U c .Piles cannot be reliable during typical food conditions [28].Tere is no guarantee that there will be a complete elimination of local scour.Terefore, further research is needed to confrm the potential efectiveness of this countermeasure.Te principal objective of this study was to evaluate the efectiveness of sacrifcial piles as a function of (N P D P /D) and (α), where, N P D P / D � blockage ratio of sacrifcial piles and α � angle of the wedge and of the combined countermeasures, composed of sacrifcial piles and a bed sill downstream of the pier (Figure 1).

Turbulent Flow
Structure.Te results of the previous studies have shown that research has mainly focused on determining the scour depth and how it can be controlled.In addition, although there have been studies on the evaluation of the complex fow structure around the pier, more research is needed.Some researchers have tried to understand the complex fow structure, but this feld still needs more research [25,29,30].Keshavarzi et al. [31] used the 3D analysis of the bursting process (octant analysis) to investigate the fow structure around the bridge pier.It should be noted that 2D and 3D bursting processes have been used on ripples as well as in meandering channels [32][33][34].
Multiple studies were performed in an open channel using 2D quadrant analysis.However, the fow around the piers is fully 3D [31].Terefore, the technique used in this study (octant analysis) provides more resolution to the efect of transverse velocity fuctuations in the sediment particle entrainment process.Although Keshavarzi et al. [31] investigated the characteristics of turbulent fow around a single bridge pier using three-dimensional analysis of bursting processes, to the writers' knowledge, in the literature, the coherent turbulent fow structure in the pier combination with BSSP has not been investigated.Te objective of this study is to provide a better understanding of the 3D fow around this model, the interactions between its elements, and their efects on this fow feld.Here, after determining the efciency of the best type of combination of BSSP, experiments were conducted with the aim of obtaining the contribution of eight diferent bursting events.

Dimensional Analysis.
Te dimensional analysis presented in this section is used to discuss the efect of dimensionless groups on local scour depth.For a smooth circular pier with countermeasures, the relation between the local scour depth at the bridge pier d s and its dependent parameters can be expressed as follows: 2 Shock and Vibration where   Shock and Vibration where F P � U/ ��� gD  � pier Froude number, y/D � fow shallowness, ρ s ′ /ρ � submerged sediment specifc gravity, D/d 50 � sediment coarseness, σ g � sediment nonuniformity, U/U c � fow intensity, B/D � sidewall efects, Ut/D � time scale for the scour development, N P D P /D � blockage ratio of sacrifcial piles, α � angle of the wedge, and β � deviation angle between the approach fow and pier axis (skew angle).
Te following considerations can be applied to determine the efect of dimensionless groups in equation ( 2): (1) if y/D ≥ 2.5, shallowness efects are insignifcant and can be ignored [26,35], (2) for sand and gravel, Δ � ρ s ′ /ρ is almost constant and equal to ≈1.65, (3) for uniform sediment with σ g <1.5 and 25 ≤ D/d 50 ≤ 130 can be maximized as d s [27], (4) if U/U c ≈1, the maximum scour depth is obtained under clear-water fow conditions, (5) if B/D ≥ 10, the channel sidewall (or blockage) efects on the local scour, which is due to the pier presence, are ignored [26,36], (6) for the bed sill attached to the back of the pier, L bs /D is practically inefective, (7) in the pile arrangement, D P , S P and X are assumed to be constant and there is no β, and (8) in this study, the constant fow conditions were considered, so Fr is constant.According to the abovementioned considerations for the present study, the dimensionless local scour depth in equation ( 2) becomes simple which is described as follows: At equilibrium, the variation of d s /D against time is almost negligible, so Ut/D is practically inefective.To maximize the efciency of the two countermeasure combinations, such as bed sill and sacrifcial piles, particular values should be considered for the dimensionless groups, which will be explained in the subsequent sections.

Experimental Setup and Procedure.
Te experiments of this study were carried out in a glass fume with a recirculating fow system in the hydraulic laboratory of the Isfahan University of Technology.Te foor and side walls of this fume were made of glass.Tis helped us to have a better side view of the fow and sediment movement in the fume.Te fume consisted of a rectangular cross-section with a foor width of 0.9 m, a height of 0.6 m, and a length of 15 m.
It should be noted that an electromagnetic fow meter and a point gauge were used to measure the discharge and the fow depth, respectively.A tailgate at the downstream end of the fume was also used to control the fow depth.Te length of the test section was 3 m, which consisted of 3 sections 0.18 m deep.A recess (middle section) of one meter length was embedded between two upstream and downstream Tefon plates (where the pier was located).Te upstream Tefon plates were installed at 0.16 m above the fume bottom and covered with sediments up to 0.02 m.Te downstream Tefon plate was considered to be fush with the bed (deep � 0.18 m) for the full development of the bed morphology.Te pier was mounted vertically on the fume bottom at a distance of 10 m from the fume inlet, where the fow was fully developed.Te fully developed fow region was determined by measuring the velocity profles along the fow from the fume inlet when no bed was installed in the channel.Te fully developed fow region is where there was no detectable change in velocity profles in the fow direction.Te recess was flled with the uniform sediment (d 50 � 0.77 mm and σ g � 1.06).A thin layer of uniform sand of the same size was glued over the false foor to roughen it.A 6 cm-diameter circular PVC was used as the pier model.According to Chiew and Melville [26], the pier diameter should not be more than 10% of the width of the channel to prevent the efect of the channel sidewalls on scour.Te pier was embedded at the centerline of the channel.All experiments were conducted in clear-water conditions, because the maximum scour depth in these conditions occurred at the threshold of the bed material motion [37].Te value of U was determined by preliminary tests before the pier was installed.Te experiments were carried out under fow conditions with constant fow depth and fow intensity.Te fow conditions in the experimental tests and dimensionless groups were considered according to Table 2. Tese could satisfy the conditions presented in the Dimensional Analysis section.U * c was calculated from the Shields diagram.Scour depth in front of the pier was measured by a meter attached to the pier body.Contraction scour was not observed in any experiment, since the scour holes were completely developed in the transverse direction.
In this study, the countermeasure of sacrifcial piles was used to reduce scour, and fnally, it was combined with the bed sill.Triangular and transverse arrangements of sacrifcial piles were used.Table 3 shows the geometric parameters of sacrifcial piles.A 1 cm-thick PVC as wide as the channel, fush with the bed and extended to the foor of the channel, was used as the bed sill.According to Grimaldi et al. [10] and Tafarojnoruz et al. [8], the best confguration of the bed sill is when it is attached to the back of the pier.In this study, the bed sill was attached to the downstream end of the pier according to the suggested best confguration.Te circular pier model, the arrangement of sacrifcial piles with geometric parameters, and the combination of BSSP are shown in Figure 1.
Fourteen experiments were performed.Te scour depth was measured in both unprotected and protected piers for comparison.A summary of the experiments and various combinations of the sacrifcial piles' group and bed sill with their geometric parameters and efciency are given in Table 4. Te frst column shows the name of the test.Test C1, which was for the pier without countermeasures, was used as the reference to evaluate the efectiveness of the countermeasures.Te experiments were designed based on neglecting the efect of side walls, sediment particle size, fow Shock and Vibration viscosity, and fow shallowness, as described in the previous section.Te percent efciency of BSSP at the end of each test, r de can be calculated by the following equation: where d se0 and d se are the equilibrium scour depths in front of the unprotected and protected piers, respectively.Also, d se0 and d se were measured at the end of each experiment.
According to the literature, there are various criteria to identify the equilibrium conditions [38][39][40][41][42][43].However, in general, it takes several days to achieve an acceptable equilibrium scour depth.Terefore, in this study, all experiments were not continued until reaching the equilibrium state.Te duration of stopping the experiments was determined as follows.
First, a relatively long experiment (36 hours) was performed (Figure 2).Ten, using the following two standard criteria, the duration of stopping the experiments was obtained: (1) slope change in the semilogarithmic plot by plotting d s versus log t [39] and (2) it was found that 90% of the fnal scour depth occurred during the frst eight hours, which was consistent with the fndings of [44].Terefore, in this study, all experiments continued for 8 hours.

Flow Structure.
In this study, a 3D downward-facing ADV (accuracy ± 0.1 m/s) was used to measure the 3D velocity components at the pier centerline at a distance of 2 mm from the bed surface (Figure 3).Te ADV probe was placed 5.5 cm above the bed, and the velocities were measured in the sampling volume with a height of 5 mm and a diameter of 6 mm.Te velocity components in the centerline from upstream to downstream were taken frst for the unprotected pier (test C1) and then for the best combination of BSSP (Figure 4).Te sampling frequency was set at 200 Hz [45].Moreover, the sampling durations were assumed to be 120 s in order to have a statistically independent timeaveraged velocity, as done by Ge et al. [46].Velocity components were measured at each point with these settings.Measurements were made by a bed fxed at the end of the experiment.Investigation of the fow structure was performed by removing the weakly measured data.For this purpose, the data were fltered by the WinADV software.Two parameters, including signal-to-noise ratio (SNR) and correlation coefcient (COR), were constantly controlled during the experiment to collect good data.In the best ranges, to provide good data, SNR and COR should be greater than 15 dB and 70%, respectively [31,47,48].Tese values were applied to flter the data in the WinADV software.In addition, the flter provided by Goring and Nikora [45] has been used for phase-space threshold despiking to detect and eliminate the spurious data.

Turbulence Characteristics.
Velocity components were measured in three directions: streamwise or x-axis (u-velocity), transverse or y-axis (w-velocity), and vertical or z-axis (v-velocity).Turbulence characteristics could be determined and investigated by velocity fuctuations.Te following relations are defned for the velocity fuctuations u′, w ′ , and v ′ : ( Te temporal-averaged velocities are determined by using the following relationships: Turbulence characteristics have multiple parameters.Here, turbulent kinetic energy and Reynolds' shear stress will be reviewed.Te total turbulent kinetic energy of the fow (TKE xyz ) is defned according to the following equation.TKE relationships in diferent directions are also given here:     Shock and Vibration 7 Reynolds' shear stress in the xz and yz planes is calculated as follows:

3D Analysis of Bursting
Events.3D bursting events include eight types of events, which are classifed into class A (internal) and class B (external).Te classifcation of these events is performed based on the sign of the velocity fuctuations, as presented in Table 5.
Based on octant analysis, 3D bursting events exist in 8 octant zones.P k is calculated based on n k , and "k (subscript) represents each octant zone (k � 1-8)": Occurrence probabilities alone are unable to determine and diagnose the state of sediment entrainment, so it is necessary to determine the transition probabilities.Based on eight events of the 3D bursting process, 64 probable movements can be considered.A change in the situation from one zone to the same zone or another zone in a time series is defned as movement.Te movement of events is determined based on the Markov process.According to the Markov process, the transition probabilities of events from zone i to zone j in a time series from t to t + 1 are determined by using the following relationship: where Considering the abovementioned defnition, 64 probable movements can be recognized for each point.Figure 5 shows the matrix view of 64 probable movements.

Validation of Local Scour Depth Results.
A review of the related literature shows that to improve the design of bridges, eforts have been made to understand the scour phenomenon and temporal variation of scour depth around the bridge piers [5,7,41,49].Some researchers have also proposed relationships to estimate the scour depth at different times [41,50,51].As can be seen in Figure 6, the comparison of the temporal variations of the experimental values of d s /D and the values calculated from these equations can be seen.A good agreement between the results of the present study and those of Barkdoll [50] and Guo [51] was observed at the equilibrium time.Te fndings showed that a high percentage of scour depth occurred in the early 8 Shock and Vibration hours.According to Ettema [35], the scour process consists of three separate phases, including the initial phase, the principal phase, and the equilibrium phase.In the initial phase, the most intense state of scour formation occurs.Te diference in the results could be attributed to the diferences in diferent experimental conditions, including fow intensity (U/U c ).

Performance of the BSSP.
As can be seen in Table 4, the test results at the same fow conditions for all tests are expressed in terms of percentage scour depth reduction and compared to the pier without countermeasures.In clearwater conditions, the scoured sediments around the sacrifcial piles are partially deposited around the pier, leading to a reduction in the scour depth around the pier and consequently, increasing the efciency [8,11].In the combination of two countermeasures, the performance is better when the protection mechanism of one device also supports the other device [9].According to Table 4, the simultaneous combination of BSSP had good efciency in reducing the local scour depth and could be quite efective.Te efciency of this combination was approximately equal to the sum of the efciency of each individual countermeasure.Te good efciency in the results obtained from the combination of these two countermeasures could be attributed to the good interaction between these two countermeasures.Te strength of the wake vortices at downstream of the pier is reduced by the bed sill.On the other hand, the wake vortices created behind the piles have low erosive power and transfer fewer sediments to the back of the pier.Tus, these two wake vortices together have led to a far greater scour depth reduction than any individual countermeasure.Te results of Table 4 show that the combination of BSSP can be considered as an efcient combination to reduce the local scour.
Field applications of countermeasures have several problems, which can limit their practical use.Among these problems, we can point out the accumulation of foating debris around the sacrifcial piles, which afects the performance of the piles.Rivers carry appreciable quantities of foating debris during foods.Such material accumulates in the form of large masses around the sacrifcial piles, sometimes referred to as debris rafts.Additional fow obstruction causes scour depths in excess of the scouring depth of the pier without pile [28,52].Terefore, debris accumulation reduces the efciency of sacrifcial piles.In the literature, there are several studies that have investigated the efect of debris accumulation [53][54][55].It should be noted that in this study, the efect of debris accumulation on the efciency of sacrifcial piles was not studied.
Te efectiveness of sacrifcial piles is dependent on the number of piles, the diameter of piles, partial or full submergence, fow intensity (U/U c ), geometric arrangement in relation to each other, and bridge pier [6,9,28].Te results show that with the increase in pile numbers, the performance decreased for both individual sacrifcial piles and their combination with bed sill.Melville and Hadfeld [6] showed that by increasing the number of piles in the same arrangement, the performance increased from 48% to 56%.

Shock and Vibration 9
Meanwhile, Tafarojnoruz et al. [8] found that the performance was decreased from 32.2% to 5.5% with increasing the number of piles in the same arrangement.By increasing the pile number, the wake region produced by the sacrifcial piles was enlarged, and local scour reduction was expected to be improved [9].However, the piles should be placed such that the piles that are rear can be on the edge of the wake region of an upstream pile [6].In this case, the width of the wake of the entire group is increased, and as a result, the local scour reduction is improved; otherwise, we will witness the opposite result.Tis is because when the rear piles are not placed on the edge of the wake region of an upstream pile, the high-velocity fow enters the regions between the piles, afecting the pier.Tus, the performance decreased.Te results, as represented in Table 4, showed that increasing the wedge angle decreased the efciency.In an arrangement with the same number and the same spacing between piles and bridge pier, when the wedge angle was increased, the transverse edge-to-edge distance of the rear piles with the upstream piles was raised too.As a result, the fow could easily pass between the piles and afect the pier, thus reducing the performance of the piles.Melville and Hadfeld [6] also reported a decrease in the performance of piles with an increase in the wedge angle.
In past studies, the triangular arrangement of sacrifcial piles with the apex of the triangle pointing upstream has been considered one of the best confgurations among the other tested cases [6].According to Table 4, the highest and best efciency in the combination of BSSP was related to test C9, whose efciency was as much as 51.1% in front of the pier.Terefore, in the following sections, we focus on the fow structure around this combination (test C9).For comparison, the results of the pier without countermeasures (test C1) are included.Figure 7 shows the pictures related to the tests performed for C1 and C9.As in test C9, it can be seen that while the bed sill protects the pier, excess scouring occurs downstream (Figure 7(B3)).A similar problem was found when using the bed sill downstream of hydraulic structures [56,57].

Turbulent Kinetic Energy.
In this section, as in other subsequent sections, an investigation of the fow structure along the channel centerline (the pier centerline) from upstream to downstream has been carried out around the two models C1 and C9.Variations of TKE xyz along the centerline are shown in Figure 8.For comparison, the longitudinal variations of TKE x , TKE y , and TKE z are included.Right in the two positions in front and behind the unprotected pier, the TKE values in the transverse direction are higher than those in the longitudinal and vertical directions.Meanwhile, in the same position at the protected pier (the position between the pier and sacrifcial piles), the TKE values in the longitudinal direction are higher than those in other directions.Terefore, using the simultaneous combination of BSSP decreases the transverse efect of velocity on the sediment particle entrainment; it also reduces the local scour depth in front of the pier.It also impedes the development of a scour hole in front of the pier.A signifcant decrease in TKE xyz and TKE x values was observed in the downstream of the protected pier with BSSP compared to the unprotected pier.Similar results were also observed by Gerami et al. [25] and Nezhadian and Hamidifar [58].Te transverse component of the velocity has a signifcant value, i.e., in the downstream of the pier, a high shear layer is created and the fow is very turbulent [31].Te high TKE xyz in the downstream of the pier is directly related to the erosive sediment particles, which could be visible in the case of the unprotected pier in Figure 7(a).9. Reynolds' shear stress was signifcantly diferent from upstream to downstream for both the C1 and C9 models.Te results obtained for the downstream of both models, and for the position between the pier and sacrifcial piles, showed a diferent and signifcant trend; however, no signifcant variations were found for the upstream regions in both models.Due to the high turbulence in front and behind the pier, Reynolds' stress was increased in the C9 model.Te results, thus, showed that when the fow is very turbulent, the shear stress is high.A 3D analysis of bursting events was also used to investigate various fow and turbulence characteristics with higher accuracy.

Occurrence Probabilities.
Te contribution of occurrence probabilities related to the points near the bed for the two models C1 and C9 is shown in Figure 10.For the position in front of the pier, the highest occurrence probability for unprotected and protected piers is related to events IV-A and II-A, respectively.Terefore, the use of BSSP caused sediments to be suspended and inclined to move to the upper edge of the scour hole, until they would move towards the downstream side of the pier; as a result, the scour depth could be decreased.Te results obtained for the upstream of the pier showed that the sweep and ejection events had increased while approaching the pier.
According to Figure 10(d), events II-A, IV-A, II-B, and IV-B have the highest occurrence probability and events I-A, III-A, I-B, and III-B have the lowest occurrence probability.Te increase in ejection and sweep events in two classes A and B downstream of the pier could be mostly due to the formation of two symmetrical scour holes downstream of the bed sill.According to the obtained results, although the occurrence probabilities of events causing sediment transport increased in the region between the pier and sacrifcial piles, as well as downstream of the pier, eventually, the simultaneous combination of BSSP efectively reduced the scour depth in front of the pier.Tis is because the sediments scoured from around the sacrifcial piles were deposited on inside the scour hole in front of the pier.On the other hand, the bed sill, by reducing the strength of wake vortices behind the pier, could reduce the transport of sediment from the front of the pier to the back of the pier.As a result, the scour depth could be reduced by using a simultaneous combination of BSSP.
Figure 11 shows the occurrence probabilities' contribution in classes A and B. Te highest average occurrence probabilities in the upstream of both models were related to event II-A.In the downstream of the pier, the highest average occurrence probabilities for the C1 and C9 models were related to III-A and II-A events, respectively.Ejection events produced pulses with a low speed from the boundary layer into the main fow towards the water surface and against the fow direction.Inward interaction events could

Transition Probabilities.
Based on the sign of the velocity fuctuations at a moment of time, one of the events of the bursting process could occur.Transition probabilities in octant analysis are classifed into 64 sections; each of these sections shows the probability of movement from one state to another.By using the Markov process, the transition probabilities in these 64 sections were determined for points near the bed in the centerline of the C1 and C9 models.For the upstream and downstream of these two models, the average transition probabilities were determined separately.Te results of the average transition probabilities are presented in Tables 6-9 for the upstream and downstream of the C1 and C9 models, respectively.According to the 64 probable movements, three specifc movements (marginal movement, cross-movement, and stable movement) were recognizable [31,34,59].Marginal movements such as II-B ⟷ III-B, cross-movements such as II-B ⟷ IV-B, and stable movements such as II-B ⟷ II-B could be observed.Stable movement occurs when each of the eight octant zone events at time (t) stays in the same zone after a one-time step (t + 1).Tis type of movement has the highest transition probability (Tables 6-9).Terefore, this section focuses on the transition probabilities of stable movement.Tese results are consistent with those of the previous studies [25,31,60].Te highest transition probability in the upstream of both C1 and C9 models was related to stable movement II-A ⟷ II-A (Tables 6 and 7); meanwhile, in the downstream of the pier, the highest transition probability for the C1 model was related to I-A ⟷ I-A (Table 8); for the C9 model, it was related to II-A ⟷ II-A (Table 9).Tese values are bolded.Te transition probabilities of stable movement in the upstream of the pier for the C9 model were decreased as compared to the C1 model; meanwhile, in the downstream of the pier, except for I-A ⟷ I-A and I-B ⟷ I-B movements, the transition probabilities of stable movement for the C9 model were increased, as compared to the C1 model.Examination of the results showed that the events with the highest occurrence probability also had the highest stable transition probability.It could also be stated that the occurrence probabilities alone may not be able to determine the situation of bursting events.Terefore, the results of the transition probabilities could be regarded as a complement to the results of occurrence probabilities, but in this study, it does not help much to investigate the sediment condition and their type of movement.In addition, as can be seen in Figure 12, the longitudinal variations of the stable transition probabilities from the upstream to the downstream of both pier models could be seen.

Conclusions
Tis study investigated the combination of two countermeasures (BSSP) in terms of efciency.It was found that this combination was quite efective in reducing scour depth.Te best confgurations of BSSP showed an efciency of 51.1% in reducing the local scour depth.Te combination of BSSP could be, therefore, recommended as a suitable solution in design and construction to reduce the local scour.

Shock and Vibration
In order to investigate the complex fow structure and how it could afect the scour mechanism, the coherent fow structure was carried out at the points near the bed from the upstream to the downstream of the C1 and C9 models.A 3D analysis of the bursting process was used to identify the most probable bursting events.It was found that the stable transition probabilities, among other movements, had the highest transition probabilities.Also, the results showed that the event that had the highest occurrence probability also had the highest transition probability.Te efect of the simultaneous use of BSSP on the reduction of the scour depth was confrmed by the results obtained from the investigation of the fow structure [61].Instantaneous velocity in the streamwise direction u ′ : Velocity fuctuation in the streamwise direction u:

Notations
Temporal average velocity in the streamwise direction v i : Instantaneous velocity in the vertical direction v ′ : Velocity fuctuation in the vertical direction v: Temporal average velocity in the vertical direction w i : Instantaneous velocity in the transverse direction w ′ : Velocity fuctuation in the transverse direction w: Temporal average velocity in the transverse direction X: Displacement distance y: Flow depth α: Angle of the wedge β: Deviation angle between the approach fow and pier axis (skew angle) ρ: Water density ρ s ′ : Submerged sediment density ]: Kinematic viscosity of water σ g : Geometric standard deviation ( �������� (d 84 /d 16 ) ).

Figure 2 :
Figure 2: Time development of scour to determine the equilibrium time.

Figure 4 :
Figure 4: Measuring positions of velocity components from upstream to downstream of the centerline: (a) test C1 and (b) test C9.

Figure 6 :Figure 7 :Figure 8 :
Figure 6: Temporal variations of the local scour around unprotected pier (C1) and comparison with other studies.

Figure 9 :Figure 10 :
Figure 9: Longitudinal variation of Reynolds' shear stress in the channel centerline for the unprotected pier (test C1) and protected pier with bed sill and sacrifcial piles (test C9): (a) RSS xz and (b) RSS yz .

Figure 11 :
Figure 11: Average occurrence probabilities in the channel centerline for (a) upstream of C1, (b) upstream of C9, (c) downstream of C1, and (d) downstream of C9.

Figure 12 :
Figure 12: Longitudinal variations of the stable transition probabilities in the channel centerline for (a) unprotected pier (test C1) and (b) protected pier with bed sill and sacrifcial piles (test C9).

Table 1 :
A summary of the results of the combined countermeasures.

Table 2 :
Experimental conditions and dimensionless groups.

Table 4 :
Details of various combinations from the group of bed sill and sacrifcial piles with geometric parameters and efciency.

Table 6 :
Average transition probability at upstream of the unprotected pier (test C1).In table, among the bolded values, these values have the highest value.

Table 7 :
Average transition probability at upstream of the pier with bed sill and sacrifcial piles (test C9).In table, among the bolded values, these values have the highest value.

Table 8 :
Average transition probability at downstream of the unprotected pier (test C1).In table, among the bolded values, these values have the highest value.

Table 9 :
Average transition probability at downstream of the pier with bed sill and sacrifcial piles (test C9).In table, among the bolded values, these values have the highest value.
Scour depth at the end of the test for protected pier d se0 : Scour depth at the end of the test for