Scour Mitigation at Bridge Abutments Using Spur Dikes Scour Mitigation at Bridge Abutments Using Spur Dikes

One of the main reasons for bridge failure is local scour at the bridge abutments. For protection of existing bridge abutment laboratory experiments, under clear water scour condition, were carried out to investigate scour reduction around the vertical bridge abutment by adding one upstream spur dike. Sand with a median and geometric standard deviation of diameter equal to 0.80 mm and 2.27, respectively, formed the bed material. Three different stages of spur dikes with varying sets, i.e., distances from the abutment, orientation angles, and lengths were considered. Each set of the considered spur dike was studied under nine ﬂ ow conditions, three approach ﬂ ow depths with three Froude numbers, with 99 experimental runs in total. Empirical equation was developed for each set between the relative scour depth and the Froude number. In addition, four dimensional equations were developed for each stage, to represent different relative dimensions of the scour hole. It is concluded that using spur dikes leads to good reduction on scour depth at the abutment. Maximum reduction in the scour depth, with percentage 81.56%, is observed for spur dike set with touched distance of the ﬂ ume wall, between abutment and spur dike, of three times the abutment length, orientation angle of 90 (cid:1) , and spur dike length normal to ﬂ ow direction equals the abutment length. The scour is just shifted from the vicinity of the abutment to the vicinity of the spur dike. Moreover, the scour area is increased at the vicinity of the spur dike in some cases.


Introduction
S COUR is a phenomenon that occurs around the foundations of the structures naturally.It is the removal of the sediment particles away from the bed by the flowing water, causing a significant decrease in the original bed level named by the scour depth.Scour occurrence at the hydraulic structures' foundations may cause possible collapses of these structures, Klingeman and colleagues (Klingeman et al., 1984).Melville and Coleman (2000), stated that scour process that can occur at a crossing bridge is classified into three types (general scour, contraction scour, and local scour).Localized scour which is referred to as general, contraction, and local scour can occur collectively.Melville and Coleman (2000), Coleman and colleagues (Coleman et al., 2003) and Arneson and colleagues (Arneson et al., 2012), showed that at crossing structure, the acceleration of flowing water and vortices lead to sediment removal from the scour hole.In the case of clear water scour, there is no transport or movement of bed soil from the upstream reach to the scour hole.It occurs under condition, V/Vc less than 1, where V is average approach flow velocity and Vc is critical flow velocity required for motivating the bed particles.When flow passes through a pier, the vortex systems, i.e., the primary downflow, the horseshoe vortices, and the wake vortices, cause local scour at the pier, Melville and Coleman (2000) and Li (2005).Complicated interactions between the bed material and the vortices are the main reason for scouring at abutments, Li (2005).Dogan (Do gan, 2008) stated that different countermeasures are usually used for the purpose of controlling abutments instability.They protect the foundations of the abutments from the scour, also they keep and rehabilitate the past-built abutments against excessive re-scouring.The selection of the optimum countermeasure that either for protecting a new structure or rehabilitation of an old existing structure, depends on the site case, functional sides, and the mechanism of the flowing water.Li (2005) and Kothyari and Ranga Raju (Kothyari and Ranga Raju, 2001) explained that the local scour patterns at bridge abutments and spur dikes are very similar, because they have comparable river configurations and are essentially similar buildings.The maximum depth of scour at vertical flat plates, without overtopping flow, occurs at the structure's tip.The geometry of the scour hole may change for more complex spur dike shapes with overtopping flows.Kothyari and Ranga Raju (Kothyari and Ranga Raju, 2001) used the parameters affecting the flow drag forces around a spur dike to conclude a function for determining the diameter of analogous pier.Using the abundant information of scour around piers, the scour around the spur dike can be estimated.
Copeland (1983) indicated that the objectives of using spur dikes as river training are to promote navigation, defined erodible banks and enhance flood control.He showed that the spur dikes oriented downstream are better than the spur dikes oriented upstream.He also noted that, when providing bank protection, the projection length of the spur dike is more influential than the spur dike orientation angle.Schaaf (1953), Richardson and Simons (1973) and Kuhnle and colleagues (Kuhnle et al., 2002) indicated that due to the small impact caused by spur dikes orientations, they are usually considered perpendicular to the channel.Zhang and colleagues (Zhang et al., 2009) explained in 3dimensional details, both numerically and experimentally, the different types of vortices around a spur dike.
Karami and colleagues (Karami et al., 2011) studied reducing scour at three existing series of consecutive parallel spur dikes by using an additional upstream spur dike with different lengths, upstream distances, and angles.Spur dikes were perpendicular to the flow alignment, and had a length (L f ) of 25 cm.The studied parameters were the length of the protective spur dike (L P Þ, its space from the main spur dikes (X p ), and the protective spur dike's angle with respect to the wall of the flume (q), the diameters of the uniform bed sediments, and flow intensity.It is concluded that using a protective spur dike leads to significant reduction on scour depth, where the set of spur dike , 90 ] is the optimum sets.The same experiments are used to verify a 3-dimensional numerical model of the problem Karami and colleagues (Karami et al., 2014), and to predict the temporal scour depth at the preexiting spur dikes using the artificial neural network Karami and colleagues (Karami et al., 2012).
Recent study of temporal scour depth at a spur dike, using experiments and literature data, for nonuniform mixture bed were presented by Pandey and colleagues (Pandey et al., 2021).Later, the experiments of Karami and colleagues (Karami et al., 2011) were extended and used to find optimum parameters of the protective spur dike, by learning two support vector regression methods with the experimental data Basser and colleagues (Basser et al., 2014), and by using a combination of particle swarm method and adaptive network based fuzzy inference system Basser and colleagues (Basser et al., 2015).
Zhang and colleagues (Zhang et al., 2012) studied the effect of bed heterogeneity on characteristics of the scour hole at a spur dike, and they concluded a linear reduction on the maximum scour depth with increasing the geometric standard deviations of the bed material.Bahrami-Yarahmadi and colleagues (Bahrami-Yarahmadi et al., 2020) found that the upstream triangular protective spur dike produces a lesser value of the maximum scour depth than the rectangular one, in case of protecting a series of existing three identical parallel consecutive spur dikes.Optimal upstream distance of the protective spur dike, from the first downstream spur dike, is found to be 5.5 the exiting spur dike.
Kadota and colleagues (Kadota et al., 2010) showed that the formation of a spur dike in plan and the elapsed time are critical factors.Numerical analysis is used to examine the effects of different Lshape, T-shape, and straight spur dike directions on mean flow structures and instantaneous coherent flow, the results indicate that L-shaped groins, which have significant sand wave forms downstream, have more variations in coherent patterns than the other shapes.
Delavari and colleagues (Delavari et al., 2022) performed laboratory experiments to evaluate the scour depth at the bridge abutment using a protective spur dike with various distances and lengths that are located at the upstream corner of the abutment.The methodology used for predicting the scour depth is the group method of data handling (GMDH), nonlinear regression method (NLR), and neural networks Multilayer Perceptron (MLP).
The previous papers show that many researchers have investigated different sets of spur dike as a countermeasure at a bridge abutment or a series of spur dikes against scour, but these studies concluded different sets for the optimum protective spur dike.For all previous works, scour has just shifted from the vicinity of the protected abutment/ spur dike to the vicinity of the protector spur dike, with a possibility of increase in the scour hole maximum depth in some studies.Therefore, the major objective of this research is to identify the optimal set of spur dike as a countermeasure to limit local scour at the vertical wall bridge abutment using laboratory experiments, under clear water scour condition and nonuniform bed material.Three parameters are studied as: 1) longitudinal distance between the spur dike and the abutment, 2) downstream orientation of the spur dike, and 3) its length.However, during the process of the present work, a semi-similar one was conducted by Bhatia and Setia (2021) for uniform bed material with diameter and geometric standard deviation of 0.28 mm and 0.6, respectively.They studied only two parameters, i.e., the spur dike length and its upstream location, with maximum run duration of 5 h and contraction ratio of 11.6%.

Experimental work
The hydraulic experiments were conducted at the Laboratory of Irrigation and Hydraulics Department in the Faculty of Engineering, Mansoura University, Mansoura, Egypt.The experiments were carried out in a horizontal straight flume with rectangular cross section.The flume was 1000 cm long, 74 cm width, and 40 cm depth.The bed and the sides of flume were covered by Epoxy material to close the voids and the pores between the steel plates, composing the bed and the vertical sides of the channel.The layout of the flume is shown in (Fig. 1).There were two centrifugal pumps; the maximum capacity for both pumps was 47.015 Lit/sec.The re-circulating water was lifted by the two pumps from the sump across two delivery pipes to the two tanks to supply the flume with a prespecified flow.These two tanks were used to deliver the discharge of water to the flume across a rectangular weir.
At the upstream of the flume, especially at the outlet of the second tank, there was a rectangular weir which was used to measure the water discharge.A double screen was installed downstream of the approaching basin and filled with gravel to reduce flow turbulence.Also, to reduce the effect of disturbance, there was an inclined wood side behind the double screen.At the downstream of the flume, there was a tail gate which was used to control the depth of water whether by increasing or decreasing the gate crest by using a screw wheel.For the process of measuring, a point gauge with accuracy of 0.1 mm was installed on the carriage.So, the point gauge could measure in X and Y axes horizontal directions, where the carriage had two scales that were perpendicular to each other.The first scale was parallel to the axis of flume; consequently, it could measure the longitudinal positions (X-axis direction).The second scale was in the transversal direction (Y-axis direction); consequently, it could determine the measurements of Y direction.The length of the flume under study was covered with sand of 15 cm thickness.A sand trap was installed at the flume's downstream end to prevent sand movement from the flume to the underground tank.By a sand bed preparing tool, the sand was initially flattened before the onset of every run.At the beginning of every run the flume was gently filled with water, to saturate the bed material, using a tab to the prespecified water depth.Then, starting the pump to the required discharge and using the downstream tail gate to adjust the required water depth.On the other hand, at the end of each run the water was drained gradually to prevent any movement of the sand particles.
Two runs were carried out, at maximum examined values of the Froude number (i.e., F r ¼ 0.34, 0.31, respectively), to determine the required time to reach the steady state of the scour hole dimension.Most of the total scour depth, 85%, was formed during the first 80 min, and 90e93% of scour was noticed to occur in the first 2 h.Measurements were taken every 20 min until the steady scour depth was reached.After 4 h, the equilibrium condition was assured, and the scour hole characteristics stabilized.The change in the scour with elapsed time is indicated in (Figs. 2 and 3) for the first and the second runs, respectively.
The length of the study flume was covered with sand that was 15 cm thickness, d 50 was equal to 0.80 mm.Sieve analysis for the sample of sand is presented in (Fig. 4).Soil classification was as follows: 0.60 mm less than d 50 ¼ 0.8 mm less than 2.0 mm, therefore description of the soil was coarse sand (CS) according to particle size classification (M.I.T. classification), where d 50 was diameter that passed 50% of the bed particles.The uniformity coefficient (C u ) which showed the variety in particle sizes of the soil and was presented as C u ¼ d 60 / d 10 ¼ 1.00/0.21¼ 4.762 greater than 4. Thus, the soil was classified as well graded according to Unified Soil Classification System (USCS); therefore, the soil of the study was well graded sand 'WS'.The geometric standard deviation of the non-uniform sand, 27.In this study, three water depths (Y) in combination with three discharges (Q)/Froude numbers, were performed for each examined set of the spur dikes.Also, all experiments were achieved under steady clear water scour condition, where the considered discharges were 28.11, 24.36 and 20.80 Lit/sec.For determining a specific water depth, it was adjusted to get a ratio of bed shear velocity to critical velocity less than one to satisfy the clear water condition (V/V a < 1.0).Melville and Coleman (2000) suggested the following formulas, which used in the present work to determine V a : Where, d max ¼ maximum particle size, V ¼ mean velocity of flow, u * c ¼ the critical shear velocity for d 50 , V a ¼ the critical mean velocity for transition from clear water condition to live bed for non-uniform sediments, y ¼ approach flow depth, and V c ¼ critical mean approach velocity for transporting flow or velocity at the condition of sediment transport threshold.(Table 1) illustrates different data used throughout the experimental sets.

Physical models and experimental procedures
All the models in this study were made of wood and were coated with a varnish as a glue material to keep the pores closed and prevent water infiltration.In all sets the top of the vertical wall bridge abutment and all spur dikes were higher than the water surface.
The Abutment Model: was a vertical wall bridge abutment (i.e., the reference case which intended to be protected) and its results were used to determine the changing ratios in the scour hole dimensions.The abutment was fixed to the flume perpendicular to flow direction and placed vertically in the middle of the right wall of the channel.The abutment had a square face (16 cm Â 16 cm) with 35 cm height.The abutment protruding length was adjusted to be 0.22% of the channel width (74 cm).This ratio was safe for the abutment not to be exposed to contraction ratio, Manual et al. (Manual, 2002) and Masjedi and colleagues (Masjedi Alireza Dehkordi et al., 2010) (Plate 1), and (Fig. 5) show the vertical wall bridge abutment.
The First Stage: in this stage, spur dike with 16 cm length and 2 cm thickness was used as a countermeasure against local scour at the vertical wall bridge abutment.The first stage studied the effect of spur dike location with respect to the abutment on the scour hole.The values of the touched distance of the flume wall between abutment and spur dike (D s ) were L, 2L, 3L, 4L, 5L, 6L, where L ¼ projected length of abutment (16 cm).This stage was based on variation of the parameter, D s , and contained six sets (one set for each D s ), where each set consisted of nine runs, so the total number of the experiments runs was equal to 54 runs.This stage aimed to find the best, D s , which caused the lesser scour depth ratio, from the six sets, at the upstream corner of abutment.The best D s was considered for the subsequent second and third stages (Fig. 6).shows plan sketch for the first stage sets, and (Fig. 7) shows the spur dike dimensions as a countermeasure used in the first stage.
The Second Stage; in this stage, spur dike was used as a countermeasure against the abutment local scour with the parameter, D s ¼ 3L, corresponding to the best performance in reducing the scour depth within the first stage.The second stage studied the effect of spur dike orientation angle with respect to the abutment (q), where the flow perpendicular length of spur dike was fixed to be L ¼ length of abutment.This stage included four sets.The values of q ¼ 45 , 60 , 70 , and 90 (Fig. 8), illustrates the second stage.The flow perpendicular length of the spur dikes, used in the second stage had a constant    value equal to L. Consequently, different lengths of the spur dikes were determined corresponding to different angles of orientation q (Figs.9e11).show dimensions of the spur dikes corresponding to q ¼ 45 , 60 , 70 , which represent the seventh, the eight, and the ninth set, respectively.The tenth set had q ¼ 90 , which was the same as the third set in the first stage, see (Fig. 7).Therefore, the additional runs in the second stage were equal to 27.The set which achieved the best performance in reducing the scour depth was fixed in the third stage.
The third stage: sets in this stage were restricted to constant parameter D s ¼ 3L, from the first stage, and constant q ¼ 90 , from the second stage.The third stage studied the effect of spur dike projection length normal to flow direction ðL sp Þ, see (Fig. 12).The values of L sp were considered as 0.5L, 0.75L, and L. This stage included three sets, the additional two sets correspond to L sp ¼ 0.5L, and 0.75L, are represented in (Figs. 13 and 14), respectively.While the thirteenth set, corresponding to L sp ¼ L, was the same as the third set, see (Fig. 7).This stage was concerned with finding the best L sp in reducing the scour depth and needed 18 runs.

Dimensionless analysis
Dimensionless analysis is used to study the relationship between the different scour whole dimensions and other affecting parameters connected to the scour phenomenon.In this study, parameters are classified into dependent and independent parameters as follows: Dependent variables are the maximum depth of scour at the abutment (d s ), the upstream length of scour hole (L u ), the downstream length of scour hole (L d Þ, and the width of scour hole (L w Þ: These variables can be shown as a function of other independent parameters as follows: 1e Constant Characteristics: L ¼ length of abutment, B ¼ width of channel, K s ¼ abutment shape factor, S o ¼ slope of bed channel, and K g ¼ Geometry of channel. 2 e Geometry Applying the Buckingham p theorem to achieve maximum information from minimum number of experiments, enhance correlation between parameters, and after considering only the studied  parameters.The final dimensionless equations can be concluded as follows: where, F r ¼ V= ffiffiffiffiffi yg p , is the Froude number.The flow in the studied experimental runs is taken as a turbulent flow, consequently the effect of Reynolds number can be ignored. Empirical dimensionless equation, for each set in every stage, is derived to represent the relationship between the relative scour depth and the Froude number.Four general equations for each stage are developed to estimate maximum relative scour dimensions as, d s /y, L u /y, L d /y, L w /y, using the available software Statistical Package for the Social Sciences (SPSS).All these equations are shown in (Table 2) for the three stages.To check the accuracy of any equation, the statistical performance indices are used to check the different relative errors.The considered indices are: 1) mean absolute error (MAE), 2) root mean square error (RMSE), 3) mean absolute percent errors (MAPE), and 4) coefficient of determination (R 2 ), were determined as follows, Najafzadeh and Barani (2011) and Pandey and colleagues (Pandey et al., 2016): Where: N is the total number of observations,  Everitt and Skrondal (2010) showed that MAPE works best if there are no extremes within the data (i.e., the observed relative scour depths) and no zero of those data.Drudi and colleagues (Drudi et al., 2019) showed that MAPE indicator less than 10 % gives a high ability, 10 % less than MAPE indicator less than 20 % gives a good ability, 20 % less than MAPE indicator less than 50 % gives an acceptable ability, and MAPE indicator greater than or equal to 50 % gives unacceptable ability.
If there are some of the observed relative scour depths that have very small values that almost equal to zero, the MAPE indicator is skipped because it doesn't work accurately in this case of data.
Each flow discharge is treated with three different water depths, for a total number of flow discharges equal three.It is noticed from the experimental results from the three stages that there are some runs that caused sedimentation, instead of scouring, at the upstream corner of the abutment.This happened at some sets in these stages at lower values of the Froude number [Q ¼ 28.11 Lit/sec, y ¼ 15 cm, Fr ¼ 0.21], [Q ¼ 24.36 Lit/sec, y ¼ 13 cm, Fr ¼ 0.22], and [Q ¼ 20.80 Lit/sec, y ¼ 13 cm, Fr ¼ 0.19].The present work concerns with studying only the scour phenomena, consequently, runs that causes sedimentation at the upstream corner of the abutment are excluded from the analysis of the results.

Analyses of experimental results
The effect of the scour at the upstream corner of the abutment will be discussed in the present section.The maximum scour depths, d s , corresponding to the higher value of the Froude number (i.e., the worst scour case at Fr ¼ 0.34) are mentioned for all sets (Figs. 15 and 16).present scour hole measurements, where X is the flume's longitudinal direction cartesian coordinate, y is cartesian coordinate perpendicular to the direction of flow, the maximum scour depth at the countermeasure is (d c cm).

The result of the first stage
From the results of the first stage of runs, it is concluded that scour depth changes with changing the parameter (D s ), see (Table 3).The percentage of reduction in the scour depth with respect to the reference scour depth (i.e., the case of no spur dike as D s ¼ 13.88 cm), increases from 43.08% at D s ¼ L to optimum reduction 81.56% at D s ¼ 3L.As D s increases over 3L, the percentage of the reduction in the scour depth diminishes significantly to 13.62% at D s ¼ 6L.From the results it is obvious the distinguished improvement in the reduction of the scour depth within the first stage occurs at D s ¼ 3L, which is considered as a fixed parameter in the subsequent second and third stages.It can be observed that the change in D s has a pronounced reduction effect in  the scour depth with a final range from 11.99 cm to 2.56 cm.The scour along the longitudinal axis (X) of the flume at the upstream abutment corner, i.e., y ¼ 0, is presented at the maximum Froude number ¼ 0.34 as shown in (Fig. 17), for different sets of the first stage.For all the six sets maximum d s /y, along the longitudinal section, is always nearly found around the upstream spur dike.At the origin coordinate, i.e., X ¼ 0 and Y ¼ 0, minimum and maximum scour depths occur at D s ¼ 3L, 6L, respectively.The scour depth at the upstream tip of the spur dike is around 14 cm for the six studied sets.
Fig. 18 shows a good correlation between observed and calculated values of d s /y, using Eq. ( 20).Comparisons between sets consisting of the first stage for the relative scour depth, d s /y, and F r are shown in (Fig. 19).The scour depth decreases with decreasing the Froude number for all values of D s .It must be noticed that decreasing the Froude number to be lesser than 0.22, will reverse the process from scouring to produce a sedimentation at the abutment tip.For the next studied sets of runs, within the second and third stages, the parameter D s will be fixed at the location of the best performance of the spur dike at D s ¼ 3L.
The relationships between different relative horizontal dimensions of the scour hole against various Froude numbers are presented in (Figs.20e22).From those figures, it is appeared that as the Froude number increases the three relative horizontal dimensionless parameters of the scour hole, Lu/y, Ld/y, Lw/y increase.From (Fig. 20), it is evident that the relative width of scour hole, Lw/y, is not clearly affected by changing, D s .From (Fig. 21), it is evident that as distance between the abutment and the spur dike (Ds) increases the relative upstream length of scour hole, Lu/y, increases (Fig. 22), shows that, Ld/ y, have minimum values for all various Froude numbers when D s ¼ 3L.Unregular behavior between Ld/y and F r is noticed for the remaining sets of D s .

The result of the second stage
The scour depth, d s , at the upstream abutment corner is affected with the orientation angle of the spur dike with respect to the abutment, q, with a   range for percentage of decreasing from 71.18% to 81.56% as q increases from 45 to 90 , see (Table 4).
Maximum scour depth is 2.56 cm at q ¼ 90 , with insignificant increase in ds to 2.7 cm, as q decreases to 70 .As q goes smaller a higher rate of increasing in ds is observed.Thus, for the next studied runs of the third stage, the orientation angle of the spur dike with respect to the abutment will be fixed at q ¼ 90 .
Longitudinal cross sections in the bed, at the abutment corner are presented, for the four sets within the second stage, as shown in (Fig. 23).Maximum scour locates around the upstream spur dike with a slight movement to the downstream direction, and a significant decrease in scour depth, as q decreases to 45 (Fig. 24).shows acceptable agreement between observed values of d s /y and the corresponding calculated ones using Eq. ( 27).For the four sets, in the second stage, a comparison between, d s /y, and F r is presented in (Fig. 25).Values of ds/y, increase with increasing F r .At maximum value of F r maximum reduction in d s /y is located for spur dike orientation ¼ 90 . But, for F r of values between 0.31 and 0.26, maximum reduction in the scour depth is located at q ¼ 70 .
The relationships between different relative horizontal dimensions of the scour hole with Froude number for the second stage are presented from (Figs. 26e28).From those figures, it is shown that as Froude number increases the horizontal dimensionless of the scour hole Lu/y, Ld/y, Lw/y, increase.From (Fig. 26), it is concluded that the relative width of scour hole Lw/y, is not clearly affected by changing spur dike orientation angle.From (Fig. 27), it is shown that as spur dike orientation angle q increases the relative upstream length of scour hole Lu/y increases.The relative downstream length of scour hole Ld/y does not change significantly as q changes between 60 to 90 for the same value of the Froude number, but as q goes to 45 a noticeable increase in Ld/y can be observed, see (Fig. 28).

The result of the third stage
The Spur dike projection length normal to flow direction, L sp , has a pronounced effect on d s /y, see (Table 5).As Lsp, increases from 0.5L to 1L the scour depth, d s , decreases from 6.68 cm to 2.56 cm, respectively.The percentage of reduction in, d s , varies from 51.87 to 81.56%.
Fig. 29 shows different longitudinal cross sections at the abutment corner for the three sets.Accuracy of Eq. ( 33) is presented in (Fig. 30), from the figure an acceptable correlation between observed and calculated values of, d s /y, are noticed.As shown in (Fig. 31), as Froude number F r increases d s /y     From (Figs. 32 and 33), it is shown that as L sp increases the relative width of scour hole Lw/y and the relative upstream length of scour hole Lu/y increase.From (Fig. 34), it is noticed that as L sp increases the relative downstream length of scour hole Ld/y decreases.
Contour maps and profiles of bed topography, at axes pass with abutment corner, are presented at the maximum Froude number ¼ 0.34 as shown from (Figs. 35e43) for the vertical wall bridge abutment (the reference case) and the third, ninth, twelfth sets, respectively.The ninth and twelfth sets are not the optimum sets, but they have high efficiency in reducing the scour depth at the upstream corner of the abutment.From these figures, it is concluded that using spur dike as a countermeasure leads to significant reduction on scour depth at the upstream corner of the abutment, where the set of spur dike, Ds ¼ 3L, q ¼ 90 , and L sp ¼ 1.0L, has the optimum parameters in reduction scour depth at the abutment, with percentage of scour reduction is 81.56 %, therefore this set is the optimum set of spur dike as a countermeasure against scour at the abutment.Bhatia and Setia (2021) concluded that optimum distance of the protective spur dike is ranged between 3 and 5 length of the abutment.

Conclusions
(1) For all spur dike sets used as countermeasures for the abutment in this study, as the Froude number increases the relative scour depth increases.Also, different relative horizontal dimensions, L w /y, L u /y, L d /y, of the scour hole increases.(2) When several sets of spur dikes with varying distances, orientation angles, and lengths with respect to the abutment were carried out, it is concluded that using spur dikes as countermeasures lead to          (4) The concluded results are valid only to the simulations conditions in the present study.

Fig. 1 .
Fig. 1.The layout of the flume used in the study.

Fig. 8 .
Fig. 8. Plan sketch of the spur dike in the second stage.

Fig. 11 .
Fig. 11.Sketch of the spur dike as countermeasure for the ninth set.

Fig. 13 .
Fig. 13.Sketch of the spur dike as countermeasure for the eleventh set.

Fig. 14 .
Fig. 14.Sketch of the spur dike as countermeasure for the twelfth set.

Fig. 18 .
Fig. 18.Comparison between observed and calculated relative scour depths for the first stage using Eqn.(20).

Fig. 17 .
Fig. 17.Along the longitudinal axis (X) at y ¼ 0, variations of maximum scour depth at Fr ¼ 0.34 for the first stage.

Fig. 23 .
Fig. 23.Along the longitudinal axis (X) at y ¼ 0, variations of maximum scour depth at Fr ¼ 0.34 for the second stage.

Fig. 29 .
Fig. 29.Along the longitudinal axis (X) at y ¼ 0, variations of maximum scour depth at Fr ¼ 0.34 for the third stage.

D
.H. Al Sirtasy et al. / Mansoura Engineering Journal 48 (2023) 1e20 good reduction on scour depth at the upstream corner of the abutment.(3) The set of spur dike represented as: touched distance of the flume wall between abutment and spur dike, Ds ¼ three times length of abutment, orientation angle, q ¼ 90 , and spur dike projection length normal to flow direction Lsp ¼ length of abutment, has the optimum

Fig. 38 .
Fig. 38.Longitudinal cross section on the scour hole around the third set at Fr ¼ 0.34.

Fig. 42 .
Fig. 42.Longitudinal cross section at section 1-1 on the scour hole around the twelfth set at Fr ¼ 0.34.

( 1 )
Considering both triangular protector spur dike and a shorter spur dike with a closer distance from the abutment.(2) Studying the effects of spur dikes in reducing the scour around the bridge abutment under livebed scour condition.(3) Studying the effects of different median grain sizes (d 50 ) on the scour phenomenon for investigating the effects of soil characteristics on scour hole dimensions.(4) Applying a group of spur dike from the concluded optimum set of spur dike of this research as a countermeasure against local scour at the bridge abutment.(5) Changing the construction material of spur dikes by applying rock spur dikes instead of solid spur dikes in reduction the scour around the bridge abutment.NOTATION In this paper, the following symbols are employed: d 50 ¼ Geometric median of sediment practical size (mm) d max ¼ Maximum particle size (mm) V ¼ Mean velocity of flow (m/s) u * c ¼ Critical shear velocity for d 50 (m/s) V a ¼ Critical mean velocity for transition from clear water condition to live bed for non-uniform sediments (m/s) y ¼ Approach flow depth (cm) V c ¼ Critical mean approach velocity for transporting flow or velocity at condition of sediment transport threshold for uniform sediments (m/s) Q ¼ Discharge of flow (Lit/s) F r ¼ Froude number (V/ ffiffiffiffiffi ffi gy p ) g ¼ The gravitational acceleration (cm=sec 2 Þ; T ¼ Time (s) d s ¼ Maximum depth of scour hole around the abutment (cm) L u ¼ Upstream length of scour hole (cm) L d ¼ Downstream length of scour hole (cm) L w ¼ Scour hole width (cm) L ¼ Length of abutment (cm) B¼Width of channel (cm) K s ¼ Abutment shape factor S o ¼ Slope of bed channel K g ¼ Geometry factor of channel D s ¼ The touched distance of the flume wall between abutment and spur dike (cm) q ¼ Spur dike orientation angle with respect to the abutment, or attracting spur dike, or oriented downstream (radian) L sp ¼ Spur dike projection length normal to flow direction (cm) r ¼ Water density s ¼ Water surface tension s g ¼ Geometric standard deviation m ¼ Water dynamic viscosity; and r s ¼ Sediment density Authors contribution M. T. E. S. S. and D. H. M. A. S. conceived of the presented idea.D. H. M. A. S. developed the theory and conducted the laboratory experiments and computations.M. T. E. S. S. and D.H. M.A. S.

Fig. 43 .
Fig.43.Along the longitudinal axis (X) at y ¼ 0, variations of maximum scour depth at Fr ¼ 0.34 for the bridge abutment and the third, ninth, twelfth sets, respectively.

Table 1 .
Critical velocity values and froude numbers.

Table 2 .
Empirical equations for the first, second, third stages, respectively.

Table 3 .
Percentage of scour reduction in the first stage compared with the reference scour depth (13.88 cm).

Table 4 .
Percentage of scour reduction in the second stage compared with the reference scour depth (13.88 cm).

Table 5 .
Percentage of scour reduction in the third stage compared with the reference scour depth (13.88 cm).