a new analytical bridge pier scour equationiwtc.info/2004_pdf/09-2.pdf · a new analytical bridge...

Eighth International Water Technology Conference, IWTC8 2004, Alexandria, Egypt

587

A NEW ANALYTICAL BRIDGE PIER SCOUR EQUATION

Youssef I. Hafez Associate Professor

Hydraulics Research Institute, El Kanater, Egypt E Mail: [email protected]

Abstract

When a bridge is built across an alluvial channel, the obstruction of the flow by the bridge piers induces higher velocities and vortices that cause scour of the channel bed around the piers. If this scour reaches the foundation level of the bridge piers, the bridge might collapse. Bridge pier scour is the leading cause of bridge failure. In Egypt, concerns about bridge pier scour is one of the important reasons for limiting the increase of the current flow releases from High Aswan Dam above the current maximum. Due to the importance of bridge pier scour, many investigators have worked on this critical subject but most have built their analysis on laboratory flume data that have simplified conditions and scale effects. When applying the existing empirical equations for predicting bridge pier scour to field cases, the scour depths are over-predicted which means increased construction costs. A new analytical equation for predicting bridge pier scour is developed herein based on an energy balance theory. The developed equation expresses equilibrium bridge pier scour depth in terms of flow velocity, flow depth, bed sediment specific gravity and porosity, bed sediment angle of repose, pier width over channel width ratio, and a momentum transfer coefficient. The equation has the advantages that it explains the physics of bridge pier scour in a direct way, relates the flow hydrodynamics to scour and most of all avoids the wide pier problem. The developed equation yielded much superior agreement with field data than any other existing empirical equation when applied to the average and maximum of 515 field data points. This was also the case in the application of the equation to bridge pier scour for two bridges near Cairo, Egypt; namely Imbaba and El-Tahreer bridges. Key Words: Bridge Pier Scour, Sediment Transport 1. Introduction: When a bridge is built across an alluvial channel, the obstruction of the flow by a bridge pier induces higher velocities and horseshoe vortices that cause intensive sediment transport out of the area around the pier and consequent scour of the channel bed around the pier. If this scour reaches the foundation level of a bridge pier, the bridge might collapse. Bridge pier scour is the leading cause of bridge failure. In the United States alone, bridge pier scour is the leading cause of failure among more than 487,000 bridges over watercourses (Landers and Mueller 1996). In Egypt, concerns about bridge pier scour is one of the important reasons for limiting the increase of the current flow releases from High Aswan Dam (HAD) above the current maximum of 270 Million m3/day. In

Eighth International Water Technology Conference, IWTC8 2004, Alexandria, Egypt 588

order to release higher flows than the current maximum, knowledge is required about how much scour is expected around bridges built on the Nile River. Other scour types such as general scour, constriction scour, bend scour, abutment scour and bank scour are equally important, however they are not discussed at this stage. Due to the importance of bridge pier scour, many investigators have worked on this critical subject but most have built their analysis on laboratory data; for example: Laursen (1956) at the University of Iowa and Shen et al. (1969) at Colorado State University. Chang (1988) reports: “more than 10 different formulas have been developed for predicting local scour around bridge piers, based on essentially laboratory data”. This empirical approach suffers from its associated simplified conditions and scale effects. When applying the existing empirical equations for predicting bridge pier scour to field cases, the scour depths are over-predicted (Babaeyan-Koopaei and Valentine, 1999). This means increased construction and maintenance costs as the foundation levels are required to be deeper than it should be. In this study, application of several well-known bridge- pier-scour prediction equations is implemented in addition to testing a newly developed analytically based equation with the objective of predicting realistically the scour depth. The already existing equations used herein are those of: The Modified Laursen by Neill (1964), Shen et al. (1969), The Colorado State University (1975), Jain and Fischer (1979), and Modified Froehlich (1999). The new analytical equation for predicting bridge pier scour is developed by Youssef I. Hafez based on an energy balance theory. It is the objective of this paper to find out which of the existing formulae works for the Nile River and how well the newly developed formula performs?. Utilization is made of valuable field data about local scour at Imbaba and Tahreer bridges at Cairo, Egypt and the average and maximum of 515 field data points reported in Johnson (1995). 2. Bridge-Pier-Scour Equations: In this section a list is made of the bridge pier scour equations used in this study. In all the formulae listed below, it is assumed that the flow angle of attack is negligible and that the pier shape is rectangular. Chang (1988) reports that the scour depth of circular piers is 90% of that for rectangular piers and 80% of that for sharp-nosed piers. As the flow angle of attack increases the scour depth, it will be assumed that the effect of flow angle of attack and the circular shape of the pier will mutually cancel each other. This is done because of the lack of information about these factors in the data. 2.1. The Modified Laursen by Neill (1964) Equation: Neill (1964) used Laursen and Toch’s (1956) design curve to obtain the following explicit formula for the scour depth:

3.0)(35.1bH

bDs = (1)

Where Ds is the equilibrium scour depth, b is the obstruction width (or pier width) and H is the approach water-depth. This equation does not include the Froude number or in other words the velocity of the attacking stream.


589

2.2 Shen et al. (1969) Formula: Shen et al. (1969) used the Froude number in their scour-depth prediction in addition to the pier width as given by:

31

32

)()(4.3bH

FbD

os = (2)

Where Fo is the Froude number and the other variables are as defined before. 2.3 The Colorado State University or CSU Formula (1975): This equation is developed as a best fit to the data (laboratory) available at the time. The formula is given as:

43.065.0 )()(2.2 os F

Hb

HD = (3)

The CSU (1975) formula is similar in form to Shen et al (1969) equation. Later on correction factors were added for effects of flow angle, pier shape and bed conditions. 2.4 Jain and Fischer (1979) Equations: Jain and Fischer (1979) developed a set of equations based on laboratory data. For (Fo-Fc) > 0.2, the formula reads as:

5.025.0 )()(0.2bH

FFbD

cos −= (4)

Where Fc is the critical Froude number. For (Fo-Fc) < 0.2, the formula is

3.025.0 )()(84.1bH

FbD

os = (5)

2.5 Modified Froelich (1999) Formula: Fischenich and Landers (1999) modified Froelich’s (1988) equations for live-bed scour at bridge crossings as

1)()90

(2 61.043.013.0 += os F

Hb

HD θ

(6)

Where θ is the angle of flow attack (degrees). This equation does include a safety factor (+1.0) that accounts for contraction scour in most cases. To compare this formula with other formulae, this factor will not be considered, as only local bridge pier scour is considered herein. 2.6 Youssef I. Hafez’ Analytical Equation: An analytical equation is developed by Youssef Hafez using energy balance theory. The energy balance theory assumes that at the equilibrium geometry of the scour hole, the work done by the attacking fluid flow upstream the bridge pier is equal to the work done in removing the volume of the scoured bed material. In other words the energy contained in the fluid flow attacking the bridge pier is converted to an energy consumed in removing or transporting the bed material, thus forming a scour hole. When all the flow


energy is consumed in transporting the sediment out of the scour hole, scour ceases and the scour hole becomes stable and at its maximum scour-depth. The following assumptions are made: (1) the shape of the upstream slope of the scour hole in the stagnation vertical symmetry plane is linear, i.e. the scour hole has a triangular shape, See Fig. 1 (2) the equilibrium scour hole has an upstream slope that is equal to the angle of repose of the bed material, (3) The scour hole is formed due to the conversion of the horizontal momentum of water coming to the pier to downward or vertical momentum attacking the bed surface, See Fig. 1a (4) The down flow component is responsible for transferring the momentum of the attacking fluid to the bed material particles which is raised or transported to the original bed level and carried away by the stream currents or horseshoe vortices (5) the analysis is done for a jet thickness of one sediment particle diameter which is close to working only in the stagnation symmetry plane (plane stress type analysis), (6) the moment arm of the horizontal force of the attacking flow is half the water depth plus half the scour depth, and (6) the volume of the scoured bed which is assumed triangular in shape is moved to the original bed level out of the scour hole with equivalent vertical distance equal to 1/3 of the scour depth, see Fig. 1b. The work done by the fluid flow of the horizontal jet coming from upstream the bridge pier in the stagnation symmetry plane can be expressed as

��

��

� +

��

��

� −22

12

22sX DH

Bb

dHV ηρ (7)

Where � is the fluid (water) density, Vx is the longitudinal flow velocity of the jet attacking the bridge in the direction normal to the pier, H is the water depth, d is the bed material sediment diameter, � is a transfer coefficient of the horizontal momentum into a vertical momentum in the downward direction, b is the pier width, B is the channel width in case of one pier or the bridge span or pier centerline to centerline distance in case of multiple piers and Ds is the maximum or equilibrium scour depth. The work done in removing the bed material from the scour hole is equal to:

)()1(3

)tan

(21 γγθ −−

Φ sss

s

Dd

DD (8)

Where � is the slope in of the scour hole in the symmetry plane (assumed here equal to the bed material angle of repose), θ is the bed material porosity, �s is the bed material unit weight and � is fluid unit weight. Under the conditions of equal work at the equilibrium conditions (or maximum scour) equations 7 and 8 are equated and after some manipulation yield:

)1()1(

1)1()1(

tan3)(

22

2

3

HD

HgV

BbSH

D sx

G

s +��

��

�

��

�

�

��

�

�

−��

��

�

−−= η

θφ

(9)


591

where SG is the sediment specific gravity. Equation 9 expresses the equilibrium bridge pier scour depth in terms of the local velocity, local flow depth, bed material specific gravity and porosity, bed material angle of repose, pier width over channel width ratio, and a momentum transfer coefficient. The Froude number can be easily made to appear in Eq. 9. The equation has the advantages that it explains the physics of bridge pier scour in a direct way, relates the flow hydrodynamics to scour and most of all avoids the wide pier problem. Equation 9 is a cubic non-linear equation. Though a closed form expression for the scour depth could be obtained, a few iterations could be used instead to solve for the scour depth. Fischenich and Landers (1999) state that “Though not addressed by most empirical relations, the ratio of obstruction width to channel width is probably a better measure of scour potential than is the obstruction width alone”. Indeed such is the case in Eq. 9 where the ratio of obstruction width to channel width (b/B) appears in the equation. In Equations 1-6, the obstruction width has a direct effect on the scour depth, the wider the obstruction the deeper the scour. However, for obstructions having large widths, Eqs. 1-6 would predict considerably larger scour depths than would be practically existing which leads to the wide-pier problem. Eq. 9, however, does not suffer from the wide-pier problem because the obstruction width is not directly related to the scour depth. The combination (η Vx = Vz) reflects the down flow component of the velocity caused by the pier obstruction where Vz is the vertical down flow velocity in front of the pier. Indeed, the down flow is responsible for the upstream scour and should be determined from 2D or 3D numerical modeling or experimental measurements. For the sake of simplicity herein, the η factor that represents the transformation of the incoming or approach horizontal momentum to vertical downward momentum will be assumed based on personal judgment. It could be postulated that Eq. 9 is also valid for predicting scour depths downstream bridge piers when a proper selection of the momentum transfer coefficient is made. In this case η represents the transformation of the momentum from either of the horseshoe or wake turbulent eddies to the bed material particles. Indeed this is an added advantage of Eq. 9 over Eqs. 1-6 that seems to predict only upstream scour depths. Another added advantage of Eq. 9 is that the bed material characteristics appear through inclusion of the bed material specific gravity, porosity and angle of repose. Regarding sediment size effect on the scour depth, Fischenich and Landers (1999) state that “…sediment size may not affect the ultimate or maximum scour but only the time it takes to reach it”. Therefore, it is no surprise that Eq. 9 does not contain the sediment size. 3. Verification of the Bridge Pier Scour Equations with Field Data: 3.1. Case of Imbaba Bridge at Cairo, Egypt: Imbaba bridge (Km 934.7 from Aswan Dam) is located several kilometers upstream the Delta Barrages (km 946 from Aswna Dam) north of Cairo. Imbaba-bridge has seven piers each with 3 m diameter except pier No. 6 that has diameter of 10 m, Fig. 2. The distance between the piers is about 65 m. The scour holes of Imbaba-bridge have been going under detailed monitoring programs by The Hydraulics Research Institute (HRI)


since 1981. The monitoring programs reveal that the scour holes at Imbaba-bridge and nearby El-Tahreer-bridge are stable under current flow conditions after HAD (HRI 1993, HRI 1997). This is because the peak flood flows released from HAD are dramatically reduced after its completion in 1968. Therefore, these scour holes are believed to be resulting from very large historic flows occurred before HAD. It is true that the higher the flow discharges, the deeper the scour holes around bridge piers. This can be seen from Eqs. 1-6 and Eq. 9 where the Froude number and the velocity (both are related to the discharge) appearing in the equations are proportional to the scour depth. Therefore, the historic data are searched for maximum flow conditions that are believed to cause scour. Historic data (Nile Research Institute 1992) show that the peak of the flood season occurs in the month of September every year. The data in the period from 1923 to 1968 reveal the highest September flood to occur in 1959 with a monthly total of 31.0 Billion m3 at Aswan (Km 7.0). Converting this value to a daily value assuming uniform conditions, the corresponding maximum daily flow is about 1033 Million m3/day (11,960 m3/s) at Aswan. This value is to be compared to the current maximum of 270 Million m3/day. It is believed that Imbaba-bridge was built before 1959, therefore the 1959 flood or a similar flood with this magnitude could have caused scour at Imbaba-bridge. For example, the Sept. flood in 1964 had a total volume of 27.9 Billion m3/month. Now it is required to find out how much of the flood discharge reached the site of Imbaba bridge in 1959?. This can be answered by making use of existing records for the year 1962 at a nearby gauging station, namely at El Ekhsas (Km 887 from Aswna Dam). In 1962 the Sept. total flow at Aswan was 24 Billion m3 which amounts to nearly 800 Million m3/day (9259 m3/s) while a measured flow at El Ekhsas of 7896 m3/s (El Moatassem 1985) was recorded in Sept. 10, 1962. From the 1962 records the ratio of El Ekhsas flow to that of Aswan flow becomes 0.85. This ratio is assumed to hold for the 1959 flood from which the flow at El Ekhsas or Imbaba is 0.85 * 11,960 m3/s = 10,202 m3/s (881.5 Million m3/day). The 1996 field survey cross sections at Imbaba (cross section No. 9 in Hydraulic Research Institute Report 1997) show a bank level of about 20.0 m and average bed level of 10.0 m. The bank level of 20 m is assumed to be the highest possible water level at this site as could also be seen in Fig. 3. Therefore a water depth of about 10.0 m could be assumed corresponding to the estimated flood discharge of 10,202 m3/s. The 1962 data at the nearby El Ekhsas show water depths in the order of 10.0 m, thus supporting the above finding. The average channel width at Imbaba-bridge could be estimated from Fig.2 or Fig. 3 as 428 m. Based on the foregoing data, the average approach flood flow velocity at Imbaba bridge site is estimated as (10,202) / (428*10) = 2.384 m/s. The most recent scour investigation at Imbaba-bridge is that by HRI in 1997 while the oldest one might be in 1980. No data about the dimensions of the scour holes at pre-HAD flood conditions exist. This makes it difficult for obtaining the exact dimensions of scour holes that are thought to be resulting from the 1959 flood or from a different flood with nearly the same magnitude. The deposition that might have occurred upstream the piers after HAD might have caused change in the scour holes dimensions after the time of


593

their formation. Deposition of the Nile bed load occurs because Imbaba bridge is upstream the Delta Barrages where back-water-effects occur. Before HAD, all gates of the Nile barrages used to be opened without back-water-effects. Therefore, some assumptions must be made to cope with this situation. Downstream the piers, little sediment deposition can be expected and therefore it can be assumed that the scour hole dimensions resemble conditions at the time of scour formation. The scour equations are therefore assumed valid for predicting the downstream scour depths. Fig. 2 shows the contours of the scoured bed around the piers where the enclosure of the contour lines around piers 1-4 supports the close equivalence between the upstream and downstream scour depths at Imbaba-bridge. Fig.3 shows cross section No. 11 just downstream Imbaba-bridge where the scour holes at piers 1,2,3 and 4 (numbering start from the right bank facing the downstream flow direction) are clearly feasible. The transverse bed slope pertinent to curved river reaches appears clearly and local scour depths at piers 1-4 are superimposed on it. A large scour hole to the left enveloping piers 5, 6 and 7 is the result from flow curvature (bend scour), contraction scour, local bridge pier scour and scour due to flow convergence around the upstream Island of Zamalek. As there are several factors and mechanisms affecting this large left scour hole, its formation is very complex and beyond the scope of the scour predictive equations cited herein. In addition, the scour holes near piers number 5,6 and 7 are away from the bridge and appear to be filled with filling materials and have floating fenders that make determining their original dimensions difficult. The scour holes around piers 1,2,3 and 4 of Imbaba-bridge are clearly feasible and have depths of about 1.90 m, 3.29 m, 4.29 m, and 5.25 m, respectively as seen in Fig.3. Table 1 shows the field data extracted from Fig. 3 and from the assumptions in the foregoing and coming discussions where a water level of 20.0 m is assumed and an average bed level of 11.0 m at the bridge. Consequently the centerline depth at the bridge becomes 9.0 m (level 20.0 – level 11.0 m).

Table 1. Data used in Scour Hole Predictions at Imbaba Bridge

Pier No. Local Bed Level (m)

Local Water Depth (m)

Local Velocity

(m/s)

Local Froude Number

η

Pier No. 1 15.0 5.0 1.897 0.271 0.56 Pier No. 2 13.0 7.0 2.162 0.261 0.78 Pier No. 3 12.0 8.0 2.277 0.257 0.89 Pier No. 4 10.5 9.5 2.435 0.252 1.00

Due to the curvature of the flow at Imbaba-bridge, the longitudinal velocity must have a transversal distribution that needs to be included in the scour calculations. From investigation by Odgaard (1982), the velocity distribution is expressed with reference to the centerline quantities as follow:


4118

7

��

��

��

��

�=

rr

HH

VV C

CC

(10)

As the radius of curvature of the river channel at Imbaba-bridge is large (about 2000 m) compared to the channel width (about 400 m), it can be assumed that the velocity distribution is only proportional to the depth distribution in Eq. 10. In other words, the maximum of (rc/r) is (2000/1800) which when is raised to the ¼ power amounts to 1.027, a value that can be neglected. Eq. 10 including only the depth term on the right hand side is the basis for calculating the local velocity at each pier shown in Table 1. The momentum transformation factor, η, can be assumed to be proportional to the ratio of (the local depth/ the centerline depth) which reflects curvature effects and sediment deposition in the transverse direction. The maximum value of η is unity, which is taken at pier 4 where the local depth exceeds the centerline depth. The sediment specific gravity is taken as 2.65, sediment porosity of 0.4, and bed material angle of repose of 30 �. In applying Jain and Fischer (1978) formula, a mean sediment diameter of 0.00027 m and D90 of 0.00051 m were taken as from 1962 data at El Ekhsas (El Motassem 1985). Table 2 shows results of applying Eqs. 1-6 and Eq. 9 to the four piers of Imbaba-bridge. It is clear from the table that the developed equation by Youssef Hafez gives better match with the observed field data than the other empirical formulae using the same set of data. This case is a complex case where river meandering curvature induced transverse slope due to sediment deposition and the transverse slope attained equilibrium conditions. 3.2. Case of El Tahreer Bridge at Cairo, Egypt: El Tahreer bridge is located on the eastern Nile branch at Zamalek Island few kilometers upstream Imbaba-bridge, Fig.4. As in the case of Imbaba-bridge, it seems that scour occurred due to pre-HAD at historic flows such as the 1959 flood. The flow in the eastern branch reaches about 80 % of total flow (HRI 1981). Taking the same maximum flow of 1,202 m3/s as at Imbaba-bridge for the whole river cross-section, the estimated maximum flow in the eastern branch is about 8162 m3/s. Assuming that the discharge is proportional to the 5/3 power of water depth (as in the Manning’s equation) yields a water depth of 8.79 m at the site of El Tahreer-bridge using the 1,202 m3/s discharge and the 10 m water depth at Imbaba-bridge. The river width at the bridge is 373 m (CS No. 3, HRI 1997). With these data, an average velocity of 2.489 m/s results in at El Tahreer-bridge. The most clear upstream scour hole at El Tahreer bridge is seen at pier No. 4 from the right bank as seen in Fig. 5 where the scour depth reaches 3.5 m (level 10.0m - level 6.5 m). The rest of the scour holes are related to flow curvature and are located downstream the bridge. The plan view of the bridge shown in Fig. 4 shows that the bridge is angled to the main flow direction with an angle of about 33�. This angle was used explicitly when applying Eq.6. The velocity component normal to the bridge becomes 2.087 m/s (2.489 times Cosine 33�) and the corresponding Froude number is 0.225. The bridge span is 46 m and the pier width is 3 m. The same sediment parameters as in Imbaba-bridge case were used also herein. The momentum transfer factor, �, is taken as 0.75 in applying Eq.9. Kwan


595

and Melville (1994) reported that the maximum down-flow component was measured to be 0.75 Uo, where Uo is the approach flow velocity at an abutment. Melville (1997), and Kothyari and Ranga Raju (2001) agree that considerable similarity also exists between the flow patterns and scour processes at a bridge pier and at a bridge abutment. Table 3 shows comparison of applying Eqs.1-6 and Eq. 9. It can be seen again that the developed equation of Youssef Hafez gives the best match with the observed scour depth. 3.3. Case of the Average and Maximum of 515 Field Data: Johnson (1995) reports a summary of 515 field data where the pier width, flow depth, flow velocity and observed scour depth are seen in Table 4. The application of Eqs.1-6 and Eq. 9 is seen in Table 5. It is clear from Table 5 that at average conditions the empirical equations (Eqs. 1-6) overestimated the scour depth but still in the same order of magnitude. At maximum conditions where wide pier conditions occur, the empirical equations yielded results that is way too much. In both case, the developed analytical equation by Youssef Hafez yields predictions very close to the observed scour depths.

Table 2. Scour Calculation at Imbaba Bridge at Cairo, Egypt

Pier Number

Measured Scour Depth

(m)

Predicted Scour Depth

Youssef Hafez

(m)


Modified Froelich (1988)

(m)

Predicted Scour Depth Jain & Fischer (1978)

(m)

Predicted Scour Depth CSU

Formula (1975)

(m)


Shen et al.

(1969) (m)


Modified Laursen (1969)

(m) Pier No. 1 1.90 1.98 3.62 4.79 4.05 4.55 4.73 Pier No. 2 3.29 3.44 3.86 5.64 4.48 4.95 5.22 Pier No. 3 4.29 4.30 4.12 6.02 4.67 5.12 5.62 Pier No. 4 5.25 5.49 4.49 6.54 4.91 5.36 5.95

Table 3. Scour Calculation at El Tahreer Bridge at Cairo, Egypt

Pier Number

Measured Scour Depth

(m)


Youssef Hafez

(m)



(m)


(m)


Formula (1975)

(m)


Shen et al.

(1969) (m)



(m) Pier No. 4 3.50 3.81 3.92 6.40 4.46 5.44 5.59


Table 4. Data used in for the Average and Maximum of 515 Field Data Points

Case Pier Width

(m)

Local Water Depth (m)

Local Velocity (m/s)

Local Froude Number

�

Average 2.92 3.18 1.52 0.272 1.00 Maximum 19.5 19.5 4.70 0.340 0.75

Table 5. Scour Calculation for the Average and Maximum of 515 Field Data Points

Case Measured Scour Depth

(m)


Youssef Hafez

(m)



(m)


(m)


Formula (1975)

(m)

Predicted Scour Depth Shen et

al. (1969)

(m)



(m) Average 1.99 2.00 2.77 3.98 3.78 4.29 4.04

Maximum 10.61 10.97 20.20 27.40 26.98 32.29 26.33

ϕ

Pier

HH2H2

(a)

ϕ+

Ds

tam φ

Ds

tam φ

Ds/3

(b)

Pier

Ds

Pier

Ds

Figure 1. Schematic Diagrams of Flow At a Bridge Pier in the Symmetry Plane, (a) Longitudinal Flow Transformation into Down Flow, (b) Scour Hole Shape


597

Figure 2. Layout of Imbaba- Bridge and Contour Map of the Bed Surface and Scour Holes at the Piers

Figure 3. Cross Section No. 11 Showing Scour Holes at Piers 1,2,3 and 4.


Figure 4. Layout of El-Tahreer Bridge and Contour Map of the Bed Surface and Scour Holes

Figure 5. Cross Section No. 7at El-Tahreer Bridge Showing Scour Holes at the Bridge Piers


599

4. Conclusions and Recommendations: The developed analytical equation herein, Eq.9, by Youssef Hafez based on an energy balance theory yields much superior agreement with field data than other existing empirical equations when applied to two bridges near Cairo, Egypt; namely Imbaba and El-Tahreer bridges and to the average and maximum of 515 data points reported by Johnson (1995). The developed equation has the advantages of: (1) being analytical that explains the physics of bridge pier scour in a direct way, (2) relating the flow hydrodynamics to the induced scour, (3) avoiding the wide pier problem, and (4) predicting realistically bridge scour depths of field cases, i.e. no overestimation of scour depths occurs especially for wide piers. It is recommended to test the developed equation, Eq. 9, using more field data and more exploration of the momentum transfer coefficient in Eq. 9 is needed. The developed equation provides a strong theoretical and analytical framework for tackling the scour phenomena of other hydraulic structures. References: Babaeyan-Koopaei K., and Valentine, E.M. (1999), “Bridge Pier Scour in Self-Formed Laboratory Channels,” The XXVIII IA HR congress 22-27 August 1999. Chang, H.H. (1988), “ Fluvial Processes in River Engineering”, John Wiley & Sons. Colorado State University, (1975) “Highways in the River Environment: Hydraulic and Environmental Design Considerations,” prepared for the Federal Highway Administration, U.S. Department of Transportation, May 1975. Fischenich, C., and Landers, M. (1999) “Computing Scour,” EMRRP Technical Notes Collection (ERDC TN-EMRRP-SR-05), U.S. Army Engineer Research and Development Center, Vicksburg, MS. Froelich, D.C., (1988). “Abutment Scour Prediction.” 68th Transportation Research Board Annual Meeting, DC. Hydraulic Research Institute (HRI), (1981). “Study of Nile River Bed at the Cairo Bridges”, in Arabic, Cairo, Egypt. Hydraulic Research Institute (HRI), (1993). “Monitoring Local Scour in the Nile River at Imbaba Bridge”, in Arabic, Cairo, Egypt. Hydraulic Research Institute (HRI), (1997). “Monitoring Local Scour in the Nile River at Imbaba and El-Tahreer Bridges”, in Arabic, Cairo, Egypt. Jain, S.C. and Fischer, E. E. (1979). “Scour around circular bridge piers at high Froude numbers.” Rep. No.FHwa-RD-79-104, Federal Hwy. Administration (FHwa), Washington, D.C.


Johnson, P. A., (1995) “Comparison of Pier Equations Using Field Data”, J. of Hydraulic Engineering, Technical Note, Vol. 121, No.8. Kothyari, U. C. and Ranga Raju K. G., (2001), “Scour around spur dikes and bridge abutments”, Journal of Hydraulic Research, Vol. 39, No.4. Kwan, R. T. F. and Melville B. W., (1994) “Local scour and flow measurements at bridge abutments”, Journal of Hydraulic Research, Vol., 32, No.5. Landers M.N. and Mueller D.S., (1996) “Channel Scour at Bridges in the United States” Federal High Way Administration, Report number FHWA/RD-95/184, 1996. Laursen, E.M., and Toch, A. (1956) “Scour around bridge piers and abutments”, Bull. No. 4, Iowa Hwy. Res. Board, Ames, Iowa. Melville, B. W. (1997), “ Pier and abutment scour, integrated approach”, Journal of Hydr. Engrg., ASCE, 118(4):615-630. Motassem, M. (1985),“Recognition of River Nile Regime at Ekhsas Flood 1962,”, Nile Research Institute, Formerly Research Institute of the High Aswan Dam Side Effects, Cairo. Neill, C. R. (1964), “River bed Scour, a review for bridge engineers.” Contract No. 281, Res. Council of Alberta, Calgary, Alberta, Canada. Nile Research Institute (1992), “Impact of Water Resources Projects on the Nile in Egypt”, Motassem, M., Editor-in-Chief, Nile Research Institute, Cairo. Odgaard, A.J., (1982) “Bed Characteristics in Alluvial Channel Bends”, J. Hydraul. Div. ASCE, 108 (HY11), pp. 1268-1281, November 1982. Shen, H.W., Schneider, V. R., and Karaki, S. S., (1969) “Local Scour Around Bridge Piers”, J. Hydraul. Div. ASCE, 95 (HY11), pp. 1919-1940, November 1969.

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