Suitable Bridge Pier Section for a Bridge over a Natural River

Estimation of maximum scour depth at the bridge pier is necessary for the safety and economy of the bridge design. Therefore, the phenomenon of scour around bridge piers was extensively studied from the literature to find the effect of pier shapes and inclined flow on scour depth at bridge piers. It was found from the analysis that scour depth increases with the increase of the flow angle relative to the pier axis, but for a cylindrical pier, maximum scour depth does not change with flow angle. When the flow angle is at 300, the scour depth for the cylindrical pier is smaller than other pier shapes; hence circular pier shape is more suitable for natural rivers which have possibility of changing flow direction.


Introduction
Scour is the local lowering of stream bed elevation which takes place in the vicinity or round a structure constructed in flowing water. Scour take placed around bridge piers, abutments, around spur, jetties and breakwaters due to modification of flow pattern in such a way as to cause increase in local shear stress. This in turn dislodges the material on the stream bed resulting in local scour. In the case of bridges, the estimation of correct depth of scour below the stream bed is very important since that determines the depth of foundation. Hurber [1] has stated that since 1950 over 500 bridges in USA have failed and that the majority of the failures were related to the scour of foundation material. Such data are not available for the PNG (Papua New Guinea) bridges. However, it is known to all of us that longest bridge in PNG, Markham Bridge is not fully functioning due to scour and settlement of one of its major pier. The concern about safety of bridges is primarily due to three reasons which are: 1).inadequate knowledge about scour phenomenon when the bridges were constructed; 2). inadequate data on which the design flood was chosen and 3). increase in the loading on the bridges due to increase in size of trucks and other vehicles and their frequency of operation.
The stream bed lowering at the bridge can take place due to four primary reasons. If the bridge is located downstream of a large dam, there is a slow lowering of the bed and reduction of stream slope due to degradation. Degradation takes place when the stream transporting sediment becomes deficient in sediment supply due to sediment being stored upstream of the dam. In extreme case this lowering can be as much as 4 to 6 meters. Secondly, if for reducing the cost of the bridge the stream is contracted by building guide bunds etc…, such contraction can cause additional lowering of the stream bed.
The third type of lowering that takes place around the bridge pier is due to modification of flow structure due to presence of pier. Depending on the pier shape and free stream condition, an eddy structure comprising of one or more of the three eddy structures, namely horseshoe vortex, wave vortex and the trailing vortex system can form; which increases the local shear on the bed and causes scour. Typical formation of horseshoe vortex and wake vortex are shown in figure 1. Lastly; additional scour can also take placed if the flow direction is inclined to the pier axis.  Eventhough, number of researchers have studied the factors affecting scouring depth and hence derived formulas to evaluate the sour depth for pier. It is not considered the combined effect of flow direction and the pier shape to select an optimum section for piers. It can be described, when the axis of the pier makes an angle θ with the general direction of the flow, two major changes take place in the flow field. Except in the case of cylindrical pier, the separation pattern is drastically changed resulting in change in vortices. Secondly, the open width between the piers, perpendicular to the flow direction reduces as the angle of inclination θ increases. Therefore, the combined effect of pier shapes and angle of inclination of pier axis to the flow direction on scouring depth is extremely important in pier designing. Since the depth of foundation of pier decided by the maximum scour depth, the finding of this study is more important for selecting a correct pier shape to reduce the depth of scour. Further, most of natural river banks are not stable for long times, it may change the direction of flow due to erosion. It also possible due to deposition of sediment inside the river. Therefore it is risky to select a pier section in traditional way, just thinking that the river flow is axial. Hence, it is better to select a suitable pier section for natural river by studying the effect of flow direction.

Literature Review
A number of papers have been published since 1940 on various aspects of scour around bridge piers. Based on the experimental work and some theoretical analysis it is found that the following factors affect the scour depth at the bridge pier. i) Whether the incoming flow is clear water flow or it carries sediment: clear water flow occurs when u * /u *c is less than unity while for sediment transporting flow U * /U *c is greater than unity. Here U * =√ gDS is the shear velocity of flow and U *c is the shear velocity at which bed material starts moving, D is the depth of flow in the river and S is the river slope. Average shear stress on the bed is τ 0 =ζ f U *se γ f DS where γ f is the unit weight of water and ζ f its mass density . All factors remaining the same clear water scour is found to be about 10 % more than scour in scour in sediment transporting flows. Further, whereas in clear water flow it takes several hours to reach the maximum scour below river bed d sc , in sediment transporting flow corresponding equilibrium scour depth d se is reached in relatively shorter time.
ii) Effect of change in depth of flow: experiments by Melville and Sutherland have shown that when (depth of flow/ pier width) ration i.e., D/b is greater than 2.6, scour depth does not depend on the depth of flow; for smaller depths the scour depth depends on the depth of flow. iii) Effect of shape of pier nose: the shape of the pier nose affects the strength of horse-shoe vortex as well as the separation of the flow around the bridge pier; hence it affects the maximum scour depth. The following table 1 prepared on the basis of studies by Laursen and Toch [4], Chabert and Engeldinger [3], Garde [7], and Paintal and Garde [6], gives relative effect of pier -nose shape on the maximum scour if for cylindrical pier the maximum scour is taken as unity.  iv) Effect of angle of inclination of pier on scour depth: In this case, two major changes take place in the flow field except in the case of ENGINEER cylindrical pier, the flow separation pattern is drastically changed and secondly, the open width between the piers, perpendicular to the flow direction reduces as the angle of inclination increases. v) Effect of opening ration on scour depth: the opening ratio α is defined as α = (B-b)/B where B is centre to centre spacing of the piers and b is the pier width. When b is very small compared to B, α is close to unity and flow around one pier does not affect that around the other. However, as α decreases, the interference affect becomes more pronounced and scour depth increases; in such a case Dse/D or Dsc/ d-α -n . Here Dse and Dsc are scour depths below the water surface for sediment transporting and clear water flows respectively. The analysis of extensive data collected by Garde [8] indicate that n = 0.30. vi) Effect of bed material characteristics: in the case of non cohesive materials, the characteristics of bed material that affect the scour depth are sediment density, median size d of the bed material, its standard deviation and stratification. For all practical purposes the density of natural sediments can be taken as 2.65, a constant value. As regard the sediment size, lacey-inglis approach suggests that D se ≈ d -1/6 . Since the average shear stress on the bed (= γ f DS) at which bed material moves-known as the critical shear stress-increases as the sediment size increases, it stands to reason that scour depth should be affected by the size of the bed material. Hence, for given flow condition, larger than the sediment size d, smaller should be the scour depth. The clear water scour depth should decrease with increase in sediment size. Analysis of data over large of sediment size by Kothyari [9,10] has indicated that d sc ≈ d -0.31 while for sediment transporting flow d se ≈ d -0.07 . Here d sc and d se are the scour depths below general bed level for sediment transporting and clear water flows respectively. The effect of size distribution of the bed material on the scour depth is more significant. When the standard deviation σ g of the bed material is large and the bed material contains some nonmoving sizes for a given discharge, the coarser material would tend to accumulate in the scour hole and inhibit further development of scour depth. Hence for the same median size, scour depth will be smaller for material with larger geometric standard deviation σ g .Here σ g = ½ (d 84 /d 50 + d 50 /d 16 ) and , d 84 , d 50 and d 16 are such sizes that 84%, 50% and 16% material is finer than d 84 , d 50 and d 16   Almost all these formulae were developed based on the laboratory data. This is because the scour is a very complex phenomenon that has resulted from the interaction between the flow around a bridge pier and the erodible bed surrounding it. Based on this, only very limited attempts have been successful in modeling the scour computationally. However, the formulae and models derived from these attempts are usually applied by the civil engineers to evaluate the depth of local scour for new bridges and existing bridges that have local scour problems.
In the earlier part of this century Lacey-Inglis analysed the data from stable irrigation canals flowing through loose noncohesive sandy material in Indo-Gangetic plain and obtained the following equations for depth (or hydraulic radius) D LQ and perimeter (or width) P.
Where d s is scour depth, y is flow depth at the upstream of the pier, K 1 is correction factor for pier nose shape, K 2 is correction factor for the angle of attack flow, b is the pier width and F r1 is the Froude number at up stream of the pier. L is the pier length. K 1 and K 2 are obtained from Table 4 and 5. Group of cylinders 1.0

Calculation of Maximum Scour
Eventhough, few acceptable equations are available to find maximum depth of scour , In this section, the most widely used Colorado State University Equation was used. Maximum scour depths were calculated for three different flow conditions with sediment size of 1mm. The flow condition were selected by referring to the local river, namely Markham River and selected three set of data as follows: Further, in the first part of the calculation, four different pier shapes were considered to find the effect of pier shape on scour depth. In the second part of the calculation, effects of flow directions were considered.

Results and Discussion
It can be seen from the table 6 that maximum scour depth varies with the pier shape eventhough the flow and sediment conditions are equal. These results are in comparable nature since all the pier sections have equal cross sectional areas. Therefore, it can be stated that maximum scour depth occurs when the pier shape is cylindrical. Also it can be concluded that minimum scour occur when the pier shape is sharp nose. The depth of scour is decreased with flow velocity decreases, while maintaining the maximum scour and minimum scour at circular and sharp nose respectively. On the other hand, it can be seen from the reading at table 7 to 9 that scour depth increases with the increase of the flow angle. But, the scour depth for cylindrical pier does not change with the flow angle. This is due to the flow properties and geometrical properties of cylinder are not changed with the direction of the flow. But in other cases it will increases due to modification of flow properties and contraction of flow due to changing clear width of flow. This is represented by K 2 value at table 4 and also taken into account in the calculation. It also can be seen from the values of table 7 to 9, when the flow angle is 30 0 , the calculated scour depths for square nose, round nose and sharp nose are larger than the cylindrical pier and further increases with the increase of the flow angle.

Conclusion
In a natural river, it is always possible to change the flow direction due to erosion or deposition of sediments. Therefore any bridge pier constructed in a natural river could experience angular flow attack. Hence it is not recommended to evaluate maximum scour depth for a bridge pier by considering the flow as axial. It is clearer from the analysis results optimum pier section for the pier is circular section, since it has a minimum scour depth with considering all possible scenarios on scour at bridge pier. However if the engineer need to design bridge with different shapes of pier, it is necessary to consider the scour for angular flow conditions. If the pier shape is not a constrain for the design of a bridge, it is economical and safer to design the bridge with circular piers.