AFFLUX UPSTREAM OF CIRCULAR BRIDGE PIER

Masoud Ghodsian and Mehdi Shafieefar

Assistant Professors of Civil Engineering, Tarbiat Modarres University

P.O. Box: 14115/143, Tehran-IRAN

Tel: +98 21 8011001(Ext. 3325), Fax: +98 21 8006544

E-mail: ghods@modares.ac.ir

Abstract: Experimental study was conducted to study the effect of different parameters on the amount of the  rise in upstream water level  of circular bridge piers in an open channel. It was found that the rise in water level (afflux) due to bridge pier is a function of  contraction ratio and  Froude number. A regression-based model was developed which enables determination of  afflux.

Keywords: rise in water level, afflux, bridge pier, contraction ratio, froude number

1    INTRODUCTION

When a bridge or similar hydraulic structure is constructed in a channel, an increase in depth of flow occurs immediately upstream of the structure, which is generally termed as afflux. The afflux phenomenon is  of interest in the context of flood protection and other engineering applications (Banner, 1987). It is also important in river training and bridge design. In spite of importance of afflux, comparatively less attention has been paid to study its characteristics. Bradley (1960) showed that the amount of afflux is a function of channel Froude number and contraction ratio. Yarnell (1934a and 1934b) examined the flow through bridge piers experimentally and found that the amount of afflux is a function of downstream Froude number and contraction ratio for different shapes of piers. Al-Nassri (1994) obtained an equation relating afflux to downstream Froude number, contraction ratio and shape of pier. Ghodsian et al. (2000) obtained new equation for estimation of afflux due to rectangular bridge pier.

In order to study the effect of different parameters on the amount of afflux due to circular bride pier, experiments were conducted, the results of which are presented in this paper.

2    DIMENSIONAL ANALYSIS

A schematic view of flow through circular bridge piers is shown in Figure 1. The afflux due to bridge Dh (i.e. the difference between water level after and before installing the pier or rise in water level due to pier) can be assumed to be a function of normal depth of flow upstream of pier  h, approach velocity of flow V, contraction ratio s (s = 1¨Cd/B, here d is diameter of piers and B is width of channel), acceleration due to gravity g and shape of pier which may be  represented by Sc. Therefore, one can write:

Dh = f (h, V, s, g, Sc)                            (1)

Dimensional analysis of above equation gives:

Dh/h = f (Fr_, s, Sc)                              (2)

in which Fr is upstream Froude number given by Fr = V/(gh)^0.5 . In this study circular shape of pier is used, hence Sc can be eliminated from equation (2) to get:

Dh/h = f (F_r, s)                              (3)

The correlation between the parameters of equation (3) can be obtained with the help of experimental data.

3    EXPERIMENTAL SETUP AND PROCEDURE

Experiments were conducted in a nearly horizontal recirculating type flume with a length of 6 m, width of 0.48m and depth of 0.5m. Circular piers with diameter of 7.5 cm were fixed to the bed at the mid length of the flume. Baffle walls were provided in the upstream of channel to get inflow with little and acceptable disturbances. Water was supplied to the upstream end of channel through a supply pipe, from an overhead tank at a constant head and the flow was controlled by a gate valve. Calibrated sharp crested triangular weir was used for discharge measurement. Flow depths were measured with the help of a point gauge having accuracy of ¡À 0.01 mm.

Initially a certain discharge was allowed into the flume and the flow profile, after stabilization of flow, was measured. Then a pier was fixed to the bed of the flume and the flow profile, after stabilization of flow, was measured. The experiments were conducted for various values of depth (70mm to 120mm) and discharge (8.04 l/s to 31.01 l/s) and contraction ratio (0.38 to 0.84). Table (1) shows the experimental data obtained  in the present study. 

  Table 1    Experimental data

4    RESULTS

Figure 2 shows a typical  flow profiles at the upstream of the pier with different contraction ratio. For the comparison  with the condition with no pier (s = 1) , the corresponding flow profile for s = 1 is also plotted (with dotted lone) in the same figure. It is obvious that  by increasing the contraction  ratio ( i.e. decreasing number of piers), water surface level decreases, which means afflux is inversely proportional to the contraction ratio. The experimental data was used to establish the relationship between the dimensionless parameters appearing in equation (3). Figures (3) shows a typical representation of equation (3) for circular pier. It is obvious that by increasing Froude number the afflux increases.

Figures 2 and 3 show that the assumed functional relationship given by equation (1) and hence that by equation (3) is acceptable. Therefore, considering the nature of variation of Dh/h and in accordance with the equation obtained by Ghodsian et al. (2000), one can assume the following functional shape of equation for Dh/h:

                             (4)

in which K, a and b are constant which can be obtained from experimental data. Further, by using the experimental data, the following best fit equation for Dh/h was obtained for circular pier:

                        (5)

with regression coefficient of R²=0.939. Figure 4 shows the comparison of computed  values of Dh/h using equation (5) and measured values of Dh/h .This figure shows that equation (5) can be used to compute afflux due to circular piers with sufficient accuracy.

5    CONCLUSION

The results of experiments, which were conducted to study the effects of different parameters on afflux due to circular pier, are presented. It was observed that the amount of afflux is influenced by the variables such as upstream Froude number and contraction ratio. A new equation for computation of afflux is introduced which contains above mentioned parameters. The introduced equation enables estimation of afflux due to circular pier in a channel.

Acknowledgement

This study was partially supported by Iran Water Resources Management Organization, Ministry of Energy, Tehran, Iran.

References

Bonner, V. R. (1987), Computing water surface profiles with HEC-2 on a personal   computer, The hydraulic engineering center, Water resources support center, U.S. Army corps of engineers, Davis, California.

Bradley, J. N., (1960), Hydraulics of bridge water ways, Hydraulic design series, No. 1, U.S. Department of commerce, Bureau of public roads.

Al-Nassri, S. (1994), Effect of bridge pier shape and contraction ratio on backwater profile, hydraulic Engineering 94.

Ghodsian, M., Shafeefar, M. and Hashemi, S. J. (2000), Afflux due to rectangular bridge pier, 2000 Joint conference on water resources engineering and water resources planning and management, American Society of Civil Engineers, July 30- August 2, Minneapolis, Minnesota, USA.

Yarnell, D. L. (1934-a), Pile trestles as channel obstructions, Technical Bulletin 429, U.S. Department of agriculture, Washington.

Yarnell, D. L. (1934-b), Bridge pier as channel obstructions, Technical Bulletin 422, U.S. Department of agriculture, Washington.

  Fig.1    Flow through circular bridge pier

Fig. 2    Water surface profile upstream of pier, in this figure S=s

Fig. 3    Variation of Dh/h with Fr, in this figure S = s

Fig. 4    Comparison of computed and measured values of Dh/h