Scouring around different shapes of bridge pier

Scour is the removal of soil and rocks from the beds and the banks of streams under the action of flowing water. As water passes around any obstruction in the flow path, scouring occurs. The obstruction, commonly a bridge pier, causes the water to change direction, producing turbulence. This in turn detaches soil particles and becomes suspended in the water stream. The United States Geological Survey (USGS) defines scour as the hole left when sediment is washed from the bottom of a river (Leopold & Maddock 1953). Although scour may occur at any time, scour action is especially strong during floods because swiftly flowing water has more energy than calm water to lift and carry sediment.

The flow of water over an erodible surface, such as the bed of a natural stream or an unlined channel, can cause scouring. This is accelerated if the water channel/stream is constricted by any hydraulic structure component such as a bridge pier. In such a case, the general scouring is accompanied by substantial local scour around the pier, which may prove detrimental to the latter's stability. The extent of scour is greatly affected by the presence of structures encroaching the channel (May et al. 2002; Abdul Aziz 2011). Many studies (Melville 1992; Landers & Mueller 1996; Melville & Coleman 2000; Hong et al. 2012; Akib & Rahman 2013) report that hydraulic structures fail mostly because of scouring around a structural element, most commonly a pier, in the case of bridges, especially during large floods. This highlights the importance of local scour depth estimation to reduce the probability of structural failure. Mohammadpour et al. (2021) conducted experiments to predict local scour around complex abutments and compared the results with complex piers. Inamdeen et al. (2021) studied riverbed scour to focus on the fundamental mechanisms and patterns governing bridge scour; a bathymetric survey was used to map the scour holes downstream on the Ronne River, Sweden to analyze the possible causes of scouring. Local scour is a function of many variables involving flow, channel, and pier/obstacle parameters (Raudkivi & Ettema 1983; Mir et al. 2017, 2018; Link et al. 2020). Channel scouring and its estimation are substantially governed by various phenomena including runoff, sediment transport mechanisms, etc. (Fakhri et al. 2014; MohammadzadeMiyab et al. 2017; Zalaki-Badil et al. 2017).

Lacey's model (1930) estimates general scour, and is extensively used for scour estimation and protection works design in India, with suitable factors. Almost all relevant IS/IRC/RDSO codes recommend this method. Shahriar et al. (2021) investigated five statistical scour estimation models; all based on deterministic approaches, to predict scour depth for clear-water conditions, and compared the results with the measured data base. The models were assessed in terms of uncertainty in predictions and were found satisfactory.

It is likely that the factors affecting general scour also affect local scour, but in addition, the shape of the obstacle may also affect it (Mir et al. 2017). Baghhbadorani et al. (2018) investigated scouring for complex pier shapes that arise when scouring exposes pile caps and piles. Fifty-two tests were conducted on four different complex pier models, in clear-water conditions, to help improve the accuracy of the published HEC-18 equations (Richardson & Davis 2001). Aly & Dougherty (2021) investigated the effect of bridge pier geometry on local scour, and the results indicated how pier geometry could reduce the bed shear stress considerably leading to reduced scour depth around the piers. Thus, there is scope to develop the local scour model, depending on the shape of the obstacle and general scour capacity of a flowing stream. In this study, Lacey's general scour model was used because of its relevance and extensive use. The aim of the study was the physical modeling of local scour for piers of commonly encountered shapes (circular, round-nosed, and elliptical) and to develop the relationships of local and general scour.

Investigations were carried out in a laboratory flume for the three obstacle model shapes – circular, round-nosed, and elliptical. The data were analyzed to determine the relations between the local and corresponding general scour.

As stated earlier, three commonly encountered shapes of the obstacles were used in the present study. These were circular, round-nosed, and elliptical. Wooden models of the three obstacle shapes, whose cross-sections are given in Table 1, were prepared. The obstacles' standard section was taken as 10cm, in accordance with previous studies (Chiew & Melville 1987), which state that the maximum channel obstruction should not exceed 10% of its width to study scouring free from channel side effects.

Table 1

Obstacle shapes used

Shape .	Designation .	Obstacle shapes .
Circular	S1
Round-ended	S2
Elliptical	S3

Shape .	Designation .	Obstacle shapes .
Circular	S1
Round-ended	S2
Elliptical	S3

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Two non-cohesive soils of different gradations were used as bed materials to fill the glass-sided flume, both having varying particle distribution characteristics. Both materials were studied to find their characteristics and determine their effect on local scour depth around the obstructions. Table 2 gives the bed material parameters.

The scouring along the obstacle model peripheries was noted down for different discharges using a laser meter.

That discharge has the main effects in scouring is already well known and widely reported. In this study, discharges were varied using discharge heads between 0.4 and 4.5 cm, for each obstruction type and both types of bed material. The flow parameters of the study are given in Table 3.

During the experiments, it was clear that scour showed dependence on pier shape. Changes in obstacle shape cause considerable variations in scour depth. The maximum scour depths for each obstacle for different discharges are given in Table 4.

The circular cross section was found to have the greatest scour, the round-ended the least. The trend was similar at all five discharge flows and with both types of bed material.

The best-fit models for the shapes follow a power trend. The models' statistical results are given in Table 5.

The data indicate a trend between local and general scour. Equations (2)–(4) were developed by analyzing the experimental data for the three shapes used in the study. In the equations, S_L stands for local scour, S_G for general scour.

Using these models, the preliminary scour depth can be estimated with respect to the general scour in the channel. This concept is different from the conventional methods used till now. But, further comparison of the models obtained here with the previous studies after adjusting the parameters of the studies accordingly can help in scour prevention and mitigation measures to a great extent. This has been listed as the future recommendation of the present study.

In the study, local scour was found to vary with general scour with a significant coefficient of correlation. The local-general scour relations developed for the three shapes used are different, indicating a definite effect of the obstacle's shape on local scouring.

The above relation is based on limited data and only two different bed materials, but can be used for preliminary estimation of local scour for a proposed obstacle shape that may encounter streamflow. The relations give a better estimate of local scour than multiplying general scour values with some factors, where the shape effect is usually ignored. The conclusions that can be drawn from the study are:

• General scour can be used effectively to estimate local scour.

• Local scour models are subject to greater variation with changes in laboratory testing conditions than general local scour models.

• Local scour depth is affected significantly by the shape of the obstacle encountered.

The authors acknowledge the cooperation of Water Resources Management Centre, NIT Srinagar, India where the experimental work was done.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.