STUDY ON ABUTMENT SCOUR IN TWO-STAGE CHANNELS

Siow-Yong Lim¹ and Guoliang Yu²

¹Assoc. Prof. and ²Research Fellow, School of Civil & Structural Engineering,

Nanyang Technological University, Singapore 639798

E-mail: csylim@ntu.edu.sg ; cglyu@ntu.edu.sy 

Abstract: This paper presents the results of an experimental study on clear water scour around a vertical-wall abutment terminating in the main channel of two-stage channels. The abutment is orientated perpendicular to the approach flow direction. A total of 24 experiments were conducted in two flumes under different approach flow conditions in the main channel. The scour depth prediction formula proposed by Lim (1997) for a single rectangular channel is modified for the abutment scour in the two-stage channels. Comparisons between the calculated and experimental results from the present study and Dongol (1994) showed that the modified formula is reasonable in predicting the maximum scour depth for abutment terminating in the main channel (Type II abutment scour).

Keywords: abutment scour, two-stage channels, floodplain, scour prediction, maximum scour depth

1    INTRODUCTION

Large number of bridge failure has been documented and one of the main causes was due to abutment scour during flood events (Melville, 1992, Richardson and Richardson, 1993). Most previous laboratory studies of local scour at bridge abutments were performed in rectangular channels in which the distributions of flow velocity and bed shear stress were considered uniform in the transverse direction (Laursen, 1963, Gill, 1972, Melville, 1992, Lim, 1997). In reality, however, bridge abutments are often located in two-stage river channels where the velocity and shear stress are not uniformly distributed. Due to the presence of the abutment and the redistribution of flow and bed shear stress between the floodplain and main channel, the down flows, turbulence, and vortices near the nose of the abutment are quite different compared to that in a rectangular channel. In addition, the abutment may be terminating in the floodplain or the main channel, and each case would produce different dimension of scour holes. In this respect, Melville (1995) has classified the abutment scour into three types. Type I refers to abutment scour in a rectangular channel. Type II refers to the case where the abutment spans the floodplain and extends into the main channel of a two-stage channel. In Type III, the abutment may span only part of the floodplain or right up to the edge of the main channel.

The problem of abutment scour in two-stage channels has not been extensively investigated. For Type III abutment scour, Sturm and Janjua (1994) conducted experiments under clear-water condition in a horizontal two-stage channel with wide and shallow floodplain flow. To account for the effect of the abutment length on the flow redistribution in the contracted section for a particular two-stage channel geometry and roughness, they considered the approach Froude number, the critical Froude number and the discharge contraction ratio of that portion of the flow in the approach section with a width equal to the opening width to the total discharge, as the significant parameters influencing the scouring process. Sturm and Chrisochoides (1998) further used one- and two-dimensional numerical models to investigate which were the suitable hydraulics variables that can be used to predict abutment scour in a two-stage channel. Dongol (1994) conducted 27 experiments of the Type II abutment scour, with different lengths of a wing-wall abutment extending into the main channel. He used uniform sediment with a median size of d₅₀ = 0.9 mm. All the experiments were conducted at the incipient motion condition for the approach flow bed of the main channel. Melville (1995) proposed an approach channel geometry factor to take into account the effect of the channel geometry on the abutment scour. With this modification, an equivalent length of the abutment was formed such that his earlier formula for abutment scour in rectangular channel (Melville 1992) can be used for the two-stage cases. Up to threefold reduction in scour depth from that in the corresponding rectangular channel were observed. 

Kouchakzadeh and Townsend (1997) commented that Sturm and Janjua’s study (1994) involved a two-stage channel having insignificant main channel width. This means that the velocity distribution in the floodplain would be uniform because the impact of lateral momentum transfer on the floodplain flows is weak. Their analysis of the flow data showed that the discharge ratio is an important parameter contributing to local scour.

Cardoso and Bettess (1999) studied the time evolution of scour depth in a two-stage channel using abutments that extended different distances on the floodplain including right up to the edge of the main channel (Type III abutment scour). Their experiments confirmed Melville’s (1995) suggestion for configuration modification.

This paper focuses on the maximum scour depth caused by the abutment which terminates into the main channel (Type II abutment scour). 24 experiments have been conducted for varying approach flow conditions up to the incipient motion condition for the bed material used. The scour depth prediction formula proposed by Lim (1997) for a single rectangular channel (Type I abutment scour) is modified to predict the abutment scour in two-stage channels.

2    ANALYSIS

Lim (1997) proposed the following generalized scour depth prediction formula for abutment in a single rectangular channel (Type I abutment scour),

         (1)

where d_ser = equilibrium scour depth in a rectangular channel, = sediment densimetric Froude number; is the Shields parameter = , U = mean flow velocity in a rectangular channel, u_*c = critical shear velocity, K_s = abutment shape factor, S = specific gravity of sediment, g = gravitational acceleration, h = flow depth, L = abutment length, and d₅₀ = median sediment size.

The following approach is used to modify (1) for Type II abutment scour in two-stage channels. For Type I abutment scour in a rectangular channel, it is found that (Melville 1995, Lim 1997) the scour depth around an abutment is proportional to the flow area blocked by the abutment, i.e.

                         (2)

where A is the area of flow obstructed by the abutment sited in a rectangular channel.  Melville (1995) further proposed an equivalent weighting factor for the areas of flow obstructed by the abutment in the “corresponding” two-stage channel with the same overall width and having the same flow depth in the main channel,

                         (3)

where d_sec = abutment scour depth in the two-stage (compound) channel; U_i = mean approach flow velocity in a sub-area, A_i of the two-stage channel and the summation is taken over that area of the two-stage channel for which the flow is obstructed by the abutment; U_m = mean approach flow velocity in the corresponding rectangular channel;  = cumulative discharge in the sub-area upstream of the abutment; Q_r = discharge in the corresponding rectangular channel; and A_r is the flow area obstructed by the abutment sited in the corresponding rectangular channel.

Melville’s (1995) study showed that the scour depth in Type II abutment scour is much shallower compared to that in the corresponding rectangular channel. Suppose L is the abutment length in both the rectangular and two-stage channels, then it is possible to define an equivalent abutment length, L_e to be sited in the rectangular channel such that it would induce the same scour depth as the actual abutment (of length L) in the corresponding two-stage channel. Using of (2), Melville (1995) proposed a channel geometry factor, K_G, to account for the scour reduction in Type II  abutment scour

                                   (4)

Substituting (2) and (3) into (4) yields

                           (5)

where B_f = width of the floodplain, h_f and h_m are the flow depths in the floodplain and the main channel, respectively.

Equating (4) and (5), we obtained the equivalent length

                        (6)

Using Manning’s equation and assuming equal slope for the main channel and floodplain, (6) becomes

                   (7)

where n_m and n_f are the Manning roughness coefficients for the main channel and floodplain respectively. When the Manning roughness coefficients are the same, the equivalent length can be simplified to

                           (8)

In (1), the characteristic approach velocity in F_o needs to take into account the flow redistribution and interaction because of the two-stage channel geometry. Since the scour depth is expected to be a function of the blockage created by the abutment spanning across the floodplain and into the main channel, we proposed a width-averaged equivalent velocity, U_e as follows

                           (9)

Using (9), the equivalent densimetric Froude number, . Taking the above-mentioned modifications into consideration, the scour depth prediction formula for two-stage channels takes the form:

         (10)

From the two modifications, it is clear that the discharge ratio, which is closely related to the velocity ratio, is an important parameter contributing to the local scour in two-stage channels. This is consistent with the findings of Kouchakzadeh and Townsend (1997).

3    Experiments

The experiments were conducted in two flumes and the geometric parameters of the flumes as well as the range of test conditions are listed in Table 1. In Series A experiments, the flume bed slope is horizontal and is 7 m long by 1.6 m wide. In Series B the flume is 20 m long by 0.492 m wide with a bed slope of 0.002. The floodplains were made of unplaned wood and were sealed with silicon gel to the walls of the flumes. Two different quartz sediment sizes were used. The median sediment size, d₅₀ were 0.52 mm with a geometric sediment gradation, s_g of 1.26 for the wide flume, and 2.92 mm with s_g = 1.29 for the narrow flume, respectively. The main channel was composed of loose uniform sediments, and the bed surface of the other part of the flume was glued using the same sediment.

Table 1    The range of experimental data

The abutments used were square-edged vertical wall types made from 10 mm-thick transparent Perspex. They were box-like with 30-mm internal width so that a periscope can be inserted to read the elevation of the scoured bed. As shown in Fig.1, the abutment spanned the floodplain and terminated in the main channel and was aligned perpendicularly to the approach flow direction at a location approximately 2/3 times the length of the flume measuring from the inflow sections. The experiments were performed under clear-water conditions for the approach flow. The approach flow velocities were measured at a cross section 2-m (for 20 m flume) and 1-m (for 7 m flume) upstream of the abutment location. A mini propeller-type Streamflo meter was used and the measurements were taken at various verticals in both the main channel and the floodplain. The point velocities were measured at 0.2x and 0.8x of the flow depth so that the depth averaged velocity can be computed for each vertical. The velocities were measured at 3 equally spaced verticals on both the floodplain and 10 verticals in the main channel.

4    Verification

To test the validity of (10), the present experimental results and Dongol’s (1994) 27 data points were used. For the present study, the shape factor for a vertical-wall abutment is K_s = 1. Dongol used a wing-wall abutment and K_s = 0.75 (Melville 1992). For Dongol's data, the velocity was not quoted in Melville's (1995) paper. However, it was mentioned that the experiments were conducted at approximately the incipient sediment condition, or u_*/u_*c » 0.98 (assumed), where u_* = shear velocity of the approach flow. For local scour problems, Lim and Cheng (1998) proposed the following equation relating the shear velocity ratio to the approach flow quantities,

 or                  (11)

Fig. 2    Comparison of measured and predicted scour depths

Eq. (11) is used to calculate F_oe for Dongol's data. As shown in Fig. 2, the agreement between the computed scour depths using (10) and the measured results of d_sec/h_m was good to within ±20% of the limit lines. This result is encouraging and the generality of (10) will be tested further when new data become available in the near future.

5    CONCLUSION

Based on a modification to the clear-water scour depth prediction formula proposed by Lim (1997) for a single rectangular channel, an equation (10) is proposed for Type II abutment scour in two-stage channels. The modifications involved an equivalent abutment length (8) and a width-averaged equivalent velocity (9) to account for the effect of the two-stage channel geometry on the original equation by Lim (1997). Comparisons between the calculated and experimental results from the present study and Dongol (1994) showed that the modified formula is reasonable in predicting the maximum scour depth for abutment terminating in the main channel (Type II abutment scour).

References

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