TEMPORAL SCOUR DEVELOPMENT AT BRIDGE ABUTMENTS

Christine S. Lauchlan¹, Stephen E. Coleman² and Bruce W. Melville³

^1*Senior Research Fellow, Delft Technical University, Delft, the Netherlands,
Faculty of Civil Engineering and Geosciences, Steinweg 1, PO Box 5048, NL-2600 GA Delft, the Netherlands

ph: (015) 278 5476, fax: (015) 278 5124, E-mail: c.lauchlan@ct.tudelft.nl;

^2,3Senior Lecturer, Associate Professor, The University of Auckland,
Department of Civil and Resource Engineering, Private Bag 92019, Auckland, New Zealand.

Abstract: Laboratory studies were undertaken to assess the temporal development of clear-water local scour depths at bridge abutments in uniform sand beds. A series of experiments was performed using a range of vertical wall abutments to quantify the influence of flow duration on the depth of local scour. Comparison of results is also made with a number of previous local abutment scour studies. Similar to previous studies of temporal local scour at bridge piers, a dimensionless equilibrium time scale is defined, namely t^* = t_eV/L, where V = flow velocity and L = abutment length. The data show that both t^* and the equilibrium local scour depth d_se are subject to the influences of flow, sediment and abutment parameters. An expression is presented for determination of the time t_e for development of d_se for a given abutment, sediment and approach flow velocity, the results indicating that t_e increases with V/V_c and y/L, where V_c = flow velocity for sediment entrainment, and y = flow depth. A second expression enables estimation of the local scour depth d_s at any stage during the development of the equilibrium scour hole. The expressions for t_e and d_s = f(t) are consistent with the findings for temporal development of pier scour.

Keywords: local scour, abutment, temporal scour, bridge

1    INTRODUCTION

Local scour holes form around bridge piers and abutments due to the action of the flow against these flow impediments. Estimates can be made of the maximum local scour likely to occur for a given location under given flow conditions. However, it takes time for scour holes to form and often adverse flow conditions at a site occur for limited time frames, for example, the length of the flood wave. It then becomes necessary to understand the development of the local scour hole with time.

Melville and Chiew (1999) studied temporal development of local scour at bridge piers and developed equations to allow the estimation of local scour depths under clear water flow conditions from initiation of the scour hole until equilibrium is reached. The corresponding analysis for abutments is the focus of this present investigation.

The framework for analysis of the present study data is similar to that used by Melville and Chiew (1999) for bridge piers. This allows the results of the analysis to be incorporated into existing local scour prediction equations.

Melville and Coleman (2000) and Melville and Chiew (1999) show that for bridge piers the equilibrium time scale increases rapidly with flow intensity for clear water scour conditions, attaining a maximum at the threshold condition. They both mention the interdependence between the time required to reach equilibrium scour t_e and the depth of scour at equilibrium d_se. Melville and Chiew (1999) show that both parameters have similar dependence on the same set of parameters. The following discussion shows that the functional relationships for t^* = t_eV/L (equilibrium time scale) and scour depth as a function of time, d_s = f(t), for bridge abutments are similar to those for bridge piers.

2    EXPERIMENTS

The present study experiments were conducted in two different flumes at The University of Auckland (AU). Table 1 gives details of the experiments. Uniform sands were used in each flume, with median particle sizes, d₅₀, of 0.8 to 1.02 mm. Flow intensity (V/V_c, where V is average flow velocity and V_c is critical flow velocity for sediment entrainment) was varied between 0.46 and 0.99 and flow shallowness (y/L; where y = flow depth and L = abutment length) varied from 0.007 to 4. In all tests, a vertical wall abutment was used. The abutments used can be classified as short (y/L>1) or medium (0.04<y/L<1.0) length as per the classifications of Melville and Coleman (2000). Additional data by Kwan (1984), Tey (1984) and Dongol (1994) have been incorporated in the analysis of the experimental results to complement the new data measurements. These three studies all measured the development of local scour at abutments under threshold conditions. Kwan (1984) and Tey (1984) used short abutments, while Dongol (1994) used both types. The additional data are contained in Table 1 with references “K”, “T” and “D” used to define Kwan (1984), Tey (1984) and Dongol (1994) respectively.

3    TEMPORAL DEVELOPMENT OF SCOUR

Attempts to describe the time varying development of abutment scour have been made by various authors. The problem is one of determining a time factor, defined as the function relating the scour depth d_s at any particular time to the equilibrium scour depth d_se occurring at the equilibrium time t_e. The value of such a factor will depend on the flow conditions, i.e. clear water or live bed.  The rapid development of scour depths under live bed conditions means that the equilibrium scour depth is obtained rapidly and the rate of temporal development is less important to the designer. However, under clear water conditions, the scour hole develops more slowly and it may be many days before an equilibrium scour depth is reached.

Melville and Coleman (2000) provide empirical expressions for time effects on local scour at both bridge piers and abutments. For local scour at bridge abutments under clear water conditions, the local scour depth as a function of the equilibrium local scour depth is given by the following preliminary function

                          (1)

where t_e is the time it takes to reach the equilibrium scour depth and t is the time for which the scour depth d_s is required. To estimate t_e, equations (2) and (3) are suggested, depending on the abutment type.

  ,                         (2)

  ,                      (3)

Equations (1) to (3) were developed based on laboratory experiments AU1 to AU8 of Table 1. The preliminary nature of the above equations is highlighted by equation (1) being physically invalid for small times, with d_s ® –¥ as t ® 0.

Equation 1 indicates that clear-water scour depths increase at rates varying with time and asymptotically approach an equilibrium level. It can therefore take a very long time for the equilibrium scour hole to form. As with temporal scour development at bridge piers, experiments show that an apparently equilibrium scour hole may continue to deepen at a relatively slow rate long after equilibrium conditions were thought to exist.

The key consideration is then determining an appropriate definition of equilibrium time for scour hole development. The equilibrium time definition of Melville and Chiew (1999) is used in the present study. This states that the equilibrium time t_e is the time at which the scour hole develops to a depth (the equilibrium depth, d_se) at which the rate of increase in scour does not exceed 5% of the abutment length in the succeeding 24-hour period. Melville and Chiew (1999) nondimensionalise t_e as t^* = t_eV/D, where D is the pier diameter. For the present abutment data, t_e is similarly nondimensionalised as t^* = t_eV/L, where L is the abutment length.

Figures 1 and 2 present the dimensionless time to equilibrium data for abutments, with the data grouped according to flow intensity (V/V_c) and flow-depth-to-abutment-size ratio (y/L). The data of Figure 2 suggest that for short abutments, y/L > 1, t^* is approximately constant, with t^* » 2 x 10⁶. As y/L decreases, t^* becomes increasingly sensitive to V/V_c. The data of V/V_c > 0.95 in Figure 1 similarly indicate an upper limit of t^* » 2×10⁶, with t^* becoming increasingly sensitive to y/L as V/V_c decreases. Generally, t^* reduces with decreasing V/V_c and decreasing y/L.

The trends in t^* with y/L and V/V_c highlighted in Figures 1 and 2 are used to collapse the t^* data into the single relation (Figure 3) of

                    (4)

Differences apparent in the experimental results of Figure 3 may be exacerbated by differences in author determinations of equilibrium scour, difficulties in measuring small changes in scour depth, and small variations in flow intensity. These differences become increasingly significant as the threshold of sediment motion V/V_c = 1 is approached, increases in scour depth near equilibrium conditions taking increasingly longer time steps as V/V_c ® 1.

Figure 4 shows typical scour development data plotted as d_s/d_se versus t/t_e, the selected runs covering ranges of y/L from 0.2 to 4 and V/V_c from 0.56 to 0.99. Comparison of all of the results indicates that 50% of the equilibrium local scour depth is attained in a time varying from 0.5% to 8% of t_e, depending principally on the flow intensity. Similarly 80% of the equilibrium local scour depth is developed in a time varying from only 8% to almost 50% of the time to equilibrium. The significance of time in the measurement and estimation of scour depth is clearly demonstrated.

Based on the complete data set of Table 1, equation (1) has been refined to

                 (5)

The relation of equation (5) is plotted on Figure 4 as a series of curves for varying V/V_c. This relation, similar in form to that of Melville and Chiew (1999) for local pier scour, provides a good fit to the abutment scour data over large ranges of t/t_e. Equation (5) furthermore gives the appropriate limits of d_s ® 0 as t ® 0 and d_s ® d_se as t ® t_e.

For a given flow, sediment and abutment configuration, equation (4) can be used to predict the time t_e required to establish the equilibrium scour depth and equation (5) can be used to predict d_s = f(t). It is hoped that additional ongoing experimental work, especially data obtained for abutments and flows satisfying both y/L < 0.1 and V/V_c < 0.9, will help to further refine the equilibrium time scale formula, particularly in regard to long abutments.

4    CONCLUSIONS

This study is limited to local scouring at vertical wall abutments in uniform sand beds. The following conclusions are drawn from this study:

(1) The equilibrium depth of scour at bridge abutments under clear water conditions is approached asymptotically, as for bridge piers.

(2) 50% of the equilibrium local scour depth can be attained (from plane bed conditions) in a time, depending principally on the flow intensity, varying from 0.5% to 8% of t_e.

(3) 80% of the equilibrium local scour depth can be attained (from plane bed conditions) in a time, depending principally on the flow intensity, varying from 8% to 50% of t_e.

(4) The equilibrium time scale (t^* = t_eV/L) for development of a clear-water local scour hole at a bridge abutment can be predicted using t^* = 1.1x10⁶(y/L)^(0.75Vc/V)(V/V_c)³.

(5) The local scour depth variation with time at an abutment can be predicted using.

d_s/d_se = exp[-0.09(V/V_c)^-0.75|ln(t/t_e)|^1.4]

where d_se can be predicted using Melville and Coleman (2000) with a time factor of K_t = 1.

Acknowledgements

The authors would like to acknowledge to work of undergraduate students Florian Ladage, Richard Body and Tracy Choi, and laboratory technicians Raymond Hoffman and Jim Bickner, for undertaking the collection and analysis of experimental data for this study.

References

[1]    Melville, B.W. and Chiew, Y.M. (1999). Time Scale for Local Scour at Bridge Piers. Journal of Hydraulic Engineering, ASCE, 125(1), 59-65.

[2]    Melville, B.W. and Coleman, S.E. (2000). Bridge Scour. Water Resources Publications, Colorado, USA, 550pp.

[3]    Tey, C.B. (1984). Local Scour at Bridge Abutments. Report No. 329, School of Engineering, The University of Auckland, Auckland, New Zealand, 111pp.

[4]    Kwan, T.F. (1984). Study of Abutment Scour. Report No. 328, School of Engineering, The University of Auckland, Auckland, New Zealand, 225pp.

[5]    Dongol, D.M.S. (1994). Local Scour at Bridge Abutments. Report No. 544, School of Engineering, The University of Auckland, Auckland, New Zealand, 409pp.

Table 1    Local abutment scour experimental data

Table 2    Local abutment scour experimental data – continued

¹ A number of the results of Dongol (1994) have been estimated based on limited d_s = f(t) data.

² The equilibrium scour depth data are unavailable.

Fig. 1    Equilibrium time scale for local abutment scour: grouped by v/v_c ratio.

Fig. 2    Equilibrium time scale for local abutment scour: grouped by y/L ratio.

Fig. 3    Equilibrium time scale for local abutment scour.

Fig. 4    Measured and predicted local scour development at an abutment.