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Estimation of maximum scour depths at upstream of front and rear piers for two in-line circular columns


Previous investigations indicate that scour around bridge piers is one of the most important factors for the failure of waterway bridges. Hence, it is essential to determine the accurate scour depth around the bridge piers. Most of the previous studies were based on scour around a single pier; however, in practice, new bridges are usually wide and then piers comprise two circular piers aligned in the flow direction that together support the loading of the structure. In this study, the effect on maximum scour depth of the spacing between two piers aligned in the flow direction was investigated experimentally under clear water scour conditions. The results show that the maximum scour depth at upstream of the front pier occurs when the spacing between the two piers is 2.5 times the diameter of the pier. Two semi empirical equations have been developed to predict the maximum scour depth at upstream of both front and rear piers as a function of the spacing between the piers, in terms of a pier-spacing factor. If the new equations for the pier-spacing factor are used with some of the existing equations for scour at a single pier, the predicted scouring depths are in good agreement with observed results. The S/M equation exhibited the best performance among the various equations tested and was recommended for use in prediction of the equilibrium scour depth. The findings of this study can be used to facilitate the positioning of piers when scouring is a design concern.

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Diameter of piers

d50 :

Median grain size of sediment


Froude number


Depth of approach flow

d1 :

Scour depth upstream of single pier case

ds :

Scour depth upstream of front pier for double-pier case

dse1 :

Equilibrium scour depth upstream of front pier for two in-line circular piers

dse2 :

Equilibrium scour depth upstream of rear pier for two in-line circular piers

Ks :

Factors for the effect of spacing between two piers

Kt :

Time factor to extrapolate the scour depth to equilibrium scour depth


Centre to centre distance between two piers


Flow rate

Re :

Reynolds number


Normalised spacing between two piers, L/D

te :

Time to reach equilibrium scour depth


Free stream velocity

Vc :

Critical velocity of flow for sediment

σg :

Geometric standard deviation of the grain size distribution


Width of the flume


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Correspondence to Alireza Keshavarzi.

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Keshavarzi, A., Shrestha, C.K., Melville, B. et al. Estimation of maximum scour depths at upstream of front and rear piers for two in-line circular columns. Environ Fluid Mech 18, 537–550 (2018).

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  • Local scour
  • Bridge piers
  • Two in-line circular piers
  • Piers–flow interaction