Abstract
In this study, three kinds of pier arrangements were tested. They are (i) two piers in tandem, (ii) two piers in staggered arrangement, and (iii) three piers in symmetrically staggered arrangements. In the arrangement of two piers in tandem, the equilibrium scour depth at downstream pier decreases with an increase in downstream distance up to approximately eight times pier diameter and then increases with further increase in downstream distance. However, the scour depth at downstream pier is always smaller than that at upstream pier. In the arrangement of two staggered piers, the scour depth at the downstream pier for L/b = 4, where L is the offset distance and b is the pier diameter, is the same as that of the upstream pier at S = 8b, where S is the streamwise spacing or distance between piers. Further, for three piers in staggered arrangement, as the lateral spacing between downstream piers increases, the equilibrium scour depth at downstream pier decreases.
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Abbreviations
- B :
-
Channel width
- b :
-
Pier diameter
- d s :
-
Instantaneous scour depth
- d se :
-
Equilibrium scour depth at an isolated single pier
- d s1 :
-
Equilibrium scour depth at upstream pier
- d s2 :
-
Average value of equilibrium scour depth at downstream piers
- d s2a :
-
Equilibrium scour depth at downstream pier (right pier)
- d s2b :
-
Equilibrium scour depth at downstream pier (left pier)
- d s2c :
-
Computed scour depth at downstream pier
- d s2m :
-
Measured scour depth at downstream pier
- d 16 :
-
16% finer sediment size
- d 50 :
-
Median sediment size
- d 84 :
-
84% finer sediment size
- F :
-
Flow Froude number
- g :
-
Gravitational acceleration
- h :
-
Flow depth
- k e :
-
Equivalent roughness height
- K T :
-
Spacing factor in tandem arrangement
- L :
-
Lateral offset distance
- R p :
-
Pier Reynolds number
- S :
-
Streamwise spacing
- s :
-
Relative density of sediments
- T :
-
Time scale
- T * :
-
T(Δg \(d_{ 50}^{3}\))0.5/b 2
- t :
-
Time
- U :
-
Approaching flow velocity
- U c :
-
Critical flow velocity
- U * c :
-
Critical shear velocity
- u :
-
Time-averaged streamwise velocity
- x :
-
Streamwise distance
- \(\hat{x}\) :
-
Nondimensional streamwise distance (=x/b)
- z :
-
Vertical flow depth
- \(\hat{z}\) :
-
Nondimensional vertical distance (=z/b)
- Δ:
-
s − 1
- Θ c :
-
Threshold shields parameter
- θ :
-
Angle between upstream and downstream piers
- ρ :
-
Mass density of water
- σ g :
-
Geometric standard deviation of sediment size
- τ c :
-
Threshold bed shear stress
- ϕ :
-
Angle of repose of sediment
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Khaple, S., Hanmaiahgari, P.R., Gaudio, R. et al. Interference of an upstream pier on local scour at downstream piers. Acta Geophys. 65, 29–46 (2017). https://doi.org/10.1007/s11600-017-0004-2
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DOI: https://doi.org/10.1007/s11600-017-0004-2