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Scour Evolution Around Bridge Piers Under Hydrographs with High Unsteadiness

  • Gökçen BombarEmail author
Research Paper
  • 26 Downloads

Abstract

The temporal development of scour at both the side and the front of circular bridge piers is studied under clear-water conditions with artificially generated, linearly rising and falling, asymmetric triangular-shaped hydrographs categorized as highly unsteady with relatively short rising durations. The base flow conditions are kept well below the conditions for scour inception so as to investigate the hysteresis in initialization of the scour. A conceptual model consisting of an S-shaped time–depth relationship is generated, and actual and effective time of scour inception, duration and finalization parameters are defined. Both the effective and the actual time of scour inception decreased with increasing unsteadiness, either at the side or at the front nose of the piers; however, scour finalization does not depend on the hydrograph unsteadiness The effect of flow deceleration during the falling phase of the hydrograph on scouring was weaker than the effect of flow acceleration during the rising phase. A five-step procedure is proposed involving the calculation of (1) the densimetric Froude number corresponding to effective scour inception at piers side, (2) the final scour depth at piers side, (3) and at the front nose, (4) the exponent n and finally (5) the scour depth time evolution for both side and front nose of the piers. The method is verified both by experimental and literature data.

Keywords

Bridge pier Final scour depth High unsteadiness Hydrograph Temporal scour evolution 

List of Symbols

b

Pier width (m)

B

Channel width (m)

d16

Particle size at which 16% by weight of the sample is finer (m)

d50

Median diameter (m)

d84

Particle size at which 84% by weight of the sample is finer (m)

ds

Scour depth (m)

dsf

Final scour depth (m)

\(D_{*}\)

\(D_{*} = \left( {\Delta g/\nu^{2} } \right)^{1/3} d_{50}\) is dimensionless grain size (–)

Fd

Densimetric Froude number \(\text{F}_{\text{d}} = V/\sqrt {\Delta gd_{50} }\) (–)

Fdi

Densimetric particle Froude number for inception of sediment movement (–)

Fdim

\(\text{F}_{ \dim } = \text{F}_{\text{di}} \;\sigma^{1/3}\) (–)

Fdim β

Densimetric Froude number for sediment entrainment at pier \(\text{F}_{{{ \dim }\;\beta }} = \text{F}_{ \dim } \;\Phi_{\beta }\) (–)

g

Gravitational acceleration (m s−2)

g

g′ = g (ρ − ρs)/ρ (m s−2)

hb

Base flow depth (m)

hp

Peak flow depth (m)

m

Slope of scour evolution curve (m s−1)

n

Parameter given by Hager and Unger (2010) (–)

QFM

The discharge measured by the flow meter (m3 s−1)

QVM

Discharge in the flume (m3 s−1)

r

Correlation coefficient (–)

Rh

Hydraulic radius (m)

t

Time (s)

ta

Effective time of inception (s)

tb

Effective time of finalization (s)

ted

Effective duration (s)

tf

Actual time of finalization of the scour (s)

ti

Actual time of inception of the scour (s)

trh

The rising duration of the hydrographs based on the flow depth (s)

tfh

The falling duration of the hydrographs based on the flow depth (s)

tR

Reference time \(t_{\text{R}} = z_{\text{R}} /V_{\text{R}}\) (s)

trV

Rising duration of the hydrographs based on the velocity measured in the flume (s)

trQ

Rising duration of the hydrograph based on the discharge (s)

u*

Shear velocity (m s−1)

u*c

Critical shear velocity for incipient motion (m s−1)

Uc

Uc = (Vb + Vp)/2 (m s−1)

V

Mean velocity (m s−1)

VR

Reference velocity (m s−1)

Vc

Critical velocity for incipient motion (m s−1)

x

Cartesian coordinate system (m)

zR

Reference length \(z_{\text{R}} = \left( {h\;b^{2} } \right)^{1/3}\) (m)

Δh

Δh = hp − hb (m)

ΔV

ΔV = Vp − Vb (m s−1)

\(\Phi\)β

\(\Phi _{\beta } = 1 - (2/3)\beta^{{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-0pt} 4}}}\) (–)

α

Dimensionless unsteadiness parameter (–)

β

Constant accounted for bridge pier as a blockage \(\beta = b/B\) (–)

ν

Kinematic viscosity (m2 s−1)

ρ

Density of the water (kg m−3)

ρs

Density of sediment (kg m−3)

σ

Non-uniformity parameter (gradation coefficient) (–)

Subscripts

b

Base of hydrograph

p

Peak of hydrograph

Side

Side of the pier at 70° from the nose of the pier

Front

Front of the pier at 0°

Eff in

Effective initiation

Act in

Actual initiation

Eff fin

Effective finalization

Act fin

Actual finalization

Notes

Acknowledgements

The author is grateful to Prof. Şebnem ELÇİ for supplying the ultrasonic velocimeter used during the execution of the experiments. Author would like to acknowledge Prof. António Heleno CARDOSO for his contributions to the manuscript. This study was not founded by any project.

Supplementary material

40996_2019_321_MOESM1_ESM.xlsx (304 kb)
Supplementary material 1 (XLSX 304 kb)
40996_2019_321_MOESM2_ESM.jpg (82 kb)
Supplementary material 2 (JPEG 82 kb)
40996_2019_321_MOESM3_ESM.jpg (26 kb)
Supplementary material 3 (JPEG 25 kb)
40996_2019_321_MOESM4_ESM.jpg (910 kb)
Supplementary material 4 (JPEG 910 kb)
40996_2019_321_MOESM5_ESM.jpg (700 kb)
Supplementary material 5 (JPEG 700 kb)

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Copyright information

© Shiraz University 2019

Authors and Affiliations

  1. 1.Civil Engineering Departmentİzmir Katip Çelebi UniversityIzmirTurkey

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