Scour Evolution Around Bridge Piers Under Hydrographs with High Unsteadiness

  • Gökçen BombarEmail author
Research Paper


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.


Bridge pier Final scour depth High unsteadiness Hydrograph Temporal scour evolution 

List of Symbols


Pier width (m)


Channel width (m)


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


Median diameter (m)


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


Scour depth (m)


Final scour depth (m)


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


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


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


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

Fdim β

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


Gravitational acceleration (m s−2)


g′ = g (ρ − ρs)/ρ (m s−2)


Base flow depth (m)


Peak flow depth (m)


Slope of scour evolution curve (m s−1)


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


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


Discharge in the flume (m3 s−1)


Correlation coefficient (–)


Hydraulic radius (m)


Time (s)


Effective time of inception (s)


Effective time of finalization (s)


Effective duration (s)


Actual time of finalization of the scour (s)


Actual time of inception of the scour (s)


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


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


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


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


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


Shear velocity (m s−1)


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


Uc = (Vb + Vp)/2 (m s−1)


Mean velocity (m s−1)


Reference velocity (m s−1)


Critical velocity for incipient motion (m s−1)


Cartesian coordinate system (m)


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


Δh = hp − hb (m)


ΔV = Vp − Vb (m s−1)


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


Dimensionless unsteadiness parameter (–)


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


Kinematic viscosity (m2 s−1)


Density of the water (kg m−3)


Density of sediment (kg m−3)


Non-uniformity parameter (gradation coefficient) (–)



Base of hydrograph


Peak of hydrograph


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


Front of the pier at 0°

Eff in

Effective initiation

Act in

Actual initiation

Eff fin

Effective finalization

Act fin

Actual finalization



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)


  1. Aksoy AÖ, Bombar G, Arkış T, Güney MŞ (2017) Study of the time-dependent clear water scour around circular bridge piers. J Hydrol Hydromech 65(1):26–34. CrossRefGoogle Scholar
  2. Bombar G (2014) Clear-water bridge scour under triangular-shaped hydrographs with different peak discharges. Paper presented at the 2014 River Flow Conference, Lausanne, Switzerland, pp 1519–1525Google Scholar
  3. Bombar G (2016) The hysteresis and shear velocity in unsteady flows. J Appl Fluid Mech 9(2):839–853. CrossRefGoogle Scholar
  4. Borghei SM, Kabiri-Samani A, Banihashem SA (2012) Influence of unsteady flow hydrograph shape on local scouring around bridge pier. Water Manag 165(9):473–480. CrossRefGoogle Scholar
  5. Çetin OK, Saçan C, Bombar G (2016) Investigation of the relation between bridge pier scour depth and vertical velocity component. Pamukkale Universitesi Muhendislik Bilimleri Dergisi 22(6):427–432. CrossRefGoogle Scholar
  6. Chang WY, Lai JS, Yen CL (2004) Evolution of scour depth at circular bridge piers. J Hydraul Eng 130(9):905–913. CrossRefGoogle Scholar
  7. Güney MŞ, Aksoy AÖ, Bombar G (2011) Experimental study of local scour versus time around circular bridge pier. Paper presented at the 6th International Advanced Technologies Symposium (IATS’11), Elazığ, TurkeyGoogle Scholar
  8. Güney MŞ, Bombar G, Aksoy AÖ, Doğan M (2013) Use of UVP to investigate the evolution of bed configuration. KSCE Kor J Civil Eng 17(5):1188–1197. CrossRefGoogle Scholar
  9. Gunsolus EH, Binns AD (2018) Effect of morphologic and hydraulic factors on hysteresis of sediment transport rates in alluvial streams. River Res Appl 34(2):183–192. CrossRefGoogle Scholar
  10. Hager WH, Unger J (2010) Bridge pier scour under flood waves. J Hydraul Eng 136(10):842–847. CrossRefGoogle Scholar
  11. Li H (2005) Countermeasures against scour at bridge abutments. Dissertation, Michigan Technological University.
  12. Li Z, Qian H, Cao Z, Liu H, Pender G, Hu P (2018) Enhanced bed load sediment transport by unsteady flows in a degrading channel. Int J Sedim Res 33(3):327–339. CrossRefGoogle Scholar
  13. Lopez G, Luis T, Ortega-Sanchez M, Simarro G (2014) Estimating final scour depth under clear water flood waves. J Hydraul Eng 140(3):328–332. CrossRefGoogle Scholar
  14. Mao L (2018) The effects of flood history on sediment transport in gravel-bed rivers. Geomorphology 322(1):196–205. CrossRefGoogle Scholar
  15. Melville BW, Chiew YM (1999) Time scale for local scour at bridge piers. J Hydraul Eng 125(1):59–65. CrossRefGoogle Scholar
  16. Melville BW, Coleman SE (2000) Bridge scour. Water Resources Publication, LondonGoogle Scholar
  17. Mrokowska MM, Rowiński PM (2019) Impact of unsteady flow events on bedload transport: a review of laboratory experiments. Water 11(5):907. CrossRefGoogle Scholar
  18. Mrokowska MM, Rowiński PM, Książek L, Strużyński A, Wyrębek M, Radecki-Pawlik A (2018) Laboratory studies on bedload transport under unsteady flow conditions. J Hydrol Hydromech 66(1):23–31. CrossRefGoogle Scholar
  19. Nezu I, Sanjou M (2006) Numerical calculation of turbulence structure in depth-varying unsteady open-channel flows. J Hydraul Eng 132(7):681–695. CrossRefGoogle Scholar
  20. Nezu I, Kadota A, Nakagawa H (1997) Turbulent structure in unsteady depth-varying open-channel flows. J Hydraul Eng 123(9):752–763. CrossRefGoogle Scholar
  21. Niazkar M, Afzali SH (2019) Developing a new accuracy-improved model for estimating scour depth around piers using a hybrid method. Iran J Sci Technol Trans Civil Eng 43(2):179–189. CrossRefGoogle Scholar
  22. Oliveto G, Hager WH (2002) Temporal evolution of clear-water pier and abutment scour. J Hydraul Eng 128(9):811–820.!0733-9429~2002!128:9~811 CrossRefGoogle Scholar
  23. Oliveto G, Hager WH (2005) Further results to time-dependent local scour at bridge elements. J Hydraul Eng 131(2):97–105. CrossRefGoogle Scholar
  24. Phillips CB, Hill KM, Paola C, Singer MB, Jerolmack DJ (2018) Effect of flood hydrograph duration, magnitude, and shape on bed load transport dynamics. Geophys Res Lett. CrossRefGoogle Scholar
  25. Pizarro A, Ettmer B, Manfreda S, Rojas A, Link O (2017) Dimensionless effective flow work for estimation of pier scour caused by flood waves. J Hydraul Eng. CrossRefGoogle Scholar
  26. Richardson EV, Davis SR (1995) Evaluating scour at bridges, 3rd edn. HEC-18, FHWA Report FHWA-IP-90-017, Washington, DCGoogle Scholar
  27. Schillinger MW (2011) Temporal pier scour evolution under stepped hydrographs. M.Sc. Thesis no: 1225, Clemson University, SC, USGoogle Scholar
  28. Schillinger MW, Khan AA (2013) Temporal pier scour evolution under stepped hydrographs. In: Khan AA, Wu W (eds) Sediment transport monitoring, modeling and management. Nova Publishers, New YorkGoogle Scholar
  29. Tabarestani MK, Zarrati AR (2016) Local scour calculation around bridge pier during flood event. KSCE J Civil Eng 21(4):1462–1472. CrossRefGoogle Scholar
  30. Talebbeydokhti N, Aghbolaghi MA (2006) Investigation of scour depth at bridge piers using bri-stars model. Iran J Sci Technol Trans B Eng 30(No. B4):541–554Google Scholar

Copyright information

© Shiraz University 2019

Authors and Affiliations

  1. 1.Civil Engineering Departmentİzmir Katip Çelebi UniversityIzmirTurkey

Personalised recommendations