Advertisement

A new mathematical model to calculate the equilibrium scour depth around a pier

  • Ainal Hoque Gazi
  • Mohammad Saud AfzalEmail author
Research Article - Hydrology
  • 59 Downloads

Abstract

This paper sheds light on the formulation of a new equilibrium local scour depth equation around a pier. The total bed materials removed from the scour hole due to the force exerted by the flowing fluid after colliding with the pier in the flow field are estimated. At the equilibrium condition, the shape of the scour hole around the pier may take any form, viz. linear, circular, parabolic, triangular, or combination of different shapes. To consider that, two functions are assumed at the stoss and the lee sides of the pier. The total volume of bed materials removed from the scour hole of an arbitrary shape at the stoss and the lee sides of the pier is obtained by integrating the two functions. The equilibrium scour depth is formed by applying the energy balance theorem. An example problem is illustrated and the results are compared with the equations presented by Melville and Coleman (Bridge scour. Water Resources Publication, Colorado, 2000) and HEC-18 (Richardson and Davis in Evaluating scour at bridges, HEC-18. Technical report no. FHWA NHI, 2001).

Keywords

Analytical solution Scour Energy balance Sediment transport 

Notes

Acknowledgements

This work was carried out as part of the Institute Scheme for Innovative Research and Development (ISIRD) titled “3D CFD Modeling of the Hydrodynamics and Local Scour Around Offshore Structures Under Combined Action of Current and Waves” from IIT Kharagpur.

Compliance with ethical standards

Conflict of interest

The authors declare no conflicts of interest in the current paper.

References

  1. AASHTO, LRFD (2010) Bridge design specificationsGoogle Scholar
  2. Afzal MS, Bihs H, Kamath A, Arntsen ØA (2015) Three-dimensional numerical modeling of pier scour under current and waves using level-set method. J Offshore Mech Arct Eng 137(3):032001.  https://doi.org/10.1115/1.4029999 CrossRefGoogle Scholar
  3. Ahmad N, Bihs H, Chella MA, Arntsen ØA, Aggarwal A et al (2017) Numerical modelling of arctic coastal erosion due to breaking waves impact using REEF3D. In: The 27th international ocean and polar engineering conference. International Society of Offshore and Polar EngineersGoogle Scholar
  4. Arneson L, Zevenbergen L, Lagasse P, Clopper P (2012) Evaluating scour at bridges. HEC-18. Federal Highway Administration (FHWA)Google Scholar
  5. Bouratsis P, Diplas P, Dancey CL, Apsilidis N (2017) Quantitative spatio-temporal characterization of scour at the base of a cylinder. Water 9(3):227.  https://doi.org/10.3390/w9030227 CrossRefGoogle Scholar
  6. Chabert J, Engeldinger P (1956) Study of scour around bridge piers. Technical report, prepared for the Laboratoire National d’HydrauliqueGoogle Scholar
  7. Chang H (1988) Fluvial processes in river engineering. Wiley, New YorkGoogle Scholar
  8. Dey S (1995) Three-dimensional vortex flow field around a circular cylinder in a quasi-equilibrium scour hole. Sadhana 20(6):871–885.  https://doi.org/10.1007/BF02745871 CrossRefGoogle Scholar
  9. Dey S (1996) Sediment pick-up for evolving scour near circular cylinders. Appl Math Model 20(7):534–539.  https://doi.org/10.1016/0307-904X(95)00172-G CrossRefGoogle Scholar
  10. Dey S (1997) Local scour at piers, part I: a review of developments of research. Int J Sediment Res 12(2):23–46Google Scholar
  11. Dey S (2014) Scour. In: Fluvial hydrodynamics, Springer, Berlin, pp. 563–639.  https://doi.org/10.1007/978-3-642-19062-9_10
  12. Dey S, Bose S, Sastry G (1992a) Clear water scour at circular piers, part I: flow model. In: Proceedings of 8th conference on IAHR Asian and Pacific Division, pp 69–80Google Scholar
  13. Dey S, Bose S, Sastry G (1992b) Clear water scour at circular piers, part II: design formula. In: Proceedings of 8th conference on IAHR Asian and Pacific Division, pp 81–92Google Scholar
  14. Dey S, Bose SK (1994) Bed shear in equilibrium scour around a circular cylinder embedded in a loose bed. Appl Math Model 18(5):265–273.  https://doi.org/10.1016/0307-904X(94)90334-4 CrossRefGoogle Scholar
  15. Dey S, Bose SK, Sastry GL (1995) Clear water scour at circular piers: a model. J Hydraul Eng 121(12):869–876.  https://doi.org/10.1061/(ASCE)0733-9429(1995)121:12(869) CrossRefGoogle Scholar
  16. Dey S, Raikar RV (2007) Characteristics of horseshoe vortex in developing scour holes at piers. J Hydraul Eng 133(4):399–413.  https://doi.org/10.1061/(ASCE)0733-9429(2007)133:4(399) CrossRefGoogle Scholar
  17. Ettema R, Melville BW, Constantinescu G (2011) Evaluation of bridge scour research: Pier scour processes and predictions. CiteseerGoogle Scholar
  18. Gioia G, Bombardelli FA (2005) Localized turbulent flows on scouring granular beds. Phys Rev Lett 95(1):014501CrossRefGoogle Scholar
  19. Gioia G, Chakraborty P (2006) Turbulent friction in rough pipes and the energy spectrum of the phenomenological theory. Phys Rev Lett 96(4):044502CrossRefGoogle Scholar
  20. Graf W, Istiarto I (2002) Flow pattern in the scour hole around a cylinder. J Hydraul Res 40(1):13–20.  https://doi.org/10.1080/00221680209499869 CrossRefGoogle Scholar
  21. Hafez YI (2016) Mathematical modeling of local scour at slender and wide bridge piers. J Fluids.  https://doi.org/10.1155/2016/4835253
  22. Harik I, Shaaban A, Gesund H, Valli G, Wang S (1990) United states bridge failures, 1951–1988. J Perform Constr Facil 4(4):272–277.  https://doi.org/10.1061/(ASCE)0887-3828(1990)4:4(272) CrossRefGoogle Scholar
  23. Kamojjala S, Gattu N, Parola A, Hagerty D (1994) Analysis of 1993 upper Mississippi flood highway infrastructure damage. In: Water resources engineering, ASCE, pp 1061–1065Google Scholar
  24. Kattell J, Eriksson M (1998) Bridge scour evaluation: screening, analysis, and countermeasures. Technical report, USDA Forest Service, San Dimas Technology and Development CenterGoogle Scholar
  25. Khaple S, Hanmaiahgari PR, Gaudio R, Dey S (2017) Interference of an upstream pier on local scour at downstream piers. Acta Geophys 65(1):29–46.  https://doi.org/10.1007/s11600-017-0004-2 CrossRefGoogle Scholar
  26. Kothyari UC, Hager WH, Oliveto G (2007) Generalized approach for clear-water scour at bridge foundation elements. J Hydraul Eng 133(11):1229–1240.  https://doi.org/10.1061/(ASCE)0733-9429(2007)133:11(1229) CrossRefGoogle Scholar
  27. Lagasse PF (2007) Countermeasures to protect bridge piers from scour, vol 593, Transportation Research BoardGoogle Scholar
  28. Lança RM, Fael CS, Maia RJ, Pêgo JP, Cardoso AH (2013) Clear-water scour at comparatively large cylindrical piers. J Hydraul Eng 139(11):1117–1125.  https://doi.org/10.1061/(ASCE)HY.1943-7900.0000788 CrossRefGoogle Scholar
  29. Manes C, Brocchini M (2015) Local scour around structures and the phenomenology of turbulence. J Fluid Mech 779:309–324.  https://doi.org/10.1017/jfm.2015.389 CrossRefGoogle Scholar
  30. Melville BW, Coleman SE (2000) Bridge scour. Water Resources Publication, ColoradoGoogle Scholar
  31. Melville BW, Raudkivi AJ (1977) Flow characteristics in local scour at bridge piers. J Hydraul Res 15(4):373–380.  https://doi.org/10.1080/00221687709499641 CrossRefGoogle Scholar
  32. Mutlu Sumer B (2007) Mathematical modelling of scour: a review. J Hydraul Res 45(6):723–735.  https://doi.org/10.1080/00221686.2007.9521811 CrossRefGoogle Scholar
  33. Nurtjahyo P, Chen H, Briaud J, Li Y, Wang J (2002) Bed shear stress around rectangular pier: numerical approach. In: First international conference on scour of foundations international society of soil mech and foundationsGoogle Scholar
  34. Olsen NR, Melaaen MC (1993) Three-dimensional calculation of scour around cylinders. J Hydraul Res 119(9):1048–1054.  https://doi.org/10.1061/(ASCE)0733-9429(1993)119:9(1048) CrossRefGoogle Scholar
  35. Raikar R, Dey S (2005a) Scour of gravel beds at bridge piers and abutments, vol 158, Thomas Telford Ltd, pp 157–162Google Scholar
  36. Raikar RV, Dey S (2005b) Clear-water scour at bridge piers in fine and medium gravel beds. Can J Civ Eng 32(4):775–781.  https://doi.org/10.1139/l05-022 CrossRefGoogle Scholar
  37. Raikar RV, Dey S (2008) Kinematics of horseshoe vortex development in an evolving scour hole at a square cylinder. J Hydraul Res 46(2):247–264.  https://doi.org/10.1080/00221686.2008.9521859 CrossRefGoogle Scholar
  38. Richardson E, Davis S (2001) Evaluating scour at bridges, HEC-18. Technical report, Rep. No. FHWA NHIGoogle Scholar
  39. Roulund A, Sumer BM, Fredsøe J, Michelsen J (2005) Numerical and experimental investigation of flow and scour around a circular pile. J Fluid Mech 534:351–401.  https://doi.org/10.1017/S0022112005004507 CrossRefGoogle Scholar
  40. Salaheldin TM, Imran J, Chaudhry MH (2004) Numerical modeling of three-dimensional flow field around circular piers. J Hydraul Eng 130(2):91–100.  https://doi.org/10.1061/(ASCE)0733-9429(2004)130:2(91) CrossRefGoogle Scholar
  41. Shatanawi KM, Aziz NM, Khan AA (2008) Frequency of discharge causing abutment scour in South Carolina. J Hydraul Eng 134(10):1507–1512.  https://doi.org/10.1061/(ASCE)0733-9429(2008)134:10(1507) CrossRefGoogle Scholar
  42. Sheppard DM, Odeh M, Glasser T (2004) Large scale clear-water local pier scour experiments. J Hydraul Eng 130(10):957–963.  https://doi.org/10.1061/(ASCE)0733-9429(2004)130:10(957) CrossRefGoogle Scholar
  43. Wardhana K, Hadipriono FC (2003) Analysis of recent bridge failures in the united states. J Perform Constr Facil 17(3):144–150.  https://doi.org/10.1061/(ASCE)0887-3828(2003)17:3(144) CrossRefGoogle Scholar
  44. Yang Y, Qi M, Li J, Ma X (2018) Evolution of hydrodynamic characteristics with scour hole developing around a pile group. Water 10(11):1632CrossRefGoogle Scholar

Copyright information

© Institute of Geophysics, Polish Academy of Sciences & Polish Academy of Sciences 2019

Authors and Affiliations

  1. 1.Department of Civil EngineeringIndian Institute of Technology KharagpurKharagpurIndia

Personalised recommendations