Technical Papers
Aug 11, 2022

Clear Water Scour at Circular Piers: A New Formula Fitting Laboratory Data with Less Than 25% Deviation

Publication: Journal of Hydraulic Engineering
Volume 148, Issue 10

Abstract

In this paper, we propose a new predictor for the time-dependent, spatially-maximum scour depth at a circular pier in clear-water flow conditions. In spite of a number of approaches used in scour research, a simple predictor based on data correlation still has merit because more insightful studies of the process dynamics lack engineering impact. Furthermore, the simple condition of a circular pier is a reference for several variabilities to be considered afterwards. The present formula is obtained using laboratory data from 30 sources, corresponding to 328 experiments over 66 years. The predictor accounts for 5 dimensionless parameters (pier slenderness, flow intensity. sediment coarseness, sediment uniformity. and time) and has a good predictive ability, largely outperforming that of 27 literature equations. The proposal of a new formula is accompanied by several considerations based on additional parameters and operational conditions, as well as by an analysis of the uncertainty of the computed scour values and recommendations for conservative predictions of the scour depth in engineering practice.

Get full access to this article

View all available purchase options and get full access to this article.

Data Availability Statement

All the data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.

Acknowledgments

The authors wish to thank Seyed Kamran Jalali, Javad Mahmoudi, Federico Mantovani, Roberto Paleari, Andrea Pellegrinelli, Matteo Pezzullo, Riccardo Robbiani, Marzia Rullo, Elio Sepe, and Francesco Vento for contributing to this study within their M.Sc. (S.K.J. and J.M.) and B.Sc. (the others) theses.

References

Alabi, P. D. 2006. “Time development of local scour at a bridge pier fitted with a collar.” M.Sc. thesis, Dept. of Civil and Geological Environmental Engineering, Univ. of Saskatchewan.
Arneson, L. A., L. W. Zevenbergen, P. F. Lagasse, and P. E. Clopper. 2012. Evaluating scour at bridges. Hydraulic engineering circular no. 18. Washington, DC: DOT.
Azzaroli, D. 1983. “Analisi sperimentale dell’erosione localizzata attorno ad una coppia di pile inserite in una canaletta di laboratorio.” [In Italian.] M.Sc. thesis, Forestry and Environmental Sciences, Università di Padova.
Baker, C. J. 1980. “Theoretical approach to prediction of local scour around bridge piers.” J. Hydraul. Res. 18 (1): 1–12. https://doi.org/10.1080/00221688009499564.
Ballio, F., C. Bettoni, and S. Franzetti. 1998. “A survey of time-averaged characteristics of laminar and turbulent horseshoe vortices.” J. Fluids Eng. 120 (2): 233–242. https://doi.org/10.1115/1.2820639.
Ballio, F., A. Teruzzi, and A. Radice. 2009. “Constriction effects in clear-water scour at abutments.” J. Hydraul. Eng. 135 (2): 140–145. https://doi.org/10.1061/(ASCE)0733-9429(2009)135:2(140).
Beg, M. 2013. “Predictive competence of existing bridge pier scour depth predictors.” Eur. Int. J. Sci. Technol. 2 (1): 161–178.
Blench, T. 1969. Mobile-bed fluviology. Edmonton, Canada: Univ. of Alberta Press.
Bouratsis, P., P. Diplas, C. L. Dancey, and N. Apsilidis. 2017. “Quantitative spatio-temporal characterization of scour at the base of a cylinder.” Water 9 (3): 227. https://doi.org/10.3390/w9030227.
Breusers, H. N. C. 1965. “Scour around drilling platforms.” Bull. Hydraul. Res. 19: 276.
Breusers, H. N. C., G. Nicollet, and H. W. Shen. 1977. “Local scour around cylindrical pier.” J. Hydraul. Res. 15 (3): 211–252. https://doi.org/10.1080/00221687709499645.
Breusers, H. N. C., and A. J. Raudkivi. 1991. Vol. 2 of Scouring: Hydraulic design considerations. IAHR hydraulic structures design manual series. New York: Taylor & Francis.
Buffington, J. M., and D. R. Montgomery. 1997. “A systematic analysis of eight decades of incipient motion studies, with special reference to gravel-bedded rivers.” Water Resour. Res. 33 (8): 1993–2029. https://doi.org/10.1029/96WR03190.
Chabert, J., and P. Engeldinger. 1956. Étude des affouillements autour des piles de ponts. Technical Rep. [In French.] Chatou, France: Laboratoire National d’Hydraulique.
Chang, W. Y., J. S. Lai, and C. L. Yen. 2004. “Evolution of scour depth at circular bridge piers.” J. Hydraul. Eng. 130 (9): 905–913. https://doi.org/10.1061/(ASCE)0733-9429(2004)130:9(905).
Chee, R. K. W. 1982. Live-bed scour at bridge piers. Rep. No. 290. Auckland, New Zealand: School of Engineering, Univ. of Auckland.
Chiew, Y. M. 1984. Local scour at bridge piers. Rep. No. 355. Auckland, New Zealand: School of Engineering, Univ. of Auckland.
Chiew, Y. M. 1995. “Mechanics of riprap failure at bridge piers.” J. Hydraul. Eng. 121 (9): 635–643. https://doi.org/10.1061/(ASCE)0733-9429(1995)121:9(635).
Chitale, S. V. 1962. “Scour at bridge crossings.” Trans. ASCE 127 (1): 191–196.
Coleman, N. L. 1971. “Analyzing laboratory measurements of scour at cylindrical piers in sand beds.” In Vol. 3 of Proc., 14th Congress of the International Association for Hydraulic Research (IAHR), 307–313. Madrid, Spain: International Association for Hydraulic Research.
Coscarella, F., R. Gaudio, and C. Manes. 2020. “Near-bed eddy scales and clear-water local scouring around vertical cylinders.” J. Hydraul. Res. 58 (6): 968–981. https://doi.org/10.1080/00221686.2019.1698668.
Darcy, M. H., and M. H. Bazin. 1865. Recherches experimentales sur l’écoulement de l’eau dans les canaux découverts. [In French.] Paris: Libraire des Corps Impériaux des Ponts et Chausséès et des mines.
Dargahi, B. 1989. “The turbulent flow around a circular cylinder.” Exp. Fluids 8 (1): 1–12. https://doi.org/10.1007/BF00203058.
Dargahi, B. 1990. “Controlling mechanism of local scouring.” J. Hydraul. Eng. 116 (10): 1197–1214. https://doi.org/10.1061/(ASCE)0733-9429(1990)116:10(1197).
Dey, S. 1999. “Time-variation of scour in the vicinity of circular piers.” Proc. Inst. Civ. Eng. Water Marit. Energy 136 (2): 67–75. https://doi.org/10.1680/iwtme.1999.31422.
Dey, S. 2014. Fluvial hydrodynamics. Berlin: Springer-Verlag.
Dey, S., S. K. Bose, and G. L. N. Sastry. 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).
Diab, R., O. Link, and U. Zanke. 2010. “Geometry of developing and equilibrium scour holes at bridge piers in gravel.” Can. J. Civ. Eng. 37 (4): 544–552. https://doi.org/10.1139/L09-176.
Ettema, R. 1976. Influence of bed gradation on local scour. Rep. No. 124. Auckland, New Zealand: School of Engineering, The Univ. of Auckland.
Ettema, R. 1980. “Scour at bridge piers.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of Auckland.
Ettema, R., G. Constantinescu, and B. W. Melville. 2017. “Flow-field complexity and design estimation of pier-scour depth: Sixty years since Lausen and Toch.” J. Hydraul. Eng. 143 (9): 03117006. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001330.
Ettema, R., G. Kirkil, and M. Muste. 2006. “Similitude of large-scale turbulence in experiments on local scour at cylinders.” J. Hydraul. Eng. 132 (1): 33–40. https://doi.org/10.1061/(ASCE)0733-9429(2006)132:1(33).
Ettema, R., B. W. Melville, and B. Barkdoll. 1998. “Scale effect in pier-scour experiments.” J. Hydraul. Eng. 124 (6): 639–642. https://doi.org/10.1061/(ASCE)0733-9429(1998)124:6(639).
Ettmer, B., F. Mueller, and O. Link. 2015. “Live-bed scour at bridge piers in a lightweight Polystyrene bed.” J. Hydraul. Eng. 141 (9): 04015017. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001025.
Franzetti, S., E. Larcan, and P. Mignosa. 1982. “Influence of scour tests duration on the evaluation of ultimate scour around circular piers.” In Proc., Int. Conf. on Hydraulic Modelling of Civil Engineering Structures, 381–396. Bedford, UK: BHRA Fluid Engineering.
Franzetti, S., E. Larcan, and P. Mignosa. 1989. “Erosione alla base di pile circolari di ponte: Verifica sperimentale di esistenza di una situazione di equilibrio.” [In Italian.] Idrotecnica 3: 135–141.
Franzetti, S., S. Malavasi, and C. Piccinin. 1994. “Sull’erosione alla base delle pile di ponte in acque chiare.” [In Italian.] In Vol. T4 of Proc., 24 Convegno di Idraulica e Costruzioni Idrauliche, 13–24. Naples, Italy: Istituto di idraulica e costruzioni idrauliche.
Froelich, D. C. 1988. “Analysis of onsite measurements of scour at piers.” In Proc., ASCE National Conf. on Hydraulic Engineering, 534–539. Reston, VA: ASCE.
Gao, D., G. L. Posada, and C. F. Nordin. 1993. Pier scour equations used in the People’s Republic of China. Washington, DC: USDOT, Federal Highway Administration.
Gaudio, R., C. Grimaldi, A. Tafarojnoruz, and F. Calomino. 2010. “Comparison of formulae for the prediction of scour depth at piers.” In Proc., 1st European IAHR Congress, Madrid, Spain: International Association for Hydraulic Research.
Graf, W. H., and M. S. Altinakar. 1998a. Fluvial hydraulics. Chichester, UK: Wiley.
Graf, W. H., and I. Istiarto. 2002. “Flow pattern in the scour hole around a cylinder.” J. Hydraul. Res. 40 (1): 13–20. https://doi.org/10.1080/00221680209499869.
Graf, W. H., and B. Yulistiyanto. 1998b. “Experiments on flow around a cylinder: The velocity and vorticity fields.” J. Hydraul. Res. 36 (4): 637–654. https://doi.org/10.1080/00221689809498613.
Guo, J. 2014. “Semi-analytical model for temporal clear-water scour at prototype piers.” J. Hydraul. Res. 52 (3): 366–374. https://doi.org/10.1080/00221686.2013.877527.
Hancu, S. 1971. “On the estimation of local scour in the bridge piers zone.” In Vol. 3 of Proc., 14th Congress of the International Association for Hydraulic Research (IAHR), 299–313. Madrid, Spain: International Association for Hydraulic Research.
Hancu, S., and L. Predescu. 1989. “Experimental results on local scour around bridge piers in free surface water currents and pressurized air currents.” In Proc., 23rd Congress of the International Association for Hydraulic Research (IAHR), Madrid, Spain: International Association for Hydraulic Research.
Hoffmans, G. J. C. M., and H. J. Verheij. 1997. Scour manual. Rotterdam, Netherlands: A.A. Balkema.
Jain, S. C. 1981. “Maximum clear-water scour around circular piers.” ASCE J. Hydraul. Div. 107 (5): 611–626. https://doi.org/10.1061/JYCEAJ.0005667.
Jain, S. C., and E. E. Fischer. 1979. Scour around circular piers at high Froude numbers. Washington, DC: USDOT.
Jain, S. C., and E. E. Fischer. 1980. “Scour around bridge piers at high flow velocity.” ASCE J. Hydraul. Div. 106 (11): 1827–1842. https://doi.org/10.1061/JYCEAJ.0005560.
Johnson, P. A., and E. F. Torrico. 1994. “Scour around wide piers in shallow water.” Transp. Res. Rec. 1471 (Dec): 66–70.
Kandasamy, J. K., and B. W. Melville. 1998. “Maximum local scour depth at bridge piers and abutments.” J. Hydraul. Res. 36 (2): 183–198. https://doi.org/10.1080/00221689809498632.
Khosronejad, A., S. Kang, and F. Sotiropoulos. 2012. “Experimental and computational investigation of local scour around bridge piers.” Adv. Water Res. 37: 73–85. https://doi.org/10.1016/j.advwatres.2011.09.013.
Kothyari, U. C., R. J. Garde, and K. G. Ranga Raju. 1992. “Temporal variation of scour around circular bridge piers.” J. Hydraul. Eng. 118 (8): 1091–1106. https://doi.org/10.1061/(ASCE)0733-9429(1992)118:8(1091).
Kothyari, U. C., W. H. Hager, and G. Oliveto. 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).
Kothyari, U. C., and A. Kumar. 2010. “Temporal variation of scour around circular bridge piers.” ISH J. Hydraul. Eng. 16 (Suppl 1): 35–48. https://doi.org/10.1080/09715010.2010.10515014.
Lança, R., C. S. Fael, R. J. Maia, J. P. Pêgo, and A. Cardoso. 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.
Lança, R., G. Simarro, C. M. S. Fael, and A. H. Cardoso. 2016. “Effect of viscosity on the equilibrium scour depth at single cylindrical piers.” J. Hydraul. Eng. 142 (3): 06015022. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001102.
Laursen, E. M., and A. Toch. 1956. Scour around bridge piers and abutments. Bulletin No. 4. Ames, IA: Iowa Highway Research Board.
Lee, S. O., and T. W. Sturm. 2009. “Effect of sediment size scaling on physical modeling of bridge pier scour.” J. Hydraul. Eng. 135 (10): 793–802. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000091.
Liang, F., C. Wang, and B. Yu. 2019. “Performance of existing methods for estimation and mitigation of local scour around bridges: Case studies.” J. Perform. Constr. Facil. 33 (6): 04019060. https://doi.org/10.1061/(ASCE)CF.1943-5509.0001329.
Link, O., S. Henriquez, and B. Ettmer. 2019. “Physical scale modelling of scour around bridge piers.” J. Hydraul. Res. 57 (2): 227–237. https://doi.org/10.1080/00221686.2018.1475428.
Link, O., F. Pfleger, and U. Zanke. 2008. “Characteristics of developing scour-holes at a sand-embedded cylinder.” Int. J. Sediment Res. 23 (3): 258–266. https://doi.org/10.1016/S1001-6279(08)60023-2.
May, R., and I. Willoughby. 1990. Local scour around large obstructions. Technical Rep. Wallingford, UK: Hydraulics Research.
Melville, B. W. 1984. “Live-bed scour at bridge piles.” J. Hydraul. Eng. 110 (9): 1234–1247. https://doi.org/10.1061/(ASCE)0733-9429(1984)110:9(1234).
Melville, B. W. 1997. “Pier and abutment scour: Integrated approach.” J. Hydraul. Eng. 123 (2): 125–136. https://doi.org/10.1061/(ASCE)0733-9429(1997)123:2(125).
Melville, B. W., and Y. M. Chiew. 1999. “Time scale for local scour at bridge piers.” J. Hydraul. Eng. 125 (1): 59–65. https://doi.org/10.1061/(ASCE)0733-9429(1999)125:1(59).
Melville, B. W., and S. E. Coleman. 2000. Bridge scour. Highlands Ranch, CO: Water Resources Publications.
Melville, B. W., and A. J. Raudkivi. 1977. “Flow characteristics in local scour at bridge piers.” J. Hydraul. Res. 15 (4): 373–380. https://doi.org/10.1080/00221687709499641.
Melville, B. W., and A. J. Sutherland. 1988. “Design methods for local scour at bridge piers.” J. Hydraul. Eng. 114 (10): 1210–1226. https://doi.org/10.1061/(ASCE)0733-9429(1988)114:10(1210).
Mia, F., and H. Nago. 2003. “Design method of time-dependent local scour at circular bridge pier.” J. Hydraul. Eng. 129 (6): 420–427. https://doi.org/10.1061/(ASCE)0733-9429(2003)129:6(420).
Mignosa, P. 1980. “Fenomeni di erosione locale alla base delle pile dei ponti.” [In Italian.] M.Sc. thesis, Politecnico di Milano.
Miller, W. 2003. “Model for the time rate of local sediment scour at a cylindrical structure.” Ph.D. thesis, Civil and Coastal Engineering Dept., Univ. of Florida.
Ming, Z., L. Cheng, and Z. Zang. 2010. “Experimental and numerical investigation of local scour around a submerged vertical circular cylinder in steady currents.” Coast. Eng. 57 (8): 709–721. https://doi.org/10.1016/j.coastaleng.2010.03.002.
Nicollet, S. 1971. Deformation des lits alluvionnaires—Affouillement autour des piles de pont cylindriques. HC7043/689. Chatou, France: Laboratoire National d’Hydraulique.
Oliveto, G., and W. H. Hager. 2002. “Temporal evolution of clear-water pier and abutment scour.” J. Hydraul. Eng. 128 (9): 811–820. https://doi.org/10.1061/(ASCE)0733-9429(2002)128:9(811).
Olsen, N. R. B., and H. M. Kjellesvig. 1998. “Three-dimensional numerical flow modeling for estimation of maximum local scour depth.” J. Hydraul. Res. 36 (4): 579–590. https://doi.org/10.1080/00221689809498610.
Olsen, N. R. B., and M. C. Melaaen. 1993. “Three-dimensional calculation of scour around cylinders.” J. Hydraul. Eng. 119 (9): 1048–1054. https://doi.org/10.1061/(ASCE)0733-9429(1993)119:9(1048).
Pandey, M., P. K. Sharma, Z. Ahmad, and N. Karna. 2018. “Maximum scour depth around bridge pier in gravel bed streams.” Nat. Hazard. 91 (2): 819–836. https://doi.org/10.1007/s11069-017-3157-z.
Qi, M., J. Li, and Q. Chen. 2016. “Comparison of existing equations for local scour at bridge piers: Parameter influence and validation.” Nat. Hazard. 82 (3): 2089–2105. https://doi.org/10.1007/s11069-016-2287-z.
Qi, M., J. Li, and Q. Chen. 2018. “Applicability analysis of pier-scour equations in the field: Error analysis by rationalizing measurement data.” J. Hydraul. Eng. 144 (8): 04018050. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001497.
Radice, A., G. Porta, and S. Franzetti. 2009. “Analysis of the time-averaged properties of sediment motion in a local scour process.” Water Resour. Res. 45 (3): W03401. https://doi.org/10.1029/2007WR006754.
Radice, A., and C. K. Tran. 2012. “Study of sediment motion in scour hole of a circular pier.” J. Hydraul. Res. 50 (1): 44–51. https://doi.org/10.1080/00221686.2011.641764.
Raikar, R. V., and S. Dey. 2005. “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.
Rajaratnam, N., and D. Muralidhar. 1969. “Boundary shear stress distribution in rectangular open channels.” La Houille Blanche 55 (6): 603–610. https://doi.org/10.1051/lhb/1969047.
Roulund, A., B. M. Sumer, J. Fredsøe, and J. Michelsen. 2005. “Numerical and experimental investigation of flow and scour around a circular pile.” J. Fluid Mech. 534 (Jul): 351–401. https://doi.org/10.1017/S0022112005004507.
Shahriar, A., A. Ortiz, B. Montoya, and M. Gabr. 2021. “Bridge pier scour: An overview of factors affecting the phenomenon and comparative evaluation of selected models.” Transp. Geotech. 28 (May): 100549. https://doi.org/10.1016/j.trgeo.2021.100549.
Shalmani, Y. A., and H. Hakimzadeh. 2015. “Experimental investigation of scour around semi-conical piers under steady current action.” Eur. J. Environ. Civ. Eng. 19 (6): 717–732. https://doi.org/10.1080/19648189.2014.968742.
Shen, H. W., V. R. Schneider, and S. S. Karaki. 1969. “Local scour around bridge piers.” J. Hydraul. Div. 95 (6): 1919–1940. https://doi.org/10.1061/JYCEAJ.0002197.
Sheppard, D. M., H. Demir, and B. Melville. 2011. Scour at wide piers and long skewed piers. NCHRP Rep. No. 682. Washington, DC: Transportation Research Board.
Sheppard, D. M., B. Melville, and H. Demir. 2014. “Evaluation of existing equations for local scour at bridge piers.” J. Hydraul. Eng. 140 (1): 14–23. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000800.
Sheppard, D. M., and W. Miller Jr. 2006. “Live-bed local pier scour experiments.” J. Hydraul. Eng. 132 (7): 635–642. https://doi.org/10.1061/(ASCE)0733-9429(2006)132:7(635).
Sheppard, D. M., M. Odeh, and T. Glasser. 2002. Clearwater local sediment scour experiments. Coastal Engineering Technical Rep. No. 131. Gainesville, FL: Dept. of Civil and Coastal Engineering, Univ. of Florida.
Sheppard, D. M., B. Ontowirjo, and G. Zhao. 1999. “Conditions of maximum local scour.” In Proc., Stream Stability and Scour at Highway Bridges, Resources Engineering Conf., edited by E. V. Richardson and P. F. Lagasse, 1991–1998. Reston, VA: ASCE.
Simarro-Grande, G., and J. P. Martìn-Vide. 2004. “Exponential expression for time evolution in local scour.” J. Hydraul. Res. 42 (6): 663–665. https://doi.org/10.1080/00221686.2004.9628320.
Vonkeman, J. K., and G. R. Basson. 2019. “Evaluation of empirical equations to predict bridge pier scour in a non-cohesive bed under clear-water conditions.” J. South Afr. Inst. Civ. Eng. 61 (2): 2–20. https://doi.org/10.17159/2309-8775/2019/v61n2a1.
Wilson, K. V. 1995. Scour at selected bridge sites in Mississippi. Water-Resources Investigations Rep. No. 94–4241. Reston, VA: US Geological Survey.
Yanmaz, A. M., and H. D. Altinbilek. 1991. “Study of time-dependent local scour around bridge piers.” J. Hydraul. Eng. 117 (10): 1247–1268. https://doi.org/10.1061/(ASCE)0733-9429(1991)117:10(1247).

Information & Authors

Information

Published In

Go to Journal of Hydraulic Engineering
Journal of Hydraulic Engineering
Volume 148Issue 10October 2022

History

Received: Nov 6, 2021
Accepted: May 19, 2022
Published online: Aug 11, 2022
Published in print: Oct 1, 2022
Discussion open until: Jan 11, 2023

Permissions

Request permissions for this article.

ASCE Technical Topics:

Authors

Affiliations

Silvio Franzetti [email protected]
Retired, Professor, Dept. of Civil and Environmental Engineering, Politecnico di Milano, Piazza L. da Vinci 32, Milano 20133, Italy. Email: [email protected]
Associate Professor, Dept. of Civil and Environmental Engineering, Politecnico di Milano, Piazza L. da Vinci 32, Milano 20133, Italy (corresponding author). ORCID: https://orcid.org/0000-0001-5024-3199. Email: [email protected]
Daniel Rebai [email protected]
Ph.D. Student, Dept. of Civil and Environmental Engineering, Politecnico di Milano, Piazza L. da Vinci 32, Milano 20133, Italy. Email: [email protected]
Francesco Ballio [email protected]
Professor, Dept. of Civil and Environmental Engineering, Politecnico di Milano, Piazza L. da Vinci 32, Milano 20133, Italy. Email: [email protected]

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

  • Effect of Transversal Bed Slope on the Equilibrium Scour Depth at Bridge Piers, Journal of Hydraulic Engineering, 10.1061/JHEND8.HYENG-13756, 150, 4, (2024).
  • Method for Estimating Clear-Water Local Scour Rate at Complex Piers, Journal of Hydraulic Engineering, 10.1061/JHEND8.HYENG-13656, 149, 10, (2023).
  • Process-Based Design Method for Pier Local Scour Depth under Clear-Water Condition, Journal of Hydraulic Engineering, 10.1061/JHEND8.HYENG-13371, 149, 12, (2023).

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share