Technical Papers
Jan 21, 2020

Theoretical Approach for Shear-Stress Estimation at 2D Equilibrium Scour Holes in Granular Material due to Subvertical Plunging Jets

Publication: Journal of Hydraulic Engineering
Volume 146, Issue 4

Abstract

The estimation of flow-induced shear stresses acting on the surface of scour holes still represents a challenge for scientists and engineers. From the practical point of view, excessive shear stresses can lead to significant scour depths, resulting eventually in the failure of the structure. From the scientific point of view, detailed knowledge of the shear stresses can yield novel insights for further understanding of scour in particular and of two-phase flows in general. Numerous studies have focused on the interaction between the water flow and a granular bed in order to furnish usable expressions for design and to provide knowledge of the erosive mechanisms. Most of those approaches are empirical, and are characterized by rather significant limitations due to tested conditions. Conversely, only a few studies have derived general theoretical equations for the prediction of the shear stresses based on the phenomenological theory of turbulence. To the best of the authors’ knowledge, no works have taken into consideration the effect of the amount of suspended sediment on the value of the shear stress at the dynamic equilibrium configuration. This paper proposes a model based on the conservation of the angular momentum in the turbulent pothole to address those stresses. Novel experimental tests allowed for the validation of the derived equation, which is consistent with accepted theoretical and semitheoretical results.

Get full access to this article

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

Data Availability Statement

All data used during the study appear in the published article.

References

Beltaos, S., and N. Rajaratnam. 1973. “Plane turbulent impinging jets.” J. Hydraul. Res. 11 (1): 29–59. https://doi.org/10.1080/00221687309499789.
Beltaos, S., and N. Rajaratnam. 1974. “Impinging circular turbulent jets.” J. Hydraul. Div. 100 (10): 1313–1328.
Beltaos, S., and N. Rajaratnam. 1977. “Impingement of axisymmetric developing jets.” J. Hydraul. Res. 15 (4): 311–326. https://doi.org/10.1080/00221687709499637.
Bollaert, E., and A. Schleiss. 2003. “Scour of rock due to the impact of plunging high velocity jets Part I: A state-of-the-art review.” J. Hydraul. Res. 41 (5): 451–464. https://doi.org/10.1080/00221680309499991.
Bombardelli, F. A., and G. Gioia. 2005. “Towards a theoretical model for scour phenomena.” In Vol. 2 of Proc., RCEM 2005, 4th IAHR Symp. on River, Coastal, and Estuarine Morphodynamics, edited by G. Parker and M. García, 931–936. London: CRC Press.
Bombardelli, F. A., and G. Gioia. 2006. “Scouring of granular beds by jet-driven axisymmetric turbulent cauldrons.” Phys. Fluids 18 (8): 088101. https://doi.org/10.1063/1.2335887.
Bombardelli, F. A., and S. K. Jha. 2011. “Discussion on ‘closure problem to jet scour’.” J. Hydraul. Res. 49 (2): 277–279. https://doi.org/10.1080/00221686.2011.568601.
Bombardelli, F. A., M. Palermo, and S. Pagliara. 2018. “Temporal evolution of jet induced scour depth in cohesionless granular beds and the phenomenological theory of turbulence.” Phys. Fluids 30 (8): 085109. https://doi.org/10.1063/1.5041800.
Bormann, N. E., and P. Y. Julien. 1991. “Scour downstream of grade-control structures.” J. Hydraul. Eng. 117 (5): 579–594. https://doi.org/10.1061/(ASCE)0733-9429(1991)117:5(579).
Breusers, H. N. C., and A. J. Raudkivi. 1991. Scouring: Hydraulic structures design manual series. Rotterdam, Netherlands: A.A. Balkema.
Castillo, L. G., J. M. Carrillo, and A. Blazquez. 2015. “Plunge pool dynamic pressures: A temporal analysis in the nappe flow case.” J. Hydraul. Res. 53 (1): 101–118. https://doi.org/10.1080/00221686.2014.968226.
Castillo, L. G., J. M. Carrillo, and F. A. Bombardelli. 2017. “Distribution of mean flow and turbulence statistics in plunge pools.” J. Hydroinf. 19 (2): 173–190. https://doi.org/10.2166/hydro.2016.044.
Chee, S. P., and T. Kung. 1974. “Piletas de derrubio autoformadas.” In Proc., 6th IAHR Latin American Congress. Madrid, Spain: IAHR.
Chee, S. P., and P. V. Padiyar. 1969. “Erosion at the base of flip buckets.” Eng. J. Inst. Can. 52 (111): 22–24.
Ervine, D. A., and H. T. Falvey. 1987. “Behavior of turbulent water jets in the atmosphere and in plunge pools.” Proc. Inst. Civ. Eng. 83 (1): 295–314. https://doi.org/10.1680/iicep.1987.353.
Ervine, D. A., H. T. Falvey, and W. Withers. 1997. “Pressure fluctuations on plunge pool floors.” J. Hydraul. Res. 35 (2): 257–279. https://doi.org/10.1080/00221689709498430.
Franke, P. G. 1960. “Uber Kolkbildung und Kolkformen.” Oesterr. Wasserwirtsch. 12 (1): 11–16.
Gioia, G., and F. A. Bombardelli. 2002. “Scaling and similarity in rough channel flows.” Phys. Rev. Lett. 88 (1): 014501. https://doi.org/10.1103/PhysRevLett.88.014501.
Gioia, G., and F. A. Bombardelli. 2005. “Localized turbulent flows on scouring granular beds.” Phys. Rev. Lett. 95 (1): 014501. https://doi.org/10.1103/PhysRevLett.95.014501.
Graf, W. H. 1971. Hydraulics of sediment transport. New York: McGraw-Hill.
Hoffmans, G. J. C. M. 1998. “Jet scour in equilibrium phase.” J. Hydraul. Eng. 124 (4): 430–437. https://doi.org/10.1061/(ASCE)0733-9429(1998)124:4(430).
Hoffmans, G. J. C. M. 2009. “Closure problem to jet scour.” J. Hydraul. Res. 47 (1): 100–109. https://doi.org/10.3826/jhr.2009.3179.
Hoffmans, G. J. C. M., and H. J. Verheij. 1997. Scour manual. Rotterdam, Netherlands: A.A. Balkema.
Jia, Y., T. Kitamura, and S. S. Y. Wang. 2001. “Simulation of scour process in plunging pool of loose bed-material.” J. Hydraul. Eng. 127 (3): 219–229. https://doi.org/10.1061/(ASCE)0733-9429(2001)127:3(219).
Julien, P. Y. 2010. Erosion and sedimentation. 2nd ed. Cambridge, UK: Cambridge University Press.
Kotoulas, D. 1967. “Das Kolkproblem unter besonderer Beruecksichtigung der Faktoren Zeit und Geschiebemischung in Rahmen der Wildbachverbauung.” Ph.D. dissertation, Dept. of Civil, Environmental and Geomatic Engineering—Laboratory of Hydraulics, Hydrology and Glaciology (VAW), Technischen Hochschule Zurich.
Machado, L. I. 1980. “Formulas to calculate the scour limit on granular or rock beds.” In Proc., 13th National Workshop on Large Dams, 35–52. Paris: International Commission on Large Dams.
Mason, P. J., and K. Arumugam. 1985. “Free jet scour below dams and flip buckets.” J. Hydraul. Eng. 111 (2): 220–235. https://doi.org/10.1061/(ASCE)0733-9429(1985)111:2(220).
Mueller, R., and W. Eggenberger. 1944. “Experimentelle und theoretische Untersuchungen ueber das Kolkproblem.” [In German.] In Mitt. Versuchanstalt Wasserbau, No. 5. Zurich, Switzerland: ETH Zurich.
Nguyen, V., J. R. Courivaud, P. Pinettes, H. Souli, and J. M. Fleureau. 2017. “Using and improved jet-erosion test to study the influence of soil parameters on the erosion of a silty soil.” J. Hydraul. Eng. 143 (8): 1–11. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001305.
Pagliara, S., M. Amidei, and W. H. Hager. 2008a. “Hydraulics of 3D plunge pool scour.” J. Hydraul. Eng. 134 (9): 1275–1284. https://doi.org/10.1061/(ASCE)0733-9429(2008)134:9(1275).
Pagliara, S., W. H. Hager, and H.-E. Minor. 2006. “Hydraulics of plane plunge pool scour.” J. Hydraul. Eng. 132 (5): 450–461. https://doi.org/10.1061/(ASCE)0733-9429(2006)132:5(450).
Pagliara, S., W. H. Hager, and J. Unger. 2008b. “Temporal evolution of plunge pool scour.” J. Hydraul. Eng. 134 (11): 1630–1638. https://doi.org/10.1061/(ASCE)0733-9429(2008)134:11(1630).
Pagliara, S., and M. Palermo. 2008. “Plane plunge pool scour with protection structures.” J. Hydro-environ. Res. 2 (3): 182–191. https://doi.org/10.1016/j.jher.2008.06.002.
Pagliara, S., M. Palermo, and I. Carnacina. 2009. “Scour and hydraulic jump downstream of block ramps in expanding stilling basins.” J. Hydraul. Res. 47 (4): 503–511. https://doi.org/10.1080/00221686.2009.9522026.
Pagliara, S., D. Roy, and M. Palermo. 2010. “3D plunge pool scour with protection measures.” J. Hydro-environ. Res. 4 (3): 225–233. https://doi.org/10.1016/j.jher.2009.10.014.
Papanicolaou, A. N. T., F. Bressan, J. Fox, C. Kramer, and L. Kjos. 2018. “Role of structure submergence on scour evolution in gravel bed rivers: Application to slope-crested structures.” J. Hydraul. Eng. 144 (2): 1–14. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001447.
Phares, D. J., G. T. Smedley, and R. C. Flagan. 2000. “The wall shear stress produced by the normal impingement of a jet on a flat surface.” J. Fluid Mech. 418: 351–375. https://doi.org/10.1017/S002211200000121X.
Poreh, M., Y. G. Tsuei, and J. E. Cermak. 1967. “Investigation of a turbulent radial wall jet.” J. Appl. Mech. 34 (2): 457–463. https://doi.org/10.1115/1.3607705.
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. 1976. “Turbulent jets.” In Vol. 5 of Development in water science. Amsterdam, Netherlands: Elsevier.
Rajaratnam, N. 1981. “Erosion by plane turbulent jets.” J. Hydraul. Res. 19 (4): 339–358. https://doi.org/10.1080/00221688109499508.
Rajaratnam, N. 1982. “Erosion by unsubmerged plane water jets.” In Proc., Applying Research to Hydraulic Practice, 280–288. Reston, VA: ASCE.
Rajaratnam, N., and K. A. Mazurek. 2005. “Impingement of circular turbulent jets on rough boundaries.” J. Hydraul. Res. 43 (6): 689–695. https://doi.org/10.1080/00221680509500388.
Scheingross, J. S., and M. P. Lamb. 2016. “Sediment transport through self-adjusting, bedrock-walled waterfall plunge pools.” J. Geophys. Res. F: Earth Surf. 5 (1): 939–963. https://doi.org/10.1002/2015JF003620.
Schoklitsch, A. 1932. “Kolkbildung unter Ueberfallstrahlen.” [In German.] Wasserwirtschaft 25 (24): 343.
Shields, A. F. 1936. “Anwendung der Aehnlichkeitsmechanik und der Turbulenzforschung auf die Geschiebebewegung” [Application of similarity mechanics and turbulence research on the bed-load motion]. [In German.] Mitt. Preuss. Versuchsanst Wasserbau Schiffbau 26: 1–26.
Stein, O. R., and P. Y. Julien. 1990. “Sediment concentration measurements below small headcuts.” In Proc., 1990 National Conf., 293–298. Reston, VA: ASCE.
Stein, O. R., and P. Y. Julien. 1993. “Criterion delineating the mode of headcut migration.” J. Hydraul. Eng. 119 (1): 37–50. https://doi.org/10.1061/(ASCE)0733-9429(1993)119:1(37).
Stein, O. R., and P. Y. Julien. 1994. “Sediment concentration below free overfall.” J. Hydraul. Eng. 120 (9): 1043–1059. https://doi.org/10.1061/(ASCE)0733-9429(1994)120:9(1043).
Stein, O. R., P. Y. Julien, and C. V. Alonso. 1993. “Mechanics of jet scour downstream of a headcut.” J. Hydraul. Res. 31 (6): 723–738. https://doi.org/10.1080/00221689309498814.
Veronese, A. 1937. Erosion of a bed downstream from an outlet. Fort Collins, CO: Colorado A&M College.
White, F. M. 2016. Fluid mechanics. 8th ed. New York: McGraw-Hill.
Whittaker, J. G., and A. Schleiss. 1984. “Scour related to energy dissipaters for high head structures.” Vol. 73 of Mitteilungen Versuchsanstalt Wasserbau: Hydrologie und Glaziologie. Zurich, Switzerland: VAW.
Yalin, M. S. 1977. The mechanics of sediment transport. Oxford, UK: Pergamon.

Information & Authors

Information

Published In

Go to Journal of Hydraulic Engineering
Journal of Hydraulic Engineering
Volume 146Issue 4April 2020

History

Received: May 23, 2018
Accepted: Aug 13, 2019
Published online: Jan 21, 2020
Published in print: Apr 1, 2020
Discussion open until: Jun 21, 2020

Permissions

Request permissions for this article.

Authors

Affiliations

Senior Researcher, Dept. of Energy, Systems, Territory, and Construction Engineering, Univ. of Pisa, Pisa 56122, Italy (corresponding author). ORCID: https://orcid.org/0000-0002-4225-1823. Email: [email protected]
Stefano Pagliara, Aff.M.ASCE [email protected]
Professor, Dept. of Energy, Systems, Territory, and Construction Engineering, Univ. of Pisa, Pisa 56122, Italy. Email: [email protected]
Fabián A. Bombardelli, A.M.ASCE [email protected]
Professor, Dept. of Civil and Environment Engineering, Univ. of California, Davis, CA 95616. Email: [email protected]; [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

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