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International Journal for Multiscale Computational Engineering
Factor de Impacto: 1.016 Factor de Impacto de 5 años: 1.194 SJR: 0.554 SNIP: 0.82 CiteScore™: 2

ISSN Imprimir: 1543-1649
ISSN En Línea: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2020031422
pages 181-197


Carlo Callari
DiBT Engineering Division, University of Molise, Campobasso, Italy, 86100
Francesco Froiio
Univ Lyon, École Centrale de Lyon, LTDS, 69134 Écully, France


We have recently proposed a finite element formulation able to simulate the localization of propagating internal erosion in rigid porous media. In the present paper, such method is extended to deformable porous solids, in order to also model the interaction between backward erosion piping and soil movements. We present the equations governing the exchange and transport of solid and fluid mass in a saturated poro-elastoplastic solid embedding a propagating erosion conduit conveying a multiphase flow. The full set of coupled finite element equations is then obtained from the weak formulations of mechanical equilibrium and fluid mass balance. The performance of the proposed formulation is assessed through an analysis of the soil response to the progressive dewatering of a cofferdam. The hydromechanical coupling and the ability in capturing both the onset and propagation of piping are crucial for an interpretation of the limit states typically observed in these structures.


  1. Abati, A. and Callari, C., Finite Element Formulation of Unilateral Boundary Conditions for Unsaturated Flow in Porous Continua, WaterResour. Res., vol. 50, no. 6, pp. 5114-5130,2014.

  2. Bauer, G.E., Scott, J.D., Shields, D.H., and Wilson, N.E., The Hydraulic Failure of a Cofferdam, Can. Geotech. J, vol. 17, no. 4, pp. 574-583,1980.

  3. Biot, M.A., General Theory of Three-Dimensional Consolidation, J. Appl. Phys., vol. 12, no. 2, pp. 155-164,1941.

  4. Bligh, W., Dams, Barrages and Weirs on Porous Foundations, Eng. News, vol. 64, no. 26, pp. 708-710, 1910.

  5. Bonelli, S. and Brivois, O., The Scaling Law in the Hole Erosion Test with a Constant Pressure Drop, Int. J. Numer. Anal. Methods Geomechan, vol. 32, no. 13, pp. 1573-1595,2008.

  6. Bonelli, S., Brivois, O., Borghi, R., and Benahmed, N., On the Modelling of Piping Erosion, C. R. Mec., vol. 334, nos. 8-9, pp. 555-559,2006.

  7. BSI, Eurocode 7: GeotechnicalDesign - Part 1: General Rules (BSEN 1997-1:2004), London: British Standards Institution, 2004.

  8. Callari, C. and Abati, A., Finite Element Methods for Unsaturated Porous Solids and Their Application to Dam Engineering Problems, Comput. Struct., vol. 87, nos. 7-8, pp. 485-501,2009.

  9. Callari, C. and Abati, A., Hyperelastic Multiphase Porous Media with Strain-Dependent Retention Laws, Transp. Porous Media, vol. 86, no. 1,pp. 155-176,2011.

  10. Callari, C., Armero, F., and Abati, A., Strong Discontinuities in Partially Saturated Poroplastic Solids, Comput. Methods Appl. Mech. Eng., vol. 199, nos. 23-24, pp. 1513-1535,2010.

  11. Callari, C. and Casini, S., Tunnels in Saturated Elasto-Plastic Soils: Three-Dimensional Validation of a Plane Simulation Procedure, in Mechanical Modelling and Computational Issues in Civil Engineering, Berlin: Springer, pp. 143-164,2005.

  12. Carman, P., Flow of Gases through Porous Media, 1sted., London, UK: Butterworth, 1956.

  13. Chanson, H., The Hydraulics of Open Channels Flows: An Introduction, 1st ed., Oxford, UK: Butterworth-Heinemann, 1999.

  14. Duann, S., Wang, R., and Wang, C., Piping Failure of a Cofferdam in Southern Taiwan, in Proc. of Int. Conf. on Foundation Failures, pp. 12-13, 1997.

  15. Froiio, F., Callari, C., and Rotunno, A.F., A Numerical Experiment of Backward Erosion Piping: Kinematics and Micromechanics, Meccanica, vol. 54,no. 14,pp. 2099-2117,2019.

  16. Hanson, G.J., Tejral, R., Hunt, S., and Temple, D., Internal Erosion and Impact of Erosion Resistance, in Proc. 30th US Society on Dams Annual Meeting and Conf., pp. 773-784,2010.

  17. HTG, Recommendations of the Committee for Waterfront Structures Harbours and Waterways (EAU 2012), John Wiley & Sons, 2015.

  18. Hughes, T.J.R., The Finite Element Method, Englewood Cliffs, NJ: Prentice-Hall, 1987.

  19. Hughes, T.J.R., Engel, G., Mazzei, L., and Larson, M., The Continuous Galerkin Method is Locally Conservative, J. Comput. Phys, vol. 163, no. 2, pp. 467-488,2000.

  20. Indraratna, B., Athukorala, R., and Vinod, J., Estimating the Rate of Erosion of a Silty Sand Treated with Lignosulfonate, J. Geotech. Geoenviron. Eng., vol. 139, no. 5, pp. 701-714,2012.

  21. Landau, L.D. and Lifshitz, E.M., Fluid Mechanics, Vol. 6, Oxford, UK: Pergamon Press, 1959.

  22. Lane, E., Security from Under-Seepage-Masonry Dams on Earth Foundations, Trans. Am. Soc. Civil Eng., vol. 100, no. 1, pp. 1235-1272,1935.

  23. Marsland, A., Model Experiments to Study the Influence of Seepage on the Stability of a Sheeted Excavation in Sand, Geotechnique, vol. 3, no. 6, pp. 223-241,1953.

  24. Ojha, C., Singh, V., and Adrian, D., Determination of Critical Head in Soil Piping, J. Hydraul. Eng., vol. 129, no. 7, pp. 511-518, 2003.

  25. Papamichos, E. and Vardoulakis, I., Sand Erosion with a Porosity Diffusion Law, Comput. Geotech., vol. 32, no. 1, pp. 47-58, 2005.

  26. Pope, S., Turbulent Flows, 1st ed., Cambridge: Cambridge University Press, 2000.

  27. Regazzoni, P. andMarot, D., A Comparative Analysis of Interface Erosion Tests, Nat. Hazards, vol. 67, no. 2, pp. 937-950,2013.

  28. Rotunno, A.F., Callari, C., and Froiio, F., Computational Modeling of Backward Erosion Piping, in Models, Simulation, and Experimental Issues in Structural Mechanics, Berlin: Springer, pp. 225-234,2017.

  29. Rotunno, A.F., Callari, C., and Froiio, F., A Finite Element Method for Localized Erosion in Porous Media with Applications to Backward Piping in Levees, Int. J. Numer. Anal. Methods Geomech., vol. 43, no. 1, pp. 293-316,2019a.

  30. Rotunno, A.F., Callari, C., and Froiio, F., A Numerical Approach for the Analysis of Piping Erosion in Hydraulic Works, in Internal Erosion in Earthdams, Dikes and Levees: Proc. of EWG-IE 26th Annual Meeting 2018, S. Bonelli, C. Jommi, and D. Sterpi, Eds., Vol. 17 of Lecture Notes in Civil Engineering, Switzerland: Springer Nature, pp. 159-167,2019b.

  31. Tanaka, T., Toyokuni, E., and Ozaki, E., A Case Study on Piping during Excavation for Bridge Abutments, in Underground Constructionin Soft Ground, Rotterdam, Netherlands: Balkema, pp. 159-162,1995.

  32. Tanaka, T. and Verruijt, A., Seepage Failure of Sand behind Sheet Piles: The Mechanism and Practical Approach to Analyze, Soils Found, vol. 39, no. 3, pp. 27-35,1999.

  33. Taylor, R.L., FEAP - A Finite Element Analysis Program: Version 8.2 Theory Manual, Berkley, CA: University of California at Berkley, 2008.

  34. Terzaghi, K., Der Grundbruch an Stauwerken und Seine Verhutung, Wasserkraft, vol. 17, pp. 445-449,1922. Terzaghi,K., Theoretical Soil Mechanics, New York: Wiley, 1943.

  35. Terzaghi, K., Peck, R.B., and Mesri, G., Soil Mechanics in Engineering Practice, New York: John Wiley & Sons, 1948.

  36. Tran, D., Prime, N., Froiio, F., Callari, C., and Vincens, E., Numerical Modelling of Backward Front Propagation in Piping Erosion by DEM-LBM Coupling, Eur. J. Environ. Civil Eng., vol. 21, nos. 7-8, pp. 960-987,2017.

  37. Vardoulakis, I., Stavropoulou, M., and Papanastasiou, P., Hydro-Mechanical Aspects of the Sand Production Problem, Transp. Porous Media, vol. 22, no. 2, pp. 225-244,1996.

  38. Wan, C. and Fell, R., Investigation of Rate of Erosion of Soils in Embankment Dams, J. Geotech. Geoenviron. Eng., vol. 130, no. 4, pp. 373-380, 2004a.

  39. Wan, C. and Fell, R., Laboratory Tests on the Rate of Piping Erosion of Soils in Embankment Dams, Geotech. Testing J, vol. 27, no. 3, pp. 295-303,2004b.

  40. Zhang, X., Wong, H., Leo, C., and Bui, T., A Thermodynamics-Based Model on the Internal Erosion of Earth Structures, Geotech. Geol. Eng., vol. 31, no. 2, pp. 479-492,2013.

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