Hisham El Safti, Matthias Kudella, Hocine Oumeraci


A finite volume model is developed for modelling the behaviour of the seabed underneath monolithic breakwaters. The fully coupled and fully dynamic Biot’s governing equations are solved in a segregated approach. Two simplifications to the governing equations are presented and tested: (i) the pore fluid acceleration is completely neglected (the u-p approximation) and (ii) only the convective part is neglected. It is found that neglecting the pore fluid convection does not reduce the computational time for the presented model. Verification of the model results with the analytical solution of the quasi-static equations is presented. A multi-yield surface plasticity model is implemented in the model to simulate the foundation behaviour under cyclic loads. Preliminary validation of the model with large-scale physical model data is presented.


caisson breakwater; sand foundation; porous flow; pore pressure; plasticity

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Detournay, E. and Cheng, A.H.-D. 1993. Fundamentals of Poroelasticity, Chapter 5 in Comprehensive Rock Engineering: Principles, Practice and Projects, Vol. II, Analysis and Design Method, ed. C. Fairhurst, Pergamon Press, pp. 113-171.

El Safti, H. and Oumeraci, H. 2012. Wave-structure-foundation interaction: structural model, Internal Report, Leichtweiß-Institute for Hydraulic Engineering and Water Resources, TU-Braunschweig, Germany.

Elgamal, A., Yang, Z., Parra, E., and Ragheb, A. 2003. Modeling of Cyclic Mobility in Saturated Cohesionless Soils, International Journal of Plasticity, Pergamon, Elsevier Science Ltd., Vol. 19, Issue 6, pp. 883-905.

Jasak, H. 1996. Error analysis and estimation for the Finite Volume method with applications to fluid flows, PhD. Thesis, Imperial College, University of London.

Jasak, H. and Weller, H.G. 2000a. Application of the Finite Volume Method and Unstructured Meshes to Linear Elasticity, Int. J. Num. Meth. Engineering 2000, v 48, n 2, pp 267-287<267::AID-NME884>3.0.CO;2-Q

Jasak, H. and Weller, H.G. 2000b. Finite volume methodology for contact problems of linear elastic solids, Proceedings of 3rd International Conference of Croatian Society of Mechanics, Cavtat/Dubrovnik, September 2000.

Jeng, D.-S. 2003. Wave-induced sea floor dynamics. Applied Mechanics Reviews, ASME, 56(4), 407-429, pp.

Jeng, D.-S., and Ou, J. 2010. 3D models for wave-induced pore pressures near breakwater heads. Acta Mechanica. doi: 10.1007/s00707-010-0303-z.

Kudella, M., Oumeraci, H., de Groot, M.B. and Meijers, P. 2006. Large-Scale Experiments on Pore Pressure Generation underneath a Caisson Breakwater. Journal of Waterway, Port, Coastal, and Ocean Engineering, Vol. 132, No. 4, pp. 310-324.

Liu, X. and García, M.H. 2006. Numerical Simulation of sea bed response under waves with coupled solver of Biot consolidation equations and free surface water flow. In proceeding of ISOPE PACOMS, Dalian, China.

Mroz, Z. 1967. On the description of anisotropic work hardening. J. Mech. Phys. Solids, 15, 163–175.

Oumeraci, H. 1994. Review and Analysis of Vertical Breakwater Failures - Lessons learned. Coastal Engineering, Special Issue on "Vertical Breakwaters", Amsterdam, The Netherlands: Elsevier Science Publishers B.V., vol. 22, nos. 1/2, pp 3- 29.

Oumeraci, H. 2004. Breakwaters, Part 2. In: Agerschou, H. (ed.): Planning and design of ports and marine terminals, London, U.K.: Thomas Telford, pp. 155-262.

Oumeraci, H., Kortenhaus, A. 1994. Analysis of Dynamic Response of Caisson Breakwaters. Coastal Engineering, Special Issue on "Vertical Breakwaters", Oumeraci, H. et al., Amsterdam, The Netherlands: Elsevier Science Publishers B.V., vol. 22, nos. 1/2, pp. 159-183.

Oumeraci, H., Kortenhaus, A., Allsop, N.W.H., De Groot, M.B., Crouch, R.S., Vrijling, J.K., Voortman, H.G. 2001. Probabilistic design tools for vertical breakwaters. Rotterdam, The Netherlands: Balkema, 392 pp.

Oumeraci, H., Kudella, M. 2004. Liquefaction around marine structures (LIMAS) – Work package 3, large scale experiments on a caisson breakwater. Technical report of Leichtweiß-Institute for Hydraulic Engineering and Water Resources, Technical University Braunschweig, Braunschweig, Germany, 119 pp.

Prévost, J. H. 1985. A simple plasticity theory for frictional cohesionless soils. Soil Dyn. Earthquake Eng., 4(1), 9–17.

Sheng, D., Wriggers, P., Sloan, S. W. 2007. Application of Frictional Contact in Geotechnical Engineering. International journal of geomechanics. ASCE / May/June 2007.

Stickle, M.M., Pastor, M. and Dutto, P. 2012. Mathematical and Numerical Modeling in Maritime Geomechanics. Pensamiento Matemático ISSN-e 2174-0410, Nº. 2 (April), 2012, 21 pp.

Ülker, M.B.C., Rahman, M.S., and Guddati, M.N. 2012. Breaking wave-induced response and instability of seabed around caisson breakwater. Int. J. Numer. Anal. Meth. Geomech. 2012; 36:362–390.

Yang, Z., Elgamal, A., and Parra, E. 2003. Computational Model for Cyclic Mobility and Associated Shear Deformation, J. Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 129, Nr. 12, pp. 1119-1127

Yang, Z., Lu, J. and Elgamal, A. 2008. OpenSees Soil Models and Solid-Fluid Fully Coupled Elements. User's Manual. Ver 1.0. University of California, San Diego, 25 pp.

Zienkiewicz, O.C., Chan, A.H.C., Pastor, M., Schrefler, B.A. and Shiomi, T. 1999. Computational Geomechanics (with Special Reference to Earthquake Engineering). UK: John Wiley & Sons Ltd, 383 pp.

Zienkiewicz, O.C. and Shiomi., T 1984. Dynamic Behaviour of Saturated Porous Media; The Generalized Biot Formulation And Its Numerical Solution. International, Journal for Numerical Methods in Engineering, 8:71–96.