Dynamic Finite Element Investigation of Wave Attack on Sea Dikes: A Coupled Approach using Plate and Volume Elements

Abstract

Approximately 400 kilometres of Dutch sea dikes are protected by bituminous concrete revetments to prevent damage from erosion and repeated wave attacks during storms. The numerical analysis of sea dikes subjected to cyclic wave loading needs to consider the behaviour of the bituminous concrete revetment, and the behaviour of the subsoil including the generation and dissipation of the excess pore pressures, as well as the interaction between the revetment and subsoil. This thesis develops and evaluates numerical methods for investigating this problem, using the dynamic Finite Element Method with the coupling of plate and volume elements. In dynamic finite element analysis, the arbitrary selected boundary generates wave reflections which normally causes oscillation problems. Absorbing boundary conditions are therefore adopted to minimise the wave reflection at the artificial boundaries. The effects of the absorbing boundary conditions are investigated in detail for both solid and water phases, and appropriate sets of parameters are recommended. In order to model the bituminous concrete revetment, which is a thin layer of material with a high stiffness, a very fine mesh is often needed in order to obtain accurate results. However, an explicit time integration algorithm is normally needed for dynamic analysis, which reduces the critical time step size required for numerical stability if the same element type is used for both the revetment and the soil, severely affecting simulation performance. In order to avoid this problem, in this thesis a structural plate element is developed based on the classical Kirchhoff thin plate bending theory for modelling thin layer materials instead of the volume element. For consideration of both stretching and bending problems, the Kirchhoff thin plate bending theory has been extended. Specifically, a more conventional 3-noded triangular plate element, with 1 translational and 2 rotational degrees of freedom per node, has been extended to include 2 extra translational degrees of freedom per node, i.e. giving a total of 3 translational and 2 rotational degrees of freedom per node. Moreover, an enhanced lumped mass matrix for the plate element has been constructed by considering both translational and rotational degrees of freedom. Numerical validations indicate that the use of plate elements for simulating the thin layer material provides a great improvement on the accuracy of the results, as well as a significant decrease in the computational cost. For the limit state design of some engineering problems, non-linear material models provide more accurate results than elastic material models. Here an elastic viscoplastic model is investigated and implemented for the new plate element, using the Drucker-Prager yield condition and a non-associated flow rule. Typical creep behaviour of the bituminous concrete is presented and a parametric study of the viscoplastic model has been carried out for modelling the behaviour of Delft bituminous concrete. It is concluded that the viscosity value for a particular material changes from different conditions, that it depends not only on the material model and stress level, but also on the temperature. The developed numerical methods have been used to investigate the behaviour of sea dikes subjected to wave attacks. The results of the bending moments and stresses in the bituminous concrete, as well as the excess pore pressures and displacements in the soil, are presented. The tendency of a so-called shake down behaviour is observed after 10 cycles of wave attack during a severe storm, indicating that the displacement of the dike converges asymptotically to a particular final deformation.