Numerical modeling of poroelastic seabed soil–structure systems under cyclic loading in geotechnical coastal engineering

Geotechnical engineers are in charge of evaluating the behavior of the foundation soil in designing coastal and offshore structures which are under constant development. In problems of geotechnical engineering, it is necessary to know how the response of saturated soils under external loads are evaluated. Dynamics of saturated soils under cyclic loadings have been studied for many years especially under earthquake and wave loadings. The theory of 'coupled flow and deformation' has long been one of the most fundamental and mathematically sound approaches in the analysis of saturated porous media. The theory describes the mechanical changes in saturated porous soils under external loads in terms of the relative motion of solid and fluid phases together. The analyses of the dynamic response of saturated soils are performed depending upon the mathematical formulations defined by the governing equations of coupled flow and deformation. In general, it is not quite possible to obtain analytical solutions to the problems involving complex soil behavior. In those cases, one seeks alternative methods to obtain approximate solutions to the problem. The 'finite element method', a very well known numerical method utilized in this study, has been such a powerful and robust way of dealing with the solutions to complex engineering problems. The finite element formulation of the equation of motion describing the dynamic behavior of geotechnical engineering systems is derived by discretizing the governing coupled flow and deformation equations of the two-phase saturated porous media. Equation of motion is written in terms of the presence of the inertial terms of the two-phases in porous media. If all the inertial terms are kept in the equations, this formulation is called the 'fully dynamic formulation' (FD). Neglecting the inertial terms associated with the pore fluid motion gives the 'partly dynamic formulation' (PD), and finally by neglecting all the inertial terms in the equations, we arrive at the 'quasi static formulation' (QS). For a single soil element, dynamic response can be evaluated by integrating the equation of motion in temporal and spatial domains once the stiffness modules of the two-phases are derived. Constitutive relations of the soil model are introduced into the equation set in terms of stress-strain relations. In practice, the soil behavior defined as a simple linearly elastic element does not reflect the actual situation in real life. Thus, the stress-strain behavior of soils must be defined by employing theoretical constitutive models which allow the calculation of plastic shear strains that the soil exhibits during the course of loading. Therefore, stress-strain behavior of soils under cyclic loads can be calculated using constitutive models. It is important that related constitutive model describes the response of the soil under cyclic loads as closely as possible the behavior observed in the laboratory experiments. In order to obtain dynamic behavior of the coastal structure-saturated porous seabed system as accurately as possible, firstly the nonlinear behavior of the soil skeleton should be defined. The latter is then incorporated into the governing equations in terms of theoretical models and the dynamic analysis of the entire system is made for each time step. In this dissertation, firstly the seabed soil is considered as a linear isotropic elastic porous medium. The static and dynamic response of the seabed soil are studied through one and two-dimensional analyses using the finite element method. The response of the system is analyzed by one of the appropriate simplified formulations of the coupled flow and deformation equations considering the physical structure and the loading situation. The validity of this numerical study is confirmed by the available analytical solutions. Subsequently, two coastal structures are examined for their cyclic loading-induced linear poroelastic response and instability conditions under the assumption of plane strain stress states. Firstly, the dynamic response of a bridge pier foundation-granular seabed system under earthquake loading is investigated. Caisson foundation sitting on a gravel layer is considered and the seabed-gravel-caisson foundation system is modeled using finite elements. The dynamic response of the porous seabed-caisson system is assumed to be governed by poroelastic equations. A number of parametric analyses investigating the effect of hydraulic conductivity of seabed and amplitude of earthquake loading on the dynamic response are carried out. Secondly, the dynamic response and instantaneous liquefaction potential of granular seabed around a rubble mound breakwater is investigated under standing waves. Only the PD and QS formulations are considered in the analyses and a number of parametric studies are performed to draw a complete picture of the response of the system. Vertical displacement, shear stress and pore water pressure distributions are considered as the most representative variables defining the variations of response of the whole system. Standing wave-induced instantaneous liquefaction of the system is also investigated. While it is important to make use of the actual stress-strain relationship of the sandy seabed as observed in tests in the dynamic analyses, such simulations require a prior study of modeling the actual soil stress-strain behavior at the elemental level. Thus, a number of elemental level analyses are conducted in both static and dynamic states of granular soil material using the UBCSAND constitutive model for a single soil element. As a result, the constitutive behavior of sand is simulated and the results are verified with their experimental counterparts in drained, partially drained and undrained triaxial shear situations under both monotonic and cyclic loads. For the dynamic case, UBCSAND model is slightly modified with the contribution of the Generalized Plasticity Theory. Finally, the new formulation is tested on the nonlinear harmonic response of a soil column with the finite element method. A 1-D finite element code is developed in MATLAB to analyze a multi degree of freedom soil column under any dynamic loading. These nonlinear finite element analyses involve solution of the equation of motion using the 'Newton-Raphson Method' which essentially calculates the degree of freedoms in terms of displacement and pore water pressure at the nodal points iteratively for each time-step. Subsequently the stresses are updated at the integration points which are then used to get the internal force vector. Here, the strains obtained from the degrees of feedom are used to update stresses obtained from the elasto-plastic stress-strain relationship. In this study, UBCSAND constitutive model is used to calculate the stress increment. In order to increase the chances of convergence of the analyses, each spatial integration step is progressed by dividing the total strains into smaller substeps prior to updating elastoplastic stresses, which is termed in this study as one form of 'substepping method'. Early results of pore pressure build-up and resulting effective stress reduction prove that the numerical model developed using MATLAB along with the late UBCSAND model, in its slightly modified form, was capable of capturing saturated sand liquefaction under harmonic loading. Important results obtained from each chapter are deduced and presented at the end of the dissertation followed by a brief summary of currently ongoing works.