Finite element dynamic shakedown analysis of a gravity type offshore structure-foundation system

Haldar, A.K. (1984) Finite element dynamic shakedown analysis of a gravity type offshore structure-foundation system. Doctoral (PhD) thesis, Memorial University of Newfoundland.

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Abstract

The shakedown deformation of a gravity type offshore foundation subjected to dynamic cyclic wave loading is determined based on the two dimensional finite element formulation of a fluid saturated porous medium. The soil is assumed to behave in an undrained manner and modelled as a two-phase material. The undrained characteristics of the soil leads the Poisson's ratio to be one-half and thus results in a singular stiffness matrix. The reduced integration technique is used in order to circumvent the problem. The dynamic shakedown load factor is obtained by first computing the elastodynamic response of the caisson-foundation (saturated) medium for some adjusted initial conditions (e.g. displacement and velocity) and then solving a linear programming problem based on the dual form of kinematic shakedown theory. -- A finite element computer code OPFA (Offshore Platform foundation Analysis) is developed which computes the dynamic shakedown load factor of a gravity type offshore foundation and then determines the response quantities such as displacements and stresses in the saturated soil medium. The nonlinear stress-strain characteristics of the soil medium is considered in the analysis by use of an equivalent linear and an elastic-perfectly plastic model. -- Several problems are solved in order to check the accuracy of the computer programme. The results are in excellent agreement with the available analytical solutions. The shakedown analysis for a flexible foundation shows – that limit pressures depend on the inclination angle and the eccentricity of the load. The shakedown limit pressure decreases as the eccentricity and the angle of inclination of the load increase. Also, shakedown analyses indicate that the footing pressures are below those predicted by the approximate bearing capacity formula. These shakedown pressures are obtained from an upper bound solution and therefore the use of the above formula will not produce a conservative estimate of the bearing capacity of the foundation when the loading is cyclic in nature. -- The dynamic shakedown load factor for the gravity foundation is only 10% lower than its static counterpart. The reason for the decrease of this load factor is due to the amplification of stresses under dynamic loading condition. In computing the response quantities for three different soil models, it is observed that the equivalent linear analysis predicts lower deformation as opposed to other linear and nonlinear models. However, for the quasi-static analysis of the gravity foundation, the permanent vertical shakedown deformation is within 0.085% of the footing width. In all cases it is observed that shakedown occurs with respect to the deformation of the foundation.

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