Numerical Methods Of Shakedown Analysis Of Soil Structure And Its Applications In Evaluation Of Bearing Capacity Of Offshore Foundations

Under varied loads such as cyclic and/or transient loading, soil structures or foundation will induce permanent and/or fluctuating plastic deformations. Such plastic deformations are cumulative and/or alternating in nature with increase of time of loading during a sequence of cyclic loading. If the resulting accumulated deformations is limited within a given bound or the alternating deformations will be adapted to a given plastic state after a certain cycle numbers or a certain period of loading, the soils will be in shakedown state. Otherwise, incremental collapse or alternating plasticity will occur. For foundations subjected to loads varying in time in a non-proportional manner within prescribed limits, the limit equilibrium analyses based on the classical limit theorems may overestimate ultimate bearing capacity, as collapse under cyclic loads may occur at a level well below the static collapse loads. In such cases, shakedown analyses are of practical significance. Shakedown analyses are aimed to evaluate ultimate bearing capacity of soil structures or foundations under varied loads. Shakedown theorems, which are generalizations of the limit theorems, can provide appropriate bounds of externally-applied loads for such complex loading programs.At present an important issue with respect to the limit analyses and shakedown analyses is to work out effective computational strategies and numerical algorithm for applying the fundamental theories of limit analyses and shakedown analyses to engineering practice. In this paper, the numerical techniques and computational methods for limit analyses and shakedown analyses of soil structures and foundations are systematically investigated and then are employed to the assessment of the safety of the non-homogeneous foundations and the offshore platform foundations.In this dissertation, the computational method which combines elasto-plastic analysis with Melan's theorem is developed and then applied to evaluate limit load and shakedown load of soil structures. Elasto-plastic analyses are performed to obtain elasto-plastic stress field and elastic stress field. Accordingly a residual stress field is constructed. This methodology avoids the operation of mathematical programming in traditional method of shakedown analysis and therefore obstruction due to large scale mathematical programming is overcome. The method for constructing a residual stress field based on the elasto-plastic analysis for soil structures do not need the linearization of the yield condition. The accuracy of numerical solution depends on elasto-plastic analysis.Because the kinematically-admissble cyclic strain rate field required in kninematical-type theorem of shakedown analysis is rather difficult to be constructed, shakedown analysis based on kinematcal theorem cannot be directly applied. Some conditions of kinematical-type shakedown theorem are released by KSnig and then the shakedown rules respectively for alternating plasticity and incremental collapse are obtained, for the numerical method based on the upper-bound theorem is formulated. In this thesis,two shakedown rules respectively for alternating plasticity and incremental collapse is given as the theoretical basis of upper-bound shakedown analyses, numerical procedures for solving for the upper shakedown loads respectively for alternating plasticity and incremental collapse are provided. And then numerical computations are conducted.The numerical methods developed in this thesis are employed to conduct both limit analysis and shakedown analysis for non-homogeneous foundations and offshore platform foundations. Comparative studies are performed. Both ultimate bearing capacity and shakedown loads of non-homogeneous foundations are computed. Based on numerical results computed for different load modes, limit loads and shakedown loads of non-homogeneous foundation and offshore platform foundations are compared. The ultimate loads and shakedown loads for different combinations of horizontal component and vertical component and momen...