Wang, Zhe
(2016)
Numerical simulations of geotechnical engineering problems considering the principal stress rotation.
PhD thesis, University of Nottingham.
Abstract
Soil behaviors are quite complex under dynamic loadings, such as wave loading, earthquake loading, etc, but they share common characteristics that the soil is subjected to considerable principal stress rotations (PSR). PSR can generate plastic deformation even without a change of principal stress magnitudes. Continuous PSR can also generate excess pore water pressures and cumulative shear strains in undrained condition. Therefore, the PSR from the dynamic loadings can accelerate undrained soil liquefaction because it can cause cumulative plastic volumetric deformations. Ignoring PSR induced deformation may lead to unsafe design. It is therefore important to understand the soil behaviors under cyclic loadings with the PSR and take account of this PSR impact in the numerical simulations of corresponding geotechnical problems.
Although researchers have recognized the importance of the PSR in real geotechnical problems under diverse loading conditions and conducted extensive experimental studies, there are limited considerations of the PSR impact on numerical simulations of boundary value problems. Moreover, most of the constitutive models widely-used in the numerical investigations at present cannot simulate this PSR behavior properly. Therefore, a new kinematic hardening soil model (PSR model) developed on the basis of a well-established model with bounding surface concept is used to simulate the PSR behavior in this research. It can take account of the PSR impact by treating the stress rate generating the PSR independently.
To investigate the impacts of PSR in numerical simulations of geotechnical problems, the PSR model is implemented into both the single element and finite element analysis of a series of geotechnical problems by a constitutive model subroutine written in Fortran. In this subroutine, an explicit substepping integration algorithm with automatic error controls is used to perform the constitutive formulations. The imposed strain increment can be automatically divided and the sizes of the sub-increments are also automatically determined based on the prescribed error tolerance in this numerical integration scheme. The single element analyses include the simulations of the triaxial and hollow cylinder tests with monotonic, rotational and torsional loading paths, while the finite element analyses consist of the simulations of the centrifuge experimental tests under wave loadings and earthquake loadings. The predicted results by using the soil model with and without considering the PSR impact, as well as the experimental results will be compared.
From these single element and finite element analyses, it is evident that the rotational, torsional and dynamic loadings such as wave and earthquake loadings can produce the PSR and non-coaxiality in the soil. The comparisons between the predicted results from the modified PSR model, the original model, and the laboratory results from these experimental tests all show that although the original model can reflect some non-coaxiality, it can produce very limited build-up of pore water pressure and cumulative shear strain under cyclic loading path. However, due to consideration of the PSR impact, the modified PSR model can generate higher pore water pressure and shear strain than the original model, thus bringing the soil to the liquefaction and agrees better with the experimental results. Therefore, it is important to consider the PSR effect in the simulation of geotechnical problems such as wave-seabed interactions and the earthquake induced liquefactions, and the PSR model presented in this research has a great ability and plays an important role in these numerical simulations.
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