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Title: Numerical and analytical solutions for consolidation analysis of soils without and with vertical drains
Authors: Zhu, Guofu
Degree: Ph.D.
Issue Date: 1999
Abstract: Consolidation analysis of soils with and without vertical drains taking into consideration time dependent loading is of practical and theoretical importance in geotechnical engineering. For example, the prediction of settlement of reclamation is a consolidation analysis with time dependent fill loading in soil mechanics. In this research, new specific analytical solutions for the consolidation analysis of a single layered soil and a double layered soil with a depth-dependent ramp loading are obtained. The solutions are described in detail. Results are presented as figures and tables for practical applications. Many analytical solutions in soil mechanics are only special cases of these solutions. An analytical solution for consolidation analysis of soil with vertical drainage wells under ramp load is also obtained. A new normalized time, T' is suggested. It is shown that the average degree of consolidation exhibits very good normalized feature using this new T. The average degree of consolidation for various parameters are plotted and tabulated for applications. A general one-dimensional (1-D) finite element (FE) procedure is derived for consolidation analysis of layered clay soils with an emphasis on a non-linear 1-D Elastic Visco-Plastic (1-D EVP) model proposed by Yin and Graham (1989, 1994). A new definition of excess porewater pressure is suggested to consider the situations that water heads at boundaries are fluctuating with time or there is an initial hydraulic gradient. In formulating the 1-D FE procedure, a trapezoidal formula is used to avoid the unsymmetry and to increase the positiveness of the stiffness matrix for a Newton (Modified Newton) iteration scheme. Unlike many other 1-D FE approaches in which the initial in-situ stresses (or stress/strain states) are considered indirectly or even not considered, the initial in-situ stress/strain states are taken into account directly. The proposed FE procedure shows very good numerical stability characteristics and is used for analysis of 1-D consolidation of clay with published test results in the literature The FE modeling results are in good agreement with the measured results. The FE model and procedure is also used to analyze the consolidation of a multi-layered clay soils with a parametric study on the effects of various parameters. Furthermore, a case modeling for the Berthierville test embankment in Quebec, Canada is carefully carried out. A finite element procedure for the analysis of consolidation of layered soils with vertical drain using general one-dimensional constitutive models is formulated in this research. The related FE program is developed. In deriving the finite element procedure, a Newton-Cotes type integration formula is used to avoid the unsymmetry and increase the positiveness of the stiffness matrix for a Newton (Modified Newton) iteration scheme. The proposed procedure is then applied to the consolidation analysis of a number of typical problems using both linear and non-linear soil models. Results from this simplified method are compared with those from a fully coupled consolidation analysis using a well-known finite element package ABAQUS. The average degree of consolidation, excess porewater pressure and average vertical effective stress are almost the same as those from the fully coupled analysis for both the linear and non-linear cases studied. The differences in vertical effective stresses are tolerable except for the values near the vertical drain boundaries. The high vertical effective stress near the vertical drain from fully coupled finite element analysis also demonstrates that a zone of low permeability will form near the vertical drain regardless of the installation methods. The consolidation behaviour of soils below a certain depth of the bottom of vertical drain is actually one-dimensional for the partially penetrating case. Therefore there are no much differences whether or not using a one-dimensional model or a three-dimensional model in this region. The average degree of consolidation has good normalized feature with respect to the ratio of well radius to external drainage boundary for the cases of fully penetrating vertical drain using a normalized time even in the non-linear case. Numerical results clearly demonstrate that the proposed simplified finite element procedure is efficient for the consolidation analysis of soils with vertical drain and it has better numerical stability characteristics. This simplified method can easily account for layered systems, time-dependent loading, well resistance, smear effects and inelastic stress-strain behaviour. This method is also very suitable for the design of vertical drain, since it greatly reduces the unknown variables in the calculation and the 1-D soil model parameters can be more easily determined. Finally the consolidation behaviour of the test embankment at the site of new international airport at Chek Lap Kok is analyzed based on a true prediction nature.
Subjects: Soil consolidation
Soil mechanics
Soils -- Analysis
Hong Kong Polytechnic University -- Dissertations
Pages: xxv, 258 leaves : ill. ; 30 cm
Appears in Collections:Thesis

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