Numerical implementation of advanced soil constitutive models: finite element method and applications

Zhang, Y 2017, Numerical implementation of advanced soil constitutive models: finite element method and applications, Doctor of Philosophy (PhD), Engineering, RMIT University.

Document type: Thesis
Collection: Theses

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Title Numerical implementation of advanced soil constitutive models: finite element method and applications
Author(s) Zhang, Y
Year 2017
Abstract Numerical analysis of various problems involving the hydro-mechanical or thermo-mechanical coupling of soils remains a challenge in the geotechnical engineering. An important element in a coupled analysis is the constitutive model adopted for the soil. A great number of advanced soil constitutive models have been developed based on experimental observations of coupled behaviours of soils and plasticity theories (e.g, subloading plasticity). As no analytical solutions for the coupled constitutive relations, it is essential to employ numerical techniques, e.g., the Finite Element Method (FEM), to analyse practical engineering problems. For such an approach to be possible, advanced soil constitutive models need to be implemented in numerical codes.

This thesis investigates three following aspects when implementing advanced soil constitutive models in Finite Element (FE) codes, and solutions developed in this research are also provided as follows:

The advanced soil models generally require additional variables (e.g. suction, the degree of saturation and temperature) to predict the coupled behaviours of soils. These variables apart from the stress and strain have to be considered in the stress integration for the FE analysis. A general form of constitutive equations for the stress integration is proposed in this research with using generalised stress and strain vectors. The suction and temperature are treated as strain-like variables, whereas, the degree of saturation is contained in the generalised stress vector. This general form is similar to constitutive equations developed for saturated soil models, which are purely strain driven. The formulation is also consistent with the conventional displacement FEM, where the displacement, pore pressure, and temperature are found first and then strains and then stresses. The derivation and applications of the general form are presented in Technical Paper 1, 2 & 3 in this thesis.
Incorrect loading-unloading decisions may happen when the conventional loading-unloading decision method is implemented in the stress integration scheme for subloading elastoplasticity models. In the conventional method, the decision is mainly made based on the location of the trail stress. For the subloading elastoplasticity, however, the stress point stays on the subloading surface conditionally. This fact may result in overestimating an elastic part within a given increment for the stress integration. A new loading-unloading decision scheme is developed in this research for the subloading elastoplasticity. The decision is mainly dependent on the direction of the stress path, and the cosine of the angle between the Outward Normal Vector (ONV) to the subloading surface at the current stress point is used to determine the stress path directions. The new loading-unloading scheme requires two main procedures including a tentative decision and a rechecking procedure, and it can successfully find the transition point from elastic state to elastoplastic state within a given increment. The performance of the new proposed scheme including accuracy and efficiency has been studied, and results and discussions are given in Technical Paper 1 & 2 in this thesis.

The governing equations used in FEM for the coupled analysis have to be consistent with the constitutive model including the stress variables and hydraulic behaviours adopted, as this will affect individual terms in the system equations. In this research, an alternative approach of the governing equations is proposed for a fully hydro-mechanical coupled constitutive model of unsaturated soils. The net stress increment is adopted in mechanical equilibrium, although the constitutive model adopted is developed in the space of Bishop’s effective stress and the degree of saturation. The degree of saturation is also considered as a coupled term in the mass conservation, as it is affected by both net stress and suction. The new developed governing and system equations have been turned into practical FE code for the coupled consolidation analyses of unsaturated soils in this research. The verifications and applications can be found in Technical Paper 3 in this thesis.
Degree Doctor of Philosophy (PhD)
Institution RMIT University
School, Department or Centre Engineering
Subjects Geomechanics and Resources Geotechnical Engineering
Civil Geotechnical Engineering
Keyword(s) Constitutive model
Subloading surface elastoplasticity
Nonconvex surface
Adaptive substeppin
Unsaturated soil
Loading-unloading decision
Finite element method
Footing analysis
Explicit integration
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Created: Thu, 13 Jul 2017, 11:52:06 EST by Adam Rivett
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