Numerical Modelling using Finite Element Analysis with Advanced Soil Constitutive Models: Static and Quasi-static Approaches
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2019-07-12
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Abstract
The analysis of geostructures with failure as a central topic has been traditionally pursued through limit equilibrium methods in geotechnical engineering. In this thesis, the finite element approach together with advanced constitutive models encompassing micromechanics-based ingredients are used to examine discontinuous failure modes such as strain localization in a boundary value problem setting like in a plane-strain (biaxial) test on sand. The constitutive models used in the numerical simulations are: (1) a non-associated plasticity and fabric-based model, and (2) a micromechanically enriched model via multiscaling. These are implemented into a finite element solver following a time integration scheme that is either implicit or explicit. Under static conditions, an implicit scheme is typically adopted where a stiffness matrix needs to be inverted. Unfortunately, when a limit state, e.g. failure, is encountered, solution uniqueness is lost, thus leading to a bifurcation problem. The static problem can be alternatively formulated as a dynamic one involving velocity, acceleration and a properly chosen loading rate. This allows for an explicit time integration scheme in which the displacement field can be obtained without solving any system of equations -- so obviating the inversion of a stiffness matrix. This gives the method great potential in resolving difficulties encountered in a static simulation or in any numerical approach using the implicit scheme. To mimic the static problem in dynamic simulations, the loading rate is kept sufficiently small so that the response of the system can be quasi-static. Also, damping might be introduced to aid these simulations to converge properly toward the static equilibrium. Localized modes of failure are examined within bifurcation theory whereby there is a transition from an initially homogeneous deformation mode into one which involves localized deformations as a shear band. The anatomy of failure is examined and analyzed using the two constitutive models. It is shown that the micromechanically-enriched model gives important microstructural information such as coordination number and anisotropy at the particle level inside and outside the shear band to help understand the genesis of failure in soils.
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Bach, T. D. (2019). Numerical Modelling using Finite Element Analysis with Advanced Soil Constitutive Models: Static and Quasi-static Approaches (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.