Nonlocal regularisation of anisotropic sand models

Li, Xin (2024) Nonlocal regularisation of anisotropic sand models. PhD thesis, University of Glasgow.

Abstract

Nonlocal regularisation is frequently used to resolve the mesh-dependency issue caused by strain softening in finite element (FE) simulations. Nonlocal methods are proposed based on the hypothesis that the response of materials depends on the deformation field of a local material point and a weighted average of its neighbouring points. The nonlocal regularisation of an anisotropic critical state sand model which can capture the strain-softening and state-dependent dilatancy response of sand is presented. The evolution of the void ratio is assumed nonlocal in this method. The regularisation method has been implemented using the explicit stress integration method.

A comprehensive comparison of three weighting functions (including the Gaussian distribution (GD), Galavi and Schweiger (G&S) and over-nonlocal (ON) functions) has been investigated in different boundary value problems (BVPs). All functions give mesh-independent force-displacement relationships in drained and undrained plane strain compression tests. The shear band thickness shows a slight variation when the mesh size is smaller than the internal length. None of them can eliminate the mesh dependency of shear band orientation. The G&S method is the most efficient in eliminating the mesh dependency, especially in the strip footing problem. The ON method can give excessive overprediction of volume expansion around strip footings, leading to unrealistic low reaction forces on strip footings at large deformation. All three weight functions give mesh-independent results for the earth pressure acting on a retaining wall.

A more in-depth investigation of the G&S method is presented. The plane strain compression tests with rough boundary conditions under both drained and undrained conditions are simulated. Mesh-independent predictions of force-displacement relationship curves, shear band orientation and shear band thickness are given. After applying nonlocal regularisation, the evolution of state variables obtained from selected elements and cross-sections reduces the fluctuation in their changes and significantly diminishes the differences in peak values observed across various mesh sizes in the local model. The effectiveness of reducing mesh dependency in the nonlocal method increases when the void ratio is higher or when the confining pressure increases.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Subjects: T Technology > TA Engineering (General). Civil engineering (General)
• Colleges/Schools: College of Science and Engineering > School of Engineering
• Supervisor's Name: Gao, Dr. Zhiwei and Grassl, Dr. Peter
• Date of Award: 2024
• Depositing User: Theses Team
• Unique ID: glathesis:2024-84407
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 26 Jun 2024 15:04
• Last Modified: 26 Jun 2024 15:11
• Thesis DOI: 10.5525/gla.thesis.84407
• URI: https://theses.gla.ac.uk/id/eprint/84407

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