Abstract

This paper presents a fabric tensor-based bounding surface model accounting for anisotropic behaviour (e.g. the dependency of peak strength on loading direction and non-coaxial deformation) of granular materials. This model is developed based on a well-calibrated isotropic bounding surface model. The yield surface is modified by incorporating the back stress which is proportional to a contact normal-based fabric tensor for characterising fabric anisotropy. The evolution law of the fabric tensor, which is dependent on both rates of the stress ratio and the plastic strain, rules that the material fabric tends to align with the loading direction and evolves towards a unique critical state fabric tensor under monotonic shearing. The incorporation of the evolution law leads to a rotational hardening of the yield surface. The anisotropic critical state is assumed to be independent of the initial values of void ratio and fabric tensor. The critical state fabric tensor has the same intermediate stress ratio (i.e. b value) and principal directions as the critical state stress tensor. A non-associated flow rule in the deviatoric plane is adopted, which is able to predict the non-coaxial flow naturally. The stress–strain relation and fabric evolution of model predictions show a satisfactory agreement with DEM simulation results under monotonic shearing with different loading directions. The model is also validated by comparing with laboratory test results of Leighton Buzzard sand and Toyoura sand under various loading paths. The comparison results demonstrate encouraging applicability of the model for predicting the anisotropic behaviour of granular materials.

Highlights

  • Fabric anisotropy has a significant influence on the strength and deformation characteristics of granular materials as reported in both experimental [3, 41, 46,47,48, 50, 77, 84, 88] and numerical observations [34, 69, 81, 86]

  • This paper presents a fabric tensor-based bounding surface model accounting for anisotropic behaviour of granular materials

  • The yield surface is modified by incorporating the back stress which is proportional to a contact normal-based fabric tensor for characterising fabric anisotropy

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Summary

Introduction

Fabric anisotropy has a significant influence on the strength and deformation characteristics of granular materials as reported in both experimental [3, 41, 46,47,48, 50, 77, 84, 88] and numerical observations [34, 69, 81, 86]. Evolution laws associated with the stress (or elastic strain) rate alone (the first type) can capture the characteristics of peak strength under monotonic shearing with various loading directions They rarely show a unique critical state fabric tensor. Fabric evolution laws associated with the plastic strain rate alone (the second type) tend to give a unique critical value of the fabric tensor, but they cannot capture the characteristics of peak strength upon monotonic shearing . These types of evolution laws may be able to qualitatively account for some experimental and numerical observations, quantitative calibrations with microscale fabric evolution data have rarely been achieved. It is demonstrated that the new constitutive model can capture both the stress–strain relation and the evolution of the fabric tensor with a high degree of satisfaction

Definition of fabric tensor
Description of the anisotropic critical state
Fabric evolution law
Constitutive model
Elastic model
Yield surface
Hardening law
Flow rule in the deviatoric space
Dilatancy
Bounding surface and mapping law
Effects of shear mode
Effect of shear mode on the critical state
Effect of shear mode on the yield function
Stress–strain relationship in the rate form
Prediction and comparison
Comparison with DEM simulations
Fabric evolution
Strength and volumetric response
Comparison with laboratory tests
Drained behaviour of Leighton Buzzard sand
Undrained true triaxial tests of Toyoura sand
Undrained torsional simple shear test of Toyoura sand
Drained triaxial test of Toyoura sand
Drained simple shear test of Toyoura sand
Findings
Conclusions
Full Text
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