A Thermodynamically Consistent 3D Breakage Model Considering Intermediate Principal Stress for Granular Crushing Problems
Publication: International Journal of Geomechanics
Volume 23, Issue 11
Abstract
A thermodynamically consistent three-dimensional (3D) continuum breakage model was developed to study the effect of intermediate principal stress. Such an effect has been long overlooked in most existing constitutive models, which might result in a considerable difference in the strength estimation of crushable granular materials. Following basic thermodynamic laws, the proposed 3D breakage model was based on a new explicit mathematical expression of the original Matsuoka–Nakai failure criterion and 3D stress transformation. This proposed 3D breakage model was verified against the corresponding true triaxial constant-hydrostatic-pressure loading tests and true triaxial constant-minor-principal-stress loading tests of sand. The results confirmed that the proposed 3D breakage model accurately captures the effect of intermediate principal stress on granular crushing behaviors.
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Acknowledgments
The project was supported by the National Natural Science Foundation of China (42172305, 52278367, and 52208426) and the Fundamental Research Funds for the Central Universities (2242023K5006).
Notation
The following symbols are used in this paper:
- B
- breakage index;
- b
- intermediate principal-stress coefficient;
- EB
- breakage energy;
- EC
- critical breakage energy;
- G
- shear modulus;
- K
- bulk modulus;
- M
- critical stress ratio;
- pcr
- critical isotropic confining pressure;
- mean stress;
- triaxial shear stress;
- W
- mechanical work;
- elastic strain tensor;
- plastic strain tensor;
- elastic volumetric strain;
- elastic shear strain;
- plastic volumetric strain;
- plastic shear strain;
- grading index;
- λ
- plastic multiplier;
- σN
- normal stress in the spatial mobilized plane;
- stress tensor;
- τ
- shear stress in the spatial mobilized plane;
- Ψ
- Helmholtz free energy;
- Φ
- energy dissipation;
- plastic volumetric dissipation;
- plastic shear dissipation;
- ΦB
- breakage dissipation;
- ω
- coupling parameter;
- φ
- frictional angle; and
- θ
- Lode’s angle.
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Published In
International Journal of Geomechanics
Volume 23 • Issue 11 • November 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Nov 17, 2022
Accepted: Apr 25, 2023
Published online: Aug 24, 2023
Published in print: Nov 1, 2023
Discussion open until: Jan 24, 2024
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