Four-Modulus Incremental Nonlinear Model of Granular Soils Considering Stress Path and Particle Breakage
Publication: International Journal of Geomechanics
Volume 24, Issue 9
Abstract
The mechanical properties of granular soils are significantly influenced by stress paths and particle breakage. In this study, a four-modulus incremental nonlinear model that incorporates the effects of the stress path and particle breakage was established based on an analysis of triaxial compression test results conducted on calcareous sands subjected to varying stress paths. A mathematical expression for this model and the process of determining its parameters was proposed. Subsequently, the model was experimentally verified. Our findings revealed that the isotropic compression consolidation volumetric strain modulus exhibited a curvilinear relationship with the average effective principal stress, whereas it demonstrated a linear correlation with the relative breakage index. Furthermore, a four-parameter nonlinear model was constructed, integrating the dilatancy equation to consider stress path effects and establishing a functional relationship between the stress ratio and shear strain. By comparing the experimental results with the calculated results for calcareous sands and rockfill materials, the model effectively simulated the stress ratio-axial strain behavior of granular soils under different stress paths. However, it failed to fully capture the volumetric strain-axial strain characteristics of granular soils after reaching the peak stress ratio. Therefore, further research is necessary to develop a more comprehensive correction method for incremental nonlinear models.
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Data Availability Statement
The data used in this study are available from the corresponding author upon request.
Acknowledgments
The authors acknowledge the financial support from the National Natural Science Foundation of China (Grant No. 42172295), the Hubei Provincial Science and Technology Department Natural Science Foundation Youth Project (2023AFB339), the Hubei Provincial Education Department Science and Technology Research Project (Grant No. Q20222701), and the project funded by of Natural Science Foundation of Xiaogan (Grant No. XGKJ2022010101). The authors thank all the reviewers who participated in the review and MJEditor (www.mjeditor.com) for providing English editing services during the preparation of this manuscript.
Notation
The following symbols are used in this paper:
- A
- parameter is related to σc, β, and material properties;
- at
- positive constant reflecting the effect of p on K;
- aB
- positive constant reflecting the effect of particle breakage on Kt;
- a1, a2
- intermediate parameters related to the stress path β;
- A, B
- test constants;
- Br
- relative breakage index;
- Brp
- particle breakage index caused by p;
- Brq
- particle breakage index caused by q;
- D
- compressive hardening coupling modulus;
- Dr
- initial relative density;
- dp
- average principal stress increment;
- dq
- deviatoric stress increment;
- dɛv
- volumetric strain increment;
- dɛs
- shear strain increment;
- d
- dilatancy ratio;
- dm, dn
- test constants;
- dmax
- dilatancy ratio corresponding to Mp;
- G
- shear modulus;
- Gt
- deviatoric shear modulus;
- J
- dilatancy coupling modulus;
- K
- volumetric strain modulus;
- Ki
- initial isotropic compression consolidation volumetric strain modulus;
- Kt
- isotropic compression consolidation volumetric strain modulus;
- Mc
- critical stress ratio;
- Mp
- peak stress ratio, stress ratio at peak state;
- M1, M2, M3
- test constants;
- m, n, h
- test constants;
- m1, m2
- test constants;
- m3, m4
- test constants;
- n1, n2
- test constants;
- n3, n4
- test constants;
- p
- average effective principal stress;
- q
- deviator stress;
- β
- stress increment ratio;
- ɛs
- shear strain;
- ɛv
- volumetric strain;
- ɛsqB
- shear strain caused by particle breakage Brq;
- ɛspB
- shear strain caused by particle breakage Brp;
- ɛvpB
- volumetric strain caused by particle breakage Brp;
- ɛvqB
- volumetric strain caused by particle breakage Brq;
- ɛsf
- shear strain corresponding to Mp;
- ɛ1
- axial strain;
- η
- stress ratio;
- σc
- initial consolidation pressure;
- σ1
- axial stress; and
- σ3
- confining stress.
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Published In
International Journal of Geomechanics
Volume 24 • Issue 9 • September 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Jun 7, 2023
Accepted: Mar 18, 2024
Published online: Jul 3, 2024
Published in print: Sep 1, 2024
Discussion open until: Dec 3, 2024
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