Calculating the State Parameter in Crushable Sands
Publication: International Journal of Geomechanics
Volume 20, Issue 7
Abstract
The state parameter (ψ) measures the distance from the current state to the critical state line (CSL) in the compression plane. The existence of a correlation between both the peak angle of shearing resistance and peak dilatancy and ψ is central to many constitutive models used to predict granular soil behavior. These correlations do not explicitly consider particle crushing. Crushing-induced evolution of the particle size distribution influences the CSL position, and recent research supports the use of a critical state plane (CSP) to account for changes in grading. This contribution evaluates whether the CSP can be used to calculate ψ and thus enable the prediction of the peak angle of and peak dilatancy where crushing takes place. The data considered were generated from a validated DEM model of Fontainebleau sand that considers particle crushing. It is shown that where ψ is calculated by considering the CSL of the original uncrushed material, there can be a significant error in predicting the material response. However, where the CSP is used, there is a significant improvement in our ability to predict behavior irrespective of whether the CSP is accurately determined using a large number of tests or approximated using crushing yield envelopes. It is shown that the state parameter calculated using the previously available definition can give a false sense of security when assessing the liquefaction potential of potentially crushable soils. This contribution also highlights the stress-path dependency of the relationship between and ψ whichever approach is used to determine ψ.
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Acknowledgments
A part of this research was supported by the first Author's Junior Research Fellowship at Imperial College London.
Notation
The following symbols are used in this paper:
- dilatancy at the point where the peak stress ratio is mobilized;
- e
- void ratio;
- void ratio on CSL;
- initial void ratio;
- I G
- grading state index following Muir Wood and Maeda (2008);
- I G,0
- grading state index based on initial grading;
- p′
- mean effective stress;
- rate of change of mean effective stress with respect to time;
- mean effective stress at the critical state;
- q
- deviator stress;
- η
- stress obliquity, q/p′;
- ψ
- state parameter;
- state parameter as the distance to CSL from the initial stress and the void ratio;
- within multiple CSLs, state parameter as the distance to the corresponding CSL from the initial stress and the void ratio;
- state parameter as the distance to CSP from the initial stress, the void ratio, and IG ;
- state parameter as the distance to CSP from the initial stress, the void ratio, and the measured IG at CS;
- state parameter as the distance to CSP from the initial stress, the void ratio, and the predicted IG at CS;
- rate of change of radial effective stress with respect to time;
- rate of change of vertical effective stress with respect to time;
- critical state angle of shearing resistance; and
- peak angle of shearing resistance.
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Published In
International Journal of Geomechanics
Volume 20 • Issue 7 • July 2020
Copyright
© 2020 American Society of Civil Engineers.
History
Received: May 13, 2019
Accepted: Dec 17, 2019
Published online: Apr 22, 2020
Published in print: Jul 1, 2020
Discussion open until: Sep 22, 2020
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