Abstract
Elastoplastic constitutive equations for soils often employ the nonlinear rate-type isotropic Hooke’s law, which is based on the additive decomposition of strain rate and considers the pressure dependency in the elastic part. Hooke’s law has independent isotropic and deviatoric components, and therefore, it cannot express elastic dilatancy as confirmed in experiments. In this model, although the elastic volume change is path-independent, the shear strain exhibits a significant residual when subjected to an effective stress cycle. This study proposes a rate-type elastic constitutive equation for soil applicable to elastoplastic constitutive equations based on finite deformation theory using an objective stress rate and additive decomposition of stretching; these equations cover these shortcomings of the rate-type Hooke’s law. The proposed rate-type elasticity constitutive equation is based on the hyperelastic body in the infinitesimal deformation theory proposed by Einav and Puzrin or Houlsby et al. and has confining pressure dependence, path independence of elastic volume change, and elastic dilatancy. Further, the residual strain is considerably smaller than that of the rate-type Hooke’s law. Moreover, this study improves the elasto-plastic constitutive equation, SYS Cam-Clay model, based on the skeleton structure concept by introducing the proposed elastic constitutive equation. The basic behavior of the elastoplastic constitutive equation for clay and sand is demonstrated to show that the newly acquired elastic dilatancy improves the mean effective stress reduction behavior during shear stress unloading under undrained conditions and the stiffness recovery behavior during liquefaction, which is essential for describing cyclic mobility.
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Data Availability Statement
All data, models, and codes generated or used during the study appear in the published article.
Acknowledgments
This study was supported by JSPS Grants-in-Aid for Scientific Research (Grant Nos. 19H02402 and 17H01289).
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Published In
International Journal of Geomechanics
Volume 23 • Issue 2 • February 2023
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This work is made available under the terms of the Creative Commons Attribution 4.0 International license, https://creativecommons.org/licenses/by/4.0/.
History
Received: Jul 13, 2021
Accepted: Sep 21, 2022
Published online: Nov 22, 2022
Published in print: Feb 1, 2023
Discussion open until: Apr 22, 2023
ASCE Technical Topics:
- Clays
- Constitutive relations
- Continuum mechanics
- Deformation (mechanics)
- Effective stress
- Elastic analysis
- Elastoplasticity
- Engineering fundamentals
- Engineering mechanics
- Geomechanics
- Geotechnical engineering
- Mathematics
- Shear stress
- Soil dilatancy
- Soil mechanics
- Soil properties
- Soil stress
- Soils (by type)
- Solid mechanics
- Stress (by type)
- Structural analysis
- Structural engineering
- Structural mechanics
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