Energy equation and stress–dilatancy relationship for sand

The energy equation is an expression of the first law of thermodynamics or the law of conservation of energy. According to the first law of thermodynamics, the externally applied work to a system is equal to the sum of dissipation energy and Helmholtz free energy of the system. However, most of the...

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Bibliographic Details
Published in:Acta geotechnica 2022-07, Vol.17 (7), p.2675-2696
Main Authors: Chang, Ching S., Deng, Yibing
Format: Article
Language:English
Subjects:
Complex Fluids and Microfluidics
Deformation
Deformation mechanisms
Dilatancy
Dissipation
Energy
Energy conservation
Energy conservation law
Energy equation
Engineering
Foundations
Free energy
Geoengineering
Geotechnical Engineering & Applied Earth Sciences
Hydraulics
Research Paper
Sand
Silica
Soft and Granular Matter
Soil Science & Conservation
Solid Mechanics
Thermodynamics
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Summary:The energy equation is an expression of the first law of thermodynamics or the law of conservation of energy. According to the first law of thermodynamics, the externally applied work to a system is equal to the sum of dissipation energy and Helmholtz free energy of the system. However, most of the currently available stress–dilatancy relationships are based on the energy equation of Taylor-Cam Clay type, which hypothesizes that the applied plastic work is equal solely to the frictional dissipation energy. The Helmholtz free energy has been completely neglected. Recently, observed from acoustic experiments, it has been recognized that Helmholtz free energy can be caused by deformation mechanisms other than friction between particles. Thus, it is necessary to include additional terms in the energy equation in order to correctly model the stress-dilatancy behavior. This paper addresses the issue regarding the balance of this energy equation. Analyses of experimental results are presented. Specific forms of the frictional energy and Helmholtz free energy are proposed. The proposed energy equation is verified with the experimental data obtained from Silica sand, Ottawa sand, and Nevada sand.
ISSN:1861-1125
1861-1133
DOI:10.1007/s11440-021-01389-1