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| − | ==1 Title, abstract and keywords<!-- Your document should start with a concise and informative title. Titles are often used in information-retrieval systems. Avoid abbreviations and formulae where possible. Capitalize the first word of the title. | + | ==Abstract== |
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| − | Provide a maximum of 6 keywords, and avoiding general and plural terms and multiple concepts (avoid, for example, 'and', 'of'). Be sparing with abbreviations: only abbreviations firmly established in the field should be used. These keywords will be used for indexing purposes.
| + | The net stress plus suction and the average skeleton stress plus modified suction are two alternative sets of energetically consistent stress variables for modelling the hydro-mechanical behaviour of unsaturated soils. When used in conjunction with their work-conjugate strains, both sets of stress variables correctly calculate the first-order term of the hydro-mechanical work input into a soil element subjected to infinitesimal changes of deformation and water content. They therefore also correctly calculate the increment of internal energy along a given stress–strain path, that is the integral of the first-order term of the infinitesimal work input. This paper shows, however, that the above two sets of stress variables lead to different values of the second-order term of the hydro-mechanical work input. They are therefore no longer equivalent with respect to other aspects of material behaviour governed by the second-order work such as the flow rule of elasto-plastic models. The flow rule assumes the normality between plastic strains and equipotential surfaces defined in the conjugate stress–strain space. This normality is however lost when an elasto-plastic model originally formulated in terms of net stress plus suction is recast in terms of average skeleton stress plus modified suction (or vice versa) by means of standard mapping relationships between stress variables. To restore normality in both stress spaces, it is necessary to impose specific forms of elastic and plastic behaviour. |
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| + | ==Full Document== |
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| − | ==2 The main text<!-- You can enter and format the text of this document by selecting the ‘Edit’ option in the menu at the top of this frame or next to the title of every section of the document. This will give access to the visual editor. Alternatively, you can edit the source of this document (Wiki markup format) by selecting the ‘Edit source’ option.
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| − | Divide your article into clearly defined and numbered sections. Subsections should be numbered 1.1, 1.2, etc. and then 1.1.1, 1.1.2, ... Use this numbering also for internal cross-referencing: do not just refer to 'the text'. Any subsection may be given a brief heading. Capitalize the first word of the headings.
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| − | 2.2 General guidelines
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| − | ==4 Acknowledgments<!-- Acknowledgments should be inserted at the end of the document, before the references section. -->==
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| − | ==5 References<!--[1] Author, A. and Author, B. (Year) Title of the article. Title of the Publication. Article code. Available: http://www.scipedia.com/ucode.
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The net stress plus suction and the average skeleton stress plus modified suction are two alternative sets of energetically consistent stress variables for modelling the hydro-mechanical behaviour of unsaturated soils. When used in conjunction with their work-conjugate strains, both sets of stress variables correctly calculate the first-order term of the hydro-mechanical work input into a soil element subjected to infinitesimal changes of deformation and water content. They therefore also correctly calculate the increment of internal energy along a given stress–strain path, that is the integral of the first-order term of the infinitesimal work input. This paper shows, however, that the above two sets of stress variables lead to different values of the second-order term of the hydro-mechanical work input. They are therefore no longer equivalent with respect to other aspects of material behaviour governed by the second-order work such as the flow rule of elasto-plastic models. The flow rule assumes the normality between plastic strains and equipotential surfaces defined in the conjugate stress–strain space. This normality is however lost when an elasto-plastic model originally formulated in terms of net stress plus suction is recast in terms of average skeleton stress plus modified suction (or vice versa) by means of standard mapping relationships between stress variables. To restore normality in both stress spaces, it is necessary to impose specific forms of elastic and plastic behaviour.
