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Time stepping schemes for coupled displacement and pore pressurē analysis.

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Title: Time stepping schemes for coupled displacement and pore pressurē analysis.
Authors: Sheng, D.1, Sloan, S. W.1
Source: Computational Mechanics. May2003, Vol. 31 Issue 1/2, p122-134. 13p.
Subjects: Temporal integration, Engineering tolerances, Structural analysis (Engineering), Measurement, Strains & stresses (Mechanics), Engineering
Abstract: The paper investigates the performance of various time stepping schemes for coupled displacement and pore pressure analysis. A number of alternative forms of the automatic time stepping method proposed by Sloan and Abbo (1999a) are also presented. These alternative schemes use different updates for the displacements and pore pressures and also adopt different starting conditions for the iterations. The automatic schemes are compared with an implicit θ-method, as well as an explicit method, through analysis of a variety of problems involving undrained loading, drained loading, and consolidation for Mohr-Coulomb and critical state models. As expected, the numerical results confirm that the explicit scheme is neither accurate nor robust. Although the implicit θ-method is accurate and fast, it fails to give a solution in a number of cases where the time step is large. The automatic schemes are shown to be accurate, fast and generally robust. Two of the automatic schemes proposed never fail to furnish a solution for the cases considered. In addition, all the automatic schemes are able to constrain the time-stepping (temporal integration) error in the displacements and pore pressures to lie near a prescribed tolerance, provided the iteration error tolerance is properly chosen. For complex soil models, it is important that the latter is set sufficiently small in order for the schemes to be able to constrain the time-stepping error to lie within a prescribed tolerance. [ABSTRACT FROM AUTHOR]
Copyright of Computational Mechanics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: The paper investigates the performance of various time stepping schemes for coupled displacement and pore pressure analysis. A number of alternative forms of the automatic time stepping method proposed by Sloan and Abbo (1999a) are also presented. These alternative schemes use different updates for the displacements and pore pressures and also adopt different starting conditions for the iterations. The automatic schemes are compared with an implicit θ-method, as well as an explicit method, through analysis of a variety of problems involving undrained loading, drained loading, and consolidation for Mohr-Coulomb and critical state models. As expected, the numerical results confirm that the explicit scheme is neither accurate nor robust. Although the implicit θ-method is accurate and fast, it fails to give a solution in a number of cases where the time step is large. The automatic schemes are shown to be accurate, fast and generally robust. Two of the automatic schemes proposed never fail to furnish a solution for the cases considered. In addition, all the automatic schemes are able to constrain the time-stepping (temporal integration) error in the displacements and pore pressures to lie near a prescribed tolerance, provided the iteration error tolerance is properly chosen. For complex soil models, it is important that the latter is set sufficiently small in order for the schemes to be able to constrain the time-stepping error to lie within a prescribed tolerance. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Computational Mechanics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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