Evaluation of numerical stress-point algorithms on elastic–plastic models for unsaturated soils with hardening dependent on the degree of saturation
Constitutive models of unsaturated soils, and in particular those based on constitutive variables which include both degree of saturation and suction, are characterised by strong non linearities due to hydromechanical coupling. In this paper, a refined Runge–Kutta–Dormand–Prince explicit algorithm a...
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| Published in: | Computers and geotechnics Vol. 55; pp. 404 - 415 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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01.01.2014
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| ISSN: | 0266-352X, 1873-7633 |
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| Abstract | Constitutive models of unsaturated soils, and in particular those based on constitutive variables which include both degree of saturation and suction, are characterised by strong non linearities due to hydromechanical coupling. In this paper, a refined Runge–Kutta–Dormand–Prince explicit algorithm and a fully implicit Euler scheme are compared for the integration of the latter class of models. The explicit and implicit procedures have been tested along different hydromechanical paths, involving various hydraulic and mechanical external control conditions. Accuracy and efficiency of the algorithms have been investigated. The results confirm that substepping is mandatory for the explicit algorithm to converge regardless the initial step size and to remain sufficiently accurate. The value of the incremental hydromechanical work per unit volume was calculated during the explicit integration procedure. The numerical results show that the maximum size of the substep which can be adopted to meet a given tolerance depends on the gradient of the incremental work per unit volume. Therefore, the latter appears a good candidate to identify problematic integration steps in terms of convergence. Accuracy of the implicit algorithm also depends on the chosen step size, although the algorithm proved to be convergent in all the paths analysed. |
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| AbstractList | Constitutive models of unsaturated soils, and in particular those based on constitutive variables which include both degree of saturation and suction, are characterised by strong non linearities due to hydromechanical coupling. In this paper, a refined Runge–Kutta–Dormand–Prince explicit algorithm and a fully implicit Euler scheme are compared for the integration of the latter class of models. The explicit and implicit procedures have been tested along different hydromechanical paths, involving various hydraulic and mechanical external control conditions. Accuracy and efficiency of the algorithms have been investigated. The results confirm that substepping is mandatory for the explicit algorithm to converge regardless the initial step size and to remain sufficiently accurate. The value of the incremental hydromechanical work per unit volume was calculated during the explicit integration procedure. The numerical results show that the maximum size of the substep which can be adopted to meet a given tolerance depends on the gradient of the incremental work per unit volume. Therefore, the latter appears a good candidate to identify problematic integration steps in terms of convergence. Accuracy of the implicit algorithm also depends on the chosen step size, although the algorithm proved to be convergent in all the paths analysed. Constitutive models of unsaturated soils, and in particular those based on constitutive variables which include both degree of saturation and suction, are characterised by strong non linearities due to hydromechanical coupling. In this paper, a refined Runge-Kutta-Dormand-Prince explicit algorithm and a hilly implicit Euler scheme are compared for the integration of the latter class of models. The explicit and implicit procedures have been tested along different hydromechanical paths, involving various hydraulic and mechanical external control conditions. Accuracy and efficiency of the algorithms have been investigated. The results confirm that substepping is mandatory for the explicit algorithm to converge regardless the initial step size and to remain sufficiently accurate. The value of the incremental hydromechanical work per unit volume was calculated during the explicit integration procedure. The numerical results show that the maximum size of the substep which can be adopted to meet a given tolerance depends on the gradient of the incremental work per unit volume. Therefore, the latter appears a good candidate to identify problematic integration steps in terms of convergence. Accuracy of the implicit algorithm also depends on the chosen step size, although the algorithm proved to be convergent in all the paths analysed. |
| Author | Cattaneo, F. Della Vecchia, G. Jommi, C. |
| Author_xml | – sequence: 1 givenname: F. surname: Cattaneo fullname: Cattaneo, F. email: fcattaneo@stru.polimi.it organization: Universitá degli Studi di Brescia, Via Branze 38, 25121 Brescia, Italy – sequence: 2 givenname: G. surname: Della Vecchia fullname: Della Vecchia, G. email: gabriele.dellavecchia@polimi.it organization: Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy – sequence: 3 givenname: C. surname: Jommi fullname: Jommi, C. email: C.Jommi@tudelft.nl, cristina.jommi@polimi.it organization: Delft University of Technology, P.O. Box 5048, 2600 GA Delft, The Netherlands |
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| Cites_doi | 10.1002/nag.296 10.1016/j.compgeo.2008.08.011 10.1016/j.compgeo.2008.08.004 10.1016/j.cma.2003.12.067 10.1002/(SICI)1097-0207(19960530)39:10<1737::AID-NME927>3.0.CO;2-5 10.1002/nag.217 10.1002/nme.1620210902 10.1016/0045-7825(90)90152-C 10.1201/9780203884430.ch96 10.1201/b10551-60 10.1680/geot.2011.61.4.313 10.1002/nag.1116 10.1680/geot.1997.47.1.193 10.1002/nag.690 10.1002/nag.295 10.1016/j.compgeo.2009.07.004 10.1108/02644400110365842 10.1007/s00466-003-0545-x 10.1061/(ASCE)1532-3641(2008)8:4(266) 10.1002/nme.1620240505 10.1016/0093-6413(86)90047-9 10.1108/02644400110365941 10.1029/2007WR006558 10.1016/S0749-6419(99)00033-9 10.1002/nag.231 10.1016/j.compgeo.2009.07.003 10.1002/nag.645 10.1016/0045-7825(94)90094-9 10.1016/0045-7825(95)00957-4 |
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Part I: Theory publication-title: Int J Numer Anal Methods Geomech doi: 10.1002/nag.295 – volume: 37 start-page: 59 issue: 1–2 year: 2010 ident: 10.1016/j.compgeo.2013.09.018_b0045 article-title: Explicit stress integration with error control for the barcelona basic model: Part I: Algorithms formulations publication-title: Comput Geotech doi: 10.1016/j.compgeo.2009.07.004 – volume: 18 start-page: 121 issue: 1/2 year: 2001 ident: 10.1016/j.compgeo.2013.09.018_b0010 article-title: Refined explicit integration of elastoplastic models with automatic error controls publication-title: Eng Comput doi: 10.1108/02644400110365842 – volume: 33 start-page: 453 issue: 6 year: 2004 ident: 10.1016/j.compgeo.2013.09.018_b0025 article-title: A constitutive model for unsaturated soils: thermomechanical and computational aspects publication-title: Comput Mech doi: 10.1007/s00466-003-0545-x – volume: 8 start-page: 266 issue: 4 year: 2008 ident: 10.1016/j.compgeo.2013.09.018_b0065 article-title: Implicit algorithm for modeling unsaturated soil response in three-invariant stress space publication-title: Int J Geomech doi: 10.1061/(ASCE)1532-3641(2008)8:4(266) – ident: 10.1016/j.compgeo.2013.09.018_b0105 – volume: 24 start-page: 893 issue: 5 year: 1987 ident: 10.1016/j.compgeo.2013.09.018_b0005 article-title: Substepping schemes for the numerical integration of elastoplastic stress–strain relations publication-title: Int J Numer Methods Eng doi: 10.1002/nme.1620240505 – volume: 13 start-page: 341 issue: 6 year: 1987 ident: 10.1016/j.compgeo.2013.09.018_b0150 article-title: An anisotropic critical state soil plasticity model publication-title: Mech Res Commun doi: 10.1016/0093-6413(86)90047-9 – volume: vol. 2 start-page: 1075 year: 2011 ident: 10.1016/j.compgeo.2013.09.018_b0050 article-title: Explicit stress integration with reduced drift for barcelona basic model – volume: 18 start-page: 314 issue: 1/2 year: 2001 ident: 10.1016/j.compgeo.2013.09.018_b0060 article-title: Implicit integration of a generalized plasticity constitutive model for partially saturated soil publication-title: Eng Comput doi: 10.1108/02644400110365941 – volume: 44 year: 2008 ident: 10.1016/j.compgeo.2013.09.018_b0145 article-title: An insight into the role of hydraulic history on the volume changes of anisotropic clayey soils publication-title: Water Resour Res doi: 10.1029/2007WR006558 – volume: 16 start-page: 121 issue: 2 year: 2000 ident: 10.1016/j.compgeo.2013.09.018_b0055 article-title: A stress point algorithm for an elastoplastic model in unsaturated soils publication-title: Int J Plast doi: 10.1016/S0749-6419(99)00033-9 – volume: 26 start-page: 963 issue: 10 year: 2002 ident: 10.1016/j.compgeo.2013.09.018_b0120 article-title: A generalized backward Euler algorithm for the numerical integration of an isotropic hardening elastoplastic model for mechanical and chemical degradation of bonded geomaterials publication-title: Int J Numer Anal Methods Geomech doi: 10.1002/nag.231 – volume: 37 start-page: 68 issue: 1–2 year: 2010 ident: 10.1016/j.compgeo.2013.09.018_b0040 article-title: Explicit stress integration with error control for the barcelona basic model. 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| SubjectTerms | Accuracy Algorithms Constitutive modelling Constitutive relationships Explicit integration Implicit integration Incremental work Mathematical analysis Mathematical models Saturation Soils Unsaturated Unsaturated soil |
| Title | Evaluation of numerical stress-point algorithms on elastic–plastic models for unsaturated soils with hardening dependent on the degree of saturation |
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