Unconditional convergence of theoretical solutions to u-p formulation
Dynamic soil-water coupling analyses, based on the u-p formulation, are inapplicable to highly permeable soils, causing numerical instability. In this study, it is demonstrated that theoretical solutions to the u-p formulation itself certainly exhibit unconditional convergence regardless of the perm...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2024-02-01
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| Series: | Soils and Foundations |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0038080623001506 |
| _version_ | 1797304619865473024 |
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| author | Tomohiro Toyoda Toshihiro Noda |
| author_facet | Tomohiro Toyoda Toshihiro Noda |
| author_sort | Tomohiro Toyoda |
| collection | DOAJ |
| description | Dynamic soil-water coupling analyses, based on the u-p formulation, are inapplicable to highly permeable soils, causing numerical instability. In this study, it is demonstrated that theoretical solutions to the u-p formulation itself certainly exhibit unconditional convergence regardless of the permeability coefficient. This suggests that the instability is only numerical and can be observed in a temporally discretized system. Firstly, the linearized governing equation for the u-p formulation was proven to be reduced to a damped wave equation under a one-dimensional condition, similar to the Full formulation. Secondly, theoretical solutions for the u-p formulation were derived and their unconditional convergence was confirmed. Then, the essential characteristics of the u-p theoretical solutions, that is, the underestimation of permeability, overestimation of compression wave celerity, and occurrence of negative pore water pressure against positive load application, were described and compared with theoretical solutions for the Full formulation. |
| first_indexed | 2024-03-08T00:13:02Z |
| format | Article |
| id | doaj.art-627ea127af144f7c83f89c7bef002b73 |
| institution | Directory Open Access Journal |
| issn | 2524-1788 |
| language | English |
| last_indexed | 2024-03-08T00:13:02Z |
| publishDate | 2024-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Soils and Foundations |
| spelling | doaj.art-627ea127af144f7c83f89c7bef002b732024-02-17T06:37:09ZengElsevierSoils and Foundations2524-17882024-02-01641101421Unconditional convergence of theoretical solutions to u-p formulationTomohiro Toyoda0Toshihiro Noda1Corresponding author.; Nagoya University, JapanNagoya University, JapanDynamic soil-water coupling analyses, based on the u-p formulation, are inapplicable to highly permeable soils, causing numerical instability. In this study, it is demonstrated that theoretical solutions to the u-p formulation itself certainly exhibit unconditional convergence regardless of the permeability coefficient. This suggests that the instability is only numerical and can be observed in a temporally discretized system. Firstly, the linearized governing equation for the u-p formulation was proven to be reduced to a damped wave equation under a one-dimensional condition, similar to the Full formulation. Secondly, theoretical solutions for the u-p formulation were derived and their unconditional convergence was confirmed. Then, the essential characteristics of the u-p theoretical solutions, that is, the underestimation of permeability, overestimation of compression wave celerity, and occurrence of negative pore water pressure against positive load application, were described and compared with theoretical solutions for the Full formulation.http://www.sciencedirect.com/science/article/pii/S0038080623001506Soil-water couplingu-p formulationUnconditional convergence |
| spellingShingle | Tomohiro Toyoda Toshihiro Noda Unconditional convergence of theoretical solutions to u-p formulation Soils and Foundations Soil-water coupling u-p formulation Unconditional convergence |
| title | Unconditional convergence of theoretical solutions to u-p formulation |
| title_full | Unconditional convergence of theoretical solutions to u-p formulation |
| title_fullStr | Unconditional convergence of theoretical solutions to u-p formulation |
| title_full_unstemmed | Unconditional convergence of theoretical solutions to u-p formulation |
| title_short | Unconditional convergence of theoretical solutions to u-p formulation |
| title_sort | unconditional convergence of theoretical solutions to u p formulation |
| topic | Soil-water coupling u-p formulation Unconditional convergence |
| url | http://www.sciencedirect.com/science/article/pii/S0038080623001506 |
| work_keys_str_mv | AT tomohirotoyoda unconditionalconvergenceoftheoreticalsolutionstoupformulation AT toshihironoda unconditionalconvergenceoftheoreticalsolutionstoupformulation |