Exact solutions for one-dimensional consolidation of single-layer unsaturated soil
SUMMARY Based on the Fredlund consolidation theory of unsaturated soil, exact solutions of the governing equations for one‐dimensional consolidation of single‐layer unsaturated soil are presented, in which the water permeability and air transmission are assumed to be constants. The general solution...
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| Veröffentlicht in: | International journal for numerical and analytical methods in geomechanics 2012-04, Vol.36 (6), p.708-722 |
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| container_title | International journal for numerical and analytical methods in geomechanics |
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| creator | Shan, Zhendong Ling, Daosheng Ding, Haojiang |
| description | SUMMARY
Based on the Fredlund consolidation theory of unsaturated soil, exact solutions of the governing equations for one‐dimensional consolidation of single‐layer unsaturated soil are presented, in which the water permeability and air transmission are assumed to be constants. The general solution of two coupled homogeneous governing equations is first obtained. This general solution is expressed in terms of two functions psi1 and ψ2, where ψ1 and ψ2, respectively, satisfy two second‐order partial differential equations, which are in the same form. Using the method of separation of variables, the two partial differential equations are solved and exact solutions for three typical homogeneous boundary conditions are obtained. To obtain exact solutions of nonhomogeneous governing equations with three typical nonhomogeneous boundary conditions, the nonhomogeneous boundary conditions are first transformed into homogeneous boundary conditions. Then according to the method of undetermined coefficients and exact solutions of homogenous governing equations, the series form exact solutions are put forward. The validity of the proposed exact solutions is verified against other analytical solutions in the literature. Copyright © 2011 John Wiley & Sons, Ltd. |
| doi_str_mv | 10.1002/nag.1026 |
| format | Article |
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Based on the Fredlund consolidation theory of unsaturated soil, exact solutions of the governing equations for one‐dimensional consolidation of single‐layer unsaturated soil are presented, in which the water permeability and air transmission are assumed to be constants. The general solution of two coupled homogeneous governing equations is first obtained. This general solution is expressed in terms of two functions psi1 and ψ2, where ψ1 and ψ2, respectively, satisfy two second‐order partial differential equations, which are in the same form. Using the method of separation of variables, the two partial differential equations are solved and exact solutions for three typical homogeneous boundary conditions are obtained. To obtain exact solutions of nonhomogeneous governing equations with three typical nonhomogeneous boundary conditions, the nonhomogeneous boundary conditions are first transformed into homogeneous boundary conditions. Then according to the method of undetermined coefficients and exact solutions of homogenous governing equations, the series form exact solutions are put forward. The validity of the proposed exact solutions is verified against other analytical solutions in the literature. Copyright © 2011 John Wiley & Sons, Ltd.</description><identifier>ISSN: 0363-9061</identifier><identifier>EISSN: 1096-9853</identifier><identifier>DOI: 10.1002/nag.1026</identifier><identifier>CODEN: IJNGDZ</identifier><language>eng</language><publisher>Chichester, UK: John Wiley & Sons, Ltd</publisher><subject>Applied sciences ; Buildings. Public works ; Computation methods. Tables. Charts ; consolidation ; Exact sciences and technology ; exact solution ; general solution ; Geotechnics ; nonhomogeneous boundary condition ; Stabilization. Consolidation ; Structural analysis. Stresses ; unsaturated soil</subject><ispartof>International journal for numerical and analytical methods in geomechanics, 2012-04, Vol.36 (6), p.708-722</ispartof><rights>Copyright © 2011 John Wiley & Sons, Ltd.</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-a3566-b0133f176023600a1a5830edc260269cf806599f0d7264e4aeaa0e6514ac01503</citedby><cites>FETCH-LOGICAL-a3566-b0133f176023600a1a5830edc260269cf806599f0d7264e4aeaa0e6514ac01503</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fnag.1026$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fnag.1026$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,776,780,1411,27901,27902,45550,45551</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=25727958$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Shan, Zhendong</creatorcontrib><creatorcontrib>Ling, Daosheng</creatorcontrib><creatorcontrib>Ding, Haojiang</creatorcontrib><title>Exact solutions for one-dimensional consolidation of single-layer unsaturated soil</title><title>International journal for numerical and analytical methods in geomechanics</title><addtitle>Int. J. Numer. Anal. Meth. Geomech</addtitle><description>SUMMARY
Based on the Fredlund consolidation theory of unsaturated soil, exact solutions of the governing equations for one‐dimensional consolidation of single‐layer unsaturated soil are presented, in which the water permeability and air transmission are assumed to be constants. The general solution of two coupled homogeneous governing equations is first obtained. This general solution is expressed in terms of two functions psi1 and ψ2, where ψ1 and ψ2, respectively, satisfy two second‐order partial differential equations, which are in the same form. Using the method of separation of variables, the two partial differential equations are solved and exact solutions for three typical homogeneous boundary conditions are obtained. To obtain exact solutions of nonhomogeneous governing equations with three typical nonhomogeneous boundary conditions, the nonhomogeneous boundary conditions are first transformed into homogeneous boundary conditions. Then according to the method of undetermined coefficients and exact solutions of homogenous governing equations, the series form exact solutions are put forward. The validity of the proposed exact solutions is verified against other analytical solutions in the literature. Copyright © 2011 John Wiley & Sons, Ltd.</description><subject>Applied sciences</subject><subject>Buildings. Public works</subject><subject>Computation methods. Tables. Charts</subject><subject>consolidation</subject><subject>Exact sciences and technology</subject><subject>exact solution</subject><subject>general solution</subject><subject>Geotechnics</subject><subject>nonhomogeneous boundary condition</subject><subject>Stabilization. Consolidation</subject><subject>Structural analysis. Stresses</subject><subject>unsaturated soil</subject><issn>0363-9061</issn><issn>1096-9853</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><recordid>eNp1kMFKAzEQhoMoWKvgI-xF8BKdbJps99gWW5VaQRTFSxizSYmmuyXZYvv2prT05mmG-T--gZ-QSwY3DCC_rXGellwekQ6DUtKyL_gx6QCXnJYg2Sk5i_EbAERKO-Tlbo26zWLjV61r6pjZJmRNbWjlFqaO6YQ-0ylovKtwi2SNzaKr595QjxsTslUdsV0FbE2VPM6fkxOLPpqL_eySt_Hd6-ieTp8nD6PBlCIXUtIvYJxbVkjIuQRAhqLPwVQ6TxdZatsHKcrSQlXksmd6aBDBSMF6qIEJ4F1yvfPq0MQYjFXL4BYYNoqB2nahUhdq20VCr3boEqNGbwPW2sUDn4siL8r0vkvojvt13mz-9anZYLL37nkXW7M-8Bh-lCx4IdT7bKIex8Ppx1A8qU_-B8AtfCc</recordid><startdate>20120425</startdate><enddate>20120425</enddate><creator>Shan, Zhendong</creator><creator>Ling, Daosheng</creator><creator>Ding, Haojiang</creator><general>John Wiley & Sons, Ltd</general><general>Wiley</general><scope>BSCLL</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20120425</creationdate><title>Exact solutions for one-dimensional consolidation of single-layer unsaturated soil</title><author>Shan, Zhendong ; Ling, Daosheng ; Ding, Haojiang</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a3566-b0133f176023600a1a5830edc260269cf806599f0d7264e4aeaa0e6514ac01503</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Applied sciences</topic><topic>Buildings. Public works</topic><topic>Computation methods. Tables. Charts</topic><topic>consolidation</topic><topic>Exact sciences and technology</topic><topic>exact solution</topic><topic>general solution</topic><topic>Geotechnics</topic><topic>nonhomogeneous boundary condition</topic><topic>Stabilization. Consolidation</topic><topic>Structural analysis. Stresses</topic><topic>unsaturated soil</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Shan, Zhendong</creatorcontrib><creatorcontrib>Ling, Daosheng</creatorcontrib><creatorcontrib>Ding, Haojiang</creatorcontrib><collection>Istex</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><jtitle>International journal for numerical and analytical methods in geomechanics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Shan, Zhendong</au><au>Ling, Daosheng</au><au>Ding, Haojiang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Exact solutions for one-dimensional consolidation of single-layer unsaturated soil</atitle><jtitle>International journal for numerical and analytical methods in geomechanics</jtitle><addtitle>Int. J. Numer. Anal. Meth. Geomech</addtitle><date>2012-04-25</date><risdate>2012</risdate><volume>36</volume><issue>6</issue><spage>708</spage><epage>722</epage><pages>708-722</pages><issn>0363-9061</issn><eissn>1096-9853</eissn><coden>IJNGDZ</coden><abstract>SUMMARY
Based on the Fredlund consolidation theory of unsaturated soil, exact solutions of the governing equations for one‐dimensional consolidation of single‐layer unsaturated soil are presented, in which the water permeability and air transmission are assumed to be constants. The general solution of two coupled homogeneous governing equations is first obtained. This general solution is expressed in terms of two functions psi1 and ψ2, where ψ1 and ψ2, respectively, satisfy two second‐order partial differential equations, which are in the same form. Using the method of separation of variables, the two partial differential equations are solved and exact solutions for three typical homogeneous boundary conditions are obtained. To obtain exact solutions of nonhomogeneous governing equations with three typical nonhomogeneous boundary conditions, the nonhomogeneous boundary conditions are first transformed into homogeneous boundary conditions. Then according to the method of undetermined coefficients and exact solutions of homogenous governing equations, the series form exact solutions are put forward. The validity of the proposed exact solutions is verified against other analytical solutions in the literature. Copyright © 2011 John Wiley & Sons, Ltd.</abstract><cop>Chichester, UK</cop><pub>John Wiley & Sons, Ltd</pub><doi>10.1002/nag.1026</doi><tpages>15</tpages></addata></record> |
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| source | Wiley Online Library Journals Frontfile Complete |
| subjects | Applied sciences Buildings. Public works Computation methods. Tables. Charts consolidation Exact sciences and technology exact solution general solution Geotechnics nonhomogeneous boundary condition Stabilization. Consolidation Structural analysis. Stresses unsaturated soil |
| title | Exact solutions for one-dimensional consolidation of single-layer unsaturated soil |
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