{"id":"https://openalex.org/W4293169081","doi":"https://doi.org/10.3390/sym14091757","title":"Improved Analytical Solution for Air\u2013Boosted Vacuum Consolidation of Saturated Soil Using Eigenfunction Expansion Method","display_name":"Improved Analytical Solution for Air\u2013Boosted Vacuum Consolidation of Saturated Soil Using Eigenfunction Expansion Method","publication_year":2022,"publication_date":"2022-08-23","ids":{"openalex":"https://openalex.org/W4293169081","doi":"https://doi.org/10.3390/sym14091757"},"language":"en","primary_location":{"id":"doi:10.3390/sym14091757","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091757","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1757/pdf?version=1662608476","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/9/1757/pdf?version=1662608476","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053191262","display_name":"Liquan Xie","orcid":"https://orcid.org/0000-0001-8287-9706"},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liquan Xie","raw_affiliation_strings":["College of Civil Engineering, Tongji University, Shanghai 200092, China"],"affiliations":[{"raw_affiliation_string":"College of Civil Engineering, Tongji University, Shanghai 200092, China","institution_ids":["https://openalex.org/I116953780"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037299329","display_name":"Zelong Liang","orcid":"https://orcid.org/0000-0002-8011-8572"},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zelong Liang","raw_affiliation_strings":["College of Civil Engineering, Tongji University, Shanghai 200092, China"],"affiliations":[{"raw_affiliation_string":"College of Civil Engineering, Tongji University, Shanghai 200092, China","institution_ids":["https://openalex.org/I116953780"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101187987","display_name":"Guangrui Feng","orcid":null},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Guangrui Feng","raw_affiliation_strings":["College of Civil Engineering, Tongji University, Shanghai 200092, China"],"affiliations":[{"raw_affiliation_string":"College of Civil Engineering, Tongji University, Shanghai 200092, China","institution_ids":["https://openalex.org/I116953780"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100420252","display_name":"Yanhong Li","orcid":"https://orcid.org/0000-0002-2579-0526"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yanhong Li","raw_affiliation_strings":["School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China"],"affiliations":[{"raw_affiliation_string":"School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084606625","display_name":"Tongqing Wu","orcid":"https://orcid.org/0000-0003-4232-7784"},"institutions":[{"id":"https://openalex.org/I168337820","display_name":"Chongqing University of Science and Technology","ror":"https://ror.org/03n3v6d52","country_code":"CN","type":"education","lineage":["https://openalex.org/I168337820"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tongqing Wu","raw_affiliation_strings":["School of Civil Engineering and Architecture, Chongqing University of Science and Technology, Chongqing 401331, China"],"affiliations":[{"raw_affiliation_string":"School of Civil Engineering and Architecture, Chongqing University of Science and Technology, Chongqing 401331, China","institution_ids":["https://openalex.org/I168337820"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5037299329","https://openalex.org/A5101187987"],"corresponding_institution_ids":["https://openalex.org/I116953780"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.8015,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.6834894,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"14","issue":"9","first_page":"1757","last_page":"1757"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13596","display_name":"Grouting, Rheology, and Soil Mechanics","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13596","display_name":"Grouting, Rheology, and Soil Mechanics","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12233","display_name":"Geotechnical Engineering and Underground Structures","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10233","display_name":"Geotechnical Engineering and Soil Mechanics","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/consolidation","display_name":"Consolidation (business)","score":0.8599951267242432},{"id":"https://openalex.org/keywords/separation-of-variables","display_name":"Separation of variables","score":0.7242787480354309},{"id":"https://openalex.org/keywords/eigenfunction","display_name":"Eigenfunction","score":0.6844576597213745},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4759233295917511},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.4340529441833496},{"id":"https://openalex.org/keywords/rotational-symmetry","display_name":"Rotational symmetry","score":0.42773470282554626},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40687257051467896},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3834778368473053},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32434719800949097},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.22230863571166992},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20944899320602417},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.1622684895992279},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11204949021339417}],"concepts":[{"id":"https://openalex.org/C2776014549","wikidata":"https://www.wikidata.org/wiki/Q3050847","display_name":"Consolidation (business)","level":2,"score":0.8599951267242432},{"id":"https://openalex.org/C159722891","wikidata":"https://www.wikidata.org/wiki/Q913323","display_name":"Separation of variables","level":3,"score":0.7242787480354309},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.6844576597213745},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4759233295917511},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.4340529441833496},{"id":"https://openalex.org/C33026886","wikidata":"https://www.wikidata.org/wiki/Q593950","display_name":"Rotational symmetry","level":2,"score":0.42773470282554626},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40687257051467896},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3834778368473053},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32434719800949097},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.22230863571166992},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20944899320602417},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.1622684895992279},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11204949021339417},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14091757","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091757","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1757/pdf?version=1662608476","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:5a716e6d59f54e1285f1c4f8885bbd92","is_oa":true,"landing_page_url":"https://doaj.org/article/5a716e6d59f54e1285f1c4f8885bbd92","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 14, Iss 9, p 1757 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/9/1757/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14091757","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry; Volume 14; Issue 9; Pages: 1757","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14091757","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091757","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1757/pdf?version=1662608476","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Life in Land","score":0.6700000166893005,"id":"https://metadata.un.org/sdg/15"}],"awards":[{"id":"https://openalex.org/G1231421488","display_name":null,"funder_award_id":"under","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2366476780","display_name":null,"funder_award_id":"51479137","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4293169081.pdf","grobid_xml":"https://content.openalex.org/works/W4293169081.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W2154975019","https://openalex.org/W2200261846","https://openalex.org/W2281619614","https://openalex.org/W2364486728","https://openalex.org/W2366971800","https://openalex.org/W2394101123","https://openalex.org/W2438553621","https://openalex.org/W2463569655","https://openalex.org/W2773573105","https://openalex.org/W2783797474","https://openalex.org/W2913216129","https://openalex.org/W2944105159","https://openalex.org/W2971518184","https://openalex.org/W3010340555","https://openalex.org/W3129490800","https://openalex.org/W3140493962","https://openalex.org/W3158534037","https://openalex.org/W3159789280","https://openalex.org/W3165835528","https://openalex.org/W3180596863","https://openalex.org/W3197644370","https://openalex.org/W3213389622","https://openalex.org/W3214560166","https://openalex.org/W6746475300","https://openalex.org/W6792350256"],"related_works":["https://openalex.org/W2393344178","https://openalex.org/W3127755322","https://openalex.org/W2006136514","https://openalex.org/W2168468275","https://openalex.org/W3046760077","https://openalex.org/W2289225949","https://openalex.org/W4242711400","https://openalex.org/W2089206232","https://openalex.org/W33477008","https://openalex.org/W4241338871"],"abstract_inverted_index":{"Soft":[0],"foundation":[1],"consolidation":[2,22,34,51,97,173],"engineering":[3],"applications":[4],"and":[5,114],"experimental":[6],"studies":[7],"have":[8],"proven":[9],"the":[10,13,32,37,53,67,70,84,90,96,99,105,122,127,135,141,145,172],"effectiveness":[11],"of":[12,36,52,75,98,140,150,159,174],"air\u2013boosted":[14,41,49,178],"vacuum":[15,42,50,179],"preloading":[16,180],"method":[17,101,108,130,143],"(AVP).":[18],"The":[19,44,163],"sand":[20],"well":[21],"theory,":[23],"a":[24,62,155],"typical":[25],"axisymmetric":[26],"consolidation,":[27],"is":[28,56,77,80,112,131],"adapted":[29],"to":[30,154,170],"analyze":[31],"whole":[33],"process":[35],"saturated":[38,54],"soil":[39,55],"by":[40,126,148,177],"preloading.":[43],"present":[45],"analytical":[46,124,165],"solution":[47,72,125,137,147,166],"for":[48,59,83,94,109],"more":[57,132],"suitable":[58],"application":[60],"in":[61,116],"deep":[63,175],"soft":[64],"foundation.":[65],"With":[66],"solving":[68,95],"method,":[69],"general":[71,146],"through":[73],"separation":[74,149],"variables":[76],"used,":[78],"which":[79,152],"mathematically":[81],"used":[82,169],"homogeneous":[85],"partial":[86,91],"differential":[87,92],"equations.":[88],"However,":[89],"equations":[93,111],"AVP":[100],"are":[102],"nonhomogeneous.":[103],"Therefore,":[104],"eigenfunction":[106,128],"expansion":[107,129],"nonhomogeneous":[110],"proposed":[113],"validated":[115],"this":[117],"study.":[118],"Results":[119],"showed":[120],"that":[121,139],"improved":[123,164],"consistent":[133],"with":[134],"numerical":[136],"than":[138,161],"previous":[142],"using":[144],"variables,":[151],"leads":[153],"lower":[156],"error":[157],"ratio":[158],"less":[160],"2%.":[162],"can":[167],"be":[168],"predict":[171],"foundations":[176],"effectively.":[181]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2}],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2022-08-27T00:00:00"}