{"id":"https://openalex.org/W4296020995","doi":"https://doi.org/10.3390/sym14091904","title":"Modification of the Peck Formula for a Double-Track Shield Tunnel under Expressway Subgrade","display_name":"Modification of the Peck Formula for a Double-Track Shield Tunnel under Expressway Subgrade","publication_year":2022,"publication_date":"2022-09-12","ids":{"openalex":"https://openalex.org/W4296020995","doi":"https://doi.org/10.3390/sym14091904"},"language":"en","primary_location":{"id":"doi:10.3390/sym14091904","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091904","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1904/pdf?version=1662981285","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/2073-8994/14/9/1904/pdf?version=1662981285","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100341662","display_name":"Yuxiang Li","orcid":"https://orcid.org/0009-0002-1170-8189"},"institutions":[{"id":"https://openalex.org/I3133134087","display_name":"Lanzhou Jiaotong University","ror":"https://ror.org/03144pv92","country_code":"CN","type":"education","lineage":["https://openalex.org/I3133134087"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuxiang Li","raw_affiliation_strings":["School of Civil Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Civil Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China","institution_ids":["https://openalex.org/I3133134087"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073542762","display_name":"Juncen Lin","orcid":"https://orcid.org/0009-0002-1397-2282"},"institutions":[{"id":"https://openalex.org/I3133134087","display_name":"Lanzhou Jiaotong University","ror":"https://ror.org/03144pv92","country_code":"CN","type":"education","lineage":["https://openalex.org/I3133134087"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Juncen Lin","raw_affiliation_strings":["School of Civil Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Civil Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China","institution_ids":["https://openalex.org/I3133134087"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009434332","display_name":"Songhong Yan","orcid":"https://orcid.org/0000-0002-9739-192X"},"institutions":[{"id":"https://openalex.org/I3133134087","display_name":"Lanzhou Jiaotong University","ror":"https://ror.org/03144pv92","country_code":"CN","type":"education","lineage":["https://openalex.org/I3133134087"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Songhong Yan","raw_affiliation_strings":["School of Civil Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Civil Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China","institution_ids":["https://openalex.org/I3133134087"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038047426","display_name":"Jiaxuan Du","orcid":null},"institutions":[{"id":"https://openalex.org/I3133134087","display_name":"Lanzhou Jiaotong University","ror":"https://ror.org/03144pv92","country_code":"CN","type":"education","lineage":["https://openalex.org/I3133134087"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiaxuan Du","raw_affiliation_strings":["School of Civil Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Civil Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China","institution_ids":["https://openalex.org/I3133134087"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5009434332"],"corresponding_institution_ids":["https://openalex.org/I3133134087"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.3983,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.79225075,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"14","issue":"9","first_page":"1904","last_page":"1904"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11046","display_name":"Geotechnical Engineering and Analysis","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2213","display_name":"Safety, Risk, Reliability and Quality"},"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/T11046","display_name":"Geotechnical Engineering and Analysis","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2213","display_name":"Safety, Risk, Reliability and Quality"},"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/T14446","display_name":"Civil and Geotechnical Engineering Research","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2200","display_name":"General 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"}}],"keywords":[{"id":"https://openalex.org/keywords/subgrade","display_name":"Subgrade","score":0.8086040019989014},{"id":"https://openalex.org/keywords/peck","display_name":"Peck (Imperial)","score":0.7924796342849731},{"id":"https://openalex.org/keywords/shield","display_name":"Shield","score":0.7886375188827515},{"id":"https://openalex.org/keywords/settlement","display_name":"Settlement (finance)","score":0.6260150074958801},{"id":"https://openalex.org/keywords/geotechnical-engineering","display_name":"Geotechnical engineering","score":0.5908886790275574},{"id":"https://openalex.org/keywords/excavation","display_name":"Excavation","score":0.5034434199333191},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.39833948016166687},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.32784566283226013},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2819939851760864},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.26672422885894775},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21761876344680786},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20793411135673523}],"concepts":[{"id":"https://openalex.org/C182377489","wikidata":"https://www.wikidata.org/wiki/Q337829","display_name":"Subgrade","level":2,"score":0.8086040019989014},{"id":"https://openalex.org/C189338036","wikidata":"https://www.wikidata.org/wiki/Q351646","display_name":"Peck (Imperial)","level":2,"score":0.7924796342849731},{"id":"https://openalex.org/C138081364","wikidata":"https://www.wikidata.org/wiki/Q852013","display_name":"Shield","level":2,"score":0.7886375188827515},{"id":"https://openalex.org/C2777063073","wikidata":"https://www.wikidata.org/wiki/Q1553237","display_name":"Settlement (finance)","level":3,"score":0.6260150074958801},{"id":"https://openalex.org/C187320778","wikidata":"https://www.wikidata.org/wiki/Q1349130","display_name":"Geotechnical engineering","level":1,"score":0.5908886790275574},{"id":"https://openalex.org/C31858485","wikidata":"https://www.wikidata.org/wiki/Q959782","display_name":"Excavation","level":2,"score":0.5034434199333191},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.39833948016166687},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.32784566283226013},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2819939851760864},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.26672422885894775},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21761876344680786},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20793411135673523},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0},{"id":"https://openalex.org/C5900021","wikidata":"https://www.wikidata.org/wiki/Q163082","display_name":"Petrology","level":1,"score":0.0},{"id":"https://openalex.org/C145097563","wikidata":"https://www.wikidata.org/wiki/Q1148747","display_name":"Payment","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14091904","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091904","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1904/pdf?version=1662981285","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:d9eb5ae18ad146eab014fb16f1bf6e9e","is_oa":true,"landing_page_url":"https://doaj.org/article/d9eb5ae18ad146eab014fb16f1bf6e9e","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 14, Iss 9, p 1904 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/9/1904/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14091904","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","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14091904","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091904","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1904/pdf?version=1662981285","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":"Sustainable cities and communities","score":0.5400000214576721,"id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G8529638987","display_name":"\u8de8\u6d3b\u65ad\u5c42\u533a\u96a7\u9053\u6297\u9519\u65ad\u53ca\u5730\u9707\u7834\u574f\u673a\u7406\u4e0e\u6297\u51cf\u9707\u6280\u672f\u7814\u7a76","funder_award_id":"52068044","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/W4296020995.pdf","grobid_xml":"https://content.openalex.org/works/W4296020995.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1131012703","https://openalex.org/W2165831329","https://openalex.org/W2357280374","https://openalex.org/W2360340699","https://openalex.org/W2368390680","https://openalex.org/W2584498326","https://openalex.org/W2884125794","https://openalex.org/W2888753662","https://openalex.org/W3046131239","https://openalex.org/W4283071617","https://openalex.org/W4283458524","https://openalex.org/W6706331285","https://openalex.org/W6708503771"],"related_works":["https://openalex.org/W4245821237","https://openalex.org/W2201985621","https://openalex.org/W606555680","https://openalex.org/W2811264828","https://openalex.org/W4213330903","https://openalex.org/W2351532073","https://openalex.org/W2382237715","https://openalex.org/W2369683634","https://openalex.org/W4386521185","https://openalex.org/W3008760781"],"abstract_inverted_index":{"In":[0],"practice,":[1],"asymmetric":[2],"formation":[3],"disturbance":[4],"occurs":[5],"due":[6],"to":[7,48,60,64],"the":[8,31,36,39,57,65,69,75,83,97,101,109,123,129,133,143,154,165,168,173,185,197],"sequence":[9],"of":[10,27,30,38,68,108,132,167],"excavation":[11],"though":[12],"parallel":[13],"double-track":[14],"tunnel":[15,99,103,187],"is":[16],"a":[17,23,28,42,50,148],"typical":[18],"symmetrical":[19],"engineering.":[20],"Based":[21],"on":[22],"shield":[24,70,137,174],"tunneling":[25],"project":[26],"section":[29],"Suzhou":[32],"Rail":[33],"Transit":[34],"under":[35,136],"subgrade":[37,135,170],"Shanghai\u2013Nanjing":[40],"Expressway,":[41],"finite":[43],"element":[44],"model":[45],"was":[46,54,104,113],"established":[47],"obtain":[49],"numerical":[51,124],"solution":[52,125],"that":[53,122],"validated":[55],"by":[56,115,142,172],"measured":[58,155],"data":[59],"guarantee":[61],"reliability.":[62],"According":[63],"construction":[66],"characteristics":[67],"method,":[71],"two":[72],"correction":[73,79,87],"coefficients\u2014namely":[74],"soil":[76],"loss":[77],"rate":[78],"coefficient":[80,88],"\u03b1":[81],"and":[82,100,180,188,192],"settlement":[84,131,166],"trough":[85],"width":[86],"\u03b2\u2014were":[89],"introduced.":[90],"A":[91],"modified":[92,110,158],"Peck":[93,111,145],"formula":[94,112,146,160],"suitable":[95],"for":[96,184,196],"preceding":[98,186],"subsequent":[102,198],"proposed.":[105],"The":[106,119,139,157],"applicability":[107],"verified":[114],"another":[116],"similar":[117],"project.":[118],"results":[120,140],"showed":[121],"can":[126],"better":[127],"reflect":[128],"actual":[130],"highway":[134],"tunneling.":[138],"calculated":[141],"classic":[144],"had":[147],"large":[149],"error":[150],"in":[151],"comparison":[152],"with":[153],"data.":[156],"empirical":[159],"could":[161],"more":[162],"accurately":[163],"predict":[164],"expressway":[169],"caused":[171],"method":[175],"when":[176],"\u03b11":[177],"=":[178,182,190,194],"0.38":[179],"\u03b21":[181],"2.08":[183],"\u03b12":[189],"0.29":[191],"\u03b22":[193],"1.99":[195],"tunnel.":[199]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3}],"updated_date":"2026-06-06T09:05:17.133730","created_date":"2025-10-10T00:00:00"}