{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T02:43:25Z","timestamp":1771469005702,"version":"3.50.1"},"reference-count":27,"publisher":"Wiley","license":[{"start":{"date-parts":[[2023,11,15]],"date-time":"2023-11-15T00:00:00Z","timestamp":1700006400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100013066","name":"Key Scientific Research Project of Colleges and Universities in Henan Province","doi-asserted-by":"publisher","award":["23B560001"],"award-info":[{"award-number":["23B560001"]}],"id":[{"id":"10.13039\/501100013066","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013066","name":"Key Scientific Research Project of Colleges and Universities in Henan Province","doi-asserted-by":"publisher","award":["U1504505"],"award-info":[{"award-number":["U1504505"]}],"id":[{"id":"10.13039\/501100013066","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["23B560001"],"award-info":[{"award-number":["23B560001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U1504505"],"award-info":[{"award-number":["U1504505"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2023,11,15]]},"abstract":"<jats:p>In order to consider the influence of liquid phase and soil anisotropy, the soil around the pile is considered a transversely isotropic saturated porous medium, and a horizontal dynamic model of transversely isotropic saturated soil-pile is established. Based on Beor\u2019s saturated porous medium theory and the constitutive equation of transversely isotropic media, the horizontal dynamic control equation of transversely isotropic saturated soil is obtained without considering the vertical displacement. The horizontal vibration of transversely isotropic soil layers was solved using the potential function and separation of the variable method, and the horizontal and radial displacements of the solid soil skeleton of transversely isotropic saturated soil were obtained. The horizontal force of transversely isotropic saturated soil on a single pile was also obtained. On this basis, the horizontal dynamic equation of a single pile in transversely isotropic saturated soil was established, and the horizontal vibration of the pile foundation was solved using the initial parameter method, and the horizontal dynamic impedance of a single pile in transversely isotropic saturated soil is obtained. The influence of soil anisotropy parameter, liquid-solid coupling coefficient, diameter-length ratio, and modulus ratio on the horizontal dynamic impedance of a single pile in transversely isotropic saturated soil was analyzed through numerical examples. The analysis results show that the anisotropy parameters <jats:inline-formula>\n                     <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\">\n                        <a:msub>\n                           <a:mrow>\n                              <a:mi>\u03b4<\/a:mi>\n                           <\/a:mrow>\n                           <a:mrow>\n                              <a:mn>1<\/a:mn>\n                           <\/a:mrow>\n                        <\/a:msub>\n                     <\/a:math>\n                  <\/jats:inline-formula>, diameter-length ratio <jats:inline-formula>\n                     <c:math xmlns:c=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\">\n                        <c:msub>\n                           <c:mrow>\n                              <c:mi>r<\/c:mi>\n                           <\/c:mrow>\n                           <c:mrow>\n                              <c:mn>0<\/c:mn>\n                           <\/c:mrow>\n                        <\/c:msub>\n                        <c:mo>\/<\/c:mo>\n                        <c:mi>H<\/c:mi>\n                     <\/c:math>\n                  <\/jats:inline-formula>, and modulus ratio <jats:inline-formula>\n                     <e:math xmlns:e=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\">\n                        <e:msub>\n                           <e:mrow>\n                              <e:mi>E<\/e:mi>\n                           <\/e:mrow>\n                           <e:mrow>\n                              <e:mi>p<\/e:mi>\n                           <\/e:mrow>\n                        <\/e:msub>\n                        <e:mo>\/<\/e:mo>\n                        <e:msub>\n                           <e:mrow>\n                              <e:mi>C<\/e:mi>\n                           <\/e:mrow>\n                           <e:mrow>\n                              <e:mn>66<\/e:mn>\n                           <\/e:mrow>\n                        <\/e:msub>\n                     <\/e:math>\n                  <\/jats:inline-formula> have a significant impact on the horizontal dynamic impedance of pile foundation in transversely isotropic saturated soil, and the influence of anisotropy on the horizontal vibration of pile foundation should not be ignored. The influence of the liquid-solid coupling coefficient on the horizontal dynamic impedance factor is related to frequency to a certain extent.<\/jats:p>","DOI":"10.1155\/2023\/8103614","type":"journal-article","created":{"date-parts":[[2023,11,15]],"date-time":"2023-11-15T19:05:40Z","timestamp":1700075140000},"page":"1-12","source":"Crossref","is-referenced-by-count":3,"title":["Horizontal Vibration of Pile in Transversely Isotropic Saturated Soil Based on Saturated Porous Medium Theory"],"prefix":"10.1155","volume":"2023","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1492-2703","authenticated-orcid":true,"given":"Linchao","family":"Liu","sequence":"first","affiliation":[{"name":"College of Architecture and Civil Engineering, Xinyang Normal University, Xinyang, Henan 464000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5864-9297","authenticated-orcid":true,"given":"Qifang","family":"Yan","sequence":"additional","affiliation":[{"name":"College of Architecture and Civil Engineering, Xinyang Normal University, Xinyang, Henan 464000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1139\/t74-059"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1002\/eqe.4290050305"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1002\/eqe.4290040308"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1002\/eqe.230"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1007\/s11803-015-0020-7"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1002\/nag.2670"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.compgeo.2019.103276"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.soildyn.2021.107126"},{"key":"9","article-title":"Analytical solution for vertical vibration of partially embedded large-diameter floating pile","volume":"167, article 107799","author":"K. Meng","year":"2003","journal-title":"Soil dynamics and Earthquake Engineering"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.compstruc.2004.10.015"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.compgeo.2008.08.013"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/j.soildyn.2020.106211"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/j.compgeo.2020.103942"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)GM.1943-5622.0001881"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1007\/s001610100069"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1007\/s11803-016-0340-2"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.compgeo.2007.05.009"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1142\/S0219455422500444"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/j.compgeo.2020.103772"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1016\/j.soildyn.2018.11.003"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1007\/s10706-022-02307-2"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1155\/2023\/9132285"},{"key":"23","volume-title":"Elasticity of Transversely Isotropic Materials","author":"H. 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