{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:17:15Z","timestamp":1760235435503,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,8,20]],"date-time":"2021-08-20T00:00:00Z","timestamp":1629417600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Fundamental Research Fund for Beijing University of Civil Engineering and Architecture","award":["X20033"],"award-info":[{"award-number":["X20033"]}]},{"DOI":"10.13039\/501100004826","name":"Beijing Municipal Natural Science Foundation","doi-asserted-by":"publisher","award":["8204058"],"award-info":[{"award-number":["8204058"]}],"id":[{"id":"10.13039\/501100004826","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Program for Scientific Research of Beijing Education Commission","award":["KM202110016013"],"award-info":[{"award-number":["KM202110016013"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The characteristics of bridge pile-group foundation have a significant influence on the dynamic performance of the superstructure. Most of the existing analysis methods for the pile-group foundation impedance take the trait of strong specialty, which cannot be generalized in practical projects. Therefore, a project-oriented numerical solution algorithm is proposed to compute the dynamic impedance of bridge pile-group foundation. Based on the theory of viscous-spring artificial boundary, the derivation and solution of the impedance function are transferred to numerical modeling and harmonic analysis, which can be carried out through the finite element method. By taking a typical pile-group foundation as a case study, the results based on the algorithm are compared with those from existing literature. Moreover, an impact experiment of a real pile-group foundation was implemented, the results of which are also compared with those resulting from the proposed numerical algorithm. Both comparisons show that the proposed numerical algorithm satisfies engineering precision, thus showing good effectiveness in application.<\/jats:p>","DOI":"10.3390\/a14080247","type":"journal-article","created":{"date-parts":[[2021,8,20]],"date-time":"2021-08-20T08:44:45Z","timestamp":1629449085000},"page":"247","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Numerical Algorithm for Dynamic Impedance of Bridge Pile-Group Foundation and Its Validation"],"prefix":"10.3390","volume":"14","author":[{"given":"Chenyu","family":"Wang","sequence":"first","affiliation":[{"name":"School of Civil and Transportation Engineering, Beijing University of Civil Engineering and Architecture, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4070-7564","authenticated-orcid":false,"given":"Hong","family":"Qiao","sequence":"additional","affiliation":[{"name":"School of Civil and Transportation Engineering, Beijing University of Civil Engineering and Architecture, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yi","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xianting","family":"Du","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zhang, L.X., and Gu, Y. 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