{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:22:12Z","timestamp":1760149332103,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,7,17]],"date-time":"2023-07-17T00:00:00Z","timestamp":1689552000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002921","name":"China State Construction Engineering Corporation","doi-asserted-by":"publisher","award":["CSCEC-2020-Z-46"],"award-info":[{"award-number":["CSCEC-2020-Z-46"]}],"id":[{"id":"10.13039\/501100002921","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A semi-analytical method is developed to study the visco-elastic interface effect on the dynamic stress of a non-circular symmetrical tunnel in a half-plane subjected to P waves, and the interaction between the visco-elastic interface around the tunnel and the traction free boundary at the half-plane is analyzed. The complex variable function method combined with the wave function expansion method is introduced to obtain the theoretical expressions of waves around the non-circular tunnel. To satisfy the traction-free boundary condition at the half-plane, the large circle assumption is applied. The expanded coefficients are determined by using appropriate boundary conditions with stiffness parameters and viscosity coefficients of the interface. Selected numerical results are presented, and the interface effect on the dynamic stress under different embedded depths is discussed. It is found that the interacting effect of the visco-elastic interface and the traction-free boundary is quite related with the wave frequency. Comparison with existing results is also given to validate the semi-analytical method.<\/jats:p>","DOI":"10.3390\/sym15071434","type":"journal-article","created":{"date-parts":[[2023,7,18]],"date-time":"2023-07-18T01:31:32Z","timestamp":1689643892000},"page":"1434","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Visco-Elastic Interface Effect on the Dynamic Stress of Symmetrical Tunnel Embedded in a Half-Plane Subjected to P Waves"],"prefix":"10.3390","volume":"15","author":[{"given":"Hexin","family":"Jin","sequence":"first","affiliation":[{"name":"China Construction Sixth Engineering Bureau Co., Ltd., Tianjin 300171, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaomin","family":"Liu","sequence":"additional","affiliation":[{"name":"China Construction Sixth Engineering Bureau Co., Ltd., Tianjin 300171, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junlong","family":"Zhou","sequence":"additional","affiliation":[{"name":"China Construction Sixth Engineering Bureau Co., Ltd., Tianjin 300171, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2217","DOI":"10.1080\/19648189.2019.1624395","article-title":"Interaction between a tunnel and alluvial valley under plane SV waves of earthquakes by IBIEM","volume":"25","author":"Huang","year":"2021","journal-title":"Eur. 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