Semi-analytical solution for the dynamic response of a cylindrical structure embedded in a homogeneous half-space

Mingjuan Zhao*, Karel N. van Dalen, João M. Barbosa, Andrei V. Metrikine

*Corresponding author for this work

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

4 Citations (Scopus)
40 Downloads (Pure)


This paper addresses the dynamic response of an infinitely long cylindrical structure embedded in an elastic half-space. The structure has a circular cross-section and its axis is parallel to the half-space surface. Excitation can be incident body waves or forces applied on the surface of the half-space and/or the structure. The model can be used to assess the integrity of structures when acted upon by seismic waves, to predict ground-borne vibration due to circulation of vehicles, and to infer about the safety of vehicles during earthquake events. Because the half-space and the structure surfaces possess different symmetries, the solution is not straightforward. In order to circumvent this difficulty, the physical domain is conformally mapped onto an auxiliary domain with a cylindrical symmetry, in which the free surface of the half-space and the surface of the structure are located at concentric cylindrical surfaces. The solution of the original boundary value problem is finally obtained by solving a set of algebraic equations. Truncation of the summation over circumferential modes is needed in the numerical implementation. Convergence tests, validations and comparisons of stresses and motions for twoand three-dimensional cases are presented and discussed as well as the advantages and disadvantages of the proposed method. Additionally, the effect of the presence of the tunnel is analysed by considering a limiting case of the half-space with just a cylindrical cavity of the same radius as the outer radius of the tunnel.
Original languageEnglish
Title of host publicationEnvironmental Vibrations and Transportation Geodynamics
Subtitle of host publicationISEV 2016, Hangzhou China
EditorsXuecheng Bian, Yunmin Chen, Xiaowei Ye
Place of PublicationSingapore
Number of pages20
ISBN (Electronic)978-981-10-4508-0
ISBN (Print)9789811045073
Publication statusPublished - 2018
Event7th international symposium on environmental vibration and transportation geodynamics - Zhejiang University, Hangzhou, China
Duration: 28 Oct 201630 Oct 2016
Conference number: 7


Conference7th international symposium on environmental vibration and transportation geodynamics
Abbreviated titleISEV2016
Internet address

Bibliographical note

Accepted Author Manuscript


  • Three-dimensional wave propagation
  • dynamic soil-structure interaction
  • Underground structure
  • conformal mapping
  • steady state dynamic response
  • semi-analytical solution


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