Seismic Response of Soil-Structure Systems via BIEM and FEM in Absolute Coordinates

  • Evtim ZaharievEmail author
  • Petia Dineva
Conference paper
Part of the IUTAM Bookseries book series (IUTAMBOOK, volume 33)


The motivation for this work is to model the seismic response of a structure taking into account the base three Earth components (seismic source, wave path and local soil profile) plus the engineering structure at the end of the line and modelling all of them in one system. The main aim is to develop an efficient hybrid hi-performance methodology and software that model the dynamic response of structures during earthquake accounting for the main characteristics and mechanical properties of the soil and seismic source, plus the specific structural peculiarities and mechanical behavior of the building/underground structure. The present study investigates the soil-foundation-structure interaction and the influence of the structural dynamics over the whole system’s motion. The boundary integral equation method (BIEM) is applied to model the semi-infinite part of the geological domain, while the finite soil profile is described via finite element method (FEM). The structural dynamics is simulated using finite elements in absolute coordinates (FEAC), which allows the geometrical nonlinearity in dynamic behavior of the engineering structure to be taken into account. Example of forced motion of the rigid foundation as a result of wave propagation overlapped by a four stroke structural displacements illustrates the efficiency of the hybrid model.


Finite elements in absolute coordinates (FEAC) Boundary integral equation method (BIEM) Seismic excitations Multibody system dynamics Structural dynamics 



The second author acknowledges the support of the Bilateral Bulgarian - Greek Project, based Personnel Program between BAS and AUTH.


  1. 1.
    Chapman, C.H.: A new method for computing synthetic seismograms. Geophys. J. R. Astron. Soc. 54, 481–518 (1978)CrossRefGoogle Scholar
  2. 2.
    Panza, G.F., Romanelli, F., Vaccari, F.: Seismic Wave Propagation in Laterally Heterogeneous An elastic Media: Theory and Applications to Seismic Zonation. Adv. Geophys. 43, 1–95 (2000)Google Scholar
  3. 3.
    Fuchs, K., Müller, G.: Computation of synthetic seismograms with the reflectivity method and comparison with observations. Geophys. J. R. Astron. Soc. 23, 417–433 (1971)CrossRefGoogle Scholar
  4. 4.
    Kind, R.: The reflectivity method for a buried source. J. Geophys. Res. 44, 603–612 (1978)Google Scholar
  5. 5.
    Wuttke F.: Beitrag zur Standortidentifzierung mit Oberfachenwellen. PhD thesis, Bauhaus Universitat, Weimar (2005)Google Scholar
  6. 6.
    Moczo, P.: Finite-difference technique for SH waves in 2-D media using irregular grids: application to the seismic response problem. Geophys. J. Intell. 99, 321–329 (1989)Google Scholar
  7. 7.
    Gatmiri, B., Arson, C., Nguyen, K.V.: Seismic site effects by an optimized 2D BE/FE method. I. Theory, numerical optimization and application to topographical irregularities. Soil Dyn. Earthq. Eng. 28(8), 632–645 (2008)CrossRefGoogle Scholar
  8. 8.
    Gatmiri, B., Arson, C.: Seismic site effects by an optimized 2D BE/FE method. II. Quantification of site effects in two-dimensional sedimentary valleys. Soil Dyn. Earthq. Eng. 28(8), 646–661 (2008)CrossRefGoogle Scholar
  9. 9.
    Bouchon, M., Sanchez-Sesma, F.J.: Boundary integral equations and boundary elements methods in elastodynamics. Adv. Geophys. 48, 157–189 (2007)CrossRefGoogle Scholar
  10. 10.
    Dineva, P., Borejko, P., Hadjikov, L., Zigler, F.: Transient elastic waves in a half-space: comparison of the DBIE – method with the method of generalized ray. Acta Mech. 115, 203–211 (1996)CrossRefGoogle Scholar
  11. 11.
    Manolis, G., Dineva, P., Rangelov, Ts., Wuttke, Fr: Seismic Wave Propagation in Non-Homogeneous Elastic Media by Boundary Elements, Series: Solid Mechanics and Its Applications, Volume 240, 294 pages. Springer, ISBN 978-3-319-45205-0 (2017)CrossRefGoogle Scholar
  12. 12.
    Manolis, G.D., Beskos, D.E.: Boundary Element Methods in Elastodynamics. Unwin and Allen, London (1987)Google Scholar
  13. 13.
    Schanz, M., Steinbach, O.: Boundary Element Analysis. Mathematical Aspects and Applications. Lectures Notes in Applied and Computational Mechanics, 29, Springer (2007). Google Scholar
  14. 14.
    Vasilev, G., Parvanova, S., Dineva, P., Wuttke, F.: Soil-structure interaction using BEM-FEM coupling through ANSYS software package. Soil Dyn. Earthq. Eng. 70, 104–117 (2015)CrossRefGoogle Scholar
  15. 15.
    Basnet, M.B., Aji, H.D.B., Wuttke, F., Dineva, P.: Wave propagation through poroelastic soil with underground structures via hybrid BEM-FEM. Z. Angew. Math. Mech. 2018, 1–22 (2018). CrossRefGoogle Scholar
  16. 16.
    Zahariev, E.: Numerical Multibody System Dynamics, Rigid and Flexible Systems, Lambert Academic Publishing GmbH & Co. KG (2012)Google Scholar
  17. 17.
    Shabana, A.A.: An absolute nodal coordinate formulation for the large rotation and deformation analysis of flexible bodies, Technical Report MBS96-1-UIC. Dept of Mechanical Engineering, Univ of Illinois, Chicago (1996)Google Scholar
  18. 18.
    Shabana, A., Christensen, A.P.: Three-dimensional absolute nodal co-ordinate formulation: plate problem. Int. J. Numer. Methods Eng. 40(15), 2775–2790 (1997)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Gerstmayr, J., Sugiyama, H., Mikkola, A.: Review on the absolute nodal coordinate formulation for large deformation analysis of multibody systems. ASME J. Comput. Nonlinear Dyn. 8(3), 031016 (12p), (2013)CrossRefGoogle Scholar
  20. 20.
    Zahariev, E.V.: Generalized Finite Element Approach to Dynamics Modeling of Rigid and Flexible Systems, Mechanics Based Design of Structures and Machines. Taylor & Francis Group,. 34,. 1,. 81–109 (2006)Google Scholar
  21. 21.
    Zahariev, E.: Earthquake dynamic response of large flexible multibody systems. Mech. Sci. 4, 131–137 (2013)CrossRefGoogle Scholar
  22. 22.
    Santana, A., Aznarez, J., Padron, L., Maeso, O.: A BEM-FEM model for the gynamic analysis of building structure founded on elastic or poroelastic soils. Bull. Earthq. Eng. 14(1), 115–138 (2015)CrossRefGoogle Scholar
  23. 23.
    Dominguez, J.: Boundary elements in dynamics. Computational Mechanics Publications, Southampton Boston. Co-published with Elsevier Applied Science, London New York (1993)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Mechanics, Bulgarian Academy of SciencesSofiaBulgaria

Personalised recommendations