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Hybrid modelling of multi-layered geological structure under seismic excitation

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Abstract

This paper deals with seismic response evaluation of a finite multilayered geological structure with non-parallel boundaries rested on semi-infinite elastic half-plane subjected to transient seismic wave. The hybrid modelling approach is applied. It is based on the decomposition of the whole domain under consideration into two subregions: a finite-sized near-field zone and the open semi-infinite far-field region. The near-field range is presented by a finite geological profile, which is heterogeneous due to non-parallel layering. The far-field region is semi-infinite elastic isotropic homogeneous medium where the finite layered structure is located. An efficient 2D hybrid computational tool based on the boundary element method (BEM) for the far-field zone and the finite element method (FEM) for the finite layered domain is developed and verified in frequency domain. The BEM model of the seismically active far-field zone is inserted as a macro-finite element (MFE) in the FEM commercial program ANSYS. The hybrid model is of the FEM hosted type, where the boundary element domain (BED) is converted into macro-finite element, the nodal forces along the interface between two zones are expressed through the BED nodal tractions and the entire BEM formulation is converted to FEM-like approach. This hybrid model is applied for modelling of a real geological profile of the main wall of the “Liulyakovitsa” tailing pond, near Panagyurishte town, Bulgaria. Simulation results are given in the form of free surface synthetic seismograms stemming from the real seismic signals recorded at bedrock so as to establish the tailing pond’s seismic response.

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References

  • Apsel RJ (1979) Dynamic Green's functions for layered media and applications to boundary-value problems. University of California at San Diego, Dissertation

    Google Scholar 

  • Apsel RJ, Luco E (1983) On the Green’s functions for a layered half-space Part I. Bulletin of the Seismological Society of America 73(4):909–929

    Google Scholar 

  • Bouchon M (1981) A simple method to calculate Green's functions for elastic layered media. Bull Seismol Soc Am 71(4):959–971

    Google Scholar 

  • Chaillat S, Bonnet M, Semblat JF (2009) A new fast multi-domain BEM to model seismic wave propagation and amplification in 3-D geological structures. Geophys J Int 177:509–531

    Article  Google Scholar 

  • Contract D III-27/27.02.2014 (2014) Assessment of the sustainability of Lyulyukovitsa tailing pond, at the stage of its operating building up to the beginning of 2014, according to the working project’, HIDROINJENERING "Ltd., Sofia

  • Contract D ІІІ-37/12.05.2017 (2018) Detailed micro-seismic zoning and determination of the seismic characteristics of Lyulyukovitsa tailing pond. National Institute of Geophysics, Geodesy and Geography, Bulgarian Academy of Sciences, Sofia

    Google Scholar 

  • Dineva P, Manolis GD, Rangelov TV (2004) Transient seismic wave propagation in a multilayered cracked geological region. J Sound Vib 273(1-2):1–32

    Article  Google Scholar 

  • Dineva P, Manolis GD, Rangelov T (2008) Site effect due to wave path in homogeneity by BEM. Engineering Analysis with Boundary Elements 32:1025–1036

    Article  Google Scholar 

  • Dineva P, Parvanova S, Vasilev G, Wuttke F (2014) BEM modeling of seismic soil-tunnels interaction. Seismic soil-tunnels interaction via BEM I. Mechanical model (Part I). J Theor Appl Mech 44(3):31–48

    Article  Google Scholar 

  • Fuchs K (1968) The reflection of spherical waves from transition zones with arbitrary depth dependent elastic moduli and density. J Phys Earth 16:27–41

    Article  Google Scholar 

  • Gilbert F, Backus GE (1966) Propagator matrices in elastic wave and vibration problems. Geophysics 31:326–332

    Article  Google Scholar 

  • Google maps (n.d.). Liulyakovitsa tailings pond. Retrieved from https://www.google.com/maps/@42.5506919,24.1109321,4387m/data=!3m1!1e3?hl=en. Accessed October, 2019

  • Guzina BB, Pak RYS (2001) On the analysis of wave motions in a multi-layered solid. Q J Mech Appl Math 54(1):13–37

    Article  Google Scholar 

  • Haskell NA (1953) The dispersion of surface waves on multilayered media. Bull Seismol Soc Am 43(1):17–34

    Google Scholar 

  • Kausel E (1974) Forced vibrations of circular foundations on layered media. Research Report R74-11, Soils Publication No. 336, Dept. of Civil Engineering, MIT, Cambridge, Massachusetts

  • Kausel E, Roësset JM (1981) Stiffness matrices for layered soils. Bull Seismol Soc Am 71(6):1743–1761

    Google Scholar 

  • Kennett BLN, Kerry NJ (1979) Seismic waves in a stratified half-space. Geophys. J. R.Astron. Soc. 44:557–583

    Google Scholar 

  • Knopoff L (1964) A matrix method for elastic wave problems. Bull Seismol Soc Am 54(1):431–438

    Google Scholar 

  • Komatitsch D, Erlebacher G, Göddeke D, Michéa D (2010) High-order finite-element seismic wave propagation modeling with MPIon a large GPU cluster. J Comput Phys 229:7692–7714

    Article  Google Scholar 

  • Lamb H (1904) On the propagation of tremors over the surface of an elastic solid. Philos Trans R Soc Lond A 203:1–42

    Article  Google Scholar 

  • Love AEH (1892) A Treatise on the Mathematical Theory of Elasticity Oxford. Reprinted in 1944 as a Dover Publication, New York

    Google Scholar 

  • Manolis G, Makra K, Dineva P, Rangelov T (2013) Seismic motions in a non-homogeneous soil deposit with tunnels by a hybrid computational technique, earthquake and structures. 5(2):161–205

    Article  Google Scholar 

  • Manolis G, Parvanova S, Makra K, Dineva P (2015) Seismic response of buried metro tunnels by a hybrid FDM-BEM approach. Bull Earthq Eng 13(7):1953–1977

    Article  Google Scholar 

  • Moczo P, Kristek J, Galis M (2004) Simulation of planar free surface with near-surface lateral discontinuities in the finite-difference modeling of seismic motion. Bull Seismol Soc Am 94:760–768

    Article  Google Scholar 

  • Pao YH, Gajewski R (1977) The generalized ray theory and transient responses of layered elastic solids. In: Mason WP & Thurston RN (ed) Physical acoustics, vol. 13, ch. 6, pp 183-265

  • Parvanova SL, Dineva PS, Manolis GD (2014a) Elastic wave field in a half-plane with free surface relief, tunnels and multiple buried inclusions. Acta Mech 225(7):1843–1865

    Article  Google Scholar 

  • Parvanova SL, Dineva PS, Manolis GD, Wuttke F (2014b) Seismic response of lined tunnels in the half-plane with surface topography. Bull Earthq Eng 12:981–1005

    Article  Google Scholar 

  • Rayleigh L (1888) On the free vibration of an infinite plate of homogeneous isotropic elastic matter. Proc Lond Math Soc 20(357):225–234

    Article  Google Scholar 

  • Santare MH, Thamburaj P, Gazonas GA (2003) The use of graded finite elements in the study of elastic wave propagation in continuously nonhomogeneous materials. International Journal Solid Structures 40:5621–5634

    Article  Google Scholar 

  • Stokes GG (1849) On the dynamical theory of diffraction. Transactions of the Cambridge Philosophical Society 9:1–62

    Google Scholar 

  • Mostafa Tazarv (2019). Elastic Response Spectrum. MATLAB Central File Exchange. https://www.mathworks.com/matlabcentral/fileexchange/31254-elastic-response-spectrum,

  • Thomson WT (1950) Transmission of elastic waves through a stratified soil medium. J Appl Phys 21:89–93

    Article  Google Scholar 

  • Todorovska M, Paskaleva I, Glavcheva R (1995) Earthquake source parameters for seismic hazard assessment: Examples in Bulgaria. 10th European Conference on Earthquake Engineering, Duma (ed.) 1995 Balkema, Rotterdam, ISBN 90 5410 528 3, pp 2573-2578

  • Vasilev G, Parvanova S, Dineva P, Wuttke F (2015) Soil-structure interaction using BEM–FEM coupling through ANSYS software package. Soil Dyn Earthq Eng 70:104–117

    Article  Google Scholar 

  • Wuttke F, Dineva P, Schanz T (2011) Seismic wave propagation in laterally inhomogeneous geological region via a new hybrid approach. J Sound Vib 330:664–684

    Article  Google Scholar 

Download references

Acknowledgement

The first and third authors are grateful for support provided by the project BG05M2OP001-1.002, MIRACle 2019-2023. The third author is partially supported by the research grant IB-RA2014-178-EnTranEmiss.

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Authors and Affiliations

  1. Department of Structural Engineering, University of Architecture, Civil Engineering and Geodesy (UACEG), 1046, Sofia, Bulgaria

    Sonia Parvanova & Georgi Vasilev

  2. Institute of Mechanics, Bulgarian Academy of Sciences (BAS), 1113, Sofia, Bulgaria

    Petia Dineva

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  1. Sonia Parvanova
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  2. Georgi Vasilev
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  3. Petia Dineva
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Correspondence to Sonia Parvanova.

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Parvanova, S., Vasilev, G. & Dineva, P. Hybrid modelling of multi-layered geological structure under seismic excitation. J Seismol 24, 183–202 (2020). https://doi.org/10.1007/s10950-019-09896-1

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