Area-wide protection of buildings and structures from surface waves using a seismic barrier implemented as an above-ground liquid storage tank
https://doi.org/10.33979/2073-7416-2026-123-1-33-50
Abstract
An approach is proposed for area-wide protection of buildings and structures from surface seismic waves using a seismic barrier in the form of an above-ground liquid storage tank placed on the surface of an elastic half-space. A mathematical model of the interaction between surface waves and the seismic barrier is developed, accounting for contact conditions at the interface between media and the weak compressibility of the fluid. A dispersion relation is obtained for Rayleigh waves beneath a finite-thickness liquid layer, which correctly reduces to the classical limiting cases of no fluid, infinite depth, and an incompressible fluid. For a barrier of finite length, based on continuity conditions at the lateral boundaries, the Rayleigh-wave transfer function TR is derived and analytical approximations are proposed. Resonances kL=nπ, corresponding to no attenuation, are identified, along with zones of exponential suppression between them; the magnitude of the suppression is governed by a parameter αf, proportional to the added mass of the fluid and dependent on the ratio of velocities. It is shown that for Love (SH) waves the liquid barrier provides no shear stiffness and does not produce attenuation, necessitating alternative solutions for area-wide seismic protection. Contour plots of the transfer function are presented to support preliminary design choices of the tank height and length needed to achieve a specified level of Rayleigh-wave attenuation.
About the Authors
S. G. Saiyan
Moscow State University of Civil Engineering (National Research University) (MGSU); Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences
Russian Federation
Russian Federation
Saiyan Sergey G. - Researcher, A. B. Zolotov Research and Education Center for Computer Modeling of Unique Buildings, Structures and Complexes; Senior Lecturer, Department of Structural and Theoretical Mechanics; Lecturer, Department of Computer Science and Applied Mathematics, Moscow State University of Civil Engineering (National Research University, NRU MGSU); Junior Research Fellow, A. Yu. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences
26 Yaroslavskoye Shosse, Moscow, 129337
101 Vernadsky Avenue, Bldg. 1, Moscow, 119526
A. V. Vasilev
Gubkin Russian State University of Oil and Gas (National Research University)
Russian Federation
Russian Federation
Vasilev Artemiy V. - Second-year Master’s student
65 Leninsky Prospekt, Moscow, 119991
References
1. Viktorov I.A. Fizicheskiye osnovy primeneniya ul'trazvukovykh voln Releya i Lemba v tekhnike [Physical fundamentals of the application of Rayleigh and Lamb ultrasonic waves in engineering]. Moscow: Nauka, 1966. 169 p. (rus)
2. Tarasenko A., Čtvrtlík R., Kudělka R. Theoretical and experimental revision of surface acoustic waves on the (100) plane of silicon. Scientific Reports. 2021;11(1):2845. https://doi.org/10.1038/s41598-021-82211-6
3. Jauhari N., Hegde A., Chakrabortty P. Full scale field studies for assessing the vibration isolation performance of single and dual trenches. Transportation Geotechnics. 2023;39:100932. https://doi.org/10.1016/j.trgeo.2023.100932
4. Povkolas K.E., Shaulouskaya O.A. Otsenka effektivnosti konstruktsii vertikal'nogo bar'yera v vide otkrytoy transhei s krepleniem stenok dlya snizheniya vibratsiy, rasprostranyayushchikhsya v gruntovoy srede [Assessment of the efficiency of the vertical barrier design in the form of an open trench with fastening of walls to reduce vibrations propagation in the ground environment]. Vestnik Polotskogo gosudarstvennogo universiteta. Seriya F: Stroitel'stvo. Prikladnye nauki. 2024;(4):33–39. DOI: 10.52928/2070-1683-2024-39-4-33-39. (rus)
5. Israilov M.S. Diffraction and Vibration Attenuation by Obstacles in Elastic Media. Moscow Univ. Mech. Bull. 2021;76:1–6. https://doi.org/10.3103/S0027133021010039
6. Kamchybekova A.T. Modelirovaniye effektivnosti gruntovykh i gruntosilikatnykh svaynykh bar'yerov dlya snizheniya seysmicheskikh vozdeystviy na zdaniya [Modeling the effectiveness of groundwater and grunt silicate pile barriers for reducing seismic impacts on buildings]. Vestnik nauki [Science Bulletin]. 2025;2(85):850–854. (rus)
7. Mitroshin V.A. Seismic protection of buildings and structures using metamaterials: current status and development prospects. Architecture, Construction, Transport. 2024;(2):67-83. (In Russ.) https://doi.org/10.31660/2782-232X-2024-2-67-83
8. Brûlé S., Javelaud E.H., Enoch S., Guenneau S. Experiments on seismic metamaterials: molding surface waves. Physical Review Letters. 2014;112(13):133901. https://doi.org/10.1103/PhysRevLett.112.133901
9. Colombi A., Roux P., Guenneau S., Gueguen P., Craster R.V. Forests as a natural seismic metamaterial: Rayleigh wave bandgaps induced by local resonances. Scientific Reports. 2016;6(1):19238. https://doi.org/10.1038/srep19238
10. Kuznetsov S.V., Saiyan S.G. Nonlinear acoustic waves in hyperelastic rods. Mechanics of Solids. 2025;60(2):923-931. DOI: 10.31857/S1026351925020129. (rus)
11. Grinchenko V.T., Komissarova G.L. Poverkhnostnye volny v sisteme uprugiy sloy na zhidkom poluprostranstve [Surface waves in the system elastic layer on liquid half-space]. Akusticheskii vestnik [Acoustic Bulletin]. 2005;8(4):38–45. (rus)
12. Kovtun Al.A. Poverkhnostnye volny na granitse uprugo-poristoy sredy i zhidkosti [The surface waves at the interface of poroelastic medium and liquid]. Voprosy geofiziki [Problems of Geophysics]. 2013;(46):14–25. (rus)
13. Pradhan N., Samal S.K. Surface waves propagation in a homogeneous liquid layer overlying a monoclinic half-space. Applied Mathematics and Computation. 2022;414:126655. https://doi.org/10.1016/j.amc.2021.126655
14. Bagheri A., Greenhalgh S., Khojasteh A., Rahimian M. Dispersion of Rayleigh, Scholte, Stoneley and Love waves in a model consisting of a liquid layer overlying a two-layer transversely isotropic solid medium. Geophysical Journal International. 2015;203(1):195–212. https://doi.org/10.1093/gji/ggv278
15. Kumari M., Kaswan P., Kumar M., Lewis R.W., Oztop H.F., Singh N., Obalalu A.M., Pushkarna M., Berhanu M. Seismic wave reflection characteristics and wave-induced fluid flow in unsaturated porous solid. Scientific Reports. 2025;15(1):18840. https://doi.org/10.1038/s41598-025-97275-x
16. Russillo A.F., Failla G. Seismic metamaterials for Rayleigh wave attenuation: a novel concept of soilembedded water-tank metabarrier. International Journal of Solids and Structures. 2025;113656. https://doi.org/10.1016/j.ijsolstr.2025.113656
17. Li L., Fang Y., Aziz M.M., Shi Y., Zhang L., Dong X., Li L. Adjustable embedded seismic metamaterial based on fluid-solid coupling mechanism. Structures. 2025;81:110429. https://doi.org/10.1016/j.istruc.2025.110429
18. Besedina A.N., Tubanov Ts.A., Predein P.A., Sanzhieva D.P.-D., Ivanchenko G.N. Osobennosti mikroseysm ozera Baykal po dannym seti seysmicheskikh stantsiy [Lake Baikal Microseisms Based on Regional Seismic Network Data]. Fizika Zemli [Physics of the Solid Earth]. 2024;(3):30–50. DOI: 10.31857/S0002333724030041. (rus)
19. Tumanov V.V., Novgorodtseva L.A., Borodin D.S., Gritsaenko A.Y., Yalputa E.A. Sravneniye kharakteristik amplitudno-chastotnykh spektrov slozhnogo signala, poluchennykh po dannym seysmicheskogo monitoringa na shakhtnom pole [Comparison of characteristics of the amplitude-frequency spectra of a complex signal received from seismic monitoring data in a mine field]. Trudy RANIMI [Proceedings of the Russian Academy of Sciences]. 2024;(3(41)-2):202–213. DOI: 10.24412/2519-2418-2024-341-202-213. (rus)
20. Tanimoto T., Anderson A. Seismic noise between 0.003 Hz and 1.0 Hz and its classification. Progress in Earth and Planetary Science. 2023;10(1):56. https://doi.org/10.1186/s40645-023-00603-8
21. Landau L.D., Lifshitz E.M. Teoriya uprugosti [Theory of Elasticity]. Moscow: Nauka, 1987. 246 p. (rus)
22. Grigor'yev Yu.M., Gavrilieva A.A. Zadacha rasprostraneniya poverkhnostnoy volny Releya v poluprostranstve sredy Kossera v sluchaye odnorodnykh i uprugo-stesnennykh granichnykh usloviy [Propagation problem of a Rayleigh surface wave in the half-space of a Cosserat medium in the case of homogeneous and elastically constrained boundary condition]. Matematicheskiye zametki SVFU [Mathematical Notes of NEFU]. 2023;30(4):81–104. DOI: 10.25587/2411-9326-2023-4-81-104. (rus)
23. Ewing M., Jardetzky W., Press F. Elastic Waves in Layered Media. New York: McGraw-Hill, 1957. 405 p.
24. Brekhovskikh L.M. Waves in Layered Media. New York: Academic Press, 1980. 503 p.
25. Sidorovskaia N.A. Systematic studies of pulse propagation in ducted oceanic waveguides in normal mode representation. The European Physical Journal – Applied Physics. 2004;25(2):113–131. DOI: 10.1051/epjap:2003089
26. Labarbe J., Kirillov O.N. Membrane flutter induced by radiation of surface gravity waves on a uniform flow. Journal of Fluid Mechanics. 2020;901:A4. https://doi.org/10.1017/jfm.2020.533
27. Perturbation theory. In: Encyclopedia of Mathematics. European Mathematical Society (EMS). [Online]. URL: https://encyclopediaofmath.org/wiki/Perturbation_theory (accessed 30 July 2025).
28. Dzhakal'ya G.E.O. Metody teorii vozmushcheniy dlya nelineynykh sistem [Methods of perturbation theory for nonlinear systems]. Moscow: Nauka, 1979. 320 p. (rus)
29. Watt S.M., Jeffrey D.J. An abstraction-preserving block matrix implementation in Maple. 26th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC). IEEE, 2024. Pp. 49–52. DOI: 10.1109/SYNASC65383.2024.00021
30. Viktorov I.A. Zvukovye poverkhnostnye volny v tverdykh telakh [Acoustic surface waves in solids]. Moscow: Nauka, 1981. 288 p. (rus)
31. Saiyan S.G., Vasiliev А.V. Numerical Simulation of the Dynamic Response of the “Evolution” Tower under Wind Action Considering Surrounding Buildings and Turbulence Resolution. Vestnik MGSU [Monthly Journal on Construction and Architecture]. 2025;20(2):246–279. DOI: 10.22227/1997-0935.2025.2.246-279 (rus.)
Review
For citations:
Saiyan S.G., Vasilev A.V. Area-wide protection of buildings and structures from surface waves using a seismic barrier implemented as an above-ground liquid storage tank. Building and Reconstruction. 2026;(1):33-50. (In Russ.) https://doi.org/10.33979/2073-7416-2026-123-1-33-50
Views:
94
JATS XML
Email this article 