Influence of the foundation bed stiffness on the dynamic properties of the building as of a multi-mass cantilever bar


Relevance. The study of the interaction of buildings and structures with the base during an earthquake is one of the most important tasks of the theory of earthquake resistance. The response of the structure to seismic impact depends to a large extent on the ratio of the stiffness characteristics of the soil, foundation, and foundation structure. Moreover, taking into account a rather high degree of statistical variability of the characteristics of the soil foundation, it is possible to ensure the required level of safety of a structure only through the use of probabilistic models and a quantitative assessment of the reliability of the construction-base system as a whole. At present, for the calculation of the “construction - base” system for seismic loads, deterministic discrete models of the finite element method are mainly used. But these models are poorly adapted for probabilistic calculations and require extensive statistical data, which are currently insufficient. Therefore, in problems of reliability assessment, it is advisable to use simplified analytical models, which make it possible to derive the value of the statistical variability of its reaction with relatively small initial information about the system. The aim of the work - based on the well-known solution for the single-mass model to present an analytical solution in the matrix form of the problem of free horizontal vibrations of a multi-mass cantilever rod on the foundation specified by the elastic half-space model. Methods. A study was made of the effect of the compliance of the soil foundation on the frequencies and forms of horizontal vibrations of the structure. A comparison of the results with the calculation performed by the finite element method is given. Results. The obtained solution is intended to conduct a probabilistic calculation of the construction-base system under seismic loads and evaluate its reliability.

About the authors

Valeriya A. Pshenichkina

Volgograd State Technical University

Author for correspondence.
SPIN-code: 3399-0668

Head of Engineering Structures, Foundations and Safety of Constructions Department, Doctor of Technical Sciences, Professor

28 Lenina Ave, Volgograd, 400005, Russian Federation

Vyacheslav V. Drozdov

Volgograd State Technical University

SPIN-code: 3403-5982

Associate Professor of Engineering Structures, Foundations and Safety of Constructions Department, Candidate of Technical Sciences

28 Lenina Ave, Volgograd, 400005, Russian Federation

Sergey I. Strok

Volgograd State Technical University

SPIN-code: 6209-1218

postgraduate student of Engineering Structures, Foundations and Safety of Constructions Department

28 Lenina Ave, Volgograd, 400005, Russian Federation


  1. Clough Ray W., Penzien Joseph. Dynamics of structures. 3rd ed. Berkeley: Computers & Structures, Inc.; 2003.
  2. Uzdin A.M., Sandovich T.A., Al'-Naser-Mohomad Samih Amin. Osnovy teorii sejsmostojkogo stroitel'stva zdanij i sooruzhenij [Fundamentals of the theory of earthquake-resistant construction of buildings and structures]. Saint Petersburg: VNIIG imeni B.E. Vedeneeva Publ.; 1993. (In Russ.)
  3. Datta T.K. Seismic analysis of structures. Singapore: John Wiley & Sons (Asia) Pte. Ltd.; 2010.
  4. Newmark N.M., Rosenblueth E. Fundamentals of earthquake engineering. Englewood Cliffs: Prentice-Hall, Inc.; 1971.
  5. Mkrtychev O.V., Reshetov A.A. Sejsmicheskie nagruzki pri raschete zdanij i sooruzhenij [Seismic loads when calculating buildings and structures]. Moscow: ASV Publ.; 2017. (In Russ.)
  6. SP 14.13330.2018. Stroitelstvo v seismicheskikh raionakh [Seismic building design code]. Updated version of SNiP II-7-81*. Moscow: Standartinform Publ.; 2018. (In Russ.)
  7. Pshenichkina V.A. Nadezhnost zdanij kak prostranstvennyh sostavnyh sistem pri sejsmicheskih vozdejstvijah [Reliability of buildings as spatial composite systems in case of seismic impacts]: monograph. Volgograd: VolgGASU Publ.; 2010. (In Russ.)
  8. Drozdov V.V., Pshenichkina V.A., Evtushenko S.I. Inzhenernaja metodika ocenki sejsmicheskoj nadezhnosti zdanij po predel'no dopustimomu risku [Engineering methodology for assessing the seismic reliability of buildings based on the maximum allowable risk]. Vestnik VolgGASU. 2013; 2(27):10. (In Russ.)
  9. Sargsjan A.E. Ocenka intensivnosti sejsmicheskogo vozdejstvija na sooruzhenie s uchetom podatlivosti ego osnovanija [Assessment of the intensity of seismic impact on the structure, taking into account the pliability of its base]. Stroitel'naja mehanika i raschet sooruzhenij. 1986;(4):55–59. (In Russ.)
  10. Sargsjan A.E., Gukova E.G., Shaposhnikov N.N. Dinamicheskaja mehanicheskaja model osnovanija sooruzhenija s uchetom inercionnyh svojstv gruntov [Dynamic mechanical model of bases of structures that takes account of inertial properties of soils]. Vestnik MGSU. 2012;(2):66–69. (In Russ.)
  11. Pshenichkina V.A., Drozdov V.V., Strok S.I., Sukhina K.N., Alkneume M.H. Converging of analytical solution of pile under horizontal static load with analysis through finite element method. Advances in engineering research conference proceedings. 2018;157:520–523.
  12. Pshenichkina V.A., Shchitov D.V., Sidyakin P.A. Problems of forecasting the resource of buildings of the historical construction of the resort region of the Caucasian Mineral Waters. IOP conference series: materials science and engineering. 2018;463(3):032027.
  13. Volgin G.A., Rozhkov A.F., Inzhutov I.S., Goncharov Ju.M. Chislenno-jeksperimental'noe issledovanie dinamicheskih parametrov krupnopanel'nogo zdanija [Experimental and Numerical Analysis of Dynamic Parameters of Large-Panel Building]. Vestnik TGASU. 2016;(3):111–120. (In Russ.)
  14. Galiullin R.R., Izotov V.S., Nurieva D.M. Chislennye issledovanija dinamicheskih harakteristik zdanij s zhelezobetonnym karkasom [Numerical researches of dynamic characteristics of buildings with the ferro-concrete skeleton]. Izvestija KazGASU. 2011;2(16):81–85. (In Russ.)
  15. Pshenichkina V.A., Drozdov V.V., Strok S.I. Sravnitel'nyj analiz vlijanija zhestkosti osnovanija na dinamicheskie harakteristiki zdanij [Contrastive analysis of influence of soil bases stiffness on dynamic characteristics of buildings]. Mehanika gruntov v geotehnike i fundamentostroenii: materialy mezhdunarodnoj nauchno-tehnicheskoj konferencii (Novocherkassk, May 29–31, 2018). Novocherkassk: JuRGPU (NPI) Publ.; 2018. p. 733–744. (In Russ.)
  16. Poljakov S.V. Sejsmostojkie konstrukcii zdanij [Earthquake-resistant building structures]: textbook for universities. 2nd ed. Moscow: Vysshaja shkola Publ.; 1983. (In Russ.)
  17. Kiselev V.A. Stroitel'naja mehanika: special'nyj kurs. Dinamika i ustojchivost' sooruzhenij [Construction mechanics: special course. Dynamics and stability of structures]: textbook for universities. 3rd ed., rev. and exp. Moscow: Strojizdat Publ.; 1980. (In Russ.)
  18. Cejtlin A.I., Guseva N.I. Statisticheskie metody rascheta sooruzhenij na gruppovye dinamicheskie vozdejstvija [Statistical methods of calculating of structures for group dynamic impacts]. Moscow: Strojizdat Publ.; 1979. (In Russ.)
  19. Birbraer A.N. Raschet konstrukcij na sejsmostojkost [Seismic analysis of structures]. Saint Petersburg: Nauka Publ.; 1998. (In Russ.)
  20. Strok S.I., Pshenichkina V.A., Drozdov V.V. Analiz vlijanija zhestkosti gruntovogo osnovanija na chastoty i formy kolebanij sooruzhenij [Analysis of the influence of subgrade stiffness on the frequencies and mode shapes of structures]. Stroitel'stvo i arhitektura. 2018;(2):13–21. (In Russ.)

Copyright (c) 2020 Pshenichkina V.A., Drozdov V.V., Strok S.I.

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies