Frequency sensitive dynamic stiffness of the soil base

DOI: 10.37153/2618-9283-2023-6-82-91

Authors:  
Rubric:     Theoretical and experimental studies   
Key words: soil-structure interaction, frequency domain, dynamic calculation, earthquake engineering, foundation vibration, soil dynamic, perfectly matched layers
Annotation:

This article describes a method for calculating the frequency sensitive dynamic stiffness of the soil base using the finite element method. The main advantage of the method is the ability to take into account the heterogeneity of the properties of the base when calculating dynamic stiffness. Requirements for creating a design model, special boundary conditions, size and type of finite elements, and processing of results are presented. Based on the calculation results, a comparison with standard dynamic stiffnesses was made. It is shown that due to the presence of layering in the base, the standard and numerical dynamic stiffness have significant discrepancies. A solution to the test problem of determining the dynamic stiffness for a rectangular stamp on a layered base is presented. A comparison of the calculation results with a known solution shows the acceptable accuracy and reliability of the solution and confirms the correctness of the proposed calculation method.

Used Books:

1. СП 14.13330.2018 «Строительство в сейсмических районах. Актуализированная редакция СНиП II-7-81*». М.: ФАУ ФЦС, 2014. / SP 14.13330.2018 «Stroitel'stvo v sejsmicheskih rajonah. Aktualizirovannaya redaktsiya SNiP II-7-81*». M.: FAU FCS, 2014. [In Russian]

2. НП-031-01 Нормы проектирования сейсмостойких атомных станций, 2001. / NP-031-01 Normy proektirovaniya sejsmostojkikh atomnykh stantsij, 2001. [In Russian]

3. Seismic Analysis of Safety-Related Nuclear Structures and Commentary. ASCE-4-16 / American Society of Civil Engineers (ASCE), 2017. 229 p.

4. Саргсян А.Е. Динамика и сейсмостойкость сооружений атомных станций: монография / А.Е. Саргсян. – Саров: ФГУП «РФЯЦ-ВНИИЭФ», 2013. 550 с. / Sargsyan A.E. Dinamika i sejsmostojkost' sooruzhenij atomnykh stantsij: monografiya / A.E. Sargsyan. – Sarov: FGUP «RFYAC-VNIIEF», 2013. 550 p. [In Russian]

5. Gazetas G. Analysis of Machine Foundation Vibrations: State of The Art. International Journal of Soil Dynamics and Earthquake Engineering, 1983, 2(1), pp. 2–42. DOI: 10.1016/0261-7277(83)90025-6

6. Gazetas G. Static and dynamic displacements of foundations on heterogeneous multilayered soils. Geotechnique, 1980, vol. 30, pp. 159–177.

7. Froio D. A true PML approach for steady-state vibration analysis of an elastically supported beam under moving load by a DLSFEM formulation / Froio D., Rizzi E., Simoes F.M.F., da Costa A.P. Computers and Structures, 2020, vol. 239(4), 765–790. DOI:10.1016/j.compstruc.2020.106295

8. Basu U., Chopra A.K. Perfectly matched layered for transient elastodynamics of unbounded domains. International Journal for Numerical Methods in Engineering, 2004, vol. 59(8), pp. 1039–1074. DOI:10.1002/nme.896

9. Wong H.L. Tables of impedance functions for square foundations on layered media / Wong H.L., Luco J.E. International Journal of Soil Dynamics and Earthquake Engineering, 1985, vol. 4, pp. 64–81.

10. Luco J.E. Impedance functions for a rigid foundation on layered medium. Nuclear Engineering and Design, 1974, vol. 31, pp. 204–217.

11. Mohan C., Parmar S. A comparative study of various methods to evaluate impedance function for shallow foundations. International Journal of Advances in Engineering & Technology, 2017, vol. 10, pp. 592–603.

12. Chen M., Li J., Li Z. An efficient numerical algorithm for solving the dynamic impedance function of arbitrary-shaped foundations in layered soil. Computers & Structures, 2023, vol. 285. DOI:10.1016/j.compstruc.2023.107085