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Energy-based dynamic parameter identification for Pasternak foundation model

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Abstract

Parameter identification of Pasternak foundation models (PFM) is never satisfactory, which discourages the application and popularization of PFM. In the present study, an energy-based model to predict the dynamic foundation coefficients was proposed using the vibration kinetic energy and potential energy of a Pasternak foundation-rigid plate system. On the basis of the Pasternak foundation, the relationship among the natural frequency, dynamic foundation coefficients, rigid plate configuration, and vibrating soil equivalent mass per unit area was considered. To obtain the natural frequencies of the Pasternak foundation-rigid plate system, dynamic tests were performed. Using two or more dynamic test results of various rigid plates on a foundation, a set of equations of dynamic foundation coefficients was set up to directly identify the foundation coefficients and equivalent mass per unit area of vibrating soil. The feasibility of the proposed method was verified by comparing it with the outdoor and indoor test results and finite element analysis results. When the proposed method is used to obtain the dynamic parameters, PFM can be generalized and applied more widely in engineering practice.

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References

  • ATC-40 (1996), Seismic Evaluation and Retrofit of Concrete Buildings, Applied Technology Council, California, USA.

    Google Scholar 

  • Binesh SM (2012), “Analysis of Beam on Elastic Foundation using the Radial Point Interpolation Method,” Scientia Iranica, 19(3): 403–409.

    Article  Google Scholar 

  • Bycroft GN (1956), “Forced Vibrations of a Rigid Circular Plate on a Semi-Infinite Elastic Space and on an Elastic Stratum,” Philosophical Transactions of the Royal Society of London, 248: 327–368.

    Google Scholar 

  • Bycroft GN (1959), “Machine Foundation Vibration,” Proc Inst Mech Eng, 173: 469–473.

    Article  Google Scholar 

  • Bycroft GN (1977), “Soil-Structure Interaction at Higher Frequency Factors,” Earthquake Engineering & Structural Dynamics, 5(3): 235–248.

    Article  Google Scholar 

  • Carrier WD and Christian JT (1973), “Rigid Circular Plate Resting on a Non-Homogeneous Elastic Halfspace,” Geotechnique, 23(1): 67–84.

    Article  Google Scholar 

  • EN 1992-1-2 (2004), Eurocode 2: Design of Concrete Structures — Part 1–2: General Rules — Structural Fire Design, European Committee for Standardization, Brussels, British, Belgium.

    Google Scholar 

  • EN 1997-1 (2005), Eurocode 7: Geotechnical Design — Part 1: General Rules, European Committee for Standardization, Brussels, British, Belgium.

    Google Scholar 

  • FEMA 303 (1997), NEHRP (National Earthquake Hazards Reduction Program) Recommended Provisions for Seismic Regulations for New Buildings and Other Structures, Building Seismic Safety Council, Washington DC, USA.

    Google Scholar 

  • Fillonenko-Borodich MM (1940), “Some Approximate Theories of the Elastic Foundation,” Uchenyie Zapiski Moskovskogo Gosudarstuennogo Universiteta Mechanika, 46: 3–18. (in Russian)

    Google Scholar 

  • GB 50007-2011 (2011), Code for Design of Building Foundation, Ministry of Housing and Urban-rural Development of the People’s Republic of China, China Architecture & Building Press, Bei**g, China. (in Chinese)

    Google Scholar 

  • GB 50040-1996 (1996), Code for Design of Dynamic Machine Foundation, State Bureau of Technology Supervision and Ministry of Construction of the People’s Republic of China, China Architecture & Building Press, Bei**g, China. (in Chinese)

    Google Scholar 

  • GB 50307-2012 (2012), Code for Geotechnical Investigations of Urban Rail Transit, Ministry of Housing and Urban-rural Development of the People’s Republic of China and General Administration of Quality Supervision, Inspection and Quarantine of the People’s Republic of China, China Planning Press, Bei**g, China. (in Chinese)

    Google Scholar 

  • GB/T 50269-2015 (2015), Code for Measurement Methods of Dynamic Properties of Subsoil, Ministry of Housing and Urban-rural Development of the People’s Republic of China and General Administration of Quality Supervision, Inspection and Quarantine of the People’s Republic of China, China Planning Press, Bei**g, China. (in Chinese)

    Google Scholar 

  • Han JB and Liew KM (1997), “Numerical Differential Quadrature Method for Reissner/Mindlin Plates on Two-parameter Foundations,” International Journal of Mechanical Sciences, 39(9): 977–989.

    Article  Google Scholar 

  • He FS, Huang Y and Huo YY (2006), “The Dynamic Problem of Plates on the Bi-Parameter Elastic Foundations,” Journal of **’an University of Architecture & Technology (Natural Science Edition), 38(1): 130–134. (in Chinese)

    Google Scholar 

  • Hetényi M (1950), “A General Solution for the Bending of Beams on an Elastic Foundation of Arbitrary Continuity,” Journal of Applied Physics, 21(1): 55–58.

    Article  Google Scholar 

  • Huang J, Yuan TY, Peng LM, Yu J and Ding ZD (2015), “Model Test on Dynamic Characteristics of Invert and Foundation Soils of High-Speed Railway Tunnel,” Earthquake Engineering and Engineering Vibration, 14(3): 549–559.

    Article  Google Scholar 

  • JTG F10-2006 (2006), Technical Specification for Construction of Highway Subgrades, Ministry of Transport of the People’s Republic of China, China Communications Press, Bei**g, China. (in Chinese)

    Google Scholar 

  • Kerr AD (1965), “A Study of a New Foundation Model,” Acta Mechanica, 1(2): 135–147.

    Article  Google Scholar 

  • Lamb H (1904), “On the Propagation of Tremors over the Surface of an Elastic Solid,” Royal Society, 203: 1–42.

    Google Scholar 

  • Li B, Cheng Y, Zhu Z and Zhang F (2019), “A Closed-form Solution for a Double Infinite Euler-Bernoulli Beam on a Viscoelastic Foundation Subjected to Harmonic Line Load,” Earthquake Engineering and Engineering Vibration, 18(1): 129–140.

    Article  Google Scholar 

  • Lu Z, Yao HL, Luo HN, Yang Y and Yang ML (2008), “Parameter Analysis of Continuously Reinforced Concrete Pavement Resting on Two-Parameter Foundation,” Rock and Soil Mechanics, 29(8): 2177–2182. (in Chinese)

    Google Scholar 

  • Matsunaga H (1999), “Vibration and Bucking of Deep Beam-Columns on Two-Parameter Elastic Foundations,” Journal of Sound and Vibration, 228(2): 359–376.

    Article  Google Scholar 

  • Mei FX, Liu D and Luo Y (1991), Advanced Analytical Mechanics, Bei**g Institute of Technology Press, Bei**g, China. (in Chinese)

    Google Scholar 

  • Miao Y, Shi Y, Wang GB and Zhong Y (2017), “Closed-form Solution of Beam on Pasternak Foundation Under Inclined Dynamic Load,” Acta Mechanica Solida Sinica, 30(6): 596–607.

    Article  Google Scholar 

  • Mindlin RD (1951), “Influence of Rotatory Inertia and Shear on Flexural Motions of Isotropic, Elastic Plates,” ASME Journal of Applied Mechanics, 18(1): 31–38.

    Article  Google Scholar 

  • Obara P (2014), “Vibrations and Stability of Bernoulli-Euler and Timoshenko Beams on Two-parameter Elastic Foundation,” Archives of Civil Engineering, 60(4): 421–440.

    Article  Google Scholar 

  • Pasternak PL (1954), “On a New Method of Analysis of an Elastic Foundation by Means of Two Foundation Constants,” Gosudarstvennoe Izdatelstvo Literaturi po Stroitelstvui Arkhitekture, 1–56, MSCOW, USSR. (in Russian)

    Google Scholar 

  • Patela BP, Ganapathia M and Touratierb M (1999), “Nonlinear Free Flexural Vibrations Post-Buckling Analysis of Laminated Orthotropic Beams/Columns on a Two Parameter Elastic Foundation,” Composite Structures, 46(2): 189–196.

    Article  Google Scholar 

  • Reissner E (1936), “Stationäre, Axialsymmetrische, Durch Eine Schüttelnde Masse Erregte Schwingungen Eines Homogenen Elastischen Halbraumes,” Ingenieur-Archiv, 7(6): 381–396.

    Article  Google Scholar 

  • Reissner E (1945), “The Effect of Transverse Shear Deformation on the Bending of Elastic Plates,” ASME Journal of Applied Mechanics, 12(2): A68–A77.

    Article  Google Scholar 

  • Rosa D (1993), “Stability and Dynamic Analysis of Two-parameter Foundation Beams,” Computers & Structures, 49(2): 341–349.

    Article  Google Scholar 

  • Rosa D (1995). “Free Vibrations of Timoshenko Beams on Two-parameter Elastic Foundation,” Computers & Structures, 57(1): 151–156.

    Article  Google Scholar 

  • Sung TY (1954), “Vibration in Semi-infinite Solids Due to Periodic Surface Loadings,” Symposium on Dynamic Testing of Soils, 156: 35–64.

    Google Scholar 

  • Tahouneh V (2014), “Free Vibration Analysis of Thick CGFR Annular Sector Plates Resting on Elastic Foundations,” Structural Engineering and Mechanics, 50(6): 773–796.

    Article  Google Scholar 

  • Tahouneh V (2017), “An Elasticity Solution for Vibration Analysis of Laminated Plates with Functionally Graded Core Reinforced by Multi-Walled Carbon Nanotubes,” Periodica Polytechnica Mechanical Engineering, 61(4): 11254.

    Article  Google Scholar 

  • Vlasov VZ and Leont’ev NN (1966), Beams, Plates and Shells on Elastic Foundations, Israel Program for Scientific Translations, Jerusalem, Israel and Palestine.

    Google Scholar 

  • Wolf JP and Somaini DR (1986), “Approximate Dynamic Model of Embedded Foundation in Time Domain,” Earthquake Engineering & Structure Dynamic, 14(5): 683–703.

    Article  Google Scholar 

  • **e HY and Wang YH (2007), “Dynamic Analysis of Elastic Plate Resting on Two-Parameter Foundation,” Rock and Soil Mechanics, 28(S1): 753–758. (in Chinese)

    Google Scholar 

  • **e HY, Zhao LL and Wang S (2009), “Dynamic Analysis of Elastic Plate Resting on Two-Parameter Foundation by Isoperimetric Element,” Chinese Journal of Underground Space and Engineering, 5(6): 1155–1160. (in Chinese)

    Google Scholar 

  • Yan KZ, **a TD and Huang LK (2005), “Dynamic Response of Strip on Two-Parameter Viscoelastic Foundation under Impact Loading,” Chinese Journal of Rock Mechanics and Engineering, 24(24): 4576–4580. (in Chinese)

    Google Scholar 

  • Yang DS, Huang Y and Pan J (2004), “Free Vibration of Plates on the Bi-Parameter Elastic Foundation,” Journal of Dynamics and Control, 2(1): 92–96. (in Chinese)

    Google Scholar 

  • Zhang JL, Ge RY and Zhang LJ (2019), “Transverse Free Vibration Analysis of a Tapered Timoshenko Beam on Visco-Pasternak Foundations Using the Interpolating Matrix Method,” Earthquake Engineering and Engineering Vibration, 18(3): 567–578.

    Article  Google Scholar 

  • Zhang WX and Yi WJ (2003), “A Generalized Conforming Element for Thick-Thin Slabs on DoubleParameter Foundation and Inverse Analysis of Deflection for Foundation Parameter Identification,” Engineering Mechanics, 20(6): 46–51. (in Chinese)

    Google Scholar 

  • Zhang ZD, Ma DW and He Q (2015), “Dynamic Response of a Multi-Layer Rectangular Plate on a Two-Parameter Foundation Under a Circular Rigid Bearing Plate’s Load,” Journal of Vibration and Shock, 34(17): 199–206. (in Chinese)

    Google Scholar 

Download references

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Correspondence to Hyeon-Jong Hwang.

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Zhang, WX., Lv, WL., Zhang, JY. et al. Energy-based dynamic parameter identification for Pasternak foundation model. Earthq. Eng. Eng. Vib. 20, 631–643 (2021). https://doi.org/10.1007/s11803-021-2043-6

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  • DOI: https://doi.org/10.1007/s11803-021-2043-6

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