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Abstract

Foundation damping incorporates combined effects of energy loss from waves propagating away from a vibrating foundation (radiation damping) and hysteretic action in supporting soil (material damping). Foundation damping appears in analysis and design guidelines for force- and displacement-based analysis of seismic building response (ASCE-7, ASCE-41), typically in graphical form (without predictive equations). We derive closed-form expressions for foundation damping of a flexible-based single degree-of-freedom oscillator from first principles. The expressions are modular in that structure and foundation stiffness terms, along with radiation and hysteretic damping ratios, appear as variables. Assumptions inherent to our derivation have been employed previously, but the present results are differentiated by: (1) the modular nature of the expressions; (2) clearly articulated differences regarding alternate bases for the derivations and their effects on computed damping; and (3) completeness of the derivations. Resulting expressions indicate well-known dependencies of foundation damping on soil-to-structure stiffness ratio, structure aspect ratio, and soil damping. We recommend a preferred expression based on the relative rigor of its derivation.

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References

American Society of Civil Engineers (ASCE), 2006. Seismic Evaluation and Retrofit of Existing Buildings, ASCE/SEI 41-06, Reston, VA.

American Society of Civil Engineers (ASCE), 2010. Minimum Design Loads for Buildings and Other Structures, ASCE/SEI 7-10, Reston, VA.

Apsel

R. J.

and Luco

J. E.

1987. Impedance functions for foundations embedded in a layered medium: an integral equation approach, Earthquake Eng. and Struct. Dynamics 15, 213–231.

Assimaki

and Gazetas

2009. A simplified model for lateral response of large diameter caisson foundations-linear elastic formulation, Soil Dyn. Earthquake Eng. 29, 268–291.

Avilés

and Pérez-Rocha

L. E.

1996. Evaluation of interaction effects on the system period and the system damping due to foundation embedment and layer depth, Soil Dyn. Earthquake Eng. 15, 11–27.

Bielak

1971. Earthquake Response of Building-Foundation Systems, Ph.D. Thesis, California Institute of Technology, Pasadena, CA.

Bielak

1974. Dynamic behavior of structures with embedded foundations, Earthquake Eng. and Struct. Dynamics 3, 259–274.

Clough

R. W.

and Penzien

1993. Dynamics of Structures, 2nd Edition, McGraw-Hill, NY.

Crouse

C. B.

and McGuire

2001. Energy dissipation in soil-structure interaction, Earthquake Spectra 17, 235–259.

10.

Esmaeilzadeh

Jeong

and Taciroglu

2016. On numerical computation of impedance functions for arbitrary rigid foundations embedded in heterogeneous halfspaces, Computers and Geotechnics 72, 15–27.

11.

Givens

M. J.

2013. Dynamic Soil-Structure Interaction of Instrumented Buildings and Test Structures. Ph.D. Thesis, University of California, Los Angeles.

12.

Jennings

P. C.

and Bielak

1973. Dynamics of building-soil interaction, Bull. Seism. Soc. Am. 63, 9–48.

13.

Luco

J. E.

and Westmann

R. A.

1971. Dynamic response of circular footings, J. Engrg. Mech. 97, 1381–1395.

14.

Maravas

Mylonakis

and Karabalis

D. L.

2014. Simplified discrete systems for dynamic analysis of structures on footings and piles, Soil Dyn. Earthquake Eng. 61, 29–39.

15.

Mylonakis

Nikolaou

and Gazetas

2006. Footings under seismic loading: Analysis and design issues with emphasis on bridge foundations, Soil Dyn. Earthquake Eng. 26, 824–853.

16.

National Institute of Standards and Technology (NIST), 2012. Soil-structure Interaction for Building Structures, Report No. NIST GCR 12-917-21, U.S. Department of Commerce, Washington, D.C.

17.

Parmelee

R. A.

1967. Building-foundation interaction effects, Journal of Eng. Mech. Div. 93, 131–155.

18.

Pais

and Kausel

1988. Approximate formulas for dynamic stiffnesses of rigid foundations, Soil Dyn. and Earthquake Eng. 7, 213–227.

19.

Roesset

J. M.

1980. Seismic Safety Margins Research Program (Phase I), Project III – Soil-Structure Interaction, A Review of Soil-Structure Interaction, UCRL-15262, Nuclear Test Engineering Division, Lawrence Livermore Laboratory, Livermore, CA.

20.

Star

L. M.

Givens

M. J.

Nigbor

R. L.

and Stewart

J. P.

2015. Field testing of structure on shallow foundation to evaluate SSI effects, Earthquake Spectra, 31, 2511–2534.

21.

Stewart

J.P.

Seed

R.B.

and Fenves

G.L.

1999. Seismic soil-structure interaction in buildings. II: empirical findings, J. Geotech. Geoenviron. Eng. 125, 38–48.

22.

Veletsos

A.S.

1977. Dynamics of soil-foundation systems, in Structural and Geotechnical Mechanics ( Hall

W. J.

, editor), Prentice-Hall, Englewood Cliffs, NJ, 261–333.

23.

Veletsos

A. S.

and Meek

J. W.

1974. Dynamic behavior of building-foundation systems, J. Earthquake Eng. Struct. Dyn. 3, 121–138.

24.

Veletsos

A. S.

and Nair

V. V.

1975. Seismic interaction of structures on hysteretic foundations, J. Struct. Eng. 101, 109–129.

25.

Veletsos

A. S.

and Ventura

C. E.

1986. Modal analysis of non-classically damped linear systems, Earthquake Eng. Struct. Dyn. 14, 217–243.

26.

Veletsos

A. S.

and Verbic

1973. Vibrations of viscoelastic foundations, J Earthquake Eng. and Struct. Dynamics 2, 87–102.

27.

Veletsos

A. S.

and Wei

Y. T.

1971. Lateral and rocking vibrations of footings, J. Soil Mechanics and Foundations Div. 97, 1227–1248.

28.

Wolf

J. P.

1985. Dynamic Soil-Structure Interaction, Prentice-Hall, Englewood Cliffs, NJ.

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Modular Analytical Solutions for Foundation Damping in Soil-Structure Interaction Applications

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