Dynamic Stiffness of Foundations on Inhomogeneous Soils for a Realistic Prediction of Vertical Building Resonance
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 134, Issue 3
Abstract
The aim of this contribution is a practice-oriented prediction of environmental building vibrations. A Green’s functions method for layered soils is used to build the dynamic stiffness matrix of the soil area that is covered by the foundation. A simple building model is proposed by adding a building mass to the dynamic stiffness of the soil. The vertical soil-building transfer functions with building-soil resonances are calculated and compared with a number of measurements of technically induced vibrations of residential buildings. In a parametrical study, realistic foundation geometries are modeled and the influence of incompressible soil, deep stiff soil layering, soft top layers, and increasing soil stiffness with depth is analyzed. All these special soil models reduce the resonant frequency compared to a standard homogeneous soil. A physically motivated model of a naturally sedimented soil has a stiffness increasing with the square root of the depth and yields a foundation stiffness that decreases with foundation area considerably stronger than the relatively insensitive homogeneous soil. This soil model is suited for the Berlin measuring sites and reproduces satisfactorily the experimental results.
Get full access to this article
View all available purchase options and get full access to this article.
References
Auersch, L. (1988). “Wechselwirkung starrer und flexibler Strukturen mit dem Baugrund insbesondere bei Anregung durch Bodenerschütterungen.” Forschungsbericht 151 Ph.D. thesis, Bundesanstalt für Materialforschung und -prüfung, Berlin.
Auersch, L. (1994). “Wave propagation in layered soil: Theoretical solution in wavenumber domain and experimental results of hammer and railway traffic excitation.” J. Sound Vib., 173, 233–264.
Auersch, L. (1995). “Some effects of the layering of the soil on wave propagation and foundation vibration.” Proc., 7th Conf. Soil Dynamics and Earthquake Engineering, Computational Mechanics Publ., Crete, Greece, 283–290.
Auersch, L. (2005). “Dynamics of the railway track and the underlying soil: The boundary-element solution, theoretical results and their experimental verification.” Veh. Syst. Dyn., 43, 671–695.
Auersch, L., Said, S., Schmid, W., and Rücker, W. (2004). “Erschütterungen im Bauwesen: Messergebnisse an verschiedenen Gebäuden und eine einfache Berechnung von Fundament-, Wand- und Deckenschwingungen.” Bauingenieur, 79, 185–192, and 291–299.
Auersch, L., and Schmid, G. (1990). “A simple boundary element formulation and its application to wavefield excited soil-structure interaction.” Earthquake Eng. Struct. Dyn., 19, 931–947.
Auersch, L., Semrau, N., Schmid, W., Said, S., and Rücker, W. (2002). “Theory and experiments on wave propagation, on track-soil and on soil-building interaction related to railway induced vibration.” Proc., 5th Int. Conf. on Structural Dynamics (Eurodyn 2002), Swets and Zeitlinger, Munich, Germany, 1137–1142.
Barkan, D. (1962). Dynamics of bases and foundations, McGraw-Hill, New York.
Gazetas, G. (1983). “Analysis of machine foundation vibrations: State of the art.” Soil Dyn. Earthquake Eng., 2, 2–41.
Gazetas, G. (1987). “Simple physical methods for foundation impedances.” Dynamic behaviour of foundations and buried structures, Elsevier Applied Science, London, New York, 45–94.
Gazetas, G., and Stokoe, K. (1991). “Free vibration of embedded foundations: Theory versus experiment.” J. Geotech. Engrg., 117(9), 1382–1401.
Holzlöhner, U. (1999). “Der nichtlineare heterogene Halbraum.” Geotechnik, 22, 96–113.
Jakobsen, J. (1989). “Transmission of ground borne vibration in buildings.” Low Freq. Noise, Vib., Act. Control, 8, 75–80.
Kalinchuk, V. V., Belyankova, T. I., and Tosecky, A. (2005). “The effective approach to the inhomogeneous media dynamics modelling.” Proc., 6th Int. Conf. on Structural Dynamics (Eurodyn 2005), Millpress, Paris, 2199–2207.
Kausel, E. (1974). “Forced vibrations of circular foundations on layered media.” Ph.D. thesis, Massachussetts Institute of Technology, Cambridge, Mass.
Kausel, E., and Roesset, J. M. (1981). “Stiffness matrices for layered soils.” Bull. Seismol. Soc. Am., 71, 1743–1761.
Kim, S., and Stewart, J. (2003). “Kinematic soil-structure interaction from strong motion records.” J. Geotech. Geoenviron. Eng., 129(4), 323–335.
Luco, J. (1974). “Impedance functions for a rigid foundation on a layered medium.” Nucl. Eng. Des., 31, 204–217.
Meinhardt, C., and Wuttke, W. (2006). Erschütterungsmessungen bei Bahnverkehr an Gebäuden im Südosten von Berlin und Umgebung. Bericht zum BMBF-Vorhaben 19U0039B, Bundesanstalt für Materialforschung und -prüfung, Berlin.
Mylonakis, G., Nikolaou, S., and Gazetas, G. (2006). “Footings under seismic loading: Analysis and design issues with emphasis on bridge foundations.” Soil Dyn. Earthquake Eng., 26, 824–853.
Nelson, J. T., and Saurenmann, H. J. (1983). “State of the art review: Prediction and control of ground-borne vibration from rail transit trains.” Rep. No. UMTA-MA-06-0049-83-4, U.S. Dept. of Transportation, Washington, D.C.
Nii, Y. (1987). “Experimental half-space dynamic stiffness.” J. Geotech. Engrg., 113(11), 1359–1373.
Reissner, E. (1936). “Stationäre axialsymmetrische durch eine schüttelnde Masse erregte Schwingungen eines homogenen elastischen Halbraumes.” Ing.-Arch., 7, 381–396.
Richart, F. E., Hall, J. R., and Wood, R. D. (1970). Vibrations of soils and foundations, Prentice-Hall, Englewood Cliffs, N.J.
Richart, F. E., and Whitman, R. V. (1967). “Comparison of footing vibration tests with theory.” J. Soil Mech. and Found. Div., 127, 863–898.
Rücker, W., Auersch, L., Gerstberger, U., and Meinhardt, C. (2005). “A practical method for the prediction of railway vibration.” Proc., 6th Int. Conf. on Structural Dynamics (Eurodyn 2005), Millpress, Paris, France, 601–606.
Verbic, B., and Meler, S. (1991). “Experimentally determined impedance functions of surface foundations.” Proc., 5th Conf. on Soil Dynamics and Earthquake Engineering, Karlsruhe, Germany, 479–489.
Vrettos, C. (1991). “Time-harmonic Boussinesq problem for a continuously nonhomogeneous soil.” Earthquake Eng. Struct. Dyn., 20, 961–977.
Waas, G. (1972). “Linear two-dimensional analysis of soil dynamic problems in semi-infinite layered media.” Ph.D. thesis, Univ. of California, Berkeley, Calif.
Waas, G., Hartmann, H., and Werkle, H. (1988). “Damping and stiffness of foundations on inhomogeneous media.” Proc., World Conf. on Earthquake Engineering, Tokyo.
Wolf, J. (1985). Dynamic soil-structure interaction, Prentice-Hall, Englewood Cliffs, N.J.
Wolf, J. (1994). Foundation vibration analysis using simple physical models, Prentice-Hall, Englewood Cliffs, N.J.
Information & Authors
Information
Published In
Journal of Geotechnical and Geoenvironmental Engineering
Volume 134 • Issue 3 • March 2008
Pages: 328 - 340
Copyright
© 2008 ASCE.
History
Received: Apr 24, 2006
Accepted: Jul 23, 2007
Published online: Mar 1, 2008
Published in print: Mar 2008
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.