Evaluation of Rocking and Coupling Rotational Linear Stiffness Coefficients of Adjacent Foundations
Publication: International Journal of Geomechanics
Volume 18, Issue 1
Abstract
This paper presents closed-form expressions for rocking spring stiffnesses and coupling interaction rotational spring stiffnesses for a set of closely spaced footings. Substructuring is used to derive analytically the exact reduced order spring models of the system. The stiffness coefficients of this reduced order model are determined by using (1) an extended, novel application of Boussinesq’s surface displacement of a point-loaded half-space and (2) an empirically derived formulation that makes use of both finite-element and experimental results. Further validation suggests that, within the scope of epistemic uncertainty present in the physical world, the interaction formulas between two footings are sufficient for more general multifooting interaction cases.
Get full access to this article
View all available purchase options and get full access to this article.
References
Aldaikh, H. (2013). “Discrete models for the study of dynamic structure-soil-structure interaction.” Ph.D. thesis, Queen’s School of Engineering, Univ. of Bristol, Bristol, U.K.
Aldaikh, H., Alexander, N. A., Ibraim, E., and Knappett, J. (2016). “Shake table testing of the dynamic interaction between two and three adjacent buildings (SSSI).” Soil Dyn. Earthquake Eng., 89(Oct), 219–232.
Aldaikh, H., Alexander, N. A., Ibraim, E., and Oddbjornsson, O. (2015). “Two dimensional numerical and experimental models for the study of structure–soil–structure interaction involving three buildings.” Comput. Struct., 150(Apr), 79–91.
Alexander, N. A., Ibraim, E., and Aldaikh, H. (2013). “A simple discrete model for interaction of adjacent buildings during earthquakes.” Comput. Struct., 124(Aug), 1–10.
ATC (Applied Technology Council). (1978). “Tentative provisions for the development of seismic regulations for buildings.” ATC-3-06, Redwood City, CA.
Azizi, F. (2000). Applied analysis in geotechnics, E & FN Spon, London.
Barkan, D. (1962). Dynamics of bases and foundations, McGraw Hill, New York.
Boas, M. L. (2006). Mathematical methods in the physical sciences Wiley, Hoboken, NJ.
Bowles, J. E. (1996). Foundation analysis and design, McGraw-Hill Education India, New Delhi, India.
Bycroft, G. N. (1956). “Forced vibrations of a rigid circular plate on a semi-infinite elastic space and on an elastic stratum.” Philos. Trans. R. Soc. London, Ser. A, 248(948), 327–368.
de Barros, F. C. P., and Luco, J. E. (1990). “Discrete models for vertical vibrations of surface and embedded foundations.” Earthquake Engrg. Struct. Dyn., 19(2), 289–303.
Dobry, R., and Gazetas, G. (1986). “Dynamic response of arbitrarily shaped foundations.” J. Geotech. Engrg., 109–135.
Dutta, S. C., and Roy, R. (2002). “A critical review on idealization and modeling for interaction among soil–foundation–structure system.” Comput. Struct., 80(20–21), 1579–1594.
Gazetas, G. (1991). “Formulas and charts for impedances of surface and embedded foundations.” J. Geotech. Engrg., 1363–1381.
Gorbunov-Possadov, M. I., Malikova, T. A., and Solomin, V. I. (1961). “Design of structures upon elastic foundations.” Proc., 5th Int. Conf. on Soil Mechanics and Foundation Engineering, Dunod Editeur, Paris, 1, 643–648.
Guyan, R. J. (1965). “Reduction of stiffness and mass matrices.” AIAA J., 3(2), 380.
Idriss, I., and Seed, H. (1967). “Response of horizontal soil layers during earthquakes.” Soil Mechanics and Bituminous Materials Research Laboratory, Univ. of California, Berkeley, CA.
Jennings, P. C., and Bielak, J. (1973). “Dynamics of building-soil-Interaction.” Bull. Seismol. Soc. Am., 63(1), 9–48.
Kobori, T., and Kusakabe, K. (1980). “Cross-interaction between two embedded structures in earthquakes.” Proc., 7th World Conf. on Earthquake Engineering, International Association of Earthquake Engineering, Tokyo.
Kobori, T., and Minai, R. (1974). “Dynamical interaction of multiple structural systems on a soil medium.” Proc., 5th World Conf. on Earthquake Engineering, Editrice Libraria, Rome, Italy.
Kobori, T., Minai, R., and Kusakab, K. (1973). “Dynamical characteristics of soil-structure cross-interaction system.” Bull. Disaster Prev. Res. Inst., 22(2), 111–151.
Kobori, T., Minai, R., and Kusakabe, K. (1977). “Dynamical cross-interaction between two foundations.” Proc., 6th World Conf. on Earthquake Engineering, International Association of Earthquake Engineering, Tokyo, Vol II, 1484–1489.
Lee, T. H., and Wesley, D. A. (1973). “Soil-structure interaction of nuclear reactor structures considering through-soil coupling between adjacent structures.” Nucl. Eng. Des., 24(3), 374–387.
Luco, J. E., and Contesse, L. (1973). “Dynamic structure-soil-structure interaction.” Bull. Seismol. Soc. Am., 63(4), 1289–1303.
Lysmer, J., and Richart, F. (1966). “Dynamic response of footings to vertical loading.” J. Soil Mech. Found. Div., ASCE, 92(1), 65–91.
Mulliken, D. L., and Karabalis, J. S. (1995). “Discrete model for foundation-soil-foundation interaction.” WIT Trans. Environ., 15, 501–508.
Mulliken, J. S., and Karabalis, D. L. (1998). “Discrete model for dynamic through-the-soil coupling of 3-D foundations and structures.” Earthquake Eng. Struct. Dyn., 27(7), 687–710.
Mykoniou, K., Butenweg, C., Holtschoppen, B., and Klinkel, S. (2016). “Seismic response analysis of adjacent liquid-storage tanks.” Earthquake Eng. Struct. Dyn., 45(11), 1779–1796.
Petersen, K. B., and Pedersen, M. S. (2012). “The matrix cookbook.” ⟨http://www2.imm.dtu.dk/pubdb/views/edoc_download.php/3274/pdf/imm3274.pdf⟩ (Oct. 26, 2017).
PLAXIS 2D 2011 [Computer software]. Plaxis bv, Delft, Netherlands.
Plaxis bv. (2011). PLAXIS 2D reference manual, Delft, Netherlands.
Poulos, H. G., and Davis, E. H. (1974). Elastic solutions for soil and rock mechanics, Wiley, New York.
Qian, J., and Beskos, D. E. (1995). “Dynamic interaction between 3-D rigid surface foundations and comparison with the ATC-3 provisions.” Earthquake Eng. Struct. Dyn., 24(3), 419–437.
Soubestre, J., et al. (2012). “Dynamic behaviour of reinforced soils–Theoretical modelling and shaking table experiments.” Role of seismic testing facilities in performance-based earthquake engineering, 22, Springer, Dordrecht, Netherlands, 247–263.
Stewart, J. P., Seed, R. B., and Fenves, G. L. (1998). Empirical evaluation of inertial soil-structure interaction effects, Pacific Earthquake Engineering Research Center, Univ. of California, Berkeley, CA.
Warburton, G. B., Richardson, J. D., and Webster, J. J. (1971). “Forced vibration of two masses on an elastic half space.” J. Appl. Mech., 38(1), 148–156.
Wolf, J. P. (1985). Dynamic soil structure interaction, Prentice-Hall, Englewood Cliffs, NJ.
Wolf, J. P. (1988). Soil-structure-interaction analysis in time domain, Prentice-Hall, Englewood Cliffs, NJ.
Wolf, J. P. (1991). “Classification of analysis methods for dynamic soil-structure interaction.” Proc., 2nd Int. Conf. on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, St. Louis, MO, Paper No. SOA9.
Wolf, J. P. (1994). Foundation vibration analysis using simple physical models, Prentice-Hall, Englewood Cliffs, NJ.
Zaman, M. M. U. (1982). “Influence of interface behavior in dynamic soil-structure interaction problems.” Ph.D. thesis, Univ. of Arizona, Tucson, AZ.
Zienkiewicz, O. C., Taylor, R. L., and Zhu, J. Z. (2013). The finite element method: Its basis and fundamentals, 7th Ed., Butterworth-Heinemann, Oxford, U.K.
Information & Authors
Information
Published In
Copyright
© 2017 American Society of Civil Engineers.
History
Received: Nov 17, 2016
Accepted: Jul 27, 2017
Published online: Nov 7, 2017
Published in print: Jan 1, 2018
Discussion open until: Apr 7, 2018
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.