Discrete model for dynamic through-the-soil coupling of 3-D foundations and structures
Jeffrey S. Mulliken
The LPA Group Inc., 2530 Devine Str., P.O. Box 5805, Columbia, SC 29250, U.S.A.
Search for more papers by this authorCorresponding Author
Dimitris L. Karabalis
Department of Civil Engineering, University of Patras, 26500 Patras, Greece
Department of Civil Engineering, University of Patras, 26500 Patras, GreeceSearch for more papers by this authorJeffrey S. Mulliken
The LPA Group Inc., 2530 Devine Str., P.O. Box 5805, Columbia, SC 29250, U.S.A.
Search for more papers by this authorCorresponding Author
Dimitris L. Karabalis
Department of Civil Engineering, University of Patras, 26500 Patras, Greece
Department of Civil Engineering, University of Patras, 26500 Patras, GreeceSearch for more papers by this authorAbstract
An efficient discrete model for predicting the dynamic through-the-soil interaction between adjacent rigid, surface foundations supported by a homogeneous, isotropic and linear elastic half-space is presented. The model utilizes frequency-independent springs and dashpots, and the foundation mass, for the consideration of soil–foundation interaction. The through-the-soil coupling of the foundations is attained by frequency-independent stiffness and damping functions, developed in this work, that interconnect the degrees of freedom of the entire system of foundations. The dynamic analysis of the resulting coupled system is performed in the time domain and includes the time lagging effects of coupled dynamic input due to wave propagation using an appropriate modification of the Wilson-θ method. The basic foundation interaction model is also extended to the evaluation of coupled building-foundation systems. © 1998 John Wiley & Sons, Ltd.
References
- 1 J. Qian and D. E. Beskos, ‘Dynamic interaction between 3-D rigid surface foundations and comparison with the ATC-3 provisions’, Earth. Engng. Struct. Dyn. 24, 419–437 (1995).
- 2 J. Qian and D. E. Beskos, ‘Harmonic wave response of two 3-D rigid surface foundations’, Soil Dyn. Earth. Engng. 15, 95–110 (1996).
- 3 M. Mohammadi and D. L. Karabalis, ‘Dynamic 3-D soil-railway track interaction by BEM-FEM’, Earth. Engng. Struct. Dyn. 24, 1177–1193 (1995).
- 4 J. Lysmer and F. E. Richart, ‘Dynamic response of footings to vertical loading’, J. Soil Mech. Found. Div. ASCE 92 (SM 1), 65–91 (1966).
- 5 R. V. Whitman, ‘The current status of soil dynamics’, Appl. Mech. Rev. 22, 1–8 (1969).
- 6 F. E. Richart, J. R. Hall and R. D. Woods, Vibrations of Soils and Foundations, Prentice-Hall, Englewood Cliffs, N.J., 1970.
- 7 N. M. Newmark and E. Rosenblueth, Fundamentals of Earthquake Engineering, Prentice-Hall, Englewood Cliffs, N.J., 1971.
- 8
G. Gazetas,
‘Analysis of machine foundation vibrations: state of the art review’,
Soil Dyn. Earth. Engng.
2,
2–42
(1983).
10.1016/0261-7277(83)90025-6 Google Scholar
- 9 J. P. Wolf, Dynamic Soil–Structure Interaction, Prentice-Hall, Englewood Cliffs, N.J., 1985.
- 10 J. P. Wolf, Soil–Structure-Interaction Analysis in Time Domain, Prentice-Hall, Englewood Cliffs, N.J., 1988.
- 11 J. W. Meek and A. S. Veletsos, ‘ Simple models for foundations in lateral and rocking motion’, Proc. 5th World Conf. on Earth. Engng. vol. 2, 1973, pp. 2610–2613.
- 12 F. C. P. De Barros and J. E. Luco, ‘Discrete models for vertical vibrations of surface and embedded foundations’, Earth. Engng. Struct. Dyn. 19, 289–303 (1990).
- 13 J. P. Wolf and D. R. Somaini, ‘Approximate dynamic model of embedded foundation in time domain’, Earth. Engng. Struct. Dyn. 14, 683–703 (1986).
- 14 J. P. Wolf and A. Paronesso, ‘ Lumped-parameter model for foundation on layer’, Proc. 10th European Conf. on Soil Mech. Engng., vol. 1, 1991, pp. 287–290.
- 15 J. P. Wolf and A. Paronesso, ‘Lumped-parameter model for a rigid cylindrical foundation embedded in a soil layer on rigid rock’, Earth. Engng. Struct. Dyn. 21, 1021–1038 (1992).
- 16 J. P. Wolf, ‘Consistent lumped-parameter models for unbounded soil: physical representation’, Earth. Engng. Struct. Dyn. 20, 11–32 (1991).
- 17 J. P. Wolf, ‘Consistent lumped-parameter models for unbounded soil: frequency-independent stiffness, damping and mass matrices’, Earth. Engng. Struct. Dyn. 20, 33–41 (1991).
- 18 G. B. Warburton, J. D. Richardson and J. J. Webster, ‘Forced vibrations of two masses on an elastic half space’, J. Appl. Mech. ASME 38, 148–156 (1971).
- 19
G. B. Warburton,
J. D. Richardson and
J. J. Webster,
‘Harmonic responses of masses on an elastic half space’,
J. Engng. Ind. ASME
194,
193–200
(1972).
10.1115/1.3428111 Google Scholar
- 20 P. B. MacCalden and R. B. Matthiesen, ‘ Coupled response of two foundations’, Proc. 5th World Conf. on Earthquake Engng., vol. 2, 1973, pp. 1913–1922.
- 21 T. Triantafyllidis, ‘Dynamic stiffness of rigid rectangular foundations on the half-space’, Earth. Engng. Struct. Des. 14, 391–441 (1986).
- 22
T. Triantafyllidis and
B. Prange,
‘Dynamic subsoil coupling between rigid, rectangular foundations’,
Soil Dyn. Earth. Engng.
6,
164–179
(1987).
10.1016/0267-7261(87)90013-3 Google Scholar
- 23 F. Guan and M. Novak, ‘Transient response of multiple rigid foundations on an elastic, homogeneous half-space’, Trans. ASME 61, 656–663 (1994).
- 24 F. Guan and M. Novak, ‘Transient Response of an elastic homogeneous half-space to suddenly applied rectangular loading’, Trans. ASME 61, 256–263, (1994).
- 25 C.-F. D. Huang, ‘ Dynamic soil–foundation and foundation–soil–foundation interaction’, in 3-D', Ph.D. Dissertation, Dept. Civil Engng., Univ. South Carolina, Columbia, 1993.
- 26 D. L. Karabalis and C.-F. D. Huang, ‘ 3-D foundation–soil–foundation interaction’, in C. A. Brebbia and A. J. Kassab (eds), Boundary Element Technology IX (BETECH 94), CMP, Southampton, 1994, pp. 197–209.
- 27
D. L. Karabalis and
M. Mohammadi,
‘ 3-D dynamic foundation–soil–foundation interaction on a layered soil medium’,
in B. H. V. Topping (ed.),
Advances in Boundary Element Methods,
Civil-Comp Press, Edinburgh,
1996,
pp. 73–80.
10.4203/ccp.44.3.1 Google Scholar
- 28 M. Mohammadi and D. L. Karabalis, ‘ 3-D dynamic foundation–soil foundation interaction on layered soil’, Soil Dyn. Earth. Engng., in print.
- 29 J. Luco and L. Contesse, ‘Dynamic structure–soil–structure interaction’, Bull. Seism. Soc. Am. 63, 1289–1303 (1973).
- 30 H. L. Wong and M. D. Trifunac, ‘Two-dimensional, antiplane, building–soil–building interaction for two or more buildings and for incident plane SH waves’, Bull. Seism. Soc. Am. 65, 1863–1885 (1975).
- 31 H. Murakami and J. Luco, ‘Seismic response of a periodic array of structures’, J. Engng. Mech. Div. ASCE 103, 965–977 (1977).
- 32 T. H. Lee and D. A. Wesley, ‘Soil–structure interaction of nuclear reactor structures considering through-soil coupling between adjacent structures’, Nucl. Engng. Des. 24, 374–387 (1973).
- 33
M. Paz,
Structural Dynamics Theory and Computation,
3rd edn,
Van Nostrand Reinhold, New York,
1991.
10.1007/978-1-4684-9907-0 Google Scholar
- 34 J. S. Mulliken, ‘ Discrete models for foundation–soil–foundation interaction in time domain’, M.S. Thesis, Dept. of Civil Engineering, Univ. of South Carolina, 1994.
- 35 J. S. Mulliken and D. L. Karabalis, ‘ Discrete model for foundation–soil–foundation interaction’, in A. S. Cakmak and C. A. Brebbia (eds), Soil Dynamics and Earthquake Engineering VII, CMP, Southampton, 1995, pp. 501–508.
- 36 D. L. Karabalis and D. E. Beskos, ‘ Numerical methods in earthquake engineering’, in D. E. Beskos and S. A. Anagnostopoulos (eds), Computer Analysis and Design in Earthquake Resistant Structures: A Handbook, Chapter 1, CMP, Southampton, 1997, pp. 1–102.
- 37 J. Lysmer, Tabatabaie-Raissi, M. Tajirian, F. Vahdani and F. Ostadan, ‘ SASSI—a system for analysis of soil–structure interaction’, Report UCB/GT/81–02, Geot. Engng, Univ. of California, Berkeley, 1981.