Nonlinear Response of Vertically Oscillating Rigid Foundations
Publication: Journal of Geotechnical Engineering
Volume 119, Issue 5
Abstract
The dynamic response of vertically excited rigid foundations on an elasto‐viscoplastic half‐space is investigated in the context of nonlinear finite element (FE) analysis. A deviatoric viscoplastic theory with a linear combination of isotropic and kinematic hardening is used to model the soil constitutive response. Large‐scale nonlinear FE computations are made feasible by the use of a composite Newton‐preconditioned conjugate gradient (PCG) iteration technique, which requires the factorization of the consistent tangent operator no more than once during the solution process. Time‐domain analyses are used to investigate the nonlinear responses of vertically oscillating circular and square foundations to harmonic loads, using two‐ and three‐dimensional FE modeling, respectively. For low‐frequency excitations, resonance is created, which amplifies the motion of the foundation at amplitudes well above those obtained at the zero‐frequency level. This behavior is in stark contrast to the linear elastic response of vertically oscillating finite‐size foundations on a homogeneous half‐space, in which the amplitude of the motion is known to decrease monotonically with increasing values of the excitation frequency. The resonance phenomenon is explained in the context of a single‐degree‐of‐freedom oscillator analog that has been used successfully by previous investigators to model prototype continuum soil‐structure interaction problems.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Borja, R. I. (1991a). “Composite Newton‐PCG and quasi‐Newton iterations for nonlinear consolidation.” Comput. Methods Appl. Mech. Engrg., 86(1), 27–60.
2.
Borja, R. I. (1991b). “Modeling the monotonic and cyclic viscoplastic soil behavior.” Proc., 2nd Int. Conf. Recent Advances Geotech. Earthquake Engrg. Soil Dynamics, S. Prakash, ed., 37–40.
3.
Dafalias, Y. F., and Herrmann, L. R. (1982). “Bounding surface formulation of soil plasticity.” Soil mechanics—Transient and cyclic loads, G. N. Pande and O. C. Zienkiewicz, eds., John Wiley and Sons, New York, N.Y., 253–282.
4.
Duvaut, G., and Lions, J. L. (1976). Inequalities in mechanics and physics. Springer‐Verlag, New York, N.Y.
5.
Gazetas, G. (1983). “Analysis of machine foundation vibrations: State of the art.” Soil Dynamics Earthquake Engrg., 2(1), 2–42.
6.
Gazetas, G. (1991). “Formulas and charts for impedances of surface and embedded foundations.” J. Geotech. Engrg., ASCE, 117(9), 1363–1381.
7.
Givoli, D. (1988). “A finite element method for large‐domain and problems,” PhD thesis, Stanford University, Stanford, Calif.
8.
Hilber, H. M., Hughes, T. J. R., and Taylor, R. L. (1977). “Improved numerical dissipation for the time integration algorithms in structural dynamics.” Earthquake Engrg. Struct. Dyn., 5(3), 283–292.
9.
Hsieh, T. K. (1962). “Foundation vibrations.” Proc., Institution of Civil Engineers (U.K.), 22(Jun), 211–226.
10.
Hughes, T. J. R. (1984). “Numerical implementation of constitutive models: Rate‐independent deviatoric plasticity.” Theoretical foundations for large‐scale computations for nonlinear material behavior, S. Nemat‐Nasser, R. J. Asaro, and G. A. Hegemier, eds., Martinus Nijhoff Publishers, Boston, Mass., 26–57.
11.
Hughes, T. J. R. (1987). The finite element method. Prentice‐Hall, Englewood Cliffs, N.J.
12.
Jakub, M., and Roesset, J. M. (1977). “Dynamic stiffness of foundations: 2‐D vs 3‐D solutions.” Research Report R77‐36, Massachusetts Inst. of Tech., Cambridge, Mass.
13.
Kausel, E. (1974). “Forced vibrations of circular foundations on layered media.” Research Report R74‐11, Massachusetts Inst. of Tech., Cambridge, Mass.
14.
Kausel, E., Roesset, J. M., and Christian, J. T. (1976). “Nonlinear behavior in soil‐structure interaction.” J. Geotech. Engrg. Div., ASCE, 102(11), 1159–1170.
15.
Kausel, E., and Ushijima, R. (1979). “Vertical and torsional stiffness of cylindrical footings.” Research Report R76‐6, Massachusetts Inst. of Tech., Cambridge, Mass.
16.
Krieg, R. D., and Key, S. W. (1976). “Implementation of a time‐independent plasticity theory into structural computer programs.” Constitutive equations in viscoplasticity: Computational and engineering aspects (AMD‐20), J. A. Stricklin and K. J. Saczalski, eds., Am. Soc. of Mech. Engrs., New York, N.Y.
17.
Luco, J. E. (1974). “Impedance functions for a rigid foundation on a layered medium.” Nuclear Engrg. Design, 31(2), 204–217.
18.
Luco, J. E., and Westman, R. A. (1971). “Dynamic response of circular footings.” J. Engrg. Mech. Div., ASCE, 97(5), 1381–1395.
19.
Lysmer, J. (1965). “Vertical motions of rigid footings,” PhD. thesis, University of Michigan, Ann Arbor, Mich.
20.
Lysmer, J., and Kuhlemeyer, R. L. (1969). “Finite dynamic model for infinite media.” J. Engrg. Mech. Div., ASCE, 95(4), 859–877.
21.
Lysmer, J. et al. (1974). “FLUSH—A computer program for complex response analysis of soil‐structure systems.” Report No. EERC 74‐4, Univ. of California, Berkeley, Calif.
22.
Manolis, G. D. (1983). “A comparative study on three boundary element method approaches to problems in elastodynamics.” Int. J. Numer. Methods Engrg., 19(1), 73–91.
23.
Mróz, Z. (1967). “On the description of anisotropic work‐hardening.” J. Mech. Phys. Solids, 15(3), 163–175.
24.
Mróz, Z., Norris, V. A., and Zienkiewicz, O. C. (1979). “Application of an anisotropic hardening model in the analysis of elastoplastic deformation of soils.” Geotechnique, London, England, 29(1), 1–34.
25.
Ortega, J. M., and Rheinboldt, W. C. (1970). Iterative solution of nonlinear equations in several variables. Academic Press, Inc., San Diego, Calif.
26.
Perzyna, P. (1971). “Thermodynamic theory of viscoplasticity.” Advances in applied mechanics, 11, Academic Press, New York, N.Y.
27.
Pinsky, P. M., and Abboud, N. N. (1991). “Finite element solution of the transient exterior structural acoustics problem based on the use of radially asymptotic boundary operators.” Comput. Methods Appl. Mech. Engrg., 85(3), 311–348.
28.
Prager, W. (1956). “A new method of analyzing stresses and strains in work‐hardening plastic solids.” J. Appl. Mech., 23(4), 493–496.
29.
Prevost, J. H. (1977). “Mathematical modelling of monotonic and cyclic undrained clay behaviour.” Int. J. Num. Analyt. Methods Geomech., 1(2), 195–216.
30.
Reissner, E. (1936). “Stationare, axialsymmetrische, durch eine schut‐telnde Masse erregte Schwingungen eines homogenen elastischen Halbraumes.” Ingenieur Archiv, Berlin, Germany, 7(6), 381–396 (in German).
31.
Richart, F. E., and Whitman, R. V. (1967). “Comparison of footing vibration tests with theory.” J. Soil Mech. Found. Engrg. Div., ASCE, 93(6), 143–168.
32.
Richart, F. E., Woods, R. D., and Hall, J. R. (1970). Vibrations of soils and foundations. Prentice‐Hall, Englewood Cliffs, N.J.
33.
Roesset, J. M. (1980). “Stiffness and damping coefficients of foundations.” Dynamic response of pile foundations, M. W. O'Neill and R. Dobry, eds., ASCE, New York, N.Y., 1–30.
34.
Simo, J. C., and Taylor, R. L. (1985). “Consistent tangent operators for rate‐independent elasto‐plasticity.” Comput. Methods Appl. Mech. Engrg., 48(1), 101–118.
35.
Simo, J. C., Kennedy, J. G., and Govindjee, S. (1988). “Nonsmooth multisurface plasticity and viscoplasticity. Loading/unloading conditions and numerical algorithms.” Int. J. Num. Methods Engrg., 26(10), 2161–2185.
36.
Tassoulas, J. L. (1981). “Elements for the numerical analysis of wave motion in layered media.” Research Report R81‐2, Massachusetts Inst. of Tech., Cambridge, Mass.
37.
Veletsos, A. S., and Wei, Y. T. (1971). “Lateral and rocking vibrations of footings.” J. Soil Mech. Found. Div., ASCE, 97(9), 1227–1248.
38.
Veletsos, A. S., and Verbic, B. (1973). “Vibration of viscoelastic foundation.” Int. J. Earthquake Engrg. Struct. Dyn., 2(1), 87–102.
39.
Veletsos, A. S., and Tang, Y. (1987). “Vertical vibration of ring foundations.” Int. J. Earthquake Engrg. Struct. Dyn., 15(1), 1–21.
40.
Wu, W. H. (1991). “Soil‐structure interaction effects of simple structures supported on rectangular foundations,” MS thesis, Rice University, Houston, Tex.
Information & Authors
Information
Published In
Copyright
Copyright © 1993 American Society of Civil Engineers.
History
Received: Jan 27, 1992
Published online: May 1, 1993
Published in print: May 1993
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.