Torsional Stiffness of Arbitrarily Shaped Embedded Foundations
Publication: Journal of Geotechnical Engineering
Volume 118, Issue 8
Abstract
A theoretical investigation of the static and dynamic torsional stiffness of arbitrarily shaped rigid foundations embedded in a homogeneous half‐space, using a quadratic‐element‐based boundary element algorithm, is presented. Extensive parametric results are displayed in the form of dimensionless graphs for a variety of basemat shapes and a wide range of embedment depths and types of contact between the foundation sidewalls and the surrounding soil. Based on these results, simple algebraic expressions are also developed, which can be readily used by engineers in practical applications. Discussion of the results provides insight into the nature of torsional response. A numerical example illustrates the practical applicability of the developed formulas, while a companion paper studies the torsional radiation damping of embedded foundations.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Ahmad, S. (1986). “Linear and nonlinear dynamic analysis by boundary element method,” Ph.D. thesis, State Univ. of New York at Buffalo, Buffalo, N.Y.
2.
Ahmad, S., and Banerjee, P. K. (1988). “Time‐domain transient elastodynamic analysis of 3‐D Solids by BEM.” Int. J. Numer. Methods Engrg., 26(8), 1709–1728.
3.
Ahmad, S., and Gazetas, G. (1992). “Radiation damping of arbitrarily shaped embedded foundations.” J. Geotech. Engrg., ASCE, 118(8), 1186–1199.
4.
Ahmad, S., and Manolis, G. D. (1987). “Dynamic analysis of 3‐D structures by a transformed boundary element method.” Comput. Mech., 2, 185–196.
5.
Ahmad, S., Israil, A. S. M., and Chen, K. (1988). “Comparison of dynamic stiffness of rigid rectangular foundations by DBEM and IBEM.” Int. J. Numer. Anal. Methods Geomech., 12(6), 657–678.
6.
Constantinou, M. C., and Gazetas, G. (1984). “Torsional vibration on anisotropic half‐space.” J. Geotech. Engrg., ASCE, 110(11), 1549–1558.
7.
Day, S. M. (1977). “Finite element analysis of seismic scattering problems.” Ph.D. thesis, Univ. of California at San Diego, La Jolla, Calif.
8.
Dobry, R., and Gazetas, G. (1986). “Dynamic response of arbitrarily shaped foundations.” J. Geotech. Engrg., ASCE, 112(2), 109–135.
9.
Dominguez, J. (1978). “Dynamic stiffness of rectangular foundations.” Report No. 8‐20, Massachusetts Inst. of Tech., Cambridge, Mass.
10.
Dominguez, J., and Abascal, R. (1987). “Dynamics of foundations.” Topics in boundary element research, Vol. 4, C. A. Brebbia, ed., Springer‐Verlag, New York, N.Y. 27–72.
11.
Erden, S. M. (1974). “Influence of shape and embedment on foundation response,” Ph.D. thesis, Univ. of Massachusetts, Amherst, Mass.
12.
Fotopoulou, M., Kotsanopoulos, P., Gazetas, G., and Tassoulas, J. L. (1989). “Rocking damping of arbitrarily shaped embedded foundation.” J. Geotech. Engrg., ASCE, 115(4), 472–485.
13.
Gazetas, G. (1983). “Analysis of machine foundation vibrations: State‐of‐the‐art.” Int. J. Soil Dyn. Earthquake Engrg., 2(1), 2–42.
14.
Gazetas, G., and Tassoulas, J. L. (1987a). “Horizontal stiffness of arbitrarily shaped embedded foundations.” J. Geotech. Engrg., ASCE, 113(5), 440–457.
15.
Gazetas, G., and Tassoulas, J. L. (1987b). “Horizontal damping of arbitrarily shaped embedded foundations.” J. Geotech. Engrg., ASCE, 113(5), 458–475.
16.
Gazetas, G., Dobry, R., and Tassoulas, J. L. (1985). “Vertical response of arbitrarily shaped embedded foundations.” J. Geotech. Engrg., ASCE, 111(6), 750–771.
17.
Hatzikonstantinou, E., Tassoulas, J. L., Gazetas, G., Kotsanopoulos, P., and Fotopoulou, M. (1989). “Rocking stiffness of arbitrarily shaped embedded foundations.” J. Geotech. Engrg., ASCE Vol. 115(4), 457–471.
18.
Kaldjian, M. J. (1971). “Torsional stiffness of embedded footings.” J. Soil Mech. Found. Div., ASCE, 97(7), 969–980.
19.
Kausel, E., and Ushijima, R. (1976). “Vertical and torsional stiffness of cylindrical footings.” Report No. R76‐6, Massachusetts Inst. of Tech., Cambridge, Mass.
20.
Kobayashi, S., and Nishimura, N. (1983). “Analysis of dynamic soil‐structure interaction by boundary integral equation method.” Numer. Methods Engrg., Proc. 3rd Int. Symp., Vol. 1, Pluralis Publishing, 353–362.
21.
Luco, J. E. (1976). “Torsion of a rigid cylinder embedded in an elastic halfspace.” J. Appl. Mech., 419–423.
22.
Novak, M. (1985). “Experiments with shallow and deep foundations.” Vibration problems in geotechnical engineering, G. Gazetas and E. T. Selig, eds., ASCE, New York, N.Y., 1026.
23.
Novak, M., and Sachs, K. (1973). “Torsional and coupled vibrations of embedded footings.” Earthquake Engrg. & Struct. Dyn., 2(1), 11–33.
24.
Pais, A., and Kausel, E. (1988). “Approximate formulas for dynamic stiffnesses of rigid foundations.” Soil Dyn. Earthquake Engrg., 7(4), 213–227.
25.
Reissner, E., and Sagoci, H. F. (1944). “Forced torsional oscillations of an elastic half‐space.” J. Appl. Physics, 15, 652–662.
26.
Riccardella, P. (1973). “An implementation of the boundary integral techniques for plane problems in elasticity and elasto‐plasticity,” PhD thesis, Carnegie Mellon Univ., Pittsburgh, Pa.
27.
Stokoe, K. H., and Richart, F. E. (1974). “Dynamic response of embedded machine foundations.” J. Geotech. Engrg., ASCE, 100(4), 427–447.
28.
Veletsos, A. S., and Dotson, K. W. (1987). “Vertical and torsional vibration of foundations in inhomogeneous media.” Tech. Report NCEER‐87‐0010, Nat. Ctr. for Earthquake Engrg. Res., State Univ. of New York at Buffalo, Buffalo, N.Y.
29.
Veletsos, A. S., and Nair, V. V. D. (1974). “Torsional vibration of viscoelastic foundations.” J. Geotech. Engrg. Div., ASCE, 100(3), 225–246.
30.
Weissmann, G. F. (1971). “Torsional vibrations of circular foundations.” J. Soil. Mech. Found. Div., ASCE, 97(9), 1293–1316.
31.
Wolf, J. P. (1988). Soil structure interaction in time domain. Prentice‐Hall, Inc., Englewood Cliffs, N.J.
32.
Wong, H. L., and Luco, J. E. (1978). “Tables of impedance functions and input motions for rectangular foundations.” Report no. CE78‐15, Univ. of Southern, California, Los Angeles, Calif.
Information & Authors
Information
Published In
Copyright
Copyright © 1992 ASCE.
History
Published online: Aug 1, 1992
Published in print: Aug 1992
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.