Dynamic Response of Arbitrarily Shaped Foundations
Publication: Journal of Geotechnical Engineering
Volume 112, Issue 2
Abstract
The paper presents a method to compute the effective dynamic stiffnesses and dashpots (C) of arbitrarily shaped, rigid surface machine foundations placed on reasonably homogeneous and deep soil deposits. The method is based on a comprehensive compilation of a number of analytical results, augmented by additional numerical studies and interpreted by means of simple physical models. All results are offered in the form of easily understood dimensionless graphs and formulas, covering the six modes of vibration and a wide range of frequencies, for both saturated and unsaturated soils. Comparisons are made with the widely used equivalent circle approximation. The proposed method is applicable to a variety of area foundation shapes, ranging from circular to strip and including rectangles of any aspect ratio as well as odd shapes differing substantially from rectangle or circle. The results confirm that both frequency and foundation shape may significantly affect and C. Insight is gained into the mechanics of radiation damping and a general conclusion is drawn regarding its magnitude at high frequencies for different foundation shapes and vibrational modes. The practical application of the method is illustrated with a specific example, while a companion paper (7) presents supporting experimental evidence from model tests.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Barkan, D. D. (1962), Dynamics of Bases and Foundations (translated from Russian), McGraw‐Hill Book Co., New York.
2.
Berger, E., Makin, S. A., and Pyke, R. (1977), “Simplified Method for Evaluating Soil‐Pile Structure Interaction Effects,” Proceedings of the 9th Offshore Technology Conference, OTC Paper 2954, Houston, TX, pp. 589–598.
3.
Borochadev, N. M. (1964), “Determination of the Settlement on Rigid Plates,” Soil Mechanics and Foundation Engineering (USSR), 1, 210.
4.
Chae, Y. S. (1969), “Vibrations of Noncircular Foundations,” Journal of the Soil Mechanics and Foundations Division, Vol. 95, No. SM6, Nov., pp. 1411–1430.
5.
Day, S. M. (1977), “Finite‐Element Analysis of Seismic Scattering Problems,” Ph.D. Thesis in Earth Sciences, Univ. of California at San Diego.
6.
Dobry, R., and Gazetas, G. (1985), “Dynamic Response of Arbitrarily Shaped Foundations,” Research Report, Dept. of Civ. Engrg., Rensselaer Polytechnic Institute.
7.
Dobry, R., Gazetas, G., and Stokoe, K. H., II (1986), “Dynamic Response of Arbitrarily Shaped Foundations: Experimental Verification,” Journal of Geotechnical Engineering, ASCE, 112(2), Feb., 136–154.
8.
Dominguez, J., and Roesset, J. M. (1978), “Dynamic Stiffness of Rectangular Foundations,” Research Report R78‐20, Dept. of Civ. Engrg., M.I.T.
9.
Erden, S. M. (1974), “Influence of Shape and Embedment on Dynamic Foundation Response,” Ph.D. Thesis, Dept. of Civ. Engrg., Univ. of Massachusetts.
10.
Gazetas, G. (1982), “ANILAY—A Computer Program for Dynamic Response of Strip Footings on Layered Cross‐Anisotropic Soils,” Research Report CE82‐05, Dept. of Civ. Engrg.
11.
Gazetas, G. (1983), “Analysis of Machine Foundation Vibrations: State of the Art,” Journal of Soil Dynamics and Earthquake Engineering, Vol. 2, No. 1, pp. 2–42.
12.
Gazetas, G., and Roesset, J. M. (1976), “Forced Vibrations of Strip Footings on Layered Soils,” Proceedings of the ASCE Specialty Conference on Methods of Structural Analysis, Madison, WI, pp. 115–131.
13.
Gazetas, G., and Roesset, J. M. (1979), “Vertical Vibrations of Machine Foundations,” Journal of the Geotechnical Engineering Division, ASCE, Vol. 105, No. GT12, pp. 1435–1454.
14.
Gazetas, G., and Dobry, R. (1984), “Horizontal Response of Piles in Layered Soils,” Journal of Geotechnical Engineering, ASCE, Vol. 110, No. 1, Jan., pp. 20–40.
15.
Gazetas, G., and Dobry, R. (1984), “Simple Radiation Damping Model for Piles and Footings,” Journal of Engineering Mechanics, ASCE, Vol. 110, No. 6, June, pp. 937–956.
16.
Gazetas, G., Dobry, R., and Tassoulas, J. L. (1985), “Vertical Response of Arbitrarily Shaped Embedded Foundations,” Journal of Geotechnical Engineering, ASCE, Vol. 111, No. 6, June, pp. 750–771.
17.
Gorbunov‐Possadov, M. I., and Serebrajanyi, V. (1961), “Design of Structures Upon Elastic Foundations,” Proceedings of the 5th International Conference on Soil Mechanics and Foundation Engineering, held in Paris, France, Vol. I, pp. 643–648.
18.
Karasudhi, P., Keer, L. M., and Lee, S. L. (1968), “Vibratory Motion of a Body on an Elastic Half Plane,” Journal of Applied Mechanics, ASME, 35E, pp. 697–705.
19.
Kausel, E., and Roesset, J. M. (1975), “Dynamic Stiffness of Circular Foundations,” Journal of the Engineering Mechanics Division, ASCE, Vol. 101, No. EM6, pp. 771–785.
20.
Luco, J. E., and Westmann, R. A. (1971), “Dynamic Response of Circular Footings,” Journal of the Engineering Mechanics Division, ASCE, Vol. 97, No. EM5, pp. 1381–1395.
21.
Luco, J. E., and Westmann, R. A., (1972), “Dynamic Response of a Rigid Footing Bonded to an Elastic Half Space,” Journal of Applied Mechanics, ASME, June, pp. 527–534.
22.
Lysmer, J., and Richart, F. E., Jr. (1966), “Dynamic Response of Footing to Vertical Loading,” Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 92, No. SM1, pp. 65–91.
23.
Lysmer, J. (1980), “Foundation Vibrations with Soil Damping,” Proceedings, 2nd ASCE Conference on Civil Engineering and Nuclear Power, Knoxville, TN, Vol. II, Paper 10‐4, pp. 1–18.
24.
Massa, F. (1972), “Radiation of Sound,” American Institute of Physics Handbook, Third Edition, McGraw‐Hill Book Co., New York, pp. 3–139.
25.
Miller, G. F., and Pursey, H. (1954), “The Field and Radiation Impedance of Mechanical Radiators on the Free Surface of a Semi‐Infinite Isotropic Solid,” Proceedings of the Royal Society, London, A, Vol. 223, pp. 521–541.
26.
Miller, G. F., and Pursey, H. (1955), “On the Partition of Energy Between Elastic Waves in a Semi‐Infinite Solid,” Proceedings of the Royal Society, London, A, Vol. 233, pp. 55–69.
27.
Morse, P. M., and Ingard, K. U. (1968), Theoretical Acoustics, McGraw Hill Book Co., NY.
28.
Muskhelishvili, N. I. (1953), Some Basic Problems of the Mathematical Theory of Elasticity, Groningen, P. Noordhoff.
29.
O'Rourke, M. J., and Dobry, R. (1982), “Spring and Dashpot Coefficients for Machine Foundations on Piles,” Foundations for Equipment and Machinery, Publication SP‐78, American Concrete Institute, pp. 177–198.
30.
Richart, F. E., Jr., and Whitman, R. V. (1967), “Comparison of Footing Vibration Tests with Theory,” J. Soil Mechanics and Foundations Div., ASCE, Vol. 93, No. SM6, pp. 143–168.
31.
Richart, F. E., Jr., Hall, J. R., Jr., and Woods, R. D. (1970), Vibrations of Soils and Foundations, Prentice‐Hall International, Inc., NJ.
32.
Rücker, W. (1982), “Dynamic Behavior of Rigid Foundations of Arbitrary Shape on a Half Space,” Earthquake Engineering and Structural Dynamics, Vol. 10, pp. 675–690.
33.
Savidis, S. A. (1977), “Analytical Methods for the Computation of Wavefields,” Dynamic Methods in Soil and Rock Mechanics, 1, 225.
34.
Selvadurai, A. P. S. (1979), Elastic Analyses of Soil‐Foundation Interaction, Elsevier Scientific Publishing Co.
35.
Veletsos, A. J., and Wei, Y. T. (1971), “Lateral and Rocking Vibration of Footings,” J. Soil Mechanics and Foundation Div., ASCE, Vol. 97, No. SM9, pp. 1227–1249.
36.
Veletsos, A. J., and Nair, V. V. (1974), “Torsional Vibration of Viscoelastic Foundations,” J. Geotechnical Engineering Div., ASCE, Vol. 100, No. GT3, pp. 225–246.
37.
Veletsos, A. J., and Verbic, B. (1974), “Basic Response Functions for Elastic Foundations,” J. Engineering Mechanics Div., ASCE, Vol. 100, No. EM2, pp. 189–201.
38.
Wong, H. L., and Luco, J. E. (1976), “Dynamic Response of Rigid Foundations of Arbitrary Shape,” Earthquake Engineering and Structural Dynamics, Vol. 4, pp. 579–587.
39.
Whitman, R. V., and Richart, F. E., Jr. (1967), “Design Procedures for Dynamically Loaded Footings,” J. Soil Mechanics and Foundations Div., ASCE, Vol. 93, No. SM6, pp. 169–193.
Information & Authors
Information
Published In
Journal of Geotechnical Engineering
Volume 112 • Issue 2 • February 1986
Pages: 109 - 135
Copyright
Copyright © 1986 ASCE.
History
Published online: Feb 1, 1986
Published in print: Feb 1986
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.