Research on vibration of soils and foundations has yielded several fundamental methods for formulation of interaction problems. This paper is intended to survey the development of the current state-of-practice for design and analysis of dynamically loaded foundations. Extensive studies in this field utilize various linear mathematical models for interaction between foundations and different soil media. The effective analytical, numerical and experimental techniques and their methodologies which are well established for treating problems in dynamic soil-foundation interaction are outlined. Described techniques are categorized based upon formulation procedures and their applications. Some areas are indicated where further research is needed.

1.
Lamb
H.
, “
On the propagation of tremors over the surface of an elastic solid
.”
Phil. Trans. Roy. Soc.
,
203, A
,
1
42
,
1904
.
2.
Nakano
H.
, “
Some problems concerning the propagation of the disturbances in and on semi-infinite elastic solid
.”
Geophys. Mag. Tokyo
,
2
,
189
348
,
1930
.
3.
Barkan, D.D., “Dynamics of bases and foundations,” McGraw-Hill, 1962.
4.
Shekhter, O.Y., “Consideration of inertial properties of soil in the computations of vertical forced vibrations of massive foundation.” NII Symp., 12, Vibratasii, Osnovaniy i Fundementov, Moscow, 1948.
5.
Pekeris
C. L.
, “
The seismic buried pulse
.”
Proc. Nat. Acad. Sci., USA
,
41
,
629
639
,
1955
.
6.
Pekeris
C. L.
, “
The seismic surface pulse
.”
Proc. Nat. Acad. Sci., USA
,
41
,
469
480
,
1955
.
7.
Elorduy, J., Nieto, J.A. and Szekely, E.M., “Dynamic response of bases of arbitrary shape subjected to periodic vertical loading.” Proc. Int. Symp. on Wave Propagation and Dynamic Properties of Earth Materials, Albuquerque, University of New Mexico, 105–123, 1967.
8.
Heller, L.W. and Weiss, R.A., “Ground motion transmission from surface sources.” Proc. Int. Symp. on Wave Propagation and Dynamic Properties of Earth Materials, Albuquerque, University of New Mexico, 71–84, 1967.
9.
Chao
C. C.
, “
Dynamical response of an elastic half-space to tangential surface loadings
.”
J. Appl. Mech. ASME
,
27
,
559
567
,
1960
.
10.
Papadopulus
M.
, “
The use of singular integrals in wave propagation problems with application to the point source in a semi-infinite elastic medium
.
Proc. Roy. Soc., London, A
,
276
,
204
237
,
1963
.
11.
Aggarwal
H. R.
and
Ablow
C. M.
, “
Solution to a class of three-dimensional pulse propagation problems in an elastic half-space
.”
Int. J. Eng. Sci.
,
5
,
663
679
,
1967
.
12.
Johnson
L. R.
, “
Green’s function for Lamb’s problem
,”
Geophys. J. Roy. Astr. Soc.
37
,
99
131
,
1974
.
13.
Apsel, R.J., “Dynamic Green’s functions for layered media and applications to boundary value problems,” Ph.D. Dissertation, University of California, San Diego, USA, 1979.
14.
Kausel, E., “An explicit solution for the Green functions for dynamic loads in layered media,” MIT Research Report R 81–13, Cambridge, Massachusetts, USA, 1981.
15.
Davies, T.G., and Banerjee, P.K., “Elastodynamic Green’s function for half-space,” Report GT/1983/1, Department of Civil Engineering, State University of New York at Buffalo, USA, 1983.
16.
Kobayashi, S. and Nishimura, N., “Green’s tensors for elastic half-space - An application of boundary integral equation method,” Memories-Fac. Eng. Kyoto University, XLII 228–241, 1980.
17.
Banerjee
P. K.
and
Mamoon
S. M.
, “
A fundamental solution due to a periodic point force in the interior of an elastic half-space
,”
Int. J. Earthquake Eng. Struct. Dyn.
,
19
,
91
105
,
1990
.
18.
Hamidzadeh, H.R. “Dynamics of rigid foundations on the surface of an elastic half-space,” Ph.D. Dissertation, University of London, England, 1978.
19.
Hamidzadeh
H. R.
and
Chandler
D. E.
, “
Elastic waves on semi-infinite solid due to a harmonic vertical surface loading
.”
Proc. Canadian Cong. Appl. Mech.
,
1
,
370
371
,
1991
.
20.
Hamidzadeh, H.R. and A. C. J. Luo, “Surface Vibration on an Elastic Half-Space,” Symposium on “Vibrations of continuous Systems,” ASME International Mechanical Engineering Congress and Exposition, Vol. DE 107, pp. 39–44, 2000.
21.
Reissner, E., “Stationare, axialsymmetrische durch eine schuttelnde masseerregte schwingungen eines homogenen elastischen habraumes.” Ingenieur Archiv., 7, Part 6, 381–397, 1936.
22.
Reissner
E.
and
Sagoci
H. F.
, “
Forced torsional oscillations of an elastic half-space
.”
J. Appl. Phys.
,
15
,
652
662
,
1944
.
23.
Miller
G. F.
and
Pursey
H.
, “
The field and radiation impedance of mechanical radiators on the free surface of a semi-infinite isotropic solid
.”
Proc. Roy. Soc., London, Series A
,
223
,
521
541
,
1954
.
24.
Miller
G. F.
and
Pursey
H.
On the partition of energy between elastic waves in a semi-infinite solid
.”
Proc. Roy. Soc., London, Series A
,
233
,
55
69
,
1955
.
25.
Quinlan, P.M., “The elastic theory of soil dynamics.” Symp. on Dynamic Testing of Soils, ASTM STP, No. 156, 3–34, 1953.
26.
Sung, T.Y., “Vibration in semi-infinite solids due to periodic surface loadings.” Symp. on Dynamic Testing of Soils, ASTM, STP No. 156, 35–64, 1953.
27.
Arnold
R. N.
,
Bycroft
G. N.
and
Warburton
G. B.
, “
Forced vibrations of a body in an infinite elastic solid
.”
J. Appl. Mech.
,
22
,
391
400
,
1955
.
28.
Bycroft
G. N.
, “
Forced vibrations of circular plate on a semi-infinite elastic space and on an elastic stratum
.”
Phil. Trans. Roy. Soc., Series A
,
248
, No.
948
,
327
368
,
1956
.
29.
Bycroft, G.N., “Machine foundation vibration.” Proc. Inst. of Mech. Eng., 173, No. 18, 1959.
30.
Thomson, W.T. and Kobori, T., “Dynamical compliance of rectangular foundations on an elastic half-space.” J. Appl. Mech., Trans. ASME, 579–584, 1963.
31.
Kobori, T., Minai, R., Suzuki, T. and Kusakabe, K., “Dynamical ground compliance of rectangular foundations.” Proc. 16th Japan Nat. Congress Appl. Mech. Eng., 301–315, 1966.
32.
Kobori, T., Minai, R. and Suzuki, T., “Dynamic ground compliance of rectangular foundation on an elastic stratum.” Proc. 2nd Japan Nat. Symp. Earthquake Eng., 261–266, 1966.
33.
Kobori, T., Minai, R., Suzuki, T. and Kusakabe, K., “Dynamic ground compliance of rectangular foundation on a semi-infinite viscoelastic medium.” Annual Report, Disaster Prevention Research Institute of Kyoto University, No. 11A, 349–367, 1968.
34.
Kobori, T. and Suzuki, T., “Foundation vibrations on a viscoelastic multilayered medium.” Proc. 3rd Japan Earthquake Eng. Symp., Tokyo, 493–499, 1970.
35.
Kobori
T.
,
Minai
R.
and
Suzuki
T.
, “
The dynamical ground compliance of a rectangular foundation on a viscoelastic stratum
.”
Bull. Disaster Prevention Research Institute
, Kyoto University,
20
,
289
329
,
1971
.
36.
Harding
J. W.
and
Sneddon
I. N.
, “
The elastic stresses produced by the indentation of the plane surface of a semi-infinite solid by a rigid punch
.”
Proc. Camb. Phil. Soc.
,
41
,
16
26
,
1945
.
37.
Sneddon, I.N., “Fourier transform.” McGraw Hill, New York, 1959.
38.
Awojobi
A. O.
and
Grootenhuis
P.
, “
Vibration of rigid bodies on semi-infinite elastic media
.”
Proc. Roy. Soc.
,
287
, Series A,
27
63
,
1965
.
39.
Awojobi
A. O.
, “
Harmonic rocking of a rigid rectangular body on a semi-infinite elastic medium
.”
J. Appl. Mech., ASME
,
33
,
547
552
,
1966
.
40.
Awojobi
A. O.
, “
Torsional vibration of a rigid circular body on an infinite elastic stratum
.”
Int. J. Solids Structures
,
5
,
369
378
,
1969
.
41.
Awojobi
A. O.
, “
Vertical vibration of a rigid circular body and harmonic rocking of a rigid rectangular body on an elastic stratum
.”
Int. J. Solids Structures
,
8
,
759
774
,
1972
.
42.
Awojobi
A. O.
, “
Vertical vibration of a rigid circular foundation on Gibson soil
.”
Geotechnique
,
22
, No.
2
,
333
343
,
1972
.
43.
Titchmarsh, E.C., “Introduction to the theory of Fourier integrals.” Oxford, New York, 1937.
44.
Robertson
I. A.
, “
Forced vertical vibration of a rigid circular disc on a semi-infinite elastic solid
.”
Proc. Camb. Phil. Soc.
,
62, A
,
547
553
,
1966
.
45.
Robertson
I. A.
, “
On a proposed determination of the shear modules of an isotropic, elastic half-space by the forced torsional oscillations of a circular disc
.”
Appl. Sci. Res.
,
17
,
305
312
,
1967
.
46.
Gladwell
G. M. L.
, “
The calculation of mechanical impedances relating to an indenter vibrating on the surface of a semi-infinite elastic body
.”
J. Sound Vib.
,
8
,
215
228
,
1968
.
47.
Gladwell
G. M. L.
, “
Forced tangential and rotatory vibration of a rigid circular disc on a semi-infinite solid
.”
Int. J. Eng. Sci.
,
6
,
591
607
,
1968
.
48.
Gladwell
G. M. L.
, “
The forced torsional vibration of an elastic stratum
.”
Int. J. Eng. Sci.
,
7
,
1011
1024
,
1969
.
49.
Karasudhi
P.
,
Keer
L. M.
and
Lee
S. L.
, “
Vibratory motion of a body on an elastic half-space
.”
J. Appl. Mech.
,
35
,
697
705
,
1968
.
50.
Housner
G. W.
and
Castellani
A.
,
Discussion of “Comparison of footing vibration tests with theory,” by F.E. Richart, Jr. and R.V. Whitman
,
J. SMFD, ASCE
,
95
,
360
364
,
1969
.
51.
Richardson, J.D., “Forced vibrations of rigid bodies on a semi-infinite elastic medium.” Ph.D. Thesis, University of Nottingham, 1969.
52.
Luco
J. E.
and
Westmann
R. A.
, “
Dynamic response of circular footings
.”
J. EMD., ASCE
,
97
, pp.
1381
1395
,
1971
.
53.
Luco
J. E.
and
Westmann
R. A.
, “
Dynamic response of a rigid footing bonded to an elastic half-space
.”
J. Appl. Mech., ASME
,
39
,
527
534
,
1972
.
54.
Veletsos
A. S.
and
Wei
Y. T.
, “
Lateral and rocking vibration of footings
.”
J. SMFD, ASCE
,
97
,
1227
1248
,
1971
.
55.
Bycroft
G. N.
, “
Soil-structure interaction at higher frequency factors
.”
Int. J. of Earthquake Eng. and Struct. Dyn.
,
5
,
235
248
,
1977
.
56.
Veletsos
A. S.
and
Verbic
B.
, “
Basic response functions for elastic foundation
.”
J. EMD, ASCE
,
100
,
189
201
,
1974
.
57.
Clemmet, J.F., “Dynamic response of structures on elastic media.” Ph.D. Thesis, Nottingham University, 1974.
58.
Luco
J. E.
, “
Vibrations of a rigid disc on a layered visco-elastic medium
.”
Nuclear Eng. and Design
,
36
,
325
340
,
1976
.
59.
Tabiowo, P.H., “Vertical vibration of rigid bodies with rectangular bases on elastic media.” Ph.D. Thesis, University of Lagos, Nigeria, 1973.
60.
Awojobi
A. O.
and
Tabiowo
P. H.
, “
Vertical vibration of rigid bodies with rectangular bases on elastic media
.”
Int. J. of Earthquake Eng. and Struct. Dyn.
,
4
,
439
454
,
1976
.
61.
Wong
H. L.
and
Luco
J. E.
, “
Dynamic response of rigid foundations of arbitrary shape
.”
Int. J. Earthquake Eng. Struct. Dyn.
4
,
579
587
,
1976
.
62.
Wong, H.L. and Luco, J.E., “Table of impedance functions and input motions for rectangular foundations,” Report CE 78–15, Department of Civil Engineering, USC, Los Angeles, CA, 1978.
63.
Hamidzadeh
H. R.
and
Grootenhuis
G.
, “
The dynamics of a rigid foundation on the surface of an elastic half-space
,”
Int. J. Earthquake Eng. Struct. Dyn.
,
9
,
501
515
,
1981
.
64.
Rucker
W.
, “
Dynamic behavior of rigid foundations of arbitrary shape on a half-space
,”
Int. J. Earthquake Eng. Struct. Dyn.
,
10
,
675–
675–
,
1982
.
65.
Chow
Y. K.
, “
Vertical vibration of three-dimensional rigid foundations on layered media
,”
Int. J. Earthquake Eng. Struct. Dyn.
,
15
,
585
594
,
1987
.
66.
Triantafyllidis
T.
, “
Dynamic stiffness of rigid rectangular foundations on the half-space
,”
Int. J. Earthquake Eng. Struct. Dyn.
,
14
,
391
411
,
1986
.
67.
Hsieh
T. K.
, “
Foundation vibration
.”
Proc. Inst. Civ. Eng.
,
22
,
211
226
,
1962
.
68.
Lysmer, J., “Vertical motion of rigid footings.” Dept. of Civil Eng., University of Michigan, Report to WES Contract Report, No. 3.115, 1965.
69.
Lysmer
J.
and
Richart
F. E.
, “
Dynamic response of footings to vertical loading
.”
J. SMFD, Proc. ASCE
,
92
,
65
91
,
1966
.
70.
Weissmann
G. F.
, “
A mathematical model of a vibrating soil-foundation system
.”
The Bell System Tech. J.
,
45
, No.
1
,
177
228
,
1966
.
71.
Whitman
R. V.
and
Richart
F. E.
, “
Design procedures for dynamic loaded foundations
.”
J. SMFD, ASCE
,
93
,
169
193
,
1967
.
72.
Hall, J.R. Jr., “Coupled rocking and sliding oscillations of rigid circular footings.” Proc. Int. Symp. on Wave Propagation and Dynamic Properties of Earth Materials, Albuquerque, University of New Mexico, 139–149, 1967.
73.
Roesset
J. M.
,
Whitman
R. V.
and
Dobry
R.
, “
Model analysis for structures with foundation interaction
.”
J. of STD, ASCE
,
99
,
399
416
,
1973
.
74.
Oner, M. and Janbu, N., “Dynamic soil-structure interaction in offshore storage tank.” Proc. Int. Conf. on Soil Mechanics and Found. Eng., March, Istanbul, 1975.
75.
Hall, J.R. Jr., Kissenpfenning, J.F. and Rizzo, P.C., “Continuum and finite element analyses for soil-structure interaction analysis of deeply embedded foundations.” 3rd Int. Conf. on Structural Mechanics in Reactor Technology, Vol. 4, Part K, Paper K 2/4, 1975.
76.
Veletsos, A.S., “Dynamics of structure-foundation systems.” Proc. Symp. on Structural and Geotechnical Mechanics, Honoring N.M. Newmark, University of Illinois, 333–361, 1975.
77.
Wolf, J.P., Dynamic Soil-Structure Interaction, Prentice-Hall, Englewood Cliffs, NJ, 1985.
78.
Wolf
J. P.
and
Somaini
D. R.
, “
Approximate dynamic model of embedded foundation in time domain
,”
Int. J. Earthquake Eng. Struct. Dyn.
,
14
,
683
703
,
1986
.
79.
Dobry
R.
and
Gazetas
G.
, “
Dynamic response of arbitrary shaped foundation
,”
J. Geotech. Eng., ASCE
,
112
,
109
135
,
1986
.
80.
Dobry
R.
,
Gazetas
G.
, and
Strohoe
K. H.
, “
Dynamic response of arbitrary shaped foundation II
,”
J. Geotech. Eng., ASCE
,
112
,
136
154
,
1986
.
81.
Terzaghi, K., “Theoretical soil mechanics.” John Wiley & Sons Inc., New York, 1943.
82.
Terzaghi
K.
, “
Evaluation of coefficients of Subgrade Reaction
.”
Geotechnique
,
5
,
297
326
,
1955
.
83.
Girard
J.
, “
Vibrations des massifs sur supports elastiques
.”
Ann. Inst. Tech., Batiment et Trayaux Publics
23–24
,
407
425
,
1968
.
84.
Duns, C.S. and Butterfield, R., “The dynamic analysis of soil-structure system using the finite element method.” Proc. Int. Symp. on Wave Propagation and Dynamic Properties of Earth Materials, Albuquerque, University of New Mexico, 615–631, 1967.
85.
Lysmer
J.
and
Kuhlemeyer
R. L.
, “
Closure to finite dynamic model for infinite media
.”
J. of EMD, ASCE
,
97
,
129
131
,
1971
.
86.
Seed, H.B., Lysmer, J. and Whitman, R.V., “Soil structure interaction effects on the design of nuclear power plants.” Proc. Symp. on Structural and Geotechnical Mechanics, Honoring N.M. Newmark, University of Illinois, 220–241, 1975.
87.
Day
S. M.
and
Frazier
G. A.
, “
Seismic response of hemispherical foundation
,”
J. Eng. Mech. Div. ASCE
,
105
,
29
41
,
1979
.
88.
Bettess
P.
and
Zienkiewicz
O. C.
, “
Diffraction and refraction of surface waves using finite and infinite elements
,”
Int. J. Numer. Methods Eng.
,
11
,
1271
1290
,
1977
.
89.
Roesset
J. M.
and
Ettouney
M. M.
, “
Transmitting boundaries: a comparison
,”
Int. J. Numer. Anal. Methods Geomech.
1
,
151
176
,
1977
.
90.
Kausel
E.
and
Tassoulas
J. L.
, “
Transmitting boundaries: a closed form comparison
,”
Bull. Seism. Soc. Am.
,
71
,
143
159
,
1981
.
91.
Chuhan
Z.
and
Chongbin
Z.
, “
Coupling method of finite and infinite elements for strip foundation wave problems
,”
Int. J. Earthquake Eng. Struct. Dyn.
,
15
,
839
851
,
1987
.
92.
Dominguez, J., “Dynamic stiffness of rectangular foundation,” Report R78-20, Department of Civil Engineering, M.I.T., 1978.
93.
Dominguez, J. and Roesset, J.M., “Dynamic stiffness of rectangular foundations,” Report R78-20, Department of Civil Engineering, MIT, Cambridge, MA, 1978.
94.
Karabalis
D. I.
and
Beskos
D. E.
, “
Dynamic response of 3-D rigid surface foundations by time domain boundary element
,”
Int. J. Earthquake Eng. Struct. Dyn.
,
12
,
73
93
,
1984
.
95.
Spyrakos
C. C.
and
Beskos
D. E.
, “
Dynamic response of rigid strip foundation by time domain boundary element method
,”
Int. J. Numer. Method. Eng.
,
23
,
1547
1565
,
1986
.
96.
Spyrakos
C. C.
and
Beskos
D. E.
, “
Dynamic response of flexible strip foundation by boundary and finite elements
,”
Soil Dyn. Earthquake Eng.
,
5
,
84
96
,
1986
.
97.
Luco
J. E.
and
Apsel
R. J.
, “
On the Green’s function for a layered half space parts I & II
,
Bull. Seism. Soc. Am.
73
,
909
929
,
1983
.
98.
Chapel, F. and Tsakalidis, C., “Computation of the Green’s functions of elastodynamics for a layered half-space through a Hankel transform - applications to foundation vibration and seismology,” Proc. Numerical Methods in Geomechanics, Nagoya, Japan, 1311–1318, 1985.
99.
Kausel
E.
and
Roesset
J. M.
, “
Dynamic stiffness of circular foundations
,”
J. Eng. Mech. Div., ASCE
,
111
,
771
785
,
1975
.
100.
Israil
A. S. M.
and
Ahmad
S.
, “
Dynamic vertical compliance of strip foundations in layered soils
,”
Int. J. Earthquake Eng. Struct. Dyn.
,
18
,
933
950
,
1989
.
101.
Richart
F. E.
and
Whitman
R. V.
, “
Comparison of footing vibration tests with theory
.”
J. SMFD, ASCE
, Vol.
93
,
143
168
,
1967
.
102.
Fry, Z.B., “Development and evaluation of soil bearing capacity, foundation of structures.” WES, Tech. Rep. No. 3 - 632, 1963.
103.
Ratay
R. T.
, “
Sliding-rocking vibration of body on elastic medium
.”
J. SMFD, ASCE
,
97
,
177
192
,
1971
.
104.
Beredugo
J. O.
and
Novak
M.
, “
Coupled horizontal and rocking vibration of embedded footings
.”
Canadian Geotechnical J.
,
9
, No.
4
.,
477
497
,
1972
.
105.
Krizek
R. O.
,
Gupta
D. C.
and
Parmelee
R. A.
, “
Coupled sliding and rocking of embedded foundations
.”
J. SMFD, ASCE
, Vol.
98
,
1347
1358
,
1972
.
106.
Wolf, J.P., “Approximate soil-structure interaction with separation of base mat from soil lifting-off.” 3rd Int. Conf. On “Structural Mechanics in Reactor Technology,” 4, park K, pp. K 3/6, 1975.
107.
Hamidzadeh, H.R. and Minor, G.R., “Horizontal and rocking vibration of foundation on an elastic half-space.” Proc. Canadian Cong. Appl. Mech., will be published, 1993.
108.
Iljitchov, V.A., “Towards the soil transmission of vibrations from one foundation to another.” Proc. Int. Symp. on Wave Propagation and Dynamic Properties of Earth Materials, Albuquerque, University of New Mexico, 641–654, 1967.
109.
Richardson
J. D.
,
Webster
J. J.
,
Warburton
G. B.
, “
The response on the surface of an elastic half-space near to a harmonically excited mass
.”
J. Sound Vib.
,
14
,
307
316
,
1971
.
110.
Warburton
G. B.
,
Richardson
J. D.
and
Webster
J. J.
, “
Forced vibrations of two masses on an elastic half-space
.”
J. Appl. Mech., ASME
,
38
,
148
156
,
1971
.
111.
Warburton
G. B.
,
Richardson
J. D.
and
Webster
J. J.
, “
Harmonic response of masses on an elastic half-space
.”
J. EI, ASME
,
94
,
193
200
,
1972
.
112.
Lee, T.H. and Wesley, D.A., “Soil-structure interaction of nuclear reactor structure considering through-soil coupling between adjacent structures.” Nuclear Eng. and Design, Vol. 24, 1973.
113.
MacCalden, P.B. and Matthiesen, R.B., “Coupled response of two foundations.” 5th World Conf. on Earthquake Eng., Rome, 1913–1922, 1973.
114.
Snyder, M.D., Shaw, D.E. and Hall, J.R. Jr., “Structure-soil-structure interaction of nuclear structures.” 3rd Int. Conf. on “Structural Mechanics in Reactor Technology,” Vol. 4, Park K, K2/9, 1975.
115.
Awojobi, A.O., “Vibrations of rigid bodies on elastic media,” Ph.D. Thesis, University of London, 1964.
116.
Jones
R.
, “
In-situ measurement of the dynamic properties of soil by vibration method
.”
Geotechnique
,
8
, No.
1
,
1
21
,
1958
.
117.
Jones, R., “Interpretation of surface vibrations measurements.” Proc. Symp. Vibration Testing of Road and Runways, Koninklijke/Shell-Laboratorium, Amsterdam, 1959.
118.
Maxwell, A.A. and Fry, Z.B., “A procedure for determining elastic modulii of in-situ soils by dynamic technique.” Proc. Int. Symp. on Wave Propagation and Dynamic Properties of Earth Materials, Albuquerque, University of New Mexico, 913–920, 1967.
119.
Stokoe
K. H.
and
Richart
F. E.
, “
Dynamic response of embedded machine foundations
.”
J. GTD, ASCE
, Vol.
100
, No.
GT4
, April, Proc. Paper 10499,
427
447
,
1974
.
120.
Beeston
H. E.
and
McEvilly
T. V.
, “
Shear wave velocities from down hole measurements
.”
Int. J. Earthquake Eng. and Struct. Dyn.
,
5
,
181
190
,
1977
.
121.
Grootenhuis, P. and Awojobi, A.O., “The in-situ measurement of the dynamic properties of soils.” Proc. Symp. Vibration i Civ. Eng., Inst. Civil Eng., 181–187, 1965.
122.
Hamidzadeh, H. R. and Dehghani, M. “The Measurement of the Dynamic Properties for an Elastic Half-Space Medium,” Proceedings of 2005 IDETC/CIE, No. DETC2005-85600, 2005.
123.
Hardin
B. O.
and
Drnevich
V. P.
, “
Shear modulus and damping in soils. I. Measurement and parameter effects
.”
J. SMFD, ASCE
,
98
,
603
624
,
1972
.
124.
Hardin
B. O.
and
Drnevich
V. P.
, “
Shear modulus and damping in soils. II. Design equations and curves
.”
J. SMFD, ASCE
,
98
,
667
692
,
1972
.
125.
Cunny
R. W.
and
Fry
Z. B.
, “
Vibratory in situ and laboratory soil modules compared
.”
J. SMFD, ASCE
,
99
,
1055
1076
,
1973
.
126.
Lawrence, F.V. Jr., “Ultrasonic shear wave velocities in sand and clay.” Rep. R65–05., WES, Dept. Civil Eng., Massachusetts Inst. of Technology, Cambridge, Mass., 1965.
127.
Theirs
G. R.
and
Seed
H. B.
, “
Cyclic stress-strain characteristics of clay
.”
J. SMFD, ASCE
,
94
,
555
569
,
1968
.
128.
Kovacs
W. D.
,
Seed
H. B.
and
Chan
C. K.
, “
Dynamic modules and damping ratios for a soft clay
.”
J. SMFD, ASCE
,
97
,
59
75
,
1971
.
129.
Kanai
K.
and
Yoshizawa
S.
, “
On the period and the damping of vibration in actual buildings
.”
BERI
,
39
,
477
477
,
1961
.
130.
Eastwood
W.
, “
Vibrations in Foundations
.”
Struct. Eng.
,
82
,
82
98
,
1953
.
131.
Chae, Y.S., “The material constants of soils as determined from dynamic testing.” Proc. Int. Symp. on Wave Propagation and Dynamic Properties of Earth Materials, Albuquerque, Univ. of New Mexico, 759–771, 1967.
132.
Hamidzadeh, H.R., “Dynamics of foundation on a simulated elastic half-space.” Proc. Intl. Symp. on Geotechnical Engineering of Soft Soils, Mexico City, 1, 339–345, 1987.
133.
Luco, J.E., Trifunac, M.D., and Wong, H.L, “On the apparent changes in dynamic behavior of a nine-story reinforced concrete building,” Bull. Seism. Soc. Am. 77, 1987.
134.
Luco
J. E.
,
Trifunac
M. D.
, and
Wong
H. L.
, “
Isolation of soil-structure interaction effects by full-scale forced vibration tests
,”
Int. J. Earthquake Eng. Struct. Dyn.
,
16
,
1
21
,
1988
.
135.
Wong
H. L.
,
Luco
J. E.
, and
Trifunac
M. D.
, “
Contact stresses and ground motion generated by soil-structure interaction
,”
Int. J. Earthquake Eng. Struct. Dyn.
,
5
,
67
79
,
1977
.
This content is only available via PDF.
You do not currently have access to this content.