Advertisement

On Analytical Methods for Vibrations of Soils and Foundations

  • H. R. Hamidzadeh
Conference paper

Abstract

Research on dynamics 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.

Keywords

Simultaneous Motion Dual Integral Equation Strip Foundation Circular Footing Foundation Block 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Lamb H (1904) On the propagation of tremors over the surface of an elastic solid. Phil Trans Roy Soc 203(A):1–42Google Scholar
  2. 2.
    Nakano H (1930) Some problems concerning the propagation of the disturbances in and on semi-infinite elastic solid. Geophys Mag Tokyo 2:189–348Google Scholar
  3. 3.
    Barkan DD (1962) Dynamics of bases and foundations. McGraw-Hill, New YorkGoogle Scholar
  4. 4.
    Shekhter OY (1948) Consideration of inertial properties of soil in the computations of vertical forced vibrations of massive foundation. NII Symposium, 12, Vibratasii, Osnovaniy i Fundementov, MoscowGoogle Scholar
  5. 5.
    Pekeris CL (1955) The seismic buried pulse. Proc Nat Acad Sci USA 41:629–639MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Pekeris CL (1955) The seismic surface pulse. Proc Nat Acad Sci USA 41:469–480MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Elorduy J, Nieto JA, Szekely EM (1967) Dynamic response of bases of arbitrary shape subjected to periodic vertical loading. Proceedings of the international symposium on wave propagation and dynamic properties of earth materials, Albuquerque, University of New Mexico, pp 105–123Google Scholar
  8. 8.
    Heller LW, Weiss RA (1967) Ground motion transmission from surface sources. Proceedings of the international symposium on wave propagation and dynamic properties of earth materials, Albuquerque, University of New Mexico, pp 71–84Google Scholar
  9. 9.
    Chao CC (1960) Dynamical response of an elastic half-space to tangential surface loadings. J Appl Mech ASME 27:559–567CrossRefMATHGoogle Scholar
  10. 10.
    Papadopulus M (1963) 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 276:204–237CrossRefGoogle Scholar
  11. 11.
    Aggarwal HR, Ablow CM (1967) Solution to a class of three-dimensional pulse propagation problems in an elastic half-space. Int J Eng Sci 5:663–679CrossRefMATHGoogle Scholar
  12. 12.
    Johnson LR (1974) Green’s function for Lamb’s problem. Geophys J Roy Astr Soc 37:99–131CrossRefMATHGoogle Scholar
  13. 13.
    Apsel RJ (1979) Dynamic Green’s functions for layered media and applications to boundary value problems, Ph.D. Dissertation, University of California, San Diego, CAGoogle Scholar
  14. 14.
    Kausel E (1981) An explicit solution for the Green functions for dynamic loads in layered media, MIT Research Report R 81–13, Cambridge, MAGoogle Scholar
  15. 15.
    Davies TG, Banerjee PK (1983) Elastodynamic Green’s function for half-space, Report GT/1983/1, Department of Civil Engineering, State University of New York at BuffaloGoogle Scholar
  16. 16.
    Kobayashi S, Nishimura N (1980) Green’s tensors for elastic half-space – an application of boundary integral equation method. Memories-Fac Eng Kyoto Univ XLII:228–241Google Scholar
  17. 17.
    Banerjee PK, Mamoon SM (1990) A fundamental solution due to a periodic point force in the interior of an elastic half-space. Int J Earthquake Eng Struct Dyn 19:91–105CrossRefGoogle Scholar
  18. 18.
    Hamidzadeh HR (1978) Dynamics of rigid foundations on the surface of an elastic half-space, Ph.D. Dissertation, University of London, EnglandGoogle Scholar
  19. 19.
    Hamidzadeh HR (1986) Surface vibration of an elastic half-space. Proc SECTAM XIII 2:637–642Google Scholar
  20. 20.
    Hamidzadeh HR, Chandler DE (1991) Elastic waves on semi-infinite solid due to a harmonic vertical surface loading. Proc Canadian Cong Appl Mech 1:370–371Google Scholar
  21. 21.
    Reissner E (1936) Stationare, axialsymmetrische durch eine schuttelnde masseerregte schwingungen eines homogenen elastischen habraumes. Ingenieur Archiv 7(6):381–397CrossRefMATHGoogle Scholar
  22. 22.
    Reissner E, Sagoci HF (1944) Forced torsional oscillations of an elastic half-space. J Appl Phys 15:652–662MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Miller GF, Pursey H (1954) The field and radiation impedance of mechanical radiators on the free surface of a semi-infinite isotropic solid. Proc R Soc Lond A 223:521–541MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Miller GF, Pursey H (1955) On the partition of energy between elastic waves in a semi-infinite solid. Proc R Soc Lond A 233:55–69CrossRefMATHGoogle Scholar
  25. 25.
    Quinlan PM (1953) The elastic theory of soil dynamics. Symp Dyn Test Soils ASTM STP 156:3–34Google Scholar
  26. 26.
    Sung TY (1953) Vibration in semi-infinite solids due to periodic surface loadings. Symp Dyn Test Soils ASTM STP 156:35–64Google Scholar
  27. 27.
    Arnold RN, Bycroft GN, Warburton GB (1955) Forced vibrations of a body in an infinite elastic solid. J Appl Mech 22:391–400MATHGoogle Scholar
  28. 28.
    Bycroft GN (1956) Forced vibrations of circular plate on a semi-infinite elastic space and on an elastic stratum. Phil Trans R Soc A, 248(948):327–368MathSciNetCrossRefMATHGoogle Scholar
  29. 29.
    Bycroft GN (1959) Machine foundation vibration. Proc Inst Mech Eng 173:18Google Scholar
  30. 30.
    Thomson WT, Kobori T (1963) Dynamic compliance of rectangular foundations on an elastic half-space. J Appl Mech Trans ASME 30:579–584CrossRefGoogle Scholar
  31. 31.
    Kobori T, Minai R, Suzuki T, Kusakabe K (1966) Dynamical ground compliance of rectangular foundations. In: Proceedings of 16th Japan national congress on applied mechanical engineering, pp 301–315Google Scholar
  32. 32.
    Kobori T, Minai R, Suzuki T (1966) Dynamic ground compliance of rectangular foundation on an elastic stratum. In: Proceedings of 2nd Japan national symposium on earthquake engineering, pp 261–266Google Scholar
  33. 33.
    Kobori T, Minai R, Suzuki T, Kusakabe K (1968) Dynamic ground compliance of rectangular foundation on a semi-infinite viscoelastic medium. Annual Report, Disaster Prevention Research Institute of Kyoto University, vol 11A. 349–367Google Scholar
  34. 34.
    Kobori T, Suzuki T (1970) Foundation vibrations on a viscoelastic multilayered medium. In: Proceedings of the 3rd Japan earthquake engineering symposium, Tokyo, pp 493–499Google Scholar
  35. 35.
    Kobori T, Minai R, Suzuki T (1971) The dynamical ground compliance of a rectangular foundation on a viscoelastic stratum. Bull Disas Prev Res Inst Kyoto Univ 20:289–329Google Scholar
  36. 36.
    Harding JW, Sneddon IN (1945) The elastic stresses produced by the indentation of the plane surface of a semi-infinite solid by a rigid punch. Proc Camb Phil Soc 41:16–26MathSciNetCrossRefMATHGoogle Scholar
  37. 37.
    Sneddon IN (1959) Fourier transform. McGraw Hill, New YorkGoogle Scholar
  38. 38.
    Awojobi AO, Grootenhuis P (1965) Vibration of rigid bodies on semi-infinite elastic media. Proc R Soc A 287:27–63MathSciNetCrossRefGoogle Scholar
  39. 39.
    Awojobi AO (1966) Harmonic rocking of a rigid rectangular body on a semi-infinite elastic medium. J Appl Mech ASME 33:547–552CrossRefMATHGoogle Scholar
  40. 40.
    Awojobi AO (1969) Torsional vibration of a rigid circular body on an infinite elastic stratum. Int J Solids Struct 5:369–378CrossRefMATHGoogle Scholar
  41. 41.
    Awojobi AO (1972) Vertical vibration of a rigid circular body and harmonic rocking of a rigid rectangular body on an elastic stratum. Int J Solids Struct 8:759–774CrossRefMATHGoogle Scholar
  42. 42.
    Awojobi AO (1972) Vertical vibration of a rigid circular foundation on Gibson soil. Geotechnique 22(2):333–343CrossRefGoogle Scholar
  43. 43.
    Titchmarsh EC (1937) Introduction to the theory of Fourier integrals. Oxford, New YorkGoogle Scholar
  44. 44.
    Robertson IA (1966) Forced vertical vibration of a rigid circular disc on a semi-infinite elastic solid. Proc Camb Philos Soc 62A:547–553CrossRefGoogle Scholar
  45. 45.
    Robertson IA (1967) 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 17:305–312CrossRefGoogle Scholar
  46. 46.
    Gladwell GML (1968) The calculation of mechanical impedances relating to an indenter vibrating on the surface of a semi-infinite elastic body. J Sound Vib 8:215–228CrossRefGoogle Scholar
  47. 47.
    Gladwell GML (1968) Forced tangential and rotatory vibration of a rigid circular disc on a semi-infinite solid. Int J Eng Sci 6:591–607CrossRefMATHGoogle Scholar
  48. 48.
    Gladwell GML (1969) The forced torsional vibration of an elastic stratum. Int J Eng Sci 7:1011–1024CrossRefMATHGoogle Scholar
  49. 49.
    Karasudhi P, Keer LM, Lee SL (1968) Vibratory motion of a body on an elastic half-space. J Appl Mech 35:697–705CrossRefMATHGoogle Scholar
  50. 50.
    Housner GW, Castellani A (1969) Discussion of “Comparison of footing vibration tests with theory” by F.E. Richart, Jr. and R.V. Whitman. J SMFD ASCE 95:360–364Google Scholar
  51. 51.
    Richardson JD (1969) Forced vibrations of rigid bodies on a semi-infinite elastic medium. Ph.D. Thesis, University of NottinghamGoogle Scholar
  52. 52.
    Luco JE, Westmann RA (1971) Dynamic response of circular footings. J EMD ASCE 97:1381–1395Google Scholar
  53. 53.
    Luco JE, Westmann RA (1972) Dynamic response of a rigid footing bonded to an elastic half-space. J Appl Mech ASME 39:527–534CrossRefGoogle Scholar
  54. 54.
    Veletsos AS, Wei YT (1971) Lateral and rocking vibration of footings. J SMFD ASCE 97:1227–1248Google Scholar
  55. 55.
    Bycroft GN (1977) Soil-structure interaction at higher frequency factors. Int J Earthquake Eng Struct Dyn 5:235–248CrossRefGoogle Scholar
  56. 56.
    Veletsos AS, Verbic B (1974) Basic response functions for elastic foundation. J EMD ASCE 100:189–201Google Scholar
  57. 57.
    Clemmet JF (1974) Dynamic response of structures on elastic media. Ph.D. Thesis, Nottingham UniversityGoogle Scholar
  58. 58.
    Luco JE (1976) Vibrations of a rigid disc on a layered visco-elastic medium. Nuclear Eng Des 36:325–340CrossRefGoogle Scholar
  59. 59.
    Tabiowo PH (1973) Vertical vibration of rigid bodies with rectangular bases on elastic media. Ph.D. Thesis, University of Lagos, NigeriaGoogle Scholar
  60. 60.
    Awojobi AO, Tabiowo PH (1976) Vertical vibration of rigid bodies with rectangular bases on elastic media. Int J Earthquake Eng Struct Dyn 4:439–454CrossRefGoogle Scholar
  61. 61.
    Wong HL, Luco JE (1976) Dynamic response of rigid foundations of arbitrary shape. Int J Earthquake Eng Struct Dyn 4:579–587CrossRefGoogle Scholar
  62. 62.
    Wong HL, Luco JE (1978) Table of impedance functions and input motions for rectangular foundations, Report CE 78–15, Department of Civil Engineering, USC, Los Angeles, CAGoogle Scholar
  63. 63.
    Hamidzadeh HR, Grootenhuis G (1981) The dynamics of a rigid foundation on the surface of an elastic half-space. Int J Earthquake Eng Struct Dyn 9:501–515CrossRefGoogle Scholar
  64. 64.
    Rucker W (1982) Dynamic behavior of rigid foundations of arbitrary shape on a half-space. Int J Earthquake Eng Struct Dyn 10:675–690CrossRefGoogle Scholar
  65. 65.
    Chow YK (1987) Vertical vibration of three-dimensional rigid foundations on layered media. Int J Earthquake Eng Struct Dyn 15:585–594CrossRefGoogle Scholar
  66. 66.
    Triantafyllidis T (1986) Dynamic stiffness of rigid rectangular foundations on the half-space. Int J Earthquake Eng Struct Dyn 14:391–411CrossRefGoogle Scholar
  67. 67.
    Hsieh TK (1962) Foundation vibration. Proc Inst Civ Eng 22:211–226CrossRefGoogle Scholar
  68. 68.
    Lysmer J (1965) Vertical motion of rigid footings. Department of Civil Engineering, University of Michigan, Report to WES Contract Report, vol 3. p 115Google Scholar
  69. 69.
    Lysmer J, Richart FE Jr (1966) Dynamic response of footings to vertical loading. J SMFD Proc ASCE 92:65–91Google Scholar
  70. 70.
    Weissmann GF (1966) A mathematical model of a vibrating soil-foundation system. Bell Syst Tech J 45(1):177–228Google Scholar
  71. 71.
    Whitman RV, Richart FE (1967) Design procedures for dynamic loaded foundations. J SMFD ASCE 93:169–193Google Scholar
  72. 72.
    Hall JR Jr (1967) Coupled rocking and sliding oscillations of rigid circular footings. In: Proceedings of International Symposium on Wave Propagation and Dynamic Properties of Earth Materials, University of New Mexico, Albuquerque, NM, pp 139–149Google Scholar
  73. 73.
    Roesset JM, Whitman RV, Dobry R (1973) Model analysis for structures with foundation interaction. J STD ASCE 99:399–416Google Scholar
  74. 74.
    Oner M, Janbu N (1975) Dynamic soil-structure interaction in offshore storage tank. In: Proceedings of the international conference on soil mechanics and foundation engineering, Istanbul, March 1975Google Scholar
  75. 75.
    Hall JR Jr, Kissenpfenning JF, Rizzo PC (1975) Continuum and finite element analyses for soil–structure interaction analysis of deeply embedded foundations. In: 3rd international conference on structural mechanics in reactor technology, vol 4. Part K, Paper K 2/4Google Scholar
  76. 76.
    Veletsos AS (1975) Dynamics of structure-foundation systems. In: Proceedings of the symposium on structural and geotechnical mechanics, Honoring Newmark NM, University of Illinois, pp 333–361Google Scholar
  77. 77.
    Wolf JP (1985) Dynamic soil–structure interaction, Prentice-Hall, Englewood Cliffs, NJGoogle Scholar
  78. 78.
    Wolf JP, Somaini DR (1986) Approximate dynamic model of embedded foundation in time domain. Int J Earthquake Eng Struct Dyn 14:683–703CrossRefGoogle Scholar
  79. 79.
    Dobry R, Gazetas G (1986) Dynamic response of arbitrary shaped foundation. J Geotech Eng ASCE 112:109–135CrossRefGoogle Scholar
  80. 80.
    Dobry R, Gazetas G, Strohoe KH (1986) Dynamic response of arbitrary shaped foundation II. J Geotech Eng ASCE 112:136–154CrossRefGoogle Scholar
  81. 81.
    Terzaghi K (1943) Theoretical soil mechanics. Wiley, New YorkCrossRefGoogle Scholar
  82. 82.
    Terzaghi K (1955) Evaluation of coefficients of subgrade reaction. Geotechnique 5:297–326CrossRefGoogle Scholar
  83. 83.
    Girard J (1968) Vibrations des massifs sur supports elastiques. Ann Inst Tech Batiment et Trayaux Publics 23–24:407–425Google Scholar
  84. 84.
    Duns CS, Butterfield R (1967) The dynamic analysis of soil–structure system using the finite element method. In: Proceedings of the international symposium on wave propagation and dynamic properties of earth materials, University of New Mexico, Albuquerque, NM, pp 615–631Google Scholar
  85. 85.
    Lysmer J, Kuhlemeyer RL (1971) Closure to finite dynamic model for infinite media. J EMD ASCE 97:129–131Google Scholar
  86. 86.
    Seed HB, Lysmer J, Whitman RV (1975) Soil structure interaction effects on the design of nuclear power plants. In: Proceedings of the symposium on structural and geotechnical mechanics, Honoring N.M. Newmark, University of Illinois, 220–241Google Scholar
  87. 87.
    Day SM, Frazier GA (1979) Seismic response of hemispherical foundation. J Eng Mech Div ASCE 105:29–41Google Scholar
  88. 88.
    Bettess P, Zienkiewicz OC (1977) Diffraction and refraction of surface waves using finite and infinite elements. Int J Numer Methods Eng 11:1271–1290MathSciNetCrossRefMATHGoogle Scholar
  89. 89.
    Roesset JM, Ettouney MM (1977) Transmitting boundaries: a comparison. Int J Numer Anal Methods Geomech 1:151–176CrossRefGoogle Scholar
  90. 90.
    Kausel E, Tassoulas JL (1981) Transmitting boundaries: a closed form comparison. Bull Seism Soc Am 71:143–159MathSciNetGoogle Scholar
  91. 91.
    Chuhan Z, Chongbin Z (1987) Coupling method of finite and infinite elements for strip foundation wave problems. Int J Earthquake Eng Struct Dyn 15:839–851CrossRefGoogle Scholar
  92. 92.
    Dominguez J (1978) Dynamic stiffness of rectangular foundation, Report R78–20, Department of Civil Engineering, MIT, Cambridge, MAGoogle Scholar
  93. 93.
    Dominguez J, Roesset JM (1978) Dynamic stiffness of rectangular foundations, Report R78–20, Department of Civil Engineering, MIT, Cambridge, MAGoogle Scholar
  94. 94.
    Karabalis DI, Beskos DE (1984) Dynamic response of 3-D rigid surface foundations by time domain boundary element, Int J Earthquake Eng Struct Dyn 12:73–93CrossRefGoogle Scholar
  95. 95.
    Spyrakos CC, Beskos DE (1986) Dynamic response of rigid strip foundation by time domain boundary element method. Int J Numer Method Eng 23:1547–1565CrossRefMATHGoogle Scholar
  96. 96.
    Spyrakos CC, Beskos DE (1986) Dynamic response of flexible strip foundation by boundary and finite elements. Soil Dyn Earthquake Eng 5:84–96CrossRefGoogle Scholar
  97. 97.
    Luco JE, Apsel RJ (1983) On the Green’s function for a layered half space parts I & II. Bull Seism Soc Am 73:909–929, 931–951Google Scholar
  98. 98.
    Chapel F, Tsakalidis C (1985) Computation of the Green’s functions of elastodynamics for a layered half-space through a Hankel transform – applications to foundation vibration and seismology. In: Proceedings of the numerical methods in geomechanics, Nagoya, Japan, pp 1311–1318Google Scholar
  99. 99.
    Kausel E, Roesset JM (1975) Dynamic stiffness of circular foundations. J Eng Mech Div ASCE 111:771–785Google Scholar
  100. 100.
    Israil ASM, Ahmad S (1989) Dynamic vertical compliance of strip foundations in layered soils. Int J Earthquake Eng Struct Dyn 18:933–950CrossRefGoogle Scholar
  101. 101.
    Richart FE Jr, Whitman RV (1967) Comparison of footing vibration test with theory. J SMFD ASCE 93:143–168Google Scholar
  102. 102.
    Fry ZB (1963) Development and evaluation of soil bearing capacity, foundation of structures. WES Technical Report No. 3, 632Google Scholar
  103. 103.
    Ratay RT (1971) Sliding-rocking vibration of body on elastic medium. J SMFD ASCE 97:177–192Google Scholar
  104. 104.
    Beredugo JO, Novak M (1972) Coupled horizontal and rocking vibration of embedded footings. Can Geotech J 9(4):477–497CrossRefGoogle Scholar
  105. 105.
    Krizek RO, Gupta DC, Parmelee RA (1972) Coupled sliding and rocking of embedded foundations. J SMFD ASCE 98:1347–1358Google Scholar
  106. 106.
    Wolf JP (1975) Approximate soil-structure interaction with separation of base mat from soil lifting-off. In: 3rd international conference on structural mechanics in reactor technology, vol 4. park K, pp. K 3/6Google Scholar
  107. 107.
    Hamidzadeh HR, Minor GR (1993) Horizontal and rocking vibration of foundation on an elastic half-space. Proc Canadian Cong Appl Mech 2:525–526Google Scholar
  108. 108.
    Iljitchov VA (1967) Towards the soil transmission of vibrations from one foundation to another. In: Proceedings of the international symposium on wave propagation and dynamic properties of earth materials, University of New Mexico, Albuquerque, NM, 641–654Google Scholar
  109. 109.
    Richardson JD, Webster JJ, Warburton GB (1971) The response on the surface of an elastic half-space near to a harmonically excited mass. J Sound Vib 14:307–316CrossRefGoogle Scholar
  110. 110.
    Warburton GB, Richardson JD, Webster JJ (1971) Forced vibrations of two masses on an elastic half-space. J Appl Mech ASME 38:148–156CrossRefGoogle Scholar
  111. 111.
    Warburton GB, Richardson JD, Webster JJ (1972) Harmonic response of masses on an elastic half-space. J EI ASME 94:193–200CrossRefGoogle Scholar
  112. 112.
    Lee TH, Wesley DA (1973) Soil–structure interaction of nuclear reactor structure considering through-soil coupling between adjacent structures. Nucl Eng Des 24:374–387CrossRefGoogle Scholar
  113. 113.
    MacCalden PB, Matthiesen RB (1973) Coupled response of two foundations. In: 5th world conference on earthquake engineering, Rome, 1913–1922Google Scholar
  114. 114.
    Snyder MD, Shaw DE, Hall JR Jr (1975) Structure–soil–structure interaction of nuclear structures. In: 3rd international conference on structural mechanics in reactor technology, vol 4. Park K, K2/9Google Scholar
  115. 115.
    Awojobi AO (1964) Vibrations of rigid bodies on elastic media, Ph.D. Thesis, University of LondonGoogle Scholar
  116. 116.
    Jones R (1958) In-situ measurement of the dynamic properties of soil by vibration method. Geotechnique 8(1):1–21CrossRefGoogle Scholar
  117. 117.
    Jones R (1959) Interpretation of surface vibrations measurements. In: Proceedings of the symposium on vibration testing of road and runways, Koninklijke/Shell-Laboratorium, AmsterdamGoogle Scholar
  118. 118.
    Maxwell AA, Fry ZB (1967) A procedure for determining elastic moduli of in-situ soils by dynamic technique. In: Proceedings of the international symposium on wave propagation and dynamic properties of earth materials, University of New Mexico, Albuquerque, NM, pp 913–920Google Scholar
  119. 119.
    Stokoe KH, Richart FE Jr (1974) Dynamic response of embedded machine foundations. J GTD ASCE 100(GT4):427–447, Proc. Paper 10499Google Scholar
  120. 120.
    Beeston HE, McEvilly TV (1977) Shear wave velocities from down hole measurements. Int J Earthquake Eng Struct Dyn 5:181–190CrossRefGoogle Scholar
  121. 121.
    Dawance G, Guillot M (1963) Vibration des massifs de foundations de machines. Ann Inst Tech Batiment et Travaux Publics, 116(185):512–531Google Scholar
  122. 122.
    Grootenhuis P, Awojobi AO (1965) The in-situ measurement of the dynamic properties of soils. Proceedings of symposium vibration in civil engineering, Institute of Civil Engineering, pp 181–187Google Scholar
  123. 123.
    Hardin BO, Drnevich VP (1972) Shear modulus and damping in soils. I. Measurement and parameter effects. J SMFD ASCE 98:603–624Google Scholar
  124. 124.
    Hardin BO, Drnevich VP (1972) Shear modulus and damping in soils. II. Design equations and curves. J SMFD ASCE 98:667–692Google Scholar
  125. 125.
    Cunny RW, Fry ZB (1973) Vibratory in situ and laboratory soil moduli compared. J SMFD ASCE 99:1055–1076Google Scholar
  126. 126.
    Lawrence FV Jr (1965) Ultrasonic shear wave velocities in sand and clay. Report R65–05., WES, Department of Civil Engineering, MIT, Cambridge, MAGoogle Scholar
  127. 127.
    Theirs GR, Seed HB (1968) Cyclic stress–strain characteristics of clay. J SMFD ASCE 94:555–569Google Scholar
  128. 128.
    Kovacs WD, Seed HB, Chan CK (1971) Dynamic moduli and damping ratios for a soft clay. J SMFD ASCE 97:59–75Google Scholar
  129. 129.
    Kanai K, Yoshizawa S (1961) On the period and the damping of vibration in actual buildings. BERI 39:477Google Scholar
  130. 130.
    Eastwood W (1953) Vibrations in foundations. Struct Eng 82:82–98Google Scholar
  131. 131.
    Chae YS (1967) The material constants of soils as determined from dynamic testing. In: Proceedings of the international symposium on wave propagation and dynamic properties of earth materials, University of New Mexico, Albuquerque, NM, 759–771Google Scholar
  132. 132.
    Hamidzadeh HR (1987) Dynamics of foundation on a simulated elastic half-space. Proc Intl Symp Geotech Eng Soft Soils 1:339–345Google Scholar
  133. 133.
    Luco JE, Trifunac MD, Wong HL (1987) On the apparent changes in dynamic behavior of a nine-story reinforced concrete building. Bull Seism Soc Am 77:1961–1983Google Scholar
  134. 134.
    Luco JE, Trifunac MD, Wong HL (1988) Isolation of soil–structure interaction effects by full-scale forced vibration tests. Int J Earthquake Eng Struct Dyn 16:1–21CrossRefGoogle Scholar
  135. 135.
    Wong HL, Luco JE, Trifunac MD (1977) Contact stresses and ground motion generated by soil–structure interaction. Int J Earthquake Eng Struct Dyn 5:67–79CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Mechanical and Manufacturing EngineeringTennessee State UniversityNashvilleUSA

Personalised recommendations