The document discusses various theoretical and simplified solutions to machine foundation problems, highlighting the contributions of several authors and their methodologies from 1904 to 1991. Specific solutions for vertical and horizontal loading, as well as comparisons with dynamic finite element results, are detailed. The content is primarily focused on the dynamics of foundations in civil engineering.

1. Machine Foundation
Prof. Samirsinh P Parmar
Mail: spp.cl@ddu.ac.in
Asst. Prof. Dept. of Civil Engg.
Dharmsinh Desai University, Nadiad,
Gujarat , Bharatvarsh.

2. Machine Foundation Problem
Machine Foundation, M.Tech, Dynamics of Foundations,
SPP-DoCL, DDU, Nadiad.
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3. What Would a Simplified
Solution Look Like?
Machine Foundation, M.Tech, Dynamics of Foundations,
SPP-DoCL, DDU, Nadiad.
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4. What Would a Simplified
Solution Look Like?
Machine Foundation, M.Tech, Dynamics of Foundations,
SPP-DoCL, DDU, Nadiad.
4

5. Simplified Solution Vertical Loading
(Lysmer and Richart, 1966)
Machine Foundation, M.Tech, Dynamics of Foundations,
SPP-DoCL, DDU, Nadiad.
5

6. Comparison Between Lysmer’s Analog and Exact
Solution
(Lysmer and Richart, 1966)
Machine Foundation, M.Tech, Dynamics of Foundations,
SPP-DoCL, DDU, Nadiad.
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7. Theoretical and Simplified
Solutions to Machine Foundation
Problem
Author(s) Year Contribution
Lamb 1904 Solution for concentrated vertical force on surface of half
space (Dynamic Boussinesq Problem)
Reissner 1936 Solution for flexible circular foundation assuming uniform
load
Quinlan 1953 Approximate solution for rigid circular foundation assuming
static pressure distribution
Sung 1953 Solutions for various assumed pressure distributions
Bycroft 1956 Simplified solution by averaging displacements over
foundation area
Hsieh 1962 Introduced idea of frequency-dependent equivalent spring
and dashpot
Lysmer and Richart 1966 Obtained exact frequency-dependent spring dashpot for
rigid circular foundation using computer.
Proposed approximate frequency-independent spring and
dashpot as Simplified Solution for engineers (Lysmer’s
Analog)
Richart and Whitman
Whitman and Richart
1967
1967
Validated Lysmer’a Analog with field footing vibration tests
Design procedure based on Lysmer’s Analog
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8. Simplified Solution Horizontal Loading
(Arnold, 1955; Bycroft, 1956; Hall, 1967)
Machine Foundation, M.Tech, Dynamics of Foundations,
SPP-DoCL, DDU, Nadiad.
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9. Equivalent Simplified Systems for Design
(Whitman and Richart, 1967)
Machine Foundation, M.Tech, Dynamics of Foundations,
SPP-DoCL, DDU, Nadiad.
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10. Radiation of Energy by Waves
Propagating from Foundation
(Lambe and Whitman, 1979)
Machine Foundation, M.Tech, Dynamics of Foundations,
SPP-DoCL, DDU, Nadiad.
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11. Horizontal Radiation Dashpot
Machine Foundation, M.Tech, Dynamics of Foundations,
SPP-DoCL, DDU, Nadiad.
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12. Perfect Viscous Dashpot Analog for 1D
Shear Wave Propagation
Machine Foundation, M.Tech, Dynamics of Foundations,
SPP-DoCL, DDU, Nadiad.
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13. Perfect Viscous Dashpot Analog for 1D
Compression-Extension Wave Propagation
Machine Foundation, M.Tech, Dynamics of Foundations,
SPP-DoCL, DDU, Nadiad.
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14. Waves and Radiation Damping in Vertical
and Horizontal Vibrations
Machine Foundation, M.Tech, Dynamics of Foundations,
SPP-DoCL, DDU, Nadiad.
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15. Simplified Radiation Dashpot for
Embedded Circular Foundation
(Gazetas, Dobry and Tassoulas, 1985)
Machine Foundation, M.Tech, Dynamics of Foundations,
SPP-DoCL, DDU, Nadiad.
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16. Comparison with Dynamic
Finite Element Results
(Gazetas et al.,1985; Day, 1977)
Machine Foundation, M.Tech, Dynamics of Foundations,
SPP-DoCL, DDU, Nadiad.
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17. Static Spring for Embedded Circular
Foundation
(Gazetas et al.,1985)
Machine Foundation, M.Tech, Dynamics of Foundations,
SPP-DoCL, DDU, Nadiad.
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18. Effect of Soil-Wall Contact on Dynamic Response of
Embedded Foundation
(Novak, 1970)
Machine Foundation, M.Tech, Dynamics of Foundations,
SPP-DoCL, DDU, Nadiad.
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19. Simplified Solutions for Noncircular
Surface and Embedded Foundations
(Gazetas and co-workers, 1985-91)
Author(s) Year Contribution Stiffness Damping Experiment
Dobry and Gazetas
Dobry et al.
1986
1986
Surface foundations, all six DOF’s
Experimental verification for surface
foundations
X X
X
Gazetas et al. 1985 Embedded foundations, vertical X X
Gazetas and Tassoulas 1987a Embedded foundations, horizontal X
Gazetas and Tassoulas 1987b Embedded foundations, horizontal X
Hatzikonstantinou et al. 1989 Embedded foundations, rocking X
Fotopoulou et al. 1989 Embedded foundations, rocking X
Ahmad and Gazetas 1991 Embedded foundations, torsional X X
Gazetas
Gazetas
Gazetas and Stokoe
1990
1991
1991
Surface and embedded foundations, all six
DOF’s; formulas, charts & numerical examples
Experimental verification for embedded
foundations
X
X
X
X
X
X X
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20. Reference paper:
https://www.ijaet.org/media/3I42-IJAET1005914-v10-i6-pp592-603.pdf
Mohan C & Parmar S.P. (2017), A comparative study of various methods to
evaluate impedance function for shallow foundations, IJAET, Dec-2017, ISSN: 22311963. pp 592-603.
Machine Foundation, M.Tech, Dynamics of Foundations,
SPP-DoCL, DDU, Nadiad.
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21. Machine Foundation, M.Tech, Dynamics of Foundations,
SPP-DoCL, DDU, Nadiad.
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