1. Machine Foundation Problem
FIGURE XXX (MIWA, 20XX)
A number of investigations have been done after earthquakes where pile foundations have been excavated or photographed with special cameras, and which have shown clearly how the lateral pressure of the soil moving against the pile has displaced, bent and cracked the piles. The figure on the right (Show) shows how the pipe piles bent under one of the piers of a bridge in Niigata in Japan in 1964, causing again the collapse of the girders of the bridge.

2. What Would a Simplified Solution Look Like?
FIGURE XXX (MIWA, 20XX)
A number of investigations have been done after earthquakes where pile foundations have been excavated or photographed with special cameras, and which have shown clearly how the lateral pressure of the soil moving against the pile has displaced, bent and cracked the piles. The figure on the right (Show) shows how the pipe piles bent under one of the piers of a bridge in Niigata in Japan in 1964, causing again the collapse of the girders of the bridge.

3. What Would a Simplified Solution Look Like?
FIGURE XXX (MIWA, 20XX)
A number of investigations have been done after earthquakes where pile foundations have been excavated or photographed with special cameras, and which have shown clearly how the lateral pressure of the soil moving against the pile has displaced, bent and cracked the piles. The figure on the right (Show) shows how the pipe piles bent under one of the piers of a bridge in Niigata in Japan in 1964, causing again the collapse of the girders of the bridge.

4. Simplified Solution Vertical Loading (Lysmer and Richart, 1966)
FIGURE XXX (MIWA, 20XX)
A number of investigations have been done after earthquakes where pile foundations have been excavated or photographed with special cameras, and which have shown clearly how the lateral pressure of the soil moving against the pile has displaced, bent and cracked the piles. The figure on the right (Show) shows how the pipe piles bent under one of the piers of a bridge in Niigata in Japan in 1964, causing again the collapse of the girders of the bridge.

5. Comparison Between Lysmer’s Analog and Exact Solution (Lysmer and Richart, 1966)
FIGURE XXX (MIWA, 20XX)
A number of investigations have been done after earthquakes where pile foundations have been excavated or photographed with special cameras, and which have shown clearly how the lateral pressure of the soil moving against the pile has displaced, bent and cracked the piles. The figure on the right (Show) shows how the pipe piles bent under one of the piers of a bridge in Niigata in Japan in 1964, causing again the collapse of the girders of the bridge.

6. 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
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
Validated Lysmer’a Analog with field footing vibration tests
Design procedure based on Lysmer’s Analog
We also want to acknowledge the people and organizations listed on the screen. They include research partners in the U.S. and Japan, students and staff at three universities, and the Network for Earthquake Engineering Simulation and National Science Foundation here in the U.S.A.
I want to single out especially two of our team members in this project who are sitting here in the audience: Prof. Elgamal from UCSD and Prof. Thevanayagam from the U. at Buffalo.

7. Simplified Solution Horizontal Loading (Arnold, 1955; Bycroft, 1956; Hall, 1967)
FIGURE XXX (MIWA, 20XX)
A number of investigations have been done after earthquakes where pile foundations have been excavated or photographed with special cameras, and which have shown clearly how the lateral pressure of the soil moving against the pile has displaced, bent and cracked the piles. The figure on the right (Show) shows how the pipe piles bent under one of the piers of a bridge in Niigata in Japan in 1964, causing again the collapse of the girders of the bridge.

8. Equivalent Simplified Systems for Design (Whitman and Richart, 1967)
FIGURE XXX (MIWA, 20XX)
A number of investigations have been done after earthquakes where pile foundations have been excavated or photographed with special cameras, and which have shown clearly how the lateral pressure of the soil moving against the pile has displaced, bent and cracked the piles. The figure on the right (Show) shows how the pipe piles bent under one of the piers of a bridge in Niigata in Japan in 1964, causing again the collapse of the girders of the bridge.

9. Radiation of Energy by Waves Propagating from Foundation (Lambe and Whitman, 1979)
FIGURE XXX (MIWA, 20XX)
A number of investigations have been done after earthquakes where pile foundations have been excavated or photographed with special cameras, and which have shown clearly how the lateral pressure of the soil moving against the pile has displaced, bent and cracked the piles. The figure on the right (Show) shows how the pipe piles bent under one of the piers of a bridge in Niigata in Japan in 1964, causing again the collapse of the girders of the bridge.

10. Horizontal Radiation Dashpot
FIGURE XXX (MIWA, 20XX)
A number of investigations have been done after earthquakes where pile foundations have been excavated or photographed with special cameras, and which have shown clearly how the lateral pressure of the soil moving against the pile has displaced, bent and cracked the piles. The figure on the right (Show) shows how the pipe piles bent under one of the piers of a bridge in Niigata in Japan in 1964, causing again the collapse of the girders of the bridge.

11. Perfect Viscous Dashpot Analog for 1D Shear Wave Propagation
FIGURE XXX (MIWA, 20XX)
A number of investigations have been done after earthquakes where pile foundations have been excavated or photographed with special cameras, and which have shown clearly how the lateral pressure of the soil moving against the pile has displaced, bent and cracked the piles. The figure on the right (Show) shows how the pipe piles bent under one of the piers of a bridge in Niigata in Japan in 1964, causing again the collapse of the girders of the bridge.

12. Perfect Viscous Dashpot Analog for 1D Compression-Extension Wave Propagation
FIGURE XXX (MIWA, 20XX)
A number of investigations have been done after earthquakes where pile foundations have been excavated or photographed with special cameras, and which have shown clearly how the lateral pressure of the soil moving against the pile has displaced, bent and cracked the piles. The figure on the right (Show) shows how the pipe piles bent under one of the piers of a bridge in Niigata in Japan in 1964, causing again the collapse of the girders of the bridge.

13. Waves and Radiation Damping in Vertical and Horizontal Vibrations
FIGURE XXX (MIWA, 20XX)
A number of investigations have been done after earthquakes where pile foundations have been excavated or photographed with special cameras, and which have shown clearly how the lateral pressure of the soil moving against the pile has displaced, bent and cracked the piles. The figure on the right (Show) shows how the pipe piles bent under one of the piers of a bridge in Niigata in Japan in 1964, causing again the collapse of the girders of the bridge.

14. Simplified Radiation Dashpot for Embedded Circular Foundation (Gazetas, Dobry and Tassoulas, 1985)
FIGURE XXX (MIWA, 20XX)
A number of investigations have been done after earthquakes where pile foundations have been excavated or photographed with special cameras, and which have shown clearly how the lateral pressure of the soil moving against the pile has displaced, bent and cracked the piles. The figure on the right (Show) shows how the pipe piles bent under one of the piers of a bridge in Niigata in Japan in 1964, causing again the collapse of the girders of the bridge.

15. Comparison with Dynamic Finite Element Results (Gazetas et al
Comparison with Dynamic Finite Element Results (Gazetas et al.,1985; Day, 1977)
FIGURE XXX (MIWA, 20XX)
A number of investigations have been done after earthquakes where pile foundations have been excavated or photographed with special cameras, and which have shown clearly how the lateral pressure of the soil moving against the pile has displaced, bent and cracked the piles. The figure on the right (Show) shows how the pipe piles bent under one of the piers of a bridge in Niigata in Japan in 1964, causing again the collapse of the girders of the bridge.

16. Static Spring for Embedded Circular Foundation (Gazetas et al.,1985)
FIGURE XXX (MIWA, 20XX)
A number of investigations have been done after earthquakes where pile foundations have been excavated or photographed with special cameras, and which have shown clearly how the lateral pressure of the soil moving against the pile has displaced, bent and cracked the piles. The figure on the right (Show) shows how the pipe piles bent under one of the piers of a bridge in Niigata in Japan in 1964, causing again the collapse of the girders of the bridge.

17. Effect of Soil-Wall Contact on Dynamic Response of Embedded Foundation (Novak, 1970)
FIGURE XXX (MIWA, 20XX)
A number of investigations have been done after earthquakes where pile foundations have been excavated or photographed with special cameras, and which have shown clearly how the lateral pressure of the soil moving against the pile has displaced, bent and cracked the piles. The figure on the right (Show) shows how the pipe piles bent under one of the piers of a bridge in Niigata in Japan in 1964, causing again the collapse of the girders of the bridge.

18. Simplified Solutions for Noncircular Surface and Embedded Foundations (Gazetas and co-workers, )
Author(s)
Year
Contribution
Stiffness
Damping
Experiment
Dobry and Gazetas
Dobry et al.
1986
Surface foundations, all six DOF’s
Experimental verification for surface foundations X
Gazetas et al.
1985
Embedded foundations, vertical
Gazetas and Tassoulas
1987a
Embedded foundations, horizontal
1987b
Hatzikonstantinou et al.
1989
Embedded foundations, rocking
Fotopoulou et al.
Ahmad and Gazetas
1991
Embedded foundations, torsional
Gazetas
Gazetas and Stokoe
1990
Surface and embedded foundations, all six DOF’s; formulas, charts & numerical examples
Experimental verification for embedded foundations
FIGURE XXX (MIWA, 20XX)
A number of investigations have been done after earthquakes where pile foundations have been excavated or photographed with special cameras, and which have shown clearly how the lateral pressure of the soil moving against the pile has displaced, bent and cracked the piles. The figure on the right (Show) shows how the pipe piles bent under one of the piers of a bridge in Niigata in Japan in 1964, causing again the collapse of the girders of the bridge.