1. General Formulation for Surface and Embedded Foundations (Gazetas,1991)
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. Foundation of Arbitrary Shape: Main Parameters (Dobry and Gazetas, 1986)
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. Vertical Surface Static Spring for Arbitrarily-Shaped Foundation (Dobry and Gazetas, 1986)
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. Vertical Surface Dynamic Spring for Arbitrarily-Shaped Foundation (Dobry and Gazetas, 1986)
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. Vertical and Horizontal Radiation Dashpots at High Frequencies (Dobry and Gazetas, 1986)
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. Horizontal Surface Radiation Dashpot for Arbitrarily-Shaped Foundation (Dobry and Gazetas, 1986)
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.

7. Torsional Surface Radiation Dashpot for Arbitrarily-Shaped Foundation (Dobry and Gazetas, 1986)
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. Embedded Foundation of Arbitrary Shape: Horizontal Stiffness (Gazetas and Tassoulas, 1987a)
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. Embedded Foundations of Arbitrary Shape: Horizontal Static Stiffness (Gazetas and Tassoulas, 1987a)
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. Embedded Foundations of Arbitrary Shape: Horizontal Radiation Dashpot (Gazetas and Tassoulas, 1987b)
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. Embedded Foundations of Arbitrary Shape: Numerical Example (Gazetas, 1991)
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. Embedded Foundations of Arbitrary Shape: Summary Table (Gazetas, 1991)
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. Contribution of Soil Internal Damping Ratio β to Total Dashpot (Gazetas, 1991)
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. Some Conclusions
Simplified Methods play a special role in Soil Dynamics. This role is different from, and cannot be replaced by, sophisticated computer simulations
Understanding by engineer of basic Dynamics and Wave Propagation concepts increases usefulness of Simplified Methods
Simplified Methods are available to calculate equivalent soil springs and dashpots under shallow embedded foundation of arbitrary shape
Read slide.
When reading second bullet, add “…both in the free field and in terms of pile response. This is a very important objective, as you will see later in the presentation. While full scale testing is in most respects closer to the actual field conditions, the centrifuge tests are closer to the way we do other tests and characterize sands in the laboratory. So in our opinion, a good integration between centrifuge and full scale is a critical step toward development of better methods of pile analysis and design.”