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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 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.