Machine Foundation Problem What Would a Simplified Solution

Machine Foundation Problem

What Would a Simplified Solution Look Like?

Simplified Solution Vertical Loading (Lysmer and Richart, 1966)

Comparison Between Lysmer’s Analog and Exact Solution (Lysmer and Richart, 1966)

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 Quinlan 1953 Solution for flexible circular foundation assuming uniform load 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 Richart and Whitman and Richart 1967 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) Validated Lysmer’a Analog with field footing vibration tests Design procedure based on Lysmer’s Analog

Simplified Solution Horizontal Loading (Arnold, 1955; Bycroft, 1956; Hall, 1967)

Equivalent Simplified Systems for Design (Whitman and Richart, 1967)

Radiation of Energy by Waves Propagating from Foundation (Lambe and Whitman, 1979)

Horizontal Radiation Dashpot

Perfect Viscous Dashpot Analog for 1 D Shear Wave Propagation

Perfect Viscous Dashpot Analog for 1 D Compression-Extension Wave Propagation

Waves and Radiation Damping in Vertical and Horizontal Vibrations

Simplified Radiation Dashpot for Embedded Circular Foundation (Gazetas, Dobry and Tassoulas, 1985)

Comparison with Dynamic Finite Element Results (Gazetas et al. , 1985; Day, 1977)

Static Spring for Embedded Circular Foundation (Gazetas et al. , 1985)

Effect of Soil-Wall Contact on Dynamic Response of Embedded Foundation (Novak, 1970)

Simplified Solutions for Noncircular Surface and Embedded Foundations (Gazetas and co-workers, 1985 -91) Author(s) Year Contribution Dobry and Gazetas 1986 Surface foundations, all six DOF’s Dobry et al. 1986 Stiffness Damping Experiment X X Gazetas et al. 1985 Experimental verification for surface foundations Embedded foundations, vertical Gazetas and Tassoulas 1987 a Embedded foundations, horizontal X Gazetas and Tassoulas 1987 b Embedded foundations, horizontal Hatzikonstantinou et al. 1989 Embedded foundations, rocking Fotopoulou et al. Ahmad and Gazetas 1989 1991 Embedded foundations, rocking Embedded foundations, torsional Gazetas 1990 1991 Gazetas and Stokoe 1991 X X X X Surface and embedded foundations, all six DOF’s; formulas, charts & numerical examples X X Experimental verification for embedded foundations X X X