Machine Foundation Problem Machine Foundation Problem

What Would a Simplified What Would a Simplified Solution Look Like? Solution Look Like?

What Would a Simplified What Would a Simplified Solution Look Like? Solution Look Like?

Simplified Solution Vertical LoadingSimplified Solution Vertical Loading (Lysmer and Richart, 1966) (Lysmer and Richart, 1966)

Comparison Between Lysmer’s Comparison Between Lysmer’s Analog and Exact SolutionAnalog and Exact Solution

(Lysmer and Richart, 1966) (Lysmer and Richart, 1966)

Theoretical and Simplified Solutions Theoretical and Simplified Solutions to Machine Foundation Problemto 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 distributionsBycroft 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 WhitmanWhitman and Richart

19671967

Validated Lysmer’a Analog with field footing vibration testsDesign procedure based on Lysmer’s Analog

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

Equivalent Simplified Systems Equivalent Simplified Systems for Design for Design

(Whitman and Richart, 1967) (Whitman and Richart, 1967)

Radiation of Energy by Waves Radiation of Energy by Waves Propagating from FoundationPropagating from Foundation

(Lambe and Whitman, 1979) (Lambe and Whitman, 1979)

Horizontal Radiation Dashpot Horizontal Radiation Dashpot

Perfect Viscous Dashpot Analog for 1D Perfect Viscous Dashpot Analog for 1D Shear Wave PropagationShear Wave Propagation

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

PropagationPropagation

Waves and Radiation Damping in Waves and Radiation Damping in Vertical and Horizontal Vibrations Vertical and Horizontal Vibrations

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

Comparison with Dynamic Finite Comparison with Dynamic Finite Element Results Element Results

(Gazetas et al.,1985; Day, 1977)(Gazetas et al.,1985; Day, 1977)

Static Spring for Embedded Circular Static Spring for Embedded Circular Foundation Foundation

(Gazetas et al.,1985)(Gazetas et al.,1985)

Effect of Soil-Wall Contact on Dynamic Effect of Soil-Wall Contact on Dynamic Response of Embedded Foundation Response of Embedded Foundation

(Novak, 1970) (Novak, 1970)

Simplified Solutions for Noncircular Simplified Solutions for Noncircular Surface and Embedded FoundationsSurface and Embedded Foundations

(Gazetas and co-workers, 1985-91)(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 XAhmad and Gazetas 1991 Embedded foundations, torsional X X

Gazetas Gazetas

Gazetas and Stokoe

19901991

1991

Surface and embedded foundations, all six DOF’s; formulas, charts & numerical examples

Experimental verification for embedded foundations

XX

X

XX

X X