Machine Foundation Problem
What Would a Simplified
Solution Look Like?
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
Whitman and Richart
1967
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
1D Shear Wave Propagation
Perfect Viscous Dashpot Analog for
1D 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
1987a
Embedded foundations, horizontal X
Gazetas and Tassoulas
1987b
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
Gazetas
1990
1991
Gazetas and Stokoe
1991
X
X
X
X
X
X
X
X
Surface and embedded
foundations, all six DOF’s;
formulas, charts & numerical
examples
X
X
X
X
Experimental verification for
embedded foundations
X
X
X