General Formulation for Surface and General Formulation for Surface and Embedded Foundations Embedded Foundations

(Gazetas,1991)(Gazetas,1991)

Foundation of Arbitrary Shape: Foundation of Arbitrary Shape: Main Parameters Main Parameters

(Dobry and Gazetas, 1986)(Dobry and Gazetas, 1986)

Vertical Surface Static Spring for Vertical Surface Static Spring for Arbitrarily-Shaped FoundationArbitrarily-Shaped Foundation

(Dobry and Gazetas, 1986)(Dobry and Gazetas, 1986)

Vertical Surface Dynamic Spring Vertical Surface Dynamic Spring for Arbitrarily-Shaped Foundationfor Arbitrarily-Shaped Foundation

(Dobry and Gazetas, 1986)(Dobry and Gazetas, 1986)

Vertical and Horizontal Radiation Vertical and Horizontal Radiation Dashpots at High Frequencies Dashpots at High Frequencies

(Dobry and Gazetas, 1986)(Dobry and Gazetas, 1986)

Horizontal Surface Radiation Dashpot Horizontal Surface Radiation Dashpot for Arbitrarily-Shaped Foundationfor Arbitrarily-Shaped Foundation

(Dobry and Gazetas, 1986)(Dobry and Gazetas, 1986)

Torsional Surface Radiation Dashpot Torsional Surface Radiation Dashpot for Arbitrarily-Shaped Foundationfor Arbitrarily-Shaped Foundation

(Dobry and Gazetas, 1986)(Dobry and Gazetas, 1986)

Embedded Foundation of Arbitrary Embedded Foundation of Arbitrary Shape: Horizontal StiffnessShape: Horizontal Stiffness

(Gazetas and Tassoulas, 1987a)(Gazetas and Tassoulas, 1987a)

Embedded Foundations of Arbitrary Embedded Foundations of Arbitrary Shape: Horizontal Static StiffnessShape: Horizontal Static Stiffness

(Gazetas and Tassoulas, 1987a)(Gazetas and Tassoulas, 1987a)

Embedded Foundations of Arbitrary Embedded Foundations of Arbitrary Shape: Horizontal Radiation DashpotShape: Horizontal Radiation Dashpot

(Gazetas and Tassoulas, 1987b)(Gazetas and Tassoulas, 1987b)

Embedded Foundations of Arbitrary Embedded Foundations of Arbitrary Shape: Numerical ExampleShape: Numerical Example

(Gazetas, 1991)(Gazetas, 1991)

Embedded Foundations of Arbitrary Embedded Foundations of Arbitrary Shape: Summary Table Shape: Summary Table

(Gazetas, 1991)(Gazetas, 1991)

Contribution of Soil Internal Damping Contribution of Soil Internal Damping Ratio Ratio ββ to Total Dashpot to Total Dashpot

(Gazetas, 1991) (Gazetas, 1991)

Some Conclusions 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