Soil-Structure Interaction

1. Soil-Structure Interaction ECIV 724A Fall 2004

2. SSI – Problem Definition Earthquake Analysis Structures supported by rigid foundations Earthquakes=>Specified motion of base Rigid Base Analysis • Tall Buildings • Acceptable • Light & Flexible • Firm Foundations • Methods focus on modeling of structure • Displacements wrt fixed base • Finite Element Methods • Nuclear Power Plants • Wrong Assumption • Massive & Stiff • Soft Soils • Interaction with supporting soils becomes important

3. Machine Foundation Seismic Excitation SSI – Problem Definition • Parameters • Local Soil Conditions • Peak Acceleration • Frequency Content of Motion • Proximity to Fault • Travel Path etc Inertial Interaction Inertial forces in structure are transmitted to flexible soil Kinematic Interaction Stiffer foundation cannot conform to the distortions of soil TOTAL=INERTIAL + KINEMATIC

4. w Posin( t) H 2b Half Space SSI Effects

5. SSI Effects

6. 3. …Reach Receiver… 4. …and life goes on… 2. Waves Propagate… Cross Interaction Effects 1. Moment is applied

7. SSI Effects • Alter the Natural Frequency of the Structure • Add Damping • Through the Soil Interaction Effects • Traveling Wave Effects

8. Methods of Analysis Objective: Given the earthquake ground motions that would occur on the surface of the ground in the absence of the structure (control or design motions), find the dynamic response of the structure.

9. Methods of Analysis Methods Complete Idealized Direct MultiStep

10. Complete Interaction Analysis High Degree of Complexity • Account for the variation of soil properties with depth. • Consider the material nonlinear behavior of the soil • Consider the 3-D nature of the problem • Consider the nature of the wave propagation which produced the ground motion • Consider possible interaction with adjacent structures.

11. Idealized Interaction Analysis Idealization Horizontal Layers Simplified Wave Mechanisms etc

12. Idealized Interaction Analysis Preliminary description of free field motion before any structure has been built • The definition of the motion itself • the control motion in terms of response spectra, acceleration records etc • The location of the control motion • free surface, soil-rock interface • The generation mechanism at the control point vertically or obliquely incident SH or SV waves, Rayleigh waves, etc.

13. Idealized Analysis Idealized Interaction Analysis Tools: FEM, BEM, FDE, Analytical solutions • MultiStep Methods • Evaluation of Dynamic Response in Several Steps • SUPERPOSITION • Two-Step • Kinematic+Inertia Interaction • Three-Step • Rigid Foundations • Lumped Parameter Models • Substructure • Division to Subsystems • Equilibrium & Compatibility Direct Methods Evaluation of Dynamic Response in a Single Step True Nonlinear Solutions

14. Finite Element Method (FEM) Governing Equation Solution Techniques • Modal Analysis • Direct Integration • Fourier Analysis - Complex Response

15. FEM Solution Techniques Selection CriteriaCost and Feasibility Paramount ConsiderationAccuracy Differences - Handling of Damping - Ability to Handle High Frequency Components of Motion

16. FEM - Modal Analysis • Damping is neglected during early stages • Actual displacements are damped • Damping is considered in arbitrary manner • Structural Dynamics: First few modes need to be evaluated (<20) • SSI: Acceleration response spectra over a large frequency range and large number of modes need to be considered (>150) • Not recommended for Direct SSI - Stiff Massive Structure Soft Soil • OK for Substructure

17. FEM - Direct Integration • Time Marching Schemes Newmark’s Methods, WilsonJ Methods, Bathe and Wilson Cubic Inertia Method • Small Time Step for Accuracy • Stability and Convergence • Choice of Damping Matrix • Frequency Dependent Damping Ratio - filters out high frequency components • Proportional Damping • Good Choice if True Dynamic Nonlinear Analysis is feasible

18. FEM - Complex Response • Fourier Transformation - Transfer Functions • Transfer Functions Independent of External Excitation • Control of Accuracy • Efficient • Only Linear or Pseudo non-linear analysis

19. FEM - Geometric Modeling

20. FEM Modeling Max Element Size Governed by Highest frequency which must be transmitted correctly within the element

21. FEM Modeling of Infinite Space

22. FEM Modeling of Infinite Space Modeling Introduces Artificial Boundaries that Reflect Waves

23. FEM Modeling of Infinite Soil • Absorbing Boundaries • Viscous Boundary • Variable Depth Method • Damping proportional to Wave Velocities • Radiating Boundaries (Hyperelements) • Satisfy Boundary Conditions at Infinity • Eigenvalue Analysis • Frequency Domain Analysis

24. SSI – FEM Methods • FEM • Advantages • Non-Linear Analysis • Well Established • Shortcomings • Finite Domains • Volume Discretizations

25. Boundary Element Methods Governing Equation • Small Displacement Field • Homogeneous • Isotropic • Elastic

26. Boundary Element Method

27. Boundary Element Method

28. BEM – Methods • BEM • Advantages • Infinite Media • Surface Discretization • Shortcomings • Non-symmetric matrices • Not Efficient for Nonlinear

29. SSI Methods Combined BEM-FEM eliminate disadvantages of each method and retain advantages • Approach • FEM Approach • BEM Approach • Staggered Solutions

30. Governing Equations

31. FEM MethodTime Marching Scheme Governing Equation Discrete Form in Time

32. FEM BEM FEM-BEM CouplingStaggered Solutions Can be Solved in a Staggered Approach...

33. At Every Time Step... Equilibrium of Forces at Interface BEM Solver FEM Solver External Excitation External Excitation Compatibility of Displacements at Interface FEM-BEM CouplingStaggered Solutions

34. FEM-BEM CouplingAdvantages • Independent Solutions for BEM and FEM • Independent Time Step Selection • Smaller Systems of Equations • BEM System of Reduced Size • In the Absence of Incidence Displacement Field in Soil, BEM does not require Solution.

35. Lumped Parameter Models for SSI

36. Lumped Parameter Foundation Models Reissner (1936) Analytic Solutions to Vertical Vibration of Circular Footing Due to Harmonic Excitation Assumptions: Elastic ½-space Material G,v,r Uniform Vertical Pressure Formed Basis of Almost All Analytical Studies

37. Lumped Parameter Foundation Models Quinlan and Sung Assumed Different Pressure Distributions Richart & Whitman Effects of Poisson’ Bycroft (1956) Displacement Functions Hsieh K and C in terms of Soil and Foundation Parameters

38. Lumped Parameter Foundation Models Lysmer Analog Constant Lumped Parameters Richart Hall & Wood(1970) Gazetas (1983) Wolf (1988)

39. Lumped Parameter Foundation Models Representative Lumped Parameter Values - Square

40. Lumped Parameter Foundation Models Representative Lumped Parameter Values Circular

41. Lumped Parameter Foundation Models Stehmeyer and Rizos (2003) The Real System Equivalent SDOF System Properties k, and c are known to be frequency (w) dependent

42. Lumped Parameter Foundation Models wn = 3.3 x = 0.975

43. w Posin( t) H 2b Half Space SSI Effects

44. SSI Effects

45. SSI Effects Based on the Simplified Lumped Parameter Models it can be shown that Longer Period of Foundation-Structure System

46. Source Foundation Receiver Foundation SSI Effects – Cross Interaction

47. SSI Effects – Cross Interaction

48. SSI Effects – Cross Interaction

49. Traveling Wave Effects After Betti et al.

50. Traveling Wave Effects After Betti et al.