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. SSI – Problem Definition
Machine Foundation
Seismic Excitation
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. SSI Effects
Posin( w t)
Half Space 2b H

5. SSI Effects

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

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 MultiStep Methods Direct Methods
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 Criteria Cost and Feasibility
Paramount Consideration Accuracy
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. eliminate disadvantages of each method and retain advantages
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 Method Time Marching Scheme
Governing Equation
Discrete Form in Time

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

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

34. FEM-BEM Coupling Advantages
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. SSI Effects
Posin( w t)
Half Space 2b H

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. SSI Effects – Cross Interaction
Receiver Foundation
Source Foundation

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.

51. Traveling Wave Effects
After Betti et al.

52. Traveling Wave Effects
After Betti et al.

53. SH-Waves
After Betti et al.

54. P-Waves
After Betti et al.

55. SV-Waves
After Betti et al.

56. Rayleigh Waves
After Betti et al.

57. Traveling Wave Effects
Inertia Effects were Not Important but yet SSI significantly affects the response
Asynchronous Motion Excite Antisymmetric Vibration Modes
SSI effects cannot be ignored
After Betti et al.