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Soil-Structure Interaction. ECIV 724A Fall 2004. 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

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soil structure interaction

Soil-Structure Interaction

ECIV 724A Fall 2004

ssi problem definition
SSI – Problem Definition

Earthquake Analysis

Structures supported by rigid foundations

Earthquakes=>Specified motion of base




  • 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
ssi problem definition3

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


ssi effects






Half Space

SSI Effects
cross interaction effects

3. …Reach Receiver…

4. …and life goes on…

2. Waves Propagate…

Cross Interaction Effects

1. Moment is applied

ssi effects7
SSI Effects
  • Alter the Natural Frequency of the Structure
  • Add Damping
  • Through the Soil Interaction Effects
  • Traveling Wave Effects
methods of analysis
Methods of Analysis


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.

methods of analysis9
Methods of Analysis






complete interaction analysis
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.
idealized interaction analysis
Idealized Interaction Analysis


Horizontal Layers

Simplified Wave Mechanisms


idealized interaction analysis12
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.
idealized analysis
Idealized Analysis

Idealized Interaction Analysis

Tools: FEM, BEM, FDE, Analytical solutions

  • MultiStep Methods
  • Evaluation of Dynamic Response in Several Steps
  • 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

finite element method fem
Finite Element Method (FEM)

Governing Equation

Solution Techniques

  • Modal Analysis
  • Direct Integration
  • Fourier Analysis - Complex Response
fem solution techniques
FEM Solution Techniques

Selection CriteriaCost and Feasibility

Paramount ConsiderationAccuracy


- Handling of Damping

- Ability to Handle High Frequency Components of Motion

fem modal analysis
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
fem direct integration
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
fem complex response
FEM - Complex Response
  • Fourier Transformation - Transfer Functions
  • Transfer Functions Independent of External Excitation
  • Control of Accuracy
  • Efficient
  • Only Linear or Pseudo non-linear analysis
fem modeling
FEM Modeling

Max Element Size Governed by Highest frequency which must be transmitted correctly within the element

fem modeling of infinite space22
FEM Modeling of Infinite Space

Modeling Introduces Artificial Boundaries that Reflect Waves

fem modeling of infinite soil
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
ssi fem methods
SSI – FEM Methods
  • FEM
  • Advantages
  • Non-Linear Analysis
  • Well Established
  • Shortcomings
  • Finite Domains
  • Volume Discretizations
boundary element methods
Boundary Element Methods

Governing Equation

  • Small Displacement Field
  • Homogeneous
  • Isotropic
  • Elastic
bem methods
BEM – Methods
  • BEM
  • Advantages
  • Infinite Media
  • Surface Discretization
  • Shortcomings
  • Non-symmetric matrices
  • Not Efficient for Nonlinear
ssi methods
SSI Methods

Combined BEM-FEM

eliminate disadvantages of each method and retain advantages

  • Approach
  • FEM Approach
  • BEM Approach
  • Staggered Solutions
fem method time marching scheme
FEM MethodTime Marching Scheme

Governing Equation

Discrete Form in Time

fem bem coupling staggered solutions



FEM-BEM CouplingStaggered Solutions

Can be Solved in a Staggered Approach...

fem bem coupling staggered solutions33

At Every Time Step...

Equilibrium of Forces

at Interface









Compatibility of Displacements

at Interface

FEM-BEM CouplingStaggered Solutions
fem bem coupling advantages
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.
lumped parameter foundation models
Lumped Parameter Foundation Models

Reissner (1936) Analytic Solutions to Vertical Vibration of Circular Footing Due to Harmonic Excitation


Elastic ½-space

Material G,v,r

Uniform Vertical Pressure

Formed Basis of Almost All Analytical Studies

lumped parameter foundation models37
Lumped Parameter Foundation Models

Quinlan and Sung

Assumed Different Pressure Distributions

Richart & Whitman

Effects of Poisson’

Bycroft (1956)

Displacement Functions


K and C in terms of Soil and Foundation Parameters

lumped parameter foundation models38
Lumped Parameter Foundation Models

Lysmer Analog

Constant Lumped Parameters

Richart Hall & Wood(1970)

Gazetas (1983)

Wolf (1988)

lumped parameter foundation models39
Lumped Parameter Foundation Models

Representative Lumped Parameter Values - Square

lumped parameter foundation models40
Lumped Parameter Foundation Models

Representative Lumped Parameter Values Circular

lumped parameter foundation models41
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

ssi effects43






Half Space

SSI Effects
ssi effects45
SSI Effects

Based on the Simplified Lumped Parameter Models it can be shown that

Longer Period of Foundation-Structure System

traveling wave effects
Traveling Wave Effects

After Betti et al.

traveling wave effects50
Traveling Wave Effects

After Betti et al.

traveling wave effects51
Traveling Wave Effects

After Betti et al.

traveling wave effects52
Traveling Wave Effects

After Betti et al.

sh waves

After Betti et al.

p waves

After Betti et al.

sv waves

After Betti et al.

rayleigh waves
Rayleigh Waves

After Betti et al.

traveling wave effects57
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.