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 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 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

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

SSI Effects

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

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

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.

Methods of Analysis Methods Complete Idealized Direct MultiStep

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 Idealization Horizontal Layers Simplified Wave Mechanisms etc

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 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

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

FEM Solution Techniques Selection Criteria Cost and Feasibility Paramount Consideration Accuracy Differences - Handling of Damping - Ability to Handle High Frequency Components of Motion

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 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 Fourier Transformation - Transfer Functions Transfer Functions Independent of External Excitation Control of Accuracy Efficient Only Linear or Pseudo non-linear analysis

FEM - Geometric Modeling

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

FEM Modeling of Infinite Space

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

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 FEM Advantages Non-Linear Analysis Well Established Shortcomings Finite Domains Volume Discretizations

Boundary Element Methods Governing Equation Small Displacement Field Homogeneous Isotropic Elastic

Boundary Element Method

Boundary Element Method

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

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

Governing Equations

FEM Method Time Marching Scheme Governing Equation Discrete Form in Time

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

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

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.

Lumped Parameter Models for SSI

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

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

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

Lumped Parameter Foundation Models Representative Lumped Parameter Values - Square

Lumped Parameter Foundation Models Representative Lumped Parameter Values Circular

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

Lumped Parameter Foundation Models wn = 3.3 x = 0.975

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

SSI Effects

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

SSI Effects – Cross Interaction Receiver Foundation Source Foundation

SSI Effects – Cross Interaction

SSI Effects – Cross Interaction

Traveling Wave Effects After Betti et al.

Traveling Wave Effects After Betti et al.

Traveling Wave Effects After Betti et al.

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 After Betti et al.

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.