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\begin{document}
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\begin{center}
{\huge \bf
%\vspace*{1.5truecm} \\
\rule[-3mm]{0cm}{1.8cm} Soil--Foundation--Structure \\
\rule[-3mm]{0cm}{1.8cm} Interaction Simulations: \\
\rule[-3mm]{0cm}{1.8cm} Static and Dynamic Issues\\
%\rule[-3mm]{0cm}{1.3cm} \\
}
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\begin{Large}
\begin{center}
{\bf Boris Jeremi{\' c}}
\end{center}
\end{Large}
\vspace*{-0.50truecm}
\begin{large}
\begin{center}
{Department of Civil and Environmental Engineering }\\
{University of California, Davis}\\
\end{center}
\end{large}
% \begin{small}
%
% \begin{description}
% %\item Supported in part by the NSF--PEER \#~EEC-9701568,
% %Cal--EPA \#~99-01337V,
% \item Supported in part by the NSF, PEER, Caltrans, and Cal--EPA.
%
% % \item Collaborators:
% % Professors
% % Zhaohui Yang (UAA),
% % Sashi Kunnath (UCD),
% % %Bruce Kutter (UCD),
% % Gregory Fenves (UCB),
% % Jacobo Bielak (CMU),
% % %Bernd Hamann (UCD),
% % %Zhaojun Bai (UCD),
% % George Karypis (UMN),
% % Drs.
% % Francis McKenna (UCB),
% % %and
% % %graduate students
% % %Xiaoyan Wu (UCD)
% % %Ritu Jain (UCD),
% % %Qing Liu (UCD),
% % %Jinxiu Liao (UCD).
% \end{description}
%
% \end{small}
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\slide{Leitmotiv}
\begin{large}
\begin{itemize}
\vspace*{0.5cm}
\item Create high fidelity models of constructed facilities
(bridges, buildings, port structures, dams...).
\vspace*{0.5cm}
\item Models will live concurrently with the physical system
they represent.
\vspace*{0.5cm}
\item Models to provide owners and operators with the
capabilities to assess operations and future performance.
\vspace*{0.5cm}
\item Use observed performance to update and validate models
through simulations.
\end{itemize}
\end{large}
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\slide{Presentation Overview}
\begin{large}
\vspace*{0.3cm}
\begin{itemize}
\item Role of numerical simulations
\item Static (kinematic) behavior
\begin{itemize}
\item Layered soils
\item Pile groups
\end{itemize}
\item Dynamic behavior
\begin{itemize}
\item Application of seismic loads (motions)
\item Site response analysis
\item From large scale geophysical simulations to large scale soil--structure simulations
\item Application to long bridges
\end{itemize}
\end{itemize}
\end{large}
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\slide{Goal}
\begin{large}
\vspace*{1.5cm}
\begin{itemize}
\vspace*{0.5cm}
\item {\bf Develop} and {\bf use} computational models in order to
\begin{itemize}
\item Design physical tests
\item Use observed behavior to {\bf validate} and {\bf improve} models
\item Use validated models to {\bf predict} behavior of realistic bridge systems
\end{itemize}
\vspace*{0.5cm}
\item Educate users about new, exciting simulation tools that are now available
\end{itemize}
\end{large}
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\slide{Goals of Validation}
\begin{large}
Quantification of uncertainties and errors in the computational model and the
experimental measurements
\begin{itemize}
\item Goals on validation
\begin{itemize}
\item Tactical goal: Identification and minimization of uncertainties and
errors in the computational model
\item Strategic goal: Increase confidence in the quantitative predictive
capability of the computational model
\end{itemize}
\item Strategy is to reduce as much as possible the following:
\begin{itemize}
\item Computational model uncertainties and errors
\item Random (precision) errors and bias (systematic) errors in the experiments
\item Incomplete physical characterization of the experiment
\end{itemize}
\end{itemize}
\end{large}
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\slide{Validation Procedure Uncertainty}
\begin{large}
\begin{itemize}
\item Aleatory uncertainty $\rightarrow$ inherent variation associated with the
physical system of the environment (variation in external excitation, material
properties...). Also know known as irreducible uncertainty, variability and
stochastic uncertainty.
\item Epistemic uncertainty $\rightarrow$ potential deficiency in any phase of
the modeling process that is due to lack of knowledge (poor understanding of
mechanics...). Also known as reducible uncertainty, model form uncertainty and
subjective uncertainty
\end{itemize}
\begin{figure}[!h]
\begin{center}
%\vspace*{-2.5cm}
{\includegraphics[width=20.0cm]{/home/jeremic/tex/works/Presentation/2004/UCLA/uncertain01.pdf}}
%\vspace*{-5.0cm}
\end{center}
\end{figure}
\end{large}
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%--- \slide{Types of Physical Experiments}
%---
%--- \begin{large}
%--- \begin{itemize}
%---
%--- \vspace*{1.0truecm}
%--- \item {\bf Traditional Experiments}
%--- \begin{itemize}
%--- \item Improve the fundamental understanding of physics involved
%--- \item Improve the mathematical models for physical phenomena
%--- \item Assess component performance
%--- \end{itemize}
%---
%--- \vspace*{1.0truecm}
%--- \item {\bf Validation Experiments}
%--- \begin{itemize}
%--- \item Model validation experiments
%--- \item Designed and executed to quantitatively estimate mathematical
%--- model's ability to simulate well defined physical behavior
%--- \item The simulation tool (SimTool) (conceptual model, computational model,
%--- computational solution) is the customer
%--- \end{itemize}
%---
%---
%--- \end{itemize}
%--- \end{large}
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\slide{Validation Experiments }
\begin{large}
\begin{itemize}
\vspace*{0.0truecm}
\item A validation experiment should be jointly designed and executed by
experimentalist and computationalist
\begin{itemize}
\item Need for close working relationship from inception to documentation
\item Elimination of typical competition between each
\item Complete honesty concerning strengths and weaknesses of both
experimental and computational simulations
\end{itemize}
\vspace*{0.0truecm}
\item A validation Experiment should be designed to capture the relevant physics
\begin{itemize}
\item Measure all important modeling data in the experiment
\item Characteristics and imperfections of the experimental facility
should be included in the model
\end{itemize}
\end{itemize}
\end{large}
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%--- \slide{Validation Experiments (contd)}
%---
%--- \begin{large}
%--- \begin{itemize}
%---
%--- \vspace*{0.0truecm}
%--- \item A validation experiment should use any possible synergism between
%--- experiment and computational approaches
%--- \begin{itemize}
%--- \item Offset strength and weaknesses of computations and experiments
%--- \item Use high confidence simulations for simple physics to calibrate or
%--- improve the characterization of the experimental facility
%--- \item Conduct experiments with a hierarchy of physics complexity to
%--- determine where the computational simulation breaks (remember, SimTool is
%--- the customer!)
%--- \end{itemize}
%---
%---
%--- \vspace*{0.0truecm}
%--- \item Maintain independence between computational and experimental results
%--- \begin{itemize}
%--- \item Blind comparison, the computational simulations should be predictions
%--- \item Neither side is allowed to use fudge factors, parameters
%--- \end{itemize}
%---
%---
%--- \end{itemize}
%--- \end{large}
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%--- \slide{Validation Experiments (contd)}
%---
%--- \begin{large}
%--- \begin{itemize}
%---
%--- \vspace*{0.0truecm}
%--- \item Validate experiments on unit level problems, hierarchy of experimental
%--- measurements should be made which present an increasing range of
%--- computational difficulty
%--- \begin{itemize}
%--- \item Use of qualitative data (e.g. visualization) and quantitative data
%--- \item Computational data should be processed to match the experimental
%--- measurement techniques
%--- \end{itemize}
%---
%--- \vspace*{0.0truecm}
%--- \item Experimental uncertainty analysis should be developed and employed
%--- \begin{itemize}
%--- \item Distinguish and quantify random and correlated bias errors
%--- \item Use symmetry arguments and statistical methods to identify
%--- correlated bias errors
%--- \item Make uncertainty estimates on input quantities needed by the SimTool
%--- \end{itemize}
%---
%---
%---
%---
%---
%---
%--- \end{itemize}
%--- \end{large}
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%--- \slide{Prediction}
%---
%--- \begin{large}
%--- \begin{itemize}
%---
%--- \vspace*{0.7truecm}
%--- \item Prediction: use of computational model to foretell the state of a
%--- physical system under consideration under conditions for which the
%--- computational model has not been validated
%---
%--- \vspace*{0.7
%--- truecm}
%--- \item Validation does not directly make a claim about the accuracy of a prediction
%--- \begin{itemize}
%--- \item Computational models are easily misused (unintentionally or intentionally)
%--- \item How closely related are the conditions of the prediction and
%--- specific cases in validation database
%--- \item How well is physics of the problem understood
%---
%--- \end{itemize}
%---
%---
%--- \end{itemize}
%--- \end{large}
%---
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% \slide{Relation Between Validation and Prediction}
%
% \begin{large}
%
% Quantification of confidence in a prediction:
%
% \begin{itemize}
%
% \vspace*{0.8truecm}
% \item How do I quantify validation and its inference value in a predictions?
%
% \vspace*{0.8truecm}
% \item How do I quantify verification and its inference value in a prediction?
%
% \vspace*{0.8truecm}
% \item How far are individual experiments in my validation database from my
% physical system of interest?
%
% % \item
%
% \end{itemize}
% \end{large}
%
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\slide{Application Domain}
\begin{large}
\vspace*{0.3cm}
\begin{figure}[!h]
\begin{center}
%\vspace*{-2.5cm}
{\includegraphics[width=20.0cm]{/home/jeremic/tex/works/Conferences/2003/PEERScholarsCourse/Present/VPI.pdf}}
%\vspace*{-5.0cm}
\end{center}
\end{figure}
\vspace*{-0.5cm}
\begin{itemize}
\vspace*{-0.2cm}
\item Inference $\Rightarrow$ Based on {\bf physics} or {\bf statistics}
\vspace*{-0.2cm}
\item Validation domain is actually an aggregation of tests (points) and might not
be convex (bifurcation of behavior)
\vspace*{-0.2cm}
\item NEES research provides for validation domain (experimental facilities)
that are mostly (if not exclusively) {\bf non--overlapping} with the application domain.
\end{itemize}
\end{large}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%---
%---
%---
%--- \slide{Validation and Prediction Simulations}
%--- \begin{large}
%---
%--- \begin{itemize}
%---
%--- \vspace*{0.5cm}
%--- \item Non--overlapping validation domain: hierarchical set of physical experiments (simple $\rightarrow$ complicated)
%---
%--- \vspace*{0.5cm}
%--- \item Uncertainty estimates for input quantities for the simulation tool (OpenSees)
%---
%--- \vspace*{0.5truecm}
%--- \item How do I quantify validation and its inference value in a predictions?
%---
%--- %\vspace*{0.2truecm}
%--- %\item How do I quantify verification and its inference value in a prediction?
%---
%--- \vspace*{0.5truecm}
%--- \item How far are individual experiments in my validation database from my
%--- physical system of interest?
%---
%--- %
%--- % \vspace*{0.5cm}
%--- % \item
%--- %
%--- % \vspace*{0.5cm}
%--- % \item
%--- %
%--- % \vspace*{0.5cm}
%--- % \item
%--- %
%--- % \vspace*{0.5cm}
%--- % \item
%---
%---
%--- \end{itemize}
%--- %1
%---
%--- \end{large}
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\slide{Computability}
\begin{large}
\begin{description}
\vspace*{1.8cm}
\item[Physical Problem Computability]: (von Neumann computability)
how well a mathematical model can predict the response of a mechanical system
(related to validation)
\vspace*{1.8cm}
\item[Computational computability]: (Turing computability) discretized
problem is computable if there exists an algorithm that can solve the problem in
a finite number of steps
(related to verification)
%
\end{description}
%
\end{large}
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% \slide{{Presentation Overview}
% \begin{large}
%
%
% \vspace*{0.3cm}
%
% \begin{itemize}
%
%
% \item {Role of numerical simulations}
%
%
% \item Static (kinematic) behavior
% \begin{itemize}
% \item Layered soils
% \item Pile groups
% \end{itemize}
%
%
%
% \item Dynamic behavior
%
% \begin{itemize}
% \item Application of seismic loads (motions)
% \item Site response analysis
% \item From large scale geophysical simulations to large scale soil--structure simulations
% \item Application to long bridges
% \end{itemize}
%
%
%
% \end{itemize}
%
% \end{large}
%
%
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\slide{Static (Kinematic) SFSI}
\begin{large}
\begin{itemize}
\item Computational geomechanics for large scale problems
\item Single pile behavior in elastic--plastic soils, effects of layers
\item Pile group behavior
\end{itemize}
\end{large}
%
\begin{figure}[!htbp]
\begin{center}
\vspace*{-0.8truecm}
\includegraphics[width=10.0truecm]{/home/jeremic/tex/works/Proposals/2000/CalTrans/boris02.jpg}
\hfill
\includegraphics[width=15.0truecm]{/home/jeremic/tex/works/Proposals/2000/CalTrans/boris01.jpg}
\vspace*{-0.8truecm}
\end{center}
%\caption{\label{code01} \footnotesize (a) Comparison of a typical seismic code design spectrum to
%the actual response spectra of several catastrophic earthquakes with strong long
%period components ($\xi = 5\%$) eg. Gazetas and Mylonakis
%(\cite{Gazetas98}); (b) Hanshin Expressway after Kobe Earthquake of 1995.}
%\vspace*{-0.3cm}
\end{figure}
%
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\slide{Single Pile in Layered Soils}
\begin{figure}[!htbp]
\vspace*{-5.0truecm}
\begin{center}
\includegraphics[width=12.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/MQP_dsand_UFmid2hdp0.pdf}
\hfill
\includegraphics[width=12.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/MQP_sand_wsfclay_UFmid2hdp0.pdf}
\end{center}
%\vspace*{-0.3cm}
\end{figure}
\vspace*{-3.5truecm}
\begin{normalsize}
\begin{figure}[!hbpt]
\begin{center}
%{\includegraphics[height=7.5cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/spUF_plastified_clay_xz_gs.jpg}}
%{\includegraphics[height=7.5cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/spUF_plastified_clay_sand_xz_gs.jpg}}
{\includegraphics[height=7.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/spUF_plastified_sand_xz_gs.jpg}}
\hfill
\includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/spUFmesh.jpg}
\hfill
{\includegraphics[height=7.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/spUF_plastified_sand_clay_xz_gs.jpg}}
\end{center}
\vspace*{-1truecm}
\end{figure}
\end{normalsize}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\slide{$p-y$ Response for Single Pile in Layered Soils}
\begin{figure}[!htbp]
\begin{center}
\includegraphics[width=12.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/p_y_dsand_UFmid2hdp0.pdf}
\hfill
\includegraphics[width=12.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/p_y_sand_sfclay_UFmid2hdp0.pdf}
\end{center}
%\vspace*{-0.3cm}
\end{figure}
\begin{large}
\begin{itemize}
\item Influence of soft layers propagates to stiff layers and vice versa
\item Can have significant effects in soils with many layers
\end{itemize}
\end{large}
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\slide{Lateral Resistance Ratio Distributions}
\begin{figure}[!htbp]
\begin{center}
\vspace*{-6.3cm}
\includegraphics[width=18.0cm]{/home/jeremic/tex/works/Presentation/2004/UCLA/P_ReductionRatio_SCSnE_050_065.pdf}
\vspace*{-6.8cm}
\end{center}
%\vspace*{-0.3cm}
\end{figure}
\begin{large}
\begin{itemize}
\item Influence increases as the shear strength of soft layer decreases
(think of cyclic mobility of liquefaction)
\end{itemize}
\end{large}
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\slide{Pile Group Simulations}
\vspace*{-0.8cm}
\begin{figure}[!hbpt]
\begin{center}
{\includegraphics*[width=12cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/PileGroups/p4X3_Joey_iso.pdf}}
\hfill
{\includegraphics*[width=12cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/PileGroups/p4X3_PlasticZone_iso.pdf}}
%\hfill
%{\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/PileGroups/p4X3_PlasticZone_xz.pdf}}
%\\
\end{center}
\vspace*{-2.3cm}
\end{figure}
\begin{large}
\begin{itemize}
\item 4x3 pile group model and plastic zones
\end{itemize}
\end{large}
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\slide{Out of Plane Effects}
\begin{figure}[!hbpt]
\vspace*{-0.3cm}
\begin{center}
{\includegraphics[height=13cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/PileGroups/Mx_4x3_4piles_com_dense.jpg}}
%\hfill
{\includegraphics[height=13cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/PileGroups/p4X3_deformedPile_Y.jpg}}
\end{center}
\end{figure}
\vspace*{-1.0cm}
%
\begin{large}
\begin{itemize}
\item Out-of-loading-plane bending moment diagram,
\item Out-of-loading-plane deformation.
\end{itemize}
\end{large}
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\slide{Pile Spreading Stress Path}
%
\begin{figure}[!htb]
\begin{center}
%{\includegraphics[height=9truecm]{/home/jeremic/tex/works/Papers/2001/Visualization/pic70.jpg}}
%\hfill
{\includegraphics[height=16truecm]{/home/jeremic/tex/works/Papers/2001/Visualization/pic80.jpg}}
\end{center}
\vspace*{-1cm}
\end{figure}
% \begin{large}
% \begin{itemize}
% \item Stress hedgehogs
% \item Hyper--stream--sufraces
% \end{itemize}
% \end{large}
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\slide{Load Distribution per Pile}
\begin{figure}[!h]
\vspace*{-6.3cm}
\begin{center}
{\includegraphics*[width=22cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/PileGroups/LoadRatio_per_pile_Dense_pg4x3.pdf}}
\end{center}
\end{figure}
\vspace*{-8.3cm}
%\begin{large}
%\begin{itemize}
%\item Load distribution per pile.
%\end{itemize}
%\end{large}
%
%
% \begin{figure}[!htbp]
% \begin{center}
% \vspace*{-0.3cm}
% \hspace*{8.3cm}
% {\includegraphics[width=12.0cm]{/home/jeremic/tex/works/Conferences/2001/EngMechSD/Dynamics/Present/pilegroupELPLFAS.pdf}}
% \\
% \vspace*{-6.3cm}
% {\includegraphics[width=8.50cm]{/home/jeremic/tex/works/Conferences/2001/EngMechSD/Dynamics/Present/singlepile02.pdf}}
% \hfill
% {\includegraphics[width=12.0cm]{/home/jeremic/tex/works/Conferences/2001/EngMechSD/Dynamics/Present/RinaldiFAS.pdf}}
% \vspace*{-0.50cm}
% \end{center}
% %\vspace*{-0.3cm}
% \end{figure}
%
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\slide{Piles Interaction at -2.0m}
%\vspace*{-1.3cm}
\begin{figure}[!hbpt]
\begin{center}
{\includegraphics[width=20cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/PileGroups/pg4x3_p_y_allpiles_20.jpg}}
\end{center}
%\vspace*{-1.3cm}
\end{figure}
\begin{large}
\begin{itemize}
\item Note the difference in response curves (cannot scale single pile response
for multiple piles)
\end{itemize}
\end{large}
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\slide{Comparison with Centrifuge Tests}
\begin{figure}[!hbpt]
\vspace*{-6.3cm}
\begin{center}
{\includegraphics[width=22.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/PileGroups/Com_LoadRatio_per_row_Dense_pg4x3.pdf}}
\end{center}
\vspace*{-8.3cm}
\end{figure}
%
%
% \begin{large}
% \begin{itemize}
% \item Good agreement for larger loads
% \end{itemize}
% \end{large}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \slide{Tube Hyperstreamlines}
% %
% \vspace*{1cm}
%
% \begin{figure}[!htb]
% \begin{center}
% {\includegraphics[height=10truecm]{/home/jeremic/tex/works/Papers/2001/Visualization/pic71.jpg}}
% \hfill
% {\includegraphics[height=10truecm]{/home/jeremic/tex/works/Papers/2001/Visualization/pic33.jpg}}
% \end{center}
% \vspace*{-1cm}
% \end{figure}
% %
%
% % \begin{large}
% % \begin{itemize}
% % \item Tube hyper--stream--lines
% % \end{itemize}
% % \end{large}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\slide{Dynamic SFSI}
\begin{large}
\begin{itemize}
\vspace*{0.5cm}
\item Application of seismic loads (motions)
\vspace*{0.5cm}
\item Site response analysis
\vspace*{0.5cm}
\item From large scale geophysical simulations to large scale soil--structure simulations
\vspace*{0.5cm}
\item Application to long bridges
\end{itemize}
\end{large}
% \begin{normalsize}
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\slide{Domain Reduction Method (DRM)}
\begin{large}
\begin{itemize}
\vspace*{0.5cm}
\item Work by Bielak et al. (2003, Bulletin of the Seismological Society of America) at CMU.
\vspace*{0.5cm}
\item Modular, two step procedure for large 3D dynamics problems.
\vspace*{0.5cm}
\item Primary unknowns:
\begin{itemize}
\item Total wave field within the local domain,
\item Scattered wave field in the exterior domain,
\end{itemize}
\vspace*{0.5cm}
\item Free field wave field from the background structure only act on a single
concave surface.
\end{itemize}
\end{large}
% \begin{normalsize}
% \begin{figure}[!htbp]
% \vspace*{0.50cm}
% \begin{center}
% {\includegraphics[width=16cm]{/home/jeremic/tex/works/Conferences/2001/PEERInitMeet/DRM01.pdf}}
% \vspace*{-0.50cm}
% \end{center}
% %\vspace*{-0.3cm}
% \end{figure}
% \end{normalsize}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\slide{DRM: Background Wave Field}
\begin{large}
\begin{itemize}
\vspace*{-0.3cm}
\item Determination using any available numerical or measurement technique,
\vspace*{-0.35cm}
\item Need displacement and acceleration field
\vspace*{-0.35cm}
\item Green's functions solutions, Quake system, SCEC database, SHAKE...
\vspace*{-0.35cm}
\item 3D downhole arrays,
\end{itemize}
\end{large}
\begin{normalsize}
\begin{figure}[!htbp]
\vspace*{-0.70cm}
\begin{center}
{\includegraphics[width=14cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DRM0102.pdf}}
\vspace*{-2.50cm}
\end{center}
%\vspace*{-0.3cm}
\end{figure}
\end{normalsize}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\slide{DRM: Idea}
\begin{large}
\begin{itemize}
\item Simplified original model
\item Local geological feature
\end{itemize}
\end{large}
\begin{normalsize}
\begin{figure}[!htbp]
\vspace*{-3.50cm}
\begin{center}
%\hspace*{1cm}
%{\includegraphics[angle=-90,width=10cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DRM03.pdf}}
{\includegraphics[width=12cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DRM03.pdf}}
\hfill
%{\includegraphics[angle=-90,width=10cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DRM04.pdf}}
{\includegraphics[width=12cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DRM04.pdf}}
%\hspace*{1cm}
\vspace*{-2.50cm}
\end{center}
%\vspace*{-0.3cm}
\end{figure}
\end{normalsize}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\slide{DRM: Dynamics}
\vspace*{-0.5cm}
\begin{eqnarray*}
\left[\begin{array}{cc} M^\Omega_{ii} & M^\Omega_{ib} \\ M^\Omega_{bi} & M^\Omega_{bb}\end{array}\right]
\left\{\begin{array}{c}\ddot{u}_i \\ \ddot{u}_b\end{array}\right\}+\left[\begin{array}{cc} K^\Omega_{ii
} & K^\Omega_{ib} \\ K^\Omega_{bi} & K^\Omega_{bb}\end{array}\right]
\left\{\begin{array}{c} u_i \\ u_b \end{array}\right\}=\left\{\begin{array}{c} 0 \\ P_b\end{array}\right\} ,\rm{in} \ \Omega
\label{e11}
\end{eqnarray*}
\vspace*{-2.0cm}
\begin{eqnarray*}
\left[\begin{array}{cc} M^{\Omega+}_{bb} & M^{\Omega+}_{be} \\ M^{\Omega+}_{eb} & M^{\Omega+}_{ee}\end{array}\right]
\left\{\begin{array}{c}\ddot{u}_b \\ \ddot{u}_e\end{array}\right\}+\left[\begin{array}{cc}K^{\Omega+}_{bb} & K^{\Omega+}_{be} \\
K^{\Omega+}_{eb} & K^{\Omega+}_{ee}\end{array}\right]
\left\{\begin{array}{c}u_b \\ u_e \end{array}\right\}=\left\{\begin{array}{c}-P_b \\ P_e \end{array}\right\}, \rm{in} \ \Omega^+
\label{e12}
\end{eqnarray*}
%Summed up $\Rightarrow$ classical form
\vspace*{-1.5cm}
\begin{eqnarray*}
\left[\begin{array}{ccc}M^{\Omega}_{ii} & M^{\Omega}_{ib} & 0 \\
M^\Omega_{bi} & M^\Omega_{bb}+M^{\Omega+}_{bb} & M^{\Omega+}_{be}\\ 0 & M^{\Omega+}_{eb} & M^{\Omega+}_{ee} \end{array}\right]
\left\{\begin{array}{c}\ddot{u}_i \\ \ddot{u}_b \\ \ddot{u}_e\end{array}\right\}
+
\\
\left[ \begin{array}{ccc}K^\Omega_{ii} & K^{\Omega}_{ib} & 0 \\
K^{\Omega}_{bi} & K^{\Omega}_{bb}+K^{\Omega+}_{bb} & K^{\Omega+}_{be} \\
0 & K^{\Omega+}_{eb} & K^{\Omega+}_{ee} \end{array}\right] \left\{\begin{array}{c} u_i \\ u_b \\ u_e \end{array} \right\}
=
\left\{\begin{array}{c} 0 \\ 0 \\ P_e\end{array}\right\}
%\nonumber \\ \label{e13}
\end{eqnarray*}
\vspace*{-0.5cm}
\begin{normalsize}
\begin{figure}[!htbp]
\vspace*{-4.50cm}
\begin{center}
%\hspace*{1cm}
%{\includegraphics[angle=-90,width=10cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DRM03.pdf}}
{\includegraphics[width=8cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DRM03.pdf}}
%\hfill
%\hspace*{1cm}
\vspace*{-2.50cm}
\end{center}
%\vspace*{-0.3cm}
\end{figure}
\end{normalsize}
%
% \begin{large}
% \begin{itemize}
% \item Simplified original model
% \item Local geological feature
% \end{itemize}
% \end{large}
%
%
% \begin{normalsize}
% \begin{figure}[!htbp]
% \vspace*{-0.50cm}
% \begin{center}
% \hspace*{1cm}
% {\includegraphics[angle=-90,width=10cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DRM03.pdf}}
% \hfill
% {\includegraphics[angle=-90,width=10cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DRM04.pdf}}
% \hspace*{1cm}
% \vspace*{-2.50cm}
% \end{center}
% %\vspace*{-0.3cm}
% \end{figure}
% \end{normalsize}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\slide{DRM: Change of Variables}
Equations of motion in $\Omega^+$ for changed model
\vspace*{-1.5cm}
\begin{eqnarray*}
\left[\begin{array}{cc}M^{\Omega+}_{bb} & M^{\Omega+}_{be} \\ M^{\Omega+}_{eb} & M^{\Omega+}_{ee} \end{array} \right]
\left\{\begin{array}{c}\ddot{u}^0_b \\ \ddot{u}^0_e \end{array}\right\}+\left[\begin{array}{cc}K^{\Omega+}_{bb} & K^{\Omega+}_{be} \\
K^{\Omega+}_{eb} & K^{\Omega+}_{ee}\end{array}\right]
\left\{\begin{array}{c} u^0_b \\ u^0_e\end{array}\right\}=\left\{\begin{array}{c}-P^0_b \\ P_e\end{array}\right\}
\Rightarrow
\label{e14}
\end{eqnarray*}
%
\vspace*{-2.85cm}
\begin{eqnarray*}
P_e = M^{\Omega+}_{eb}\ddot{u}^0_b+ M^{\Omega+}_{ee}\ddot{u}^0_e+
K^{\Omega+}_{eb}u^0_b+K^{\Omega+}_{ee}u^0_e
\label{e15}
\end{eqnarray*}
Change of variables: $u_e=u^0_e+w_e$
\begin{itemize}
\vspace*{-0.5cm}
\item total displacement $u_e$
\vspace*{-0.5cm}
\item free field, background structure $u^0_e$
\vspace*{-0.5cm}
\item residual field, relative displacement field with respect to the reference free, background field $w_e$
\end{itemize}
\vspace*{-1.5cm}
\begin{footnotesize}
\begin{eqnarray*}
\left[\begin{array}{ccc}M^{\Omega}_{ii} & M^{\Omega}_{ib} & 0 \\
M^\Omega_{bi} & M^\Omega_{bb}+M^{\Omega+}_{bb} & M^{\Omega+}_{be}
\\ 0 & M^{\Omega+}_{eb} & M^{\Omega+}_{ee} \end{array}\right]
\left\{\begin{array}{c}\ddot{u}_i \\ \ddot{u}_b \\ \ddot{w}_e\end{array}\right\}+
\left[ \begin{array}{ccc}K^\Omega_{ii} & K^{\Omega}_{ib} & 0 \\
K^{\Omega}_{bi} & K^{\Omega}_{bb}+K^{\Omega+}_{bb} & K^{\Omega+}_{be} \\
0 & K^{\Omega+}_{eb} & K^{\Omega+}_{ee} \end{array}\right]
\left\{\begin{array}{c} u_i \\ u_b \\ w_e \end{array} \right\}
=
\left\{\begin{array}{c} P^{eff}_i \\ P^{eff}_b \\ P^{eff}_e \end{array}\right\}
%
% \nonumber \\ \left\{\begin{array}{c} 0 \\ -M^{\Omega+}_{be} \ddot{u}^0_e-K^{\Omega+}_{be}u^0_e
% \\ M^{\Omega+}_{eb}\ddot{u}^0_b+K^{\Omega+}_{eb}u^0_b\end{array}\right\}
\label{e18}
\end{eqnarray*}
\end{footnotesize}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\slide{DRM: Dynamic (Seismic) Forces}
\vspace*{1cm}
%After substitions
\begin{figure}[!htb]
%
%\unitlength 1cm
%\begin{large}
\begin{minipage}[t]{6cm}
%
\begin{eqnarray*}
\left\{\begin{array}{c} P^{eff}_i \\ P^{eff}_b \\ P^{eff}_e \end{array}\right\}
= \left\{\begin{array}{c} 0 \\ -M^{\Omega+}_{be} \ddot{u}^0_e-K^{\Omega+}_{be}u^0_e
\\ M^{\Omega+}_{eb}\ddot{u}^0_b+K^{\Omega+}_{eb}u^0_b\end{array}\right\}
\end{eqnarray*}
\end{minipage}
%\end{large}
%
\hfill
%
\begin{minipage}[t]{10cm}
\begin{normalsize}
% \begin{picture}(10.0 ,2.0)
% \begin{picture}(10.0 ,2.0)(4.0, 0.0)
\begin{figure}[!h]
%\vspace*{-0.50cm}
%\begin{center}
%\hspace*{1cm}
\vspace*{-4.50cm}
{\includegraphics[width=10cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DRM05.pdf}}
\vspace*{-5.50cm}
%\hspace*{1cm}
%\vspace*{-2.50cm}
%\end{center}
%\vspace*{-0.3cm}
\end{figure}
% \end{picture}
\end{normalsize}
\end{minipage}
%
\end{figure}
\vspace*{1.5cm}
\begin{large}
\begin{itemize}
\vspace*{-0.5cm}
\item Seismic forces $P_e$ replaced by
the effective nodal forces $P^{eff}$,
\vspace*{-0.5cm}
\item $P^{eff}$ involve only submatrices, $M_{be}$,$K_{be}$,$M_{eb}$,$K_{eb}$
\vspace*{-0.5cm}
\item They vanish everywhere except in the single layer of elements in $\Omega^+$
adjacent to $\Gamma$.
\vspace*{-0.5cm}
\item The material inside $\Omega$ does not have to be linear elastic
% \item The only input wave field is the one for the nodes of this layer of elements.
\end{itemize}
\end{large}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\slide{Application Examples}
\begin{large}
\begin{itemize}
\vspace*{1.0cm}
\item Seismic wave propagation
\begin{itemize}
\item Effects of elastic plastic soils on free field motions
\end{itemize}
\vspace*{1.0cm}
\item Soil--Structure interaction
\begin{itemize}
\item Effects of elastic--plastic soils on dynamic response of pile--column system
\end{itemize}
\end{itemize}
\end{large}
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\slide{Wave Propagation Model}
\begin{figure}[!h]
\vspace*{-0.0cm}
\begin{center}
{\includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/thesis/figures/model1a.jpg}}
\\
\vspace*{-3.8cm}
{\includegraphics[width=10.5cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/thesis/figures/Inp_acc0507.pdf}}
%\hfill
{\includegraphics[width=10.5cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/thesis/figures/Inp_dis0507.pdf}}
\vspace*{-4.8cm}
\end{center}
\end{figure}
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\slide{Wave Propagation \\ Soft Soil}
\begin{figure}[!h]
%\begin{center}
\vspace*{-3.5cm}
{\includegraphics[width=13.5cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/thesis/figures/TS/DL_SS.pdf}}
\hspace{-1.8cm}
{\includegraphics[width=13.7cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/thesis/figures/TS/DY_SS.pdf}}
\vspace*{-5.0cm}
%\end{center}
\end{figure}
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\slide{Wave Propagation \\ Stiff Soil}
\begin{figure}[!h]
%\begin{center}
\vspace*{-2.5cm}
{\includegraphics[width=13.5cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/thesis/figures/TS/DL_TS.pdf}}
\hspace{-1.8cm}
{\includegraphics[width=13.5cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/thesis/figures/TS/DY_TS.pdf}}
\vspace*{-5.0cm}
%\end{center}
\end{figure}
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\slide{SSI Model}
\begin{figure}[!h]
\vspace*{-0.0cm}
\begin{center}
{\includegraphics[width=12cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/model3.jpg}}
\\
\vspace*{-4.8cm}
{\includegraphics[width=10.5cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/newthesis/figures/Model3/AT.pdf}}
%\hfill
{\includegraphics[width=10.5cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/newthesis/figures/Model3/DT.pdf}}
\vspace*{-4.8cm}
\end{center}
\end{figure}
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\slide{SSI Model Free Field \\ Stiff Elastic--Plastic Soil}
\begin{figure}[!h]
%\begin{center}
\vspace*{-2.5cm}
{\includegraphics[width=13.5cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DL_T617.pdf}}
\hspace{-1.8cm}
{\includegraphics[width=13.5cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DY_T617.pdf}}
\vspace*{-5.0cm}
%\end{center}
\end{figure}
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\slide{SSI Model: Pile--Column \\ Stiff Elastic--Plastic Soil}
\begin{figure}[!h]
%\begin{center}
\vspace*{-2.5cm}
{\includegraphics[width=13.5cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DL_T615.pdf}}
\hspace{-1.8cm}
{\includegraphics[width=13.5cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DY_T615.pdf}}
\vspace*{-5.0cm}
%\end{center}
\end{figure}
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\slide{SSI Model Free Field \\ Soft Elastic--Plastic Soil}
\begin{figure}[!h]
%\begin{center}
\vspace*{-2.5cm}
{\includegraphics[width=13.5cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DL_M617.pdf}}
\hspace{-1.8cm}
{\includegraphics[width=13.5cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DY_M617.pdf}}
\vspace*{-5.0cm}
%\end{center}
\end{figure}
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\slide{SSI Model: Pile--Column \\ Soft Elastic--Plastic Soil}
\begin{figure}[!h]
%\begin{center}
\vspace*{-2.5cm}
{\includegraphics[width=13.5cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DL_M615.pdf}}
\hspace{-1.8cm}
{\includegraphics[width=13.5cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DY_M615.pdf}}
\vspace*{-5.0cm}
%\end{center}
\end{figure}
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\slide{SSI Model: Pile--Column Behavior}
\begin{figure}[!h]
%\begin{center}
\vspace*{-2.5cm}
{\includegraphics[width=13.5cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/Top_T615.pdf}}
\hspace{-1.8cm}
{\includegraphics[width=13.5cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/Top_M615.pdf}}
\vspace*{-5.0cm}
%\end{center}
\end{figure}
\hspace*{4cm} Stiff soil \hspace*{10cm} Soft soil
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\slide{I--880 Bridge SFSI Issues}
\begin{large}
\begin{itemize}
%\vspace*{1.0cm}
\item Seismic response of I--880 viaduct using performance based engineering
%\vspace*{1.0cm}
\item Hierarchical set of SFSI simulations models developed to represent
engineering demand parameters (EDP)
%\vspace*{1.0cm}
\item Local site conditions (inelastic SFSI interaction problem)
%\vspace*{1.0cm}
\item Wave propagation over the bridge length (scale problem)
%\vspace*{1.0cm}
\item Single point (spatial) far field input motions
%\vspace*{1.0cm}
\item Stochastic distribution of materials (properties) over spatial scales
% %\vspace*{1.0cm}
% \item
%
%
% %\vspace*{1.0cm}
% \item
%
\end{itemize}
\end{large}
%
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\slide{Geologic and Soil Conditions}
\begin{large}
\begin{figure}[!h]
%\vspace*{-0.6cm}
\begin{center}
{\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Presentation/2002/SFBayComputingDay/aerial04.jpg}}
%{\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Presentation/2002/SFBayComputingDay/aerial01.jpg}}
{\includegraphics[width=6cm]{/home/jeremic/tex/works/Presentation/2002/SFBayComputingDay/aerial02.jpg}}
{\includegraphics[width=6cm]{/home/jeremic/tex/works/Presentation/2002/SFBayComputingDay/aerial03.jpg}}
\\
\vspace*{0.3cm}
{\includegraphics[width=10cm]{/home/jeremic/tex/works/Papers/2002/PBSE/Map02.jpg}}
\vspace*{-0.9cm}
\end{center}
\end{figure}
% \vspace*{-0.3cm}
% \begin{itemize}
%
% %\vspace*{0.5cm}
% \item
%
% \item
%
%
%
%
% \end{itemize}
\end{large}
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\slide{Local Site Conditions}
\begin{large}
\begin{figure}[!h]
\vspace*{-0.5cm}
\begin{center}
{\includegraphics[width=20cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/soilmeshDEEP02.jpg}}
\end{center}
\end{figure}
\vspace*{-0.7cm}
\begin{itemize}
%\vspace*{0.5cm}
\item Adjacency of foundations in soft and stiff soil
\vspace*{-0.5cm}
\item Spatial distribution of soil materials
\vspace*{-0.5cm}
\end{itemize}
\end{large}
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\slide{Soil--Foundation System Models}
\begin{large}
%\vspace*{-0.3cm}
\begin{itemize}
%\vspace*{-0.5cm}
%\item Similar pile groups beneath all piers
\vspace*{-0.5cm}
\item Hierarchical set of models used to estimate performance
\vspace*{-0.5cm}
\item Reducing epistemic uncertainty as much as possible
\end{itemize}
\vspace*{-1.0cm}
\begin{figure}[!h]
\begin{center}
{\includegraphics[width=10cm]{/home/jeremic/tex/works/Papers/2002/PBSE/bent16meters.pdf}}
\hspace*{2cm}
{\includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/b234.jpg}}
\\
{\includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/sg.jpg}}
\hspace*{2cm}
{\includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/n2iso.jpg}}
\end{center}
\end{figure}
\vspace*{-4.0cm}
\end{large}
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\slide{I--880: Hierarchy of Models}
\begin{large}
%\vspace*{-0.3cm}
% \begin{itemize}
% %\vspace*{0.5cm}
% \item Similar pile group beneath all piers
%
% \end{itemize}
%\vspace*{-0.0cm}
\begin{figure}[!h]
\begin{center}
{\includegraphics[width=14cm]{/home/jeremic/tex/works/Presentation/2003/PEER-Site-Visit/I880_system.jpg}}
{\includegraphics[width=8cm]{/home/jeremic/tex/works/Papers/2002/PBSE/model02.jpg}}
%
\\ \vspace*{0.5cm}
{\includegraphics[height=6.50cm]{/home/jeremic/oofep/OpenSees/EXAMPLES/ExampleScripts/I-880_Bent16/Structure/HingeElement/Disp80FixSpr20hinge_a.jpg}}
{\includegraphics[height=6.50cm]{/home/jeremic/oofep/OpenSees/EXAMPLES/ExampleScripts/I-880_Bent16/Structure/HingeElement/period20Hinge_ps.jpg}}
\end{center}
\end{figure}
\vspace*{-2.0cm}
\end{large}
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\slide{I--880: Seismic Input}
\begin{large}
\vspace*{-0.3cm}
\begin{itemize}
%\vspace*{0.5cm}
\vspace*{-0.5cm}
\item Coupling free field motions to SFSI system (Domain Reduction Method)
\vspace*{-0.5cm}
\item Wave propagation over the \\ bridge length
%\vspace*{-0.5cm}
%item Large scale simulation model, parallel computing (development of Plastic
%Domain Decomposition Method)
\end{itemize}
\end{large}
\vspace*{-3.0cm}
\begin{figure}[!h]
\begin{center}
%\hspace*{4cm}
{\includegraphics[width=24cm]{/home/jeremic/tex/works/Reports/2004/PEER/NSF-Site-Visit/Presentation/I-880-sim-model01.pdf}}
\end{center}
\end{figure}
\vspace*{-3.0cm}
%\item Based on state of the art computational mechanics theories and implementation
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%\item Based on state of the art computational mechanics theories and implementation
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\slide{Seismic Amplification}
\begin{large}
\vspace*{-0.3cm}
\begin{itemize}
%\vspace*{0.5cm}
\item Adjacent bents
\item Foundation will survive but the superstructure or joints might not
\end{itemize}
\begin{figure}[!h]
%\begin{center}
\vspace*{-4.5truecm}
{\includegraphics[width=13.5truecm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/newthesis/figures/Eq_P/P_T_DL_NS.pdf}}
\hspace{-1.8truecm}
{\includegraphics[width=13.5truecm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/newthesis/figures/Eq_P/P_S_DL_NS.pdf}}
\vspace*{-6.0truecm}
%\end{center}
\end{figure}
\hspace*{4cm} Stiff soil \hspace*{10cm} Soft soil
\end{large}
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\slide{Concluding Remarks}
\begin{large}
\vspace*{0.3cm}
\begin{itemize}
\vspace*{0.6cm}
\item Static (kinematic) SFSI issues
\begin{itemize}
\item Layered soils
\item Piles in liquefied soils (layers)
% \item
\end{itemize}
\vspace*{0.6cm}
\item Dynamic (seismic) SFSI issues
\begin{itemize}
\item Free field vs. SFSI motions
\item Very large scale coupling (with geophysical simulations)
% \item Wave propagation over the bridge length (scale problem)
% \item Single point (spatial) far field input motions
% \item Stochastic distribution of materials (properties) over spatial scales
\end{itemize}
\end{itemize}
\end{large}
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\slide{Thank you}
\begin{center}
\includegraphics[height=4.5truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/PileGroups/Plastified_3X3pg_skewCOLOR.jpg}
\includegraphics[height=4.5truecm]{/home/jeremic/public_html/GeoWulf/GeoWulf_01_Nov2001a.jpg}
\includegraphics[height=4.5truecm]{/home/jeremic/tex/works/Papers/2001/Visualization/pic30.jpg}
\includegraphics[height=4.5truecm]{/home/jeremic/tex/works/Papers/2001/Visualization/pic71.jpg}
\\
\vspace*{0.2cm}
\includegraphics[height=4.0truecm]{/home/jeremic/tex/works/Papers/2001/Visualization/pic80.jpg}
\includegraphics[height=4.0truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/MQP_sand_wsfclay_UFmid2hdp0.jpg}
\includegraphics[height=4.0truecm]{/home/jeremic/tex/works/Reports/2001/PEER/FinalReport/sp2_stress_pile_isoSmall.jpg}
\includegraphics[height=4.0truecm]{/home/jeremic/tex/works/Reports/2001/PEER/FinalReport/sp2_MQP_pile.jpg}
\\
\vspace*{0.2cm}
\includegraphics[height=5.0truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cubic_el_05.jpg}
\includegraphics[height=5.0truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cubic_pl_05.jpg}
\includegraphics[height=5.0truecm]{/home/jeremic/tex/works/Conferences/2002/WCCM/Keynote/Present/p-version_slope.jpg}
\end{center}
%\vspace*{1cm}
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\end{document}
\bye