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\MyLogo{\tiny{Jeremi{\'c}, PEER Annual Meeting, 2004}}
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\vspace*{2.0truecm}
\begin{center}
{\Large \bf
%\vspace*{1.5truecm} \\
\rule[-3mm]{0cm}{1.8cm} I-880 Bridge Testbed Simulations: \\
\rule[-3mm]{0cm}{1.8cm} Soil--Foundation--Structure Interaction Issues\\
%\rule[-3mm]{0cm}{1.3cm}  \\
}
\end{center}
%%%%%%%%%%%%%%%%%%%%%%%%%%





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\vspace*{4.0truecm}


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\begin{large}
\begin{center}
{\bf Boris Jeremi{\' c}}
\end{center}
\end{large}

\vspace*{-0.50truecm}

\begin{small}
\begin{center}
{Department of Civil and Environmental Engineering }\\
{University of California, Davis}\\
\end{center}
\end{small}



% \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{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{I--880: Where in the World?}
\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{I--880: Local Site Conditions}
\begin{large}



\begin{figure}[!h]
\vspace*{-0.3cm}
\begin{center}
{\includegraphics[width=20cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/soilmeshDEEP02.jpg}}
\end{center}
\end{figure}



\vspace*{-1.2cm}
\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}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\slide{I--880: Foundation System}
\begin{large}

%\vspace*{-0.3cm}
\begin{itemize}
%\vspace*{0.5cm}
\item Similar pile group beneath all piers

\end{itemize}

\vspace*{-3.0cm}

\begin{figure}[!h]
\begin{center}
{\includegraphics[width=9cm]{/home/jeremic/tex/works/Papers/2002/PBSE/bent16meters.pdf}}
\hspace*{5cm}
{\includegraphics[width=7cm]{/home/jeremic/tex/works/Presentation/2002/SFBayComputingDay/I-880_02.jpg}}
\\
{\includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/sg.jpg}}
{\includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/n2iso.jpg}}
\end{center}
\end{figure}

\vspace*{-2.0cm}

\end{large}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\slide{I--880: Systems Approach \\ Where are we Going}
\begin{large}






%\vspace*{-0.3cm}
\begin{itemize}

\vspace*{-0.3cm}
\item Currently investigated SFSI issues
   \begin{itemize}

     \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}


\vspace*{-0.3cm}
\item Application of the Domain Reduction Method to the bridge system simulations




\end{itemize}

\vspace*{-1.0cm}
\begin{figure}[!h]
\begin{center}
\hspace*{4cm}
{\includegraphics[width=16cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DRM0101.pdf}}
\end{center}
\end{figure}

\vspace*{-3.0cm}

\end{large}




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\slide{Domain Reduction Method (DRM)}


\begin{large}
\begin{itemize}
\vspace*{-0.35cm}
  \item  Work by Bielak et al. (since 1986, current paper: 2003, Bulletin of the Seismological Society of America) at CMU.
\vspace*{-0.35cm}
  \item Modular, two step procedure for large 3D dynamics problems.
    \begin{itemize}
      \item  Background wave field on simplified domain
      \item  Local wave field (coupled through acc. and disp.)
    \end{itemize}
% 
% %\vspace*{0.5cm}
%   \item Free field wave field from the background structure only act on a single
%   concave surface.
% %    \vspace*{-0.3cm}
%   \item Determination using any available numerical or measurement technique,
% %    \vspace*{-0.35cm}
%   \item Need displacement and acceleration field
%    \vspace*{-0.35cm}
\vspace*{-0.35cm}
  \item Green's functions solutions, Quake system, SCEC database, SHAKE, 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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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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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}
% 
% 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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{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: Stiff 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/DL_T615.pdf}}
\vspace*{-5.0cm}
%\end{center}
\end{figure}

 \hspace*{4cm} Free field   \hspace*{10cm}  SFSI




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\slide{SSI Model: Soft 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/DL_M615.pdf}}
\vspace*{-5.0cm}
%\end{center}
\end{figure}


 \hspace*{4cm} Free field   \hspace*{10cm}  SFSI



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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}
% 
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%  \hspace*{4cm} Stiff soil   \hspace*{10cm}  Soft soil
% 
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\slide{SSI Model: Seismic Amplification}


\begin{figure}[!h]
%\begin{center}
\vspace*{-1.5cm}
{\includegraphics[width=13.5cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/newthesis/figures/Eq_P/P_T_DL_NS.pdf}}
\hspace{-1.8cm}
{\includegraphics[width=13.5cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/newthesis/figures/Eq_P/P_S_DL_NS.pdf}}
\vspace*{-5.0cm}
%\end{center}
\end{figure}


 \hspace*{4cm} Stiff soil   \hspace*{10cm}  Soft soil



  
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\slide{Currently in Works}

\begin{large}


\begin{itemize}


\vspace*{1.0cm}
\item  Generation of background wave fields from point seismic motions data


\vspace*{1.0cm}
\item   Development   of   full   soil--foundation--structure  bridge  model  to
investigate influences of

\begin{itemize}
  \item Local site amplifications
  \item Coherency loss (stochastic variations)
  \item Time lag (wave passage effects)

\end{itemize}


\end{itemize}

\end{large}

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%   \slide{Conclusions}
%   
%   \begin{large}
%   
%   
%   \begin{itemize}
%   
%   %\vspace*{1.0cm}
%   \item    Application  domain:  Wave propagation in solids with local ''defects''
%   (different material, change of geometry...)
%   
%   %\vspace*{1.0cm}
%   \item Excellent radiation damping (by design!), usually need to dump out small number (single) of frequencies
%   
%   %\vspace*{1.0cm}
%   \item For bridge systems, the domain is already decomposed for distributed parallel computations
%   
%   %\vspace*{1.0cm}
%   \item  Implementation available in public domain within the OpenSees framework
%   
%   %\vspace*{1.0cm}
%   %\item
%   
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%   \end{itemize}
%   
%   \end{large}

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\end{document}
\bye





