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\title[Directing Energy Dissipation in Earthquake-Soil-Structure Systems]
% (optional, use only with long paper titles)
{Directing Energy Dissipation in Earthquake-Soil-Structure Systems}

%\subtitle
%{{\tiny full set of slides available at:}\\
%%\verb{http://sokocalo.engr.ucdavis.edu/~jeremic/}
%}

\pgfdeclareimage[height=0.2cm]{university-logo}{/home/jeremic/BG/amblemi/ucdavis_logo_blue_sm}

%\author[Boris Jeremi{\'c}, CompGeoMech \includegraphics[width=8cm]{/home/jeremic/BG/amblemi/ucdavis_logo_gold_lrg}] % (optional, use only with lots of authors)
\author[Boris Jeremi{\'c}] % (optional, use only with lots of authors)
{Boris~Jeremi{\'c},\\ 
Nima Tafazzoli, Mahdi Taiebat, Guanzhou Jie}
% - Give the names in the same order as the appear in the paper.
% - Use the \inst{?} command only if the authors have different
%   affiliation.

%\institute[Computational Geomechanics Group
\institute[Computational Geomechanics Group
\pgfuseimage{university-logo} \hspace*{-0.3truecm}] % (optional, but mostly needed)
{ \vspace*{1cm} \\

  Department of Civil and Environmental Engineering\\
  University of California, Davis}
% - Use the \inst command only if there are several affiliations.
% - Keep it simple, no one is interested in your street address.

\date[CompDyn09] % (optional, should be abbreviation of conference name)
{CompDyn09}
% - Either use conference name or its abbreviation.
% - Not really informative to the audience, more for people (including
%   yourself) who are reading the slides online

\subject{}
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\end{frame}

\begin{frame}
  \frametitle{Outline}
  \tableofcontents
  % You might wish to add the option [pausesections]
\end{frame}


% Structuring a talk is a difficult task and the following structure
% may not be suitable. Here are some rules that apply for this
% solution: 

% - Exactly two or three sections (other than the summary).
% - At *most* three subsections per section.
% - Talk about 30s to 2min per frame. So there should be between about
%   15 and 30 frames, all told.

% - A conference audience is likely to know very little of what you
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%   enough. Leave out details, even if it means being less precise than
%   you think necessary.
% - If you omit details that are vital to the proof/implementation,
%   just say so once. Everybody will be happy with that.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Motivation}

\subsection*{Motivation}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Motivation}

\begin{itemize}
  


\vspace*{0.3cm}
  \item Improving seismic design for infrastructure objects

\vspace*{0.3cm}
  \item  Use of high fidelity numerical models in analyzing seismic behavior
  of soil--structure systems


\vspace*{0.3cm}
  \item Accurately (high fidelity modeling and simulations) 
  following the flow of seismic energy in the soil--structure system

\vspace*{0.3cm}
  \item Directing, in space and time, seismic energy flow in the soil--structure system

  

\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Hypothesis}

\begin{itemize}
  


\vspace*{0.5cm}
  \item    Interplay   of  Earthquake  with    Soil  and  Structure plays  major
  role in (catastrophic) failures (and successes).


\vspace*{0.5cm}
  \item   Timing  and spatial location of energy dissipation determines location
  and amount of damage.

\vspace*{0.5cm}
  \item  If timing and spatial location of energy dissipation can be controlled,
  we could  optimize soil--structure systems  for
    \begin{itemize}
      \item Safety and
      \item Economy
    \end{itemize}

\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{First Published Work on Soil--Structure  Interaction}

  \begin{itemize}
         \item Professor Kyoji Suyehiro 
         \item Ship engineer (Professor of Naval Arch. at U. of Tokyo),
         \item Was in Tokyo during Great Kant{\= o} earthquake 
               (11:58am(7.5),    12:01pm(7.3),    12.03pm(7.2)  (shaking until
               12:08pm), 1st. Sept. 1923)
         \item Saw earthquake surface waves travel and buildings sway 
         \item Founding Director of the Earthquake Engineering Research Institute  Univ. of Tokyo),
         \item  Records  shows $4 \times$ (four) more damage to soft
                wooden buildings on soft ground
  \end{itemize}

\end{frame}






%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Northridge Example}

\begin{figure}[ht]
\begin{center}
\vspace*{-0.7cm}
\includegraphics[width=8.7cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Paper/SanFernando_spatial_distribution_of_damage.jpg}
%\includegraphics[width=7cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Paper/LosAngeles-SantaMonica_spatial_distribution_of_damage.jpg}
\end{center}
\end{figure}

\vspace*{-0.9cm}
\hfill {\tiny [Trifunac and Todorovska 1998]}
\vspace*{-0.4cm}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




% 

% 
%  
%  
%    \item Slow and Fast earthquakes
%          
%    \item Uncertainty and variability (source, material...) 
%  
%  
%  \end{itemize}
%  \end{frame}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Distribution of Seismic Energy in Soil-Structure Systems}
%  
%  
%  \begin{itemize}
%  
%       \item Input: seismic waves from the source
%  
%       \item Output: various dissipation mechanisms:
%         \begin{itemize}
%           \item wave reflection and radiation
%           \item soil structure system oscilation radiation
%           \item plasticity of soil (different subdomains)
%           \item viscous coupling of porous solid with pore fluid (air, water)
%           \item plasticity/damage of the structure (different parts)
%           \item viscous coupling of structure with surounding fluid (air, water)
%           \item potential energy
%           \item kinetic energy
%         \end{itemize}
%  
%  
%     \item  Preserving  energy  in  numerical models (numerical damping and period
%     errors)
%  
%  
%  \end{itemize}
%  
%  %
%  %\item Models available (some now, some later) 
%  %\vspace*{-2.0cm}
%  \end{frame}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \subsection{High Fidelity Modeling of Soil--Foundation--Structure System}
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%   
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Verification, Validation and Prediction}
%  
%  
%  \begin{itemize}
%  
%       \item {Verification provides evidence that the
%     model is solved correctly.} Mathematics issue. 
%  
%       \item {Validation provides
%     evidence that the correct model is solved.} Physics issue. 
%  
%     \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
%  
%  \end{itemize}
%  
%  literature: \cite{Roach1998}, \cite{Oberkampf2002}.
%  %Verification, validation and predictive capability in computational
%  %  engineering and physics.
%  %In {\em Proceedings of the Foundations for Verification and
%  %  Validation on the 21st Century Workshop}, pages 1--74, Laurel, Maryland,
%  %  October 22-23 2002. Johns Hopkins University / Applied Physics Laboratory.
%  %%{\href{http://sokocalo.engr.ucdavis.edu/~jeremic/UsefulReadings/Oberkampf-Trucano-Hirsch.pdf}
%  %%{PDF available here}}
%  %
%  %
%  %\item
%  %{\sc P.~J. Roache.}
%  % {\em Verification and Validation in Computational Science and
%  %  Engineering}.
%  %Hermosa publishers, 1998.
%  %ISBN 0-913478-08-3.
%  %%
%  %\item Material from {\it Verification and Validation in Computational Mechanics}
%  %web site \texttt{http://www.usacm.org/vnvcsm/} at the USACM.
%  %
%  
%  
%  
%  %
%  %\item Models available (some now, some later)
%  %\vspace*{-2.0cm}
%  \end{frame}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%   
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Role of Verification and Validation}
%  
%  
%      
%  %   \vspace*{1.5truecm}
%  
%  \begin{figure}[!h]
%  \begin{center}
%  {\includegraphics[width=8.0cm]{/home/jeremic/tex/works/Presentation/2003/Verif_and_Valid/RoleVV.pdf}}
%  \end{center}
%  \end{figure}
%  
%  
%  %
%  %\item Models available (some now, some later)
%  %\vspace*{-2.0cm}
%  \end{frame}
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%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % \begin{frame}
%  % \frametitle{Application Domain  Complete or Partial Overlap}
%  % 
%  % 
%  % 
%  % 
%  % 
%  % %\vspace*{0.3cm}
%  % 
%  % \begin{figure}[!h]
%  % \begin{center}
%  % \hspace*{1.5cm}
%  % {\includegraphics[width=2.50cm]{/home/jeremic/tex/works/Presentation/2004/VandV/VPI01.pdf}}
%  % \hfill
%  % {\includegraphics[width=2.50cm]{/home/jeremic/tex/works/Presentation/2004/VandV/VPI02.pdf}}
%  % \hspace*{1.5cm}
%  % %\vspace*{-5.0cm}
%  % \end{center}
%  % \end{figure}
%  % 
%  % \vspace*{-0.3cm}
%  % 
%  % \begin{itemize}
%  %  \item Rarely applicable to infrastructure objects 
%  % %( bridges, buildings, port facilities, dams...
%  %  \item Environmental influences (generalized loads, conditions, wear and tare)  are hard to predict
%  %  \item Human factors (I-35 bridge failure, {\bf forgot} to multiply loads with safety  factor...)
%  % \end{itemize}
%  % 
%  % 
%  % 
%  % 
%  % \end{frame}
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%  \frametitle{Application Domain --  No Overlap}
%  
%  
%  
%  
%  
%  %\vspace*{0.3cm}
%  
%  \begin{figure}[!h]
%  \begin{center}
%  %\vspace*{-2.5cm}
%  {\includegraphics[width=2.50cm]{/home/jeremic/tex/works/Presentation/2004/VandV/VPI01.pdf}}
%  \hfill
%  {\includegraphics[width=2.50cm]{/home/jeremic/tex/works/Presentation/2004/VandV/VPI02.pdf}}
%  \hfill
%  {\includegraphics[width=2.5cm]{/home/jeremic/tex/works/Presentation/2004/VandV/VPI03.pdf}}
%  %\vspace*{-5.0cm}
%  \end{center}
%  \end{figure}
%  
%  \vspace*{-0.2cm}
%  
%  \begin{itemize}
%   \item  Inference  $\Rightarrow$  Based on {\bf physics} or {\bf statistics} (or
%   both)
%   \item  Validation domain is actually an aggregation of tests and thus might not
%   be convex (bifurcation of behavior)
%   \item      Validation      domain   for  infrastructure objects (bridges, dams,
%   buildings,  ports...)  is  exclusively  non--overlapping  with  the application
%   domain.
%  \end{itemize}
%  
%  
%  
%  
%  
%  \end{frame}
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%\section{Modeling and Simulation of Soil Structure Systems}
\section{Modeling and Simulation}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Seismic Energy Input}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Seismic Energy at the Source}

   \begin{itemize}

\vspace*{0.2cm}
     \item Large energy releases, 
        \begin{itemize}
          \item Northridge, 1994, $M_{Richter} = 6.7$, $E_r = 6.8 \times 10^{16}J$
          \item Loma Prieta, 1989, $M_{Richter} = 6.9$, $E_r =1.1 \times 10^{17}J$
          \item Sumatra-Andaman, 2004, $M_{Richter} = 9.3$, $E_r =4.8 \times 10^{20}J$
          \item Valdivia, Chile, 1960, $M_{Richter} = 9.5$, $E_r =7.5 \times 10^{20}J$
          \item Rhodes, 2008, $M_{Richter} = 6.5$, $E_r =2.4 \times 10^{16}J$
        \end{itemize}
\vspace*{0.2cm}
      \item Part that energy is radiated as waves ($\approx 1.6 \times 10^{-5}$)
      and makes it to the surface
\vspace*{0.2cm}
      \item For comparison, specific energy  of TNT is $4.2\times 10^6 J/kg$. 
\vspace*{0.2cm}
      \item Rhodes earthquake was $\approx 0.1 kt$.

  \end{itemize}


\end{frame}
%- 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Seismic Energy and the SFS System}

   \begin{itemize}

\vspace*{-1.5cm}
     \item Kinetic  energy  flux  through closed surface $\Gamma$ includes both incoming
     and outgoing waves (using Domain Reduction Method by Bielak et al.)
\begin{eqnarray*}
E_{flux} = 
\left[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 \right]_i
%
% \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]^{T}
\times u_i
%\left[
%\begin{array}{c} 
%0 \\ 
%{u}_b\\ 
%{u}_e
%\end{array}
%\right]
\end{eqnarray*}

  \item Alternatively, $E_{flux} = \rho A c \int_0^t \dot{u}_i^2 dt$

  \item  Outgoing kinetic  energy  \\
         is obtained from outgoing \\
         wave field ($w_i$, in DRM)

  \item Incoming kinetic energy \\
        is then the difference.


   \end{itemize}


\vspace*{-7.0cm}
% \begin{figure}[!hbpt]
%\begin{flushright}
\hfill \includegraphics[width=5.5cm]{/home/jeremic/tex/works/psfigures/DRMidea03.pdf}
%\end{flushright}
%\end{figure}
\vspace*{-2cm}


\end{frame}
%- 
%- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%- 
%- \begin{frame}
%-  \frametitle{Simulation of the Incomming SFS Energy}
%- 
%-    \begin{itemize}
%- 
%-      \item Domain Reduction Method
%- 
%-   \end{itemize}
%- 
%- 
%- \end{frame}
%- %- 
%- 
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\subsection{Seismic Energy Dissipation}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
% \frametitle{Seismic Energy Dissipation for \underline{Soil}--Foundation--Structure Systems}
 \frametitle{Seismic Energy Dissipation for \underline{Soil}--Structure Systems}


\begin{itemize}


\vspace*{0.2cm}
     \item Mechanical dissipation outside of SFS domain:
       \begin{itemize}
         \item wave reflection
         \item SFS system oscillation radiation
       \end{itemize}
\vspace*{0.2cm}
     \item Mechanical dissipation/conversion inside SFS domain:
       \begin{itemize}
         \item plasticity of soil (different subdomains)
         \item viscous coupling of porous solid with pore fluid (air, water)
         \item plasticity/damage of the structure (different parts)
         \item viscous coupling of structure with surrounding fluids 
%         \item potential and kinetic energy
         \item potential $\leftarrow \! \! \! \! \! \! \rightarrow$ kinetic energy
       \end{itemize}                           



\vspace*{0.2cm}
%   \item Numerical energy dissipation (numerical damping/production and period  errors)
%   \item Numerical energy dissipation (damping/production)
   \item Numerical energy dissipation/production


\end{itemize}

%
%\item Models available (some now, some later) 
%\vspace*{-2.0cm}
\end{frame}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Energy Losses (Disipation)}
%  
%     \begin{itemize}
%  
%       \item Losses outside of SFS domain
%       \item Losses within SFS domain
%       \item Numerical algorithm losses
%  
%    \end{itemize}
%  
%  
%  \end{frame}
%  %- 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Energy Dissipation by Plasticity}


   \begin{itemize}

%     \item Plastic work ($W = \int_{0}^{t} \sigma_{ij} d \epsilon_{ij}^{pl}$)
     \item Plastic work ($W = \int \sigma_{ij} d \epsilon_{ij}^{pl}$)

     \item Energy dissipation capacity for different soils


  \end{itemize}

%\vspace*{-1.0cm}
\begin{center}
\vspace*{-0.9cm}
\includegraphics[width=8.5cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/Energy-Capacity2.pdf}
\hspace*{-0.2cm}
%\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/Energy-Capacity10.pdf}
\vspace*{-1.0cm}
\end{center}


\end{frame}
%- 
%- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%- \begin{frame}
%-  \frametitle{Plasticity Energy Disipation}
%- 
%-    \begin{itemize}
%- 
%-      \item
%- 
%-   \end{itemize}
%- 
%- 
%- \end{frame}
%- %- 
%- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Energy Disipation by Viscous Coupling}


   \begin{itemize}

     \item Viscous coupling of porous solid and fluid
     \item Energy loss per unit volume is  $E_{vc}= n^2 k^{-1} (\dot{U}_i - \dot{u}_i)^2$ 
     \item Natural in $u-p-U$ formulation:

  \end{itemize}
%\vspace*{-0.4cm}




\begin{footnotesize}
%\begin{tiny}
\begin{eqnarray*}
%& &\left[ \begin{array}{ccc}
\left[ \begin{array}{ccc}
(M_s)_{KijL} & 0 & 0 \\
 0  & 0 & 0 \\
 0  & 0 & (M_f)_{KijL}
\end{array} \right]
\left[ \begin{array}{c}
\ddot{\overline{u}}_{Lj} \\
\ddot{\overline{p}}_N \\
\ddot{\overline{U}}_{Lj}
\end{array} \right]
+
\left[ \begin{array}{ccc}
(C_1)_{KijL} & 0 & -(C_2)_{KijL} \\
 0  & 0 &   0  \\
-(C_2)_{LjiK} & 0 & (C_3)_{KijL} \\
\end{array} \right]
\left[ \begin{array}{c}
\dot{\overline{u}}_{Lj} \\
\dot{\overline{p}}_N \\
\dot{\overline{U}}_{Lj}
\end{array} \right]   
\nonumber\\
+
%& &\left[ \begin{array}{ccc}
\left[ \begin{array}{ccc}
(K^{EP})_{KijL} & -(G_1)_{KiM} & 0 \\
-(G_1)_{LjM}  & -P_{MN} & -(G_2)_{LjM} \\
 0  & -(G_2)_{KiL} & 0
\end{array} \right]
\left[ \begin{array}{c}
\overline{u}_{Lj} \\
\overline{p}_M \\
\overline{U}_{Lj}
\end{array} \right]
=
\left[ \begin{array}{c}
\overline{f}_{Ki}^{solid} \\
0  \\
\overline{f}_{Ki}^{fluid}
\end{array} \right] \nonumber\\
\label{68}
\end{eqnarray*}
%\end{tiny}
\end{footnotesize}

\vspace*{-1cm}

\begin{footnotesize}
\begin{eqnarray*}
%%%%%%%%
(C_{(1,2,3)})_{KijL}   
=
\int_{\Omega} N_K^{(u,u,U)} 
n^2 k_{ij}^{-1} 
N_L^{(u,U,U)} d\Omega
% (C_1)_{KijL}   =\int_{\Omega} N_K^u n^2 k_{ij}^{-1} N_L^u d\Omega
% \;\; \mbox{;} \;\;
% (C_2)_{KijL}   =\int_{\Omega} N_K^u n^2 k_{ij}^{-1} N_L^U d\Omega 
% %%%%%%%%
% %\;\; \mbox{;}\;\;
% \\
% %%%%%%%%
% (C_3)_{KijL}   =\int_{\Omega} N_K^U n^2 k_{ij}^{-1} N_L^U d\Omega
\end{eqnarray*}
\end{footnotesize}
%
%
%
%
%\newpage




\end{frame}
%- 
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\begin{frame}
 \frametitle{Numerical Energy Dissipation}

   \begin{itemize}

     \item  Newmark  and  Hilber--Hughes--Taylor can be made non--dissipative for
     elastic system $\alpha=0.0, \beta = 0.25 ; \gamma  = 0.5,$

     \item Or dissipative (for elastic) for higher frequency modes: 
%Newmark ($\gamma     \ge     0.5,     \;\;\;    \beta    = 0.25(\gamma+0.5)^2$ ),
%Hilber--Hughes--Taylor   ($-0.3\dot{3}\le\alpha        \le0,        \;\;\;\gamma    =  
%0.5(1-2\alpha), \;\;\; \beta = 0.25(1-\alpha)^2$)
      \begin{itemize}
        \item N: $\gamma     \ge     0.5,     \;\;\;    \beta    = 0.25(\gamma+0.5)^2$,
        \item HHT: $-0.3\dot{3}\le\alpha        \le0,        \;\;\;\gamma    =  
0.5(1-2\alpha), \;\;\; \beta = 0.25(1-\alpha)^2$
      \end{itemize}

     \item  For nonlinear problems, 
            energy cannot be maintained
       \begin{itemize}
           \item Energy dissipation for steps with reduction of stiffness
           \item Energy production for steps with increase of stiffness

\hspace{1cm}
\includegraphics[width=1.80cm, angle=-90]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/EnergyDissipationReducationStiffness.pdf}
\hspace{1cm}
\includegraphics[width=1.80cm, angle=-90]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/EnergyProductionIncreaseStiffness.pdf}
\hspace{1cm}



       \end{itemize}
     

  \end{itemize}


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\section{Examples of Energy Dissipation}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Use of Soft Soil}

% - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - \begin{frame}
% -  \frametitle{Detailed 3D FEM Model (one of)}
% - 
% - %
% - \begin{figure}[!htbp] 
% - \begin{center}
% - \includegraphics[width=8.0cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
% - %\hspace*{-0.9cm}
% - %bridge.}
% - \end{center}
% - \end{figure}
% - %
% - \end{frame}
% - %- 
% - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - 
% - \begin{frame}
% -  \frametitle{Model Components}
% - 
% - %
% - \begin{itemize}
% -  \item   Soils:   elastic--plastic   solids   (yield   potential  surface
% -  Drucker-Prager, kinematic hardening Armstrong-Frederick) (UCD: Jie and Jeremi{\'c})
% - \vspace*{0.2cm}
% -  \item Structure: non--linear  beam--column elements (fiber element) 
% -   (UCB: Fenves, UW: Eberhardt) 
% - 
% - \vspace*{0.2cm}
% -   \item Piles: non--linear  beam--column elements (fiber element) (UCD: Jie and Jeremi{\'c})
% - 
% - 
% - \vspace*{0.2cm}
% -   \item Two types of soil: stiff soil (UT, UCD), soft soil (Bay Mud)
% - 
% - \vspace*{0.2cm}
% -   \item  Use of the Domain Reduction Method (DRM) (Bielak et al.) for seismic
% -   input into FEM model
% - 
% - 
% - \end{itemize}
% - 
% - \end{frame}
% - %- 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
 \frametitle{Earthquake--Soil--Bridge
             System}

%
\begin{itemize}
 \item   Inelastic soils (el--pl, 
 Armstrong-Frederick, stiff and soft), 
 inelastic structure (columns), 
 inelastic piles, DRM for seismic input,
 
%\vspace*{0.3cm}
  \item Construction process

% 
 \item Deconvolution osurface ground motions

%\vspace*{0.3cm}
  \item No artificial damping, \\
   only plastic dissipation \\
   and radiation

 
%\vspace*{0.3cm}
  \item Plastic Domain \\
  Decompisition Method \\
  for parallel computing

%  \item Element size issues (filtering of frequencies) 
%\vspace*{0.3cm}
  \item 1.6 M DOFs \\
  (15cm element size)



\end{itemize}
\vspace*{-4cm}
\hfill \includegraphics[width=5.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}


%  %
%  \begin{figure}[!htbp] 
%  \begin{center}
%  \includegraphics[width=4.0cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
%  %\hspace*{-0.9cm}
%  %bridge.}
%  \end{center}
%  \end{figure}
%  
%  
\end{frame}
%- 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Modeling Issues}
% 
%    \begin{itemize}
% 
% \vspace*{0.2cm}
%   \item Construction process
% 
% \vspace*{0.2cm}
%   \item Deconvolution of given surface ground motions
% 
% \vspace*{0.2cm}
%   \item No artificial damping (only mat. dissipation, radiation)
% 
% \vspace*{0.2cm}
%   \item Element size issues (filtering of frequencies) 
% 
% \vspace*{-0.4cm}
% \begin{table}[!htbp]
% %\caption{ }
% \begin{center}
% \begin{tabular}{|r|c|c|c|c|} 
% \hline
% elem. \# &  elem.  size  &  $f_{cutoff}$  & min. $G^{ep}/Gmax$ & $\gamma$  \\
% \hline
% %
% %
% % 100cm element model, f_cuttof=10HZ, G/Gmax=1.0, 12K elements, Gmax model
% 12K         &  1.00~m          &  10~Hz      & 1.0      & <0.5~\% \\
% %
% %
% %~90cm element model, f_cutoff ~= 3Hz, G/Gmax~=0.08, for epsilon ~= 1%, 15K
% %elements, now running...
% 15K         &  0.90~m          &  >3~Hz     & 0.08            & <1.0~\% \\
% %
% %
% %27.6cm element model, f_cutoff= 10HZ, G/Gmax=0.08, for epsilon = 1%, 150K
% %elements, finest model
% 150K        &  0.30~m          &  10~Hz      & 0.08            & <1.0~\% \\
% 500K        &  0.15~m          &  10~Hz      & 0.02            & <5.0~\% \\
% % 27.6cm element model, f_cutoff= 10HZ, G/Gmax=0.08, for epsilon = 1%, 150K
% %elements, finest model
% \hline
% \end{tabular}
% \end{center}
% \end{table}
% 
%   \end{itemize}
% 
% 
% \end{frame}
% %- 
% %-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%- 
%- \begin{frame}
%-   \frametitle{Parametric Simulation Results}
%- 
%- 
%- \vspace*{-0.5cm}
%- %\begin{landscape}
%- \begin{figure}[!htbp]
%- \begin{center}
%- \hspace*{-1cm}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispSoilBlock1.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispBent1.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispSoilBlock2.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispBent2.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispSoilBlock3.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispBent3.pdf}
%- \hspace*{-1cm}
%- \\
%- \hspace*{-1cm}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelSoilBlock1.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelBent1.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelSoilBlock2.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelBent2.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelSoilBlock3.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelBent3.pdf}
%- \hspace*{-1cm}
%- \\
%- \hspace*{-1cm}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispSoilBlock1_Spectrum.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispBent1_Spectrum.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispSoilBlock2_Spectrum.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispBent2_Spectrum.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispSoilBlock3_Spectrum.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispBent3_Spectrum.pdf}
%- \hspace*{-1cm}
%- \\
%- \hspace*{-1cm}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelSoilBlock1_Spectrum.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelBent1_Spectrum.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelSoilBlock2_Spectrum.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelBent2_Spectrum.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelSoilBlock3_Spectrum.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelBent3_Spectrum.pdf}
%- \hspace*{-1cm}
%- \\
%- \hspace*{-1cm}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/MomentBent1Pile1.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/MomentBent1Pile2.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/MomentBent2Pile1.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/MomentBent2Pile2.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/MomentBent3Pile1.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/MomentBent3Pile2.pdf}
%- \hspace*{-1cm}
%- \end{center}
%- \end{figure}
%- 
%- \vspace*{-0.8cm}
%- \begin{figure}[!htbp] 
%- \begin{center}
%- \includegraphics[width=3.2cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
%- %\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
%- %bridge.}
%- \end{center}
%- \end{figure}
%- \vspace*{-2cm}
%- 
%- 
%- \clearpage
%- 
%- 
%- 
%- 
%- \end{frame}
%- 
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%- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%






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\begin{frame}
  \frametitle{Northridge and Kocaeli Input Motions}


\vspace*{-0.7cm}
\begin{figure}[!htbp] 
\begin{center}
\hspace*{-1cm}
\includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/InputMotion_Northridge.pdf}
\hspace*{-1cm}
%\\
%\hspace*{-1cm}
%\includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/InputMotion_Northridge_Spectrum.pdf}
%\hspace*{-1cm}
%%\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
%%bridge.}
\end{center}
\end{figure}
\vspace*{-1.0cm}
%


\vspace*{-0.7cm}
\begin{figure}[!htbp] 
\begin{center}
\hspace*{-1cm}
\includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/InputMotion_Kocaeli.pdf}
\hspace*{-1cm}
%\\
%\hspace*{-1cm}
%\includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/InputMotion_Kocaeli_Spectrum.pdf}
%\hspace*{-1cm}
%%\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
%bridge.}
\end{center}
\end{figure}
%
\vspace*{-1cm}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - %\begin{frame}
% - %  \frametitle{Short Period E.: Left Bent, Structure and Soil, Disp.}
% - %  
% - %
% - %
% - %
% - %\vspace*{-1cm}
% - %\begin{figure}[!htbp] 
% - %\begin{center}
% - %\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispBent1.pdf}
% - %%\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispBent1.pdf}
% - %\\
% - %\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispSoilBlock1.pdf}
% - %%\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispSoilBlock1.pdf}
% - %%\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
% - %%bridge.}
% - %\end{center}
% - %\end{figure}
% - %
% - %
% - %\vspace*{-2.9cm}
% - %\hspace*{0.2cm}
% - %\begin{figure}[!htbp] 
% - %\begin{flushright}
% - %\includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
% - %%\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
% - %%bridge.}
% - %\end{flushright}
% - %\end{figure}
% - %\hspace*{-0.5cm}
% - %\vspace*{-2.0cm}
% - %
% - %
% - %
% - %\end{frame}
% - %%-- 
% - %%--  
% - %%--  
% - %%--  
%--  
%--  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%--  \begin{frame}
%--    \frametitle{Short Period E.:  Left Bent, Structure and Soil, Acc.}
%--    
%--  
%--  
%--  
%--  \vspace*{-1cm}
%--  \begin{figure}[!htbp] 
%--  \begin{center}
%--  \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelBent1.pdf}
%--  \\
%--  \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelSoilBlock1.pdf}
%--  %\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
%--  %bridge.}
%--  \end{center}
%--  \end{figure}
%--  
%--  
%--  \vspace*{-2.9cm}
%--  \hspace*{0.2cm}
%--  \begin{figure}[!htbp] 
%--  \begin{flushright}
%--  \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
%--  %\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
%--  %bridge.}
%--  \end{flushright}
%--  \end{figure}
%--  \hspace*{-0.5cm}
%--  \vspace*{-2.0cm}
%--  
%--  \end{frame}
%--  %-- 
%--  
%--  
%--  
%--  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%--  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - %\begin{frame}
% - %  \frametitle{Short Period E.: Left Bent, Structure and Soil, Acc.Sp.}
% - %  
% - %
% - %
% - %
% - %\vspace*{-1cm}
% - %\begin{figure}[!htbp] 
% - %\begin{center}
% - %\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelBent1_Spectrum.pdf}
% - %\\
% - %\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelSoilBlock1_Spectrum.pdf}
% - %%\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
% - %%bridge.}
% - %\end{center}
% - %\end{figure}
% - %
% - %
% - %\vspace*{-2.9cm}
% - %\hspace*{0.2cm}
% - %\begin{figure}[!htbp] 
% - %\begin{flushright}
% - %\includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
% - %%\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
% - %%bridge.}
% - %\end{flushright}
% - %\end{figure}
% - %\hspace*{-0.5cm}
% - %\vspace*{-2.0cm}
% - %
% - %
% - %\end{frame}
% - %%-- 
% - %
% - %
% - %
% - %%--  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - %%--  \begin{frame}
%--    \frametitle{Short Period E.: Left Bent, Structure and Soil, M.}
%--    
%--  
%--  
%--  
%--  \vspace*{-1cm}
%--  \begin{figure}[!htbp] 
%--  \begin{center}
%--  \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/MomentBent1Pile1.pdf}
%--  \\
%--  \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/MomentBent1Pile2.pdf}
%--  %\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
%--  %bridge.}
%--  \end{center}
%--  \end{figure}
%--  
%--  
%--  
%--  
%--  \vspace*{-2.9cm}
%--  \hspace*{0.2cm}
%--  \begin{figure}[!htbp] 
%--  \begin{flushright}
%--  \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
%--  %\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
%--  %bridge.}
%--  \end{flushright}
%--  \end{figure}
%--  \hspace*{-0.5cm}
%--  \vspace*{-2.0cm}
%--  
%--  
%--  \end{frame}
%--  %-- 
%--  
%--  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
  \frametitle{Northridge Energy: Strain (dissipated) and Kinetic}
  



\vspace*{-0.1cm}
\begin{figure}[!htbp] 
\begin{center}
\includegraphics[width=9cm,height=3.5cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/MomentBent1Pile1_25s_SC.pdf}
%\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
%bridge.}
\end{center}
\end{figure}


% \vspace*{-2.9cm}
% \hspace*{0.2cm}
% \begin{figure}[!htbp] 
% \begin{flushright}
% \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
% %\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
% %bridge.}
% \end{flushright}
% \end{figure}
% \hspace*{-0.5cm}
% \vspace*{-2.0cm}
% 


\vspace*{-1.2cm}
\begin{figure}[!htbp] 
\begin{center}
%\includegraphics[width=11cm,height=7.0cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/Northridge-Bent.pdf}
\includegraphics[width=11cm,height=7.0cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/Northridge-Diff-Comp.pdf}
%\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
%bridge.}
\end{center}
\end{figure}


%  % 
%  \vspace*{2.0cm}
%  {%
%  \begin{beamercolorbox}{section in head/foot}
%  \usebeamerfont{framesubtitle}\tiny{B.   Jeremi\'{c},  G.   Jie, 
%  M. Preisig and N. Tafazzoli.}  "Soil--Foundation--Structure  Interaction
%  in non--Uniform Soils", \textit{Earthquake Engineering and Structural Dynamics},
%  38, 5 pp 699-718, 2009.
%  %\vskip2pt\insertnavigation{\paperwidth}\vskip2pt
%  \end{beamercolorbox}%
%  }
%  


\end{frame}
%-- 

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%--  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%--  \begin{frame}
%--    \frametitle{Short Period E.: Left Bent, Free Field vs Real Disp.}
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%--  \begin{figure}[!htbp] 
%--  \begin{center}
%--  \includegraphics[width=11cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispSoilBlock1_15cm_25s_SC.pdf}
%--  %\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
%--  %bridge.}
%--  \end{center}
%--  \end{figure}
%--  
%--  
%--  \vspace*{-2.9cm}
%--  \hspace*{0.2cm}
%--  \begin{figure}[!htbp] 
%--  \begin{flushright}
%--  \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
%--  %\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
%--  %bridge.}
%--  \end{flushright}
%--  \end{figure}
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%--  \begin{frame}
%--    \frametitle{Kocaeli Input Motions}
%--  
%--  
%--  \vspace*{-0.7cm}
%--  \begin{figure}[!htbp] 
%--  \begin{center}
%--  \hspace*{-1cm}
%--  \includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/InputMotion_Kocaeli.pdf}
%--  \hspace*{-1cm}
%--  \\
%--  \hspace*{-1cm}
%--  \includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/InputMotion_Kocaeli_Spectrum.pdf}
%--  \hspace*{-1cm}
%--  %\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
%--  %bridge.}
%--  \end{center}
%--  \end{figure}
%--  %
%--  \vspace*{-1cm}
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%--    \frametitle{Long Period E.: Left Bent, Structure and Soil, Disp.}
%--    
%--  
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%--  \vspace*{-1cm}
%--  \begin{figure}[!htbp] 
%--  \begin{center}
%--  \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/DispBent1.pdf}
%--  \\
%--  \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/DispSoilBlock1.pdf}
%--  %\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
%--  %bridge.}
%--  \end{center}
%--  \end{figure}
%--  
%--  
%--  \vspace*{-2.9cm}
%--  \hspace*{0.2cm}
%--  \begin{figure}[!htbp] 
%--  \begin{flushright}
%--  \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
%--  %\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
%--  %bridge.}
%--  \end{flushright}
%--  \end{figure}
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%--    \frametitle{Long Period E.: Left Bent, Structure and Soil, Acc.}
%--    
%--  
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%--  \vspace*{-1cm}
%--  \begin{figure}[!htbp] 
%--  \begin{center}
%--  \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/AccelBent1.pdf}
%--  \\
%--  \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/AccelSoilBlock1.pdf}
%--  %\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
%--  %bridge.}
%--  \end{center}
%--  \end{figure}
%--  
%--  
%--  
%--  \vspace*{-2.9cm}
%--  \hspace*{0.2cm}
%--  \begin{figure}[!htbp] 
%--  \begin{flushright}
%--  \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
%--  %\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
%--  %bridge.}
%--  \end{flushright}
%--  \end{figure}
%--  \hspace*{-0.5cm}
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%--  \begin{frame}
%--    \frametitle{Long Period E.: Left Bent, Structure and Soil, Acc.Sp.}
%--    
%--  
%--  
%--  
%--  \vspace*{-1cm}
%--  \begin{figure}[!htbp] 
%--  \begin{center}
%--  \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/AccelBent1_Spectrum.pdf}
%--  \\
%--  \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/AccelSoilBlock1_Spectrum.pdf}
%--  %\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
%--  %bridge.}
%--  \end{center}
%--  \end{figure}
%--  
%--  
%--  \vspace*{-2.9cm}
%--  \hspace*{0.2cm}
%--  \begin{figure}[!htbp] 
%--  \begin{flushright}
%--  \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
%--  %\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
%--  %bridge.}
%--  \end{flushright}
%--  \end{figure}
%--  \hspace*{-0.5cm}
%--  \vspace*{-2.0cm}
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%--  \end{frame}
%--  %-- 
%--  
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%--  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
  \frametitle{Kocaeli Energy: Strain (dissipated) and Kinetic}



\vspace*{-0.1cm}
\begin{figure}[!htbp] 
\begin{center}
\includegraphics[width=9cm,height=3.5cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/MomentBent1Pile1.pdf}
%\\
%\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/MomentBent1Pile2.pdf}
%\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
%bridge.}
\end{center}
\end{figure}


\vspace*{-0.8cm}
\begin{figure}[!htbp] 
\begin{flushleft}
\hspace*{0.4cm}
%\includegraphics[width=7.85cm,height=7.0cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/Kocaeli-Bent.pdf}
\includegraphics[width=7.85cm,height=7.0cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/Kocaeli-Diff-Comp.pdf}
%\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
%bridge.}
\end{flushleft}
\end{figure}



% 
% \vspace*{-2.9cm}
% \hspace*{0.2cm}
% \begin{figure}[!htbp] 
% \begin{flushright}
% \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
% %\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
% %bridge.}
% \end{flushright}
% \end{figure}
% \hspace*{-0.5cm}
% \vspace*{-2.0cm}
% 

\end{frame}
%-- 


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%   \frametitle{Soft Soils: Left Bent, Structure and Soil, Moments}
%   
% 
% 
% 
% \vspace*{-1cm}
% \begin{figure}[!htbp] 
% \begin{center}
% \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/MomentBent1Pile1_25s_SC.pdf}
% %\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
% %bridge.}
% \end{center}
% \end{figure}
% \vspace*{-2cm}
% 
% 
% \end{frame}
% %-- 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%   \frametitle{Soft Soils: Left Bent, Free Field vs Real Displacements}
%   
% 
% 
% 
% \vspace*{-1cm}
% \begin{figure}[!htbp] 
% \begin{center}
% \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/DispSoilBlock1_15cm_25s_SC.pdf}
% %\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
% %bridge.}
% \end{center}
% \end{figure}
% \vspace*{-2cm}
% 
% 
% \end{frame}
% %-- 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Use of  Liquefaction}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
  \frametitle{Uniform and Layered Soils}
  



\vspace*{-0.5cm}
\begin{figure}[!htbp] 
\begin{center}
\includegraphics[width=7cm,angle=90]{/home/jeremic/tex/works/Papers/2009/SeismicIsolationLiquefaction/Mesh-Isolation.pdf}
%\\
%\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/MomentBent1Pile2.pdf}
%\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
%bridge.}
\end{center}
\end{figure}
\vspace*{-1cm}



\end{frame}
%-- 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Acceleration Time History}


\vspace*{-0.1cm}
\begin{figure}[!htbp]
%\begin{center}
\includegraphics[width=6cm]{/home/jeremic/tex/works/Papers/2009/SeismicIsolationLiquefaction/time-history-acc.jpg} \\
%\end{center}
\end{figure}
%\vspace*{-0.3cm}
%\hspace*{2.3cm} EPPR \hspace{1.5cm}  $\gamma$ \hspace{1.7cm}  $u_{hor}$


\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%--  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%--  \begin{frame}
%--   \frametitle{Stress Variation}
%--  
%--  \vspace*{-0.1cm}
%--  \begin{figure}[!htbp]
%--  %\begin{center}
%--  \includegraphics[width=6cm]{/home/jeremic/tex/works/Papers/2009/SeismicIsolationLiquefaction/variation-sigmaxz-sigmaz.jpg} \\
%--  %\end{center}
%--  \end{figure}
%--  %\vspace*{-0.3cm}
%--  %\hspace*{2.3cm} EPPR \hspace{1.5cm}  $\gamma$ \hspace{1.7cm}  $u_{hor}$
%--  
%--  
%--  
%--  \end{frame}
%--  
%--  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%--  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%--  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%--  \begin{frame}
%--   \frametitle{Stress Strain Response}
%--  
%--  \vspace*{-0.1cm}
%--  \begin{figure}[!htbp]
%--  %\begin{center}
%--  \includegraphics[width=6cm]{/home/jeremic/tex/works/Papers/2009/SeismicIsolationLiquefaction/variation-sigmaxz-gamma.jpg} \\
%--  %\end{center}
%--  \end{figure}
%--  %\vspace*{-0.3cm}
%--  %\hspace*{2.3cm} EPPR \hspace{1.5cm}  $\gamma$ \hspace{1.7cm}  $u_{hor}$
%--  
%--  
%--  
%--  \end{frame}
%--  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Excess Pore Pressure}
%  
%  
%  \vspace*{-0.3cm}
%  \begin{figure}[!htbp]
%  %\begin{center}
%  \includegraphics[width=10cm]{/home/jeremic/tex/works/Papers/2009/SeismicIsolationLiquefaction/contours-exc-pore-press.jpg} \\
%  %\end{center}
%  \end{figure}
%  %\vspace*{-0.3cm}
%  %\hspace*{2.3cm} EPPR \hspace{1.5cm}  $\gamma$ \hspace{1.7cm}  $u_{hor}$
%  
%  
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Excess Pore Pressure Ratio}

\vspace*{-0.1cm}
\begin{figure}[!htbp]
\begin{center}
\hspace*{-0.7cm}
\includegraphics[width=10cm]{/home/jeremic/tex/works/Papers/2009/SeismicIsolationLiquefaction/contours-exc-pore-press-ratio.jpg} \\
\hspace*{-1.0cm}
\end{center}
\end{figure}
%\vspace*{-0.3cm}
%\hspace*{2.3cm} EPPR \hspace{1.5cm}  $\gamma$ \hspace{1.7cm}  $u_{hor}$



\vspace*{-0.9cm}
\begin{center}
%\begin{center}
\includegraphics[width=4cm]{/home/jeremic/tex/works/Conferences/2009/GheoMat/Coupled-behavior_04/Niigata-Earthquake-tilted-buildings.jpg} \\
%\end{center}
\end{center}
%\vspace*{-0.3cm}
%\hspace*{2.3cm} EPPR \hspace{1.5cm}  $\gamma$ \hspace{1.7cm}  $u_{hor}$
               


\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%









%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
  \frametitle{Plastic Energy Dissipation in Uniform Soils}
  



\vspace*{-1cm}
\begin{figure}[!htbp] 
\begin{center}
\includegraphics[width=10cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/Uniform.pdf}
%\includegraphics[width=4cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/Layered.pdf}
%\\
%\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/MomentBent1Pile2.pdf}
%\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
%bridge.}
\end{center}
\end{figure}
\vspace*{-1cm}



\end{frame}
%-- 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
  \frametitle{Plastic Energy Dissipation in Layered Soils}
  



\vspace*{-1cm}
\begin{figure}[!htbp] 
\begin{center}
%\includegraphics[width=10cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/Uniform.pdf}
\includegraphics[width=10cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/Layered.pdf}
%\\
%\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/MomentBent1Pile2.pdf}
%\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
%bridge.}
\end{center}
\end{figure}
\vspace*{-1cm}



\end{frame}
%-- 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



 

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Kinetic Energy at the Top}


%\vspace*{-0.3cm}
\begin{figure}[h]
\begin{center}
\hspace*{-1.3cm}
\includegraphics[width=13cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/StackElements-Compare.pdf} 
\hspace*{-0.1cm}
\end{center}
\end{figure}
%\vspace*{-0.3cm}
%\hspace*{2.3cm} EPPR \hspace{1.5cm}  $\gamma$ \hspace{1.7cm}  $u_{hor}$
               
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Void Ratio Variation (Potential Energy)}

\vspace*{-0.1cm}
\begin{figure}[!htbp]
%\begin{center}
\includegraphics[width=6cm]{/home/jeremic/tex/works/Papers/2009/SeismicIsolationLiquefaction/variation-e-t.jpg} \\
%\end{center}
\end{figure}
%\vspace*{-0.3cm}
%\hspace*{2.3cm} EPPR \hspace{1.5cm}  $\gamma$ \hspace{1.7cm}  $u_{hor}$



\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%





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\section{Summary}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
  \frametitle{Summary}
  
  \begin{itemize}


%  \item  High fidelity
%  modeling and simulations for performance assessment of infrastructure systems


%\vspace*{0.5cm}
  \item  {\bf  Interplay}  of    {\bf  Earthquake}, {\bf Soil} and {\bf
  Structure} plays a major role in catastrophic failures
  and great successes

\vspace*{0.5cm}
  \item    {\bf  Opportunity to improve design}:  following  the 
  flow of seismic energy in the soil--structure systems

\vspace*{0.5cm}
  \item   {\bf  Directing} in  space  and  time,  seismic 
  energy flow in the soil--structure system might/will lead to increase in safety and
  economy

  

%
%    \item {\bf Matching Triad}: 
%    \underline{Earthquake}, 
%    \underline{Soil} and 
%    \underline{Structure}  
%    ({\bf ESS}) interaction determines 
%          possible benefits or detriments of SFSI



\end{itemize}


\end{frame}
%-- 
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\begin{frame}
  \frametitle{Colossus of Rhodes: What if?}
  
\includegraphics[height=5cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/rhodes.jpg}
\includegraphics[height=5cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/colossus_final.jpg}
\includegraphics[height=5cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/rhodes_tilted.jpg}


\end{frame}
%-- 

%--  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%--  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%--  \begin{frame}
%--    \frametitle{References}
%--  
%--  {\tiny
%--  \bibliographystyle{plainnat}
%--  
%--  \bibliography{refGuanzhou,refcomp,refmech,auxCompPlatform}
%--  
%--  
%--  }
%--  
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%--  %-- 


\end{document}


