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\title[High  Fidelity  Modeling  and Simulation of \\
SFS Interaction: \\
Energy Dissipation by Design]
% (optional, use only with long paper titles)
{High  Fidelity  Modeling  and Simulation of \\
SFS Interaction: \\
Energy Dissipation by Design}

%\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} \\ {\tiny with contributions by} \\
{\small Nima  Tafazzoli  (UCD),  Guanzhou Jie (Wachovia Corp.), Mahdi Taiebat (UBC), Zhao
Cheng (EarthMechanics Inc.)}}
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\pgfuseimage{university-logo} \hspace*{-0.3truecm}] % (optional, but mostly needed)
{ 

  CompGeoMech group, CEE Dept. UCD}
%  Department of Civil and Environmental Engineering\\
%  University of California, Davis}
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\date[SFSI Auckland, NZ] % (optional, should be abbreviation of conference name)
{SFSI Auckland, NZ}
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% 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.
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\section{Motivation}

\subsection*{Motivation}
%\subsection*{}
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\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-foundation-structure systems


\vspace*{0.3cm}
  \item      Accurate     following  of  the  flow  of  seismic  energy  in  the
  soil-foundation-structure
  system

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

  

\end{itemize}
\end{frame}
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\begin{frame}
 \frametitle{The Very First Published Work on SFSI}

  \begin{itemize}
         \item Professor Kyoji Suyehiro 
         \item Ship engineer (Professor of Naval Arch. at U. of Tokyo),
         \item Witnessed Great Kant{\= o} earthquake 
               (Tokyo, 01Sept1923
                11:58am(7.5),    
                12:01pm(7.3),    
                12.03pm(7.2),   
                shaking until 12:08pm)
         \item Saw earthquake surface waves travel and buildings sway 
         \item  Became  founding Director of the 
                Earthquake Engineering Research
                Institute at the Univ. of Tokyo,
         \item  His published records (ASCE 1932) show 
                four times more damage to soft
                wooden buildings on soft ground 
                then same buildings on stiff soil
  \end{itemize}

\end{frame}


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\begin{frame}
 \frametitle{Hypothesis}

\begin{itemize}
  


%\vspace*{0.5cm}
  \item    Interplay   of  the  Earthquake  with the   
  Soil, Foundation  and  Structure in time domain plays  major
  role in  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 (directed, designed),
         we could  optimize soil-foundation-structure system for
    \begin{itemize}
      \item Safety and
      \item Economy
    \end{itemize}

\end{itemize}
\end{frame}
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%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \subsection{Predictive Capabilities}
%  
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\begin{frame}
 \frametitle{Predictive Capabilities}
% \frametitle{High Fidelity Modeling of SFS System:
% Verification, Validation and Prediction}


\begin{itemize}


     \item {{\bf Verification} provides evidence that the
   model is solved correctly.} Mathematics issue. 

%\vspace*{0.2cm}
     \item {{\bf Validation} provides
   evidence that the correct model is solved.} Physics issue. 

%\vspace*{0.2cm}
   \item {\bf 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*{0.2cm}
   \item Goal: predictive capabilities 
   with {\bf low Kolmogorov Complexity}



% \vspace*{0.2cm}
   \item {\bf The Finite Element 
   Interpreter  \FEI{}} might be one such 
   predictive tool (application program)
   


\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}
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%\section{Modeling and Simulation of Soil Structure Systems}
\section{Seismic Energy Flow}
%\section{High Fidelity Modeling and 
%         Simulation of Seismic Energy Flow}



%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \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{Input}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Seismic Energy 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 LARGE JAPANESE EQ.
%          \item LARGE NEW ZEALAND EQ.
          \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*{0.5cm}
      \item Part that energy is radiated as mechanical 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}
%- 
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\begin{frame}
 \frametitle{Seismic Energy Input Into 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}
%- 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Dissipation}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
% \frametitle{Seismic Energy Dissipation for \underline{Soil}-Foundation-Structure Systems}
 \frametitle{Seismic Energy Dissipation for 
             \underline{\bf S}FS System}
% \frametitle{Seismic Energy Dissipation for 
%             \underline{Soil}-Foundation-Structure Systems}


\begin{itemize}


\vspace*{0.2cm}
     \item Mechanical dissipation outside of SFS domain:
       \begin{itemize}
         \item reflected wave radiation
         \item SFS system oscillation radiation
       \end{itemize}
\vspace*{0.2cm}
     \item Mechanical dissipation/conversion inside SFS domain:
       \begin{itemize}
         \item plasticity of soil subdomains
         \item viscous coupling of porous solid with pore fluid (air, water)
         \item plasticity/damage of the parts of structure/foundation
         \item viscous coupling of structure/foundation with 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}

%
\end{frame}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
 \frametitle{Energy Dissipation by Soil 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}
%- 
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%- \begin{frame}
%-  \frametitle{Plasticity Energy Disipation}
%- 
%-    \begin{itemize}
%- 
%-      \item
%- 
%-   \end{itemize}
%- 
%- 
%- \end{frame}
%- %- 
%- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
 \frametitle{Energy Disipation by Soil 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}


\end{frame}
%- 
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\section{Energy Dissipation Examples}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Soft Soil}

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

\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 of surface ground motions

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

 
%\vspace*{0.3cm}
  \item Plastic Domain \\
  Decomposition 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*{-5.2cm}
%\hfill
\hspace*{4.8cm} 
\includegraphics[width=6.5cm]{/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{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{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{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}
%


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\subsection{Liquefaction}



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\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}
%

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\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{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}
% 
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\begin{frame}
 \frametitle{Kinetic Energy at the Soil Surface}


%\vspace*{-0.3cm}
\begin{figure}[h]
\begin{center}
\includegraphics[width=10cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/StackElements-Compare.pdf} 
%\hspace*{-0.1cm}
\end{center}
\vspace*{-4.3cm}
\end{figure}
%\vspace*{-5.3cm}
%\hspace*{2.3cm} EPPR \hspace{1.5cm}  $\gamma$ \hspace{1.7cm}  $u_{hor}$
               

%
\begin{itemize}
 
 \item Liquefaction base isolates seismic motions

 \item Energy dissipated by plasticity and 
 viscous coupling

% \item 


\end{itemize}




\end{frame}









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% \frametitle{SPT: Shear Strength and Young's Modulus}
% 
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% 
% 
% \begin{figure}[!hbpt]
% \begin{center}
% % 
% \includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_RawData_and_MeanTrend-Mod.pdf}
% \hfill
% \includegraphics[width=4.50truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_Histogram_PearsonIV-FineTuned-Mod.pdf}
% %
% \end{center}
% \end{figure}                        
% 
% \vspace*{-0.3cm}
% \begin{figure}[!hbpt]
% \begin{center}
% %
% \includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01-Ed.pdf} 
% \hfill
% \includegraphics[width=4.50truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_Histogram_Normal_01-Ed.pdf}
% %
% \end{center}
% \end{figure}                                                          
%                                   
% 
% \vspace*{-0.2cm}
% Phoon and Kulhawy (1999B)
% 
% \end{frame}
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% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% % 
% % \frametitle{Bi-Linear von Mises Response}
% % 
% % 
% % \begin{figure}[!hbpt]
% % \begin{center}
% % \includegraphics[width=9cm]{/home/jeremic/tex/works/Papers/2007/ProbabilisticYielding/figures/vonMises_G_and_cu_very_uncertain/Contour_PDF-edited.pdf}
% % \end{center}
% % \end{figure}                                                          
% % 
% % %\vspace*{-0.3cm}
% % %linear elastic - linear hardening plastic von Mises
% % 
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% \begin{figure}[!hbpt]
% \begin{center}
% %
% \includegraphics[width=5.15truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/meanStressStrainPlot_1Point026-Mod.pdf}
% \hfill
% \includegraphics[width=4.35truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/sdStressStrainPlot_1Point026-Mod.pdf}
% %
% \end{center}
% \end{figure}                                                          
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% \begin{figure}[!hbpt]
% \begin{center}
% %
% \hspace*{-1cm}
% \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/GoverGmax-Mod.pdf}
% \hspace*{-0.5cm}
% \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/Damping-Mod.pdf}
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% \end{figure}                                                          
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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      the { Earthquake}, the { Soil},
  {Foundation} and {Structure} in {\bf time domain} plays a decisive role in
  catastrophic failures and great successes

\vspace*{0.2cm}
  \item        {\bf  Improve  design  through  high  fidelity
  simulations}: direct the flow of seismic energy in the SFS systems

%\vspace*{0.2cm}
%  \item   {\bf Ability to direct} seismic energy flow, in  space  and  time, 
%  for a complete SFS system will lead to an increase in  safety and economy

\vspace*{0.2cm}
  \item   {\bf Uncertainty} (point-wise and spatial) is very important
 
 
\vspace*{0.2cm}
  \item   {\bf Predictive tools}, will prove essential:
  \begin{itemize}
     \item The Finite Element Interpreter (\FEI{}) 
     \item {\url{www.OpenHazards.com}}
  \end{itemize}
  



\end{itemize}


\end{frame}
%

\end{document}


