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\title[ESSI Modeling and Simulation]
        {Nonlinear Time Domain \\
         Modeling and Simulation of  \\
         Surface  and Embedded NPPS }


%\subtitle
%{Include Only If Paper Has a Subtitle}

%\author[Author, Another] % (optional, use only with lots of authors)
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\author[Jeremi{\'c} et al.] % (optional, use only with lots of authors)
%{Boris~Jeremi{\'c}}
{Boris Jeremi{\'c} \\ 
{\tiny with contributions from} \\ 
Federico Pisan{\`o}, Jose Abell, Kohei Watanabe, Chao Luo}

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%{ Professor, University of California, Davis\\
{ University of California, Davis\\
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%  Faculty Scientist, Lawrence Berkeley National Laboratory, Berkeley }
  Lawrence Berkeley National Laboratory, Berkeley }
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\date[] % (optional, should be abbreviation of conference name)
{\small DOE NPH, \\  October 2014}

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\section{Introduction}




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\subsection{Motivation}



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\begin{frame}
 \frametitle{Motivation}

\begin{itemize}
  


%\vspace*{0.3cm}
  \item Improving seismic design (safety and economy) for Nuclear Facilities (NFs)


\vspace*{0.1cm}
  \item      {\bf   E}arthquake {\bf S}oil {\bf S}tructure {\bf I}nteraction
  ({\bf ESSI}) in time and space, plays a major role in successes and failures



\vspace*{0.1cm}
  \item  Accurate  following  and directing (!) the  flow  of  seismic energy in
  ESSI system to optimize ESSI system for
    \begin{itemize}
      \item Safety and
      \item Economy
    \end{itemize}


\vspace*{0.1cm}
  \item  Development of  high  fidelity  numerical modeling and simulation tools
  to analyze realistic ESSI behavior, \\ Real ESSI Simulator
%  of NFs

\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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*{0.1cm}
     \item {{\bf Validation} provides
   evidence that the correct model is solved.} Physics issue. 

%\vspace*{0.1cm}
   \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)
   

%\vspace*{0.1cm}
   \item {\bf Real ESSI Simulator}: a software, hardware and documentation system for high
   fidelity,  high  performance,  time  domain,  nonlinear,  3D,  finite element
   modeling  and  simulation  of  earthquake-soil/rock-structure  interaction of
   Nuclear  Facilities  (NFs) 
%  %    developed  in collaboration and with a financial
%  %   support  of  the
%       (US-NRC,  US-DOE, CNSC-CCSN, US-NSF, 
%        AREVA, and Shimizu)
%  %      AREVA NP GmbH, and Shimizu Corp.)

\end{itemize}


\end{frame}






%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \subsection{Flow of Seismic Energy}
% 
% 
% 
% %- 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Seismic Energy Input for the SSI 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{Seismic Energy Dissipation for \underline{Soil}-Foundation-Structure Systems}
 \frametitle{Seismic Energy Input and Dissipation for NFs}
% \frametitle{Seismic Energy Dissipation for 
%             \underline{Soil}-Foundation-Structure Systems}


\begin{itemize}


% \vspace*{0.2cm}
     \item Seismic waves input (flux) into SSI system

\vspace*{0.1cm}
     \item Mechanical dissipation outside of SSI domain:
       \begin{itemize}
         \item reflected (surface, NF) wave radiation
         \item SSI (NF) system oscillation radiation
       \end{itemize}
\vspace*{0.1cm}
     \item Mechanical dissipation/conversion inside SSI domain:
       \begin{itemize}
         \item plasticity of soil and rock
         \item nonlinear contact zone (foundation -- soil/rock)
         \item plasticity/damage of  structure, foundation
         \item viscous coupling of porous solid with pore fluid (soil)
         \item viscous coupling of structure/foundation with fluids 
%         \item potential and kinetic energy
%         \item potential $\leftarrow \! \! \! \! \! \! \rightarrow$ kinetic energy
       \end{itemize}                           



\vspace*{0.1cm}
%   \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}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \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}
%  %- 
%  %- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %- \begin{frame}
%  %-  \frametitle{Plasticity Energy Dissipation}
%  %- 
%  %-    \begin{itemize}
%  %- 
%  %-      \item
%  %- 
%  %-   \end{itemize}
%  %- 
%  %- 
%  %- \end{frame}
%  %- %- 
%  %- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Energy Dissipation 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}
%  %- 
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \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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\subsection{Modeling Uncertainty}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Modeling Uncertainty}

\begin{itemize}



\item Real ESSI goal: reduction of modeling uncertainty

\vspace*{0.2cm}
  \item  Simplified modeling:  important  features    are 
  neglected (structure complexity, 6D ground motions, non-linearities)

\vspace*{0.2cm}
     \item      Modeling      Uncertainty:   unnecessary and
     unrealistic modeling simplifications 

\vspace*{0.2cm}
     \item  Modeling  simplifications   are  justifiable  if  one  or  two  level  higher
     sophistication  model  shows  that  features  being  simplified out are not
     important

%\vspace*{0.1cm}
%     \item    Use   of  results  from  models  with  (high) modeling uncertainty
%     should be avoided
  


\end{itemize}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
% \frametitle{Complexity and Uncertainty in Ground Motions and Material Modeling}
 \frametitle{Complexity and Uncertainty in Motions and Material}

\begin{itemize}
%\vspace*{0.3cm}
  \item 6D (3 translations (horizontal and vertical), 3 rotations)

%\vspace*{0.3cm}
% \item Vertical motions usually neglected
%  
% \vspace*{0.3cm}
%   \item Rotational components usually not measured and neglected 
%  
% \vspace*{0.3cm}
%   \item Lack of models for such 6D motions (from measured data))
%   
\vspace*{0.1cm}
  \item Sources of uncertainties in ground motions (Source, Path (rock), soil (rock))  

\vspace*{0.1cm}
  \item     Most  engineering  materials  and  components  experience  inelastic
  deformations for service and hazard loads

%\vspace*{0.1cm}
%  \item This is even more so for hazard loads (earthquakes)
 
\vspace*{0.1cm}
  \item    Pressure sensitive materials (soil, rock, concrete, \&c.) have complex
  constitutive  response,  tying  together  nonlinear  stress-strain with volume
  response
 
%\vspace*{0.1cm}
%  \item  Simplistic  material  modeling  introduces
%  (significant) uncertainties in response results
  
\vspace*{0.1cm}
  \item  In  addition, man-made and natural materials are spatially variable and
  their material modeling parameters are uncertain


\end{itemize}

\end{frame}











%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame} 
% 
% \frametitle{Material Behavior Inherently Uncertain}
% 
% 
% %\begin{itemize}
% 
% %\vspace*{0.5cm}
% %\item  
% %Material  behavior  is  inherently uncertain  (concrete,  metals,  soil,  rock, 
% %bone, foam, powder \&c.)
% 
%         \begin{itemize}
% 
% \vspace*{0.5cm}
%         \item Spatial \\ 
%               variability
% 
% \vspace*{0.5cm}
%         \item Point-wise \\ 
%               uncertainty, \\
%               testing \\
%               error, \\
%               transformation \\
%               error
% 
%         \end{itemize}
% 
% % \vspace*{0.5cm}
% % \item  Failure mechanisms related to spatial variability (strain localization and
% %        bifurcation of response)
% % 
% % \vspace*{0.5cm}
% % \item Inverse problems
% % 
% %       \begin{itemize}
% %       
% %       \item New material design, ({\it point-wise})
% % 
% %       \item Solid and/or structure design (or retrofits),  ({\it spatial})
% % 
% %       \end{itemize}
%                                   
% %\end{itemize}
% 
% \vspace*{-5cm}
% \begin{figure}[!hbpt]
% %\nonumber
% %\begin{center}
% \begin{flushright}
% %\includegraphics[height=5.0cm]{/home/jeremic/tex/works/Conferences/2006/KragujevacSEECCM06/Presentation/MGMuzorak01.jpg}
% \includegraphics[height=5.5cm]{/home/jeremic/tex/works/Conferences/2006/KallolsPresentationGaTech/FrictionAngleProfile.jpg}
% \\
% \mbox{(Mayne et al. (2000) }
% \end{flushright}
% %\end{center}
% %\end{center}
% \end{figure}
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
% 
% 
% \frametitle{SPT Based Determination of Shear Strength}
% 
% 
% 
% 
% \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=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_Histogram_PearsonIV-FineTuned-Mod.pdf}
% %
% \end{center}
% \end{figure}                                                          
% 
% \vspace*{-0.3cm}
% Transformation of SPT $N$-value $\rightarrow$ un-drained shear
% strength, $s_u$ (cf. Phoon and Kulhawy (1999B)
% 
% Histogram  of  the  residual  
% (w.r.t  the  deterministic transformation
% equation) un-drained strength, 
% along with fitted probability density function 
% (Pearson IV)
% \end{frame}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}



\frametitle{SPT Based Determination of Young's Modulus}


\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=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_Histogram_Normal_01-Ed.pdf}
%
\end{center}
\end{figure}                                                          

\vspace*{-0.3cm}
 Transformation of SPT $N$-value $\rightarrow$ 1-D Young's modulus, $E$ (cf. Phoon and Kulhawy (1999B))

 Histogram of the residual (w.r.t the deterministic transformation equation) Young's modulus, along with fitted probability density function

\end{frame}






























% 
% 












 
















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\section{ESSI Modeling}





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\subsection{Modeling Issues}




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\begin{frame}
\frametitle{Important Issues for ESSI Modeling and Simulation}

   \begin{itemize}

     \item Verification and Validation

\vspace*{2mm}
     \item 6D, inclined, body and surface  seismic waves

\vspace*{2mm}
     \item Uncorrelated (incoherent) motions

\vspace*{2mm}
     \item Nonlinear material (soil, rock, concrete, steel, \&c.)

\vspace*{2mm}
     \item Nonlinear foundation-soil/rock contact (dry and saturated), slip -- gap 

\vspace*{2mm}
     \item Saturated dense vs loose soil with buoyant forces

%\vspace*{2mm}
%     \item Piles and pile groups 

\vspace*{2mm}
     \item Isolators, dissipators


\end{itemize}

\end{frame}








% %  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{ESSI Models}

\vspace*{+10mm}
Detailed \\
high\\
fidelity\\
models\\
taking\\
into\\
account\\ 
all of the\\
issues


\vspace*{-60mm}
\begin{figure}[!hbpt]
\begin{flushright}
\includegraphics[width=4.30cm]{/home/jeremic/tex/works/Conferences/2014/DOE_Natural_Phenomena_Hazards_Germantown_MD-21-22Oct/present/Model01.jpeg}
\includegraphics[width=4.30cm]{/home/jeremic/tex/works/Conferences/2014/DOE_Natural_Phenomena_Hazards_Germantown_MD-21-22Oct/present/Model02.jpeg}
\\
\includegraphics[width=4.30cm]{/home/jeremic/tex/works/Conferences/2014/DOE_Natural_Phenomena_Hazards_Germantown_MD-21-22Oct/present/Model03.jpeg}
\includegraphics[width=3.30cm]{/home/jeremic/tex/works/Conferences/2014/DOE_Natural_Phenomena_Hazards_Germantown_MD-21-22Oct/present/Model04.jpeg}
%gthumb /home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_ESSI_for_NPPs/Model01_full_view.jpg &
%gthumb /home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_ESSI_for_NPPs/Model02_full_view.jpg &
%gthumb /home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_ESSI_for_NPPs/Model03_full_view.jpg &
%gthumb /home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_ESSI_for_NPPs/SMR02_a.jpg           &
\end{flushright}
\end{figure}

\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{In Detail: Main ESSI Issues for SMRs}

\begin{figure}[!hbpt]
\begin{center}
\vspace*{-0.2cm}
\includegraphics[width=3.5cm]{/home/jeremic/tex/works/Conferences/2014/ASME_SMR_Symposium/present/SMR02_a_01-GRAY_pdf.pdf}
\includegraphics[width=3.5cm]{/home/jeremic/tex/works/Conferences/2014/ASME_SMR_Symposium/present/SMR02_a_02-GRAY_pdf.pdf}
\\
\includegraphics[width=3.5cm]{/home/jeremic/tex/works/Conferences/2014/ASME_SMR_Symposium/present/SMR02_a_03-GRAY_pdf.pdf}
\includegraphics[width=3.5cm]{/home/jeremic/tex/works/Conferences/2014/ASME_SMR_Symposium/present/SMR02_a_04-GRAY_pdf.pdf}
\vspace*{-0.6cm}
\end{center}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%  



% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{High Fidelity Modeling and Simulation \\
% Detrimental and Beneficial ESSI Effects}
% 
% 
% 
% \begin{figure}[!hb]
% \begin{center}
% \vspace*{-0.2cm}
% \includegraphics[width=3.3cm]{/home/jeremic/tex/works/consulting/2013/CNSC/ProgressReports/Progress_report_02_figs/single-NPP-FEM-model.jpg}
% \includegraphics[width=3.3cm]{/home/jeremic/tex/works/consulting/2013/CNSC/ProgressReports/Progress_report_02_figs/double-NPP-FEM-model.jpg}
% \end{center}
% \end{figure}
% %\vspace*{2.0cm}
% 
% \begin{figure}[!hbpt]
% \begin{center}
% \hspace*{-0.5cm}
% \includegraphics[width=3.3cm]{/home/jeremic/tex/works/Conferences/2014/ASME_SMR_Symposium/present/SMR01_a.jpg}
% \includegraphics[width=3.3cm]{/home/jeremic/tex/works/Conferences/2014/ASME_SMR_Symposium/present/SMR02_a.jpg}
% \end{center}
% \end{figure}
% 
% % 
% % %
% % 
% % \begin{itemize}
% %      \item 
% %      \item 
% %      \item 
% % \end{itemize}
% 
% \end{frame}
% 
       
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Current Surface NPP Models (LWRs)}
% 
% % 
% 
% \vspace*{-0.2cm}
% \begin{figure}[!hbpt]
% \begin{center}
% \raisebox{0.9cm}{\includegraphics[width=1.0cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/04_cropped.jpg}}
% \raisebox{1.2cm}{\includegraphics[width=2.2cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/02_cropped.jpg}}
% \raisebox{-0.5cm}{\includegraphics[width=4cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/03_cropped.jpg}}
% \end{center}                              
% \end{figure}
% 
% \vspace*{-1.6cm}
% \begin{itemize}
% % \item Modular models
% %\vspace*{-0.1cm}
%  \item 3D, Inclined, body and \\ surface  seismic waves
% %\vspace*{-0.1cm}
%  \item Uncorrelated (incoherent) motions
% %\vspace*{-0.1cm}
%  \item Foundation slip -- gap 
% %\vspace*{-0.1cm}
%  \item Isolators, dissipators
% %\vspace*{-0.1cm}
%  \item Saturated dense vs loose soil with buoyant forces
% %\vspace*{-0.1cm}
%  \item Piles and pile groups 
% 
% \end{itemize}
% 
% \end{frame}
% 
% 
% 
% 
% 
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Current Embedded NPP Models (SMRs)}
% 
% 
% \begin{figure}[!hbpt]
% \begin{center}
% \vspace*{-0.2cm}
% %\includegraphics[width=4cm]{/home/jeremic/tex/works/Conferences/2014/ASME_SMR_Symposium/present/SMR01_a.jpg}
% \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2014/ASME_SMR_Symposium/present/SMR02_a.jpg}
% \vspace*{-0.6cm}
% \end{center}
% \end{figure}
% 
% % OVDE stavi srdjene slike (ovu mrezu, dodaj mnan tablici, za sve probleme)...
% 
% 
% \begin{itemize}
%      \item    A  number  of ESSI modeling and simulation issues that control the
%      seismic response
%      \item Detrimental and Beneficial ESSI effects
%      \item Seismic energy propagation and dissipation
% \end{itemize}
% 
% \end{frame}
% 
% 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% % \frametitle{ESSI: Seismic Body and Surface Waves}
% % 
% % \begin{figure}[!hbpt]
% % \begin{center}
% % \vspace*{-0.2cm}
% % \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2014/ASME_SMR_Symposium/present/SMR02_a_01-GRAY_pdf.pdf}
% % \vspace*{-0.6cm}
% % \end{center}
% % \end{figure}
% % 
% % \begin{itemize}
% %      \item Seismic surface waves carry most seismic energy
% %      \item SMR bottom: body waves; SMR top: surface waves
% %      \item Incoherent seismic motions 
% % \end{itemize}
% % \end{frame}
% % 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% % \frametitle{ESSI: Nonlinear Contact and Soil/Rock Zones}
% % 
% % \begin{figure}[!hbpt]
% % \begin{center}
% % \vspace*{-0.2cm}
% % \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2014/ASME_SMR_Symposium/present/SMR02_a_02-GRAY_pdf.pdf}
% % \vspace*{-0.6cm}
% % \end{center}
% % \end{figure}
% % 
% % \begin{itemize}
% %      \item Seismic energy dissipated at the contact 
% %      \item Seismic energy dissipated within adjacent soil/rock zones
% %     \item Passive (complete) structural isolation (beneficial)
% % \end{itemize}
% % \end{frame}
% % 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% % \frametitle{ESSI: Fluid Structure Interaction}
% % 
% % \begin{figure}[!hbpt]
% % \begin{center}
% % \vspace*{-0.2cm}
% % \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2014/ASME_SMR_Symposium/present/SMR02_a_03-GRAY_pdf.pdf}
% % \vspace*{-0.6cm}
% % \end{center}
% % \end{figure}
% % 
% % \begin{itemize}
% %      \item SMR below water table, 
% %      \item Saturated soil (liquefaction, densification/stiffening)
% %      \item Buoyant forces (dynamically changing)
% % \end{itemize}
% % \end{frame}
% % 
% % 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% % \frametitle{ESSI: Uncertain Material and Uncertain Loads}
% % 
% % \begin{figure}[!hbpt]
% % \begin{center}
% % \vspace*{-0.2cm}
% % \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2014/ASME_SMR_Symposium/present/SMR02_a_04-GRAY_pdf.pdf}
% % \hspace{0.5cm}
% % \includegraphics[width=4.0cm]{/home/jeremic/tex/works/Conferences/2014/ASME_SMR_Symposium/present/SPT_Uncertain_Youngs_Modulus.jpg}
% % %
% % %\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01-Ed.pdf} 
% % %\\
% % %%\hfill
% % %\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_Histogram_Normal_01-Ed.pdf}
% % %
% % \vspace*{-0.6cm}
% % \end{center}
% % \end{figure}
% % 
% % \begin{itemize}
% %      \item Inherently uncertain material response
% %      \item Inherently uncertain (seismic) loading
% %      \item Full probabilistic modeling and simulations is desired
% % %     \item 
% % \end{itemize}
% % \end{frame}
% % 
% % 
% % 
% 
% 


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{3D, Inclined, Body and Surface Seismic Waves}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Real Earthquake Ground Motions}


   \begin{itemize}
\vspace*{0.2cm}
     \item Body waves: P and S waves
\vspace*{0.2cm}
     \item Inclined waves
\vspace*{0.2cm}
     \item Surface waves: Rayleigh, Love waves, \&c.
\vspace*{0.2cm}
     \item 6D waves (3 translations, 3 rotations)
\vspace*{0.2cm}
  \item Surface waves carry most seismic energy
\vspace*{0.2cm}
     \item Lack of correlation (incoherence)
%\vspace*{0.1cm}
%     \item Earthquake energy  dissipation

   \end{itemize}






\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Body (P, S) and Surface (Rayleigh, Love) Waves}
% 
%  
% \vspace*{-0.3cm}
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=2.5cm, angle=45]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Presentation/P_body_wave.jpeg}
% \includegraphics[width=2.5cm, angle=45]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Presentation/S_body_wave.jpeg}
% \vspace*{-0.7cm}
% \\
% \includegraphics[width=3cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Presentation/Rayleigh_surface_wave.jpeg}
% \includegraphics[width=3cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Presentation/Love_surface_wave.jpeg}
% %\caption{\label{Love_surface_wave}   Visualization  of  propagation  of  a  Love
% %surface seismic wave (illustrations are from MTU web site).}
% \end{center}
% \end{figure}
% 
% \end{frame}
% 
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame} 
% \frametitle{Spatial Variability (Incoherence, Lack of Correlation)}
% 
% Incoherence $\rightarrow$ frequency domain
% 
% \vspace*{0.2cm}
% 
% Lack of Correlation $\rightarrow$ time domain
% 
% 
% \vspace*{0.5cm}
% 
% \begin{itemize}
%   \item Wave passage effects
%   \item Attenuation effects
%   \item Extended source effects
%   \item Scattering effects
% %  \item Variable seismic energy dissipation
% \end{itemize}
% 
% %\begin{figure}[!htb]
% %\begin{center}
% \vspace*{-3.5cm}
% \hspace*{5.5cm}
% \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2011/NRC_Staff_Capacity_Building_25May2011/Lack_of_Correlation_5_points.pdf}
% %\caption{\label{LC} Four main sources contributing to the lack of correlation of
% %seismic waves as measured at two observation points.}
% %\end{center}
% %\end{figure}
% %
% %A number of models available (Abrahamson...)
% %
% \end{frame}
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Free Field, Inclined, 3D Body and Surface Waves}
% 
%   \begin{itemize}
%     
%     \item  Development  of  analytic  and  numerical  3D, inclined, uncorrelated
%     seismic motions for verification
% 
%    \vspace*{0.2cm}
%     \item Large scale models 
% 
%    \vspace*{0.2cm}
%     \item Point shear source 
% 
%    \vspace*{0.2cm}
%     \item Stress drop:
%          \begin{itemize}
% 
%            \item Wavelet (Ricker, \\
%            Ormsby, \&c.)
%   
%            \item Analytic 
% 
% 
%          \end{itemize}
% 
%    \vspace*{0.2cm}
%     \item Seismic input using DRM (Bielak et al (2003))
% 
%   \end{itemize}
% 
% 
% 
%  
%    \vspace*{-4.6cm}
% \begin{flushright}
% \includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/wave_propagation/figs/FaultSlipModel2km.pdf}
% \end{flushright}
% 
% 
% 
% \end{frame}
% 
% 
% 
% 
%  
%      
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Plane Wave Model}
% 
% \vspace*{-1cm}
% \begin{figure}[!h]
% \begin{flushright}
% \includegraphics[width=4cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_wave_propagation_figs_DRMModel.pdf}
% \label{fig:DRMModel}
% \end{flushright}
% \end{figure}
% 
% 
% \vspace*{-1.5cm}
% \begin{figure}[H]
% \begin{center}
% \includegraphics[width=8cm]{/home/jeremic/tex/works/Conferences/2011/NRC_LBNL_Review_Panel_Sept2011/2D_faul_slip_model.pdf}
% \end{center}
% \end{figure}
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Seismic Source Mechanics}
% 
% \vspace*{0.5cm}
% Stress drop, Ormsby wavelet
% 
% \vspace*{-1cm}
% \begin{figure}[H]
% \begin{flushright}
% \includegraphics[width=2cm]{/home/jeremic/tex/works/Conferences/2011/NRC_LBNL_Review_Panel_Sept2011/Seismic_source_moment_couple.pdf}
% \end{flushright}
% \end{figure}
% 
% \vspace*{-1.9cm}
% \hspace*{-1cm}
% \begin{figure}[H]
% \begin{center}
% \hspace*{-0.4cm}
% \includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FaultModel_7seconds/xz_TimeHistory/3000_3000_x_displacement.pdf}
% \hspace*{-0.4cm}
% \includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FaultModel_7seconds/xz_FFT/3000_3000_x_displacement_FFT.pdf}
% \end{center}
% \end{figure}
% 
% \end{frame}
% 
% 
% 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{3D, Body and Surface Seismic Waves}

\vspace*{-0.5cm}
\begin{figure}[H]
\begin{flushright}
\includegraphics[width=4cm]{/home/jeremic/tex/works/Conferences/2011/NRC_LBNL_Review_Panel_Sept2011/2D_faul_slip_model_MIDDLE.pdf}
\end{flushright}
\end{figure}

\vspace*{-2.0cm}
\begin{figure}[H]
\begin{center}
\hspace*{-1.0cm}
\includegraphics[width=6.5cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FreeFieldInclinedMotionModels/Ormsby/middle_top2000/middle_acceleration_x.pdf}
\hspace*{-0.5cm}
\includegraphics[width=6.5cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FreeFieldInclinedMotionModels/Ormsby/middle_top2000/middle_acceleration_z.pdf}
\hspace*{-0.5cm}
\end{center}
\end{figure}

\vspace*{-0.90cm}
{horizontal accelerations   \hfill vertical accelerations}


\end{frame}




% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Body and Surface Wave Animations}
% 
% 
% 
% \begin{itemize}
% 
% %    \item  
% % \begin{center}%
% %     \includemovie{.85\textheight}{.85\textheight}{homo_50m-mesh_45degree_Ormsby.mp4}%
% % \end{center}%
% % 
%    \item  
% 
% %\begin{figure}[h!]
% %\centering    
% \movie[label=show3,width=0.7\textwidth,poster,autostart,showcontrols,loop] 
%   {\includegraphics[width=30mm]{BJicon.png}}{homo_50m-mesh_45degree_Ormsby.mp4}
% %  \caption{caption}
% % \end{figure} 
% 
%    \item  
%   \href{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/color_high-quality/homo_50m-mesh_45degree_Ormsby.mp4}
% %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
%   {Homogeneous soil/rock, $45^{\deg}$  off  vertical}
% 
% 
% \hspace*{0.5cm}
%    \item 
%    \href{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/vector/homo_50m-mesh_45degree_Ormsby.mp4}
%    {Homogeneous soil/rock, $45^{\deg}$  off  vertical, motion vectors}
%  
%  
%  \hspace*{0.5cm}
%    \item 
%    \href{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/vector/homo_50m-mesh_45degree_Ormsby_X5000-Z5000.mp4}
%    {Homogeneous  soil/rock,  $45^{\deg}$    off    vertical,  motion vectors, NPP location}
% 
%  \hspace*{0.5cm}
%    \item 
%    \href{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/color_high-quality/layered2_50m-mesh_45degree_Ormsby.mp4}
%    {Two  layers  of  soft  soil  with  homogeneous  soil/rock,  $45^{\deg}$  off 
%    vertical }
%  
% 
%  \end{itemize}
%  
% 
% 
% %   Homogeneous soil/rock, $56^{\deg}$  off  vertical)
% % \href{/home/jeremic/lecture_notes_online_material/public_html/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/color_high-quality/homo_50m-mesh_56degree_Ormsby.mp4}
% % {(link to a movie, 39MB)}
% % 
% %     Homogeneous soil/rock, $45^{\deg}$  off  vertical)
% %   \href{http://SOKOCALO.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/color_high-quality/homo_50m-mesh_45degree_Ormsby.mp4}
% %   {(link to a movie, 32MB)}
% % 
% %     Homogeneous soil/rock, $27^{\deg}$  off  vertical)
% %   \href{http://SOKOCALO.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/color_high-quality/homo_50m-mesh_27degree_Ormsby.mp4}
% %   {(link to a movie, 37MB)}
% % 
% % 
% %     Single layer soft soil with homogeneous soil/rock, $56^{\deg}$  off  vertical)
% %   \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/color_high-quality/layered_50m-mesh_56degree_Ormsby.mp4}
% %   {(link to a movie, 30MB)}
% % 
% %     Single layer soft soil with homogeneous soil/rock, $45^{\deg}$  off  vertical)
% %   \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/color_high-quality/layered_50m-mesh_45degree_Ormsby.mp4}
% %   {(link to a movie, 34MB)}
% % 
% %     Single layer soft soil with homogeneous soil/rock, $27^{\deg}$  off  vertical)
% %   \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/color_high-quality/layered_50m-mesh_27degree_Ormsby.mp4}
% %   {(link to a movie, 32MB)}
% % 
% % 
% % 
% %     Two layers of soft soil with homogeneous soil/rock, $56^{\deg}$  off  vertical)
% %   \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/color_high-quality/layered2_50m-mesh_56degree_Ormsby.mp4}
% %   {(link to a movie, 30MB)}
% % 
% %     Two layers of soft soil with homogeneous soil/rock, $45^{\deg}$  off  vertical)
% %   \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/color_high-quality/layered2_50m-mesh_45degree_Ormsby.mp4}
% %   {(link to a movie, 31MB)}
% % 
% %     Two layers of soft soil homogeneous soil/rock, $27^{\deg}$  off  vertical)
% %   \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/color_high-quality/layered2_50m-mesh_27degree_Ormsby.mp4}
% %   {(link to a movie, 32MB)}
% % %  
% 
% 
%  
%  \end{frame}
%  
%  


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Body and Surface Wave: System Displacements}

\begin{center}
\movie[label=show3,width=0.7\textwidth,poster,autostart,showcontrols,loop] 
  {\includegraphics[width=65mm]{BJicon.png}}{homo_50m-mesh_45degree_Ormsby.mp4}
\end{center}
%homo_50m-mesh_45degree_Ormsby.mp4
%homo_50m-mesh_45degree_Ormsby_vector.mp4
%homo_50m-mesh_45degree_Ormsby_X5000-Z5000.mp4
%layered2_50m-mesh_45degree_Ormsby.mp4
\end{frame}
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Body and Surface Wave: Vectors}

\begin{center}
%\movie[label=show3,width=0.7\textwidth,poster,autostart,showcontrols,loop] 
\movie[label=show3,width=0.7\textwidth,poster,autostart,showcontrols,loop] 
  {\includegraphics[width=65mm]{BJicon.png}}{homo_50m-mesh_45degree_Ormsby_vector.mp4}
\end{center}
%homo_50m-mesh_45degree_Ormsby.mp4
%homo_50m-mesh_45degree_Ormsby_vector.mp4
%homo_50m-mesh_45degree_Ormsby_X5000-Z5000.mp4
%layered2_50m-mesh_45degree_Ormsby.mp4
\end{frame}
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Body and Surface Wave: NF Soil Motions}

\begin{center}
%\movie[label=show3,width=0.7\textwidth,poster,autostart,showcontrols] 
\movie[label=show3,width=0.7\textwidth,poster,autostart,showcontrols,loop] 
  {\includegraphics[width=65mm]{BJicon.png}}{homo_50m-mesh_45degree_Ormsby_X5000-Z5000.mp4}
\end{center}
%homo_50m-mesh_45degree_Ormsby.mp4
%homo_50m-mesh_45degree_Ormsby_vector.mp4
%homo_50m-mesh_45degree_Ormsby_X5000-Z5000.mp4
%layered2_50m-mesh_45degree_Ormsby.mp4
\end{frame}
 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Body and Surface Wave Animations \#4}
% 
% %\movie[label=show3,width=0.7\textwidth,poster,autostart,showcontrols,loop] 
% \movie[label=show3,width=0.7\textwidth,poster,autostart,showcontrols] 
%   {\includegraphics[width=65mm]{BJicon.png}}{layered2_50m-mesh_45degree_Ormsby.mp4}
% %homo_50m-mesh_45degree_Ormsby.mp4
% %homo_50m-mesh_45degree_Ormsby_vector.mp4
% %homo_50m-mesh_45degree_Ormsby_X5000-Z5000.mp4
% %layered2_50m-mesh_45degree_Ormsby.mp4
% \end{frame}
%  
 


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Nonlinear Material Behavior}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Validation: Lotung, LSST07, $G/G_{max}$ and Damping}

 \vspace*{5mm}
\begin{itemize}
 \item Nonlinear, 3D elastic-plastic, Pisan{\`o} material model for Lotung (validation)

 \item 1D wave propagation, only LSST07 is close to 1D!
 \item No volume change data (a serious issue!)
\end{itemize}

 \vspace*{-5mm}
\begin{figure}[!h]
\begin{center} 
\includegraphics[width=5.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/LLSST07_GGmax_Curves.pdf}
\includegraphics[width=5.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/LLSST07_Damping_Curves.pdf}
%  \caption{G/Gmax and Damping Curves}\label{GD}
\end{center} 
\end{figure}

\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Validation: Lotung, LSST07, Downhole Motions}



\begin{figure}[!h]
 \centering
\includegraphics[width=4.1cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/LLSST07_Time_History_of_Surface.pdf}
\includegraphics[width=4.1cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/LLSST07_Time_History_of_6m_depth.pdf}
\\
\includegraphics[width=4.1cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/LLSST07_Time_History_of_11m_depth.pdf}
\includegraphics[width=4.1cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/LLSST07_Time_History_of_17m_depth.pdf}
% \caption{Time history comparison at  different depths}\label{Time_History}
\end{figure}

\end{frame}
           
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Validation: Lotung, LSST07, Fourier Spectra}


\begin{figure}[!h] 
 \centering
\includegraphics[width=4.1cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/LLSST07_Fourier_Spectrum_of_Surface.pdf}
\includegraphics[width=4.1cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/LLSST07_Fourier_Spectrum_of_6m_depth.pdf}
\\
\includegraphics[width=4.1cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/LLSST07_Fourier_Spectrum_of_11m_depth.pdf}
\includegraphics[width=4.1cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/LLSST07_Fourier_Spectrum_of_17m_depth.pdf}
% \caption{Fourier spectrum comparison at  different depths}\label{Fourier_Spectrum}
\end{figure}


\end{frame}
           
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Soil Volume Response}
% 
% \begin{itemize}
% 
% 
%    \item  3D  elastic-plastic  material  modeling  with  (only)  $G/G_{max}$ and
%    damping curves known: Pisan{\`o} model
% 
%   \item Soil behavior is very much a function of volumetric response
% 
%   \item Dilative soils: increase  volume due to shearing
% 
%   \item Compressive soils: decrease  volume due to shearing
% 
%   \item Modulus reduction and damping curves do not provide volumetric data
% 
%   \item Soil volume change will affect response due to volume constraints
% 
% \end{itemize}
% 
%     
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{No Volume Change, Compressive and Dilative Soil}
% %\frametitle{No Volume Change and Dilative Soil}
% 
% \begin{figure}[!h]
% \begin{center}
% \hspace*{-1cm}
%   \includegraphics[width=4.3cm]{/home/jeremic/tex/works/Thesis/FedericoPisano/Pisano_model/Issue_of_dilatancy/sine1Hz-4.pdf}
% \hspace*{-0.3cm}
%   \includegraphics[width=4.3cm]{/home/jeremic/tex/works/Thesis/FedericoPisano/Pisano_model/Issue_of_dilatancy/sine1Hz_comp-4.pdf}
% \hspace*{-0.3cm}
%   \includegraphics[width=4.3cm]{/home/jeremic/tex/works/Thesis/FedericoPisano/Pisano_model/Issue_of_dilatancy/sine1Hz_dil-4.pdf}
% \end{center}
% \end{figure}
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Northridge, No Volume Change Soil}
% 
% \vspace*{-0.6cm}
% \begin{figure}[!h]
% \begin{center}
%   \includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/FedericoPisano/Pisano_model/Issue_of_dilatancy/Northridge1-2.pdf}
% \end{center}
% \end{figure}
% 
% \end{frame}
% 
% % 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Northridge, Dilatant Soil}
% 
% \vspace*{-0.6cm}
% \begin{figure}[!h]
% \begin{center}
%   \includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/FedericoPisano/Pisano_model/Issue_of_dilatancy/Northridge1-3.pdf}
% \end{center}
% \end{figure}
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Northridge, No Volume Change and Dilative Soils}
% 
% \vspace*{-0.6cm}
% \begin{figure}[!h]
% \begin{center}
%   \includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/FedericoPisano/Pisano_model/Issue_of_dilatancy/Northridge1-4.pdf}
% \end{center}
% \end{figure}
% 
% \end{frame}
% % 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Northridge, No Volume Change and Dilative Soils}
% 
% \vspace*{-0.6cm}
% \begin{figure}[!h]
% \begin{center}
%   \includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/FedericoPisano/Pisano_model/Issue_of_dilatancy/Northridge1-5.pdf}
% \end{center}
% \end{figure}
% 
% \end{frame}
% % 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%





% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Foundation Slip/Gap and Liquefiable Soils}
% 
% \begin{itemize}
% \item Slip and gap between foundation slab and the soil/rock
% 
% \vspace*{0.4cm}
% \item Passive seismic isolation by liquefaction
% 
% \end{itemize}
% 
% \end{frame}
% 
% 


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{NPP with Base Slip and Gap}

\begin{itemize}

  \item Low friction zone between \\
        concrete foundation and soil/rock

  \item Inclined, 3D, body and surface, \\
        seismic wave field (wavelets: \\
        Ricker, Ormsby; real seismic, \&c.)


\end{itemize}



\vspace*{-4.0cm}
\begin{figure}[!h]
\begin{flushright}
\includegraphics[width=2.50cm]{/home/jeremic/tex/works/Conferences/2011/NRC_LBNL_Review_Panel_Sept2011/2D_faul_slip_model_top_200m.pdf}
%{\includegraphics[width=4.0cm]{/home/jeremic/tex/works/Conferences/2011/NRC_LBNL_Review_Panel_Feb2011/Case_study_model/visit0002.jpeg}}
\end{flushright}
\end{figure}

\vspace*{-0.9cm}
\begin{figure}[!h]
\begin{flushright}
{\includegraphics[width=4.0cm]{/home/jeremic/tex/works/Conferences/2011/NRC_LBNL_Review_Panel_Feb2011/Case_study_model/visit0002.jpeg}}
\end{flushright}
\end{figure}




\vspace*{-3.6cm}
\begin{figure}[H]
\begin{center}
%\vspace*{-0.5cm}
%\includegraphics[width=2.0cm]{/home/jeremic/tex/works/Conferences/2011/NRC_LBNL_Review_Panel_Sept2011/2D_faul_slip_model_top_200m.pdf}
%\hspace*{0.5cm}
%\vspace*{0.2cm}
\includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FreeFieldInclinedMotionModels/FaultSlip_Ormsby/figs/surface_200m/middle_acceleration_x.pdf}
\hspace*{-0.5cm}
\includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FreeFieldInclinedMotionModels/FaultSlip_Ormsby/figs/surface_200m/middle_acceleration_z.pdf}
%
\vspace*{-0.5cm} 
\hspace*{0.8cm} 
\mbox{horizontal}
\hspace*{4cm} 
\mbox{vertical}
\hspace*{3cm} 
\end{center}
\end{figure}
\vspace*{-1.0cm} 
% 
%  %\vspace*{-3.5cm}
%  \begin{figure}[H]
%  \begin{center}
%  \includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FreeFieldInclinedMotionModels/FaultSlip_Ormsby/figs/surface_200m/middle_acceleration_x.pdf}
%  \hspace*{-0.5cm}
%  \includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FreeFieldInclinedMotionModels/FaultSlip_Ormsby/figs/surface_200m/middle_acceleration_z.pdf}
%  \end{center}
%  \end{figure}
%  
%  %\vspace*{-3.5cm}
%  \begin{figure}[H]
%  \begin{center}
%  \includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FaultModel_7seconds/xz_TimeHistory/5000_5000_x_acceleration.pdf}
%  \hspace*{-0.5cm}
%  \includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FaultModel_7seconds/xz_TimeHistory/5000_5000_z_acceleration.pdf}
%  \end{center}
%  \end{figure}
%  
%  \vspace*{-0.90cm}
%  {horizontal accelerations   \hfill vertical accelerations}
%  
%  
%  


\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Acc. Response for a Full 3D (at $45^\circ$) Ricker Wavelet}

\begin{figure}[H]
\begin{center}
\begin{tabular}{rr} 
%\hline 
\mbox{\tiny top X}\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/91_97/top_structure_x_acceleration.pdf}
&
\mbox{\tiny top Z}\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/91_97/top_structure_z_acceleration.pdf}
\\
\mbox{\tiny bottom X}\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/91_97/bottom_structure_x_acceleration.pdf}
&
\mbox{\tiny bottom Z}\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/91_97/bottom_structure_z_acceleration.pdf}
\end{tabular}
%\caption{Comparison of acceleration time histories of the structure between 
%slipping and no-slipping models for Ricker wave}
\label{fig:3d_ricker_acc_1000}
\end{center}
\end{figure}



\end{frame}



% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{FFT Response for a Full 3D (at $45^\circ$) Ricker Wavelet}
% 
% \begin{figure}[H]
% \begin{center}
% \begin{tabular}{rr} 
% \mbox{\tiny top X}\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/91_97/top_structure_x_acceleration_FFT.pdf}
% &
% \mbox{\tiny top Z}\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/91_97/top_structure_z_acceleration_FFT.pdf}
% \\
% \mbox{\tiny bottom X}\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/91_97/bottom_structure_x_acceleration_FFT.pdf}
% &
% \mbox{\tiny bottom Z}\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/91_97/bottom_structure_z_acceleration_FFT.pdf}
% \end{tabular}
% %\caption{Comparison of FFT of the acceleration of the structure between 
% %slipping and no-slipping models for Ricker wave}
% \label{fig:3d_ricker_fft_1000}
% \end{center}
% \end{figure}
% 
% 
% \end{frame}
% 
% 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Slipping Response and Energy Dissipated ($45^\circ$ Ricker)}





\vspace*{-0.1cm}
\begin{tiny}
\begin{figure}[H]
\begin{flushleft}
\hspace*{-1cm}
\begin{tabular}{ccc} 
%\hline 
$4.5s$
&
$4.6s$
&
$4.7s$
\\
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/slide450.pdf}
&
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/slide460.pdf}
&
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/slide470.pdf}
\\
$4.8s$
&
$4.9s$
&
$5.0s$
\\
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/slide480.pdf}
&
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/slide490.pdf}
&
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/slide500.pdf}
\\
$5.1s$
&
$5.2s$
&
$5.3s$
\\
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/slide510.pdf}
&
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/slide520.pdf}
&
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/slide530.pdf}
%\\
%
%\hline
\end{tabular}
%\caption{Distribution of sliding along the contact interface for Ricker wave
%(gray scale given in meters)}
\label{fig:3d_ricker1000_slide_9}
\end{flushleft}
\end{figure}
\end{tiny}

\vspace*{-5cm}
\begin{figure}[!H]
\begin{flushright}
\includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/energy_sliding_92/energy_time.pdf}
\hspace*{-1cm}
\end{flushright}
\end{figure}



\end{frame}


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\begin{frame}
\frametitle{Gaping Response ($45^\circ$ Ricker Wavelet)}

\vspace*{-0.1cm}
\begin{tiny}
\begin{figure}[H]
\begin{center}
\begin{tabular}{ccc} 
%\hline 
$4.5s$
&
$4.6s$
&
$4.7s$
\\
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/gap450.pdf}
&
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/gap460.pdf}
&
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/gap470.pdf}
\\
$4.8s$
&
$4.9s$
&
$5.0s$
\\
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/gap480.pdf}
&
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/gap490.pdf}
&
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/gap500.pdf}
\\
$5.1s$
&
$5.2s$
&
$5.3s$
\\
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/gap510.pdf}
&
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/gap520.pdf}
&
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/gap530.pdf}
%\\
%
%\hline
\end{tabular}
%\caption{Distribution of gap openings along the contact interface for Ricker wave
%(gray scale given in meters)}
\label{fig:3d_ricker1000_gap_9}
\end{center}
\end{figure}
\end{tiny}



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%   \frametitle{Passive Base Isolation in Uniform and Layered Soils}
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% %\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
% %bridge.}
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%   \includegraphics[width=3.3cm]{/home/jeremic/tex/works/Conferences/2007/PEERAnnualMeeting/Liquefaction/PileBridgeModel02.jpg} 
% %  \includegraphics[width=4cm]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/GMklot02.pdf}
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% \includegraphics[width=0.03\textwidth,angle=0]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/Model_IV.jpg}
% &
% \includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_4_T002.jpg}
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% \\
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \includegraphics[width=0.03\textwidth,angle=0]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/Model_V.jpg}
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% \includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_5_T002.jpg}
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% \includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_5_T080.jpg}
% \\
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \includegraphics[width=0.035\textwidth,angle=0]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/Model_VI.jpg}
% &
% \includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_6_T002.jpg}
% &
% \includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_6_T005.jpg}
% &
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% &
% \includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_6_T015.jpg}
% &
% \includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_6_T020.jpg}
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% t=
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% \includegraphics[width=7cm,height=0.45cm]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/GMklot02.pdf}\hspace*{1cm}
% \\
% \vspace*{-0.5cm}
% \includegraphics[angle=-90,width=0.4\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_scale.pdf}
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% \begin{frame}
% \frametitle{ESSI: ANIMATIONS}
% 
%  
% 
%   Homogeneous soil/rock, $56^{\deg}$  off  vertical)
% \href{/home/jeremic/lecture_notes_online_material/public_html/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/color_high-quality/homo_50m-mesh_56degree_Ormsby.mp4}
% {(link to a movie, 39MB)}
% 
%     Homogeneous soil/rock, $45^{\deg}$  off  vertical)
%   \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/color_high-quality/homo_50m-mesh_45degree_Ormsby.mp4}
%   {(link to a movie, 32MB)}
% 
%     Homogeneous soil/rock, $27^{\deg}$  off  vertical)
%   \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/color_high-quality/homo_50m-mesh_27degree_Ormsby.mp4}
%   {(link to a movie, 37MB)}
% 
% 
%     Single layer soft soil with homogeneous soil/rock, $56^{\deg}$  off  vertical)
%   \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/color_high-quality/layered_50m-mesh_56degree_Ormsby.mp4}
%   {(link to a movie, 30MB)}
% 
%     Single layer soft soil with homogeneous soil/rock, $45^{\deg}$  off  vertical)
%   \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/color_high-quality/layered_50m-mesh_45degree_Ormsby.mp4}
%   {(link to a movie, 34MB)}
% 
%     Single layer soft soil with homogeneous soil/rock, $27^{\deg}$  off  vertical)
%   \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/color_high-quality/layered_50m-mesh_27degree_Ormsby.mp4}
%   {(link to a movie, 32MB)}
% 
% 
% 
%     Two layers of soft soil with homogeneous soil/rock, $56^{\deg}$  off  vertical)
%   \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/color_high-quality/layered2_50m-mesh_56degree_Ormsby.mp4}
%   {(link to a movie, 30MB)}
% 
%     Two layers of soft soil with homogeneous soil/rock, $45^{\deg}$  off  vertical)
%   \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/color_high-quality/layered2_50m-mesh_45degree_Ormsby.mp4}
%   {(link to a movie, 31MB)}
% 
%     Two layers of soft soil homogeneous soil/rock, $27^{\deg}$  off  vertical)
%   \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/color_high-quality/layered2_50m-mesh_27degree_Ormsby.mp4}
%   {(link to a movie, 32MB)}
% %  
%  
% \end{frame}
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%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \section{Real ESSI Simulator System}
% %
% 
% 
% 
% 
% \subsection{Real ESSI Simulator Components}
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}
% \frametitle{Real ESSI Simulator System}
% 
% \begin{itemize}
% 
% \item {\bf The Real ESSI-Program} is a 3D, nonlinear, time domain, 
% parallel finite element program specifically developed for
% Hi-Fi modeling  and  simulation  of  Earthquake  Soil/Rock  Structure
% Interaction problems for NPPs (infrastructure objects) on ESSI-Computers. \
% %The NRC ESSI Program is based on
% %a  number of public domain numerical libraries developed at UCD as well as those
% %available  on  the  web,  that  are  compiled  and  linked  together to form the
% %executable  program (NRC-ESSI-Program). Significant effort is devoted to development
% %of  verification  and  validation  procedures,  as  well  as  on  development of
% %extensive  documentation.  NRC-ESSI-Program  is  in  public  domain  and is licensed
% %through the Lesser GPL.
% 
% %\vspace*{0.3cm}
% \vspace*{0.1cm}
% \item {\bf The Real ESSI-Computer} is a distributed memory 
% parallel computer, a cluster of clusters with multiple performance  
% processors and multiple performance networks.  
% %Compute  nodes are Shared Memory Parallel
% %(SMP)  computers,  that  are  connected,  using  high  speed  network(s), into a
% %Distributed Memory Parallel (DMP) computer.
% 
% %\vspace*{0.3cm}
% \vspace*{0.1cm}
% \item    {\bf        The Real  ESSI-Notes} represent a hypertext 
% documentation system
% (Theory and Formulation, Software and Hardware, Verification and Validation, and
% Case  Studies  and  Practical  Examples)   
% detailing modeling and simulation of ESSI
% problems.
% %
% %the
% %NRC-ESSI-Program  code  API (application Programming Interface) and DSLs (Domain
% %Specific Language).
% %%NRC-ESSI-Notes,    developed  by Boris Jeremic and collaborators, are in public
% %domain
% %%and  are  licensed  under a Creative Commons Attribution-ShareAlike 3.0 Unported
% %%License.
% %
% %\vspace*{0.3cm}
% \end{itemize}
% 
% \end{frame}
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}
% \frametitle{Real ESSI Simulator Program: Finite Elements}
% 
% 
% %\vspace*{-3mm} 
%    \begin{itemize}
% %\vspace*{-1.5mm} 
%      \item Dry/single phase solids (8, 20, 27, 8-27 node bricks), 
% %\vspace*{-1.5mm} 
%      \item Saturated/two phase solids (8 and 27 node bricks, liquefaction modeling),
% %\vspace*{-1.5mm} 
%      \item Shell with 6DOF per node, 
% %\vspace*{-1.5mm} 
%      \item Beams (six and variable DOFs per node), 
% %\vspace*{-1.5mm} 
%      \item Truss, 
% %\vspace*{-1.5mm} 
%      \item   Contacts      (dry   and/or   saturated   soil/rock   -  concrete,  gap
%      opening-closing, frictional slip),
% %\vspace*{-1.5mm} 
%      \item Base isolators (elastomeric, frictional pendulum)
%    \end{itemize}
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}
% \frametitle{Real ESSI Simulator Program: Material Models and Seismic Input}
% 
% \begin{itemize}
% 
% \item Material Models
% %\vspace*{-2mm} 
%    \begin{itemize}
% %\vspace*{-1.5mm} 
%       \item Linear and nonlinear, isotropic and anisotropic  elastic
% %\vspace*{-1.5mm} 
%        \item  Elastic-Plastic  (von Mises, Drucker Prager, Rounded Mohr-Coulomb,
%               Leon      Parabolic,      Cam-Clay,      SaniSand,     SaniClay,  
%               Pisan{\` o}...).  All  elastic-plastic  models can be used as perfectly
%               plastic,  isotropic  hardening/softening  and  kinematic hardening
%               models.
%    \end{itemize}
% 
% \vspace*{4mm} 
%  \item    Analytic    input    of  seismic motions (both body (P, S) and surface
%  (Rayleigh, Love, \&c., waves), including analytic radiation damping.
% 
% \end{itemize}
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}
% \frametitle{Real ESSI Simulator Program: V\&V, Parallel}
% 
% \begin{itemize}
% 
% %\vspace*{-2mm} 
% \item Verification and Validation:
%   each element, model, algorithm and procedure has been extensively verified
%   (math  issue)  and  validated  (physics issue). Verification and Validation is
%   documented in detail in Real ESSI Notes.
% 
% %%\vspace*{-2mm} 
% %\item  Documentation: available in great detail through ESSI Notes, consisting
% %of four parts: Theory/Formulation Background, Software and Hardware description,
% %Verification and Validation, Examples and Case Studies.
% 
% %\vspace*{-2mm} 
% \vspace*{4mm} 
% \item High Performance Parallel Computing:
%   both  parallel  and  sequential  version available, however, for high fidelity
%   modeling,  parallel is really the only option. Parallel Real ESSI Simulator runs on
%   clusters  of  PCs  and  on  large  supercomputers (Distributed Memory Parallel
%   machines,  all  top  national  supercomputers).  
% %  Parallel  algorithm  uses our
% %  original  Plastic Domain Decomposition method (featuring dynamic computational
% %  load  balancing) that is efficient for elastic-plastic finite element problems
% %  where  elastic-plastic  (slow)  and  elastic (fast) domains change dynamically
% %  during run time.
% 
% 
% \end{itemize}
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}
% \frametitle{Real ESSI Simulator Program: Probabilistic/Stochastic}
% %\vspace*{-2mm} 
% 
% 
%    \begin{itemize}
% %\vspace*{-2.5mm} 
%      \item   Constitutive:   Euler-Lagrange   form   of  Fokker-Planck  (forward
%      Kolmogorov) equation for probabilistic elasto-plasticity (PEP)
% %\vspace*{-1.5mm} 
%      \item Spatial: stochastic elastic plastic finite element method (SEPFEM)
%    \end{itemize}
% 
% 
%   Uncertainties  in  material  and  load  are  analytically  taken into account.
%   Resulting  displacements,  stress  and  strain  are  obtained as very accurate
%   (second  order accurate for stress) Probability Density Functions.
%   PEP  and  SEPFEM  are  not  based  on a Monte Carlo method, rather they expand
%   uncertain  input  variables  and  uncertain degrees of freedom (unknowns) into
%   spectral  probabilistic  spaces  and  solve  for  PDFs  of
%   resulting displacement, stress and strain in a single run.
% 
% 
% \end{frame}
% 
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}
% \frametitle{Real ESSI Simulator Program: Design and Users}
% 
% \begin{itemize}
% 
% %\vspace*{0.2cm}
% \item  Based  on  a  Collection  of Useful Libraries  (portable)
% 
% \vspace*{0.1cm}
% \item Library centric software design
% 
% \vspace*{0.1cm}
% \item Sequential (learning) and Parallel (production modeling and simulation)
% 
% \vspace*{0.1cm}
% \item Distributed Memory Parallel (DMP) paradigm, scales well to large supercomputers
% 
% 
% 
% \vspace*{0.1cm}
% \item Various public domain licenses (GPL, LGPL, BSD, CC)
% 
% %\vspace*{0.3cm}
% \vspace*{0.1cm}
% \item Verification (extensive) and Validation (not much)
% 
% 
% \vspace*{0.1cm}
% \item Target users: US-NRC, CNSC, IAEA, LBNL, INL, US-DOE, professional
% practice collaborators (AREVA, Shimizu)
%     
% \vspace*{0.1cm}
% \item Limited use Expert Modeling and Simulation System, and not a commercial product
% 
% %\item Sources will be available through
% %{\bf 
% %\url{http://nrc-essi-simulator.info}}
% 
% 
% \end{itemize}
% 
% \end{frame}
% 
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}[fragile]
%  \frametitle{ESSI Simulator Computer(s)}
% 
%   A distributed memory parallel (DMP) computer
%    designed for high performance,  
%    parallel finite element simulations
% 
%  \begin{itemize}
% %\vspace*{0.1cm}
%    \item Multiple performance CPUs \\
%          and Networks
% %\vspace*{0.1cm}
%    \item Most cost-performance \\
%          effective 
% %\vspace*{0.1cm}
%    \item Source compatibility with \\
%          any DMP supercomputer
% %\vspace*{0.1cm}
%    \item Current systems: 208CPUs, \\
%          and 40CPUs (8+32) and \\ 
%          160CPUs (8x5+2x16+24+64)...
% 
% %%\vspace*{0.1cm}
% %   \item Near future: 784 CPUs
% 
%  \end{itemize}
% 
%   
% \vspace*{-4.5cm}
% \begin{flushright}
% %\hspace*{-0.5cm}
% \includegraphics[width=5.0cm]{/home/jeremic/public_html/NRC_ESSI_Simulator/NRC_ESSI_Computer/photos/IMG_2607.JPG}
% %\includegraphics[width=6.0cm]{/home/jeremic/public_html/NRC_ESSI_Simulator/NRC_ESSI_Computer/photos/IMG_2609.JPG}
% %\includegraphics[width=8.0cm]{/home/jeremic/public_html/NRC_ESSI_Simulator/NRC_ESSI_Computer/photos/IMG_2611.JPG}
% \end{flushright}
% 
% 
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% \end{frame}
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\section{Summary}


\subsection*{Summary}


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


  \item    Earthquake Soil Structure Interaction,
  in  time domain, nonlinear, uncertain, plays a
  decisive role in seismic performance of Nuclear Facilities

\vspace*{0.2cm}
  \item     Improve design and retrofits (safety and economy) through  
  high fidelity, physics based modeling and simulation

\vspace*{0.2cm}
  \item    Real    ESSI    Simulator  System,   verified (extensive) and
  validated (not so extensive), for modeling and simulations used for design, retrofits and
  regulatory decision making


 
\vspace*{0.2cm}
  \item      Education  and  training  of  users  (designers, regulators,
  owners) proves essential
  
  
\end{itemize}


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


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


\vspace*{0.1cm}
  \item Funding from and collaboration with the US-NRC, US-DOE,
  US-NSF,   CNSC, LLNL, INL, 
  AREVA NP GmbH, and Shimizu Corp. is greatly appreciated,
  
\vspace*{0.4cm}
  \item  Collaborators:      
  Dr.  Budnitz  (LBNL),  Dr. Kammerer (Bechtel Corp.), Prof. Whittaker (UB), Mr.
  Orbovi{\'c} (CNSC), Prof. Pisan{\`o} (TU Delft), Prof. Sett (UB),
  and  UCD  students:  Mr. Abell, Mr. Jeong, Mr. Kamranimoghadam, Mr.
  Karapiperis, Mr. Watanabe, Mr. Chao, Dr. Tafazzoli,

%\vspace*{0.2cm}
%  \item  Contact: \\
%   {\bf \url{jeremic@ucdavis.edu}}~~~;~~~{\bf \url{bjeremic@lbl.gov}}
  
\end{itemize}


\end{frame}




\end{document}

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