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\title[Real ESSI]
        {Real Earthquake Soil Structure Interaction \\
        (Real ESSI) \\
        Modeling and Simulation }


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

%\author[Author, Another] % (optional, use only with lots of authors)
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%   affiliation.
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\pgfdeclareimage[height=0.7cm]{lbnl-logo}{/home/jeremic/BG/amblemi/lbnl-logo}


\author[Jeremi{\'c} et al.] % (optional, use only with lots of authors)
%{Boris~Jeremi{\'c}}
{Boris Jeremi{\'c} et al.}

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\institute[\pgfuseimage{university-logo}\hspace*{0.1truecm}\pgfuseimage{lbnl-logo}] % (optional, but mostly needed)
%{ Professor, University of California, Davis\\
{UCD, LBNL}
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{\small PRENOLIN \\
 December 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 for infrastructure objects, focus on Nuclear Facilities

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


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

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

  

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

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

\begin{itemize}
  


%\vspace*{0.5cm}
  \item    Interplay   of  the  Earthquake  with the   
  Soil/Rock, Foundation  and  Structure in time domain, plays a  major
  role in  successes and failures


\vspace*{0.2cm}
  \item   Timing  and spatial location of energy dissipation determines location
  and amount of damage

\vspace*{0.2cm}
  \item  If timing and spatial location of energy dissipation 
         can be controlled (directed, designed),
         we could  optimize soil structure system for
    \begin{itemize}
      \item Safety and
      \item Economy
    \end{itemize}

\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*{0.2cm}
     \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}


\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 Dissipation for  the SSI System}
% \frametitle{Seismic Energy Dissipation for 
%             \underline{Soil}-Foundation-Structure Systems}


\begin{itemize}


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

\vspace*{0.2cm}
  \item  Simplified (or inadequate/wrong) modeling:  important  features    are 
  missed (3D seismic ground motions, nonlinearities, etc.)

\vspace*{0.2cm}
     \item      Modeling      Uncertainty:   introduced   with   unnecessary and
     unrealistic modeling simplification

\vspace*{0.2cm}
     \item  Avoid  use  of  results  obtained  using models with (high) modeling
     uncertainty
  


\end{itemize}
\end{frame}


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

\begin{itemize}
%\vspace*{0.3cm}
  \item 6D (3 translations, 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*{0.3cm}
  \item Sources of uncertainties in ground motions (Source, Path (rock), soil (rock))  
\end{itemize}

\end{frame}




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

\begin{itemize}
%\vspace*{0.3cm}
  \item All engineering materials experience inelastic deformations for working loads

\vspace*{0.1cm}
  \item This is even more so for hazard loads (earthquakes)
 
\vspace*{0.1cm}
  \item  Pressure sensitive materials (soil, rock , concrete, etc) can have very
  complex constitutive response, tying together nonlinear stress-strain with volume response
 
\vspace*{0.1cm}
  \item  Simplistic  material  modeling  (elastic,  $G/G_{max}$, etc.) introduce
  (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 etc.)

        \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}

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\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}


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\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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\begin{frame}



\frametitle{Transformation Error/Uncertainty}




\begin{figure}[!hbpt]
\begin{center}
% 
\includegraphics[width=2.7truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldPhiPdf.pdf}
\includegraphics[width=2.7truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldPhiCdf.pdf}
\includegraphics[width=2.7truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldSuPdf.pdf}
\includegraphics[width=2.7truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldSuCdf.pdf}
\\
\mbox{Field $\phi$} \hspace*{4cm} \mbox{Field $c_u$}
\hfill
\includegraphics[width=2.7truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabPhiPdf.pdf}
\includegraphics[width=2.7truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabPhiCdf.pdf}
\includegraphics[width=2.7truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabSuPdf.pdf}
\includegraphics[width=2.7truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabSuCdf.pdf}
\\
\mbox{Lab $\phi$} \hspace*{4cm} \mbox{Lab $c_u$}
%
\end{center}
\end{figure}                                                          

\end{frame}


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% \section{ESSI Modeling}
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% \subsection{3D, Inclined, Body and Surface}
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% \begin{frame}
% \frametitle{Earthquake Ground Motions}
% 
% 
% 
%  Realistic earthquake ground motions 
%    \begin{itemize}
% \vspace*{0.1cm}
%      \item Body waves: P and S waves
% \vspace*{0.1cm}
%      \item Surface waves: Rayleigh, Love waves, etc.
% \vspace*{0.1cm}
%   \item Surface waves carry most seismic energy
% \vspace*{0.1cm}
%      \item Lack of correlation (incoherence)
% \vspace*{0.1cm}
%      \item Inclined waves
% \vspace*{0.1cm}
%      \item 3D waves
% %\vspace*{0.1cm}
% %     \item Earthquake energy  dissipation
% 
%    \end{itemize}
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% 
% \end{frame}
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% \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}
% 
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% \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, etc)
%   
%            \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}
% 
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% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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}
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Body and Surface Wave Animations}
% 
% 
% 
% \begin{itemize}
%   \item  
%   \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}
%   {Homogenous soil/rock, $45^{\deg}$  off  vertical}
% 
% 
% \hspace*{0.5cm}
%   \item 
%   \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/vector/homo_50m-mesh_45degree_Ormsby.mp4}
%   {Homogenous soil/rock, $45^{\deg}$  off  vertical, motions at the top $2$km $\times$ $2$km}
% 
% 
% \hspace*{0.5cm}
%   \item 
%   \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/vector/homo_50m-mesh_45degree_Ormsby_X5000-Z5000.mp4}
%   {Homogenous soil/rock, $45^{\deg}$  off  vertical, motions at the very top, location of observation point and/or structure}
% \end{itemize}
% 
% 
% \end{frame}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Verification: Displacements, Top Middle Point }
% %  \begin{itemize}
% %   \item 
% %  \end{itemize}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{figure}[!htbp] 
% \begin{center}
% \begin{tabular}{ccc} 
% %\hline 
% (X)
% &
% (Z)
% \\
% \includegraphics[width=5.0cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/wave_propagation/figs/ricker_2km/top_middle_comparison_disp_x.pdf}
% &
% \includegraphics[width=5.0cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/wave_propagation/figs/ricker_2km/top_middle_comparison_disp_z.pdf}
% &
% \end{tabular}
% %\caption{Comparison of displacements for top middle point using Ricker wave $(f=1Hz)$ as an input motion}
% %\label{fig:ricker_acc}
% \end{center}
% \end{figure}
% 
% 
% 
% \end{frame}
% 
% 
% % 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% % \frametitle{Verification: Accelerations, Top Middle Point }
% % %  \begin{itemize}
% % %    \item 
% % %  \end{itemize}
% % 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{figure}[!htbp] 
% % \begin{center}
% % \begin{tabular}{ccc} 
% % %\hline 
% % (X)
% % &
% % (Z)
% % \\
% % \includegraphics[width=5.0cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/wave_propagation/figs/ricker_2km/top_middle_comparison_accel_x.pdf}
% % &
% % \includegraphics[width=5.0cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/wave_propagation/figs/ricker_2km/top_middle_comparison_accel_z.pdf}
% % &
% % \end{tabular}
% % %\caption{Comparison of accelerations for top middle point using Ricker wave $(f=1Hz)$ as an input motion}
% % %\label{fig:ricker_acc}
% % \end{center}
% % \end{figure}
% % 
% % 
% % 
% % 
% % \end{frame}
% % 
% % 
% % 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Verification: Disp. and Acc., Out of DRM }
% %  \begin{itemize}
% %    \item 
% %  \end{itemize}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{figure}[!htbp] 
% \begin{center}
% \begin{tabular}{ccc} 
% %\hline 
% Displacement
% &
% Acceleration
% \\
% \includegraphics[width=5.0cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/wave_propagation/figs/ricker_2km/10_40_disp_x.pdf}
% &
% \includegraphics[width=5.0cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/wave_propagation/figs/ricker_2km/10_40_accel_x.pdf}
% &
% \end{tabular}
% %\caption{Displacement and acceleration time history for a point outside of DRM layer in (x) direction}
% %\label{fig:out_ricker_disp}
% \end{center}
% \end{figure}
% 
% 
% 
% \end{frame}
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% %  
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% \begin{frame}
% \frametitle{Northridge 3D FE Model}
% \vspace*{-3.5cm}
% \begin{figure}
% % \includegraphics[scale=0.35]{Present06_figs/3DModel.pdf}
%  \includegraphics[scale=0.35]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Jose_fix/presentation/Present06_figs/3DModel.pdf}
% \end{figure}
% \end{frame}
% 
% 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% % \frametitle{FE Model}
% % \begin{figure}
% % % \includegraphics[scale=0.4]{Present06_figs/3DModelxzPlane.pdf}
% %  \includegraphics[scale=0.4]{Present06_figs/3DModelxzPlane.pdf}
% % \end{figure}
% % \end{frame}
% % 
% % 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Northridge 3D Model Properties}
% \begin{itemize}
%  \item Model Properties
%  \begin{itemize}
%   \item 90 m $\times$ 90 m $\times$ 90 m dimension
%   \item Vs1 = 300 m/s, Vs2 = 400 m/s
%   \item Poisson's ratio1 = 0.25, Poisson's ratio2 = 0.25
% %  \item Density1 = 940 kg/m$^3$, Density2 = 990 kg/m$^3$
%  \end{itemize}
%  \vspace{2mm}
%  \item Input Wave Properties
%  \begin{itemize}
%   \item Northridge earthquake source properties
%   \item Generated using fk program
%  \end{itemize}
% \end{itemize}
% \end{frame}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{FEM Results, EW Component}
% \vspace*{-3.5cm}
% \begin{figure}
% % \includegraphics[scale=0.5]{Present06_figs/90m_Northridge_EW.pdf}
%  \includegraphics[scale=0.5]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Jose_fix/presentation/Present06_figs/90m_Northridge_EW.pdf}
% \end{figure}
% \end{frame}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{FEM Results, NS Component}
% \vspace*{-3.5cm}
% \begin{figure}
% % \includegraphics[scale=0.5]{Present06_figs/90m_Northridge_NS.pdf}
%  \includegraphics[scale=0.5]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Jose_fix/presentation/Present06_figs/90m_Northridge_NS.pdf}
% \end{figure}
% \end{frame}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{FEM Results, UD Component}
% \vspace*{-3.5cm}
% \begin{figure}
% % \includegraphics[scale=0.5]{Present06_figs/90m_Northridge_UD.pdf}
%  \includegraphics[scale=0.5]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Jose_fix/presentation/Present06_figs/90m_Northridge_UD.pdf}
% \end{figure}
% \end{frame}
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Model Verification: Mesh Size Effects}
% 
% \begin{itemize}
% 
%   \item Finite element mesh "filters out" \\
%        high frequencies
% 
% %\vspace*{0.2cm}
%   \item Usual rule of thumb: 10-12 elements \\
%         needed per wave length
% %  (SASSI recommends only 5 ?!)
% 
% % 
% %    \item  Maximum grid spacing should not exceed 
% %    $\Delta h \;\le\; {\lambda}/{10}\;=\;{v}/({10\,f_{max}})$
% %  where $v$ is the lowest wave velocity  (shear, elastic-plastic ?)
% %  
% %    \item  Tests  without and with numerical damping, for different element sizes 
% %  
% 
% \item 1D wave propagation model
% %\vspace*{0.2cm}
% \item 3D finite elements (same in 3D)
% %\vspace*{0.2cm}
% \item Motions applied as displacements at the bottom
% 
% 
% \end{itemize}
% 
% %\begin{figure}[H]
% \vspace*{-4.0cm}
% \begin{flushright}
% \includegraphics[width=0.7cm]{/home/jeremic/tex/works/Conferences/2011/NRC_Staff_Capacity_Building_21Nov2011/model01.pdf}
% \end{flushright}
% %\end{figure}
% 
% \vspace*{-0.4cm}
% \begin{small}
% \begin{table}[!htbp]
% \centering
% % \begin{tabular}{|c|c|c|c|c|}
% \begin{tabular}{|r|m{2.6cm}|m{1.5cm}|m{1.8cm}|m{2.3cm}|}
% \hline
% case  &  model  height  [m]  &  $V_s$ [m/s] & El.size [m] & $f_{max}$ (10el) [Hz]\\
% \hline
% %\hline
% 3 & 1000 & 1000 & 10 & 10\\
% %\hline
% 4 & 1000 & 1000 & 20 & 5\\
% %\hline
% 6 & 1000 & 1000 & 50 & 2\\
% \hline
% % \begin{tabular}{|m{1.5cm}c|m{2.8cm}c|m{2.8cm}c|m{3.0cm}c|m{4.0cm}c|}
% % \begin{tabularx}{\linewidth}{|c|c|c|c|c|}
% % \begin{tabular*}{0.75\textwidth}{@{\extracolsep{\fill}}|c|c|c|c|c|}
% \end{tabular}
% % \end{tabularx}
% \end{table}
% \end{small}
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Cases 3, 4, and 6, Ormsby Wavelet Input Motions}
% 
%  
% \begin{figure}[H]
% \begin{center}
% \includegraphics[width=9cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/MeshSize/figs/3_4_6/Input_Displacement.pdf}
% \end{center}
% \end{figure}
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% \frametitle{Cases 3, 4, and 6, Input and Surface Motions, FFT}
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%  
% \begin{figure}[H]
% \begin{center}
% \includegraphics[width=9cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/MeshSize/figs/3_4_6/FFT.pdf}
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% \frametitle{Cases 3, 4, and 6, Surface Motions}
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% \begin{figure}[H]
% \begin{center}
% \includegraphics[width=9cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/MeshSize/figs/3_4_6/displacement.pdf}
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% \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}
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% \end{frame}
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% \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}
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% \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}
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% \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}
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% \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}
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% % 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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}
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% \begin{frame}
% \frametitle{Foundation Slip/Gap and Liquefiable Soils}
% 
% \begin{itemize}
% \item Slip between foundation slab and the soil/rock
% underneath
% 
% \vspace*{0.2cm}
% \item Passive seismic isolation by liquefaction
% 
% \vspace*{0.2cm}
% \item Structural response in liquefied soil
% 
% 
% \end{itemize}
% 
% \end{frame}
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Nuclear Power Plant with Base Slip}
% 
% \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, etc.)
% 
% 
% \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}
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% \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}
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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{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}
% 
% 
% 
% \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}
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% \begin{frame}
%   \frametitle{Passive Base Isolation in Uniform and Layered Soils}
%   
% 
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% \vspace*{-0.5cm}
% \begin{figure}[!htbp] 
% \begin{flushleft}
% \includegraphics[width=5cm,angle=90]{/home/jeremic/tex/works/Papers/2009/SeismicIsolationLiquefaction/Mesh-Isolation.pdf}
% \\
% \includegraphics[width=4cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/StackElements-Compare.pdf} 
% \end{flushleft}
% \end{figure}
% \vspace*{-1cm}
% 
% 
% \vspace*{-8cm}
% %\hspace*{-0.5cm}
% \begin{figure}[!htbp] 
% \begin{flushright}
% \includegraphics[width=6cm]{/home/jeremic/tex/works/Papers/2009/SeismicIsolationLiquefaction/time-history-acc.jpg} \\
% %\\
% %\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{flushright}
% \end{figure}
% \vspace*{-1cm}
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% %
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% \begin{frame}
%  \frametitle{Pile in Liquefiable Sloping Ground}
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% 
% \vspace*{-0.8cm}
% \begin{figure}[!htbp]
% \begin{flushright}
% %  \includegraphics[width=6cm]{/home/jeremic/tex/works/Conferences/2007/PEERAnnualMeeting/Liquefaction/PileBridgeModel01.jpg} \\
%   \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}
% \end{flushright}
% \end{figure}
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% %
% \vspace*{-0.4cm}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{figure}[!htbp] 
% \begin{center}
% \hspace*{-0.5cm}
% \begin{tabular}{lllllll} 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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}
% &
% \includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_4_T005.jpg}
% &
% \includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_4_T010.jpg}
% &
% \includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_4_T015.jpg}
% &
% \includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_4_T020.jpg}
% &
% \includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_4_T080.jpg}
% \\
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \includegraphics[width=0.03\textwidth,angle=0]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/Model_V.jpg}
% &
% \includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_5_T002.jpg}
% &
% \includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_5_T005.jpg}
% &
% \includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_5_T010.jpg}
% &
% \includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_5_T015.jpg}
% &
% \includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_5_T020.jpg}
% &
% \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}
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% \includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_6_T010.jpg}
% &
% \includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_6_T015.jpg}
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% \includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_6_T020.jpg}
% &
% \includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_6_T080.jpg}
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% \\
% \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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\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 Nuclear Facilities
(NPPs and other 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} are 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}

%\vspace*{0.3cm}
\vspace*{0.1cm}
\item  Real ESSI aka, Tr{\`e}s Facile, Muy
F{\'a}cil,  {\cyss  Vrlo  Prosto},  Molto  Facile,  {\large \greektext{Pragmatik'a
E'ukolo}}, \raisebox{-1mm}{\includegraphics[height=5mm]{/home/jeremic/tex/works/Conferences/2014/PRENOLIN/Nov2014_meeting/Present/Real_ESSI_in_Japanese/sc20141217105418/Hontoni_Kantan.jpg}}



\end{itemize}

\end{frame}



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

\begin{frame}
\frametitle{Real ESSI Simulator Program: Finite Elements}


   \begin{itemize}
     \item Dry/single phase solids (8, 20, 27, 8-27 node bricks), 
     \item Saturated/two phase solids (8 and 27 node bricks, $u-p-U$ and $u-p$, liquefaction modeling),
     \item Truss, 
     \item Beams (\underline{six} and \underline{variable} DOFs per node), 
     \item Shell (ANDES) with 6DOF per node, 
     \item   Contacts      (dry   and/or   saturated   soil/rock   -  concrete,  gap
     opening-closing, frictional slip),
     \item Base isolators and dissipators (elastomeric, natural rubber, 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*{2mm} 
 \item    Analytic    input    of  seismic motions (both body (P, S) and surface
 (Rayleigh, Love, etc., 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 (not so extensively) 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*{2mm} 
\item High Performance Parallel Computing:
  both    parallel    and    sequential    version available. Parallel Real ESSI
  Simulator    (based  on  the Plastic Domain Decomposition Method, designed for
  efficient elastic-plastic parallel simulations) 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  \underline{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}

\item Library centric software design (portable, modular)

\item Sequential (initial use, learning) and Parallel (production modeling and simulation)

\item Distributed Memory Parallel (DMP) paradigm, scales well to large supercomputers


\item Public domain licenses (CC, GPL, LGPL, BSD, \&c.)

\item Verification (extensive) and Validation (not much)

\item  Target  users:  US-DOE,  US-NRC, CNSC, IAEA, AREVA NP GmbH, Shimizu Corp,
Rizzo and Assoc., Academic Collaborators, \&c.
    
\item  Real ESSI is a limited distribution expert modeling and simulation system


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



%

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

\subsection{Current NPP Modeling Issues}






% %  
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Earthquake Soil Structure Interaction (ESSI)}
% 
% 
% \begin{figure}[!hbpt]
% \begin{flushleft}
% %\hspace*{-0.5cm}
% %\includegraphics[width=2.0cm]{/home/jeremic/tex/works/Conferences/2014/ASME_SMR_Symposium/present/SMR01_a.jpg}
% %\hfill
% \includegraphics[width=2.5cm]{/home/jeremic/tex/works/Conferences/2014/ASME_SMR_Symposium/present/SMR02_a.jpg}
% \hfill
% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/consulting/2013/CNSC/ProgressReports/Progress_report_02_figs/single-NPP-FEM-model.jpg}
% \hfill
% \includegraphics[width=4.8cm]{/home/jeremic/tex/works/consulting/2013/CNSC/ProgressReports/Progress_report_02_figs/double-NPP-FEM-model.jpg}
% \end{flushleft}
% \end{figure}
% 
% 
% \begin{itemize}
%      \item   Seismic response modeling controlled by a  number  of ESSI modeling
%      and simulation issues
%      \item Detrimental and Beneficial ESSI effects
% %     \item Seismic energy propagation and dissipation
% \end{itemize}
% 
% \end{frame}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{ESSI Issues}
% 
% \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{Important Issues for ESSI Modeling and Simulation}

   \begin{itemize}

     \item Verification and Validation

\vspace*{1mm}
     \item 6D, inclined, body and surface  seismic waves

\vspace*{1mm}
     \item Uncorrelated (incoherent) motions

\vspace*{1mm}
     \item Nonlinear material (soil, rock, concrete, steel, \&c.)

\vspace*{1mm}
     \item Nonlinear foundation-soil/rock contact (dry and saturated), slip -- gap 

\vspace*{1mm}
     \item Seismic Isolators and Dissipators

\vspace*{1mm}
     \item Saturated dense vs loose soil with buoyant forces

\vspace*{1mm}
     \item Piles and pile groups 


\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{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}


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

     
\end{frame}





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Summary}


\subsection{Summary}









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


  \item              {\bf    Interplay}        of     
%  {\bf Uncertain} 
{\bf   Earthquake}, 
%  {\bf Uncertain}  
{\bf Soil},
  and  
%  {\bf  Uncertain}   
{\bf Structure}, in  time domain, 
%{\bf probably} 
plays a
  decisive role in seismic performance of NPPs  and other infrastructure objects

\vspace*{0.1cm}
  \item           Improve {\bf 
%  risk informed 
%  decision making}
design} ({\bf safety} and {\bf economy}) 
   through  
  {\bf high fidelity}, 
%  {\bf  Deterministic}  and  
%  {\bf  Stochastic Elastic-Plastic  Finite Element} 
  modeling and simulation

\vspace*{0.1cm}
  \item   {\bf   Real  ESSI  Simulator},  developed with this in mind, is used for
  modeling, simulations, design and regulatory decision making


 
\vspace*{0.1cm}
  \item      {\bf  Education}  and  {\bf training}  of  users  (designers, regulators,
  owners) will prove essential
  
  
\end{itemize}


\end{frame}
%




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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,  CNSC, US-NSF,
  AREVA NP GmbH, and Shimizu Corp. is greatly appreciated,
  
\vspace*{0.5cm}
  \item  Collaborators, students:      
  Messrs.  Abell, Jeong, Aldridge.   Kamranimoghadam, Karapiperis, Watanabe, Chao,
  Drs.  Tafazzoli, Cheng,   Profs.  Pisan{\`o}, Sett,  Taiebat, Yang 

  
\end{itemize}


\end{frame}
%



\end{document}

%  
%  
