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\title{ Time Domain Nonlinear  \\
Earthquake Soil/Rock Structure Interaction \\
Modeling and Simulation}


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

%\author[Author, Another] % (optional, use only with lots of authors)
%{F.~Author\inst{1} \and S.~Another\inst{2}}
% - Give the names in the same order as the appear in the paper.
% - Use the \inst{?} command only if the authors have different
%   affiliation.
\pgfdeclareimage[height=0.2cm]{university-logo}{/home/jeremic/BG/amblemi/ucdavis_logo_blue_sm}
\pgfdeclareimage[height=0.7cm]{lbnl-logo}{/home/jeremic/BG/amblemi/lbnl-logo}

\author[Jeremi{\'c}] % (optional, use only with lots of authors)
{Boris~Jeremi{\'c} \\ 
%{\small with
%          Dr. Tafazzoli, 
%          Mr. Abell, 
%          Mr. Jeong, 
%          Dr. Pisan{\`o}, 
%          Prof. Sett (UA), 
%          Prof. Taiebat (UBC), 
%          Prof. Yang (UAA),
%          Dr. Cheng (Itasca)} 
}
%{Boris~Jeremi{\'c},  Nima  Tafazzoli,  Babak Kamrani, Panagiota Tasiopoulou and
%Chang-Gyun Jeong}
% - Give the names in the same order as the appear in the paper.
% - Use the \inst{?} command only if the authors have different
%   affiliation.


%\institute[Computational Geomechanics Group \hspace*{0.3truecm}
\institute[\pgfuseimage{university-logo}\hspace*{0.1truecm}\pgfuseimage{lbnl-logo}] % (optional, but mostly needed)
{ Professor, University of California, Davis, CA\\
%  and\\ 
  Faculty Scientist, Lawrence Berkeley National Laboratory, Berkeley, CA }
% - Use the \inst command only if there are several affiliations.
% - Keep it simple, no one is interested in your street address.


\date[] % (optional, should be abbreviation of conference name)
{\small ASCE-4 Meeting \\ April 2013}

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\begin{document}

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\begin{frame}
  \titlepage
\end{frame}

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

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Introduction}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{The Problem}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{The Problem}

\begin{itemize}
  

  \item  Earthquake  Soil/Rock  Structure  Interaction (ESSI) response of Nuclear
  Power Plants


\vspace*{0.1cm}
  \item  3D, inclined, body and surface seismic waves

\vspace*{0.1cm}
  \item      Nonlinear behavior (elastic, damage, plastic behavior of materials:
  soil, rock, concrete, steel, rubber, etc.)

\vspace*{0.1cm}
  \item  Full coupling of pore fluids  with soil/rock skeleton

\vspace*{0.1cm}
  \item  Contact and buoyancy effects 

\vspace*{0.1cm}
  \item    Uncertainty  in  seismic  sources, path, soil/rock response and structural
  response
  

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Solution (?)}

\begin{itemize}
  


%\vspace*{0.3cm}
  \item    {\bf Physics based  modeling  and  simulation} of 
  seismic behavior of NPP soil/rock -- structure systems

\vspace*{0.1cm}
  \item             Development  and  use  of  {\bf high  fidelity} time domain,
  nonlinear  numerical  models,  in  {\bf deterministic} and {\bf probabilistic}
  spaces


\vspace*{0.1cm}
  \item   Accurate following of  the  {\bf flow  of  seismic 
  energy}    (input  and  dissipation)   within soil-structure NPP system

\vspace*{0.1cm}
  \item  {\bf  Directing},      in   space   and   time,  with {\bf high (known)
  confidence}, seismic energy flow in the soil-foundation-structure system

%\vspace*{0.1cm}
%  \item  {\bf Education} for researchers, professional practice.
  

\end{itemize}
\end{frame}













%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Uncertainties}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Modeling, Material and Loading Uncertainty}

\begin{itemize}

%\vspace*{0.3cm}
  \item  Simplified (or inadequate/wrong) modeling:  important  features    are 
  missed (seismic ground motions, etc.)

\vspace*{0.1cm}
  \item  Introduction of uncertainty and  (unknown) lack of accuracy in results due
  to  use  of  un-verified  simulation tools (software quality, etc.)

\vspace*{0.1cm}
  \item  Introduction of uncertainty and  (unknown) lack of accuracy in results due
  to    use  of  un-validated  models  (due to lack of quality validation experiments)
%    (still    missing  data, experiments under
%  uncertainty, for more see below)

\vspace*{0.1cm}
  \item  Material  (left  hand  side)  and  load (right hand side) uncertainties
  affect   (probabilities of)  overall response


\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), SSI
  (soil,rock))
\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 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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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Verification and Validation}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Verification \& Validation (V\&V) Definition}


\begin{itemize}

%   \vspace*{1.0truecm}
   \item   {\bf  Verification}:  The  process  of  determining  that    a  model
   implementation  accurately  represents the developer's conceptual description
   and specification. Mathematics issue. {\it Verification provides evidence that the
   model is solved correctly.}

   \vspace*{0.5truecm}
   \item    {\bf  Validation}:  The process of determining the degree to which a
   model  is  accurate  representation of the real world from the perspective of
   the  intended  uses  of  the  model.  Physics issue. {\it Validation provides
   evidence that the correct model is solved.}
   


\end{itemize}


\end{frame}


 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Importance of V\&V}


 \begin{itemize}

%   \vspace*{2.0truecm}
   \item  V  \&  V  procedures  are  the  primary means of assessing accuracy in
   modeling and computational simulations

   \vspace*{0.5truecm}
   \item  V  \&  V  procedures  are the tools with which we build confidence and
   credibility in modeling and computational simulations


\end{itemize}


\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Role of Verification and Validation}


\begin{figure}[!h]
\begin{center}
\hspace*{-2cm}
%{\includegraphics[width=5.0cm]{/home/jeremic/tex/works/Conferences/2012/ASME_V_and_V_symposium/presentetation/RoleVV_NEW_knowledge.pdf}}
{\includegraphics[width=8.5cm]{/home/jeremic/tex/works/Conferences/2011/USNCCM11_Minneapolis/Coupled/Present/VandV_ODEN.jpg}}
\hspace*{-2cm}
\end{center}
\end{figure}

{Oden et al.}
%{Oberkampf et al. \hspace*{4cm}  Oden et al.}
%
%\item Models available (some now, some later)
%\vspace*{-2.0cm}
\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Errors in Scientific Software: The T Experiments}


\begin{itemize}

%   \vspace*{0.2truecm}
   \item Les Hatton, Kingston University (formerly of Oakwood Comp. Assoc.)

   \vspace*{0.1truecm}
   \item "Extensive tests showed that many software codes widely used in science
   and engineering are not as accurate as we would like to think."

   \vspace*{0.1truecm}
   \item "Better software engineering practices would help solve this problem,"

   \vspace*{0.1truecm}
   \item "Realizing that the problem exists is an important first step."
   
   
   \vspace*{0.1truecm}
   \item  Large  experiment over 4 years measuring faults (T1) and failures (T2)
   of scientific and engineering codes
   
   
   
    

\end{itemize}





\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{The T2 Experiments}






\begin{itemize}

\item Specific application area: seismic data processing (inverse analysis)

\vspace*{0.2truecm}
\item Echo sounding of underground and reconstructing "images" of 
subsurface geological structure

\vspace*{0.2truecm}
\item Nine mature packages, using same algorithms, on a same data set!

\vspace*{0.2truecm}
\item 14 primary calibration points for results check

\vspace*{0.2truecm}
\item Results "fascinating and disturbing"

    

\end{itemize}

\end{frame}


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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{T2: Disagreement at Calibration Points}




\begin{figure}[!h]
\begin{center}
\hspace*{-1.5cm}
%\vspace*{-2.5cm}
{\includegraphics[width=8.0cm]{/home/jeremic/tex/works/Conferences/2009/GheoMat/VandV_01/T2_01.jpg}}
\hspace*{-1.5cm}
%\vspace*{-5.0cm}
\end{center}
\end{figure}


% \begin{itemize}
% 
%     
% 
% \end{itemize}

\end{frame}


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\section{Modeling and Simulation Issues}


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\subsection{High Fidelity Modeling}


%

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


\begin{itemize}

  \item   Energy  influx:  
       \begin{itemize}
        \item  \underline{Seismic body  and  surface waves, 3D, inclined} 
       \end{itemize}
%  $E_{flux} = \rho A c \int_0^t \dot{u}_i^2 dt$ (Aki \& Richards)

\vspace*{0.1cm}
     \item Mechanical dissipation outside of SSI domain:
       \begin{itemize}
         \item \underline{Radiation} of reflected waves
         \item \underline{Radiation} of oscillating SSI system
       \end{itemize}
\vspace*{0.1cm}
     \item Mechanical dissipation inside SSI domain:
       \begin{itemize}
         \item \underline{Plasticity} of soil/rock sub-domain
         \item \underline{Plasticity} of foundation -- soil/rock interface
         \item \underline{Viscous coupling} of porous solid with pore fluid (air,
         water)
         \item Plasticity/damage of the structure
         \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}
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%%%%%%%%%

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


\vspace*{1cm}

%\vspace*{0.5cm}
   \begin{itemize}
     \item Body: P and S waves
     \item Surface: Rayleigh,\\
           Love waves, etc.
     \item Lack of correlation \\
           (incoherence)
     \item Inclined waves
     \item 3D waves

   \end{itemize}




 
\vspace*{-5.3cm}
\begin{figure}[!hbpt]
\begin{flushright}
\includegraphics[width=2.0cm, angle=45]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Presentation/P_body_wave.jpeg}
\includegraphics[width=2.0cm, angle=45]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Presentation/S_body_wave.jpeg}
\vspace*{-0.5cm}
\\
\includegraphics[width=2.5cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Presentation/Rayleigh_surface_wave.jpeg}
\includegraphics[width=2.5cm]{/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{flushright}
\end{figure}

\end{frame}




% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame} 
\frametitle{Seismic Input: The Domain Reduction Method}


%\begin{itemize}

%  \item 
The DRM (Bielak et al.): \\
  The effective force  $P^{eff}$ \\
  is a dynamically consistent \\
  replacement the dynamic \\
  source forces  $P_{e}$

% \end{itemize}

  \begin{eqnarray}
P^{eff} = \left\{\begin{array}{c} P^{eff}_i \\ P^{eff}_b \\ P^{eff}_e \end{array}\right\}
= \left\{\begin{array}{c} 0 \\ -M^{\Omega+}_{be} \ddot{u}^0_e-K^{\Omega+}_{be}u^0_e
   \\ M^{\Omega+}_{eb}\ddot{u}^0_b+K^{\Omega+}_{eb}u^0_b\end{array}\right\}
\nonumber
\label{DRMeq09}
\end{eqnarray}
%

\begin{figure}[!h]
\begin{flushright}
%\vspace*{-0.50cm}
%\begin{center}
%\hspace*{1cm}
\vspace*{-6.50cm}
{\includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2010/NRC-LBL-ProjectReviewMeeting_21_22_Sept_2010/DRM05NPP.pdf}}
%\vspace*{-5.50cm}
%\hspace*{1cm}
%\vspace*{-2.50cm}
%\end{center}
%\vspace*{-0.3cm}
\end{flushright}
\end{figure}




\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame} 
\frametitle{DRM}





\begin{itemize}
%%\vspace*{-0.2cm}
%  \item  Seismic forces $P_e$  replaced by $P^{eff}$

%\vspace*{-0.2cm}
  \item $P^{eff}$ applied only to a  single \\
        layer of elements next to  $\Gamma$.
%\vspace*{-0.2cm}
  \item The only outgoing waves \\
        are from dynamics of \\
        the NPP (easy to damp out)
%\vspace*{-0.2cm}
  \item Material inside $\Omega$ \\
        can be elastic-plastic

  \item All types of seismic waves\\
        (body, surface...) are \\
        properly modeled 


% \item  The only input wave field is the one for the nodes of this layer of elements.
\end{itemize}

\begin{figure}[!h]
\begin{flushright}
%\vspace*{-0.50cm}
%\begin{center}
%\hspace*{1cm}
\vspace*{-5.50cm}
{\includegraphics[width=5.8cm]{/home/jeremic/tex/works/Conferences/2010/NRC-LBL-ProjectReviewMeeting_21_22_Sept_2010/DRM05NPP.pdf}}
%\vspace*{-5.50cm}
\hspace*{-0.8cm}
%\vspace*{-2.50cm}
%\end{center}
%\vspace*{-0.3cm}
\end{flushright}
\end{figure}


\end{frame}




















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\subsection{Verification and  Validation}



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\begin{frame}
\frametitle{V \& V for ESSI Modeling and Simulations}


\begin{itemize}

   \vspace*{0.3cm}
   \item Material modeling and simulation (elastic, elastic-plastic...)


   \vspace*{0.3cm}
   \item Finite elements (solids, structural, special elements...)


   \vspace*{0.3cm}
   \item Solution advancement algorithms (static, dynamic...)


   \vspace*{0.3cm}
   \item Seismic input and radiation 


   \vspace*{0.3cm}
   \item Finite element model verification!


\end{itemize}



\end{frame}

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

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Mesh Size Effects on Seismic Wave Propagation Modeling}

\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}




\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Cases 3, 4, and 6, Ormsby Wavelet Input Motions}

\vspace*{-7mm} 
\begin{figure}[H]
\begin{center}
\includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/MeshSize/figs/3_4_6/Input_Displacement.pdf}
\end{center}
\end{figure}


 
\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Cases 3, 4, and 6, Surface Motions}

 
\vspace*{-7mm} 
\begin{figure}[H]
\begin{center}
\includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/MeshSize/figs/3_4_6/displacement.pdf}
\end{center}
\end{figure}


 
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Cases 3, 4, and 6, Input and Surface Motions, FFT}

 
\vspace*{-7mm} 
\begin{figure}[H]
\begin{center}
\includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/MeshSize/figs/3_4_6/FFT.pdf}
\end{center}
\end{figure}


 
\end{frame}


 








%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection{3D  Inclined  Body  and Surface Seismic Wave Fields}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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

  \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{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}





















          
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Elastic-Plastic Material Modeling}
%\subsection{Material Modeling: $G/G_{max}$ and Damping Curves}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Modulus Reduction ($G/G_{max}$ ) and Damping Curves}

\begin{itemize}

%\vspace*{5mm}
\item Idriss and Seed 1970

\vspace*{3mm}
\item Much work gone into development of curves for different types of soils

\vspace*{3mm}
\item  However,  it is still a linear elastic (secant) approach with some energy
dissipation taken into account

\vspace*{3mm}
\item   Not good for any case where soil volume change makes a difference or where 2D
or 3D behavior is important

   
\end{itemize}
\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{$G/G_{max}$ and Damping Curves}

\vspace*{-5mm}
\begin{figure}[!htb]
 \centering
 \includegraphics[width=11.5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Staff_Capacity_Building_28Jan2013/Figure_Stiffness_Damping.pdf}
\end{figure}


\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Commonly used $G/G_{max}$ and Damping Curves: \\
 Vu{\v c}eti{\' c} and  Dobry (1991)}

\begin{figure}[!hbpt]
\begin{center}
% 
\includegraphics[width=5truecm]{/home/jeremic/tex/works/Conferences/2013/NRC_Staff_Capacity_Building_28Jan2013/Vucetic_and_Dobry_01.jpeg}
\hspace*{5mm}
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Conferences/2013/NRC_Staff_Capacity_Building_28Jan2013/Vucetic_and_Dobry_02.jpeg}
%
\end{center}
\end{figure}                                                          



\end{frame}








%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Pisan{\`o} 3D Elastic Plastic Material Model}

\begin{itemize}

  \item    Split    stress    into    frictional    and    viscous    components
  $\sigma_{ij}=\sigma_{ij}^{f} + \sigma_{ij}^{v}$

  \item Elasticity: classic, linear (can be nonlinear)

  \item  Yield  surface, Drucker-Prager cone,  collapsed  (limit  analysis,  vanishing elastic
  regions) to cylinder (von Mises), with conical bounding surface

  \item   Plastic   flow  and  rotational  kinematic  hardening,  borrowed  from
  Manzari-Dafalias model (1997)

  \item Yield (loading-unloading) condition established using stress projection
  
  \item Special (unique) developments of a stiffness tensor (used for FEM)



   
\end{itemize}

\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Pisan{\`o} Model: Triaxial  and Pure Shear Response}


\begin{figure}  [!htb]
 \centering
\includegraphics [width=5.5cm] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res1a.pdf}
\includegraphics [width=5.8cm] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res1b.pdf}
\\
\includegraphics [width=5.5cm] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res2a.pdf}
\includegraphics [width=5.5cm] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res2b.pdf}
 \label{fig:res1}
\end{figure}


    

\end{frame}



% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Pisan{\`o} Model: Calibration for $G/G_{max}$ and Damping}
% 
% 
%   
%      
% \begin{figure}  [!htb]
%  \centering
% \includegraphics [width=0.8\textwidth] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res3.pdf}
%  \hfill
%  \caption{Comparison  between  experimental and simulated $G/G_{max}$
%  and  damping  curves ($p_0$=100 kPa, T=2$\pi$ s, $\zeta$ = 0.003, $G_{max}$ = 4
%  MPa, $\nu$=0.25, $M$=1.2, $k_d$=$\xi$=0, $h$=$G$/(112$p_0$), $m$=1.38)}
%  \label{fig:res3}
% \end{figure}
%     
% 
% \end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Pisan{\`o} Model: Calibration for $G/G_{max}$ and Damping}

        
\begin{figure}  [!htb]
 \centering
\includegraphics [width=0.8\textwidth] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res4.pdf}
%\hfill
 \caption{Comparison  between  experimental and simulated $G/G_{max}$
 and  damping  curves ($p_0$=100 kPa, T=2$\pi$ s, $\zeta$ = 0.003, $G_{max}$ = 4
 MPa, $\nu$=0.25, $M$=1.2, $k_d$=$\xi$=0, $h$=$G_{max}$/(15$p_0$), $m$=1)}
 \label{fig:res4}
\end{figure}

   

\end{frame}

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Pisan{\`o} Model: Variation in Confining Pressure}


 
\begin{figure}[!htb]
 \centering
\includegraphics [width=0.8\textwidth] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res7.pdf}
% \hfill
 \caption{Simulated  $G/G_{max}$  and  damping  curves  at  varying
 confining  pressure  (T=2$\pi$  s,  $G_{max}$  =  4  MPa,  $\nu$=0.25, $M$=1.2,
 $k_d$=$\xi$=0, $h$=$G$/(15$p_0$), $m$=1)}
 \label{fig:res5}
\end{figure}


    

\end{frame}

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Soil Volume Response}

\begin{itemize}
  \item Soil behavior is very much a function of volumetric response

  \vspace*{2mm}
  \item Dilative soils: increase  volume due to shearing

  \vspace*{2mm}
  \item Compressive soils: decrease  volume due to shearing


  \vspace*{2mm}
  \item Modulus reduction and damping curves do not provide volumetric data

  \vspace*{2mm}
  \item Soil volume change will affect response due to volume constraints

\end{itemize}

    

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{No Volume Change Soil (at Critical State?)}

\begin{figure}[!h]
\begin{center}
  \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/FedericoPisano/Pisano_model/Issue_of_dilatancy/sine1Hz-4.pdf}
\end{center}
\end{figure}

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Compressive Soil}

\begin{figure}[!h]
\begin{center}
  \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/FedericoPisano/Pisano_model/Issue_of_dilatancy/sine1Hz_comp-4.pdf}
\end{center}
\end{figure}

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Dilative Soil}

\begin{figure}[!h]
\begin{center}
  \includegraphics[width=8cm]{/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}
% 


















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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Examples}
% %
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Few Illustrative Examples}
% 
% \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}
% 
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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}
% 
% 
% 
% 
% \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{Gaping Response ($45^\circ$ Ricker Wavelet)}
% 
% \vspace*{-0.1cm}
% \begin{tiny}
% \begin{figure}[H]
% \begin{center}
% \begin{tabular}{ccc} 
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% \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}
% \\
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% \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}
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% \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}
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% &
% \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}
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% \includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/slide500.pdf}
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% &
% \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}
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% %\\
% %\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/MomentBent1Pile2.pdf}
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% %  \includegraphics[width=4cm]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/GMklot02.pdf}
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\section{Current Work}



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\subsection{NRC ESSI Simulator System}

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\begin{frame}
\frametitle{NRC ESSI Simulator System}

\begin{itemize}

\item {\bf The NRC-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 on NRC-ESSI-Computer. \
%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 NRC-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    NRC-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 NPP 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}


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\begin{frame}
\frametitle{NRC ESSI Simulator Program}

\begin{itemize}

%\vspace*{0.2cm}
\item  Collection  of Useful Libraries  (modular, portable)

\vspace*{0.1cm}
\item Library centric software design

\vspace*{0.1cm}
\item Various open source licenses (GPL, LGPL, BSD, CC)

%\vspace*{0.3cm}
\vspace*{0.1cm}
\item Extensive verification and (not so much) validation


\vspace*{0.1cm}
\item  Detailed program documentation  (part of NRC ESSI Notes)
    
\vspace*{0.1cm}
\item        Target   users:  U.S.-NRC,  other  domestic (DOE) and international
agencies (CNSC, IAEA), National Labs, Testers, eventually external users
    
%\item Sources will be available through
%{\bf 
%\url{http://nrc-essi-simulator.info}}


\end{itemize}

\end{frame}



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\begin{frame}[fragile]
 \frametitle{NRC ESSI Simulator Computer}

  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 supercomputers
%\vspace*{0.1cm}
   \item Current system: 208 CPUs
%\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}

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\begin{frame}
\frametitle{NRC ESSI Simulator Notes}


A hypertext documentation system  describing in detail 
modeling and simulations of NPP ESSI
problems 

\begin{itemize}


\vspace*{0.1cm}
\item  Theoretical  and  Computational  Formulations  
\vspace*{0.1cm}
\item  Software and Hardware Platform Design 
\vspace*{0.1cm}
\item  Verification and Validation 
\vspace*{0.1cm}
\item Application Example


\end{itemize}

\end{frame}

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\subsection{Features in Development}

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\begin{frame}

\frametitle{Features in Development}

\begin{itemize}

\item Buoyancy effects for foundations

\vspace*{2mm}
\item Piles

\vspace*{2mm}
\item Isolators

%\vspace*{2mm}
%\item Liquefiable soil

\vspace*{2mm}
\item Saturated contact (dry is already in)



\end{itemize}

 
\end{frame}




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\begin{frame}

\frametitle{Models in Development \#1}


\begin{figure}[!h]
\begin{center}
 \includegraphics[width=5.5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Project_Review_LBNL_23-23Feb2013/Roche_NRC_model/FixedBase_Shell_LSDYNA_001.png}
\hspace*{1mm}
 \includegraphics[width=5.5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Project_Review_LBNL_23-23Feb2013/Roche_NRC_model/FixedBase_Shell_LSDYNA_002.png}
\\
\vspace*{1mm}
 \includegraphics[width=5.5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Project_Review_LBNL_23-23Feb2013/Roche_NRC_model/FixedBase_Shell_LSDYNA_003.png}
\hspace*{1mm}
 \includegraphics[width=5.5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Project_Review_LBNL_23-23Feb2013/Roche_NRC_model/FixedBase_Shell_LSDYNA_004.png}
\end{center}
\end{figure}

\end{frame}


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\begin{frame}
\frametitle{Models in Development \#2}

\vspace*{-0.50cm}

\begin{itemize}

\item Body and surface seismic waves

\item Seismic wave frequencies \\
      up to $50$Hz 

\item Elastic-plastic soil/rock and \\
      structural components,

\item Inelastic contact/gap 

\item Seismic isolator effects

\item Buoyant effects for deep foundation embedment 


\item High Fidelity Model: soil block: $230m \times 230m \times100m$, foundation
$90m  \times  90m$,  Containment  Structure:  $40m \times 50m$, 2.1 Million DOFs,
700,000 elements,

\end{itemize}



\vspace*{-6.0cm}
\begin{flushright}
\hspace*{1cm}
\includegraphics[width=5.0cm]{/home/jeremic/tex/works/Conferences/2012/Seismic_research_issues_for_NPPs/Large_NPP_model_01A.jpg}
\end{flushright}








\end{frame}




 

\subsection{Uncertainty Propagation}
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\begin{frame} 

\frametitle{Eulerian--Lagrangian FPK Equation and (SEP)FEM}

 

\begin{itemize}

\item Advection-diffusion equation 
%
\begin{equation}                
\nonumber
\frac{\partial P(\sigma_{ij},t)}{\partial t} 
= 
-\frac{\partial}{\partial\sigma_{ab}}
\left[N_{ab}^{(1)}P(\sigma_{ij},t)
-
\frac{\partial}{\partial \sigma_{cd}}
\left\{N_{abcd}^{(2)} P(\sigma_{ij},t)\right\} \right]
\end{equation}

%

\vspace*{0.1cm}
\item {\bf  Complete} probabilistic description of response 


\vspace*{0.1cm}
\item {\bf Second-order  exact} to covariance of time (exact mean and variance)

% - 
% -  \item Deterministic equation in probability density space
% -  
% -  \item Linear PDE in probability density space 
% -  $\rightarrow$ simplifies the numerical solution process
% -  

%\item  Applicable  to any elastic-plastic-damage material model (only coefficients $N_{ab}^{(1)}$
%and $N_{abcd}^{(2)}$ differ)


\vspace*{0.1cm}
\item  Any uncertain FEM problem
(${\bf M} \ddot{\bf u}
+
{\bf C} \dot{\bf u}
+
{\bf K} {\bf u}
=
{\bf F}
$)  
with
  \begin{itemize}
    \item uncertain material parameters (stiffness matrix ${\bf K}$),
    \item uncertain loading (load vector ${\bf F}$)
  \end{itemize}
 can  be  analyzed using PEP and SEPFEM to obtain PDFs of DOFs,
 stress, strain...

% -  %\vspace*{0.2cm}
% -  \item PEP solution is second order accurate (exact mean and standard deviation)
% -  
% -  %\vspace*{0.2cm}
% -  \item SEPFEM solution (PDFs) can be made as accurate as need be
% -  
% -  
% -  \item Tails of PDFs can than be used to develop accurate risk
% -  
% -  
% -  \item Application to a realistic case of seismic wave propagation


%\vspace*{0.2truecm}

\end{itemize}


\end{frame}






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\begin{frame} 

\frametitle{Probabilistic Elastic-Plastic Response}


\begin{figure}[!hbpt]
\begin{center}
%\includegraphics[width=8cm]{/home/jeremic/tex/works/Papers/2007/ProbabilisticYielding/figures/vonMises_G_and_cu_very_uncertain/Contour_PDF-edited.pdf}
\includegraphics[width=8cm]{/home/jeremic/tex/works/Conferences/2012/DOE-LLNL-workshop-27-28-Feb-2012/ProbabilisticYielding_vonMises_G_and_cu_very_uncertain_Contour_PDF-edited.pdf}
\end{center}
\end{figure}

\end{frame}

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\begin{frame} 

\frametitle{Probabilistic Elastic-Plastic Response}


\begin{figure}[!hbpt]
\begin{center}
%\includegraphics[height=6.0cm]{/home/jeremic/tex/works/Conferences/2011/ICASP11_Zurich/Present/PDF_Plot-Ed.pdf}
\includegraphics[width=9.5cm]{/home/jeremic/tex/works/Conferences/2012/DOE-LLNL-workshop-27-28-Feb-2012/ProbabilisticYielding_vonMises_G_and_cu_very_uncertain_PDF-edited.pdf}
\end{center}
\end{figure}

\end{frame}




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\begin{frame}

\frametitle{Stochastic Finite Element Formulation}

\begin{itemize}

\item    Input    random   field   material   properties   ($E$)   $\rightarrow$
Karhunen--Lo{\`e}ve (KL) expansion, optimal expansion, error minimizing property

\item  Unknown  solution  random field ($u$) $\rightarrow$ Polynomial Chaos (PC)
expansion



\end{itemize}

%
%
% Minimizing    norm  of  error  of  finite  representation  using Galerkin
%technique (Ghanem and Spanos 2003):

      \vspace*{-0.6truecm}
      \begin{flushright}
      \begin{equation}
      \nonumber
      \sum_{n = 1}^N K_{mn}^{ep} d_{ni} + \sum_{n = 1}^N \sum_{j = 0}^P d_{nj} \sum_{k = 1}^M C_{ijk} K_{mnk}^{'ep}  = \left< F_m \psi_i[\{\xi_r\}] \right >
      \end{equation}
      \end{flushright}

%      \begin{itemize}
%
%      \vspace*{0.5cm}
%      \item Final eqn.:
%      
%      \vspace*{-0.4cm}
%      \begin{flushright}
%      \begin{normalsize}
%      \begin{equation}
%      \nonumber
%      \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sum_{n = 1}^N K_{mn} d_{ni} + \sum_{n = 1}^N \sum_{j = 0}^P d_{nj} \sum_{k = 1}^M C_{ijk} K'_{mnk}  = \left< F_m \psi_i[\{\zeta_r\}] \right >
%      \end{equation}
%      \end{normalsize}
%      \end{flushright}

      \vspace*{-0.5cm}
      \begin{equation}
      \nonumber
      K_{mn}^{ep} = \int_D B_n \textcolor{mycolor}{E}^{ep}  B_m dV    
      \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 
      K_{mnk}^{'ep} = \int_D B_n {\sqrt \lambda_k h_k} B_m dV
      \end{equation}
      
      \vspace*{-1.0cm}
      \begin{equation}
      \nonumber
      C_{ijk} = \left < \xi_k(\theta) \psi_i[\{\xi_r\}] \psi_j[\{\xi_r\}] \right >  
      \ \ \ \ \ \ \ \ \ \ \ \  
      F_m = \int_D \phi N_m dV  \ \ \ \ \ \ \ \ \ \ \ \
      \end{equation}

%
\end{frame}

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\begin{frame}


\frametitle{Seismic Wave Propagation through Stochastic Soil}


Uniform CPT site data

%\begin{figure}
\begin{flushleft}
%\hspace*{-1.7cm}
\includegraphics[height=2.0cm]{/home/jeremic/tex/works/Thesis/KallolSett/Dissertation/figures/CPT_DataAnalysis_Plots/SamplingPlan-Edited.jpg}
\end{flushleft}

\vspace*{-2.7cm}
%\begin{figure}
\begin{flushright}
\includegraphics[height=4.7cm]{/home/jeremic/tex/works/Thesis/KallolSett/Dissertation/figures/CPT_DataAnalysis_Plots/EastWestProfile-Edited.pdf}
\end{flushright}
%\end{figure}


\end{frame}


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\begin{frame}


\frametitle{Random Field Parameters from Site Data}


%\begin{flushleft}
%\includegraphics[height=5.0cm]{PEER2007_3.jpg}
%\end{flushleft}
%\vspace*{-0.5truecm}

\begin{itemize}

\item Soil as 12.5 m deep 1--D soil column (von Mises Material) 

\begin{itemize}

\item Properties (including testing uncertainty) obtained through random field modeling of CPT $q_T$
%
$\left<q_T\right> = 4.99 ~MPa;~~Var[q_T] = 25.67 ~MPa^2; $\\
Cor. ~Length $[q_T] = 0.61 ~m; $ Testing~Error $= 2.78 ~MPa^2$

\end{itemize}

\vspace*{0.2cm}
\item $q_T$ was transformed to obtain $G$: ~~$G/(1-\nu)~=~2.9q_T$ 

\begin{itemize}
\item Assumed transformation uncertainty = 5\%
%
$\left<G\right> = 11.57MPa; Var[G] = 142.32 MPa^2$ \\
Cor.~Length $[G] = 0.61 m$

\end{itemize}


%\begin{center}
%\hspace*{-1.7cm}
%\includegraphics[height=3.5cm]{Chapter9_Schematic.jpg}
%\hspace*{0.0cm}
%\includegraphics[height=3.5cm]{Chapter9_BaseDisplacement.jpg} \\
%\small{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Base Displacement}
%\end{center}

\vspace*{0.2cm}
\item Input motions: modified 1938 Imperial Valley

% \vspace*{-0.2cm}
% \begin{center}
% \includegraphics[height=2.0cm]{Chapter9_BaseDisplacement.jpg} 
% \end{center}

\end{itemize}
\end{frame}


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\begin{frame}


\frametitle{Decision About Site (Material) Characterization}




\begin{itemize}

\item  Do nothing about site characterization (rely on experience): conservative
{\bf guess}  of  soil  data, $COV  = 225$\%, correlation length $= 12$m.


\vspace*{0.3cm}
\item  Do better than standard site characterization: $COV = 103$\%, correlation
length $= 0.61$m)


\vspace*{0.3cm}
\item Improve site (material) characterization if  probabilities of exceedance are unacceptable!


\end{itemize}

\end{frame}

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\begin{frame}


\frametitle{Full PDFs of all DOFs (and $\sigma_{ij}$, $\epsilon_{ij}$, etc.)}
%\frametitle{Full PDFs for Real Data Case}


\begin{itemize}
\vspace*{0.7cm}
  \item Stochastic Elastic-Plastic\\
        Finite Element Method \\
        (SEPFEM)  \\    
\vspace*{0.5cm}
  \item Dynamic case
\vspace*{0.5cm}
  \item Full PDF at \\
        each time step $\Delta t$
\end{itemize}


\vspace*{-4.60cm}
\begin{flushright}
\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/Plots_with_Labels/EvolutionaryPDF_Actual-Edited.pdf}
%\vspace*{-0.75cm}
%\includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2007/USC_seminar/Application_figs/Mean_and_SDElasticPlastic_ps.pdf}
\end{flushright}

% 
\end{frame}

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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}
% 
% 
% \frametitle{Evolution of Mean $\pm$ SD for Guess Case}
% 
% 
% 
% \begin{figure}
% \begin{center}
% \hspace*{-0.75cm}
% \includegraphics[width=10.0cm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/Plots_with_Labels/Evolutionary_Mean_pm_SD_NoData-Edited.pdf}
% \hspace*{-0.75cm}
% %\includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2007/USC_seminar/Application_figs/Mean_and_SDElasticPlastic_ps.pdf}
% \end{center}
% \end{figure}
% 
% % 
% \end{frame}
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% 




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\begin{frame}


\frametitle{PDF at each $\Delta t$ (say at $6$ s)}



\begin{figure}
\begin{center}
\hspace*{1.75cm}
\includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/Plots_with_Labels/PDFs_at6sec_Actual_vs_NoData-Edited.pdf}
\vspace*{-0.75cm}
%\includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2007/USC_seminar/Application_figs/Mean_and_SDElasticPlastic_ps.pdf}
\end{center}
\end{figure}

% 
\end{frame}

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\begin{frame}


\frametitle{PDF $\rightarrow$ CDF (Fragility) at $6$ s}



\begin{figure}
\begin{center}
%\hspace*{-0.75cm}                                                                                               
\includegraphics[width=8.0cm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/Plots_with_Labels/CDFs_at6sec_Actual_vs_NoData-Edited.pdf}
\vspace*{-0.75cm}
%\hspace*{-0.75cm}
%\includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2007/USC_seminar/Application_figs/Mean_and_SDElasticPlastic_ps.pdf}
\end{center}
\end{figure}

% 
\end{frame}

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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
                                        
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\begin{frame}

\frametitle{Probability of Unacceptable Deformation ($50$cm)}

\begin{figure}
\begin{center}
\vspace*{-0.3cm}
%\hspace*{-0.75cm}                                                                                               
\includegraphics[width=10.50cm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/NewPlots/with_legends_and_labels/Exceedance50cm_LomaPrieta-Edited_ps.pdf}
\vspace*{-0.5cm}
%\hspace*{-0.75cm}
%\includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2007/USC_seminar/Application_figs/Mean_and_SDElasticPlastic_ps.pdf}
\end{center}
\end{figure}
 
\end{frame}

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\section{Summary}



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


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


%\vspace*{0.5cm}
  \item  {\bf  Interplay}  of {\bf Uncertain} {\bf Earthquake}, {\bf Uncertain} 
  {\bf Soil/Rock},
%  {Foundation} 
  and  {\bf  Uncertain}  {\bf  Structure}  in time domain {\bf probably} plays a
  decisive role in seismic performance of NPPs

%\vspace*{0.1cm}
  \item  Improve  {\bf  risk  informed decision making}  through  high fidelity 
  (Verified   and   Validated)  Time Domain. {\bf   Deterministic}   and   {\bf 
  Stochastic}   Elastic-Plastic Finite Element modeling and simulation

 
%\vspace*{0.1cm}
%  \item  {\bf Education and training} of users will prove essential
  

%\vspace*{0.1cm}
  \item        {\bf Acknowledgement:} funding and collaboration with the US-NRC,
  CNSC, NSF, DOE, AREVA, Shimizu.  \\ 
 Drs. and students:
   Nima     Tafazzoli,  Federico Pisan{\`o}, Mario Martinelli,   Jos{\'e}  Abell 
   Mena, Kohei Watanabe, Babak Kamrani, Chang-Gyun Jeong...

  
\end{itemize}


\end{frame}
%


\end{document}


