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%\title{NRC Staff Capacity Building: \\
%       Micromechanical Origins of Elasto-Plasticity }
\title{Challenges and Tools for \\
       Non-Linear SSI Analysis }


%\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}}
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%   affiliation.
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\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}}


%\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\\
{ University of California, Davis\\
%  and\\ 
%  Faculty Scientist, Lawrence Berkeley National Laboratory, Berkeley }
  Lawrence Berkeley National Laboratory, Berkeley }
% - 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 UCB SSI Meeting, January 2013}

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\begin{document}

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

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\begin{frame}
  \frametitle{Presentation Goals}
\begin{itemize}

  \item  Briefly overview of most  important  current  challenges 
  for SSI modeling and simulation (personal view )

\vspace*{0.3cm}
  \item  Briefly overview select current work that aims to address some of those
  challenges

\vspace*{0.3cm}
  \item  Hope  for a discussion/information  about validation experiments
  (we are done with the verification for the most part)

\end{itemize}



\end{frame}

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%   just say so once. Everybody will be happy with that.


  


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\section{Current Challenges}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{}
% 
% \begin{itemize}
% %\vspace*{0.3cm}
%   \item   
% 
%   \item   
% \end{itemize}
% \end{frame}


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\subsection{Modeling Uncertainty}

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\begin{frame}
 \frametitle{Modeling Uncertainty}

\begin{itemize}

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

\vspace*{0.2cm}
  \item  Introduction of uncertainty and  (unknown) lack of accuracy in results due
  to  use  of  un-verified  simulation tools (software quality, etc.)

\vspace*{0.2cm}
  \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)


\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}
















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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}


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{T2: Stage 14, Interpretation of Data  }
% 
% 
% 
% 
% \begin{figure}[!h]
% \begin{center}
% %\vspace*{-2.5cm}
% \vspace*{-1.0cm}
% \hspace*{-1.5cm}
% {\includegraphics[width=8.0cm]{/home/jeremic/tex/works/Conferences/2009/GheoMat/VandV_01/T2_02.jpg}}
% \hspace*{-1.5cm}
% \vspace*{-1.5cm}
% %\vspace*{-5.0cm}
% \end{center}
% \end{figure}
% 
% % 
% % % \begin{itemize}
% % % 
% % %     
% % 
% % \end{itemize}
% 
% \end{frame}


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\subsection{Uncertainty in Material Behavior/Properties}


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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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{Soil Uncertainties and Quantification}

\begin{itemize}
%
%\vspace*{0.5cm}
\item Natural variability of soil deposit  (Fenton 1999) 

  \begin{itemize}

    \item Function of soil formation process 
 
  \end{itemize}


%
\vspace*{0.2cm}
\item Testing error (Stokoe et al. 2004)

  \begin{itemize}

    \item Imperfection of instruments 
 
    \item Error in methods to register quantities

  \end{itemize}

%
\vspace*{0.2cm}
\item Transformation error (Phoon and Kulhawy 1999)

  \begin{itemize}

    \item Correlation by empirical data fitting (e.g. CPT data $\rightarrow$ friction angle etc.)

  \end{itemize}

\end{itemize}


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



\frametitle{SPT Based Determination of Shear Strength}




\begin{figure}[!hbpt]
\begin{center}
% 
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_RawData_and_MeanTrend-Mod.pdf}
\hfill
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_Histogram_PearsonIV-FineTuned-Mod.pdf}
%
\end{center}
\end{figure}                                                          

\vspace*{-0.3cm}
Transformation of SPT $N$-value $\rightarrow$ undrained shear
strength, $s_u$ (cf. Phoon and Kulhawy (1999B)

Histogram  of  the  residual  
(w.r.t  the  deterministic transformation
equation) undrained strength, 
along with fitted probability density function 
(Pearson IV)
\end{frame}


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



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


\begin{figure}[!hbpt]
\begin{center}
%
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01-Ed.pdf} 
\hfill
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_Histogram_Normal_01-Ed.pdf}
%
\end{center}
\end{figure}                                                          

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

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

\end{frame}































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


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Types of Physical Experiments}


 \begin{itemize}

%   \vspace*{1.0truecm}
   \item {\bf Traditional Experiments}
     \begin{itemize}
       \item Improve the fundamental understanding of physics involved
       \item Improve the mathematical models for physical phenomena
       \item Assess component performance 
     \end{itemize}

   \vspace*{0.2truecm}
   \item {\bf Validation Experiments}
     \begin{itemize}
       \item Model validation experiments
       \item  Designed  and  executed  to  quantitatively estimate mathematical
       model's ability to simulate well defined physical behavior
       \item   The  simulation  tool (SimTool) (conceptual  model,  computational  model,
       computational solution) is the customer
      \item Experimental uncertainty analysis!
     \end{itemize}


\end{itemize}



\end{frame}


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Validation Experiments}
% 
% 
%  \begin{itemize}
% 
%    \vspace*{0.0truecm}
%    \item  Jointly designed and executed by
%    experimentalist and computationalist
% % 
%    \item Designed to capture the relevant physics
% 
%    \item  Use any possible synergism between
%    experiment and computational approaches
% 
%    \item  Maintain independence  between computational and experimental results
% 
%    \item  Validate experiments on unit level problems, hierarchy of experimental
%    measurements   should   be   made   which  present  an  increasing  range  of
%    computational difficulty
% 
%    \item Develop experimental uncertainty analysis
% 
% \end{itemize}
% 
% 
% 
% \end{frame}
% 

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Validation and Application Domains --  No Overlap}

     
%\vspace*{0.3cm}

\begin{figure}[!h]
\begin{center}
%\vspace*{-2.5cm}
{\includegraphics[width=4.0cm]{/home/jeremic/tex/works/Presentation/2004/VandV/VPI03.pdf}}
%\vspace*{-5.0cm}
\end{center}
\end{figure}

%\vspace*{-0.5cm}

\begin{itemize}
 \item  Inference  $\Rightarrow$ probabilistic modeling and numerical
 simulation (deterministic is a special case)
%  %  \item  Validation domain is actually an aggregation of tests and thus might not
%  %  be convex (bifurcation of behavior)
%   \item Current experiments $\Rightarrow$ non--overlapping validation and
%   application domains
%  % \item We have to rely on {\bf Modeling} and {\bf Numerical Simulation}
\end{itemize}

\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Prediction}


 \begin{itemize}

   \vspace*{0.0truecm}
   \item  Prediction:  use  of  computational  model  to foretell the state of a
   physical   system   under  consideration  under  conditions  for  which  the
   computational model has not been validated

   \vspace*{0.3truecm}
   \item Validation does not directly make a claim about the accuracy of a prediction
     \begin{itemize}
       \item Computational models are easily misused (unintentionally or intentionally)
       \item  How  closely  related  are  the  conditions  of the prediction and
       specific cases in validation database
       \item How well is physics of the problem understood

     \end{itemize}


\end{itemize}



\end{frame}




% 






















%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Brief Overview of Select Modeling and Simulations Tools}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{NRC ESSI Simulator System}

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

\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 (ESSI) 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,
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}  is a hypertext documentation system 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}



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

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

\begin{itemize}

%\vspace*{0.2cm}
\item   Based  on  a  Collection  of Useful Libraries  (library centric software
design, modular, portable)

\vspace*{0.3cm}
\item  A number of models, elements  and algorithms available 


\vspace*{0.3cm}
\item  Detailed  V\&V (actually, good validation experiments are rare!)


\vspace*{0.3cm}
\item  Current  users, testers, collaborators:  US-NRC,  UCD  students,  
National  Laboratories,   Foreign  Nuclear  Regulatory  Agencies, 
Nuclear Power Companies

%\vspace*{0.3cm}
%\item Future target user space: a very limited number of experts
    

\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*{0.2cm}
   \item Multiple performance CPUs 
         and Networks
\vspace*{0.2cm}
   \item Most cost-performance 
         effective 
\vspace*{0.2cm}
   \item Source compatibility with 
         any DMP supercomputers
\vspace*{0.2cm}
   \item Current system: 208 CPUs (near future: 784 CPUs)

 \end{itemize}

  


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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*{0.3cm}
    \item[]  {\bf Part I}: Theoretical  and  Computational  Formulations   
    
\vspace*{0.3cm}
    \item[] {\bf Part II}:    Software  and  Hardware Platform Design 
    
\vspace*{0.3cm}
    \item[] {\bf Part III}:      Verification  and  Validation  
    
\vspace*{0.3cm}
    \item[] {\bf Part IV}:      Application    to   Practical  Nuclear  Power  Plant  Earthquake 
    Soil/Rock   Structure   Interaction   Problems   

  \end{itemize}


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\subsection{Pisan{\` o} Material Model}




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\begin{frame}
 \frametitle{Pisan{\` o} Material Model: Brief Description}

\begin{itemize}


%\vspace*{0.2cm}
  \item  Primary  modeling  objective: calibration of a 3D elastic-plastic model
  from $G/G_{max}$ and damping curves
   

\vspace*{0.2cm}
  \item  3D  elastic-plastic  material  model,  with  vanishing  elastic region,
  rotational  kinematic  hardening,  bounding  surface,  and  stress  split into
  frictional and viscous components

\vspace*{0.2cm}
  \item  No  volume  change  data (since it is missing in  $G/G_{max}$ and damping
  curve  data),  however,  volume  modeling can be calibrated as well if data is
  available

   
   
\end{itemize}

\end{frame}


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Triaxial Response}
% 
% 
% \begin{figure}  [!htb]
%  \centering
% \includegraphics [width=6cm] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res1a.pdf}
% \\
% \includegraphics [width=6cm] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res1b.pdf}
% % \caption{Predicted  triaxial  responses  for  different  dilatancy  surfaces  (
% % $p_0$=100   kPa,   $G_{max}$   =   4   MPa,   $\nu$=0.25,   $M$=1.2,   $\xi$=1,
% % $h$=$G$/(1.5$p_0$), $m$=1)}
%  \label{fig:res1}
% \end{figure}
% 
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%     
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% \end{frame}
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\begin{frame}
 \frametitle{Pure Shear Cyclic}

   
\begin{figure}  [!htb]
 \centering
\includegraphics [width=6cm] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res2a.pdf}
\\
\includegraphics [width=6cm] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res2b.pdf}
% \hfill
% \caption{Predicted pure shear response at two different shear strain amplitudes ($p_0$=100 kPa, $T$=2$\pi$ s, $\zeta_0$ = 0.003,
%$G_{max}$= 4 MPa, $\nu$=0.25, $M$=1.2, $k_d$=$\xi$=0, $h$=$G$/(1.5$p_0$), $m$=1)}
% \label{fig:res2}
\end{figure}


    

\end{frame}

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\begin{frame}
 \frametitle{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}

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\begin{frame}
 \frametitle{Variation in Viscous Damping}


         
\begin{figure}  [!htb]
 \centering
\includegraphics [width=0.4\textwidth] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res9.pdf}
% \hfill
 \caption{Damping   curves   simulated  at  varying  $\zeta_0$  ($p_0$=100  kPa,
 $T$=2$\pi$   s,   $G_{max}$   =  4  MPa,  $\nu$=0.25,  $M$=1.2,  $k_d$=$\xi$=0,
 $h$=$G_{max}$/(15$p_0$), $m$=1)}
 \label{fig:res9}
\end{figure}


    

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\subsection{Fragility Curve Simulations}
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\begin{frame}




\frametitle{"Uniform" CPT  Site Data}


\vspace*{-0.7cm}
%\begin{figure}
\begin{center}
\includegraphics[height=6.7cm]{/home/jeremic/tex/works/Thesis/KallolSett/Dissertation/figures/CPT_DataAnalysis_Plots/EastWestProfile-Edited.pdf}
\end{center}
%\end{figure}


\end{frame}


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\begin{frame}


\frametitle{Seismic Wave Propagation through Stochastic Soil}


\begin{itemize}

%\item maximizing the log--likelihood of observing the spatial data under assumed joined distribution (for finite 
%scale model) or maximizing the log--likelihood of observing the periodogram estimates (for fractal model)

\item Maximum likelihood estimates

\vspace*{0.3truecm}

%\begin{figure}
\begin{flushleft}
\hspace*{-1.7cm}
\includegraphics[height=4.0cm]{/home/jeremic/tex/works/Thesis/KallolSett/Dissertation/figures/CPT_DataAnalysis_Plots/SamplingPlan-Edited.jpg}
\hspace*{0.0cm}
\includegraphics[height=4.0cm]{/home/jeremic/tex/works/Thesis/KallolSett/Dissertation/figures/CPT_DataAnalysis_Plots/TypicalDataPlotBH1-Edited.jpg} \\
\small{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Typical CPT $q_T$}
\end{flushleft}
%\end{figure}

\vspace*{-4.9truecm}

%\begin{figure}
\begin{flushright}
\includegraphics[width=4.0cm]{/home/jeremic/tex/works/Thesis/KallolSett/Dissertation/figures/CPT_DataAnalysis_Plots/TypicalAutoCovariancePlotBH1_FiniteScale-Edited.jpg} \\
\vspace*{0.01truecm}
\small{Finite Scale}
\end{flushright}
%\end{figure}

\vspace*{0.02truecm}

%\begin{figure}
\begin{flushright}
\includegraphics[width=4.0cm]{/home/jeremic/tex/works/Thesis/KallolSett/Dissertation/figures/CPT_DataAnalysis_Plots/TypicalAutoCovariancePlotBH1_Fractal-Edited.jpg} \\
\small{Fractal}
\end{flushright}
%\end{figure}

\end{itemize}


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\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}
\item  Use of {\bf Probabilistic  Elasto-Plasticity}  and  {\bf Stochastic Elastic-Plastic Finite
Element Method} 

\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}

% 
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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}

% 
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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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\begin{frame}

\frametitle{Probability of Unacceptable Deformation (say $50$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}
 
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% 
% \frametitle{Risk Informed Decision Process}
% 
% \begin{figure}
% \begin{center}
% %\hspace*{-0.75cm}                                                                                               
% \includegraphics[width=8.0cm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/NewPlots/with_legends_and_labels/Summary_LomaPrieta-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}
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\section{Summary and Credits}



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\begin{frame}
  \frametitle{Summary and Credits}
  
  \begin{itemize}

%\vspace*{0.1cm}
  \item   {\bf Interplay} of {\bf uncertain} {\bf earthquake},  {\bf  uncertain}
  {\bf  soil/rock},  and  {\bf  uncertain}  {\bf structure} in time domain, {\bf
  probably} plays a decisive role in seismic performance of NPPs

\vspace*{0.1cm}
  \item  Improve  {risk  informed  decision  making}    through  {\bf  high
  fidelity}  { deterministic}  and  {  stochastic  elastic-plastic finite
  element}  modeling and simulation

\vspace*{0.1cm}
  \item {\bf Education} and {\bf Training} are essential! 
 
%\vspace*{0.1cm}
%  \item  {\bf Education and training} will prove essential
  
\vspace*{0.1cm}
  \item   {  Post-Docs  and  Students:}  Tafazzoli,  Pisan{\`o},  Martinelli,
  Kamrani, Abell, Jeong, Aldridge, Anderson

\vspace*{0.1cm}
  \item              { Acknowledgement:} funding from and collaboration with the
  US-NRC, CNSC 
%AREVA and Shimizu 
and funding from NSF and DOE is much appreciated


  
\end{itemize}


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