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\title{On Seismic Soil Structure \\
       Interaction Simulations for \\
       Nuclear Power Plants  }


%\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=0.1cm]{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} at al.] % (optional, use only with lots of authors)
{B.~Jeremi{\'c}, 
N.~Tafazzoli, 
B.~Kamrani, 
Y.C.~Chao,\\ 
C.G.~Jeong,
P.~Tasiopoulou, 
K.~Sett, 
A.~Kammerer,\\ 
N.~Orbovi{\'c}, and 
A.~Blahoianu
 }
%{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}] % (optional, but mostly needed)
{}
%{Univ. of California, Davis, Univ. of Akron,  NTUA, U.S. NRC, CNSC }
% - 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 OECD/NEA SSI workshop, Ottawa, October  2010}

\subject{}
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\begin{document}

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\begin{frame}
  \titlepage
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\begin{frame}
  \frametitle{Outline}
  \tableofcontents
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%\section{A Historical Note}
\section{A Hypothesis}

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% \subsection{Early Works}
% 
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% \begin{frame} 
% 
% \frametitle{Historical Note on ESSI}
% 
%  
%   \begin{itemize}
%          \item   Kyoji  Suyehiro (Japanese Imperial     
%          Academy) Professor of Naval Engineering at Tokyo Imperial University, a
%          director of Mitsubishi Research Institute for Shipbuilding
%          \item    Life  changing  event  (was  present in) Tokyo  during  Great 
%          Kant{\=   o}   earthquake,   01Sept1923, 11:58am(7.5),  12:01pm(7.3),
%          12.03pm(7.2)
%          \item Saw earthquake surface waves travel and buildings sway 
%          \item   Founding   Director  of  the  Earthquake  Engineering  Research
%          Institute Univ. of Tokyo
%         \item  Observation of different damage to similar buildings on different
%         soil/rock sites.
% %        \item  Records  shows $4 \times$ (four) more damage to soft
% %                wooden buildings on soft ground (nonlinear resonance ?)
%          \item Toured USA in 1931 and gave a series of lectures at 
%               UCB, Stanford, CalTech, MIT, motivating
%               Earthquake Engineering research in the U.S.A.
%    \end{itemize}
% 
% 
%  
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\subsection*{A Hypothesis}
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\begin{frame}
 \frametitle{The ESSI Hypothesis}

\begin{itemize}

\item    NPPSSS    response  is a  function  of  a tightly coupled (in space and
time)   triad of dynamic characteristic of
 \begin{itemize}
   \item Earthquake Ground Motions
   \item Underlying Soil/Rock
   \item NPP Structure, Systems and Components (NPPSSC)
 \end{itemize}

%\item Interplay (in time and space) of dynamic characteristics of  
%  \begin{itemize}
%    \item earthquake  ground  motions
%    \item underlying soil/rock
%    \item NPP structure
%  \end{itemize}
%Determine the accumulation or prevention of damage

                  
\item Energy balance: input (seismic) and dissipated (inelasticity, radiation,
coupling) will control fate of the NPPSSS

\item  Better  understanding  of  the  timing  and  spatial  location  of energy
dissipation in Earthquake-Soil-Structure Interaction (ESSI) system 
can add significant benefit to the safety and economy of NPPSSSs

\item High Fidelity Numerical Simulations of ESSI for NPPSSS

         
    \end{itemize}



\end{frame}









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%\section{Seismic Energy Input, Dissipation, Mechanics, Modeling and Simulations}
\section{Seismic Energy}



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\subsection{Seismic Energy Input}


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%\section{Overview of the available computational tools for SSI analysis}

% 
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Seismic Energy Source}
%  
%     \begin{itemize}
%  
%  %\vspace*{0.2cm}
%       \item Large energy releases, 
%          \begin{itemize}
%            \item Northridge, 1994, $M_{Richter} = 6.7$, $E_r = 6.8 \times 10^{16}J$
%  %          \item Loma Prieta, 1989, $M_{Richter} = 6.9$, $E_r =1.1 \times 10^{17}J$
%  %          \item LARGE JAPANESE EQ.
%  %          \item LARGE NEW ZEALAND EQ.
%            \item Sumatra-Andaman, 2004, $M_{Richter} = 9.3$, $E_r =4.8 \times 10^{20}J$
%            \item Valdivia, Chile, 1960, $M_{Richter} = 9.5$, $E_r =7.5 \times 10^{20}J$
%  %          \item Rhodes, 2008, $M_{Richter} = 6.5$, $E_r =2.4 \times 10^{16}J$
%          \end{itemize}
%  \vspace*{0.5cm}
%        \item Part that energy is radiated as mechanical waves 
%  %      ($\approx 1.6 \times 10^{-5}$)
%        and makes it to the surface
%  %\vspace*{0.2cm}
%  %      \item For comparison, specific energy  of TNT is $4.2\times 10^6 J/kg$. 
%  %%\vspace*{0.2cm}
%  %%      \item Rhodes earthquake was $\approx 0.1 kt$.
%  
%    \end{itemize}
%  
%  
%  \end{frame}
%  %- 
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\begin{frame}
 \frametitle{Seismic Energy Input Into the NPPSSS}

   \begin{itemize}

\vspace*{-1.0cm}
     \item Seismic energy propagates to the NPPSSS

     \item Kinetic  energy  flux  through closed surface $\Gamma$ includes both incoming
     and outgoing waves (using DRM)
\begin{eqnarray*}
E_{flux} = 
\left[0 ; -M^{\Omega+}_{be} \ddot{u}^0_e-K^{\Omega+}_{be}u^0_e ;
M^{\Omega+}_{eb}\ddot{u}^0_b+K^{\Omega+}_{eb}u^0_b \right]_i
%
% \left[
% \begin{array}{c} 
% 0 \\ 
% -M^{\Omega+}_{be} \ddot{u}^0_e-K^{\Omega+}_{be}u^0_e \\ 
% M^{\Omega+}_{eb}\ddot{u}^0_b+K^{\Omega+}_{eb}u^0_b
% \end{array}
% \right]^{T}
\times u_i
%\left[
%\begin{array}{c} 
%0 \\ 
%{u}_b\\ 
%{u}_e
%\end{array}
%\right]
\end{eqnarray*}

  \item Alternatively, $E_{flux} = \rho A c \int_0^t \dot{u}_i^2 dt$

  \item  Outgoing kinetic  energy  \\
         is obtained from outgoing \\
         wave field ($w_i$, in DRM)

  \item Incoming kinetic energy \\
        is then the difference.


   \end{itemize}


\vspace*{-3.0cm}
% \begin{figure}[!hbpt]
\begin{flushright}
\hfill \includegraphics[width=5.5cm]{/home/jeremic/tex/works/Conferences/2010/NRC-LBL-ProjectReviewMeeting_21_22_Sept_2010/DRMideaNPP03.pdf}
\end{flushright}
%\end{figure}
\vspace*{-2cm}


\end{frame}
%- 
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Seismic Energy Dissipation}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
% \frametitle{Seismic Energy Dissipation for \underline{Soil}-Foundation-Structure Systems}
 \frametitle{Seismic Energy Dissipation within NPPSSS}
% \frametitle{Seismic Energy Dissipation for 
%             \underline{Soil}-Foundation-Structure Systems}


\begin{itemize}


\vspace*{0.2cm}
     \item Mechanical dissipation outside of NPPSSS domain:
       \begin{itemize}
         \item reflected wave radiation
         \item NPP system oscillation radiation
       \end{itemize}
\vspace*{0.2cm}
     \item Mechanical dissipation/conversion inside NPPSSS:
       \begin{itemize}
         \item plasticity of the soil/rock subdomain
         \item viscous coupling of porous solid with pore fluid (air, water)
         \item plasticity/damage of parts of the structure/foundation
         \item viscous coupling of structure/foundation with fluids 
%         \item potential and kinetic energy
%         \item potential $\leftarrow \! \! \! \! \! \! \rightarrow$ kinetic energy
       \end{itemize}                           



\vspace*{0.2cm}
%   \item Numerical energy dissipation (numerical damping/production and period  errors)
%   \item Numerical energy dissipation (damping/production)
   \item Numerical energy dissipation/production


\end{itemize}

%
\end{frame}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Energy Dissipation by Soil Plasticity}
%  
%  
%     \begin{itemize}
%  
%  %     \item Plastic work ($W = \int_{0}^{t} \sigma_{ij} d \epsilon_{ij}^{pl}$)
%       \item Plastic work ($W = \int \sigma_{ij} d \epsilon_{ij}^{pl}$)
%  
%       \item Energy dissipation capacity for different soils
%  
%  
%    \end{itemize}
%  
%  %\vspace*{-1.0cm}
%  \begin{center}
%  \vspace*{-0.9cm}
%  \includegraphics[width=8.5cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/Energy-Capacity2.pdf}
%  \hspace*{-0.2cm}
%  %\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/Energy-Capacity10.pdf}
%  \vspace*{-1.0cm}
%  \end{center}
%  
%  
%  \end{frame}
%  %- 
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Energy Dissipation by Soil Viscous Coupling}
%  
%  
%     \begin{itemize}
%  
%       \item Viscous coupling of porous solid and fluid
%       \item Energy loss per unit volume is  $E_{vc}= n^2 k^{-1} (\dot{U}_i - \dot{u}_i)^2$ 
%  %     \item Natural in $u-p-U$ formulation:
%  
%    \end{itemize}
%  %\vspace*{-0.4cm}
%  
%  
%  
%  
%  \begin{footnotesize}
%  %\begin{tiny}
%  \begin{eqnarray*}
%  %& &\left[ \begin{array}{ccc}
%  \left[ \begin{array}{ccc}
%  (M_s)_{KijL} & 0 & 0 \\
%   0  & 0 & 0 \\
%   0  & 0 & (M_f)_{KijL}
%  \end{array} \right]
%  \left[ \begin{array}{c}
%  \ddot{\overline{u}}_{Lj} \\
%  \ddot{\overline{p}}_N \\
%  \ddot{\overline{U}}_{Lj}
%  \end{array} \right]
%  +
%  \left[ \begin{array}{ccc}
%  (C_1)_{KijL} & 0 & -(C_2)_{KijL} \\
%   0  & 0 &   0  \\
%  -(C_2)_{LjiK} & 0 & (C_3)_{KijL} \\
%  \end{array} \right]
%  \left[ \begin{array}{c}
%  \dot{\overline{u}}_{Lj} \\
%  \dot{\overline{p}}_N \\
%  \dot{\overline{U}}_{Lj}
%  \end{array} \right]   
%  \nonumber\\
%  +
%  %& &\left[ \begin{array}{ccc}
%  \left[ \begin{array}{ccc}
%  (K^{EP})_{KijL} & -(G_1)_{KiM} & 0 \\
%  -(G_1)_{LjM}  & -P_{MN} & -(G_2)_{LjM} \\
%   0  & -(G_2)_{KiL} & 0
%  \end{array} \right]
%  \left[ \begin{array}{c}
%  \overline{u}_{Lj} \\
%  \overline{p}_M \\
%  \overline{U}_{Lj}
%  \end{array} \right]
%  =
%  \left[ \begin{array}{c}
%  \overline{f}_{Ki}^{solid} \\
%  0  \\
%  \overline{f}_{Ki}^{fluid}
%  \end{array} \right] \nonumber\\
%  \label{68}
%  \end{eqnarray*}
%  %\end{tiny}
%  \end{footnotesize}
%  
%  \vspace*{-1cm}
%  
%  \begin{footnotesize}
%  \begin{eqnarray*}
%  %%%%%%%%
%  (C_{(1,2,3)})_{KijL}   
%  =
%  \int_{\Omega} N_K^{(u,u,U)} 
%  n^2 k_{ij}^{-1} 
%  N_L^{(u,U,U)} d\Omega
%  % (C_1)_{KijL}   =\int_{\Omega} N_K^u n^2 k_{ij}^{-1} N_L^u d\Omega
%  % \;\; \mbox{;} \;\;
%  % (C_2)_{KijL}   =\int_{\Omega} N_K^u n^2 k_{ij}^{-1} N_L^U d\Omega 
%  % %%%%%%%%
%  % %\;\; \mbox{;}\;\;
%  % \\
%  % %%%%%%%%
%  % (C_3)_{KijL}   =\int_{\Omega} N_K^U n^2 k_{ij}^{-1} N_L^U d\Omega
%  \end{eqnarray*}
%  \end{footnotesize}
%  %
%  %
%  %
%  %
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%  
%  
%  
%  
%  \end{frame}
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%  \begin{frame}
%   \frametitle{Numerical Energy Dissipation}
%  
%     \begin{itemize}
%  
%       \item  Newmark  and  Hilber-Hughes-Taylor can be made non-dissipative for
%       elastic system $\alpha=0.0, \beta = 0.25 ; \gamma  = 0.5,$
%  
%       \item Or dissipative (for elastic) for higher frequency modes: 
%  %Newmark ($\gamma     \ge     0.5,     \;\;\;    \beta    = 0.25(\gamma+0.5)^2$ ),
%  %Hilber-Hughes-Taylor   ($-0.3\dot{3}\le\alpha        \le0,        \;\;\;\gamma    =  
%  %0.5(1-2\alpha), \;\;\; \beta = 0.25(1-\alpha)^2$)
%        \begin{itemize}
%          \item N: $\gamma     \ge     0.5,     \;\;\;    \beta    = 0.25(\gamma+0.5)^2$,
%          \item HHT: $-0.3\dot{3}\le\alpha        \le0,        \;\;\;\gamma    =  
%  0.5(1-2\alpha), \;\;\; \beta = 0.25(1-\alpha)^2$
%        \end{itemize}
%  
%       \item  For nonlinear problems, 
%              energy cannot be maintained
%         \begin{itemize}
%             \item Energy dissipation for steps with reduction of stiffness
%             \item Energy production for steps with increase of stiffness
%  
%  \hspace{1cm}
%  \includegraphics[width=1.80cm, angle=-90]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/EnergyDissipationReducationStiffness.pdf}
%  \hspace{1cm}
%  \includegraphics[width=1.80cm, angle=-90]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/EnergyProductionIncreaseStiffness.pdf}
%  \hspace{1cm}
%  
%  
%  
%         \end{itemize}
%       
%  
%    \end{itemize}
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\section{ESSI Modeling}






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\subsection{Frequency and Time Domain Techniques}




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\begin{frame} 

\frametitle{ESSI Modeling Approaches}



\begin{itemize}


\item  Analytical (closed form) solutions
  \begin{itemize}
    \item Limited application for realistic NPPSSCs
    \item Excellent for verification studies
    \item Good  for  initial  insight 
    \item Potentially large modeling uncertainty!

  \end{itemize}



\item Numerical solutions
  \begin{itemize}
    \item Integral Equations (Boundary Element Method, CLASSI)
    \item Finite Element Methods 
      \begin{itemize}
        \item Frequency domain (SASSI, etc.), widely used, linear elastic, etc.
        \item   Time   domain  (LS-DYNA,  NRC  ESSI  Simulator,  etc.),  gaining
        popularity, full non-linear, etc.
      \end{itemize}
%    \item Can be very powerful but can also be misused 
    \item Educated developers/modelers/analysts are a must
  \end{itemize}




\end{itemize}




 
\end{frame}



% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame} 
% 
% \frametitle{Frequency and Time Domain Approaches}
% 
% 
% \begin{itemize}
%     \item Frequency Domain Approach
%       \begin{itemize}
%         \item Widely used in seismic analysis of NPPSSCs
%         \item Rely on superposition (linear elasticity assumed)
%         \item Energy  dissipation  mimicked  through viscous damping
%         \item Can be very  powerful, however, can be unintentionally misused and
%         needs very educated modelers/analysts
%       \end{itemize}
% 
%     \item Time Domain Approach
% 
%       \begin{itemize}
%         \item Not as widely used for seismic analysis of NPPSSCs
%         \item   Offer    accurate,   nonlinear     modeling    of    mechanics
%         of Earthquake-Soil-Structure Interaction for NPPSSSs
%         \item    Can   be  very    powerful,  however,  can  be 
%         misused and needs very educated modelers/analysts
%         \item        Require    use    of   new  (already  available  and/or in
%         development) software and hardware tools
%       \end{itemize}
% 
% \end{itemize}
% 
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\begin{frame} 

\frametitle{NRC ESSI Simulator Program: Library Centric Design}


%Levels of abstraction
 
 \begin{itemize}
    \item  A  full 3D, non-linear Earthquake-Soil-Structure Interaction program,
    computer and documentation system


    \item   MOSS library (UCD Modified OpenSees Services: trimmed, debugged,
    verified, documented), 
    
    \item Plastic Domain Decomposition  for Parallel Computing

    \item Finite element and material libraries (FEMtools, Template3DEP)

    \item Numerical utility libraries (BLAS, lapack, nDarray, matrix...)

    \item Solver libraries (UMFPACK, PETSc, SuperLU...)

    \item Graph libraries (ParMETIS)

    \item Domain Specific Language (DSL) library

    \item Verification, Validation, Educational, and Real NPPSSS  Examples library


 \end{itemize}






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




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


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

\frametitle{NRC ESSI Simulator Program: Management}

\begin{itemize}

\vspace*{0.2cm}
  \item    Application    Programming  Interface (API): well documented, for all
  libraries and examples
  
\vspace*{0.2cm}
  \item Detailed theory background

\vspace*{0.2cm}
  \item Verification examples, extensive

\vspace*{0.2cm}
  \item Validation examples, as available 

\vspace*{0.2cm}
  \item Educational examples, extensive  
  
\vspace*{0.2cm}
  \item  NRC  ESSI    Simulation    in  public  domain, an open source
  license (LPGL)
  
\vspace*{0.2cm}
  \item    Source    files    management    by  subversion for a large number of
  developers and users
%,  currently  at code.google.com,
%  probable move to LBNL
  
%  \item Editors appointed for source libraries, example libraries, documentation
%  libraries...


\end{itemize}


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


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
  \frametitle{NRC ESSI Simulator Computer}
    \begin{itemize}
%\vspace*{0.2cm}

      \item Distributed memory parallel \\
            computer
%\vspace*{0.2cm}

% \vspace*{0.3cm}
      \item   Very   cost   effective,  \\
              affordable,  high  availability,\\
              design exportable to Companies, \\
              Regulatory Agencies, Universities
%\vspace*{0.2cm}

% \vspace*{0.3cm}
      \item  Same  architecture  as  large \\
             parallel supercomputers\\
             (SDSC, TACC, EarthSimulator...)
%\vspace*{0.2cm}

% \vspace*{0.3cm}
      \item Current version at UCD, \\
            new version to be acquired soon
      

%
\vspace*{-5.6cm}
\begin{figure}[!htbp] 
%\hspace*{6cm}
\begin{flushright}
\includegraphics[width=4.2cm]{/home/jeremic/tex/works/Conferences/2010/Ottawa_SSI_conference/Present/Geowulf.jpg}
%\includegraphics[width=5cm]{/home/jeremic/public_html/GeoWulf/Dec2006/IMG_0907.jpg}
\end{flushright}
\hspace*{-2cm}
\end{figure}

      
%      \item Local design, construction,
%      available at all times!
%\vspace*{0.2cm}

%      \item 
%%\vspace*{0.2cm}

    \end{itemize}


\end{frame}

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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%   \frametitle{NRC ESSI Simulator Computer: Architecture}
% 
% 
% %
% %\vspace*{-0.6cm}
% \begin{figure}[!htbp] 
% \begin{center}
% \includegraphics[width=11truecm]{/home/jeremic/tex/works/psfigures/ParallelGeoWulf07.pdf}
% %\hspace*{0.1cm}
% %\includegraphics[width=3truecm]{/home/jeremic/public_html/NSF-Nuggets/Students_develop_parallel_computer/StudentsConstructingGeoWulf.jpg}
% \end{center}
% \end{figure}
% 
% 
% 
% 
% 
% 
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%   \frametitle{NRC ESSI Simulator Computer: Space and Cooling}
% 
% %
% %\vspace*{-5.6cm}
% \begin{figure}[!htbp] 
% %\hspace*{6cm}
% %\begin{center}
% \includegraphics[width=8truecm]{/home/jeremic/public_html/GeoWulf/Dec2006/IMG_0907.jpg}
% %\hfill
% %%\hspace*{6cm}
% %\includegraphics[width=6truecm]{/home/jeremic/public_html/NSF-Nuggets/Students_develop_parallel_computer/StudentsConstructingGeoWulf.jpg}
% %\end{center}
% \end{figure}
% 
% 
% 
% \end{frame}
% % 
% 
% 
% 
% 
% 
% 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
  \frametitle{Illustrative Example: Free Field}

%
%\vspace*{-5.6cm}
\begin{figure}[!htbp] 
%\hspace*{6cm}
%\begin{center}
\includegraphics[width=10truecm]{/home/jeremic/tex/works/Conferences/2010/Ottawa_SSI_conference/Paper/model_FF.jpg}
%
%/home/jeremic/tex/works/Conferences/2010/NRC-LBL-ProjectReviewMeeting_21_22_Sept_2010/VisIt_Full_Model_DRM_1.jpeg}
%\hfill
%%\hspace*{6cm}
%\includegraphics[width=6truecm]{/home/jeremic/public_html/NSF-Nuggets/Students_develop_parallel_computer/StudentsConstructingGeoWulf.jpg}
%\end{center}
\end{figure}




%

\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
  \frametitle{Illustrative Example: ESSI for NPPs}

%
%\vspace*{-5.6cm}
\begin{figure}[!htbp] 
%\hspace*{6cm}
%\begin{center}
\includegraphics[width=10truecm]{/home/jeremic/tex/works/Conferences/2010/Ottawa_SSI_conference/Paper/model_SSI.jpg}
%\includegraphics[width=10truecm]{/home/jeremic/tex/works/Conferences/2010/Ottawa_SSI_conference/Paper/model_FF.jpg}
%/home/jeremic/tex/works/Conferences/2010/NRC-LBL-ProjectReviewMeeting_21_22_Sept_2010/VisIt_Excavated_Material_DRM_3.jpeg}
%\hfill
%%\hspace*{6cm}
%\includegraphics[width=6truecm]{/home/jeremic/public_html/NSF-Nuggets/Students_develop_parallel_computer/StudentsConstructingGeoWulf.jpg}
%\end{center}
\end{figure}




%

\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
  \frametitle{Seismic Input: Green's Function  and DRM}



%
%\vspace*{-5.6cm}
\begin{figure}[!htbp] 
%\hspace*{6cm}
%\begin{center}
\includegraphics[width=9truecm]{/home/jeremic/tex/works/Conferences/2010/NRC-LBL-ProjectReviewMeeting_21_22_Sept_2010/Map_of_Points.pdf}
%\hfill
%%\hspace*{6cm}
%\includegraphics[width=6truecm]{/home/jeremic/public_html/NSF-Nuggets/Students_develop_parallel_computer/StudentsConstructingGeoWulf.jpg}
%\end{center}
\end{figure}

%

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
  \frametitle{Free field Motions: Lack of Correlation}


%
\vspace*{-0.5cm}
\begin{figure}[!htbp] 
%\hspace*{6cm}
%\begin{center}
\includegraphics[width=10truecm]{/home/jeremic/tex/works/Conferences/2010/NRC-LBL-ProjectReviewMeeting_21_22_Sept_2010/Time_History_Plots.pdf}
%\hfill
%%\hspace*{6cm}
%\includegraphics[width=6truecm]{/home/jeremic/public_html/NSF-Nuggets/Students_develop_parallel_computer/StudentsConstructingGeoWulf.jpg}
%\end{center}
\end{figure}


%

\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
  \frametitle{Free field Motions: Lack of Correlation}


%
\vspace*{-0.5cm}
%\vspace*{-5.6cm}
\begin{figure}[!htbp] 
%\hspace*{6cm}
%\begin{center}
\includegraphics[width=10truecm]{/home/jeremic/tex/works/Conferences/2010/NRC-LBL-ProjectReviewMeeting_21_22_Sept_2010/Time_History_Plots_Zoomed.pdf}
%\hfill
%%\hspace*{6cm}
%\includegraphics[width=6truecm]{/home/jeremic/public_html/NSF-Nuggets/Students_develop_parallel_computer/StudentsConstructingGeoWulf.jpg}
%\end{center}
\end{figure}


%

\end{frame}

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


\subsection{Verification and Validation}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Verification, Validation and Prediction}


\begin{itemize}

     \item 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}


     \item 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}


   \item Prediction:  use  of  computational  model  to foretell the state of
   an NPPSSS under  conditions  for  which  the
   computational model has not been validated
\end{itemize}

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



\vspace*{0.5truecm}

\begin{figure}[!h]
\begin{center}
{\includegraphics[width=8.0cm]{/home/jeremic/tex/works/Presentation/2003/Verif_and_Valid/RoleVV.pdf}}
\end{center}
\end{figure}



%   \vspace*{-2.5truecm}

\end{frame}

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Verification and Validation for Prediction}



\begin{itemize}


%\vspace*{0.5cm}
\item How much can (should) we trust  model implementations (verification)?

%\vspace*{0.5cm}
\item How much can (should) we trust numerical simulations (validation)?

%\vspace*{0.5cm}
\item How good are our numerical predictions?

%\vspace*{0.5cm}
\item  Can  a  simulation  tool  (NRC ESSI Simulator) be used for assessing {\bf
public safety}?


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


%   \vspace*{0.2truecm}
   \item  Ever  present  uncertainties need to be modeled and propagated  through
   the simulation process




% %\vspace*{1.0truecm}
% \item  V  \&  V  procedures  are the tools with which we build confidence and
% credibility in modeling and computational simulations
% 

%\vspace*{2.5cm}
%\item How do we  use experimental simulations   to improve models




\end{itemize}




\end{frame}

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% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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*{1.0truecm}
%    \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{Fundamentals of Verification and Validation}
% 
% 
% 
% %--
% 
% 
% \begin{figure}[!h]
% %\vspace*{-0.5cm}                                                    
% %\hspace*{-0.5cm}                                                    
% %\begin{center}
% {\includegraphics[width=11cm]{/home/jeremic/tex/works/Conferences/2005/OpenSeesWorkshopAugust/DeveloperSymposium/VerifValidFund01.pdf}}
% %\end{center}
% \end{figure}
% 
% 
% \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*{0.5truecm}
%  %   \item Validation does not directly make a claim about the accuracy of a prediction
%     \item Validation does not claim 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}
%  
%  
%  %   \vspace*{0.2truecm}
%     \item Ever present uncertainty needs to be estimated for predictions
%  
%  %   \vspace*{0.2truecm}
%     \item  Identify  all  relevant sources of uncertainty 
%  
%  %   \vspace*{0.2truecm}
%     \item Create mathematical representation of individual sources
%  
%  %   \vspace*{0.2truecm}
%     \item Propagate representation of sources through modeling and simulation process
%  
%  
%  
%  
%  \end{itemize}
%  
%  
%  
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Uncertainty Aspects}




\subsection{Uncertain Engineering Materials}





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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}

\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{Eulerian--Lagrangian FPK Equation}
% 
% %
% 
% %\begin{itemize}
% 
% \begin{footnotesize}
% % 
% % %\noindent
% % van  Kampen's  Lemma (van Kampen 1976) $\rightarrow$  $  <\rho(\sigma,t)>=P(\sigma,t) $, 
% % ensemble average of phase density 
% % %(in stress space here) 
% % is the probability density;
% 
% 
% \begin{eqnarray}
% \nonumber
% &&\displaystyle \frac{\partial P(\sigma(x_t,t), t)}{\partial t}=
% - \displaystyle \frac{\partial}{\partial \sigma} \left[ \left\{\left< \vphantom{\int_{0}^{t} d\tau} \eta(\sigma(x_t,t), D^{el}(x_t),
% q(x_t), r(x_t), \epsilon(x_t,t)) \right> \right. \right. \\
% \nonumber
% &+& \left. \left. \int_{0}^{t} d\tau Cov_0 \left[ \displaystyle \frac{\partial \eta(\sigma(x_t,t), D^{el}(x_t), q(x_t), r(x_t),
% \epsilon(x_t,t))}{\partial \sigma}; \right. \right. \right. \\
% \nonumber
% & & \left. \left. \left. \eta(\sigma(x_{t-\tau},t-\tau), D^{el}(x_{t-\tau}), q(x_{t-\tau}), r(x_{t-\tau}),
% \epsilon(x_{t-\tau},t-\tau) \vphantom{\int_{0}^{t} d\tau} \right] \right \} P(\sigma(x_t,t),t) \right] \\
% \nonumber
% &+& \displaystyle \frac{\partial^2}{\partial \sigma^2} \left[ \left\{ \int_{0}^{t} d\tau Cov_0 \left[ \vphantom{\int_{0}^{t}}
% \eta(\sigma(x_t,t), D^{el}(x_t), q(x_t), r(x_t), \epsilon(x_t,t)); \right. \right. \right. \\
% \nonumber
% & & \left. \left. \left. \eta (\sigma(x_{t-\tau},t-\tau), D^{el}(x_{t-\tau}), q(x_{t-\tau}), r(x_{t-\tau}),
% \epsilon(x_{t-\tau},t-\tau)) \vphantom{\int_{0}^{t}} \right] \vphantom{\int_{0}^{t}} \right\} P(\sigma (x_t,t),t) \right] \\
% \nonumber
% \end{eqnarray}
% 
% \end{footnotesize}
% 
% 
% \end{frame}
% 
% 
% 
% 
% 
% 
% 
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% 

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\begin{frame} 

\frametitle{Probabilistic Elasto-Plasticity (PEP) and
Stochastic Elastic-Plastic Finite Element Method (SEPFEM)}

 

\begin{itemize}

%\vspace*{0.3cm}
\item  PEP:  Eulerian--Lagrangian  form  of  the  Fokker-Planck-Kolmogorov (FPK)
equation
%
% \begin{equation}                
% \nonumber
% \frac{\partial P(\sigma,t)}{\partial t} = -\frac{\partial}{\partial \sigma}\left[N_{(1)}P(\sigma,t)-\frac{\partial}{\partial \sigma}
% \left\{N_{(2)} P(\sigma,t)\right\} \right]
% \end{equation}
% 
%

  \begin{itemize}
    \item Input, probability distribution of material properties

%\vspace*{0.3cm}
    \item  Output:  Complete     probabilistic    description    of 
    response, solution is a Probability Density Function (PDF) of stress


%\vspace*{0.3cm}
    \item Solution PDF is second-order {\bf exact} to covariance of time (exact mean and variance)

  \end{itemize}

% \item It is deterministic equation in probability density space
% 
% \item It is linear PDE in probability density space 
% %$\rightarrow$ simplifies the numerical solution process






% 
% %\vspace*{0.3cm}
% \item   PEP: Probabilistic  Elastic-Plastic  solution  applicable to any incremental
% elasto-plasticity material model
%




\item PEP $+$ Spectral Stochastic Finite Element Method
%

  \begin{itemize}
    \item  Input:  PDF for material properties (LHS), probabilistic
    seismic loading (RHS)


    \item   Output:  accurate,  full PDF of displacements (and
    $\dot{u}_i$, $\ddot{u}_i$), stress, strain, etc.

  \end{itemize}



%\vspace*{0.2truecm}

\end{itemize}

% 
% \vspace*{0.5cm}
% {%
% \begin{beamercolorbox}{section in head/foot}
% \usebeamerfont{framesubtitle}\tiny{B. Jeremi\'{c}, K. Sett, and M. L. Kavvas, "Probabilistic
% Elasto--Plasticity: Formulation in 1--D", \textit{Acta Geotechnica}, Vol. 2, No. 3, 2007, In press (published
% online in the \textit{Online First} section)}
% %\vskip2pt\insertnavigation{\paperwidth}\vskip2pt
% \end{beamercolorbox}%
% }



\end{frame}



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% \begin{frame} 
% 
% \frametitle{{Low OCR Cam Clay  with  Random $G$, $M$ and $p_0$}}
% 
% 
% 
% 
% 
% \begin{itemize}
% 
% %\item Narrow transition between el. \& el.-pl.
% 
% 
% \vspace*{0.3cm}
% \item Non-symmetry in \\
%       probability \\
%       distribution
% 
% 
% \vspace*{0.3cm}
% \item Difference \\
%       between \\
%       mean, mode and \\
%       deterministic 
% 
% 
% 
% \vspace*{0.3cm}
% \item Divergence at \\
%       critical state \\
%       because $M$ might be \\
%       (is) uncertain?
% 
% \end{itemize}
% 
% 
% \vspace*{-6.3cm}
% %\hspace*{0.5cm}
% \begin{figure}[!hbpt]
% \begin{flushright}
% %\includegraphics[height=3.5cm]{/home/jeremic/tex/works/Conferences/2006/KallolsPresentationGaTech/PDFLowOCR_RandomG_RandomM_Randomp0-m.pdf}
% %\hfill
% \includegraphics[height=6.5cm]{/home/jeremic/tex/works/Conferences/2006/KallolsPresentationGaTech/ContourLowOCR_RandomG_RandomM_Randomp0-m.pdf}
% \end{flushright}
% \end{figure}
% 
% 
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% 
% \end{frame}
% % --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% \begin{frame} 
% 
% \frametitle{Comparison of Low OCR Cam Clay at $\epsilon$ = 1.62 \%}
% 
% 
% 
% %\vspace*{-4.50cm}
% 
% \begin{figure}[!hbpt]
% \begin{center}
% %\includegraphics[height=14cm]{/home/jeremic/tex/works/Conferences/2006/KallolsPresentationGaTech/CamClayPDFComparison-m.pdf}
% \includegraphics[height=5.0cm]{/home/jeremic/tex/works/Conferences/2007/USC_seminar/Present/LowOCR_ComparisonPDF-m_ps.pdf}
% \end{center}
% \end{figure}                                                          
% 
% \vspace*{-0.5cm}
% 
% \begin{itemize}
% 
% \item None coincides with deterministic
% 
% \item Some  very uncertain, some very certain
% 
% \item Either on safe or unsafe side
% 
% \end{itemize}
% 
%  
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% 
% 
% \end{frame}
% 
% 
% 
% 
% 
% 
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% 
% \begin{frame}
% \frametitle{Spectral Stochastic Elastic--Plastic FEM}
% 
% \begin{itemize}
% 
% \item  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}{D}^{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}
% 
% %\item Fokker--Planck--Kolmogorov approach based probabilistic constitutive integration
% %      at Gauss integration points
% 
% 
% \end{itemize}
% 
% %
% \end{frame}
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\subsection{Uncertain Seismic Motions}


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\begin{frame}


\frametitle{Decision About Site (Material) Characterization}




\begin{itemize}

\vspace*{0.3cm}
\item  Do an inadequate site characterization (rely on experience): conservative
{\bf guess}  for  soil  data, $COV  = 225$\%, large correlation length (length of
a model).


\vspace*{0.3cm}
\item  Do a good site characterization: $COV = 103$\%, correlation
length calculated ($= 0.61$m)


\vspace*{0.3cm}
\item Do an excellent (much improved) site characterization if  probabilities of exceedance
are unacceptable!


\end{itemize}

\end{frame}

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\begin{frame}


\frametitle{Random Field Parameters from Site Data}

\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}

\end{frame}


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\begin{frame}




\frametitle{"Uniform" CPT  Site Data (Courtesy of USGS)}


\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{Statistics of Stochastic Soil Profile(s)}

%\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{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}

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\end{frame}

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\begin{frame}


\frametitle{Evolution of Mean $\pm$ SD for Real Data 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_Actual-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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\begin{frame}


\frametitle{Full PDFs for Real Data Case}



\begin{figure}
\begin{center}
\vspace*{-0.75cm}
\includegraphics[width=7.0cm]{/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{center}
\end{figure}

% 
\end{frame}

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\begin{frame}


\frametitle{Example: PDF 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{Example: CDF 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 ($50$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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\begin{frame}

\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}
 
\end{frame}

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\section{Summary}
\subsection{}

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\begin{frame} 

\frametitle{Summary}


\begin{itemize}

\item There is a need for high fidelity modeling and simulations 
(verified and validated,  deterministic and probabilistic) for NPPSSSs

%\vspace*{0.2cm}
\item  Such  high  fidelity  modeling  and  simulations  will improve safety and
economy

%\vspace*{0.2cm}
\item  Education  for  Developers,  Modelers/Analysts, Researchers, Consultants,
Regulators is very important


%\vspace*{0.2cm}
\item  Presented  research  was/is funded in part and performed in collaboration
with the Caltrans, NSF, U.S. NRC and CNSC


%\vspace*{0.2cm}
\item   CompDyn2011  Corfu,  Greece,  26-28  May,  Soil-Structure  Interaction
Mini-Symposium


 
\end{itemize}

\end{frame}

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\end{document}


