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\title[Modeling and Simulation Uncertainty]
        {Modelling and Simulation Uncertainty}


%\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.
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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}}
{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 Computational Mechanics Working Group \\
  UC Davis, February 2016}

\subject{}
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%   just say so once. Everybody will be happy with that.



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\section{Introduction}




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\subsection{Motivation}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
 \frametitle{Motivation}

\begin{itemize}



%\vspace*{0.3cm}
  \item Improve seismic design of soil structure systems


\vspace*{1mm}
  \item      {E}arthquake {S}oil {S}tructure {I}nteraction
  ({ESSI}) in time and space, plays a major role in successes and failures



%\vspace*{0.1cm}
\vspace*{1mm}
  \item  Accurate  following  and directing (!) the  flow  of  seismic energy in
  ESSI system to optimize for
    \begin{itemize}
      \item Safety and
      \item Economy
    \end{itemize}


%\vspace*{0.1cm}
\vspace*{1mm}
  \item  Development of  high  fidelity  numerical modeling and simulation tools
  to analyze realistic ESSI behavior: \\
  {Real ESSI} simulator
%   ({\small aka}: {\cyrssDvanaest Stvarno  Lako},
% { Muy F{\'a}cil},
% {Molto  Facile},
% \raisebox{-1.2mm}{\includegraphics[height=5mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Chinese.jpeg}},
% \raisebox{-1.2mm}{\includegraphics[height=5mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Japanese.jpg}},
% {\greektext{Pragmatik'a E'ukolo}},
% \raisebox{-1.2mm}{\includegraphics[height=5mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Farsi.jpg}},
% {Tr{\`e}s Facile},
% {\cyrssDvanaest Vistinski Lesno}
% %{Wirklich Einfach}
% )

\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Predictive Capabilities}
% \frametitle{High Fidelity Modeling of SFS System:
% Verification, Validation and Prediction}

\begin{itemize}


     \item  {{  Verification}  provides  evidence  that  the  model is solved
     correctly.} Mathematics issue.

%\vspace*{0.1cm}
\vspace*{1mm}
     \item  {{  Validation}  provides  evidence  that  the  correct  model is
     solved.} Physics issue.

%\vspace*{0.1cm}
\vspace*{1mm}
   \item {  Prediction under Uncertainty (!)}:  use  of  computational  model
   to  predict  the  state  of SSI system under
   conditions for which the computational model has not been validated.


\vspace*{1mm}
   \item Modeling and Parametric Uncertainties


\vspace*{1mm}
   \item Predictive capabilities with {low Kolmogorov Complexity}


\vspace*{1mm}
     \item Modeling and simulation goal: \\
      predict and inform, rather than (force) fit

%
\end{itemize}


\end{frame}






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\subsection{Uncertainties}
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\begin{frame}
 \frametitle{Modeling Uncertainty}

\begin{itemize}



  \item      Simplified  modeling:    Features (important ?)   are neglected (6D
  ground motions, inelasticity)

\vspace*{4mm}
     \item   Modeling   Uncertainty:   unrealistic   and   unnecessary  modeling
     simplifications

\vspace*{4mm}
     \item  Modeling  simplifications   are  justifiable  if  one  or  two  level  higher
     sophistication  model  shows  that  features  being  simplified out are not
     important



\end{itemize}
\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Parametric Uncertainty: Material Stiffness}


%\vspace*{-3mm}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-7mm}
\includegraphics[width=7.0truecm]{/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*{-1.8cm}
% %\hspace*{-3.3cm}
% \begin{flushright}
% {\tiny
% Transformation  of SPT $N$-value: \\
% 1-D Young's modulus, $E$ \\
% (cf. Phoon and Kulhawy (1999B))\\
% ~}
% \end{flushright}
%
\end{frame}


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Parametric Uncertainty: Material Strength}
% 
% 
% \begin{figure}[!hbpt]
% \begin{center}
% %
% \hspace*{-7mm}
% \includegraphics[width=6.50truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_RawData_and_MeanTrend-Mod.pdf}
% \hspace*{-7mm}
% % \hfill
% \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_Histogram_PearsonIV-FineTuned-Mod.pdf}
% %
% \end{center}
% \end{figure}
% 
% % \vspace*{-1.8cm}
% % %\hspace*{-3.3cm}
% % \begin{flushright}
% % {\tiny
% % Transformation  of SPT $N$-value: \\
% % 1-D Young's modulus, $E$ \\
% % (cf. Phoon and Kulhawy (1999B))\\
% % ~}
% % \end{flushright}
% % %
% 
% 
% \end{frame}
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Parametric Uncertainty: Material Properties}



\begin{figure}[!hbpt]
\begin{center}
% %
\hspace*{-3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldPhiPdf.pdf}
\hspace*{-3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldPhiCdf.pdf}
\hspace*{3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldSuPdf.pdf}
\hspace*{-3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldSuCdf.pdf}
\\
%\vspace*{-2mm}
\hspace*{-2.5cm} \mbox{\tiny Field $\phi$} \hspace*{3.5cm} \mbox{\tiny Field $c_u$}
%\vspace*{45mm}
\hspace*{-3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabPhiPdf.pdf}
\hspace*{-3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabPhiCdf.pdf}
\hspace*{3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabSuPdf.pdf}
\hspace*{-3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabSuCdf.pdf}
\\
%\vspace*{-8mm}
\hspace*{-2.5cm} \mbox{\tiny Lab $\phi$} \hspace*{3.5cm} \mbox{\tiny Lab $c_u$}
\end{center}
\end{figure}

\end{frame}



% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Realistic ESSI Modeling (Uncertainties)}
% 
% 
% \begin{itemize}
% 
% 
% \item   Seismic   Motions:  6D,  inclined,  body  and  surface  waves
% (translations, rotations)
% %; Incoherency
% 
% %\vspace*{3mm}
% \vspace*{1mm}
% \item    Inelastic    material:    soil (dry, saturated),   rock,   concrete,   steel   
% 
% \vspace*{1mm}
% \item Inelastic contact: foundation--soil, dry, saturated, slip--gap
% 
% \vspace*{1mm}
% \item  Nonlinear buoyant forces 
% 
% \vspace*{1mm}
% \item Base Isolators, Dissipators
% 
% \vspace*{1mm}
%     \item Uncertain loading and material
% 
% \vspace*{1mm}
%      \item Verification and Validation  $\Rightarrow$  Predictions
% 
% 
% \end{itemize}
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% 
% 
% 
% 

%
%
















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\subsection{Real ESSI Simulator}



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

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

\begin{itemize}

\item {\bf The Real ESSI-Program} is a 3D, nonlinear, time domain,
parallel finite element program specifically developed for
Hi-Fi modeling  and  simulation  of  Earthquake  Soil/Rock  Structure
Interaction problems for NPPs (infrastructure objects) on ESSI-Computers. \
%The NRC ESSI Program is based on
%a  number of public domain numerical libraries developed at UCD as well as those
%available  on  the  web,  that  are  compiled  and  linked  together to form the
%executable  program (NRC-ESSI-Program). Significant effort is devoted to development
%of  verification  and  validation  procedures,  as  well  as  on  development of
%extensive  documentation.  NRC-ESSI-Program  is  in  public  domain  and is licensed
%through the Lesser GPL.

%\vspace*{0.3cm}
\vspace*{1mm}
\item {\bf The Real ESSI-Computer} is a distributed memory
parallel computer, a cluster of clusters with multiple performance
processors and multiple performance networks.
%Compute  nodes are Shared Memory Parallel
%(SMP)  computers,  that  are  connected,  using  high  speed  network(s), into a
%Distributed Memory Parallel (DMP) computer.

%\vspace*{0.3cm}
\vspace*{1mm}
\item    {\bf        The Real  ESSI-Notes} represent a hypertext
documentation system
(Theory and Formulation, Software and Hardware, Verification and Validation, and
Case  Studies  and  Practical  Examples)
detailing modeling and simulation of ESSI
problems.
%
%the
%NRC-ESSI-Program  code  API (application Programming Interface) and DSLs (Domain
%Specific Language).
%%NRC-ESSI-Notes,    developed  by Boris Jeremic and collaborators, are in public
%domain
%%and  are  licensed  under a Creative Commons Attribution-ShareAlike 3.0 Unported
%%License.
%
%\vspace*{0.3cm}
\end{itemize}

\end{frame}


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

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


\begin{itemize}


\item Developed with funding from US-NRC, US-NSF, CNSC-CCSN, and US-DOE



\vspace*{2mm}
\item  The  Real  ESSI  simulator  system  is  designed based on premise of high
fidelity modeling and simulation

\vspace*{2mm}
\item Reduction of modeling uncertainty and propagation of parametric uncertainty

\vspace*{2mm}
\item 
   Real ESSI simulator, also known as 
   {\small{\cyrssDvanaest Vrlo Prosto},
\raisebox{-1.2mm}{\includegraphics[height=4mm]  {/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Chinese.jpeg}},
\raisebox{-1.2mm}{\includegraphics[height=4mm]  {/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Bengali.pdf}},
{ Muy F{\'a}cil},  
{Molto  Facile},  
\raisebox{-1.2mm}{\includegraphics[height=4.2mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Japanese.jpg}},
{\greektext{Pragmatik'a E'ukolo}},
\raisebox{-1.6mm}{\includegraphics[height=5mm]  {/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Hindi.jpg}},
\raisebox{-1.2mm}{\includegraphics[height=5mm]  {/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Farsi.jpg}},
{Tr{\`e}s Facile}, 
{\cyrssJedanaest Vistinski Lesno},
{Wirklich Einfach},
\raisebox{-1.6mm}{\includegraphics[height=5mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Arabic.jpg}}.

%\raisebox{-1.2mm}{\includegraphics[height=4.5mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Chinese.jpeg}},
%{ Muy F{\'a}cil},
%{Molto  Facile},
%\raisebox{-1.2mm}{\includegraphics[height=4mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Japanese.jpg}},
%{\greektext{Pragmatik'a E'ukolo}},
%\raisebox{-1.2mm}{\includegraphics[height=4.5mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Hindi.jpg}},
%\raisebox{-1.2mm}{\includegraphics[height=4mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Farsi.jpg}},
%{Tr{\`e}s Facile},
%{\cyrssDvanaest Vistinski Lesno},
%{Wirklich Einfach},
%\raisebox{-0.80mm}{\includegraphics[height=5.2mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Arabic.jpg}}.
}


\end{itemize}


\end{frame}


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

\begin{frame}
\frametitle{Real ESSI  Modelling}


\vspace*{4mm}
\begin{figure}[!hbpt]
\begin{center}
\includegraphics[width=3.2cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Theory_Introduction/tex_works_psfigures_loading_stage-increments-iterations.pdf}
%\caption{\label{loading_stages-increments_iterations} }
\end{center}
%\vspace*{-0.5cm}
\end{figure}
%
\end{frame}

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Verification and Validation for High Fidelity Predictive Capabilities}
% \frametitle{High Fidelity Modeling of SFS System:
% Verification, Validation and Prediction}


\begin{itemize}


% \vspace*{0.2cm}
%    \item {\bf Prediction}:  use  of  computational  model  to foretell the state
%    of  a  physical  system  under  consideration  under conditions for which the
%    computational model has not been validated.


\vspace*{3mm}
     \item {{Verification} provides evidence that the
   model is solved correctly.} Mathematics issue.

\vspace*{3mm}
     \item {{Validation} provides
   evidence that the correct model is solved.} Physics issue.


\vspace*{3mm}
   \item Goal: predictive capabilities with low information (Kolmogorov) Complexity

% %% % \vspace*{0.2cm}
% %   \item {\bf The Finite Element
% %   Interpreter  \FEI{}} might be one such
% %   predictive tool (application program)

\end{itemize}

\end{frame}





























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\section{Modeling and Parametric Uncertainty}


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\subsection{Modeling Uncertainty: 3D Dam/Slope Model, Expert Opinion}


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\begin{frame} 

\frametitle{3D Dam -- Slope Stability}


\begin{itemize}

  \item 3D earth slope part of a concrete, earth dam

%  \vspace*{3mm}
  \item Movements recorded during lowering of reservoir
  
%  \vspace*{3mm}
  \item  3D  slope  unstable (?), no one could tell, all  commercial software
  does 2D slope stability

%  \vspace*{3mm}
  \item 2D vs 3D slope stability

%  \vspace*{3mm}
  \item  Shear  strength  (?)  as  the  only material parameter
  
  \item  (")Expert(") increased value of measured shear strength

   \item Load cases: lowering and raising reservoir, slow and fast
   
   \item Dam build using untreated alluvium 


\end{itemize}

\end{frame}

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

\begin{frame}
 \frametitle{Dam, Satellite Photo}

%
\begin{figure}[!htbp] 
\begin{center}
\includegraphics[width=10.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WolfCreekDam_SateliteView01.jpg}
%\hspace*{-0.9cm}
%bridge.}
\end{center}
\end{figure}
%
\end{frame}
%- 
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\begin{frame}
 \frametitle{Dam, 3D Slope, Satellite Photo}

%
\begin{figure}[!htbp] 
\begin{center}
\includegraphics[width=10.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WolfCreekDam_SateliteView02.jpg}
%\hspace*{-0.9cm}
%bridge.}
\end{center}
\end{figure}
%
\end{frame}
%- 
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\begin{frame}
 \frametitle{3D Slope}

%
\begin{figure}[!htbp] 
\begin{center}
\includegraphics[width=10.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WolfCreekDam_SatelliteView_with_slope01.jpg}
%\hspace*{-0.9cm}
%bridge.}
\end{center}
\end{figure}
%
\end{frame}
%- 
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\begin{frame}
 \frametitle{3D Slope, Ground Photo}

%
\begin{figure}[!htbp] 
\begin{center}
\includegraphics[width=9.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/img-0188.jpg}
%\hspace*{-0.9cm}
%bridge.}
\end{center}
\end{figure}
%
\end{frame}
%- 
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\begin{frame}
 \frametitle{Dam, Construction Photo}

%
\begin{figure}[!htbp] 
\begin{center}
\includegraphics[width=10.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WolfCreekDam_Q2-61_621_Embankment_Sep_30_48.jpg}
%\hspace*{-0.9cm}
%bridge.}
\end{center}
\end{figure}
%
\end{frame}
%- 
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}
 \frametitle{Dam, Section}


%
\begin{figure}[!htbp] 
\begin{center}
\includegraphics[width=10.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WolfCreekDam_PerpendicularSection.jpg}
%\hspace*{-0.9cm}
%bridge.}
\end{center}
\end{figure}
%
\end{frame}
%- 
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}
 \frametitle{Dam, Model}

%
\begin{figure}[!htbp] 
\begin{center}
\includegraphics[width=5.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/3D_final02.jpg}
\includegraphics[width=5.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/3D_final04.jpg}
//
\includegraphics[width=5.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/3D_final05.jpg}
\includegraphics[width=5.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/3D_final_Top.jpg}

%\hspace*{-0.9cm}
%bridge.}
\end{center}
\end{figure}
%
\end{frame}
%- 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}
 \frametitle{Dam Slope, Failure Modes}


 \vspace*{5mm}
 \begin{itemize}

   \item 3D failure pattern

   \item 3D has lower FS than 2D

   \item Original $S_u$ FS barely enough,
   \item  With "increased" $S_u$ a bit higher

 \end{itemize}



 \vspace*{-40mm}
\begin{figure}[!htbp] 
\begin{flushright}
\includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/Undrained-Su440-Vector-Plan_snapshot.jpg}
\end{flushright}
\end{figure}

 \vspace*{-10mm}

%
\begin{figure}[!htbp] 
\begin{center}
% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Drained_3D_AbsVal_L680_E680_Phi18_FS178.jpg}
% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Drained_3D_Vector_L680_E680_Phi18_FS178.jpg}
% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_drained_case_40_FS_1_89_displacement_vectors_factor_42_39.jpg}
% \\
% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Drained_L680_E680_Phi17_FS189.jpg}
% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_undrained_case_41_FS_1_43__displacement_vectors_factor_1_80.jpg}
% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Undrained_L680_E680_Su1200_FS167.jpg}
% \\
\includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Undrained_L680_E680_Su800_Alluvium_Su1500_FS250.jpg}
\includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Undrained_L680_E680_Su900_Alluvium_Su1000_FS222.jpg}
\includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Undrained_L680_E720_Su1300_FS154.jpg}
%\hspace*{-0.9cm}
%bridge.}
\end{center}
\end{figure}
%
\end{frame}
%- 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 




































%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Modeling Uncertainty: Bridge Model}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}
%  \frametitle{Detailed 3D Bridge Model}
% 
% %
% \begin{figure}[!htbp] 
% \begin{center}
% \includegraphics[width=8.0cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
% %\hspace*{-0.9cm}
% %bridge.}
% \end{center}
% \end{figure}
% %
% \end{frame}
% %- 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % 
% % \begin{frame}
% %  \frametitle{Model Components}
% % 
% % %
% % \begin{itemize}
% %  \item   Soils:   elastic--plastic   solids   (yield   land   potential  surface
% %  Drucker-Prager, kinematic hardening Armstrong-Frederick) (UCD: Jie and Jeremi{\'c})
% % \vspace*{0.2cm}
% %  \item Structure non--linear  beam--column elements (fiber element) 
% %   (UCB: Fenves, UW: Eberhardt) 
% % 
% % \vspace*{0.2cm}
% %   \item Piles: non--linear  beam--column elements (fiber element) (UCD: Jie and Jeremi{\'c})
% % 
% % 
% % \vspace*{0.2cm}
% %   \item Two types of soil: stiff soil (UT, UCD), soft soil (Bay Mud)
% % 
% % \vspace*{0.2cm}
% %   \item  Use of the Domain Reduction Method (DRM) (Bielak et al.) for seismic
% %   input into FEM model
% % 
% % 
% % \end{itemize}
% % 
% % \end{frame}
% % %- 
% % 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Modeling Issues}
% 
%    \begin{itemize}
% 
% \vspace*{0.2cm}
%   \item Construction process
% 
% \vspace*{0.2cm}
%   \item Deconvolution of given surface ground motions
% 
% \vspace*{0.2cm}
%   \item No artificial damping (only mat. dissipation, radiation)
% 
% \vspace*{0.2cm}
%   \item Element size issues (filtering of frequencies) 
% 
% \vspace*{-0.4cm}
% \begin{table}[!htbp]
% %\caption{ }
% \begin{center}
% \begin{tabular}{|r|c|c|c|c|} 
% \hline
% elem. \# &  elem.  size  &  $f_{cutoff}$  & min. $G^{ep}/Gmax$ & $\gamma$  \\
% \hline
% %
% %
% % 100cm element model, f_cuttof=10HZ, G/Gmax=1.0, 12K elements, Gmax model
% 12K         &  1.00~m          &  10~Hz      & 1.0      & <0.5~\% \\
% %
% %
% %~90cm element model, f_cutoff ~= 3Hz, G/Gmax~=0.08, for epsilon ~= 1%, 15K
% %elements, now running...
% 15K         &  0.90~m          &  >3~Hz     & 0.08            & <1.0~\% \\
% %
% %
% %27.6cm element model, f_cutoff= 10HZ, G/Gmax=0.08, for epsilon = 1%, 150K
% %elements, finest model
% 150K        &  0.30~m          &  10~Hz      & 0.08            & <1.0~\% \\
% 500K        &  0.15~m          &  10~Hz      & 0.02            & <5.0~\% \\
% % 27.6cm element model, f_cutoff= 10HZ, G/Gmax=0.08, for epsilon = 1%, 150K
% %elements, finest model
% \hline
% \end{tabular}
% \end{center}
% \end{table}
% 
%   \end{itemize}
% 
% 
% \end{frame}
% %- 
% %-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %-
% %-\begin{frame}
% %- \frametitle{FEM Mesh (one of)}
% %-
% %-%
% %-\begin{figure}[!htbp] 
% %-\begin{center}
% %-\includegraphics[width=8cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
% %-%\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
% %-%bridge.}
% %-\end{center}
% %-\end{figure}
% %-%
% %-\end{frame}
% %- 
% 
% %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %  \begin{frame}
% %    \frametitle{Northridge and Kocaeli Input Motions}
% %  
% %  
% %  \begin{figure}[!htbp] 
% %  \begin{center}
% %  \hspace*{-1cm}
% %  \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/InputMotion_Northridge.pdf}
% %  \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/LongMotion/InputMotion_Kocaeli.pdf}
% %  \hspace*{-1cm}
% %  \\
% %  \hspace*{-1cm}
% %  \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/InputMotion_Northridge_Spectrum.pdf}
% %  \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/LongMotion/InputMotion_Kocaeli_Spectrum.pdf}
% %  \hspace*{-1cm}
% %  %bridge.}
% %  \end{center}
% %  \end{figure}
% %  %
% %  
% %  \end{frame}
% %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %  
% %  \begin{frame}
% %    \frametitle{Simulation Results}
% %  
% %  
% %  \vspace*{-0.5cm}
% %  %\begin{landscape}
% %  \begin{figure}[!htbp]
% %  \begin{center}
% %  \hspace*{-1cm}
% %  \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispSoilBlock1.pdf}
% %  \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispBent1.pdf}
% %  \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispSoilBlock2.pdf}
% %  \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispBent2.pdf}
% %  \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispSoilBlock3.pdf}
% %  \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispBent3.pdf}
% %  \hspace*{-1cm}
% %  \\
% %  \hspace*{-1cm}
% %  \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelSoilBlock1.pdf}
% %  \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelBent1.pdf}
% %  \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelSoilBlock2.pdf}
% %  \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelBent2.pdf}
% %  \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelSoilBlock3.pdf}
% %  \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelBent3.pdf}
% %  \hspace*{-1cm}
% %  \\
% %  \hspace*{-1cm}
% %  \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispSoilBlock1_Spectrum.pdf}
% %  \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispBent1_Spectrum.pdf}
% %  \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispSoilBlock2_Spectrum.pdf}
% %  \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispBent2_Spectrum.pdf}
% %  \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispSoilBlock3_Spectrum.pdf}
% %  \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispBent3_Spectrum.pdf}
% %  \hspace*{-1cm}
% %  \\
% %  \hspace*{-1cm}
% %  \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelSoilBlock1_Spectrum.pdf}
% %  \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelBent1_Spectrum.pdf}
% %  \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelSoilBlock2_Spectrum.pdf}
% %  \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelBent2_Spectrum.pdf}
% %  \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelSoilBlock3_Spectrum.pdf}
% %  \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelBent3_Spectrum.pdf}
% %  \hspace*{-1cm}
% %  \\
% %  \hspace*{-1cm}
% %  \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/MomentBent1Pile1.pdf}
% %  \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/MomentBent1Pile2.pdf}
% %  \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/MomentBent2Pile1.pdf}
% %  \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/MomentBent2Pile2.pdf}
% %  \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/MomentBent3Pile1.pdf}
% %  \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/MomentBent3Pile2.pdf}
% %  \hspace*{-1cm}
% %  \end{center}
% %  \end{figure}
% %  
% %  \vspace*{-0.8cm}
% %  \begin{figure}[!htbp] 
% %  \begin{center}
% %  \includegraphics[width=3.2cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
% %  %bridge.}
% %  \end{center}
% %  \end{figure}
% %  \vspace*{-2cm}
% %  
% %  
% %  \clearpage
% %  
% %  
% %  
% %  
% %  \end{frame}
% %  
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%   \frametitle{Short Period (Northridge) Input Motions}
% 
% 
% \vspace*{-0.7cm}
% \begin{figure}[!htbp] 
% \begin{center}
% \hspace*{-1cm}
% \includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/InputMotion_Northridge.pdf}
% \hspace*{-1cm}
% \\
% \hspace*{-1cm}
% \includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/InputMotion_Northridge_Spectrum.pdf}
% \hspace*{-1cm}
% %bridge.}
% \end{center}
% \end{figure}
% \vspace*{-1.0cm}
% %
% 
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%   \frametitle{Short Period Eq.: Left Bent, Displacements}
%   
% 
% 
% 
% \vspace*{-1cm}
% \begin{figure}[!htbp] 
% \begin{center}
% \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispBent1.pdf}
% %\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispBent1.pdf}
% \\
% \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispSoilBlock1.pdf}
% %\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispSoilBlock1.pdf}
% %bridge.}
% \end{center}
% \end{figure}
% 
% 
% \vspace*{-2.9cm}
% \hspace*{0.2cm}
% \begin{figure}[!htbp] 
% \begin{flushright}
% \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
% %bridge.}
% \end{flushright}
% \end{figure}
% \hspace*{-0.5cm}
% \vspace*{-2.0cm}
% 
% 
% 
% \end{frame}
% %-- 
% 
% 
% 
% 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% %   \frametitle{Short Period E.:  Left Bent, Structure and Soil, Acc.}
% %   
% % 
% % 
% % 
% % \vspace*{-1cm}
% % \begin{figure}[!htbp] 
% % \begin{center}
% % \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelBent1.pdf}
% % \\
% % \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelSoilBlock1.pdf}
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% %  \begin{frame}
% %    \frametitle{Short Period E.: Left Bent, Structure and Soil, Acc.Sp.}
% %    
% %  
% %  
% %  
% %  \vspace*{-1cm}
% %  \begin{figure}[!htbp] 
% %  \begin{center}
% %  \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelBent1_Spectrum.pdf}
% %  \\
% %  \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelSoilBlock1_Spectrum.pdf}
% %  %bridge.}
% %  \end{center}
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% %  \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
% %  %bridge.}
% %  \end{flushright}
% %  \end{figure}
% %  \hspace*{-0.5cm}
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% %  
% %  
% %  \end{frame}
% %  
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% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%   \frametitle{Short Period Eq.: Left Bent, Moments.}
%   
% 
% 
% 
% \vspace*{-1cm}
% \begin{figure}[!htbp] 
% \begin{center}
% \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/MomentBent1Pile1.pdf}
% \\
% \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/MomentBent1Pile2.pdf}
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% \begin{frame}
%   \frametitle{Short Period E.: Left Bent, Bending Moments}
%   
% 
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% \vspace*{-1cm}
% \begin{figure}[!htbp] 
% \begin{center}
% \includegraphics[width=11cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/MomentBent1Pile1_25s_SC.pdf}
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% 
% \vspace*{-2.9cm}
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% \begin{figure}[!htbp] 
% \begin{flushright}
% \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
% %bridge.}
% \end{flushright}
% \end{figure}
% \hspace*{-0.5cm}
% \vspace*{-2.0cm}
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% 
% \end{frame}
% %-- 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%   \frametitle{Short Period E.: Left Bent, Free Field vs Real Disp.}
%   
% 
% 
% 
% \vspace*{-1cm}
% \begin{figure}[!htbp] 
% \begin{center}
% \includegraphics[width=11cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispSoilBlock1_15cm_25s_SC.pdf}
% %bridge.}
% \end{center}
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% \vspace*{-2.9cm}
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% \begin{figure}[!htbp] 
% \begin{flushright}
% \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
% %bridge.}
% \end{flushright}
% \end{figure}
% \hspace*{-0.5cm}
% \vspace*{-2.0cm}
% 
% 
% \end{frame}
% %-- 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%   \frametitle{Long Period (Kocaeli) Input Motions}
% 
% 
% \vspace*{-0.7cm}
% \begin{figure}[!htbp] 
% \begin{center}
% \hspace*{-1cm}
% \includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/LongMotion/InputMotion_Kocaeli.pdf}
% \hspace*{-1cm}
% \\
% \hspace*{-1cm}
% \includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/LongMotion/InputMotion_Kocaeli_Spectrum.pdf}
% \hspace*{-1cm}
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% \begin{frame}
%   \frametitle{Long Period E.: Left Bent, Bending Moments.}
%   
% 
% 
% 
% %\vspace*{-1cm}
% \begin{figure}[!htbp] 
% \begin{center}
% %\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/MomentBent1Pile1.pdf}
% %\\
% \includegraphics[width=11cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/MomentBent1Pile2.pdf}
% %bridge.}
% \end{center}
% \end{figure}
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% 
% \vspace*{-2.9cm}
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% \begin{figure}[!htbp] 
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% \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
% %bridge.}
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% \end{figure}
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% \end{frame}
% %-- 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% % \begin{frame}
% %   \frametitle{Long Period E.: Left Bent, Structure and Soil, Disp.}
% %   
% % 
% % 
% % 
% % \vspace*{-1cm}
% % \begin{figure}[!htbp] 
% % \begin{center}
% % \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/DispBent1.pdf}
% % \\
% % \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/DispSoilBlock1.pdf}
% % %bridge.}
% % \end{center}
% % \end{figure}
% % 
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% % \vspace*{-2.9cm}
% % \hspace*{0.2cm}
% % \begin{figure}[!htbp] 
% % \begin{flushright}
% % \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
% % %bridge.}
% % \end{flushright}
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% % \hspace*{-0.5cm}
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% 












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\subsection{Modeling Uncertainty: Seismic Behavior of Nuclear Power Plants}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Modeling and Simulation of Nuclear Power Plants}


\begin{itemize}


\item Nuclear Power Plants (NPPs) design based on a number of simplified assumptions!

\vspace*{1mm}
\item Linear elastic material behavior

\vspace*{1mm}
\item Seismic Motions: $1$D  or $3 \times 1$D, or real 3D (6D)


\vspace*{1mm}
\item   Savings  in  construction  cost  possible with more accurate modeling of
NPPs


\vspace*{1mm}
\item    Improvements in  safety of NPPs also possible, even with higher seismic
motions, as inelastic effects "eat up" (dissipate) seismic energy


\end{itemize}


 \end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Nuclear Power Plants: 6D or 1D Seismic Motions}


\begin{itemize}


\item Assume that a full 6D (3D) motions at the surface are only recorded in one
horizontal direction


\item  From such recorded motions one can develop a vertically propagating shear
wave in 1D

\item  Apply  such  vertically propagating shear wave to the same soil-structure
system

\end{itemize}

\vspace*{-3mm}
\begin{figure}[!H]
\begin{center}
 \includegraphics[width=6.5cm]{/home/jeremic/tex/works/Conferences/2015/CompDyn/Present/6D_to_1D_01.jpg}
\end{center}
\end{figure}



 \end{frame}


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


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Synthetic Test Motions}

\begin{itemize}

  \item Develop free field models with sources within
  
  \item Sources are simple, point (mostly), line and surface

  \item Sources will send both P and S waves

  \item Variation in strike and dip 
  
  \item Simulation programs, Real ESSI Simulator and SW4    

\end{itemize}


  
\vspace*{-2mm}
\begin{center}
\hspace*{-7mm}
\movie[label=show3,width=5.0cm,poster,autostart,showcontrols]
  {\includegraphics[width=40mm]{BJicon.png}}{movie_input_closeup.mp4}
 \movie[label=show3,width=5.0cm,poster,autostart,showcontrols]
  {\includegraphics[width=40mm]{BJicon.png}}{movie_ff_3d.mp4}
\end{center}




\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Synthetic Test Motions, 6D vs 1D}

\begin{itemize}

  \item Danger of picking one component of motions for 1D or 3$\times$1D (it is done all the time!)
  
  \item  Excellent  (forced)  fit,  but  not a prediction and information is lost
  (goal is to predict and inform and not (force) fit)


\end{itemize}


  
\vspace*{-2mm}
\begin{center}
\hspace*{-7mm}
 \movie[label=show3,width=5.0cm,poster,autostart,showcontrols]
  {\includegraphics[width=40mm]{BJicon.png}}{movie_ff_3d.mp4}
\movie[label=show3,width=5.0cm,poster,autostart,showcontrols]
  {\includegraphics[width=40mm]{BJicon.png}}{movie_ff_1d.mp4}
\end{center}




\end{frame}





% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{6D Free Field Motions}
% 
% 
% \vspace*{-2mm}
% \begin{center}
% %\movie[label=show3,width=8.5cm,poster,autostart,showcontrols,loop]
% \hspace*{-7mm}
% \movie[label=show3,width=8.8cm,autostart,showcontrols]
%   {\includegraphics[width=70mm]{BJicon.png}}{movie_input.mp4}
% \end{center}
% 
% \begin{flushleft}
% \vspace*{-15mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_01AApr2015/movie_input.mp4}
% %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
%   {\tiny (MP4)}
% %
% \end{flushleft}
% 
% 
%  \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{6D Free Field Motions (closeup)}
% 
% 
% \vspace*{-2mm}
% \begin{center}
% \hspace*{-7mm}
% \movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
%   {\includegraphics[width=70mm]{BJicon.png}}{movie_input_closeup.mp4}
% \end{center}
% 
% \begin{flushleft}
% \vspace*{-15mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_01AApr2015/movie_input_closeup.mp4}
% %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
%   {\tiny (MP4)}
% \end{flushleft}
% %
% 
% 
%  \end{frame}
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{6D Free Field at Location}
% 
% 
% \vspace*{-2mm}
% \begin{center}
% \hspace*{-7mm}
% \movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
%   {\includegraphics[width=69mm]{BJicon.png}}{movie_ff_3d.mp4}
% \end{center}
% 
% 
% \begin{flushleft}
% \vspace*{-15mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_3d.mp4}
% %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
%   {\tiny (MP4)}
% \end{flushleft}
% %
% 
% 
%  \end{frame}
% 
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{6D Earthquake Soil Structure Interaction}
% 
% \vspace*{-2mm}
% \begin{center}
% \hspace*{-7mm}
% \movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
%   {\includegraphics[width=70mm]{BJicon.png}}
%   {movie_npp_3d.mp4}
% \end{center}
% 
% \begin{flushleft}
% \vspace*{-15mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_npp_3d.mp4}
%   {\tiny (MP4)}
% \end{flushleft}
% %
% 
%  \end{frame}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{1D Free Field at Location}
% 
% 
% \vspace*{-2mm}
% \begin{center}
% \hspace*{-7mm}
% \movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
%   {\includegraphics[width=70mm]{BJicon.png}}
%   {movie_ff_1d.mp4}
% \end{center}
% 
% \begin{flushleft}
% \vspace*{-15mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_1d.mp4}
%   {\tiny (MP4)}
% \end{flushleft}
% %
% 
% 
%  \end{frame}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{1D ESSI of NPP}
% 
% 
% \vspace*{-2mm}
% \begin{center}
% \hspace*{-7mm}
% \movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
%   {\includegraphics[width=70mm]{BJicon.png}}
%   {movie_npp_1d.mp4}
% \end{center}
% 
% \begin{flushleft}
% \vspace*{-15mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_npp_1d.mp4}
%   {\tiny (MP4)}
% \end{flushleft}
% %
% 
% 
% 
% 
%  \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{6D vs 1D NPP ESSI Response Comparison}


\vspace*{-2mm}
\begin{center}
\hspace*{-7mm}
\movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
  {\includegraphics[width=69mm]{BJicon.png}}
  {movie_2_npps.mp4}
\end{center}


\begin{flushleft}
\vspace*{-15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_2_npps.mp4}
  {\tiny (MP4)}
\end{flushleft}
%



 \end{frame}





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{6D vs 1D: Containment Displacement Response}
% 
% 
% \begin{figure}[!hp]
% \begin{center}
% \hspace*{-13mm}
%  \includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/NPP_movies_19May2015/01_displacements_Containment_building_bottom.pdf}
% \hspace*{-6mm}
%  \includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/NPP_movies_19May2015/02_displacements_Containment_building_top.pdf}
% \hspace*{-10mm}
% \end{center}
% \end{figure}
% 
% 
% 
% \end{frame}
% 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{6D vs 1D: Containment Acceleration Response}


\begin{figure}[!hp]
\begin{center}
\hspace*{-13mm}
 \includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/NPP_movies_19May2015/01_accelerations_Containment_building_bottom.pdf}
\hspace*{-6mm}
 \includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/NPP_movies_19May2015/02_accelerations_Containment_building_top.pdf}
\hspace*{-10mm}
\end{center}
\end{figure}



\end{frame}




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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection{Parametric Uncertainty: Probabilistic Inelasticity}
\subsection{Parametric Uncertainty: Wave Propagation}


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

\frametitle{Uncertain Material Parameters and Loads}


\begin{itemize}

  \item Decide on modeling complexity
  
  \vspace*{3mm}
  \item Determine  model/material parameters

  \vspace*{3mm}
  \item  Model/material  parameters are uncertain! 

    \begin{itemize}
    
      \item Measurements
      
      \item Transformation

      \item Spatial variability

    \end {itemize}



\end{itemize}

\end{frame}







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

\frametitle{Uncertainty Propagation through 
Inelastic System}

% 

\begin{itemize}

\item Incremental el--pl constitutive equation
%  
    \begin{eqnarray}
    \nonumber
  \Delta \sigma_{ij} 
  = 
%  E^{EP}_{ijkl} 
     E^{EP}_{ijkl} \Delta \epsilon_{kl} 
     =  
     \left[
     E^{el}_{ijkl}
       -
       \frac{\displaystyle  E^{el}_{ijmn} m_{mn} n_{pq} E^{el}_{pqkl}}
           {\displaystyle n_{rs} E^{el}_{rstu} m_{tu} - \xi_* h_*}
           \right]
  \Delta \epsilon_{kl}
    \end{eqnarray}

 
  

\vspace*{5mm}
\item Dynamic Finite Elements
%
\begin{equation}
{\bf M} \ddot{\bf u} +
{\bf C} \dot{\bf u} +
{\bf K}^{ep} {\bf u} =
{\bf F}
    \nonumber
\end{equation}


\end{itemize}


\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame} 
%  \frametitle{Critique of our Previous Work, PEP and SEPFEM}
%  
%  \begin{itemize}
%  
%  \item Constitutive weighted coefficients $N_1$ and $N_2$ do not work well for
%  stress solution!
%  
%  \vspace{1mm}
%  \item  We  suggested   that $\sigma(t)$ be considered a $\delta$-correlated, and
%  based  on  that  simplified  stiffness  equations.  Both  the assumption and the
%  resulting equation were not right.
%  
%  
%  \vspace{1mm}
%  \item  On  a  SEPFEM  level,  stiffness  needs  update  basis  functions  and KL
%  coefficients  in  each  step.  We updated   the   eigenvalues  
%  $\lambda_i$  and kept the same structure (Karhunen-Loeve)  in  the approximation
%  of  the  stiffness, which is not physical
%  
%  \vspace{1mm}
%  \item   Implicitly  assumed    that   the  stiffness remains Gaussian, which is 
%  not the case
%  
%  
%  \end{itemize}
%  
%  
%  
%  
%  
%  
%  
%  \end{frame}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame} 
%  \frametitle{Gradient Flow Theory of Probabilistic Elasto-Plasticity}
%  
%  
%  Decomposition of an elastoplastic random process:
%  % into 
%  %the following general form:
%  %
%  \begin{eqnarray}
%  \begin{array}{c c c c c}
%   \bigg( \displaystyle{\pder[]{t}} - \mathcal{L}_{rev} \bigg) P(\boldsymbol{\sigma},t) &=& 0& \qquad &\text{if } 
%   \boldsymbol{\sigma} \in \Omega^{el} 
%   \\
%   ~
%   \\
%   \bigg( \displaystyle{\pder[]{t}} - \mathcal{L}_{irr} \bigg) P(\boldsymbol{\sigma},t) &=& 0& \qquad &\text{if } 
%   \boldsymbol{\sigma} \in \Omega^{el} \cup \Omega^{pl}
%  \end{array} 
%  \nonumber
%  \end{eqnarray}
%  
%  %
%  \begin{itemize}
%  
%  \item Reversible ($\mathcal{L}_{rev} $) and Irreversible ($\mathcal{L}_{irr} $) operators
%  %
%  
%  \vspace*{2mm}
%  \item Yield PDF is an attractor, similar to plastic corrector
%  
%  \vspace*{2mm}
%  \item Ergodicity of the elastic-plastic process can be proven!
%  
%  \end{itemize}
%  
%  
%  
%  
%  
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  
%  \begin{frame} 
%  \frametitle{Gradient Flow Theory of Probabilistic Elasto-Plasticity}
%  
%  \begin{itemize}
%  
%  \item 
%  Elastic, reversible process, Fokker-Planck (forward Kolmogorov) equation
%  %
%  \begin{equation}
%   \pder[P (\boldsymbol{\sigma},t)]{t} 
%    = -\nabla \cdot (\langle \boldsymbol{E} \dot{\boldsymbol{\epsilon}} \rangle P(\boldsymbol{\sigma},t))
%    + t ~\text{Var}[\boldsymbol{E}\dot{\boldsymbol{\epsilon}}] \Delta P(\boldsymbol{\sigma},t) 
%  \nonumber
%  \end{equation}
%  %
%  \begin{equation}
%   \mathcal{L}_{rev} = \nabla \cdot (t \,\text{Var}[\boldsymbol{C}\dot{\boldsymbol{\epsilon}}] \nabla - 
%   \langle \boldsymbol{C} \dot{\boldsymbol{\epsilon}} \rangle)
%  \nonumber
%  \end{equation}
%  
%  \item 
%  Plastic, irreversible process,  Fokker-Planck (forward Kolmogorov) equation 
%  %
%  \begin{equation}
%   \pder[P(\boldsymbol{\sigma},t)]{t} = \nabla \cdot (\nabla \Psi(\boldsymbol{\sigma})
%   P(\boldsymbol{\sigma},t)) + D \Delta P(\boldsymbol{\sigma},t)
%  \nonumber
%  \end{equation}
%  %   
%  \begin{equation}
%   \mathcal{L}_{irr} = D \nabla \cdot \bigg(\nabla - \frac{\nabla P_y(\boldsymbol{\sigma})}{P_y(\boldsymbol{\sigma})}\bigg)
%  \nonumber
%  \end{equation}
%  %
%  
%  \end{itemize}
%  
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame} 
%  \frametitle{Gradient Flow Theory of Probabilistic Elasto-Plasticity}
%  
%  \begin{itemize}
%  
%  \item Limiting (final) distribution
%  is  considered  to  be  known 
%  %(given as a material parameter) and 
%  
%  \vspace*{2mm}
%  \item Underlying potential  leading  to  this  distribution is sought
%  
%  \vspace*{2mm}
%  \item Transition from uncertain elastic to uncertain plastic response
%  
%  
%  \vspace*{2mm}
%  \item Only in a 1D   elastoplastic   problem  does  one  end  up  with  a  stationary
%  distribution
%  
%  \vspace*{2mm}
%  \item In  higher dimensional problems this yield stress distribution is
%  only   "marginally"  stationary  along  one  or  a  combination  of  the  stress
%  components.
%  
%  \end{itemize}
%  
%  
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} 
\frametitle{Probabilistic Elasto-Plasticity: von Mises Surface}


%        An example of a Mises probabilistic yield surface is given in Fig.~\ref{ProbCylinder}.

\begin{figure}[H]
\centering
\vspace*{-5mm}
%\hspace*{-30mm}
 \includegraphics
%  [scale = 0.8, trim = 0.6in 0.4in 0.6in 0.4in, clip=true]
  [width=12cm]
   {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Probabilistic_von_Mises_Surface.jpg}
% \caption{An example of a probabilistic von Mises yield surface.}
 \label{ProbCylinder}
\end{figure}



\end{frame}





%  % 
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame} 
%  \frametitle{Gradient Theory of Probabilistic Elasto-Plasticity: Numerical Solution}
%  
%  
%  \begin{itemize}
%           
%  \item  Using  radial  basis  functions  (a  meshless  method)  for solving
%  Fokker-Planck equations for uncertain elastic-plastic response
%  
%  
%  \vspace*{6mm}
%  \item   Details in a talk by Mr. Karapiperis later this afternoon (room 2, MS-6,
%  17:00-19:00, last talk) 
%  
%  
%  \end{itemize}
%  % %
%  
%  
%  \end{frame}
%  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} 
\frametitle{Gradient Theory of Probabilistic Elasto-Plasticity: 
Verification, Elastic-Perfectly Plastic}
               

%\vspace*{-3mm}
\begin{figure}[H]
\centering
 \includegraphics
% [scale = 0.55, trim = 0.0in 0.0in 0.0in 0.0in, clip=true]
 [width=8cm]
 {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/M+-SD_1D_Perf_Cyclic.pdf}
%  \caption{Combining  the  above  plots to get the evolution of mean $\pm$ std.
% deviation of stress.}
 \label{MSD_12}
\end{figure}


\end{frame}

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection{SEPFEM}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%  
%  \begin{frame}{Stochastic Elastic-Plastic FEM (SEPFEM)}
%  
%  \begin{itemize}
%   \item<1> KL-PC expansion of material random fields (stiffness, etc)
%  %
%  % \begin{equation*}
%  $
%  \mathbb{D}(\bold{x}, \theta) = \sum_{i=0}^{M} r_{i}(\bold{x}) \Phi_i[\{\xi_r(\theta)\}]
%   \label{nonGaussian1}
%  $
%  %\end{equation*}
%  
%   \item<1> PC expansion of displacement field
%  %
%  \begin{eqnarray*}
%  u(\bold{x},\theta) = \sum_{i=0}^p d_i(\bold{x}) \psi_i[\{\xi_r(\theta)\}]
%  \label{PC1}
%  \end{eqnarray*}
%  
%  \item<1> Stochastic Galerkin
%  
%  \begin{eqnarray*}
%  \sum_{n = 1} ^ N K'_{mn} d_{ni} + \sum_{n=1}^N \sum_{j=0}^P d_{nj} \sum_{k=1}^M b_{ijk} K''_{mnk} =
%  \Phi_{m}\langle\psi_i[\{\xi_r\}]\rangle
%  \label{Lognormal6}
%  \end{eqnarray*}
%  
%   \end{itemize}
%  
%  
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  \begin{frame}{SEPFEM Statistical linearization}
%  
%  Update the FE stiffness in the elastoplastic regime:
%  
%  \begin{itemize}
%   \item  Solve elastoplastic FPE for each integration point
%  %
%  \begin{eqnarray*}
%   \pder[P^{nl}(\sigma,t)]{t}
%   &=& \pder[]{\sigma} \bigg(\bigg\langle D^k (1 - P[\Sigma_y \leq \sigma]) \frac{\Delta
%   \epsilon}{\Delta t} \bigg\rangle P\bigg) \nonumber \\
%   & & + \pder[^2]{\sigma^2} \bigg( t Var\bigg[ D^k (1 - P[\Sigma_y \leq \sigma]) \frac{\Delta
%   \epsilon}{\Delta t} \bigg] P\bigg)
%   \label{SEPFEMLinearization1}
%  \end{eqnarray*}
%  
%  \item Consider an equivalent linear FPE
%  %
%  \begin{eqnarray*}
%   \pder[P^{lin}(\sigma,t)]{t}
%   &=& N_{(1)}^{eq} \pder[P]{\sigma} + N_{(2)}^{eq} \pder[^2 P]{\sigma^2}
%   \label{SEPFEMLinearization2}
%  \end{eqnarray*}
%  
%  \item Linearization of the PC coeff. as an optimization problem
%  %
%  \begin{equation*}
%   \pder[P^{lin}(\sigma,t)]{t}
%   = \pder[P^{nl}(\sigma,t)]{t}
%  \end{equation*}
%  
%  
%  \end{itemize}
%  
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  \begin{frame}{Dynamic, Time Domain, SEPFEM}
%  
%  \begin{itemize}
%   \item Gaussian formulation inadequate due to occurrence of "probabilistic softening" modes
%   $\Rightarrow$ Need for positive definite kernel
%  
%  \vspace*{2mm}
%   \item Stochastic forcing  (e.g. uncertain earthquake)
%  
%  \vspace*{2mm}
%   \item   Stability   of   time   marching  algorithm  (Newmark, Rosenbrock, Cubic Hermitian )  analyzed  using
%   amplification matrix
%  
%  \vspace*{2mm}
%   \item Long-integration error and higher order statistics phase shift
%  \end{itemize}
%  
%  %  \begin{figure}[H]
%  % \centering
%  %  \includegraphics[scale = 0.4, trim = 0.1in 0.0in 0.0in 0.0in, clip=true]{/home/jeremic/tex/Classes/2015/spring/ECI280A/SEPFEM/odKonstantinosa/figures/Sendai_1Sine_PCk2PCd8.pdf}
%  %  \label{Sendai_1Sine_PCk2PCd8.pdf}
%  % \end{figure}
%  % 
%  
%  
%  \end{frame}
%  






 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} 
\frametitle{Wave Propagation Through Uncertain Soil}

\vspace{-2mm}
 
\begin{figure}[H]
 \centering
 \includegraphics
% [scale = 0.56, trim = 0.0in 0.15in 0.2in 0.16in, clip=true]
 [width=7cm]
 {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_profile.png}
%
%  
\includegraphics
%[scale = 0.56, trim = 0.0in 0.0in 0.0in 0.0in, clip=true]
 [width=1.5cm]
{/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/meshes.png}
% \caption{Simplified profile and properties for the 1-dimensional profile considered.}
 \label{Sendai_profile}
\end{figure}
     


\vspace{-5mm}

 
\begin{figure}[htbp]
\centering
%\hspace{-0.2in}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \includegraphics
% [scale = 0.37, trim = 0.0in 0.0in 0.0in 0.0in,clip=true]
 [width=3.5cm]
 {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/ShearModulusStats.pdf}
\hfill
 \includegraphics
% [scale = 0.37, trim = 0.0in 0.0in 0.0in 0.0in, clip=true]
 [width=3.5cm]
 {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/ShearStrengthStats.pdf}
%\caption{Shear modulus and shear strength statistics in the middle of the soil column.}
\hfill
 \includegraphics
% [scale = 0.62, trim = 0in 0.15in 0in 0.22in, clip=true]
 [width=3.5cm]
 {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_1Sine_PCk2PC2_elastic_COV45_BaseInput.pdf}
% \caption{Single sine pulse excitation of the soil column at its base.}
% \label{Sendai_1Sine_PCk2PC2_elastic_COV45_BaseInput}
\end{figure}


\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} 
\frametitle{Uncertain Elastic Response at the Surface {\tiny(COV = 120\%)} }
 
 \vspace*{-2mm}
\begin{figure}[H]
 \centering
 \includegraphics
% [scale = 0.62, trim = 0in 0.16in 0in 0.26in, clip=true]
 [width=9.3cm]
 {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_1Sine_PCk2PC2_elastic_COV120.pdf}
%  \caption{Mean  $\pm$ std. deviation of the elastic response at the top of the
% soil column for the conservative COV case (COV = 120\%).}
% \label{Sendai_1Sine_PCk2PC2_elastic_COV120}
\end{figure}

\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} 
\frametitle{Displacement PDFs at the Surface {\tiny(COV = 120\%)} }

%\vspace*{-20mm} 
%\hspace*{-30mm} 
\begin{figure}[H]
 \centering
 \includegraphics
%[scale = 0.62, trim = 0in 0.16in 0in 0.26in, clip=true]
 [width=10cm]
 {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_1Sine_PCk2PC2_elastic_COV120_FullPdf.jpg}
%  \caption{Mean  $\pm$ std. deviation of the elastic response at the top of the
% soil column for the conservative COV case (COV = 120\%).}
% \label{Sendai_1Sine_PCk2PC2_elastic_COV120}
\end{figure}

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} 
\frametitle{Displacement CDFs (Fragilities) at the Surface {\tiny(COV = 120\%)}  }
 
 \vspace*{-3mm}
\begin{figure}[H]
 \centering
 \includegraphics
% [scale = 0.62, trim = 0in 0.16in 0in 0.26in, clip=true]
 [width=11cm]
 {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_1Sine_PCk2PC2_elastic_COV120_FullCdf.jpg}
%  \caption{Mean  $\pm$ std. deviation of the elastic response at the top of the
% soil column for the conservative COV case (COV = 120\%).}
% \label{Sendai_1Sine_PCk2PC2_elastic_COV120}
\end{figure}

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} 
\frametitle{Probability of Exceedance, $disp=0.1m$ {\tiny(COV = 120\%)}  }
 
\begin{figure}[H]
 \centering
 \includegraphics
% [scale = 0.62, trim = 0in 0.16in 0in 0.26in, clip=true]
 [width=9cm]
 {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_1Sine_PCk2PC2_elastic_COV120_ProbExc.pdf}
%  \caption{Mean  $\pm$ std. deviation of the elastic response at the top of the
% soil column for the conservative COV case (COV = 120\%).}
% \label{Sendai_1Sine_PCk2PC2_elastic_COV120}
\end{figure}

\end{frame}

% 

















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\section{Summary}


\subsection*{Summary}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}          
  \frametitle{Concluding Remarks}

  \begin{itemize}



%\vspace*{2mm}
  \item    Modeling and simulation of infrastructure object requires high sophistication
  

\vspace*{3mm}
  \item   Uncertainties (modeling  and parametric) influences results 
  
  
\vspace*{3mm}
  \item  Those  uncertainties need to be addressed and propagated to results and
  used in decision making
  

\vspace*{3mm}
     \item Goal is to {predict} and {inform}, and not force fit

\end{itemize}


\end{frame}


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

  \begin{itemize}



\vspace*{2mm}
  \item  Funding from and collaboration with the US-NRC, US-DOE, US-NSF,   CNSC,
  AREVA NP GmbH, and Shimizu Corp. is greatly appreciated,

\vspace*{2mm}
  \item  Collaborators:
%  Dr.    Budnitz    (LBNL),
  Prof. Yang,
  Dr Cheng, Dr. Jie, Dr. Tafazzoli,
  Prof. Pisan{\`o},
  Mr. Watanabe,
  Mr. Vlaski,
  Mr. Orbovi{\'c},
  and
  UCD students:
  Mr. Abell,
  Mr. Karapiperis,
  Mr. Feng,
  Mr. Sinha,
  Mr. Luo,
  Mr. Lacour,
  Mr. Yang,
  Ms. Behbehani
% 
% 

\vspace*{2mm}
  \item Real ESSI Simulator: 
  \url{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}

\end{itemize}


\end{frame}








































%%%%%%%%%%%%%%
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\section*[]{Real ESSI Simulator}
% invisible section trick 

%\subsection*{Summary}


% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Real ESSI Modelling and Simulation Process}
% 
%  \begin{itemize}
% 
% %\vspace*{4mm}
%    \item Mesh development: gmsh (UL), gmESSI, FeConv (Vlaski)
% 
% \vspace*{2mm}
%    \item Model Development: sublime text editor
% 
% \vspace*{2mm}
%    \item Model Simulation:
%      \begin{itemize}
%        \item Domain Specific Language (DSL) for input
%        \item Real ESSI
%        \item output in HDF5 (NCSA...)
%      \end{itemize}
% 
% \vspace*{2mm}
%    \item    Result    Visualization:    VisIt  (LLNL),   visitESSI  plug-in  (all
%    displacements, stress, strain)
% 
%  \end{itemize}
% %
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Source Code Development and Management}
% 
%  \begin{itemize}
% 
% %\vspace*{4mm}
%    \item  Real  ESSI  sources  (finite element, material models, algorithms, DSL
%    interpreter, \&c.) in a private online repository with version control
%  
%  
% \vspace*{4mm}
%    \item Real ESSI dependencies (external libraries: solvers, MPI, BLAS, LAPACK,
%    \&c.)
% 
% 
% % %\vspace*{1mm}
% %    \item   Sequential   performance   optimization  (templates,  global  linking
% %    optimization, pipeline parallel, \&c.)
% % 
% % %\vspace*{1mm}
% %    \item   Parallel  performance  optimization  (Plastic  Domain  Decomposition)
% %    for local clusters as well as large national parallel computers.
% %    
%  \end{itemize}
% %
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Real ESSI Developers}
% 
% \begin{itemize}
%          \item UC Davis:
%       Core system architecture (sequential and
%    parallel), finite elements, material models,
%    constitutive  integration,  deterministic  and  stochastic  elastic plastic
%    finite elements 
% 
% \vspace*{2mm}
% 
%         \item  LBNL: Nonlinear/inelastic beam, Nonlinear/inelastic shell (plate
%          and wall, deterministic)
% 
% \vspace*{2mm}
%          \item TU Delft: Material Models (deterministic)
% \end{itemize}
% 
% %
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Real ESSI Users}
% 
% 
%      \begin{itemize}
%        \item DOE Project Team:
%           \begin{itemize}
%              \item UC Davis: verification, system modeling, \&c.
% 
%              \item LBNL: verification, validation, validation system design, system modeling)
% 
%              \item UN Reno: validation system design, validation
%           \end{itemize}
%    
% \vspace*{2mm}
%        \item National Labs
% 
% \vspace*{2mm}
%        \item Companies: AREVA, Shimizu Corp., Rizzo and Assoc.
% 
% \vspace*{2mm}
%        \item Universities: TU Delft, NTUA, UCB
% 
%     \end{itemize}
%    
% %
% \end{frame}
% 
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%\subsection{Real ESSI Simulator: Program}


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

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


%\vspace*{-3mm}
   \begin{itemize}
%\vspace*{1mm}
     \item Dry/single phase solids (8, 20, 27, 8-27 node bricks), elastic and/or
     inelastic
%\vspace*{1mm}
     \item  Saturated/two  phase  solids  (8  and  27  node bricks, liquefaction
     modeling), elastic and/or inelastic
%\vspace*{1mm}
     \item Truss, elastic
%\vspace*{1mm}
     \item Beams (six and variable DOFs per node), elastic, inelastic
%\vspace*{1mm}
     \item Shell (ANDES) with 6DOF per node, linear elastic, inelastic shell soon 
%\vspace*{1mm}
     \item   Contacts      (dry   and/or   saturated   soil/rock   -  concrete,  gap
     opening-closing, frictional slip), inelastic
%\vspace*{1mm}
     \item Base isolators (elastomeric, frictional pendulum), inelastic
   \end{itemize}

\end{frame}

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

\begin{frame}
\frametitle{Real ESSI: Material Models}

%\vspace*{-2mm}
   \begin{itemize}
      \item Linear and nonlinear, isotropic and anisotropic  elastic
\vspace*{3mm}
       \item  Elastic-Plastic  (von Mises, Drucker Prager, Rounded Mohr-Coulomb,
              Leon      Parabolic,      Cam-Clay,      SaniSand,     SaniClay,
              Pisan{\` o}...).  All  elastic-plastic  models can be used as perfectly
              plastic,  isotropic  hardening/softening  and  kinematic hardening
              models.
\vspace*{3mm}
       \item  Viscous damping solids, Rayleigh and Caughey damping
   \end{itemize}


\end{frame}

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

\begin{frame}
\frametitle{Real ESSI: Solution Advancement Algorithms}

   \begin{itemize}
%\vspace*{-10mm}

 \item  Constitutive
   \begin{itemize}
%\vspace*{-1mm}
     \item Explicit, Implicit, Sub-incrementation, Line Search
   \end{itemize}


 \item  Nonlinear Static FEM
   \begin{itemize}
%\vspace*{-1mm}
     \item No equilibrium iteration
     \item Equilibrium Iterations (full Newton, modified N, Initial Stiff.)
     \item  Hyperspherical  constraint  (arch length, displacement control, load
     control)
     \item Line Search
     \item Convergence criteria: 
           displacement, load, energy 
   \end{itemize}

 \item  Nonlinear Dynamic FEM
   \begin{itemize}
%\vspace*{-1mm}
     \item No equilibrium iteration
     \item Equilibrium Iterations (full Newton, modified N, Initial Stiff.) 
     \item Constant or variable time stepping 
     \item Convergence criteria: displacement, load, energy
   \end{itemize}

\end{itemize}

%\vspace*{-60mm}
%%\begin{figure}[!hbpt]
%\begin{flushright}
%\hspace*{50mm}
%\includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Theory_Introduction/tex_works_psfigures_loading_stage-increments-iterations.pdf}
%%\caption{\label{loading_stages-increments_iterations} }
%\end{flushright}
%%\vspace*{-0.5cm}
%%\end{figure}



\end{frame}

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

\begin{frame}
\frametitle{Real ESSI: Seismic Input}

   \begin{itemize}
%\vspace*{-1.5mm}

\vspace*{4mm}
 \item    Analytic    input    of  seismic motions (both body (P, S) and surface
 (Rayleigh,  Love,  etc.,  waves),  including analytic radiation damping using Domain
 Reduction Method (Bielak et al.)

\end{itemize}
%
%\begin{figure}[!hbpt]
\begin{center}
\includegraphics[width=8cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/tex_works_psfigures_DRM_NPP_idea01.pdf}
%\caption{\label{DRMidea01} Large physical domain with the source of load $P_e(t)$
%and the local feature (in this case a soil-structure system.}
\end{center}
%\end{figure}


\end{frame}

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\begin{frame}
\frametitle{Real ESSI Simulator Program: Parallel, HPC}

\begin{itemize}

\item High Performance Parallel Computing:
  both  parallel  and  sequential  version available, however, for high fidelity
  modeling,    parallel  is really the only option. Parallel Real ESSI Simulator
  runs  on  clusters  of  PCs  and  on  large supercomputers (Distributed Memory
  Parallel   machines,   all   top   national  supercomputers).  Plastic  Domain
  Decomposition   Method   (PDD,   dynamic  computational  load  balancing)  for
  elastic-plastic  computations  with  multiple  types of finite elements and on
  variable speed CPUs (and networks)
%  Parallel  algorithm  uses our
%  original  Plastic Domain Decomposition method (featuring dynamic computational
%  load  balancing) that is efficient for elastic-plastic finite element problems
%  where  elastic-plastic  (slow)  and  elastic (fast) domains change dynamically
%  during run time.


\end{itemize}

\end{frame}

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\begin{frame}
\frametitle{Real ESSI Simulator Program: Probabilistic/Stochastic}
%\vspace*{-2mm}


   \begin{itemize}
%\vspace*{-2.5mm}
     \item   Constitutive:   Euler-Lagrange   form   of  Fokker-Planck  (forward
     Kolmogorov) equation for probabilistic elasto-plasticity (PEP)
%\vspace*{-1.5mm}
     \item Spatial: stochastic elastic plastic finite element method (SEPFEM)
   \end{itemize}


  Uncertainties  in  material  and  load  are  analytically  taken into account.
  Resulting  displacements,  stress  and  strain  are  obtained as very accurate
  (second  order accurate for stress) Probability Density Functions.
  PEP  and  SEPFEM  are  not  based  on a Monte Carlo method, rather they expand
  uncertain  input  variables  and  uncertain degrees of freedom (unknowns) into
  spectral  probabilistic  spaces  and  solve  for  PDFs  of
  resulting displacement, stress and strain in a single run.


\end{frame}




% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}
% \frametitle{Real ESSI Simulator Program: Design and Users}
% 
% \begin{itemize}
% 
% %\vspace*{0.2cm}
% \item  Based  on  a  Collection  of Useful Libraries  (portable)
% 
% \vspace*{0.1cm}
% \item Library centric software design
% 
% \vspace*{0.1cm}
% \item Sequential (learning) and Parallel (production modeling and simulation)
% 
% \vspace*{0.1cm}
% \item Distributed Memory Parallel (DMP) paradigm, scales well to large supercomputers
% 
% 
% 
% \vspace*{0.1cm}
% \item Various public domain licenses (GPL, LGPL, BSD, CC)
% 
% %\vspace*{0.3cm}
% \vspace*{0.1cm}
% \item Verification (extensive) and Validation (not much)
% 
% 
% \vspace*{0.1cm}
% \item  Target  users: US-DOE, US-NRC, CNSC, IAEA, Collaborators (AREVA, Shimizu,
% Rizzo...), others
% 
% \vspace*{0.1cm}
% \item Limited use Expert Modeling and Simulation System, and not a public domain
% program
% 
% 
% \end{itemize}
% 
% \end{frame}
% 
% 
% 

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}[fragile]
%  \frametitle{ESSI Simulator Computer(s)}
% 
%   A distributed memory parallel (DMP) computer
%    designed for high performance,
%    parallel finite element simulations
% 
%  \begin{itemize}
% %\vspace*{0.1cm}
%    \item Multiple performance CPUs \\
%          and Networks
% %\vspace*{0.1cm}
%    \item Most cost-performance \\
%          effective
% %\vspace*{0.1cm}
%    \item Source compatibility with \\
%          any DMP supercomputer
% %\vspace*{0.1cm}
%    \item Current systems:
%       \begin{itemize}
%         \item 208CPUs,
%         \item 40CPUs (8+32)
%         \item 160CPUs (8x5+2x16+24+64)
%         \item 32CPUs (multiple machines like this)
%       \end{itemize}
% 
%  \end{itemize}
% 
% 
% \vspace*{-4.5cm}
% \hspace*{0.5cm}
% \begin{flushright}
% \includegraphics[width=4.0cm]{/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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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Near Future Plan}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Real ESSI: Verification and Validation}
% \begin{itemize}
% %\vspace*{-2mm}
% \item Verification:
%   each element, model, algorithm and procedure has been extensively verified
%   (math  issue) 
% \vspace*{4mm}
% \item Validation: limited 
%   \begin{itemize} 
%     \item Lotung (!), 
% %    \item PRENOLIN (!?)) 
%     \item  UNR tests (!!)
%   \end{itemize} 
% \end{itemize}
% \end{frame}
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Verification and Validation}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% 




% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Fundamentals of Verifications and Validation}
% % \frametitle{High Fidelity Modeling of SFS System:
% % Verification, Validation and Prediction}
% 
%                          
% \begin{figure}[!h]
% \vspace*{-0.5cm}
% \hspace*{-0.5cm}
% %\begin{center}
% %{\includegraphics[width=11cm]{/home/jeremic/tex/works/Conferences/2005/OpenSeesWorkshopAugust/DeveloperSymposium/VerifValidFund01.pdf}}
% {\includegraphics[width=11cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present06_figs/VerifValidFund01.pdf}}
% %\end{center}
% \end{figure}
% 
% 
% 
% 
% 
% 
% \end{frame}
% 





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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Verification}


\begin{itemize}
\vspace*{1mm}
   \item    Code    Verification    (code    coverage,  memory leaks and pointer
   assignment testing, static argument list testing, \&c.)

\vspace*{1mm}
   \item  Solution  verification  (finite  elements,  constitutive  integration,
   material models, algorithms, seismic input, \&c.) based on analytic, closed form solutions 

\vspace*{1mm}
   \item Method of manufactured solutions for elasto-plastic verification


\vspace*{1mm}
   \item  Parameter bounds (finite elements, material models, algorithms, \&c.)

\vspace*{1mm}
   \item Develop error plots for elements, models, algorithms over a range of parameter

\end{itemize}

\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection{Validation}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Validation}

\begin{itemize}

  \item {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*{2mm}
   \item {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 (Real ESSI Simulator) (conceptual  model,  computational  model,
       computational solution) is the customer
       \item  New US-DOE project to validate 
       inelastic seismic wave propagation and soil-structure interaction

     \end{itemize}




\end{itemize}




\end{frame}







\end{document}

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