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%% Jose Antonio Abell Mena provided this for DSL descriptions
% (used in a file _Chapter_SoftwareHardware_Domain_Specific_Language_English.tex
% This is added for listing FEI DSL
%   since   he   customized   it,   it   needs   to   be   changed   (linked  to
% /usr/share/texmf/tex/latex/misc)
%\usepackage{myListings}
\input{essi_listings_options.tex}

      
\usepackage{multimedia}

% for inclusion of other PDF pages, in this case Frank's presentation
\usepackage{pdfpages}

%This is a macro to  convert eps to pdf files on the fly.
% make sure figure syntax uses graphicx syntax NOT epsfig syntax
%from http://mailman.mit.edu/pipermail/macpartners/2005-January/000780.html
%
% \ifx\pdfoutput\undefined
% % we are running LaTeX, not pdflatex
% \usepackage{graphicx}
% \else
% % we are running pdflatex, so convert .pdf files to .pdf
% \usepackage[pdftex]{graphicx}
% \usepackage{epstopdf}
% \fi
% %*****************************************


%% %% ovo je za cirilicu
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% % for not showing eq numbers unless eq is references
% \usepackage[fleqn,tbtags]{mathtools}
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%   }

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{{\sf \uppercase{F}\kern-0.20em\uppercase{E}\kern-0.20em\uppercase{I}}}

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%  \usetheme{Marburg} % ima naslov i sadrzaj sa desne strane
%  \usetheme{Hannover} % ima naslov i sadrzaj sa leve strane
%  \usetheme{Singapore} % ima sadrzaj i tackice gore
%  \usetheme{Antibes}  % ima sadrzaj gore i kao graf ...
%  \usetheme{Berkeley} % ima sadrzaj desno
%  \usetheme{Berlin} % ima sadrzaj gore i tackice
%  \usetheme{Goettingen} % ima sadrzxaj za desne strane
%  \usetheme{Montpellier} % ima graf sadrzaj gore
%  \usetheme{Warsaw}
%  \usetheme{Warsaw}
  \usetheme{Dresden}
    \usecolortheme[RGB={20,0,128}]{structure}

% or ...

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%  \setbeamercovered{transparent}
% or whatever (possibly just delete it)
%  \usecolortheme{albatross} % teget sa svetlim slovima
%  \usecolortheme{beetle} % siva pozadina (vrh plav)
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%%%%%%%
%  \usecolortheme{BorisJeremic}
%%%%%%%
%  \usecolortheme{rose}
%   \usefonttheme[onlylarge]{structuresmallcapsserif}
%   \usefonttheme{structuresmallcapsserif}
}

\definecolor{mycolor}{rgb}{0,0.08,0.45}%


\usepackage[greek,english]{babel}



\usepackage{amsmath}
\usepackage{mathrsfs}
\usepackage{amsfonts}

\newcommand{\ud}{{\rm d}}


\usepackage{array}



%%%%  HYPERREF  HYPERREF  HYPERREF  HYPERREF  HYPERREF
%%%%  HYPERREF  HYPERREF  HYPERREF  HYPERREF  HYPERREF
\definecolor{webgreen}{rgb}{0, 0.15, 0} % less intense green
\definecolor{webblue}{rgb}{0, 0, 0.15} % less intense blue
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\usepackage{pause}
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\usepackage[latin1]{inputenc}
% or whatever
\usepackage{times}
\usepackage[T1]{fontenc}
% Or whatever. Note that the encoding and the font should match. If T1
% does not look nice, try deleting the line with the fontenc.






\title[{\cyrosam
Modelovanje tla i konstrukcije}]
        {{\cyrsesnaest
Dinamika tla i konstrukcije pri zemljotresima, nepouzdani
modeli, nepouzdani parametri i teorija verovatno\cj{}a}}


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

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


%\author[Boris Jeremi{\'c}, CompGeoMech \includegraphics[width=8cm]{/home/jeremic/BG/amblemi/ucdavis_logo_gold_lrg}] % (optional, use only with lots of authors)
\author[{\cyrosam Jeremi\cj{}}] % (optional, use only with lots of authors)
{\cyrsesnaest Boris~Jeremi\cj{}}
% - Give the names in the same order as the appear in the paper.
% - Use the \inst{?} command only if the authors have different
%   affiliation.

%\institute[Computational Geomechanics Group \hspace*{0.3truecm}
\institute[\pgfuseimage{university-logo}\hspace*{0.1truecm}\pgfuseimage{lbnl-logo}] % (optional, but mostly needed)
%{ Professor, University of California, Davis\\
{ University of California, Davis, CA, USA\\
%  and\\
%  Faculty Scientist, Lawrence Berkeley National Laboratory, Berkeley }
  Lawrence Berkeley National Laboratory, Berkeley, CA, USA }
% - 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)
{\cyrdeset Beograd, Decembar 2016}

\subject{}
% This is only inserted into the PDF information catalog. Can be left
% out.



% If you have a file called "university-logo-filename.xxx", where xxx
% is a graphic format that can be processed by latex or pdflatex,
% resp., then you can add a logo as follows:

%\pgfdeclareimage[height=0.2cm]{university-logo}{/home/jeremic/BG/amblemi/ucdavis_logo_gold_lrg}
%\logo{\pgfuseimage{university-logo}}

% \pgfdeclareimage[height=0.5cm]{university-logo}{university-logo-filename}
% \logo{\pgfuseimage{university-logo}}




% Delete this, if you do not want the table of contents to pop up at
% the beginning of each subsection:
% \AtBeginSubsection[]
\setcounter{tocdepth}{2}
 \AtBeginSubsection[]
% \AtBeginSection[]
 {
   \begin{scriptsize}
   \begin{frame}<beamer>
%     \frametitle{\cyrsesnaest Pregled}
     \tableofcontents[currentsection,currentsubsection]
%    \tableofcontents[currentsection]
   \end{frame}
   \end{scriptsize}
 }


% If you wish to uncover everything in a step-wise fashion, uncomment
% the following command:





\begin{document}

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

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\begin{frame}
  \frametitle{\cyrdvanaest Sadrzhaj}

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

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% Structuring a talk is a difficult task and the following structure
% may not be suitable. Here are some rules that apply for this
% solution:

% - Exactly two or three sections (other than the summary).
% - At *most* three subsections per section.
% - Talk about 30s to 2min per frame. So there should be between about
%   15 and 30 frames, all told.

% - A conference audience is likely to know very little of what you
%   are going to talk about. So *simplify*!
% - In a 20min talk, getting the main ideas across is hard
%   enough. Leave out details, even if it means being less precise than
%   you think necessary.
% - If you omit details that are vital to the proof/implementation,
%   just say so once. Everybody will be happy with that.



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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{\cyrdeset Uvod}




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\subsection{\cyrdevet Motivacija}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{{\cyrsesnaest Motivacija}}

\begin{itemize}



%\vspace*{0.3cm}
  \item {\cyrdvanaest Poboljshanje modelovanja i simulacija za sisteme tla i konstrukcije}

\vspace*{1mm}
  \item {\cyrdvanaest Razvoj ekspertnog sistema za numerichke analize}

\vspace*{1mm}
  \item  {\cyrdvanaest    Upotreba preciznih modela za analize statike i dinamike
  sistema tla i konstrukcije}

%\vspace*{1mm}
%  \item  {\cyrdvanaest  Pra\cj{}enje protoka mehanichke energije kroz sistem tla
%  i konstrukcije sa ciljem}
%    \begin{itemize}
%      \item {\cyrdvanaest pove\cj{}anja sigurnosti}
%      \item {\cyrdvanaest smanjenja troshkova objekta}
%    \end{itemize}

\vspace*{1mm}
  \item  {\cyrdvanaest    Cilj  je  razvoj  metodologije za  
  numerichka predvidjanja i informisanje korisnika, struchnjaka,
  a ne rezultati koji prate neku zadatu liniju, na silu}
  


%\vspace*{1mm}
%  \item   Directing,   in   space   and   time,   seismic  energy  flow  in  the
%  soil structure system



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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{{\cyrsesnaest Pretpostavka}}

\begin{itemize}

%OVDE

%\vspace*{0.5cm}
  \item       {\cyrdvanaest  Interakcija dinamichkih karakteristika zemljotresa,
  tla i konstrukcije kontrolishe nivo oshte\cj{}enja konstrukcije}

\vspace*{3mm}
  \item  {\cyrdvanaest Mesto i vreme disipacije zemljotresne energije
           odredjuje lokaciju i
  nivo oshte\cj{}enja konstrukcije}

\vspace*{3mm}
  \item  {\cyrdvanaest Kontrolisanjem protok 
         zemljotresne energije kroz tlo i konstrukciju, 
          mozhemo da poboljshamo}
    \begin{itemize}
\vspace*{1mm}
      \item {\cyrdvanaest Sigurnost}
\vspace*{1mm}
      \item {\cyrdvanaest Ekonomichnost}
    \end{itemize}

\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{\cyrsesnaest Tachnost Modelovanja i Simulacija}
% \frametitle{High Fidelity Modeling of SFS System:
% Verification, Validation and Prediction}


\begin{itemize}


     \item  {\cyrdvanaest Verifikacija:  dokaz da je model tachno 
           reshen, matematichki problem}

\vspace*{1mm}
     \item {\cyrdvanaest Validacije: dokaz da je reshen pravi model,
            mehanichki problem}

\vspace*{1mm}
     \item {\cyrdvanaest Numerichko analiza:
           korish\cj{}enje numerichkog 
           modela za predvicjanje stanja sistema za optere\cj{}enja koja nisu 
           korish\cj{}ena pri testiranju (validaciji)}

\vspace*{1mm}
     \item  {\cyrdvanaest Predvidjanje/analiza uz teoriju verovatno\cj{}a:} 
     
        \begin{itemize}

%OVDE vidi opet kako da pravilno kazes uncertainty, pitaj Beku
          \item {\cyrdvanaest Nesigurnost modela}

          \item {\cyrdvanaest Nesigurnost parametara}

        \end{itemize}


%\vspace*{0.2cm}
%   \item Goal: predictive capabilities
%   with {\bf low Kolmogorov Complexity}

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

\end{itemize}

\end{frame}



%    
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   \begin{frame}
%    \frametitle{Role of Verification and Validation}
%   
%   
%   \begin{figure}[!h]
%   \begin{center}
%   \hspace*{-2cm}
%   {\includegraphics[width=5.0cm]{/home/jeremic/tex/works/Conferences/2012/ASME_V_and_V_symposium/presentetation/RoleVV_NEW_knowledge.pdf}}
%   {\includegraphics[width=6.5cm]{/home/jeremic/tex/works/Conferences/2011/USNCCM11_Minneapolis/Coupled/Present/VandV_ODEN.jpg}}
%   \hspace*{-2cm}
%   \end{center}
%   \end{figure}
%   
%   {Oberkampf et al. \hspace*{4cm}  Oden et al.}
%   %
%   %\item Models available (some now, some later)
%   %\vspace*{-2.0cm}
%   \end{frame}
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   
%   


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Modeling and Parametric Uncertainty}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Modeling Uncertainty: Simplified  Models}

\begin{itemize}



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

%\vspace*{1mm}
     \item   Modeling   Uncertainty:   unrealistic   and   unnecessary  modeling
     simplifications

%\vspace*{1mm}
     \item    Modeling   simplifications: justifiable  iff higher level 
     sophistication model shows are features not important


\end{itemize}

    
\begin{center}
  {\includegraphics[width=45mm]{movie_ff_3d_mp4_icon.jpeg}}
%
%\hspace*{10mm}
%
  {\includegraphics[width=45mm]{movie_ff_1d_mp4_icon.jpeg}}
\end{center}


\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Parametric Uncertainty: Material and Loads}



\begin{itemize}



  \item  Significant uncertainty in material and loads

%\vspace*{1mm}
     \item  Need  to  propagate  uncertainty through simulation, to give
     regulators and engineers information for design, licensing...


\end{itemize}

%
%\vspace{1cm}
%\hspace{-0.5cm}
%Example: Elastic 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*{-0.8cm}
%\hspace*{-3.3cm}
\begin{flushleft}
{\tiny
Transformation  of SPT $N$-value: 
1-D Young's modulus, $E$ 
(cf. Phoon and Kulhawy (1999B))
~}
\end{flushleft}

\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}
% 
% % 

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Uncertainty in Modeling Ground Motions}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Complexity of and Uncertainty in Ground Motions}
% 
% \begin{itemize}
% %\vspace*{0.3cm}
%   \item 6D (3 translations, 3 rotations)
% 
% \vspace*{0.3cm}
%   \item Vertical motions usually neglected
%  
% \vspace*{0.3cm}
%   \item Rotational components usually not measured and neglected 
%  
% \vspace*{0.3cm}
%   \item Lack of models for such 6D motions (from measured data))
%   
% \vspace*{0.3cm}
%   \item Sources of uncertainties in ground motions (Source, Path (rock), soil (rock))  
% \end{itemize}
% 
% 
% 
% \end{frame}
% 
% 
% 
% 
% 
% 
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Uncertainty in  Modeling Material}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame} 
% 
% \frametitle{Material Behavior Inherently Uncertain}
% 
% 
% %\begin{itemize}
% 
% %\vspace*{0.5cm}
% %\item  
% %Material  behavior  is  inherently uncertain  (concrete,  metals,  soil,  rock, 
% %bone, foam, powder etc.)
% 
%         \begin{itemize}
% 
% \vspace*{0.5cm}
%         \item Spatial \\ 
%               variability
% 
% \vspace*{0.5cm}
%         \item Point-wise \\ 
%               uncertainty, \\
%               testing \\
%               error, \\
%               transformation \\
%               error
% 
%         \end{itemize}
% 
% % \vspace*{0.5cm}
% % \item  Failure mechanisms related to spatial variability (strain localization and
% %        bifurcation of response)
% % 
% % \vspace*{0.5cm}
% % \item Inverse problems
% % 
% %       \begin{itemize}
% %       
% %       \item New material design, ({\it point-wise})
% % 
% %       \item Solid and/or structure design (or retrofits),  ({\it spatial})
% % 
% %       \end{itemize}
%                                   
% %\end{itemize}
% 
% \vspace*{-5cm}
% \begin{figure}[!hbpt]
% %\nonumber
% %\begin{center}
% \begin{flushright}
% %\includegraphics[height=5.0cm]{/home/jeremic/tex/works/Conferences/2006/KragujevacSEECCM06/Presentation/MGMuzorak01.jpg}
% \includegraphics[height=5.5cm]{/home/jeremic/tex/works/Conferences/2006/KallolsPresentationGaTech/FrictionAngleProfile.jpg}
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% \includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_RawData_and_MeanTrend-Mod.pdf}
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% \includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_Histogram_PearsonIV-FineTuned-Mod.pdf}
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% \end{center}
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% \vspace*{-0.3cm}
% Transformation of SPT $N$-value $\rightarrow$ undrained shear
% strength, $s_u$ (cf. Phoon and Kulhawy (1999B)
% 
% Histogram  of  the  residual  
% (w.r.t  the  deterministic transformation
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% \includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01-Ed.pdf} 
% \hfill
% \includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_Histogram_Normal_01-Ed.pdf}
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% \end{center}
% \end{figure}                                                          
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%    \item Les Hatton, Kingston University, the T Experiments
% 
%    \vspace*{0.1truecm}
%    \item "Extensive tests showed that many software codes widely used in science
%    and engineering are not as accurate as we would like to think."
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%    \item "Realizing that the problem exists is an important first step."
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%    \item  Large  experiment over 4 years measuring faults (T1) and failures (T2)
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% \item Specific application area: seismic data processing, geophysics, inverse analysis
% 
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% \item Echo sounding of underground and reconstructing "images" of 
% subsurface geological structure
% 
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% \item  Nine  mature packages, using {same algorithms (same original code)}, on a
% {same data set}!
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% \frametitle{Realistic ESSI Modeling (Uncertainties)}
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% \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
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% \includegraphics[width=2.3cm]{/home/jeremic/public_html/forDaveMcCallen/Student_pictures/YuanFeng01.jpg}
% \includegraphics[width=2.3cm]{/home/jeremic/public_html/forDaveMcCallen/Student_pictures/SumeetKumarSinha01.jpg}
% \includegraphics[width=2.3cm]{/home/jeremic/public_html/forDaveMcCallen/Student_pictures/FatmaBehbehani01.jpg}
% \includegraphics[width=2.3cm]{/home/jeremic/public_html/forDaveMcCallen/Student_pictures/MaximeLacour.jpg}
% \includegraphics[width=2.3cm]{/home/jeremic/public_html/forDaveMcCallen/Student_pictures/HanYang01.jpg}
% \end{center}
% \end{figure}
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% 
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=2.2cm]{/home/jeremic/public_html/forDaveMcCallen/Student_pictures/JoseAbell.jpg}
% \includegraphics[width=2.6cm]{/home/jeremic/tex/works/Conferences/2016/DOE_panel_review_UNR_01June2016/present/Frank02.jpg}
% \includegraphics[width=3cm]{/home/jeremic/tex/works/Conferences/2016/DOE_panel_review_UNR_01June2016/present/Boris01.jpg}
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% \begin{frame}
%  \frametitle{Recent Work}
% 
% \begin{itemize}
% 
%    \item Wave propagation in local geology
% 
%    \item Stiff (concr. to concr.) and soft
%    (concr. to soil)  contacts
% 
%    \item SW4 for development of seismic wave fields, 
%    
%    \item Coupling of SW4 with the Real ESSI (using DRM)
% 
%    \item Nonlinear/inelastic bending beam element
% 
%    \item  Detailed  modeling  of  the  UNR  cylinder, 
%      \begin{itemize} 
%      
%        \item Nonlinear/inelastic soil, (variation of soil stiffness)
% 
%        \item   Contact  zone  (frictional,  gaping)  (variation  of  frictional
%        resistance (complementary shear?)
% 
%        \item Detailed model of a wall (beams, elastomers)
% 
%        \item Static pushovers (wall, full model...)
% 
%        \item Dynamic excitations, bottom shakes 
% 
%        \item Dynamic excitations from within (dynamic sources) 
% 
%      \end{itemize} 
% 
%     \item Educational developments!!!
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\section{\cyrdeset Program}



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\subsection{Real ESSI Simulator System}



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

\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*{0.1cm}
\item {\bf The Real ESSI-Computer} is a distributed memory
parallel computer, a cluster of clusters with multiple performance
processors and multiple performance networks.
%Compute  nodes are Shared Memory Parallel
%(SMP)  computers,  that  are  connected,  using  high  speed  network(s), into a
%Distributed Memory Parallel (DMP) computer.

%\vspace*{0.3cm}
\vspace*{0.1cm}
\item    {\bf        The Real  ESSI-Notes} 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}


    
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\begin{frame}
\frametitle{Real ESSI Simulator Modeling  and Simulation Process}


\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}

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\subsection{Real ESSI Simulator Components}



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\begin{frame}
\frametitle{Real ESSI Simulator: DSL}[fragile]

 \begin{itemize}
   \item Domain Specific Language (DSL), Yacc \& Lex
\vspace*{3mm}
   \item English like modeling and simulation language
\vspace*{3mm}
   \item Parser and compiler, can define functions, models, etc.
\vspace*{3mm}
   \item Can extend models and methods
\vspace*{3mm}
   \item Requires units!
 \end{itemize}
%


%\begin{verbatim}
%add node \# 2 at (0*m, 0*m, 1*m) with 6 dofs;
%\end{verbatim}

%
%\begin{lstlisting}
%add node # 1 at (0*m, 0*m, 0*m) with 6 dofs;
%add node # 2 at (0*m, 0*m, 1*m) with 6 dofs;
%\end{lstlisting}

%
%\begin{lstlisting}
%add node # 2 at (0*m, 0*m, 1*m) with 6 dofs;
%\end{lstlisting}


\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[fragile]
 \frametitle{Real ESSI DSL Example}


 \vspace*{-2mm}
\begin{lstlisting}
model name "UNR Test Setup";
new loading stage "First, static";
add node # 1 at (0*m, 0*m, 0*m) with 6 dofs;
add node # 2 at (0*m, 0*m, 1*m) with 6 dofs;
add element # 1 type beam_elastic with
  nodes (1, 2) cross_section=1.0*m^2
  elastic_modulus=1.0e5*KN/m^2
  shear_modulus=2.0e4*KN/m^2
  torsion_Jx=2*0.083*m^4
  bending_Iy=0.083*m^4 bending_Iz=0.083*m^4
  mass_density=2500.0*kg/m^3
  xz_plane_vector = (0, -1, 0)
  joint_1_offset = (0.0*m, 0.0*m, 0.0*m)
  joint_2_offset = (0.0*m, 0.0*m, 0.0*m);
\end{lstlisting}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[fragile]
 \frametitle{Real ESSI DSL Example}


 \vspace*{-2mm}
\begin{lstlisting}
fix node No 1 dofs all;
add load # 1 to node # 2 type
  linear Fx=-9*kN;
define load factor increment 0.01;
define solver UMFPack;
define convergence test
  Norm_Displacement_Increment
  tolerance = 1e-5
  maximum_iterations = 20
  verbose_level = 4;
define algorithm Newton;
simulate 100 steps using static algorithm;

dovidjenja;
\end{lstlisting}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}[fragile]
%  \frametitle{Real ESSI DSL Example}
% 
% 
% \begin{lstlisting}
% add node # 1 at (0*m, 0*m, 0*m) with 6 dofs;
% add node # 2 at (0*m, 0*m, 1*m) with 6 dofs;
% \end{lstlisting}
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 




% 
%  % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}[fragile]
%   \frametitle{Beam Example, Model}
%  
%  
%  
%  \begin{figure}[!h]
%  \begin{center}
%  \includegraphics[width=10cm]{/home/jeremic/tex/works/Conferences/2016/Beograd_predavanje_decembar/present/Cantilever_Beam_02.pdf}
%  %\caption{8 node brick element}
%  %\label{fig:8node_command}
%  \end{center}
%  \end{figure}
%  
%  
%  %}
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}[fragile]
%   \frametitle{Real ESSI DSL Example}
%  
%  
%  \begin{lstlisting}
%  model name "UNR Test Setup";
%  new loading stage "First, static";
%  // Nodal  Coordinates
%  add node # 1 at (0*m, 0*m, 0*m) with 6 dofs;
%  add node # 2 at (0*m, 0*m, 1*m) with 6 dofs;
%  add element # 1 type beam_elastic with
%    nodes (1, 2) cross_section=1.0*m^2
%    elastic_modulus=1.0e5*KN/m^2
%    shear_modulus=2.0e4*KN/m^2
%    torsion_Jx=2*0.083*m^4
%    bending_Iy=0.083*m^4 bending_Iz=0.083*m^4
%    mass_density=2500.0*kg/m^3
%    xz_plane_vector = (0, -1, 0)
%    joint_1_offset = (0.0*m, 0.0*m, 0.0*m)
%    joint_2_offset = (0.0*m, 0.0*m, 0.0*m);
%  \end{lstlisting}
%  \end{frame}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}[fragile]
%   \frametitle{Real ESSI DSL Example}
%  
%  
%  \begin{lstlisting}
%  fix node No 1 dofs all;
%  add load # 1 to node # 2 type
%    linear Fx=-9*kN;
%  define load factor increment 0.01;
%  
%  define solver UMFPack;
%  define convergence test
%    Norm_Displacement_Increment
%    tolerance = 1e-5
%    maximum_iterations = 20
%    verbose_level = 4;
%  define algorithm Newton;
%  simulate 100 steps using static algorithm;
%  
%  bye;
%  \end{lstlisting}
%  \end{frame}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  
%  
%  
%  
%  
%  
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% \subsection{Real ESSI Program}


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


%\vspace*{-3mm}
   \begin{itemize}
     \item Dry/single phase solids (8, 20, 27, 8-27 node bricks),
%\vspace*{1mm}
     \item Saturated/two phase solids (8 and 27 node bricks, liquefaction modeling),
%\vspace*{1mm}
     \item Truss, Beams, linear and nonlinear
%\vspace*{1mm}
     \item Nonlinear concrete shell and linear shell (ANDES)
% with 6DOF per node, 
%\vspace*{1mm}
     \item   Contacts      (dry   and/or   saturated   soil/rock   -  concrete,  gap
     opening-closing, frictional slip),
%\vspace*{1mm}
     \item Base isolators (elastomeric, frictional pendulum)
%\vspace*{1mm}
     \item Stochastic Elastic-Plastic FEM (1D and 3D solid)
   \end{itemize}

\end{frame}

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

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

%\vspace*{-2mm}
   \begin{itemize}
      \item Elastic (solids): Linear,  nonlinear, isotropic and anisotropic
\vspace*{2mm}
       \item  Elastic-Plastic (solids):  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*{2mm}
       \item  Elastic-Plastic (structures, 1D fibers): concrete and steel

\vspace*{2mm}
     \item Probabilistic Elasto-Plasticity 

   \end{itemize}


\end{frame}

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

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


Analytic input of seismic motions using Domain Reduction Method (Bielak et al.)

   \begin{itemize}

\vspace*{2mm}
     \item Body (P, S) seismic waves

\vspace*{2mm}
     \item Surface (Rayleigh,  Love,  etc.) seismic  waves,

\vspace*{2mm}
     \item Analytic radiation damping.

   \end{itemize}

\end{frame}



% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}
% \frametitle{Real ESSI Simulator Program: Probabilistic/Stochastic}
% %\vspace*{-2mm}
% 
% \begin{equation}
% \boldsymbol{M \ddot{x}+C \dot{x}+Kx}=\boldsymbol{f}
% \end{equation}
% 
% Forward  propagation  of uncertainty for uncertain inelastic/nonlinear  material
% (LHS, $\boldsymbol{M, C, K}$) and uncertain loads (RHS,  $\boldsymbol{f}$)
% 
%    \begin{itemize}
% %\vspace*{-2.5mm}
%      \item   Constitutive:   Euler-Lagrange   form   of  Fokker-Planck  (forward
%      Kolmogorov)  equation  for  probabilistic elasto-plasticity (PEP) (meshless
%      finite element method for solution at each Gauss point)
% 
% \vspace*{1mm}
%      \item Spatial: stochastic elastic plastic finite element method (SEPFEM)
% 
%    \end{itemize}
% 
% 
% \end{frame}
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}
% \frametitle{Real ESSI Simulator Program: Probabilistic/Stochastic}
% %\vspace*{-2mm}
% 
% 
%    \begin{itemize}
% 
%      \item  Uncertainties  in  {\bf material}  and  {\bf load}
%      are  analytically  taken into account
% 
% \vspace*{1mm}
%      \item Resulting  displacements,  stress  and  strain  are  obtained as very
%      accurate (second order accurate for stress)
%      Probability Density Functions (PDFs)
% 
% \vspace*{1mm}
%      \item  PEP  and  SEPFEM  are  not  based  on Monte Carlo method!
% 
% \vspace*{1mm}
%      \item  PEP  and  SEPFEM  expand  uncertain  input  variables  and uncertain
%      degrees   of   freedom   (unknowns)   into  spectral  probabilistic  spaces
%      (Karhunen-Loeve, Polynomial Chaos)
% 
% \vspace*{1mm}
%      \item  Solve   for  PDFs  of resulting displacement, stress and strain in a
%      single run
% 
%    \end{itemize}
% 
% \end{frame}
% 


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}
% \frametitle{Real ESSI Simulator Program: Probabilistic/Stochastic}
% %\vspace*{-2mm}
% 
% Backward propagation of uncertainty (future work):
% 
%    \begin{itemize}
% %\vspace*{-2.5mm}
% \vspace*{3mm}
%      \item    Backward  Kolmogorov  problem: for given/required
%       final risk,
%       prescribe uncertainties in input material parameters and loads
% 
% \vspace*{3mm}
%      \item Constitutive level backward Kolmogorov to use
%      Feynman-Kac analytic
%      solution ('48, '49)
% 
% 
% \vspace*{3mm}
%      \item  Spatial  level  backward  Kolmogorov  to  use a
%      variant of Monte Carlo
%      method
% 
%    \end{itemize}
% 
% 
% \end{frame}
% 

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

\begin{frame}
\frametitle{Real ESSI Simulator Program: V\&V}

\begin{itemize}

%\vspace*{-2mm}
\item  Verification: mathematics issue,
  \begin{itemize}
\vspace*{1mm}
    \item Each  element,  model,  algorithm  and  procedure has been extensively
    verified (math issue),
  \end{itemize}

\vspace*{4mm}
\item Validation: physics issue,
  \begin{itemize}
\vspace*{1mm}
    \item Limited, current DOE project will provide a wealth of data for soil, SSI, \&c.
  \end{itemize}



\end{itemize}

\end{frame}

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



%  
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Real ESSI Simulator Status}
% 
% \begin{scriptsize}
% 
% \begin{itemize}
% 
% \item[-] Real ESSI Simulator. '05 --
% 
% \item[-] C++ standard (current !)
% 
% \item[-] Input: Domain Specific Language (DSL), Yacc and Lex,
% 
% \item[-] Model development: gmsh, gmESSI, Python,
% 
% \item[-] Output:    HDF5 (VisIt, ParaView, Matlab, Python...)
% 
% %\item[-] Vis: Visit, Paraview, Matlab ...
% 
% \item[-] E:    Solids (bricks 8n, 20n, 8-20n, 27n 8-27n)
% 
% \item[-] E:  Coupled solids,      u-p-U and u-p,
% 
% \item[-] E:   Structural  (Truss,  beams  B12,  B9,  ANDES Shell, Nonlinear Beam,
% Shell
% 
% \item[-]  E: Contact, dry and saturated
% 
% 
% \item[-]  Material:   template/template elasto-plasticity (small and large def.),
% 
% \item[-]  Seismic:   DRM for seismic input
% 
% \item[-]   Probabilistic Elasto-Plasticity and Stochastic Elastic-Plastic FEM
% 
% \item[-]  HPC: Template Metaprograms and Expression Templates
% 
% \item[-]  HPC:       Parallel, Plastic Domain Decomposition (PDD) (dyn comp load bal),
% 
% \item[-]  HPC:   Adaptive PDD (multiple networks/connectivity)
% 
% 
% \item[-]  Portable: local clusters, SDSC, TACC, NERSC (Edison)
% 
% \end{itemize}
% \end{scriptsize}
% 
% 
% \end{frame}
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Real ESSI Modelling and Simulation Process}
% 
%  \begin{itemize}
% 
% %\vspace*{4mm}
%    \item Mesh Development: gmsh, 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 everything (HDF5), Great (!) and a problem (!)
%      \end{itemize}
% 
% \vspace*{2mm}
%    \item    Result    visualization:    VisIt,   visitESSI  plug-in  (all
%    displacements, stress, strain, really large output!), ParaView
% 
%  \end{itemize}
% %
% \end{frame}
% 
%  
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   
%   \begin{frame}
%   \frametitle{Real ESSI Program Features}
%   
%   
%      
% \begin{itemize}
% 
% 
%        \item  Finite  Elements:  solids  (dry/single,  coupled);  truss;  beams;
%        shell; wall; plate; contact; base isolator/dissipator
% 
%   \vspace*{1mm}
%        \item   Material Models: Lin., nonlin, iso. and aniso. 
%        elastic; Elastic-Plastic (vMises, DrPr, R-MC, Leon-P, CClay,  SSand, SClay, P); 
%        Damping, Rayleigh and Caughey 
% 
%   \vspace*{1mm}
%        \item  Seismic  input:  the  Domain Reduction Method (DRM, Bielak et al.,
%        Analytic input of seismic motions)
%   
%   \vspace*{1mm}
%        \item  High Performance Computing: Parallel (Plastic Domain Decomposition
%        Method), Template Metaprograms
%   
%   \vspace*{1mm}
%        \item   Probabilistic Modeling: (analytic) PEP and SEPFEM
%   
% 
% \end{itemize}
% 
%   \end{frame}
%   
%   
  




  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{\cyrdeset Analize}


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

\frametitle{Examples}


\begin{itemize}

  \item  Earth  and  Concrete  Dam: level of sophistication and the influence of
  human factor (expert opinion)

  \vspace*{3mm}
  \item  Concrete  Bridge:  matching  of earthquake, soil and  structure dynamic
  characteristics
  
  \vspace*{3mm}
  \item Nuclear Power Plant: 3D (6D) vs 1D seismic motions

  \vspace*{3mm}
  \item    Stochastic    Elastic    Plastic    Finite   Element  Method: risk of
  undesirable performance



\end{itemize}

\end{frame}

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



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection{{\cyrdevet Nasuta Brana} }
\subsection{{\cyrdevet Brana} }


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

\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}
%- 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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

\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}
%- 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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

\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}
%- 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\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}
%- 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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

\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}
%- 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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 (and significant rain!)
  
%  \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 (a single) 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, 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}
%- 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\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" $S_u$, FS a bit higher

   \item Seismic: immediate slope failure

 \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{{\cyrdevet Betonski Most} }



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

\begin{frame}
 \frametitle{Post-Tensioned Concrete Bridge in Variable Soil}


\begin{itemize}
  \item Linear elastic deck/box girder, concrete, post-tensioned
  \item Nonlinear frame, r. concrete
  \item Nonlinear piles, r. concrete
  \item Nonlinear soil (Sand, Clay)

\end{itemize}


% OVDE


\vspace*{-15mm}
\begin{figure}[!htbp] 
\begin{center}
\hspace*{10mm}
\includegraphics[width=2.2cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_NEES_Bridge/tex_works_Thesis_GuanzhouJie_thesis_Verzija_Februar_Images_triaxial_test_austin.pdf}
\includegraphics[width=1.8cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_NEES_Bridge/tex_works_Thesis_GuanzhouJie_thesis_Verzija_Februar_Images_Triaxial_Austin.pdf}
\hspace*{3mm}
\includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_NEES_Bridge/tex_works_Thesis_GuanzhouJie_thesis_Verzija_Februar_Images_g_gmax_austin_1.pdf}
\includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_NEES_Bridge/tex_works_Thesis_GuanzhouJie_thesis_Verzija_Februar_Images_damping_ratio_austin_1.pdf}
\\
\includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_NEES_Bridge/tex_works_Thesis_GuanzhouJie_thesis_Verzija_Februar_Images_HingeModel.pdf}
\includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_NEES_Bridge/tex_works_Thesis_GuanzhouJie_thesis_Verzija_Februar_Images_Hinge_MomentRotation.pdf}
\includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_NEES_Bridge/tex_works_Thesis_GuanzhouJie_thesis_Verzija_Februar_Images_StructureModel.pdf}
%
\end{center}
\end{figure}

% 
% %      OVDE opisi model koristi slike LN, sa strane
% %
% %    \vspace*{2mm}
% %    \item
% %             opis modela, slike iz LN:
% %                        34.1,  34.2, 34.3, 34.4, 34.5, 34.6,  34.7, 34.8
% % 
% % 
% % 
% %             slika 34.86 da opises sta se desava kada imas razno tlo i koristi one dve slike so imaju 
% %             odgovor na Northridge in Kocaeli, za SSS i CCC tlo...
% %  \end{itemize}


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

\begin{frame}
 \frametitle{Variable Soil}

\begin{itemize}
 
  \item Stiff frames (bends) in variable stiffness soils

\vspace*{2mm}
  \item Short period \\
        earthquake

\vspace*{2mm}
  \item Matching EQ, soil \\
        and structure \\
        stiffness

\vspace*{2mm}
  \item Variable soil\\
        creates extra\\
        demand on main\\
        girder

\end{itemize}

\vspace*{-55mm}
\begin{figure}[!htbp]
\begin{flushright}
\hspace*{40mm}
\includegraphics[width=8.5cm]{/home/jeremic/tex/works/Conferences/2016/Beograd_predavanje_decembar/present/soilmeshDEEP.jpg}
\end{flushright}
\end{figure}


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

\begin{frame}
 \frametitle{Short Period Earthquake, Northridge}



\begin{itemize}
 
  \item Usual assumption: soft soil is a problem

\vspace*{1mm}
  \item Design: static pushover, single bent, soft soil

\vspace*{1mm}
  \item Actual critical behavior: system in stiff and variable soil


\end{itemize}

%\vspace*{-0.7cm} 
\begin{figure}[!htbp] 
\begin{center}
%\hspace*{-1cm}
\includegraphics[width=10.0truecm]{/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{Detailed 3D Bridge Model, 3 Bends}

%
\begin{figure}[!htbp] 
\begin{center}
%
\includegraphics[width=5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_NEES_Bridge/tex_works_Thesis_GuanzhouJie_thesis_Verzija_Februar_Images_3BentModel.pdf}
%
\hfill
%
\includegraphics[width=4.0cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
%
%\hspace*{-0.9cm}
%bridge.}
\end{center}
\end{figure}
%
\end{frame}
%- 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%OVDE
%    
%    
%  %Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_NEES_Bridge/tex_works_Thesis_GuanzhouJie_thesis_Verzija_Februar_Images_MomentBent1Pile1_25s_2ndC.pdf}
%  %Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_NEES_Bridge/tex_works_Thesis_GuanzhouJie_thesis_Verzija_Februar_Images_MomentBent2Pile1_25s_2ndC.pdf}
%  %Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_NEES_Bridge/tex_works_Thesis_GuanzhouJie_thesis_Verzija_Februar_Images_MomentBent3Pile1_25s_2ndC.pdf}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%    \frametitle{Short Period E.: Moments, Bent \#1, SSS, CSC, CCC}
%  \begin{figure}[!htbp] 
%  \begin{center}
%  \hspace*{-8mm}
%  \includegraphics[width=12cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_NEES_Bridge/tex_works_Thesis_GuanzhouJie_thesis_Verzija_Februar_Images_MomentBent1Pile1_25s_2ndC.pdf}
%  \end{center}
%  \end{figure}
%  \end{frame}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%    \frametitle{Short Period E.: Moments, Bent \#2, SSS, CSC, CCC}
%  \begin{figure}[!htbp] 
%  \begin{center}
%  \hspace*{-8mm}
%  \includegraphics[width=12cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_NEES_Bridge/tex_works_Thesis_GuanzhouJie_thesis_Verzija_Februar_Images_MomentBent2Pile1_25s_2ndC.pdf}
%  \end{center}
%  \end{figure}
%  \end{frame}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%    \frametitle{Short Period E.: Moments, Bent \#3, SSS, CSC, CCC}
%  \begin{figure}[!htbp] 
%  \begin{center}
%  \hspace*{-8mm}
%  \includegraphics[width=12cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_NEES_Bridge/tex_works_Thesis_GuanzhouJie_thesis_Verzija_Februar_Images_MomentBent3Pile1_25s_2ndC.pdf}
%  \end{center}
%  \end{figure}
%  \end{frame}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
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%  %  \includegraphics[width=12cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_NEES_Bridge/tex_works_Thesis_GuanzhouJie_thesis_Verzija_Februar_Images_MomentBent2Pile1_25s_1stS.pdf}
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%  %  \includegraphics[width=12cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_NEES_Bridge/tex_works_Thesis_GuanzhouJie_thesis_Verzija_Februar_Images_MomentBent3Pile1_25s_1stS.pdf}
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%  %  \includegraphics[width=12cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_NEES_Bridge/tex_works_Thesis_GuanzhouJie_thesis_Verzija_Februar_Images_MomentBent1Pile1_25s_2ndS.pdf}
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\begin{frame}
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\begin{figure}[!htbp] 
\begin{center}
\hspace*{-8mm}
\includegraphics[width=12cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_NEES_Bridge/tex_works_Thesis_GuanzhouJie_thesis_Verzija_Februar_Images_MomentBent1Pile1_25s_3rdS.pdf}
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\begin{figure}[!htbp] 
\begin{center}
\hspace*{-8mm}
\includegraphics[width=12cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_NEES_Bridge/tex_works_Thesis_GuanzhouJie_thesis_Verzija_Februar_Images_MomentBent2Pile1_25s_3rdS.pdf}
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  \frametitle{Short Period E.: Moments, Bent \#3, SSS, CCS, CCC}    
\begin{figure}[!htbp] 
\begin{center}
\hspace*{-8mm}
\includegraphics[width=12cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_NEES_Bridge/tex_works_Thesis_GuanzhouJie_thesis_Verzija_Februar_Images_MomentBent3Pile1_25s_3rdS.pdf}
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\subsection{{\cyrdevet Nuklearna Elektrana}}


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\begin{frame}
 \frametitle{Nuclear Power Plants, Modelling Issues}

\begin{itemize}


  \item Nuclear Power Plants (NPPs), early use of SSI analysis (SASSI, CLASSI, \&c.)

%\vspace*{2mm}
  \item State of practice for ESSI analysis of NPPs:

    \begin{itemize}

      \item Linear elastic material

      \item 1D seismic motions

      \item Incoherent seismic motions

    \end{itemize}


%\vspace*{1mm}
  \item Current state of art for ESSI analysis of NPPs:

                
    \begin{itemize}

      \item Nonlinear soil, rock, contact, structure

      \item 3D (6D) seismic motions

    \end{itemize}



%\vspace*{1mm}
  \item Seismic motions issue/problem


%
%\vspace*{1mm}
%  \item 


\end{itemize}
\end{frame}
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\begin{frame}
 \frametitle{Example Earthquake: M 6.6, Norcia, Italy, 30Oct2016}

  
%\vspace*{-10mm}
\begin{figure}[!hpbt]
%\hspace*{-30mm}
\begin{center}
\includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2016/Beograd_predavanje_decembar/present/Norcia_30Oct2016_ACC_3D.jpg}
\hspace*{10mm}
\includegraphics[width=3cm]{/home/jeremic/tex/works/Conferences/2016/Beograd_predavanje_decembar/present/Norcia_30Oct2016_ACC_2D_PGA.jpg}
\\
\vspace*{3mm}
%
\includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2016/Beograd_predavanje_decembar/present/Norcia_30Oct2016_DISP_3D.jpg}
\hspace*{10mm}
\includegraphics[width=3cm]{/home/jeremic/tex/works/Conferences/2016/Beograd_predavanje_decembar/present/Norcia_30Oct2016_DISP_2D_PGD.jpg}
\end{center}
\end{figure}

\begin{flushright}
\vspace*{-10mm}
\hspace*{50mm}
\tiny{StrongMotions.com}
\end{flushright}
%
% 
% \begin{itemize}
% %\vspace*{0.3cm}
%   \item 
% 
% \vspace*{1mm}
%   \item 
% 
% \end{itemize}
\end{frame}
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\begin{frame}
 \frametitle{1D, 2D, 3D Earthquakes?}

\vspace*{-4mm}
  
\begin{figure}[!hpbt]
\begin{center}
\hspace*{-8mm}
\includegraphics[width=6cm]{/home/jeremic/tex/works/consulting/2016/IAEA/Report/Chapter_4_Free_Field_Ground_Motions/Lotung_LSST07_FA25.jpeg}
\hspace*{3mm}
\includegraphics[width=6cm]{/home/jeremic/tex/works/consulting/2016/IAEA/Report/Chapter_4_Free_Field_Ground_Motions/Lotung_LSST12_FA25.jpeg}
\end{center}
\end{figure}
%

\vspace*{-4mm}
\begin{itemize}
  \item SMART-1 array, Lotung, Taiwan, 
  
  \item LSST07: almost 2D (the only one!)
  
  \item LSST12: full 3D

\end{itemize}


\end{frame}
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%    
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
\frametitle{3D (6D) or 1D Seismic Motions for NPPs}


\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}


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% 
% 
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Stress Testing NPP SSI Systems}
% 
% 
% 
% \begin{itemize}
% 
% \item Excite SSI system: different waves, energies and durations
% 
% \item Try to "break" the system, shake-out strong and weak links
% 
% 
% %\vspace*{3mm}
% %\item 
% 
% \end{itemize}
% 
% \vspace*{-2mm}
% \begin{figure}[!htb]
% \begin{center}
% \includegraphics[width=8cm]{/home/jeremic/tex/works/Conferences/2015/CNSC_July/Present/Stress_test_NPP_idea.jpg}
% \hspace*{-5mm}
% \end{center}
% \end{figure}
% 
% 
% 
% \end{frame}
% 

%  


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
 \frametitle{Synthetic (Realistic) Test Motions}


% online   
  \begin{center}
  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input.mp4}
    {\includegraphics[width=55mm]{movie_input_mp4_icon.jpeg}}
  %
  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input_closeup.mp4}
    {\includegraphics[width=50mm]{movie_input_closeup_mp4_icon.jpeg}}
  \end{center}
% online  

% local  % local 
% local  % local 
% local  % local 
% local  \vspace*{2mm}
% local  \begin{center}
% local  %\movie[label=show3,width=8.5cm,poster,autostart,showcontrols,loop]
% local  \hspace*{-12mm}
% local  %\movie[label=show3,width=6.0cm,poster]
% local  %  {\includegraphics[width=70mm]{movie_input_mp4_icon.jpeg}}{movie_input.mp4}
% local  %
% local  %\hspace*{-2mm}
% local  %%\hfill
% local  %%\hspace*{-7mm}
% local  \movie[label=show3,width=80mm,poster,toolbar,mouse=true]
% local    {\includegraphics[width=80mm]{movie_input_closeup_mp4_icon.jpeg}}{movie_input_closeup.mp4}
% local  \hspace*{-12mm}
% local  \end{center}
% local  % local 
% local  % local 
% local  % local 
% 


\end{frame}



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

\begin{itemize}

  \item Danger of picking one component (1D) of motions 
  
  \item  Excellent  (forced)  fit,  but it is  not a prediction
%   and information is lost
%  (goal is to predict and inform and not (force) fit)


\end{itemize}

% local  
% local  % local
% local  \vspace*{-4mm}
% local  \begin{center}
% local  \hspace*{-16mm}
% local  \movie[label=show3,width=61mm,poster]
% local    {\includegraphics[width=60mm]{movie_ff_3d_mp4_icon.jpeg}}{movie_ff_3d.mp4}
% local  %\hspace*{-2mm}
% local  %\hfill
% local  \movie[label=show3,width=61mm,poster]
% local    {\includegraphics[width=60mm]{movie_ff_1d_mp4_icon.jpeg}}{movie_ff_1d.mp4}
% local  \hspace*{-16mm}
% local  \end{center}
% local  % local  
% local  

% online 
% online 
% online 
\begin{center}
\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}
  {\includegraphics[width=50mm]{movie_ff_3d_mp4_icon.jpeg}}
%
\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}
  {\includegraphics[width=50mm]{movie_ff_1d_mp4_icon.jpeg}}
\end{center}
% online  
% online  
% online  



% 




\end{frame}





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{6D vs 1D NPP ESSI Response Comparison}

% local % local
% local \vspace*{-2mm}
% local \begin{center}
% local \hspace*{-7mm}
% local \movie[label=show3,width=88mm,poster]
% local   {\includegraphics[width=88mm]{movie_2_npps_mp4_icon.jpeg}}{movie_2_npps.mp4}
% local \end{center}
% local % local


% online
% online
% online
\begin{center}
%\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}
  {\includegraphics[width=80mm]{movie_2_npps_mp4_icon.jpeg}}
\end{center}
% online
% online
% online

\end{frame}





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} 
\frametitle{6D vs 1D NPP ESSI, Top of Containment, Differences}


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

\begin{figure}[!htbp]
\begin{center}
\hspace*{-10mm}
\includegraphics[width=6.6cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_ESSI_for_NPPs/02_displacements_Containment_building_top.jpg}
\hspace*{-5mm}
\includegraphics[width=6.6cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_ESSI_for_NPPs/02_accelerations_Containment_building_top.jpg}
\end{center}
\end{figure}



\end{frame}






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% out for now % MPa, $\nu$=0.25, $M$=1.2, $k_d$=$\xi$=0, $h$=$G_{max}$/(15$p_0$), $m$=1)}
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% out for now % \begin{tabular}{cccc} 
% out for now % %\hline 
% out for now % {\tiny $4.5s$}
% out for now % &
% out for now % {\tiny $4.6s$}
% out for now % &             
% out for now % {\tiny $4.7s$}
% out for now % &             
% out for now % {\tiny $4.8s$}
% out for now % \\            
% out for now % \includegraphics[width=1.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/slide450.pdf}
% out for now % &
% out for now % \includegraphics[width=1.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/slide460.pdf}
% out for now % &
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% out for now % &
% out for now % \includegraphics[width=1.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/slide480.pdf}
% out for now % \\
% out for now % {\tiny $4.9s$}
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% out for now % {\tiny $5.0s$}
% out for now % &             
% out for now % {\tiny $5.1s$}
% out for now % &             
% out for now % {\tiny $5.2s$}
% out for now % \\            
% out for now % \includegraphics[width=1.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/slide490.pdf}
% out for now % &
% out for now % \includegraphics[width=1.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/slide500.pdf}
% out for now % &
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% out for now % %\\
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% out for now % %\caption{Distribution of sliding along the contact interface for Ricker wave
% out for now % %(gray scale given in meters)}
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% out for now % \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/energy_sliding_92/energy_time.pdf}
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% out for now %  \frametitle{Soil Volume Response}
% out for now % 
% out for now % \begin{itemize}
% out for now %   \item Soil behavior is very much a function of volumetric response
% out for now % 
% out for now %   \item Dilative soils: increase  volume due to shearing
% out for now %   \item Compressive soils: decrease  volume due to shearing
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% out for now %   \item Modulus reduction and damping curves do not provide volumetric data
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% out for now % % \frametitle{No Volume Change, Compressive and Dilative Soil}
% out for now %  \frametitle{No Volume Change and Dilative Soil}
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% out for now % \begin{center}
% out for now % \hspace*{-1cm}
% out for now %   \includegraphics[width=6.3cm]{/home/jeremic/tex/works/Thesis/FedericoPisano/Pisano_model/Issue_of_dilatancy/sine1Hz-4.pdf}
% out for now % %\hspace*{-0.3cm}
% out for now % %  \includegraphics[width=4.3cm]{/home/jeremic/tex/works/Thesis/FedericoPisano/Pisano_model/Issue_of_dilatancy/sine1Hz_comp-4.pdf}
% out for now % \hspace*{-0.3cm}
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% out for now % %   \includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/FedericoPisano/Pisano_model/Issue_of_dilatancy/Northridge1-2.pdf}
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% out for now \frametitle{Foundation -- Soil/Rock Slip}
% out for now 
% out for now \begin{itemize}
% out for now 
% out for now   \item Foundation slab slips significantly during an earthquake
% out for now   
% out for now   \item Base isolation (?!) and energy dissipation
% out for now    
% out for now    \item Soil on the side restricts movements
% out for now 
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% out for now \begin{center}
% out for now \hspace*{-6mm}
% out for now \includegraphics[width=2.5cm]{/home/jeremic/tex/works/Conferences/2015/SMiRT_23/_XX_Use_of_Nonlinear_Time_Domain_Analysis_for_NPP_Design/Paper/slip_at_1_percent_02.jpg}
% out for now \hfill                     
% out for now \includegraphics[width=9cm]{/home/jeremic/tex/works/Conferences/2015/SMiRT_23/_XX_Use_of_Nonlinear_Time_Domain_Analysis_for_NPP_Design/Paper/Slipping.pdf}
% out for now \hspace*{-6mm}
% out for now %\caption{Snapshot  of  a  relative  displacements  between  foundation  slab and
% out for now %soil/rock  (left)  and  the  amount  of  slip  at  a center of a foundation slab
% out for now %(beneath containment and internal sticks).}
% out for now \end{center}
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% out for now 
% out for now  
% out for now \begin{itemize}
% out for now 
% out for now   \item Significant reduction of horizontal motions
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% out for now \begin{center}
% out for now \hspace*{-7mm}
% out for now %\includegraphics[width=6cm]{/home/jeremic/tex/works/Conferences/2015/SMiRT_23/_XX_Use_of_Nonlinear_Time_Domain_Analysis_for_NPP_Design/Paper/results_24June2015/SA_X_containment_building_top_3d_nonlin_vs_linear.pdf}
% out for now \includegraphics[width=6cm]{/home/jeremic/tex/works/Conferences/2015/SMiRT_23/PresentDesign/FromJose/SA_X_containment_building_top_3d_nonlin_vs_linear.pdf}
% out for now %\\
% out for now %\includegraphics[width=8cm]{/home/jeremic/tex/works/Conferences/2015/SMiRT_23/_XX_Use_of_Nonlinear_Time_Domain_Analysis_for_NPP_Design/Paper/results_24June2015/SA_Y_containment_building_top_3d_nonlin_vs_linear.pdf}
% out for now %\\
% out for now %\includegraphics[width=6cm]{/home/jeremic/tex/works/Conferences/2015/SMiRT_23/_XX_Use_of_Nonlinear_Time_Domain_Analysis_for_NPP_Design/Paper/results_24June2015/SA_Z_containment_building_top_3d_nonlin_vs_linear.pdf}
% out for now \includegraphics[width=6cm]{/home/jeremic/tex/works/Conferences/2015/SMiRT_23/PresentDesign/FromJose/SA_Z_containment_building_top_3d_nonlin_vs_linear.pdf}
% out for now %\includegraphics[width=12cm]{/home/jeremic/tex/works/Conferences/2015/SMiRT_23/_XX_Use_of_Nonlinear_Time_Domain_Analysis_for_NPP_Design/Paper/results_17June2015/Comparissons/FFT_Accel_containment_building_1percent_vs_10percent.pdf}
% out for now % \caption{\label{comparison_containment} Comparison    of  spectral  accelerations  at the top of a containment 
% out for now % structure  for 
% out for now % X directions (left), 
% out for now % %Y direction (middle) 
% out for now % and 
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% out for now % \hspace*{-10mm}
% out for now % \includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/NPP_Feb2016/fig1.png}
% out for now % \hspace*{-10mm}
% out for now % \includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/NPP_Feb2016/fig2.png}
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\subsection{{\cyrdevet Mehanika i Teorija Verovatno\cj{}a}}

            
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\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{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}

% 




                                          
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame} 
% 
% \frametitle{Uncertainty Propagation through Constitutive Eq.}
% 
% % 
% 
% \begin{itemize}
% 
%  
% 
% 
% \item Incremental el--pl constitutive equation  
%      $\displaystyle \Delta \sigma_{ij} = D_{ijkl} \displaystyle \Delta \epsilon_{kl}$
% 
%  
%   
% %\begin{normalsize}
% 
% %    
% %    \begin{equation}
% %    \nonumber
% %    \frac{d\sigma_{ij}}{dt} = D_{ijkl} \frac{d\epsilon_{kl}}{dt}
% %    \end{equation}
%     
%     
%     \begin{eqnarray}
%     \nonumber
%      D_{ijkl} = \left\{\begin{array}{ll}
% %
%      D^{el}_{ijkl}
% %
% %
%         \;\;\; & \mbox{\large{~for elastic}} \\
% %
%            \\
% %
%            D^{el}_{ijkl}
%            -
%            \frac{\displaystyle  D^{el}_{ijmn} m_{mn} n_{pq} D^{el}_{pqkl}}
%            {\displaystyle n_{rs} D^{el}_{rstu} m_{tu} - \xi_* r_*}
% 
%            \;\;\; & \mbox{\large{~for elastic--plastic}}
% %
%            \end{array} \right.
%            \end{eqnarray}
% 
% %\end{normalsize}
% 
%  
% 
% 
% 
% %\vspace{0.5cm}
% % \item Non--linear coupling in the El--Pl modulus
% 
% 
% \item What if all (any) material parameters are uncertain
% 
% \item PEP and SEPFEM methods for spatially variable and point uncertain material 
% 
% 
% %-  \item Focus on 1-D $\rightarrow$ a nonlinear ODE with random coefficient and random forcing
% %-  
% %-  
% %- 
% %-  \begin{eqnarray}
% %-  \nonumber
% %-  \frac{d\sigma(x,t)}{dt} &=& \beta(\sigma(x,t),D^{el}(x),q(x),r(x);x,t) \frac{d\epsilon(x,t)}{dt} \\
% %-  \nonumber
% %-  &=& \eta(\sigma,D^{el},q,r,\epsilon; x,t)  \mbox{\ \ \ \ with an I.C. $\sigma(0)=\sigma_0$}
% %-  \end{eqnarray}
% %- 
%  
% 
% \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} 
     =  
     \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}


\item What if all (any) material and load parameters are uncertain



\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{Probabilistic Stress Solution: \\ Eulerian--Lagrangian form of FPK Equation}

%

%\begin{itemize}
% 3D
\begin{footnotesize}

\begin{eqnarray}
\nonumber
\lefteqn{\displaystyle \frac{\partial P(\sigma_{ij}(x_t,t), t)}{\partial t} = \displaystyle \frac{\partial}{\partial \sigma_{mn}} 
\left[ \left\{\left< \vphantom{\int_{0}^{t}} \eta_{mn}(\sigma_{mn}(x_t,t), E_{mnrs}(x_t), \epsilon_{rs}(x_t,t))\right> \right. \right.} \\
\nonumber
&+&  \left.  \left.  \int_{0}^{t} d\tau Cov_0 \left[\displaystyle \frac{\partial
\eta_{mn}(\sigma_{mn}(x_t,t), E_{mnrs}(x_t),
\epsilon_{rs}(x_t,t))} {\partial \sigma_{ab}}; \right.  \right. \right. \\
\nonumber
& & \left. \left. \left. \eta_{ab} (\sigma_{ab}(x_{t-\tau}, t-\tau), E_{abcd}(x_{t-\tau}), \epsilon_{cd}(x_{t-\tau}, t-\tau) 
\vphantom{\int_{0}^{t}} \right] \right \} P(\sigma_{ij}(x_t,t),t) \right] \\
\nonumber
&+& \displaystyle \frac{\partial^2}{\partial \sigma_{mn} \partial \sigma_{ab}} \left[ \left\{ \int_{0}^{t} d\tau Cov_0 \left[ 
\vphantom{\int_{0}^{t}} \eta_{mn}(\sigma_{mn}(x_t,t), E_{mnrs}(x_t), \epsilon_{rs}(x_t,t)); \right. \right. \right. \\
\nonumber
& & \left. \left. \left. \eta_{ab} (\sigma_{ab}(x_{t-\tau}, t-\tau), E_{abcd}(x_{t-\tau}), \epsilon_{cd}(x_{t-\tau}, t-\tau)) 
\vphantom{\int_{0}^{t}} \right] \vphantom{\int_{0}^{t}} \right\} P(\sigma_{ij}(x_t,t),t) \right]
\end{eqnarray}

 
\end{footnotesize}

{\small (Jeremi{\'c} et al. 2007, Sett and Jeremi{\'c} 2010, Sett et al. 2007, 2011)}




% 1D % 1D
% 1D \begin{footnotesize}
% 1D \begin{eqnarray}
% 1D \nonumber
% 1D &&\displaystyle \frac{\partial P(\sigma(x_t,t), t)}{\partial t}=
% 1D - \displaystyle \frac{\partial}{\partial \sigma} \left[ \left\{\left< \vphantom{\int_{0}^{t} d\tau} \eta(\sigma(x_t,t), D^{el}(x_t),
% 1D q(x_t), r(x_t), \epsilon(x_t,t)) \right> \right. \right. \\
% 1D \nonumber
% 1D &+& \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),
% 1D \epsilon(x_t,t))}{\partial \sigma}; \right. \right. \right. \\
% 1D \nonumber
% 1D & & \left. \left. \left. \eta(\sigma(x_{t-\tau},t-\tau), D^{el}(x_{t-\tau}), q(x_{t-\tau}), r(x_{t-\tau}),
% 1D \epsilon(x_{t-\tau},t-\tau) \vphantom{\int_{0}^{t} d\tau} \right] \right \} P(\sigma(x_t,t),t) \right] \\
% 1D \nonumber
% 1D &+& \displaystyle \frac{\partial^2}{\partial \sigma^2} \left[ \left\{ \int_{0}^{t} d\tau Cov_0 \left[ \vphantom{\int_{0}^{t}}
% 1D \eta(\sigma(x_t,t), D^{el}(x_t), q(x_t), r(x_t), \epsilon(x_t,t)); \right. \right. \right. \\
% 1D \nonumber
% 1D & & \left. \left. \left. \eta (\sigma(x_{t-\tau},t-\tau), D^{el}(x_{t-\tau}), q(x_{t-\tau}), r(x_{t-\tau}),
% 1D \epsilon(x_{t-\tau},t-\tau)) \vphantom{\int_{0}^{t}} \right] \vphantom{\int_{0}^{t}} \right\} P(\sigma (x_t,t),t) \right] \\
% 1D \nonumber
% 1D \end{eqnarray}
% 1D 
% 1D \end{footnotesize}





\end{frame}







%-- 
%-- \item 6 equations
%-- 
%-- \item Complete description of 3-D probabilistic stress-strain response
%-- 
%-- \end{itemize}
%-- 
%--  


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

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

 

\begin{itemize}

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

%

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


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

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

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


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

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


%\vspace*{0.2truecm}

\end{itemize}


\end{frame}






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

\frametitle{Probabilistic Elastic-Plastic Response}


\begin{figure}[!hbpt]
\begin{center}
\hspace*{-10mm}
\includegraphics[width=6cm]{/home/jeremic/tex/works/Conferences/2012/DOE-LLNL-workshop-27-28-Feb-2012/ProbabilisticYielding_vonMises_G_and_cu_very_uncertain_Contour_PDF-edited.pdf}
\includegraphics[width=6.5cm]{/home/jeremic/tex/works/Conferences/2012/DOE-LLNL-workshop-27-28-Feb-2012/ProbabilisticYielding_vonMises_G_and_cu_very_uncertain_PDF-edited.pdf}
\end{center}
\end{figure}

\end{frame}

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

\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, Sett et al. 2011):

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

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

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

%\item Fokker--Planck--Kolmogorov approach based probabilistic constitutive integration
%      at Gauss integration points


\end{itemize}

%  \noindent Salient Features:
       
%      \begin{itemize}
%
%      \item Efficient representation of input random fields into finite number of random
%            variables using KL-expansion
%      
%      \item Representation of (unknown) solution random variables using polynomial chaos of
%            (known) input random variables
%
%      \item Fokker--Planck--Kolmogorov approach based probabilistic constitutive integration
%      at Gauss integration points
%
%      \end{itemize}
%      
%%   \end{itemize}
%
\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 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=9.0cm]
 {/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}

% 









%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection{Seismic Wave Propagation Through Uncertain Soils}
%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   
%   \begin{frame}
%   \frametitle{Example: "Uniform" CPT  Site Data}
%   
%   
%   %\vspace*{-0.7cm}
%   %\begin{figure}
%   \begin{center}
%   \includegraphics[height=6.0cm]{/home/jeremic/tex/works/Thesis/KallolSett/Dissertation/figures/CPT_DataAnalysis_Plots/EastWestProfile-Edited.pdf}
%   \end{center}
%   %\end{figure}
%   
%   
%   \end{frame}
%   
%   
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   
%   \begin{frame}
%   
%   
%   \frametitle{Simulation Results: PDFs of all DOFs (and $\sigma_{ij}$, $\epsilon_{ij}$, etc.)}
%   %\frametitle{Full PDFs for Real Data Case}
%   
%   
%   \begin{itemize}
%   \vspace*{7mm}
%     \item Propagate seismic \\
%           wave through \\
%           uncertain soil
%   \vspace*{3mm}
%     \item Stochastic Elastic-Plastic\\
%           Finite Element Method \\
%           (SEPFEM)  \\    
%   \vspace*{3mm}
%     \item Full PDF at \\
%           each time step $\Delta t$
%   \end{itemize}
%   
%   
%   \vspace*{-4.90cm}
%   \begin{flushright}
%   \includegraphics[width=6.0cm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/Plots_with_Labels/EvolutionaryPDF_Actual-Edited.pdf}
%   %\vspace*{-0.75cm}
%   %\includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2007/USC_seminar/Application_figs/Mean_and_SDElasticPlastic_ps.pdf}
%   \end{flushright}
%   
%   % 
%   \end{frame}
%   
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   
%   \begin{frame}
%   
%   
%   \frametitle{PDF at each $\Delta t$ (say at $6$ s)}
%   
%   
%   
%   \begin{figure}
%   \begin{center}
%   \hspace*{1.75cm}
%   \includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/Plots_with_Labels/PDFs_at6sec_Actual_vs_NoData-Edited.pdf}
%   \vspace*{-0.75cm}
%   %\includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2007/USC_seminar/Application_figs/Mean_and_SDElasticPlastic_ps.pdf}
%   \end{center}
%   \end{figure}
%   
%   % 
%   \end{frame}
%   
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   
%   
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   
%   \begin{frame}
%   
%   
%   \frametitle{PDF $\rightarrow$ CDF (Fragility) at $t=6$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}
%   
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   
%   \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}
%   
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   
%   
%   
%   
%   
%   
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   
%   \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}
%   
%   
%   
%   
%   
%   
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   
% out 
% out 
% out 
% out 
% out % out
% out % out 
% out % out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out % out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out % out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out % out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out \begin{frame} 
% out 
% out \frametitle{Uncertainty Propagation through 
% out Inelastic System}
% out 
% out % 
% out 
% out \begin{itemize}
% out 
% out \item Incremental el--pl constitutive equation
% out %  
% out     \begin{eqnarray}
% out     \nonumber
% out   \Delta \sigma_{ij} 
% out   = 
% out %  E^{EP}_{ijkl} 
% out      E^{EP}_{ijkl} 
% out      =  
% out      \left[
% out      E^{el}_{ijkl}
% out        -
% out        \frac{\displaystyle  E^{el}_{ijmn} m_{mn} n_{pq} E^{el}_{pqkl}}
% out            {\displaystyle n_{rs} E^{el}_{rstu} m_{tu} - \xi_* h_*}
% out            \right]
% out   \Delta \epsilon_{kl}
% out     \end{eqnarray}
% out 
% out  
% out   
% out 
% out \vspace*{5mm}
% out \item Dynamic Finite Elements
% out %
% out \begin{equation}
% out {\bf M} \ddot{\bf u} +
% out {\bf C} \dot{\bf u} +
% out {\bf K}^{ep} {\bf u} =
% out {\bf F}
% out     \nonumber
% out \end{equation}
% out 
% out 
% out \end{itemize}
% out 
% out 
% out \end{frame}
% out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out % 
% out %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out %  \begin{frame} 
% out %  \frametitle{Critique of our Previous Work, PEP and SEPFEM}
% out %  
% out %  \begin{itemize}
% out %  
% out %  \item Constitutive weighted coefficients $N_1$ and $N_2$ do not work well for
% out %  stress solution!
% out %  
% out %  \vspace{1mm}
% out %  \item  We  suggested   that $\sigma(t)$ be considered a $\delta$-correlated, and
% out %  based  on  that  simplified  stiffness  equations.  Both  the assumption and the
% out %  resulting equation were not right.
% out %  
% out %  
% out %  \vspace{1mm}
% out %  \item  On  a  SEPFEM  level,  stiffness  needs  update  basis  functions  and KL
% out %  coefficients  in  each  step.  We updated   the   eigenvalues  
% out %  $\lambda_i$  and kept the same structure (Karhunen-Loeve)  in  the approximation
% out %  of  the  stiffness, which is not physical
% out %  
% out %  \vspace{1mm}
% out %  \item   Implicitly  assumed    that   the  stiffness remains Gaussian, which is 
% out %  not the case
% out %  
% out %  
% out %  \end{itemize}
% out %  
% out %  
% out %  
% out %  
% out %  
% out %  
% out %  
% out %  \end{frame}
% out %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out %  
% out %  
% out %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out %  \begin{frame} 
% out %  \frametitle{Gradient Flow Theory of Probabilistic Elasto-Plasticity}
% out %  
% out %  
% out %  Decomposition of an elastoplastic random process:
% out %  % into 
% out %  %the following general form:
% out %  %
% out %  \begin{eqnarray}
% out %  \begin{array}{c c c c c}
% out %   \bigg( \displaystyle{\pder[]{t}} - \mathcal{L}_{rev} \bigg) P(\boldsymbol{\sigma},t) &=& 0& \qquad &\text{if } 
% out %   \boldsymbol{\sigma} \in \Omega^{el} 
% out %   \\
% out %   ~
% out %   \\
% out %   \bigg( \displaystyle{\pder[]{t}} - \mathcal{L}_{irr} \bigg) P(\boldsymbol{\sigma},t) &=& 0& \qquad &\text{if } 
% out %   \boldsymbol{\sigma} \in \Omega^{el} \cup \Omega^{pl}
% out %  \end{array} 
% out %  \nonumber
% out %  \end{eqnarray}
% out %  
% out %  %
% out %  \begin{itemize}
% out %  
% out %  \item Reversible ($\mathcal{L}_{rev} $) and Irreversible ($\mathcal{L}_{irr} $) operators
% out %  %
% out %  
% out %  \vspace*{2mm}
% out %  \item Yield PDF is an attractor, similar to plastic corrector
% out %  
% out %  \vspace*{2mm}
% out %  \item Ergodicity of the elastic-plastic process can be proven!
% out %  
% out %  \end{itemize}
% out %  
% out %  
% out %  
% out %  
% out %  
% out %  \end{frame}
% out %  
% out %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out %  
% out %  
% out %  \begin{frame} 
% out %  \frametitle{Gradient Flow Theory of Probabilistic Elasto-Plasticity}
% out %  
% out %  \begin{itemize}
% out %  
% out %  \item 
% out %  Elastic, reversible process, Fokker-Planck (forward Kolmogorov) equation
% out %  %
% out %  \begin{equation}
% out %   \pder[P (\boldsymbol{\sigma},t)]{t} 
% out %    = -\nabla \cdot (\langle \boldsymbol{E} \dot{\boldsymbol{\epsilon}} \rangle P(\boldsymbol{\sigma},t))
% out %    + t ~\text{Var}[\boldsymbol{E}\dot{\boldsymbol{\epsilon}}] \Delta P(\boldsymbol{\sigma},t) 
% out %  \nonumber
% out %  \end{equation}
% out %  %
% out %  \begin{equation}
% out %   \mathcal{L}_{rev} = \nabla \cdot (t \,\text{Var}[\boldsymbol{C}\dot{\boldsymbol{\epsilon}}] \nabla - 
% out %   \langle \boldsymbol{C} \dot{\boldsymbol{\epsilon}} \rangle)
% out %  \nonumber
% out %  \end{equation}
% out %  
% out %  \item 
% out %  Plastic, irreversible process,  Fokker-Planck (forward Kolmogorov) equation 
% out %  %
% out %  \begin{equation}
% out %   \pder[P(\boldsymbol{\sigma},t)]{t} = \nabla \cdot (\nabla \Psi(\boldsymbol{\sigma})
% out %   P(\boldsymbol{\sigma},t)) + D \Delta P(\boldsymbol{\sigma},t)
% out %  \nonumber
% out %  \end{equation}
% out %  %   
% out %  \begin{equation}
% out %   \mathcal{L}_{irr} = D \nabla \cdot \bigg(\nabla - \frac{\nabla P_y(\boldsymbol{\sigma})}{P_y(\boldsymbol{\sigma})}\bigg)
% out %  \nonumber
% out %  \end{equation}
% out %  %
% out %  
% out %  \end{itemize}
% out %  
% out %  \end{frame}
% out %  
% out %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out %  \begin{frame} 
% out %  \frametitle{Gradient Flow Theory of Probabilistic Elasto-Plasticity}
% out %  
% out %  \begin{itemize}
% out %  
% out %  \item Limiting (final) distribution
% out %  is  considered  to  be  known 
% out %  %(given as a material parameter) and 
% out %  
% out %  \vspace*{2mm}
% out %  \item Underlying potential  leading  to  this  distribution is sought
% out %  
% out %  \vspace*{2mm}
% out %  \item Transition from uncertain elastic to uncertain plastic response
% out %  
% out %  
% out %  \vspace*{2mm}
% out %  \item Only in a 1D   elastoplastic   problem  does  one  end  up  with  a  stationary
% out %  distribution
% out %  
% out %  \vspace*{2mm}
% out %  \item In  higher dimensional problems this yield stress distribution is
% out %  only   "marginally"  stationary  along  one  or  a  combination  of  the  stress
% out %  components.
% out %  
% out %  \end{itemize}
% out %  
% out %  
% out %  \end{frame}
% out %  
% out %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out \begin{frame} 
% out \frametitle{Probabilistic Elasto-Plasticity: von Mises Surface}
% out 
% out 
% out %        An example of a Mises probabilistic yield surface is given in Fig.~\ref{ProbCylinder}.
% out 
% out \begin{figure}[H]
% out \centering
% out \vspace*{-5mm}
% out %\hspace*{-30mm}
% out  \includegraphics
% out %  [scale = 0.8, trim = 0.6in 0.4in 0.6in 0.4in, clip=true]
% out   [width=12cm]
% out    {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Probabilistic_von_Mises_Surface.jpg}
% out % \caption{An example of a probabilistic von Mises yield surface.}
% out  \label{ProbCylinder}
% out \end{figure}
% out 
% out 
% out 
% out \end{frame}
% out 
% out 
% out 
% out 
% out 
% out %  % 
% out %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out %  \begin{frame} 
% out %  \frametitle{Gradient Theory of Probabilistic Elasto-Plasticity: Numerical Solution}
% out %  
% out %  
% out %  \begin{itemize}
% out %           
% out %  \item  Using  radial  basis  functions  (a  meshless  method)  for solving
% out %  Fokker-Planck equations for uncertain elastic-plastic response
% out %  
% out %  
% out %  \vspace*{6mm}
% out %  \item   Details in a talk by Mr. Karapiperis later this afternoon (room 2, MS-6,
% out %  17:00-19:00, last talk) 
% out %  
% out %  
% out %  \end{itemize}
% out %  % %
% out %  
% out %  
% out %  \end{frame}
% out %  
% out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out \begin{frame} 
% out \frametitle{Gradient Theory of Probabilistic Elasto-Plasticity: 
% out Verification, Elastic-Perfectly Plastic}
% out                
% out 
% out %\vspace*{-3mm}
% out \begin{figure}[H]
% out \centering
% out  \includegraphics
% out % [scale = 0.55, trim = 0.0in 0.0in 0.0in 0.0in, clip=true]
% out  [width=8cm]
% out  {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/M+-SD_1D_Perf_Cyclic.pdf}
% out %  \caption{Combining  the  above  plots to get the evolution of mean $\pm$ std.
% out % deviation of stress.}
% out  \label{MSD_12}
% out \end{figure}
% out 
% out 
% out \end{frame}
% out 
% out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out 
% out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out %\subsection{SEPFEM}
% out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out 
% out %  
% out %  \begin{frame}{Stochastic Elastic-Plastic FEM (SEPFEM)}
% out %  
% out %  \begin{itemize}
% out %   \item<1> KL-PC expansion of material random fields (stiffness, etc)
% out %  %
% out %  % \begin{equation*}
% out %  $
% out %  \mathbb{D}(\bold{x}, \theta) = \sum_{i=0}^{M} r_{i}(\bold{x}) \Phi_i[\{\xi_r(\theta)\}]
% out %   \label{nonGaussian1}
% out %  $
% out %  %\end{equation*}
% out %  
% out %   \item<1> PC expansion of displacement field
% out %  %
% out %  \begin{eqnarray*}
% out %  u(\bold{x},\theta) = \sum_{i=0}^p d_i(\bold{x}) \psi_i[\{\xi_r(\theta)\}]
% out %  \label{PC1}
% out %  \end{eqnarray*}
% out %  
% out %  \item<1> Stochastic Galerkin
% out %  
% out %  \begin{eqnarray*}
% out %  \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} =
% out %  \Phi_{m}\langle\psi_i[\{\xi_r\}]\rangle
% out %  \label{Lognormal6}
% out %  \end{eqnarray*}
% out %  
% out %   \end{itemize}
% out %  
% out %  
% out %  \end{frame}
% out %  
% out %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out %  
% out %  \begin{frame}{SEPFEM Statistical linearization}
% out %  
% out %  Update the FE stiffness in the elastoplastic regime:
% out %  
% out %  \begin{itemize}
% out %   \item  Solve elastoplastic FPE for each integration point
% out %  %
% out %  \begin{eqnarray*}
% out %   \pder[P^{nl}(\sigma,t)]{t}
% out %   &=& \pder[]{\sigma} \bigg(\bigg\langle D^k (1 - P[\Sigma_y \leq \sigma]) \frac{\Delta
% out %   \epsilon}{\Delta t} \bigg\rangle P\bigg) \nonumber \\
% out %   & & + \pder[^2]{\sigma^2} \bigg( t Var\bigg[ D^k (1 - P[\Sigma_y \leq \sigma]) \frac{\Delta
% out %   \epsilon}{\Delta t} \bigg] P\bigg)
% out %   \label{SEPFEMLinearization1}
% out %  \end{eqnarray*}
% out %  
% out %  \item Consider an equivalent linear FPE
% out %  %
% out %  \begin{eqnarray*}
% out %   \pder[P^{lin}(\sigma,t)]{t}
% out %   &=& N_{(1)}^{eq} \pder[P]{\sigma} + N_{(2)}^{eq} \pder[^2 P]{\sigma^2}
% out %   \label{SEPFEMLinearization2}
% out %  \end{eqnarray*}
% out %  
% out %  \item Linearization of the PC coeff. as an optimization problem
% out %  %
% out %  \begin{equation*}
% out %   \pder[P^{lin}(\sigma,t)]{t}
% out %   = \pder[P^{nl}(\sigma,t)]{t}
% out %  \end{equation*}
% out %  
% out %  
% out %  \end{itemize}
% out %  
% out %  \end{frame}
% out %  
% out %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out %  
% out %  \begin{frame}{Dynamic, Time Domain, SEPFEM}
% out %  
% out %  \begin{itemize}
% out %   \item Gaussian formulation inadequate due to occurrence of "probabilistic softening" modes
% out %   $\Rightarrow$ Need for positive definite kernel
% out %  
% out %  \vspace*{2mm}
% out %   \item Stochastic forcing  (e.g. uncertain earthquake)
% out %  
% out %  \vspace*{2mm}
% out %   \item   Stability   of   time   marching  algorithm  (Newmark, Rosenbrock, Cubic Hermitian )  analyzed  using
% out %   amplification matrix
% out %  
% out %  \vspace*{2mm}
% out %   \item Long-integration error and higher order statistics phase shift
% out %  \end{itemize}
% out %  
% out %  %  \begin{figure}[H]
% out %  % \centering
% out %  %  \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}
% out %  %  \label{Sendai_1Sine_PCk2PCd8.pdf}
% out %  % \end{figure}
% out %  % 
% out %  
% out %  
% out %  \end{frame}
% out %  
% out 
% out 
% out 
% out 
% out 
% out 
% out  
% out 
% out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out \begin{frame} 
% out \frametitle{Wave Propagation Through Uncertain Soil}
% out 
% out \vspace{-2mm}
% out  
% out \begin{figure}[H]
% out  \centering
% out  \includegraphics
% out % [scale = 0.56, trim = 0.0in 0.15in 0.2in 0.16in, clip=true]
% out  [width=7cm]
% out  {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_profile.png}
% out %
% out %  
% out \includegraphics
% out %[scale = 0.56, trim = 0.0in 0.0in 0.0in 0.0in, clip=true]
% out  [width=1.5cm]
% out {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/meshes.png}
% out % \caption{Simplified profile and properties for the 1-dimensional profile considered.}
% out  \label{Sendai_profile}
% out \end{figure}
% out      
% out 
% out 
% out \vspace{-5mm}
% out 
% out  
% out \begin{figure}[htbp]
% out \centering
% out %\hspace{-0.2in}
% out % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out  \includegraphics
% out % [scale = 0.37, trim = 0.0in 0.0in 0.0in 0.0in,clip=true]
% out  [width=3.5cm]
% out  {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/ShearModulusStats.pdf}
% out \hfill
% out  \includegraphics
% out % [scale = 0.37, trim = 0.0in 0.0in 0.0in 0.0in, clip=true]
% out  [width=3.5cm]
% out  {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/ShearStrengthStats.pdf}
% out %\caption{Shear modulus and shear strength statistics in the middle of the soil column.}
% out \hfill
% out  \includegraphics
% out % [scale = 0.62, trim = 0in 0.15in 0in 0.22in, clip=true]
% out  [width=3.5cm]
% out  {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_1Sine_PCk2PC2_elastic_COV45_BaseInput.pdf}
% out % \caption{Single sine pulse excitation of the soil column at its base.}
% out % \label{Sendai_1Sine_PCk2PC2_elastic_COV45_BaseInput}
% out \end{figure}
% out 
% out 
% out \end{frame}
% out 
% out 
% out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out \begin{frame} 
% out \frametitle{Uncertain Elastic Response at the Surface {\tiny(COV = 120\%)} }
% out  
% out  \vspace*{-2mm}
% out \begin{figure}[H]
% out  \centering
% out  \includegraphics
% out % [scale = 0.62, trim = 0in 0.16in 0in 0.26in, clip=true]
% out  [width=9.3cm]
% out  {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_1Sine_PCk2PC2_elastic_COV120.pdf}
% out %  \caption{Mean  $\pm$ std. deviation of the elastic response at the top of the
% out % soil column for the conservative COV case (COV = 120\%).}
% out % \label{Sendai_1Sine_PCk2PC2_elastic_COV120}
% out \end{figure}
% out 
% out \end{frame}
% out 
% out 
% out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out \begin{frame} 
% out \frametitle{Displacement PDFs at the Surface {\tiny(COV = 120\%)} }
% out 
% out %\vspace*{-20mm} 
% out %\hspace*{-30mm} 
% out \begin{figure}[H]
% out  \centering
% out  \includegraphics
% out %[scale = 0.62, trim = 0in 0.16in 0in 0.26in, clip=true]
% out  [width=10cm]
% out  {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_1Sine_PCk2PC2_elastic_COV120_FullPdf.jpg}
% out %  \caption{Mean  $\pm$ std. deviation of the elastic response at the top of the
% out % soil column for the conservative COV case (COV = 120\%).}
% out % \label{Sendai_1Sine_PCk2PC2_elastic_COV120}
% out \end{figure}
% out 
% out \end{frame}
% out 
% out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out \begin{frame} 
% out \frametitle{Displacement CDFs (Fragilities) at the Surface {\tiny(COV = 120\%)}  }
% out  
% out  \vspace*{-3mm}
% out \begin{figure}[H]
% out  \centering
% out  \includegraphics
% out % [scale = 0.62, trim = 0in 0.16in 0in 0.26in, clip=true]
% out  [width=11cm]
% out  {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_1Sine_PCk2PC2_elastic_COV120_FullCdf.jpg}
% out %  \caption{Mean  $\pm$ std. deviation of the elastic response at the top of the
% out % soil column for the conservative COV case (COV = 120\%).}
% out % \label{Sendai_1Sine_PCk2PC2_elastic_COV120}
% out \end{figure}
% out 
% out \end{frame}
% out 
% out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out \begin{frame} 
% out \frametitle{Probability of Exceedance, $disp=0.1m$ {\tiny(COV = 120\%)}  }
% out  
% out \begin{figure}[H]
% out  \centering
% out  \includegraphics
% out % [scale = 0.62, trim = 0in 0.16in 0in 0.26in, clip=true]
% out  [width=9cm]
% out  {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_1Sine_PCk2PC2_elastic_COV120_ProbExc.pdf}
% out %  \caption{Mean  $\pm$ std. deviation of the elastic response at the top of the
% out % soil column for the conservative COV case (COV = 120\%).}
% out % \label{Sendai_1Sine_PCk2PC2_elastic_COV120}
% out \end{figure}
% out 
% out \end{frame}
% out 
% out % 
% out 
% out 
% out 
% out 
% out 
% out 
% out 
% out 
% out 
% out 
% out 
% out 
% out 
% out 
% out 
% out 
% out 
% out 
% out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out \begin{frame}
% out  \frametitle{Uncertain Material and Loads, Wave Propagation}
% out 
% out \vspace*{6mm}
% out 
% out \begin{itemize}
% out 
% out %    \vspace*{2mm}
% out     \item[]
% out %
% out %\begin{figure}[!hbpt]
% out %\begin{center}
% out %%
% out %\hspace*{-7mm}
% out \hspace*{-12mm}
% out \includegraphics[width=3.5truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01-Ed.pdf}
% out %% \hfill
% out \includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_Histogram_Normal_01-Ed.pdf}
% out %%
% out %\end{center}
% out %\end{figure}
% out 
% out 
% out 
% out     \item Probabilistic Elasto-Plasticity 
% out %   \vspace*{3mm}
% out     \item Stochastic Elastic-Plastic FEM
% out     
% out 
% out 
% out 
% out \end{itemize}
% out 
% out \vspace*{-3.30cm}
% out \begin{figure}[!hbpt]
% out \begin{flushright}
% out \includegraphics[width=50mm]{/home/jeremic/tex/works/Papers/2007/ProbabilisticYielding/figures/vonMises_G_and_cu_very_uncertain/Contour_PDF-edited.pdf}
% out \hspace*{-8mm}
% out \end{flushright}
% out \end{figure}
% out %\hfill
% out 
% out \vspace*{-1.50cm}
% out \begin{figure}[!hbpt]
% out \begin{center}
% out \includegraphics[width=25mm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/Plots_with_Labels/EvolutionaryPDF_Actual-Edited.pdf}
% out %\hfill
% out \includegraphics[width=30mm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/Plots_with_Labels/PDFs_at6sec_Actual_vs_NoData-Edited.pdf}
% out %
% out \includegraphics[width=25mm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/Plots_with_Labels/CDFs_at6sec_Actual_vs_NoData-Edited.pdf}
% out %\hfill
% out \includegraphics[width=35mm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/NewPlots/with_legends_and_labels/Exceedance50cm_LomaPrieta-Edited_ps.pdf}
% out %\vspace*{-0.5cm}
% out \end{center}
% out \end{figure}
% out 
% out 
% out \end{frame}
% out 
% out 
% out 
% out 
% out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out % \begin{frame} 
% out % \frametitle{Probabilistic Elasto-Plasticity: von Mises Surface}
% out % 
% out % 
% out % %        An example of a Mises probabilistic yield surface is given in Fig.~\ref{ProbCylinder}.
% out % 
% out % \begin{figure}[H]
% out % \centering
% out % \vspace*{-5mm}
% out % %\hspace*{-30mm}
% out %  \includegraphics
% out % %  [scale = 0.8, trim = 0.6in 0.4in 0.6in 0.4in, clip=true]
% out %   [width=12cm]
% out %    {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Probabilistic_von_Mises_Surface.jpg}
% out % % \caption{An example of a probabilistic von Mises yield surface.}
% out %  \label{ProbCylinder}
% out % \end{figure}
% out % 
% out % 
% out % 
% out % \end{frame}
% out % 
% out % 
% out % 
% out % 
% out % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out % % \begin{frame} 
% out % % \frametitle{Gradient Theory of Probabilistic Elasto-Plasticity: 
% out % % Verification, Elastic-Perfectly Plastic}
% out % %                
% out % % 
% out % % %\vspace*{-3mm}
% out % % \begin{figure}[H]
% out % % \centering
% out % %  \includegraphics
% out % % % [scale = 0.55, trim = 0.0in 0.0in 0.0in 0.0in, clip=true]
% out % %  [width=8cm]
% out % %  {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/M+-SD_1D_Perf_Cyclic.pdf}
% out % % %  \caption{Combining  the  above  plots to get the evolution of mean $\pm$ std.
% out % % % deviation of stress.}
% out % %  \label{MSD_12}
% out % % \end{figure}
% out % % 
% out % % 
% out % % \end{frame}
% out % % 
% out % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out % \begin{frame} 
% out % \frametitle{Wave Propagation Through Uncertain Soil}
% out % 
% out % \vspace{-2mm}
% out %  
% out % \begin{figure}[H]
% out %  \centering
% out %  \includegraphics
% out % % [scale = 0.56, trim = 0.0in 0.15in 0.2in 0.16in, clip=true]
% out %  [width=7cm]
% out %  {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_profile.png}
% out % %
% out % %  
% out % \includegraphics
% out % %[scale = 0.56, trim = 0.0in 0.0in 0.0in 0.0in, clip=true]
% out %  [width=1.5cm]
% out % {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/meshes.png}
% out % % \caption{Simplified profile and properties for the 1-dimensional profile considered.}
% out %  \label{Sendai_profile}
% out % \end{figure}
% out %      
% out % 
% out % 
% out % \vspace{-5mm}
% out % 
% out %  
% out % \begin{figure}[htbp]
% out % \centering
% out % %\hspace{-0.2in}
% out % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out %  \includegraphics
% out % % [scale = 0.37, trim = 0.0in 0.0in 0.0in 0.0in,clip=true]
% out %  [width=3.5cm]
% out %  {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/ShearModulusStats.pdf}
% out % \hfill
% out %  \includegraphics
% out % % [scale = 0.37, trim = 0.0in 0.0in 0.0in 0.0in, clip=true]
% out %  [width=3.5cm]
% out %  {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/ShearStrengthStats.pdf}
% out % %\caption{Shear modulus and shear strength statistics in the middle of the soil column.}
% out % \hfill
% out %  \includegraphics
% out % % [scale = 0.62, trim = 0in 0.15in 0in 0.22in, clip=true]
% out %  [width=3.5cm]
% out %  {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_1Sine_PCk2PC2_elastic_COV45_BaseInput.pdf}
% out % % \caption{Single sine pulse excitation of the soil column at its base.}
% out % % \label{Sendai_1Sine_PCk2PC2_elastic_COV45_BaseInput}
% out % \end{figure}
% out % 
% out % 
% out % \end{frame}
% out % 
% out % 
% out % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out % \begin{frame} 
% out % \frametitle{Uncertain Elastic Response at the Surface {\tiny(COV = 120\%)} }
% out %  
% out %  \vspace*{-2mm}
% out % \begin{figure}[H]
% out %  \centering
% out %  \includegraphics
% out % % [scale = 0.62, trim = 0in 0.16in 0in 0.26in, clip=true]
% out %  [width=9.3cm]
% out %  {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_1Sine_PCk2PC2_elastic_COV120.pdf}
% out % %  \caption{Mean  $\pm$ std. deviation of the elastic response at the top of the
% out % % soil column for the conservative COV case (COV = 120\%).}
% out % % \label{Sendai_1Sine_PCk2PC2_elastic_COV120}
% out % \end{figure}
% out % 
% out % \end{frame}
% out % 
% out % 
% out % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out % \begin{frame} 
% out % \frametitle{Displacement PDFs at the Surface {\tiny(COV = 120\%)} }
% out % 
% out % %\vspace*{-20mm} 
% out % %\hspace*{-30mm} 
% out % \begin{figure}[H]
% out %  \centering
% out %  \includegraphics
% out % %[scale = 0.62, trim = 0in 0.16in 0in 0.26in, clip=true]
% out %  [width=10cm]
% out %  {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_1Sine_PCk2PC2_elastic_COV120_FullPdf.jpg}
% out % %  \caption{Mean  $\pm$ std. deviation of the elastic response at the top of the
% out % % soil column for the conservative COV case (COV = 120\%).}
% out % % \label{Sendai_1Sine_PCk2PC2_elastic_COV120}
% out % \end{figure}
% out % 
% out % \end{frame}
% out % 
% out % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out % \begin{frame} 
% out % \frametitle{Displacement CDFs (Fragilities) at the Surface {\tiny(COV = 120\%)}  }
% out %  
% out %  \vspace*{-3mm}
% out % \begin{figure}[H]
% out %  \centering
% out %  \includegraphics
% out % % [scale = 0.62, trim = 0in 0.16in 0in 0.26in, clip=true]
% out %  [width=11cm]
% out %  {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_1Sine_PCk2PC2_elastic_COV120_FullCdf.jpg}
% out % %  \caption{Mean  $\pm$ std. deviation of the elastic response at the top of the
% out % % soil column for the conservative COV case (COV = 120\%).}
% out % % \label{Sendai_1Sine_PCk2PC2_elastic_COV120}
% out % \end{figure}
% out % 
% out % \end{frame}
% out % 
% out % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out % \begin{frame} 
% out % \frametitle{Probability of Exceedance, $disp=0.1m$ {\tiny(COV = 120\%)}  }
% out %  
% out % \begin{figure}[H]
% out %  \centering
% out %  \includegraphics
% out % % [scale = 0.62, trim = 0in 0.16in 0in 0.26in, clip=true]
% out %  [width=9cm]
% out %  {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_1Sine_PCk2PC2_elastic_COV120_ProbExc.pdf}
% out % %  \caption{Mean  $\pm$ std. deviation of the elastic response at the top of the
% out % % soil column for the conservative COV case (COV = 120\%).}
% out % % \label{Sendai_1Sine_PCk2PC2_elastic_COV120}
% out % \end{figure}
% out % 
% out % \end{frame}
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% \begin{frame}
% \frametitle{Important Issues for ESSI Modeling and Simulation}
% 
%    \begin{itemize}
% 
%      \item Verification and Validation
% 
% \vspace*{2mm}
%      \item 6D, inclined, body and surface  seismic waves
% 
% \vspace*{2mm}
%      \item Uncorrelated (incoherent) motions
% 
% \vspace*{2mm}
%      \item Nonlinear material (soil, rock, concrete, steel, \&c.)
% 
% \vspace*{2mm}
%      \item Nonlinear foundation-soil/rock contact (dry and saturated), slip -- gap 
% 
% \vspace*{2mm}
%      \item Saturated dense vs loose soil with buoyant forces
% 
% %\vspace*{2mm}
% %     \item Piles and pile groups 
% 
% \vspace*{2mm}
%      \item Isolators, dissipators
% 
% 
% \end{itemize}
% 
% \end{frame}
% 
% 
% 
% 
% 
% 
% 
% 
% % %  
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{ESSI Models}
% 
% \vspace*{+10mm}
% Detailed \\
% high\\
% fidelity\\
% models\\
% taking\\
% into\\
% account\\ 
% all of the\\
% issues
% 
% 
% \vspace*{-60mm}
% \begin{figure}[!hbpt]
% \begin{flushright}
% \includegraphics[width=4.30cm]{/home/jeremic/tex/works/Conferences/2014/DOE_Natural_Phenomena_Hazards_Germantown_MD-21-22Oct/present/Model01.jpeg}
% \includegraphics[width=4.30cm]{/home/jeremic/tex/works/Conferences/2014/DOE_Natural_Phenomena_Hazards_Germantown_MD-21-22Oct/present/Model02.jpeg}
% \\
% \includegraphics[width=4.30cm]{/home/jeremic/tex/works/Conferences/2014/DOE_Natural_Phenomena_Hazards_Germantown_MD-21-22Oct/present/Model03.jpeg}
% \includegraphics[width=3.30cm]{/home/jeremic/tex/works/Conferences/2014/DOE_Natural_Phenomena_Hazards_Germantown_MD-21-22Oct/present/Model04.jpeg}
% %gthumb /home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_ESSI_for_NPPs/Model01_full_view.jpg &
% %gthumb /home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_ESSI_for_NPPs/Model02_full_view.jpg &
% %gthumb /home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_ESSI_for_NPPs/Model03_full_view.jpg &
% %gthumb /home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_ESSI_for_NPPs/SMR02_a.jpg           &
% \end{flushright}
% \end{figure}
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% \end{frame}
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% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{In Detail: Main ESSI Issues for SMRs}
% 
% \begin{figure}[!hbpt]
% \begin{center}
% \vspace*{-0.2cm}
% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/Conferences/2014/ASME_SMR_Symposium/present/SMR02_a_01-GRAY_pdf.pdf}
% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/Conferences/2014/ASME_SMR_Symposium/present/SMR02_a_02-GRAY_pdf.pdf}
% \\
% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/Conferences/2014/ASME_SMR_Symposium/present/SMR02_a_03-GRAY_pdf.pdf}
% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/Conferences/2014/ASME_SMR_Symposium/present/SMR02_a_04-GRAY_pdf.pdf}
% \vspace*{-0.6cm}
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% 
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% \begin{frame}
%   \frametitle{Education, Training and Refresher Courses}
% 
% 
%     \begin{itemize}
% 
%       \item Education will be the key to successful use of time domain nonlinear Earthquake Soil
%       Structure Interaction modeling and simulation
%       
%       \vspace*{2mm}
%       \item Online illustrative material available
% 
%       
%       \vspace*{2mm}
%       \item Online educational material finalized
% 
% 
%       \vspace*{2mm}
%       \item Short course, 2 or 3 days, in preparation
% 
% 
%       \vspace*{2mm}
%       \item  Refresher course, Just-in-Time  (JiT) on specific topics, in preparation,
%       will be available online
% 
% 
% 
% 
%     \end{itemize}
% 
% \end{frame}
% 
% 
% 


 













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%\subsection{Modeling Issues}





%  



% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{High Fidelity Modeling and Simulation \\
% Detrimental and Beneficial ESSI Effects}
% 
% 
% 
% \begin{figure}[!hb]
% \begin{center}
% \vspace*{-0.2cm}
% \includegraphics[width=3.3cm]{/home/jeremic/tex/works/consulting/2013/CNSC/ProgressReports/Progress_report_02_figs/single-NPP-FEM-model.jpg}
% \includegraphics[width=3.3cm]{/home/jeremic/tex/works/consulting/2013/CNSC/ProgressReports/Progress_report_02_figs/double-NPP-FEM-model.jpg}
% \end{center}
% \end{figure}
% %\vspace*{2.0cm}
% 
% \begin{figure}[!hbpt]
% \begin{center}
% \hspace*{-0.5cm}
% \includegraphics[width=3.3cm]{/home/jeremic/tex/works/Conferences/2014/ASME_SMR_Symposium/present/SMR01_a.jpg}
% \includegraphics[width=3.3cm]{/home/jeremic/tex/works/Conferences/2014/ASME_SMR_Symposium/present/SMR02_a.jpg}
% \end{center}
% \end{figure}
% 
% % 
% % %
% % 
% % \begin{itemize}
% %      \item 
% %      \item 
% %      \item 
% % \end{itemize}
% 
% \end{frame}
% 
       
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Current Surface NPP Models (LWRs)}
% 
% % 
% 
% \vspace*{-0.2cm}
% \begin{figure}[!hbpt]
% \begin{center}
% \raisebox{0.9cm}{\includegraphics[width=1.0cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/04_cropped.jpg}}
% \raisebox{1.2cm}{\includegraphics[width=2.2cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/02_cropped.jpg}}
% \raisebox{-0.5cm}{\includegraphics[width=4cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/03_cropped.jpg}}
% \end{center}                              
% \end{figure}
% 
% \vspace*{-1.6cm}
% \begin{itemize}
% % \item Modular models
% %\vspace*{-0.1cm}
%  \item 3D, Inclined, body and \\ surface  seismic waves
% %\vspace*{-0.1cm}
%  \item Uncorrelated (incoherent) motions
% %\vspace*{-0.1cm}
%  \item Foundation slip -- gap 
% %\vspace*{-0.1cm}
%  \item Isolators, dissipators
% %\vspace*{-0.1cm}
%  \item Saturated dense vs loose soil with buoyant forces
% %\vspace*{-0.1cm}
%  \item Piles and pile groups 
% 
% \end{itemize}
% 
% \end{frame}
% 
% 
% 
% 
% 
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Current Embedded NPP Models (SMRs)}
% 
% 
% \begin{figure}[!hbpt]
% \begin{center}
% \vspace*{-0.2cm}
% %\includegraphics[width=4cm]{/home/jeremic/tex/works/Conferences/2014/ASME_SMR_Symposium/present/SMR01_a.jpg}
% \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2014/ASME_SMR_Symposium/present/SMR02_a.jpg}
% \vspace*{-0.6cm}
% \end{center}
% \end{figure}
% 
% % OVDE stavi srdjene slike (ovu mrezu, dodaj mnan tablici, za sve probleme)...
% 
% 
% \begin{itemize}
%      \item    A  number  of ESSI modeling and simulation issues that control the
%      seismic response
%      \item Detrimental and Beneficial ESSI effects
%      \item Seismic energy propagation and dissipation
% \end{itemize}
% 
% \end{frame}
% 
% 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% % \frametitle{ESSI: Seismic Body and Surface Waves}
% % 
% % \begin{figure}[!hbpt]
% % \begin{center}
% % \vspace*{-0.2cm}
% % \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2014/ASME_SMR_Symposium/present/SMR02_a_01-GRAY_pdf.pdf}
% % \vspace*{-0.6cm}
% % \end{center}
% % \end{figure}
% % 
% % \begin{itemize}
% %      \item Seismic surface waves carry most seismic energy
% %      \item SMR bottom: body waves; SMR top: surface waves
% %      \item Incoherent seismic motions 
% % \end{itemize}
% % \end{frame}
% % 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% % \frametitle{ESSI: Nonlinear Contact and Soil/Rock Zones}
% % 
% % \begin{figure}[!hbpt]
% % \begin{center}
% % \vspace*{-0.2cm}
% % \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2014/ASME_SMR_Symposium/present/SMR02_a_02-GRAY_pdf.pdf}
% % \vspace*{-0.6cm}
% % \end{center}
% % \end{figure}
% % 
% % \begin{itemize}
% %      \item Seismic energy dissipated at the contact 
% %      \item Seismic energy dissipated within adjacent soil/rock zones
% %     \item Passive (complete) structural isolation (beneficial)
% % \end{itemize}
% % \end{frame}
% % 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% % \frametitle{ESSI: Fluid Structure Interaction}
% % 
% % \begin{figure}[!hbpt]
% % \begin{center}
% % \vspace*{-0.2cm}
% % \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2014/ASME_SMR_Symposium/present/SMR02_a_03-GRAY_pdf.pdf}
% % \vspace*{-0.6cm}
% % \end{center}
% % \end{figure}
% % 
% % \begin{itemize}
% %      \item SMR below water table, 
% %      \item Saturated soil (liquefaction, densification/stiffening)
% %      \item Buoyant forces (dynamically changing)
% % \end{itemize}
% % \end{frame}
% % 
% % 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% % \frametitle{ESSI: Uncertain Material and Uncertain Loads}
% % 
% % \begin{figure}[!hbpt]
% % \begin{center}
% % \vspace*{-0.2cm}
% % \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2014/ASME_SMR_Symposium/present/SMR02_a_04-GRAY_pdf.pdf}
% % \hspace{0.5cm}
% % \includegraphics[width=4.0cm]{/home/jeremic/tex/works/Conferences/2014/ASME_SMR_Symposium/present/SPT_Uncertain_Youngs_Modulus.jpg}
% % %
% % %\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01-Ed.pdf} 
% % %\\
% % %%\hfill
% % %\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_Histogram_Normal_01-Ed.pdf}
% % %
% % \vspace*{-0.6cm}
% % \end{center}
% % \end{figure}
% % 
% % \begin{itemize}
% %      \item Inherently uncertain material response
% %      \item Inherently uncertain (seismic) loading
% %      \item Full probabilistic modeling and simulations is desired
% % %     \item 
% % \end{itemize}
% % \end{frame}
% % 
% % 
% % 
% 
% 


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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \section{Summary}
% 
% 
\section{\cyrdeset Zakljuchak}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{\cyrdevet Zakljuchak}





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

  \begin{itemize}

  \item        High    fidelity  modeling  and  simulation allows  reduction of
  modeling  uncertainty  and  direct  propagation  of parametric uncertainties
  through the dynamic ESSI system

%\vspace*{1mm}
  \item  Development  and expert use of high fidelity modeling and simulation numerical
  tools:  Real  ESSI  Simulator  System 

%\vspace*{1mm}
  \item {  Education}  and  {training}  of  users  (researchers, designers, regulators,
  owners) will prove essential

%\vspace*{1mm}
  \item  Collaborators:
  Yang,  Cheng,  Jie,  Sett,  Taiebat,  Tafazzoli, Karapiperis, Abell,
  Pisan{\`o},  Feng,  Sinha,  Lacour,  Yang,  Behbehani, Wang, Petrone, Wong,
  McKenna, McCallen
       
%\vspace*{0.1cm}
   \item Funding from and collaboration with the US-NRC,
  US-NSF,  US-DOE, CNSC, LBNL, LLNL, INL, ILEE,
  AREVA NP GmbH, and Shimizu Corp. is greatly appreciated,



\end{itemize}


\end{frame}
%


% \vspace*{0.1cm}
%   \item Funding from and collaboration with the US-NRC,
%   US-NSF,  US-DOE, CNSC, LLNL, INL,
%   AREVA NP GmbH, and Shimizu Corp. is greatly appreciated,
% 
% % \vspace*{0.5cm}
% %   \item  Collaborators, students:
% %   Mr.  Abell,  Mr.  Jeong, Mr. Aldridge. Mr.   Kamranimoghadam, Mr. Karapiperis,
% %   Mr. Watanabe, Mr. Chao,
% %   Dr.  Tafazzoli,   Prof.  Pisan{\`o} (TU Delft),
% %   Prof. Sett (U. Bufallo), Prof. Taiebat (U. British Columbia), Prof. Yang (U. Alaska)
% % 
% 
% \end{itemize}
% 
% 
% \end{frame}
% %
% 


\end{document}

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