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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{threeparttable}

%\usepackage{MnSymbol}%
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\usepackage{wasysym}%
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\usepackage{subfig}
\usepackage{tabularx}
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\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
%
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%% ovo je za cirilicu
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%   }

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\newcommand{\FEI}
{{\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 ...

  \setbeamercovered{transparent}


%  \setbeamercovered{transparent}
% or whatever (possibly just delete it)
%  \usecolortheme{albatross} % teget sa svetlim slovima
%  \usecolortheme{beetle} % siva pozadina (vrh plav)
  \usecolortheme{seagull} % sivo
%%%%%%%
%  \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, 0.35, 0} % less intense green
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  pdfpagemode={None}
             colorlinks=true,
             linkcolor=webblue,
             citecolor=webblue,
             urlcolor=webblue,
}
% \usepackage[pdfauthor={Boris Jeremic},
%             colorlinks=true,
%             linkcolor=webblue,
%             citecolor=webblue,
%             urlcolor=webblue,
%             linktocpage,
%             pdftex]{hyperref}


\usepackage{pause}
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%\usepackage{url}

\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.



%      Site Specific Dynamics of Structures: 
%From Seismic Source to 
%the Safety of Occupants and Content


\title[Real-ESSI]
        { Modeling and Simulation \\
         Earthquake Soil Structure Interaction}


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

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


\author[Jeremi{\'c} et al.] % (optional, use only with lots of authors)
%{Boris~Jeremi{\'c}}
{Boris Jeremi{\'c}
}

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


\date[] % (optional, should be abbreviation of conference name)
{\small United States Society on Dams\\
         Chicago, April 2019}

\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}{3}
 \AtBeginSubsection[]
% \AtBeginSection[]
 {
   \begin{scriptsize}
   \begin{frame}<beamer>
     \frametitle{Outline}
     \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{Outline}

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

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

% 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{Introduction}




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\subsection{Motivation}



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


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

\begin{itemize}



%\vspace*{0.3cm}
  \item[]  Improve  modeling  and  simulation  for  infrastructure objects
 

% \vspace*{2mm}
%  \item[]  Expert numerical modeling and simulation tool

\vspace*{1mm}
  \item[]      Use select fidelity (high  $\leftrightarrow$ low) numerical models to
  analyze static and dynamic behavior of soil/rock structure fluid systems


\vspace*{1mm}
  \item[]  Reduction  of modeling uncertainty, ability to perform desired level
  of sophistication modeling and simulation


\vspace*{1mm}
  \item[]  Accurately   follow  the  flow   of input and dissipation of  energy 
  in a soil structure system


\vspace*{1mm}
  \item[]  Development  of  an  expert    system  for modeling and simulation of
  Earthquakes,    Soils,    Structures    and    their    Interaction,   Real-ESSI:
  \hspace*{5mm} \href{http://real-essi.info/}{http://real-essi.info/}



% \vspace*{1mm}
%   \item[]   The  goal is to create methodology and numerical tool that is used to 
%   predict and inform and not to fit
% 


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



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


%    
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Hypothesis}
% 
% \begin{itemize}
% 
% 
% 
% %\vspace*{0.5cm}
%   \item  Interplay            dynamic characteristics of  the  Dynamic Forcing /
%   Earthquake,  Soil/Rock  and  Structure  in  time domain, plays a decisive role in
%   successes and failures
% 
% 
% \vspace*{3mm}
%   \item   Timing  and spatial location of energy dissipation determines location
%   and amount of damage
% 
% \vspace*{3mm}
%   \item  If timing and spatial location of the energy dissipation
%          can be controlled (directed),
%          we could  optimize soil structure system for
%     \begin{itemize}
%       \item Safety and
%       \item Economy
%     \end{itemize}
% 
% \end{itemize}
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% % \frametitle{Seismic Energy Dissipation for \underline{Soil}-Foundation-Structure Systems}
%  \frametitle{Energy Dissipation in SSI System}
% % \frametitle{Seismic Energy Dissipation for
% %             \underline{Soil}-Foundation-Structure Systems}
% 
% 
% \begin{itemize}
% 
% 
% \vspace*{0.2cm}
%      \item Mechanical dissipation outside of SSI domain:
%        \begin{itemize}
%          \item SSI system oscillation radiation
%          \item reflected wave radiation
%        \end{itemize}
% \vspace*{0.2cm}
%      \item Mechanical dissipation/conversion inside SSI domain:
%        \begin{itemize}
%          \item plasticity of soil subdomain
%          \item plasticity/damage of the parts of structure/foundation
%          \item viscous coupling of porous solid (soil) with pore fluid (air, water)
%          \item viscous coupling of structure/foundation with fluids
% %         \item potential and kinetic energy
% %         \item potential $\leftarrow \! \! \! \! \! \! \rightarrow$ kinetic energy
%        \end{itemize}
% 
% 
% 
% \vspace*{0.2cm}
% %   \item Numerical energy dissipation (numerical damping/production and period  errors)
% %   \item Numerical energy dissipation (damping/production)
%    \item Numerical energy dissipation/production
% 
% 
% \end{itemize}
% 
% %
% \end{frame}
% % %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%


  


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

\begin{itemize}

   \item {  Prediction under Uncertainty}:  use  of  computational  model
   to  predict  the  state  of SSI system under
   conditions for which the computational model has not been validated.


\vspace*{1mm}
     \item  {{  Verification}  provides  evidence  that  the  model is solved
     correctly.} Mathematics issue.

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

\vspace*{1mm}
   \item  Modeling  and  parametric uncertainties are always present, need to be
   addressed 

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

\vspace*{1mm}
     \item Goal: Predict and Inform rather than (force) Fit


\vspace*{1mm}
     \item Engineer needs to know!




\end{itemize}


\end{frame}



% 


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


%\subsection*{Uncertainties}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Motivation: Modeling Uncertainty}

\begin{itemize}


  \item      Simplified  modeling:    Features (important ?)   are neglected (3C, 6C
  ground motions, inelasticity)

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

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


%\vspace*{3mm}
%     \item   Chief Engineer in my old company: "I would really love to know what
%     would a realistic response this object be"


\end{itemize}
\end{frame}








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


\vspace*{10mm}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-7mm}
\includegraphics[width=6.2truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01-Ed.pdf}
% \hfill
\includegraphics[width=4.8truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_Histogram_Normal_01-Ed.pdf}
%
\end{center}
\end{figure}

%\vspace*{-1.8cm}
%\hspace*{-3.3cm}
\begin{flushright}
{\small
%Transformation  of SPT $N$-value: 
%1-D Young's modulus, $E$ 
cf. Phoon and Kulhawy (1999B)
~}
\end{flushright}

\end{frame}






%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Modeling Uncertainty, 6C vs 1C Motions}

     
% local
\vspace*{-2mm}
\begin{center}
\hspace*{-7mm}
%\movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
\movie[label=show3,width=8.8cm,poster, showcontrols]
  {\includegraphics[width=92mm]
  {/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_2_npps_mp4_icon.jpeg}}
  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_2_npps.mp4}
\end{center}
% local
%  \vspace*{-2mm}
%  \begin{center}
%  \hspace*{-7mm}
%  \movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
%    {\includegraphics[width=90mm]{movie_2_npps_mp4_icon.jpeg}}{movie_2_npps.mp4}
%  \end{center}


% online
\vspace*{-12mm}
\begin{flushleft}
%\vspace*{-15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_2_npps.mp4}
  {\tiny (MP4)}
\end{flushleft}
% online





\end{frame}








%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %\subsection{Personal Experience with Dam Engineering}
%  %
%  
%  \begin{frame}
%   \frametitle{Spillway Dynamic Analysis, '88-'89}
%  
%  
%  
%  %  %  \begin{itemize}
%  %  % 
%  %  %    \item {\cyr Diplomski pre skoro 18 godina}
%  %  % 
%  %  % \vspace*{0.10cm}
%  %  %    \item {\cyr relativno mali model}
%  %  % 
%  %  % \vspace*{0.10cm}
%  %  %    \item {\cyr linearno elastichan materijal}
%  %  % 
%  %  % \vspace*{0.10cm}
%  %  %    \item {\cyr aksisimetrichni elementi sa \\
%  %  %          razvojem pomeranja u \\
%  %  %          trigonometrijske redove}
%  %  %          
%  %  % 
%  %  % \vspace*{0.10cm}
%  %  %    \item {\cyr uprosh\cj{}eno zemljtresno \\
%  %  %                optere\cj{}enje}
%  %  % 
%  %  % \vspace*{0.10cm}
%  %  %    \item {\cyr vrlo korisna analiza \\
%  %  %                interakcije zemljotresa, \\
%  %  %                tla i konstrukcije  }
%  %  % %
%  %  % %   \item {\cyr    }
%  %  % 
%  %  % 
%  %  %  \end{itemize}
%  %  % 
%  %  % 
%  % \vspace*{-6.2cm}
%  % %
%  \begin{center}
%  \begin{figure}[!htbp] 
%  \includegraphics[width=6.2cm]{/home/jeremic/tex/works/Conferences/2018/USBR_22Aug2018/present/Monticelo_dam_glory_hole_spillway_01.jpg}
%  \hfill
%  \includegraphics[width=4.2cm]{/home/jeremic/tex/works/Conferences/2018/USBR_22Aug2018/present/DiplomskiModel.pdf}
%  \end{figure}
%  \end{center}
%  %\vspace*{-2.0cm}
%  
%  
%  
%  \end{frame}
%  
%  
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Behkme Dam Project, Iraq, '89-'90}
%  
%  
%  
%  \begin{center}
%  \begin{figure}[!htbp] 
%  %\includegraphics[width=4cm]{/home/jeremic/public_html/Bekhme/Bekhme_panorama_pogled_na_istok_jug_zapad_April_1990.jpg}
%  %\\
%  %\includegraphics[width=4cm]{/home/jeremic/public_html/Bekhme/Bekhme_panorama_pogled_na_tunele_jug_zapad_April_1990.jpg}
%  %\\
%  %\includegraphics[width=4cm]{/home/jeremic/public_html/Bekhme/Bekhme_panorama_pogled_na_levu_obalu_istok_April_1990.jpg}
%  %
%  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/Bekhme/Bekhme_panorama_pogled_na_istok_jug_zapad_April_1990.jpg}
%  {\includegraphics[width=7cm]{/home/jeremic/tex/works/Conferences/2018/USBR_22Aug2018/present/Bekhme_panorama_pogled_na_istok_jug_zapad_April_1990_SMALL.jpg}}
%  \\
%  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/Bekhme/Bekhme_panorama_pogled_na_tunele_jug_zapad_April_1990.jpg}
%  {\includegraphics[width=7cm]{/home/jeremic/tex/works/Conferences/2018/USBR_22Aug2018/present/Bekhme_panorama_pogled_na_tunele_jug_zapad_April_1990_SMALL.jpg}}
%  \\
%  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/Bekhme/Bekhme_panorama_pogled_na_levu_obalu_istok_April_1990.jpg}
%  {\includegraphics[width=7cm]{/home/jeremic/tex/works/Conferences/2018/USBR_22Aug2018/present/Bekhme_panorama_pogled_na_levu_obalu_istok_April_1990_SMALL.jpg}}
%  %
%  \end{figure}
%  \end{center}
%  %\vspace*{-2.0cm}
%  
%  
%  \end{frame}
%  
%  


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Wolf Creek Dam, '09-'10}
% 
% %
% \begin{figure}[!htbp] 
% \begin{center}
% \includegraphics[width=3.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WolfCreekDam_SateliteView01.jpg}
% \hfill
% \includegraphics[width=2.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WolfCreekDam_SatelliteView_with_slope01.jpg}
% \hfill
% \includegraphics[width=2.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/img-0188.jpg}
% \hfill
% \includegraphics[width=2.6cm]{/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}
% \\
% \includegraphics[width=3.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WolfCreekDam_PerpendicularSection.jpg}
% \hfill
% \includegraphics[width=2.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/3D_final02.jpg}
% \hfill
% \includegraphics[width=2.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/3D_final04.jpg}
% \hfill
% \includegraphics[width=2.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/3D_final05.jpg}
% %\hfill
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% \\
% \includegraphics[width=2.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/Undrained-Su440-Vector-Plan_snapshot.jpg}
% \hfill
% \includegraphics[width=2.5cm]{/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}
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% \includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Undrained_L680_E720_Su1300_FS154.jpg}
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    \subsection{Modeling and Simulation of ESSI}


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\begin{frame}
 \frametitle{Energy Input and Dissipation}

\begin{itemize}

\vspace*{1mm}
     \item[] Energy input, dynamic forcing


\vspace*{4mm}
     \item[] Energy dissipation outside SSI domain:
       \begin{itemize}
         \item[] SSI system oscillation radiation
         \item[] Reflected wave radiation
       \end{itemize}
%\vspace*{1mm}
     \item[] Energy dissipation/conversion inside SSI domain:
       \begin{itemize}
         \item[] Inelasticity of soil, contact zone, structure, foundation, dissipators
         \item[] Viscous coupling with internal/pore fluids, and external fluids
% %         \item[] potential and kinetic energy
%          \item[] potential $\leftarrow \! \! \! \! \! \! \rightarrow$ kinetic energy
       \end{itemize}                           



%\vspace*{1mm}
%   \item[] Numerical energy dissipation (numerical damping/production and period  errors)
%   \item[] Numerical energy dissipation (damping/production)
   \item[] Numerical energy dissipation/production


\end{itemize}

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




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Fully Coupled Formulation, u-p-U}

% 
%
\begin{small}
\begin{eqnarray}
\hspace*{-13mm}
\left[ \begin{array}{ccc}
(M_s)_{KijL} & 0 & 0 \\
 0  & 0 & 0 \\
 0  & 0 & (M_f)_{KijL}
\end{array} \right]
\left[ \begin{array}{c}
\ddot{\overline{u}}_{Lj} \\
\ddot{\overline{p}}_N \\
\ddot{\overline{U}}_{Lj}
\end{array} \right]
+
\left[ \begin{array}{ccc}
(C_1)_{KijL} & 0 & -(C_2)_{KijL} \\
 0  & 0 &   0  \\
-(C_2)_{LjiK} & 0 & (C_3)_{KijL} \\
\end{array} \right]
\left[ \begin{array}{c}
\dot{\overline{u}}_{Lj} \\
\dot{\overline{p}}_N \\
\dot{\overline{U}}_{Lj}
\end{array} \right]    
\nonumber
\\
+ 
\left[ \begin{array}{ccc}
(K^{EP})_{KijL} & -(G_1)_{KiM} & 0 \\
-(G_1)_{LjM}  & -P_{MN} & -(G_2)_{LjM} \\
 0  & -(G_2)_{KiL} & 0
\end{array} \right]
\left[ \begin{array}{c}
\overline{u}_{Lj} \\
\overline{p}_M \\
\overline{U}_{Lj}
\end{array} \right]
=
\left[ \begin{array}{c}
\overline{f}_{Ki}^{solid} \\
0  \\
\overline{f}_{Ki}^{fluid}
\end{array} \right] \nonumber
%\\
%\label{68}
\end{eqnarray}
\end{small}
%
%
%
\end{frame}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Fully Coupled Formulation, u-p-U}

% 
% 
%
%
%
\begin{eqnarray}
\hspace*{-10mm} (M_s)_{KijL}&=&\int_{\Omega} H_K^u (1-n) \rho_s \delta_{ij} H_L^u d\Omega
\hspace*{5mm} (M_f)_{KijL}=\int_{\Omega} H_K^U n \rho_f \delta_{ij} H_L^U d\Omega \nonumber\\
\hspace*{-10mm} (C_1)_{KijL}&=&\int_{\Omega} H_K^u n^2 k_{ij}^{-1} H_L^u d\Omega 
\hspace*{5mm} (C_2)_{KijL}=\int_{\Omega} H_K^u n^2 k_{ij}^{-1} H_L^U d\Omega \nonumber\\
\hspace*{-10mm} (C_3)_{KijL}&=&\int_{\Omega} H_K^U n^2 k_{ij}^{-1} H_L^U d\Omega 
\hspace*{5mm} (K^{EP})_{KijL}=\int_{\Omega} H_{K,m}^u D_{imjn} H_{L,n}^u d\Omega \nonumber\\
\hspace*{-10mm} (G_1)_{KiM}&=&\int_{\Omega} H_{K,i}^u (\alpha-n) H_M^p d\Omega
\hspace*{5mm} (G_2)_{KiM}=\int_{\Omega} n H_{K,i}^U H_M^p d\Omega \nonumber\\
\hspace*{-10mm} P_{NM}&=&\int_{\Omega} H_N^p \frac{1}{Q} H_M^p d\Omega  \nonumber
\end{eqnarray}
%
%
%
%
%\newpage

%  \begin{eqnarray}
%  \overline{f}_{Ki}^{solid}&=&(f_1^u)_{Ki}-(f_4^u)_{Ki}+(f_5^u)_{Ki} \nonumber\\
%  \overline{f}_{Ki}^{fluid}&=&-(f_1^U)_{Ki}+(f_2^U)_{Ki}  \nonumber\\
%  (f_1^u)_{Ki}&=&\int_{\Gamma_t} H_K^u n_j \sigma_{ij}^{''} d\Gamma \nonumber\\
%  (f_4^u)_{Ki}&=&\int_{\Gamma_p} H_K^u (\alpha-n) n_i p d\Gamma \nonumber\\
%  (f_5^u)_{Ki}&=&\int_{\Omega} H_K^u (1-n) \rho_s b_i d\Omega \nonumber\\
%  (f_1^U)_{Ki}&=&\int_{\Gamma_p} n H_K^U n_i p d\Gamma \nonumber\\
%  (f_2^U)_{Ki}&=&\int_{\Omega} n H_K^U \rho_f b_i d\Omega
%  \label{69}
%  \end{eqnarray}
%

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




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\begin{frame}

\frametitle{Energy Dissipation Control Mechanisms}

\begin{figure}[!H]
%\hspace*{-10mm}
     \includegraphics[width=3.4cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_plasticity.pdf}
     \includegraphics[width=3.4cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_Rayleigh.pdf}
     \includegraphics[width=3.4cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_Newmark.pdf}
\end{figure}


% \hspace*{10mm} Numerical  \hspace*{20mm}  Viscous  \hspace*{20mm} Plasticity 
 \hspace*{10mm} Plasticity \hspace*{20mm}  Viscous  \hspace*{20mm} Numerical



\end{frame}

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\begin{frame}

\frametitle{Energy Dissipation Control}

\begin{figure}[!H]
%\hspace*{-10mm}
%     \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_a.pdf}
%     \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_b.pdf}
     \includegraphics[width=9cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_g.pdf}
%     \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_e.pdf}
\end{figure}




\end{frame}

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


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 
\frametitle{Energy Dissipation on Material Level}


\vspace*{2mm}
 
 Single elastic-plastic element under cyclic shear loading
 
\begin{itemize}
\item[] Difference between plastic work and plastic dissipation
\item[] Plastic work can decrease
\item[] Plastic dissipation always increases
\end{itemize}
 
%\vspace*{-7mm}
\begin{figure}[!hbpt]
\begin{center}
\hspace*{-5mm}
\includegraphics[width=11.0truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Dissipation_Material.png}
\end{center}
\end{figure}
  
\end{frame}
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Liquefaction as Base Isolation, Model}
% 
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=4.5truecm]{/home/jeremic/tex/works/Conferences/2017/Slovenia_IAEA_short_course/present/SSI-Site_Response_Analysis/Liquefaction_04.jpg}
% \end{center}
% \end{figure}
% 
% \end{frame}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Liquefaction, Wave Propagation}
% 
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Conferences/2017/Slovenia_IAEA_short_course/present/SSI-Site_Response_Analysis/Liquefaction_01.jpg}
% \end{center}
% \end{figure}
% 
% \end{frame}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Liquefaction, Stress-Strain Response}
% 
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Conferences/2017/Slovenia_IAEA_short_course/present/SSI-Site_Response_Analysis/Liquefaction_03.jpg}
% \end{center}
% \end{figure}
% 
% \end{frame}
% 
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}
% 
% \frametitle{Buoyant Force Simulation}
% 
% \begin{figure}[!H]
% \hspace*{-10mm}
%      \includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/upU_element_type_annotation.pdf}
%      \includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/bouyant_displacement.pdf}
% \end{figure}
% 
% % -  %
% % -  % \begin{tikzpicture}[remember picture,overlay]
% % -  %    \node[anchor=south west,inner sep=0pt] at ($(current page.south west)+(7.5cm,2.5cm)$) {
% % -  %      \includegraphics[width=0.4\textwidth]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/bouyant_displacement.pdf}};
% % -  % \end{tikzpicture}
% % -
% % -  %  \vspace{-1.4cm}
% %  \begin{itemize}
% %   \item \scriptsize Upward structural displacement under buoyant force
% %  \end{itemize}
% \end{frame}
% 
% 

%

     
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}
%  \frametitle{Solid/Structure-Fluid Interaction, Example}
% 
% 
% 
% %\vspace*{-5mm}
% \begin{center}
% % \hspace*{-15mm}
% \movie[label=show3,width=9cm,poster,autostart,showcontrols]
% {\includegraphics[width=8.5cm]
% {/home/jeremic/tex/works/Conferences/2017/DOE_Project_Review_Meeting_LBNL_09June2017/Present/Solid-Fluid-Interaction.jpg}}
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Fluid_Solid_interaction/Solid_Fluid_Interaction_NEW.mpeg}
% \end{center}
% 
% 
% \begin{flushleft}
% \vspace*{-15mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Fluid_Solid_interaction/Solid_Fluid_Interaction.mp4}
% %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
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\section{Seismic Motions, Inelasticity and Uncertainty}



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\subsection{Six Component Seismic Motions}

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

\begin{frame}
  \frametitle{3C, 6C Seismic Motions}

\vspace*{2mm}

\begin{itemize}

   \item  All (most) measured motions are full 3C, 6C

   \item  One example of an almost 2C motion (LSST07, LSST12)
\vspace*{2mm}


\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-5mm}
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Lotung_LSST07_FA25.jpeg}
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Lotung_LSST12_FA25.jpeg}
\hspace*{-5mm}
%
\end{center}
\end{figure}
   

%
%   \item  1D (?): M 6.9 San Pablo, Guatemala EQ, 14Jun2017
%
\end{itemize}


\end{frame}






% %  
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Regional Geophysical  Models}
% 
% \begin{itemize}
% 
%   \item Free Field seismic motions on regional scale
% 
% 
% \vspace*{4mm}
%   \item Knowledge of geology (deep and shallow) needed
% 
% 
% \vspace*{4mm}
%  \item Developed using SW4 and/or Real-ESSI
% 
% 
% \vspace*{4mm}
%   \item  Collaboration  with LLNL: Dr.~Rodgers, Dr.~Pitarka and Dr.~Petersson
% 
% 
% 
% 
% \end{itemize}
%  
% \end{frame}
% 
% 
%  
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Regional Geophysical  Models}
% 
%  \begin{figure}[!htb]
%  \begin{center}
%   \includegraphics[width=5truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/San_Francisco__Regional_Model_BIG.jpg}
%   \includegraphics[width=5.2truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/San_Francisco__Regional_Model.jpg}
%  \end{center}
% % \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
%  \end{figure}
% 
% Rodgers and Pitarka 
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Regional Geophysical  Models}
% 
%  \begin{figure}[!htb]
%  \begin{center}
%   \includegraphics[width=10truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/USG-Bay_Area_Model_CC_det2_sm.jpg}
%  \end{center}
% % \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
%  \end{figure}
% 
% USGS
%  
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% 
% 
% 
% %  
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% %  \begin{frame}
% %  \frametitle{Example Regional Model}
% %  
% %   \begin{figure}[!htb]
% %   \begin{center}
% %    \includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/Vs_at_top.jpg}
% %  %  \includegraphics[width=5truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/Horizontal_Velocity_at_12s.jpg}
% %    \includegraphics[width=5truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/Peak_Velocity.jpg}
% %   \end{center}
% %  % \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
% %   \end{figure}
% %   
% %  \end{frame}
% %  
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Example Regional Model (Rodgers)}
% 
% 
% 
% 
%   
% %\vspace*{5mm}
% \begin{center}
% %\hspace*{-5mm}
% %
% %\movie[label=show3,width=10.0cm,poster,autostart,showcontrols]
% \movie[label=show3,width=8.0cm,poster]
% %\movie[label=show3,width=6.0cm,poster,showcontrols]
%   {\includegraphics[width=80mm]{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/NPP_animations_August2017/M6_5_s500_BASIN_STOCHASTIC_mag_SLOW.jpg}}
%      {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/NPP_animations_August2017/M6_5_s500_BASIN_STOCHASTIC_mag_SLOW.mpg}
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% %
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% 
% 
% % online   
% \vspace*{-5mm}
% \begin{flushleft}
% \hspace*{-5mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/NPP_animations_August2017/M6_5_s500_BASIN_STOCHASTIC_mag_SLOW.mpg}
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% 


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\begin{frame}
\frametitle{ESSI: 6C or 1C Seismic Motions}


\begin{itemize}


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


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

\item  Apply  such  vertically propagating shear wave to 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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\begin{frame}
\frametitle{6C Free Field Motions (closeup)}


  
%\vspace*{-2mm}
\begin{center}
\movie[label=show3,width=80mm,poster,showcontrols]
{\includegraphics[width=80mm]{/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_input_closeup_mp4_icon.jpeg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input_closeup.mp4}
\end{center}

\begin{flushleft}
\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}
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% local
% local
%


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% out   
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% out  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_01AApr2015/movie_input_closeup.mp4}
% out  %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
% out    {\tiny (MP4)}
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% out  %
% out  

 \end{frame}



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\begin{frame}
\frametitle{1C vs 6C Free Field Motions}



 
\begin{itemize}

  \item One component of motions, 1C from  6C
%  or 3$\times$1D (it is done all the time!)

  \item  Excellent fit
%  (goal is to predict and inform and not (force) fit)


\end{itemize}




% local
%\vspace*{-2mm}
\begin{center}
\hspace*{-16mm}
%\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
\movie[label=show3,width=61mm,poster, showcontrols]
  {\includegraphics[width=60mm]{/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_ff_3d_mp4_icon.jpeg}}
  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_ff_3d.mp4}
%\hspace*{-2mm}
%\hfill
%\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
\movie[label=show3,width=61mm,poster, showcontrols]
  {\includegraphics[width=60mm]
  {/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_ff_1d_mp4_icon.jpeg}}
  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_ff_1d.mp4}
\hspace*{-16mm}
\end{center}
% local


% 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}
{\tiny (MP4)}
%
\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}
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%  
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% \begin{frame}
% \frametitle{1D vs 3$\times$1C vs 3C Seismic Motions}
% 
% 
% \begin{itemize}
% 
% \vspace{2mm}
%  \item 1D is required by the code
% 
% \vspace{4mm}
%  \item 3$\times$1D can be used depending on frequency/wave length of interest, 
% 
% \vspace{4mm}
%  \item 3C is more realistic, however it is challenging to define motions in full 3C
% 
% \end{itemize}
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{When to  use  3C and/or 3$\times$1C}
% 
% 
% \begin{figure}[!hbpt]
% \begin{center}
% %
% %\includegraphics[width=4.5truecm]{/home/jeremic/tex/works/Papers/2016/3D_vs_3_x_1D_motions/version_04Jan2017/NearFieldESSINPPs/results/3d_vs_1d_6/node_733_acce.pdf}
% %\includegraphics[width=4.5truecm]{/home/jeremic/tex/works/Papers/2016/3D_vs_3_x_1D_motions/version_04Jan2017/NearFieldESSINPPs/results/6/node_733_acce.pdf}
% % %
% % \\
% % \includegraphics[width=9.5truecm]{/home/jeremic/tex/works/Papers/2016/3D_vs_3_x_1D_motions/version_04Jan2017/NearFieldESSINPPs/results/3d_vs_1d_6/node_733_fft.pdf}
% % \\
% \includegraphics[width=11truecm]{/home/jeremic/tex/works/consulting/2017/IAEA/TECDOC/Version_14Mar2017/1Dvs3x1Dvs3D_waves.pdf}
% \end{center}
% \end{figure}
% 
% \end{frame}
% 
% 
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{6C vs 1C NPP ESSI Response Comparison}

 
% local
\vspace*{-2mm}
\begin{center}
\hspace*{-7mm}
%\movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
\movie[label=show3,width=8.8cm,poster, showcontrols]
  {\includegraphics[width=92mm]
  {/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_2_npps_mp4_icon.jpeg}}
  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_2_npps.mp4}
\end{center}
% local
%  \vspace*{-2mm}
%  \begin{center}
%  \hspace*{-7mm}
%  \movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
%    {\includegraphics[width=90mm]{movie_2_npps_mp4_icon.jpeg}}{movie_2_npps.mp4}
%  \end{center}


% online
\vspace*{-12mm}
\begin{flushleft}
%\vspace*{-15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_2_npps.mp4}
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% online



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\begin{frame}
\frametitle{Stress Testing SSI Systems}



\begin{itemize}

\item Excite SSI system with a suite of  seismic motions

\item  Waves: P, SV, SH, Surface (Rayleigh, Love, etc.)
   
\item Variation in inclination, frequency, energy and duration

\item Try to "break" the system, shake-out strong and weak links

\end{itemize}

\vspace*{-4mm}  
\begin{figure}[!htb]
\begin{center}
\hspace*{-5mm}
\includegraphics[width=6.5cm]{/home/jeremic/tex/works/Conferences/2018/BestPSHANI/Presentation/stress_test_Best_SHANI_May2018.jpg}
\end{center}
\end{figure}

 
\vspace*{-5mm}  
\begin{figure}[!htb]
\begin{center}
\hspace*{-5mm}  
%\includegraphics[width=4cm]{/home/jeremic/tex/works/consulting/2017/IAEA/TECDOC/Version_14Mar2017/1Dvs3x1Dvs3D_waves_02.pdf}
\includegraphics[width=7.5cm]{/home/jeremic/tex/works/Conferences/2018/WCCM2018/Present/1Dvs3x1Dvs3D_waves_03.pdf}
\hspace*{4mm}
\includegraphics[width=3.6cm]{/home/jeremic/tex/works/Conferences/2018/WCCM2018/Present/1Dvs3x1Dvs3D_waves_02.pdf}
\hspace*{-5mm}
\end{center}
\end{figure}


\end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Stress Test Source Signals}

\begin{itemize}


%   \item Gauss 
% \begin{figure}[!hbpt]
% \begin{flushright}
%   \vspace*{-0.5cm}
% \includegraphics[width=7.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/gauss.png}
% \end{flushright}
% \end{figure}

  \item Ricker 
\begin{figure}[!hbpt]
\begin{flushright}
  \vspace*{-1cm}
\includegraphics[width=4.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ricker2nd.pdf}
\includegraphics[width=4.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ricker2nd_FFT.pdf}
  \hspace*{-0.7cm}
\end{flushright}
\end{figure}
    
  \item Ormsby   
\begin{figure}[!hbpt]
\begin{flushright}
  \vspace*{-1cm}
\includegraphics[width=4.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ormsby.pdf}
\includegraphics[width=4.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ormsby_FFT.pdf}
  \hspace*{-0.7cm}
\end{flushright}
\end{figure}

\end{itemize}

% \begin{figure}[!hbpt]
% \begin{center}
% %
% \includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/gauss.png}
% %
% \includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ricker2nd.pdf}
% \includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ricker2nd_FFT.pdf}
% %
% \includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ormsby.pdf}
% \includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ormsby_FFT.pdf}
% %
% \end{center}
% \end{figure}


\end{frame}


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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection{Local Geology Effects}



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

\frametitle{Free Field, Variation in Input Frequency, $\theta = 60^{o}$}

% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy

     
% \vspace*{-5mm}
\begin{center}
% \hspace*{-15mm}
%\movie[label=show3,width=10cm,poster,autostart,showcontrols]
\movie[label=show3,width=10cm,poster,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/Free_Field_variation_in_wave_frequency.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/free_field_frequency.mp4}
\end{center}
        
% online   
\vspace*{-12mm}
\begin{flushleft}
\hspace*{-4mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/free_field_frequency.mp4}
  {\tiny (MP4)}
\end{flushleft}
% online  
   

\end{frame}

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



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

\frametitle{SMR ESSI, Variation in Input Frequency, $\theta = 60^{o}$}

% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy

     
% \vspace*{-5mm}
\begin{center}
% \hspace*{-15mm}
%\movie[label=show3,width=10cm,poster,autostart,showcontrols]
\movie[label=show3,width=10cm,poster,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/ESSI_SMR_variation_in_wave_frequency.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/SMR_frequency.mp4}
\end{center}
        
% online   
\vspace*{-12mm}
\begin{flushleft}
\hspace*{-4mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/SMR_frequency.mp4}
  {\tiny (MP4)}
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% online  
   

\end{frame}

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Inelasticity, Plastic  Energy Dissipation and Uncertainty}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Energy Input and Dissipation}

\begin{itemize}

\vspace*{1mm}
     \item[] Energy input, static and dynamic forcing


\vspace*{4mm}
     \item[] Energy dissipation outside SSI domain:
       \begin{itemize}
         \item SSI system oscillation radiation
         \item Reflected wave radiation
       \end{itemize}
\vspace*{1mm}
     \item[] Energy dissipation/conversion inside SSI domain:
       \begin{itemize}
         \item Inelasticity of soil, contact zone, structure, foundation, dissipators
         \item Viscous coupling with internal/pore fluids, and external fluids
% %         \item[] potential and kinetic energy
%          \item[] potential $\leftarrow \! \! \! \! \! \! \rightarrow$ kinetic energy
       \end{itemize}                           



%\vspace*{1mm}
%   \item[] Numerical energy dissipation (numerical damping/production and period  errors)
%   \item[] Numerical energy dissipation (damping/production)
%\vspace*{4mm}
   \item[] Numerical energy dissipation/production


\end{itemize}

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




   
% %  


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

\frametitle{Energy Dissipation in NPP Model}

% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy

% \vspace*{-5mm}
\begin{center}
% \hspace*{-15mm}
\movie[label=show3,width=10cm,poster,autostart,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/tex/works/Conferences/2017/SMiRT_24/present/3D_Nonlinear_Modeling_and_it_Effects/NPP_Plastic_Dissipation_grab.jpg}}
{/home/jeremic/tex/works/Thesis/HanYang/Files_10Aug2017/NPP_Plastic_Dissipation.mp4}
\end{center}




\begin{flushleft}
\vspace*{-15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/NPP_Plastic_Dissipation.mp4}
%  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
  {\tiny (MP4)}
\end{flushleft}
%



\end{frame}

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

\frametitle{Energy Dissipation for an SMR Model}

% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy


% \vspace*{-5mm}
\begin{center}
% \hspace*{-15mm}
\movie[label=show3,width=10cm,poster,autostart,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation_screen_grab.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation.mp4}
\end{center}


\begin{flushleft}
\vspace*{-15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation.mp4}
%  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
  {\tiny (MP4)}
\end{flushleft}
%





% \vspace*{-5mm}



\end{frame}

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 
 \frametitle{Wall, Regular and ASR Concrete}

\vspace{-1mm}

   \begin{figure}[!h]
    \begin{center}
     \includegraphics[width=4truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/Rebar_Plan.pdf}
     \includegraphics[width=6truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/3D_mesh.pdf}
    \end{center}
\end{figure}

   \begin{figure}[!h]
    \begin{center}
\includegraphics[width=2.7truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/Reg_A_Force_Displacement.pdf}
\includegraphics[width=2.7truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/ASR_A1_Force_Displacement.pdf}
%
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_Natural_Hazartd_Oct2018/Present/OECD_wall_damage_3_stages.jpg}
    \end{center}
\end{figure}
\vspace{-4mm}

%
%\vspace{-2mm}
%\begin{figure}[!htbp]
%\begin{center}
%\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_Natural_Hazartd_Oct2018/Present/OECD_wall_damage_3_stages.jpg}
%\end{center}
%\end{figure}
\vspace{-2mm}



% \vspace{-20mm}
% \begin{figure}[!htbp]
% \hspace*{-10mm}
% \begin{center}
% \includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/Damage_3000.pdf}
% \hspace*{-5mm}
% \includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/Damage_5000.pdf}
% \hspace*{-5mm}
% \includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/Damage_10000.pdf}
% \end{center}
% \end{figure}
% 
% 
% \vspace*{-5mm}
% \hspace*{12mm}
% \begin{footnotesize}
% $u_y$ = 1.4 mm
% \hspace{12mm}
% $u_y$ = 1.8 mm
% \hspace{12mm}
% $u_y$ = 3.0 mm
% \end{footnotesize}
  
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 



			 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
  \frametitle{Real-ESSI  Modeling Phases}



\begin{figure}[htbp]
\begin{center}
  \includegraphics[width = 2.3cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/soil-structure/overview.png}
\vspace*{-1mm}
\\
  \includegraphics[width = 0.35cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/free_field_1D/DRM_1D_motion_3D_just_column.jpg}
\hspace*{5mm}
%  \includegraphics[width = 0.1cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/free_field_1D/DRM1D_Motion3D.png}
  \includegraphics[width = 2.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/free_field_3D/motion3D_DRM3D_free_field.png}
\hspace*{5mm}
%  \includegraphics[width = 1cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/soil-foundation/soil_foundation.png}
%  \includegraphics[width = 3cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/soil-foundation/slice.png}
  \includegraphics[width = 2.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/soil-foundation/foundation_results.png}
%  \includegraphics[width = 3cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/soil-structure/overview.png}
\\
\vspace*{-3mm}
  \includegraphics[width = 1.0cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/eigen/structure-only.png}
\hfill
  \includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/eigen/eigen1.png}
\hfill
  \includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/eigen/eigen2.png}
\hfill
  \includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/eigen/eigen3.png}
\hfill
  \includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/eigen/eigen4.png}
\hfill
  \includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/eigen/eigen5.png}
\hfill
  \includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/eigen/eigen6.png}
\hfill
%  \includegraphics[width = 1.0cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/imposed_motion/structure-only.png}
%\hfill
  \includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/imposed_motion/imposed_motion_results.png}
%   \includegraphics[width = 0.1cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/soil-structure/overview.png}
\\
\vspace*{-1mm}
  \includegraphics[width = 6cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/soil-structure/DRM3D_motion3D_structure.png}
\end{center}
\end{figure}



\end{frame}










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

\frametitle{Uncertainty Propagation through 
Inelastic System}

% 

\begin{itemize}



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

 
  

\vspace*{2mm}
\item Dynamic Finite Elements
%
\begin{equation}
{ M} \ddot{ u_i} +
{ C} \dot{ u_i} +
{ K}^{ep} { u_i} =
{ F(t)}
    \nonumber
\end{equation}


\vspace*{2mm}
\item Material and load parameters are uncertain



\end{itemize}



\end{frame}






 
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\begin{frame} 

\frametitle{Probabilistic Elastic-Plastic Response}


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

\end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame} 
% 
% \frametitle{Previous Work}
% 
%  
% 
% \begin{itemize}
% 
% \item 
% Linear algebraic or differential equations:
% 
%      \begin{itemize}
%         \item Variable Transf. Method (Montgomery and Runger 2003)
%         \item Cumulant Expansion Method (Gardiner 2004)
%      \end{itemize}
% 
% \item 
% Nonlinear differential equations:
%      
%       \begin{itemize}
% 
%       \item  Monte  Carlo Simulation (Schueller 1997, De Lima et al 2001, Mellah
%       et al. 2000, Griffiths et al. 2005...) \\ $\rightarrow$ can be accurate, very costly
% 
%       \item  Perturbation  Method  (Anders and Hori 2000, Kleiber and Hien 1992,
%       Matthies  et  al. 1997) \\ $\rightarrow$ first and second order Taylor series
%       expansion  about mean - limited to problems with small C.O.V. and inherits
%       "closure problem"
% 
%       \item SFEM (Matthies et al,  2004, 2005, 2014...)
% 
% 
%       \end{itemize}
% 
% % 
% %  \item 
% %  Monte Carlo method: accurate, very costly
% %  
% %  \item 
% %  Perturbation method: 
% 
% \end{itemize}
% 
% 
%  
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \end{frame}
% 
% 


% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame} \frametitle{{3D FPK Equation}}
% 
% \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), D_{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), D_{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), D_{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), D_{mnrs}(x_t), \epsilon_{rs}(x_t,t)); \right. \right. \right. \\
% \nonumber
% & & \left. \left. \left. \eta_{ab} (\sigma_{ab}(x_{t-\tau}, t-\tau), D_{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}
% 
% 
% 
% %-- \begin{itemize}
% %-- 
% %-- 
% %-- 
% %-- \item 6 equations
% %-- 
% %-- \item Complete description of 3-D probabilistic stress-strain response
% %-- 
% %-- \end{itemize}
% %-- 
% %--  
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \end{frame}
% 
% 
% 



% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame} 
% 
% \frametitle{FPK Equation}
% 
%  
% 
% \begin{itemize}
% 
% \item Advection-diffusion equation 
% %
% \begin{equation}                
% \nonumber
% \frac{\partial P(\sigma,t)}{\partial t} = -\frac{\partial}{\partial \sigma}\left[N_{(1)}P(\sigma,t)-\frac{\partial}{\partial \sigma}
% \left\{N_{(2)} P(\sigma,t)\right\} \right]
% \end{equation}
% 
% %
% 
% \item Complete probabilistic description of response 
% 
% 
% \item Solution PDF is second-order exact to covariance of time (exact mean and variance)
% 
% 
% \item It is deterministic equation in probability density space
% 
% \item It is linear PDE in probability density space 
% $\rightarrow$ simplifies the numerical solution process
% 
% %\vspace*{0.2truecm}
% 
% \end{itemize}
% 
% % 
% % \vspace*{0.5cm}
% % {%
% % \begin{beamercolorbox}{section in head/foot}
% % \usebeamerfont{framesubtitle}\tiny{B. Jeremi\'{c}, K. Sett, and M. L. Kavvas, "Probabilistic
% % Elasto--Plasticity: Formulation in 1--D", \textit{Acta Geotechnica}, Vol. 2, No. 3, 2007, In press (published
% % online in the \textit{Online First} section)}
% % %\vskip2pt\insertnavigation{\paperwidth}\vskip2pt
% % \end{beamercolorbox}%
% % }
% 
% 
% 
% \end{frame}
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame} 
% 
% 
% 
% \frametitle{Template Solution of FPK Equation}
% 
%  
% 
% \begin{itemize}
% 
% 
% 
% 
% \item FPK diffusion--advection equation is applicable to any material model $\rightarrow$ 
% only the coefficients $N_{(1)}$ and $N_{(2)}$ are different for different material models
% % %
% % %
% % %
% % %\begin{normalsize}
% % \begin{equation}                
% % \nonumber
% % \frac{\partial P(\sigma,t)}{\partial t} = -\frac{\partial}{\partial \sigma}\left[N_{(1)}P(\sigma,t)-\frac{\partial}{\partial \sigma}
% % \left\{N_{(2)} P(\sigma,t)\right\} \right]
% % %\nonumber
% %  = -\frac{\partial \zeta}{\partial \sigma}
% % \end{equation}
% % %\end{normalsize}
% 
% %
% 
% \item Initial condition 
% 
% \begin{itemize}
% 
% \item Deterministic $\rightarrow$ Dirac delta function $\rightarrow$ $ P(\sigma,0)=\delta(\sigma) $
% 
% \item Random $\rightarrow$ Any given distribution
% 
% \end{itemize}
% 
% \item Boundary condition: Reflecting BC $\rightarrow$ conserves probability mass
% $\zeta(\sigma,t)|_{At \ Boundaries}=0$
% 
% \item Solve using finite differences and/or finite elements
% 
% 
% \item  However  (!!)  it  is a stress solution and probabilistic stiffness is an
% approximation!
% 
% \end{itemize}
% 
%  
% \end{frame}
% 
% 
% 
% 
% 
% 
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Direct Solution for Probabilistic Stiffness and Stress in 1D}
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%    BEGGINING PEP    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% \begin{frame}{Direct Probabilistic Constitutive Modeling in 1D}
% 
% 
% % \begin{itemize}
% %  
% %  \vspace{0.5cm}
% % 
% % \item<1-> Probabilistic constitutive modeling : \vspace{0.5cm}
% 
% \begin{itemize}
% 
% 
% \item  Zero elastic region elasto-plasticity with stochastic Armstrong-Frederick
% kinematic hardening
% 
% $ \Delta\sigma =\ H_a  \Delta \epsilon  -  c_r \sigma |\Delta \epsilon| ;
% \hspace{0.5cm} 
% E_t = {d\sigma}/{d\epsilon} = H_a \pm c_r \sigma $
% 
% \vspace*{2mm}
% \item Uncertain: 
%       init. stiff. $H_a$, 
%       shear strength $H_a/c_r$, 
%       strain $\Delta \epsilon$: 
% 
% $ H_a = \Sigma h_i \Phi_i; \;\;\;  
%   C_r = \Sigma c_i \Phi_i; \;\;\; 
%   \Delta\epsilon =  \Sigma \Delta\epsilon_i \Phi_i $
% 
% 
% 
% \vspace*{2mm}
% \item Resulting stress and stiffness are also uncertain 
% 
% % - 
% % - $ \sum_{l=1}^{P_{\sigma}} \Delta\sigma_i \Phi_i = \sum_{i=1}^{P_h} \sum_{k=1}^{P_e}\ h_i  \Delta \epsilon_k \Phi_i \Phi_k - \sum_{j=1}^{P_g} \sum_{k=1}^{P_e}\sum_{l=1}^{P_{\sigma}} \ c_i \Delta \epsilon_k \sigma_l \Phi_j \Phi_k \Phi_l$
% % - 
% % - $ \sum_{l=1}^{P_{E_t}} \Delta E_{t_i} \Phi_i = \sum_{i=1}^{P_h}  h_i  \Phi_i \pm \sum_{i=1}^{P_c} \sum_{l=1}^{P_{\sigma}} \ c_i  \sigma_l  \Phi_i \Phi_l$
% % - 
% 
% 
% \end{itemize}
% 
% 
% % \vspace{0.5cm}
% 
% 
% 
% % \vspace{1cm}
% 
% %\item<1-> Time integration is done via Newmark algorithm
% 
% % 
% % \end{itemize}
% % 
% \end{frame}
% 
% 
% % % % % % % % % % % % % % % % %
% 
% 


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}{Probabilistic Stiffness Solution}
%  
%  \begin{itemize}
%   
% 
% \item Analytic product for all the components, 
% 
% $ 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]
% $
% 
% 
% 
% 
% \item Stiffness: each Polynomial Chaos component is updated incrementally
% % at each Gauss Point via stochastic Galerkin projection
% 
% 
% 
%   \small{$E_{t_1}^{n+1}  =  \frac{1}{<\Phi_1\Phi_1> }\{\sum_{i=1}^{P_h} \ h_i   <\Phi_i \Phi_1> \pm \sum_{j=1}^{P_c} \sum_{l=1}^{P_{\sigma}} \ c_j  \sigma_l^{n+1} <\Phi_j  \Phi_l \Phi_1>\}$}
%   
%   $\large{\vdots}$
%   
%      \small{$E_{t_P}^{n+1}  =  \frac{1}{<\Phi_1\Phi_P> }\{\sum_{i=1}^{P_h} \ h_i   <\Phi_i \Phi_P> \pm \sum_{j=1}^{P_c} \sum_{l=1}^{P_{\sigma}} \ c_j  \sigma_l^{n+1} <\Phi_j  \Phi_l \Phi_P>\}$}
%   
%   
% \item Total stiffness is : 
%   
%   $ E_{t}^{n+1} = \sum_{l=1}^{P_{E}} E_{t_i}^{n+1} \Phi_i $
% 
% 
% 
% 
% \end{itemize}
% 
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}{Probabilistic Stress Solution}
%  
%  \begin{itemize}
%   
%   
% 
% \item Analytic product, for each stress component, 
% 
% $ \Delta \sigma_{ij} =  E^{EP}_{ijkl} \; \Delta \epsilon_{kl} $ 
% %      =  
% %      \left[
% %      E^{el}_{ijkl}
% %        -
% %        \frac{\displaystyle  E^{el}_{ijmn} m_{mn} n_{pq} E^{el}_{pqkl}}
% %            {\displaystyle n_{rs} E^{el}_{rstu} m_{tu} - \xi_* h_*}
% %            \right]
% %     \Delta \epsilon_{kl}
% % 
% 
% 
% \vspace*{1mm}
% \item Incremental stress: each  Polynomial  Chaos  component  is updated
% incrementally 
% % via stochastic Galerkin projection
% 
% 
%  
%  
%   {$\Delta\sigma_1^{n+1}  = \frac{1}{<\Phi_1\Phi_1> }\{\sum_{i=1}^{P_h} \sum_{k=1}^{P_e}\ h_i  \Delta \epsilon_k^n <\Phi_i \Phi_k \Phi_1>- \sum_{j=1}^{P_g} \sum_{k=1}^{P_e}\sum_{l=1}^{P_{\sigma}} \ c_j \Delta \epsilon_k^n \sigma_l^n <\Phi_j \Phi_k \Phi_l \Phi_1>\}$}
% 
%  ${\vdots}$ 
% 
% {$\Delta\sigma_P^{n+1}  = \frac{1}{<\Phi_P\Phi_P> }\{\sum_{i=1}^{P_h} \sum_{k=1}^{P_e}\ h_i  \Delta \epsilon_k^n <\Phi_i \Phi_k \Phi_P>- \sum_{j=1}^{P_g} \sum_{k=1}^{P_e}\sum_{l=1}^{P_{\sigma}} \ c_j \Delta \epsilon_k^n \sigma_l^n <\Phi_j \Phi_k \Phi_l \Phi_P>\}$}
% 
% 
% \vspace*{1mm}
% \item Stress  update: 
% 
% $ \sum_{l=1}^{P_{\sigma}} \sigma_i^{n+1} \Phi_i = \sum_{l=1}^{P_{\sigma}} \sigma_i^{n} \Phi_i + \sum_{l=1}^{P_{\sigma}} \Delta\sigma_i^{n+1} \Phi_i$
% 
% 
% 
% \end{itemize}
% 
% \end{frame}
% 



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

\begin{frame}
\frametitle{Probabilistic Elastic-Plastic Modeling}


% % \vspace*{-5mm}
% \begin{center}
% % \hspace*{-15mm}
% \movie[label=show3,width=7cm,poster,autostart,showcontrols]
% {\includegraphics[width=7cm]
% {/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/NPP_Plastic_Dissipation_Density.png}}
% %{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/NPP_without_Contact_vonMises.mp4}
% {NPP_without_Contact_vonMises.mp4}
% \end{center}

%\vspace*{-5mm}
\begin{center}
% \hspace*{-15mm}
\movie[label=show3,width=9cm,poster,autostart,showcontrols]
{\includegraphics[width=9cm]
{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_PEP_25.png}}
% /home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_PEP_25.pdf
%{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Animations/PEP_Animation.mp4}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Probabilistic_Elasto_Plasticity_and_Stochastic_Elastic_Plastic_Finite_Element_Method/PEP_Animation.mp4}
\end{center}

%
% \includegraphics[width = 12cm]{./img/figure_PEP_25.pdf}


\end{frame}















 



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Stochastic Elastic-Plastic Finite Element Method}



\begin{itemize}

\item Material uncertainty expanded into stochastic shape funcs.
%$E(x,t,\theta) = \sum_{i=0}^{P_d} r_i(x,t) * \Phi_i[\{\xi_1, ..., \xi_m\}]$

\vspace*{1mm}
\item Loading uncertainty expanded into stochastic shape funcs.
%$f(x,t,\theta) = \sum_{i=0}^{P_f} f_i(x,t) * \zeta_i[\{\xi_{m+1}, ..., \xi_f]$

\vspace*{1mm} 
\item Displacement expanded into stochastic shape funcs.
%$u(x,t,\theta) = \sum_{i=0}^{P_u} u_i(x,t) * \Psi_i[\{\xi_1, ..., \xi_m, \xi_{m+1}, ..., \xi_f\}]$

%\item 
%Stochastic system of equation resulting from Galerkin approach (static example):
%
%\item  Time domain integration  using Newmark and/or HHT, in probabilistic spaces


\end{itemize}


\begin{tiny}
\[
%$
\begin{bmatrix}
    \sum_{k=0}^{P_d} <\Phi_k \Psi_0 \Psi_0> K^{(k)}    & \dots & \sum_{k=0}^{P_d} <\Phi_k \Psi_P \Psi_0> K^{(k)}\\
    \sum_{k=0}^{P_d} <\Phi_k \Psi_0 \Psi_1> K^{(k)}    & \dots & \sum_{k=0}^{P_d} <\Phi_k \Psi_P \Psi_1> K^{(k)}\\  \\
    \vdots & \vdots & \vdots & \vdots\\
    \sum_{k=0}^{P_d} <\Phi_k \Psi_0 \Psi_P> K^{(k)}     & \dots & \sum_{k=0}^{M} <\Phi_k \Psi_P \Psi_P> K^{(k)}
\end{bmatrix}
\begin{bmatrix}
    \Delta u_{10} \\
    \vdots \\
    \Delta u_{N0}\\
    \vdots \\
    \Delta u_{1P_u}\\
    \vdots \\
    \Delta u_{NP_u}
\end{bmatrix}
=
%\]
%\[
\begin{bmatrix}
     \sum_{i=0}^{P_f} f_i  <\Psi_0\zeta_i> \\
    \sum_{i=0}^{P_f} f_i   <\Psi_1\zeta_i> \\
   \sum_{i=0}^{P_f} f_i    <\Psi_2\zeta_i> \\
    \vdots \\
     \sum_{i=0}^{P_f} f_i  <\Psi_{P_u}\zeta_i>\\
\end{bmatrix}
%$
\]
\end{tiny}





\end{frame}







% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}
% \frametitle{SEPFEM: System Size}
% 
% \begin{itemize}
% 
%   \item SEPFEM offers a complete solution (single step) 
% 
%   \item  It is NOT based on Monte Carlo approach
% 
%   \item  System of equations does grow (!)
% 
% \end{itemize}
% 
% 
% %   \normalsize{Typical number of terms required for a SEPFEM problem} \vspace{1cm}\\
%   \scalebox{0.7}{
%   \begin{tabular}{ c c c c}
%    \# KL terms material & \# KL terms load & PC order displacement& Total \# terms per DoF\\ \hline
%    4 & 4 & 10 & 43758 \\  
%    4 & 4 & 20 & 3 108 105 \\    
%    4 & 4 & 30 & 48 903 492 \\  
%    6 & 6 & 10 & 646 646 \\    
%    6 & 6 & 20 & 225 792 840 \\  
%    6 & 6 & 30 & 1.1058 $10^{10}$ \\    
%    8 & 8 & 10 & 5 311 735 \\  
%    8 & 8 & 20 & 7.3079 $10^{9}$ \\    
%    8 & 8 & 30 & 9.9149 $10^{11}$\\  
%    
%    ...  & ... & ... & ...\\   
% %    \hline
%   \end{tabular}}
% 
% 
% \end{frame}
% 
% 
% 
% 
% 







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\begin{frame}
\frametitle{SEPFEM: Example in 1D}


\vspace*{-2mm}
\begin{center}
% \hspace*{-15mm}
\movie[label=show3,width=9cm,poster,autostart,showcontrols]
{\includegraphics[width=9cm]{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_elastic_900.png}}
% /home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_PEP_25.pdf
%{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Animations/SEPFEM_Animation_Elastic.mp4}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Probabilistic_Elasto_Plasticity_and_Stochastic_Elastic_Plastic_Finite_Element_Method/SEPFEM_Animation_Elastic.mp4}
\end{center}

% \includegraphics[width = 12cm]{./img/figure_elastic_900.pdf}




\end{frame}


























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%\section{Energy Dissipation}
%

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\section{Pine Flat Dam}





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\subsection{Pine Flat Dam Test Model}


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Repeat of Simulations}
% 
% \begin{itemize}
% 
% \vspace*{1mm}
%      \item[]
% 
% 
% 
% \end{itemize}
% 
% %
% \end{frame}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Pine Flats Dam, Model}

\begin{itemize}

%\vspace*{1mm}
     \item Material properties provided
     \item Motions applied through DRM, from bottom
     
     \item Energy dissipation, Viscous, Numerical, Radiation

     \item Load cases as provided
%     \item 


\end{itemize}


\vspace*{-5mm}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-8mm}
\includegraphics[width=12.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Model_Mesh_No_Reservior.pdf}
%
\end{center}
\end{figure}

%
\end{frame}









%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Pine Flats Dam, Static, Displacements}

\begin{itemize}
%\vspace*{1mm}
     \item Self weight
     \item Water pressure, on dam side and lake bottom
\end{itemize}


 
\begin{small}
%
\begin{table}[!htb]
\centering
\begin{tabular}{c|c|c|c|c|c}
%\hline
                       &            & \multicolumn{3}{c|}{Disp. [m]}   & Disp. [in] \\ \hline
                       &            & Top     & Heel    & Rel.    & Rel.         \\ \hline
Mat. Prop. I  & Hor. &  0.0121   &  0.0031  &  0.00900  &  0.354             \\ \cline{2-6} 
(Soft Found.)    & Vert.   & -0.0095   & -0.0059  & -0.00348  & -0.137            \\ \hline
Mat. Prop, II & Hor. &  0.0101   &  0.0011  &  0.00904  &  0.356             \\ \cline{2-6} 
(Stiff Found.)   & Vert.   & -0.0048   & -0.0019  & -0.00298  & -0.117            \\ 
%\hline
\end{tabular}
\end{table}
\end{small}


\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Static, Displacements and \huge{$\sigma_v$}}

% \begin{itemize}
% %\vspace*{1mm}
%      \item Displacements
%      \item Vertical stress distribution
% \end{itemize}

\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-7mm}
\includegraphics[width=12.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Case_A_Vertical_Stress.png}
%
\end{center}
\end{figure}

%
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Mesh Refinement Effects}

%\begin{itemize}
%%\vspace*{1mm}
%     \item Material properties provided
%\end{itemize}
%
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-5mm}
\includegraphics[width=11.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Model_Refined_Mesh.pdf}
%
\end{center}
\end{figure}

%
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Mesh Refinement Effects}




%\begin{itemize}
%%\vspace*{1mm}
%     \item Meshing effects are small
%\end{itemize}
%  
%  \begin{figure}[!hbpt]
%  \begin{center}
%  %
%  %\hspace*{-5mm}
%  \includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/}
%  %
%  \end{center}
%  \end{figure}
%
\begin{table}[!htb]
\centering
\begin{tabular}{c|c|c|c|c}
%\hline
                          &            & \multicolumn{3}{c}{Displacements [m]} \\ 
%\hline
                          &            & Original    & Refined     & Difference \\ \hline
\multirow{2}{*}{Dam Top}  & Horizontal &  0.012121  &  0.012201  &  0.66\%     \\ \cline{2-5} 
                          & Vertical   & -0.009463  & -0.009794  &  3.51\%     \\ \hline
\multirow{2}{*}{Dam Heel} & Horizontal &  0.003124  &  0.003287  &  5.21\%     \\ \cline{2-5} 
                          & Vertical   & -0.005981  & -0.006953  & 16.25\%    \\ \hline
\multirow{2}{*}{Relative} & Horizontal &  0.008996  &  0.009064  &  0.76\%     \\ \cline{2-5} 
                          & Vertical   & -0.003481  & -0.003489  &  0.23\%     \\ 
%                          \hline
\end{tabular}
\end{table}


%
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Eigen Analysis, Dry}

\begin{itemize}
%\vspace*{1mm}
     \item Eigen frequencies: \\
 (a) 2.46945~Hz, 
 (b) 3.82403~Hz, 
 (c) 4.48795~Hz, \\
 (d) 5.25455~Hz, 
 (e) 5.32023~Hz, 
 (f) 5.60061~Hz, 

\end{itemize}

%  \begin{table}[!htb]
% \centering
% \begin{tabular}{c|c}
% %\hline
% Mode & Natural Frequency (Hz) \\ \hline
% 1    & 2.46945                \\ \hline
% 2    & 3.82403                \\ \hline
% 3    & 4.48795                \\ \hline
% 4    & 5.25455                \\ \hline
% 5    & 5.32023                \\ \hline
% 6    & 5.60061                \\ 
% %\hline
% \end{tabular}
% \end{table}
%

%
\begin{figure}[!htbp]
\centering
\subfloat[]{\includegraphics[width=3.5cm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/mode1.pdf}}
\subfloat[]{\includegraphics[width=3.5cm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/mode2.pdf}}
\subfloat[]{\includegraphics[width=3.5cm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/mode3.pdf}}
\\
\subfloat[]{\includegraphics[width=3.5cm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/mode4.pdf}}
\subfloat[]{\includegraphics[width=3.5cm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/mode5.pdf}}
\subfloat[]{\includegraphics[width=3.5cm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/mode6.pdf}}
%\caption{\label{figure_case_d1_modal_shapes}
%Modal shapes: (a) First mode; (b) Second mode; (c) Third mode; (d) Fourth mode; (e) Fifth mode; (f) Sixth mode.}
\end{figure}

% 
% \begin{figure}[!hbpt]
% \begin{center}
% %
% %\hspace*{-5mm}
% \includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/}
% %
% \end{center}
% \end{figure}
% 
%
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Taft Earthquake, Time History of \huge{$\sigma_v$}}

\begin{itemize}
%\vspace*{1mm}
     \item Vertical stress at  dam heel, there is a tension!
\end{itemize}

\begin{figure}[!hbpt]
\begin{center}
%
%\hspace*{-5mm}
\includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Heel_Vertical_Stress_IU.pdf}
%
\end{center}
\end{figure}

%
\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Taft Earthquake, {\huge $\sigma_v$} Distribution at 
 {\huge $\sigma_{min}$} and {\huge $\sigma_{max}$}}

%\begin{itemize}
%%\vspace*{1mm}
%     \item Vertical stress at max tension and max compression
%\end{itemize}

\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-5mm}
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Max_IU.pdf}
\hfill
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Min_IU.pdf}
\hspace*{-5mm}
%\\
%\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Max_US.pdf}
%\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Min_US.pdf}

%
\end{center}
\end{figure}

%
\end{frame}





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{D2, Taft Earthquake, Dam and the Reservoir}

\begin{itemize}
%\vspace*{1mm}
     \item Pressures: total at the heel, total at the upstream face, hydrodynamic at the upstream face
\end{itemize}


\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-5mm}
\includegraphics[width=3.4truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Pressure_heel_time_series.pdf}
%\hfill
\includegraphics[width=3.4truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Pressure_distribution_upstream_surface.pdf}
%\hfill
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Pressure_dynamic_distribution_upstream_surface.pdf}
\hspace*{-5mm}
%\\
%\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Max_US.pdf}
%\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Min_US.pdf}
%
%
\end{center}
\end{figure}

%
\end{frame}






%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{D2, Tafts Earthquake, Dam and the Reservoir}

\begin{itemize}
%\vspace*{1mm}
     \item Vertical stress: heel time series, along base for max stress at the heel, for min stress at the heel
\end{itemize}


\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-5mm}
\includegraphics[width=3.5truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Heel_Vertical_Stress_US_D2_taft.pdf}
\hfill
\includegraphics[width=3.5truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Max_IU_D2_taft.pdf}
\hfill
\includegraphics[width=3.5truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Min_IU_D2_taft.pdf}
\hspace*{-5mm}
%\\
%\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Max_US.pdf}
%\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Min_US.pdf}

%
\end{center}
\end{figure}

%
\end{frame}

















%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{D2, ETAF Earthquake, Dam and the Reservoir}

\begin{itemize}
%\vspace*{1mm}
     \item Pressures: total at the heel, total at the upstream face, hydrodynamic at the upstream face
\end{itemize}


\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-5mm}
\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Pressure_heel_time_series_ETAF.pdf}
\hfill
\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Pressure_distribution_upstream_surface_ETAF.pdf}
\hfill
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Pressure_dynamic_distribution_upstream_surface_ETAF.pdf}
\hspace*{-5mm}
%\\
%\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Max_US.pdf}
%\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Min_US.pdf}

%
\end{center}
\end{figure}

%
\end{frame}






%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{D2, ETAF Earthquake, Dam and the Reservoir}

\begin{itemize}
%\vspace*{1mm}
     \item Vertical stress: heel time series, along base for max stress at the heel, for min stress at the heel
\end{itemize}


\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-5mm}
\includegraphics[width=3.5truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Heel_Vertical_Stress_US_D2_ETAF.pdf}
\hfill
\includegraphics[width=3.5truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Max_IU_D2_ETAF.pdf}
\hfill
\includegraphics[width=3.5truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Min_IU_D2_ETAF.pdf}
\hspace*{-5mm}
%\\
%\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Max_US.pdf}
%\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Min_US.pdf}

%
\end{center}
\end{figure}

%
\end{frame}













% EXTRA
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\subsection{Pine Flat Dam, Additional Modeling and Simulation}
















%  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Numerical Damping Effects, Elastic
   {\Large $\ddot{u}_{hor}^{top}$}, 
		 {\Large ${\sigma}_{v}^{heel}$}}

%\begin{itemize}
%%\vspace*{1mm}
%     \item Vertical stress at max tension and max compression
%\end{itemize}

\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-5mm}
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Top_Horizontal_Acceleration_IU.pdf}
\hfill
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Different_NP_Heel_Vertical_Stress_IU.pdf}
\hspace*{-5mm}
%\\
%\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Max_US.pdf}
%\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Min_US.pdf}

%
\end{center}
\end{figure}

%
\end{frame}





%  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Numerical Damping Effects, Inelastic 
   {\Large $\ddot{u}_{hor}^{top}$}, 
		 {\Large ${\sigma}_{v}^{heel}$}}

%\begin{itemize}
%%\vspace*{1mm}
%     \item Vertical stress at max tension and max compression
%\end{itemize}

\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-5mm}
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Case_D3_Different_NP_Top_Horizontal_Acceleration_IU.pdf}
\hfill
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Case_D3_Different_NP_Heel_Vertical_Stress_IU.pdf}
\hspace*{-5mm}
%\\
%\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Max_US.pdf}
%\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Min_US.pdf}

%
\end{center}
\end{figure}

%
\end{frame}


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

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

\begin{frame}
 \frametitle{Pine Flat Dam, Dynamic Response with Reservoir}

%\vspace*{-5mm}
\begin{center}
% \hspace*{-15mm}
\movie[label=show3,width=9cm,poster,autostart,showcontrols]
{\includegraphics[width=8cm]
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/soil_fluid_interaction_dam.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/soil_fluid_interaction_dam.mp4}
\end{center}

\begin{flushleft}
\vspace*{-15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/soil_fluid_interaction_dam.mp4}
%  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
  {\tiny (MP4)}
\end{flushleft}
%

\end{frame}

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

\begin{frame}
 \frametitle{Pine Flat Dam, Hydrodynamic Pressure}

%\vspace*{-5mm}
\begin{center}
% \hspace*{-15mm}
\movie[label=show3,width=10cm,poster,autostart,showcontrols]
{\includegraphics[width=10.0cm]
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/dynamic_pressure.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/dynamic_pressure.mp4}
\end{center}

\begin{flushleft}
\vspace*{-15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/dynamic_pressure.mp4}
%  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
  {\tiny (MP4)}
\end{flushleft}
%

\end{frame}

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

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

\begin{frame}
 \frametitle{Pine Flat Dam, Inelastic Interface, Hydrostatic}

%\vspace*{-5mm}
\begin{center}
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{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/Case_D3_Gap_Open_more.mp4}
\end{center}

\begin{flushleft}
\vspace*{-15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/Case_D3_Gap_Open_more.mp4}
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{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/dynamic_response_inclination.mp4}
\end{center}

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\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/dynamic_response_inclination.mp4}
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\section{Conclusion}



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    \subsection{Real-ESSI Simulator System}





 

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\frametitle{Real-ESSI Simulator System}

The  Real-ESSI, Realistic  
{\underline {\bf M}}odeling  and  
{\underline {\bf S}}imulation  of  
{\underline {\bf E}}arthquakes,  
{\underline {\bf S}}oils,
{\underline {\bf S}}tructures  and  their  
{\underline {\bf I}}nteraction.  Simulator  is  a  software,  hardware  and
documentation   system   for  high  fidelity,  high  performance,  time  domain,
nonlinear/inelastic, deterministic or probabilistic, 3D, finite element modeling
and simulation of:

    \begin{itemize}
%\vspace*{1mm}
      \item statics and dynamics of soil,
\vspace*{1mm}
      \item    statics and dynamics of rock,
\vspace*{1mm}
      \item    statics and dynamics of structures,
\vspace*{1mm}
      \item    statics of soil-structure systems, and
\vspace*{1mm}
      \item    dynamics of earthquake-soil-structure system interaction
    \end{itemize}


\end{frame}



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\frametitle{Real-ESSI Simulator System}

 
\begin{itemize}


  \item Real-ESSI System Components
    \begin{itemize} 
     \item Real-ESSI Pre-processor (gmsh/gmESSI, X2ESSI) 
     \item Real-ESSI Program (local, remote, cloud)
     \item Real-ESSI Post-Processor (Paraview, Python, Matlab)

    \end{itemize} 

\vspace*{1mm}
  \item Real-ESSI System availability:                   
    \begin{itemize}
%\vspace*{1mm}
     \item Educational  Institutions: Amazon Web Services (AWS), free 
     \item Government Agencies, National Labs: AWS GovCloud
     \item Professional  Practice: AWS, commercial
%\vspace*{1mm}
%%\vspace*{1mm}
%      \item Sources available to collaborators
    \end{itemize}



\vspace*{1mm}
\item Quality Management System, ASME-NQA-1, ISO9003-2018, Certification in progress


\vspace*{1mm}
  \item Real-ESSI Short Courses (online, this Fall)



\vspace*{1mm}
  \item System description and documentation at  \url{http://real-essi.info/}



% \vspace*{2mm}
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\end{itemize}


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%\subsection*{Summary}


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% \item Max  Planck: 
% "A    new    scientific  truth does not triumph by convincing  its opponents and
% making  them see the light, but rather because its opponents eventually die, and
% a  new  generation  grows  up  that  is familiar with it." (Science advances one
% funeral at a time)
% 
% 
%  \vspace*{3mm}
% 
% \item  Fran{\c c}ois-Marie Arouet,  Voltaire: 
% "Le doute n'est pas une condition agr{\'e}able, mais la certitude est absurde."
% 
%  \vspace*{3mm}
% 
% \item  Niklaus  Wirth:   
% "Software is getting slower more rapidly than hardware becomes faster."
% w
% \end{itemize}
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\begin{frame}
  \frametitle{Summary}

  \begin{itemize}

%    \item Importance   of   using  proper  models  correctly  (verification,
%    validation, level of sophistication)
%     
 
%    \item Reduction of modeling uncertainty 
%
\vspace*{1mm}
    \item Numerical modeling to predict and inform, rather than fit

%\vspace*{1mm}
%    \item Change of demand due to inelastic effects

%\vspace*{-1mm}
%      \begin{itemize}
%         \item Reduction of dynamic motions
%         \item Increase in deformations
%      \end{itemize}



\vspace*{1mm}
    \item  Sophisticated inelastic/nonlinear modeling and simulations need to be
    done carefully and in phases


\vspace*{1mm}
    \item Education and Training is the key!


\vspace*{1mm}
   \item     Collaborators:    Feng,  Yang,  Behbehani,  Sinha,  Wang,
   Pisan{\'o}, Abell, Tafazzoli, Jie, Preisig, Tasiopoulou, Watanabe, Cheng, Yang...
   
   

\vspace*{1mm}
  \item  Funding  from  and  collaboration  with  the US-DOE, US-NRC, US-NSF, 
  CNSC-CCSN, UN-IAEA, and Shimizu Corp. is greatly appreciated,


\vspace*{1mm}
  \item {\large \url{http://real-essi.info/}}

      

\end{itemize}



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\end{document}

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