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\usepackage{epstopdf}

\usepackage[absolute,overlay]{textpos}

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

      
\usepackage{multimedia}

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

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


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% % for not showing eq numbers unless eq is references
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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}
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%  \setbeamercovered{transparent}
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%  \usecolortheme{beetle} % siva pozadina (vrh plav)
  \usecolortheme{seagull} % sivo
%%%%%%%
%  \usecolortheme{BorisJeremic}
%%%%%%%
%  \usecolortheme{rose}
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%   \usefonttheme{structuresmallcapsserif}
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\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
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%             colorlinks=true,
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%             citecolor=webblue,
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%             linktocpage,
%             pdftex]{hyperref}


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\usepackage[latin1]{inputenc}
% or whatever
\usepackage{times}
\usepackage[T1]{fontenc}
% Or whatever. Note that the encoding and the font should match. If T1
% does not look nice, try deleting the line with the fontenc.



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


\title[MS ESSI]
        {Modeling and Simulation of 
Earthquakes, Soils, Structures, and their 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 ETH Seminar, \\
        Zurich, Switzerland \\
        May 2018}

\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:
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%    \tableofcontents[currentsection]
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\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}

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

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

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



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\section{Introduction}




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\subsection{Motivation}



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\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*{2mm}
  \item[]    Use  of  high fidelity numerical modeling and simulation to analyze
  earthquakes, and/or soils and/or structures  and their interaction (ESSI)


\vspace*{2mm}
  \item[]  Reduce modeling uncertainty, perform desired  level
  of sophistication modeling and simulation


\vspace*{2mm}
%  \item[] Model and simulate parametric uncertainty as it evolves in time and space
  \item[] Follow evolution of parametric uncertainty


\vspace*{2mm}
  \item[] Le doute n'est pas un {\'e}tat bien agr{\'e}able, mais l'assurance est
  un {\'e}tat ridicule. (Fran{\c c}ois-Marie Arouet, Voltaire)


% \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}
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\begin{frame}
 \frametitle{Earthquake Motions, 6C vs 3$\times$1C vs 1C}

\begin{itemize}

  \item Danger of picking one component of motions (1C) from  3C 
%  or 3$\times$1C (it is done all the time!)
  
  \item  Excellent  (forced)  fit,  but  not a prediction, information is lost
%  (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]
  {\includegraphics[width=60mm]{movie_ff_3d_mp4_icon.jpeg}}{movie_ff_3d.mp4}
%\hspace*{-2mm}
%\hfill
%\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
\movie[label=show3,width=61mm,poster]
  {\includegraphics[width=60mm]{movie_ff_1d_mp4_icon.jpeg}}{movie_ff_1d.mp4}
\hspace*{-16mm}
\end{center}
% local  


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



% 




\end{frame}





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\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]{movie_2_npps_mp4_icon.jpeg}}{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
% online \begin{center}
% online %\vspace*{-15mm}
% online \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}
% online   {\includegraphics[width=80mm]{movie_2_npps_mp4_icon.jpeg}}
% online \end{center}
% online






\end{frame}
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\begin{frame}

\frametitle{Elastic and Inelastic Response: Differences}

% 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/Thesis/SumeetKumarSinha/Files_13Aug2017/NPP_Non_Linear_Effects_Sumeet.jpg}}
{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_13Aug2017/NPP_Non_Linear_Effects_Sumeet.mp4}
\end{center}



% local
% local 
% local 
% local % \vspace*{-5mm}
% local \begin{center}
% local % \hspace*{-15mm}
% local \movie[label=show3,width=10cm,poster,autostart,showcontrols]
% local {\includegraphics[width=10cm]
% local {/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_13Aug2017/NPP_Non_Linear_Effects_Sumeet.jpg}}
% local {/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_13Aug2017/NPP_Non_Linear_Effects_Sumeet.mp4}
% local \end{center}
% local 
% local 
% local 



% online% online 
% online% online 
% online% online 
% online\begin{center}
% online\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/NPP_animations_August2017/NPP_Non_Linear_Effects_Sumeet.mp4}
% online  {\includegraphics[width=90mm]{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/NPP_animations_August2017/NPP_Non_Linear_Effects_Sumeet.jpg}}
% online\end{center}
% online% online 
% online% online 
% online% online  





\end{frame}

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\begin{frame} 

\frametitle{Material Behavior Inherently Uncertain}



        \begin{itemize}

\vspace*{0.5cm}
        \item Spatial \\ 
              variability

\vspace*{0.5cm}
        \item Point-wise \\ 
              uncertainty, \\
              testing \\
              error, \\
              transformation \\
              error

        \end{itemize}


\vspace*{-5cm}
\begin{figure}[!hbpt]
%\nonumber
%\begin{center}
\begin{flushright}
%\includegraphics[height=5.0cm]{/home/jeremic/tex/works/Conferences/2006/KragujevacSEECCM06/Presentation/MGMuzorak01.jpg}
\includegraphics[height=5.5cm]{/home/jeremic/tex/works/Conferences/2006/KallolsPresentationGaTech/FrictionAngleProfile.jpg}
\\
\mbox{(Mayne et al. (2000) }
\end{flushright}
%\end{center}
%\end{center}
\end{figure}


\end{frame}







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

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


%
% \begin{itemize}
% 
% 
% 
%   \item  Significant uncertainty in material and loads
% %       
% % %\vspace*{1mm}
% %      \item  Propagate  uncertainties in space and time 
% % 
% % 
% \end{itemize}
% 
% %
%\vspace{1cm}
%\hspace{-0.5cm}
%Example: Elastic Stiffness

%\vspace*{-3mm}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-7mm}
\includegraphics[width=7.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01-Ed.pdf}
% \hfill
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_Histogram_Normal_01-Ed.pdf}
%
\end{center}
\end{figure}

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


\end{frame}





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



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

\end{frame}

% 























% 
%  
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{It is not a new Problem}
%  
%  \vspace*{10mm}
%  
%    {\Large Le doute n'est pas un {\'e}tat bien agr{\'e}able,
%    \\ 
%  \vspace*{3mm}
%          mais l'assurance est un {\'e}tat ridicule.} 
%       
%       
%       
%  \vspace*{10mm}
%  \begin{flushright}        
%          Fran{\c c}ois-Marie Arouet (Voltaire)
%  \end{flushright}        
%   
%  
%  \end{frame}
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%  
%  
%  
%  
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\section{Seismic Motions}



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\subsection{Observations}

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

\begin{frame}
  \frametitle{3C (6C) Seismic Motions}

\vspace*{2mm}

\begin{itemize}

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

   \item  Example of an almost 2D motion (LSST07, LSST12)
\vspace*{-5mm}


\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-10mm}
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Lotung_LSST07_FA25.jpeg}
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Lotung_LSST12_FA25.jpeg}
%
\end{center}
\end{figure}
   


\end{itemize}


\end{frame}





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

\begin{frame}
  \frametitle{San Pablo Earthquake, 14Jun2017}
  
  Courtesy  of \url{http://www.strongmotioncenter.org/}

\vspace*{2mm}

%\begin{itemize}
%
%   \item  San Pablo, Guatemala, 14June2017 (data from  \url{http://www.strongmotioncenter.org/}
%
%\vspace*{-5mm}
% \end{itemize}


\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-10mm}
\includegraphics[width=5.5truecm]{/home/jeremic/oofep/LJUDI/PraveenMalhotra/EQ__01_Guatemala_14Jun2017.jpg}
\\
\includegraphics[width=2.0truecm]{/home/jeremic/oofep/LJUDI/PraveenMalhotra/EQ__02_Guatemala_14Jun2017.jpg}
\includegraphics[width=1.8truecm]{/home/jeremic/oofep/LJUDI/PraveenMalhotra/EQ__03_Guatemala_14Jun2017.jpg}
\includegraphics[width=2.0truecm]{/home/jeremic/oofep/LJUDI/PraveenMalhotra/EQ__04_Guatemala_14Jun2017.jpg}
\includegraphics[width=2.0truecm]{/home/jeremic/oofep/LJUDI/PraveenMalhotra/EQ__05_Guatemala_14Jun2017.jpg}
\includegraphics[width=2.0truecm]{/home/jeremic/oofep/LJUDI/PraveenMalhotra/EQ__06_Guatemala_14Jun2017.jpg}
\includegraphics[width=2.0truecm]{/home/jeremic/oofep/LJUDI/PraveenMalhotra/EQ__07_Guatemala_14Jun2017.jpg}
%
\end{center}
\end{figure}




\end{frame}
































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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Regional Geophysical Models}

 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Regional Geophysical  Models}

\begin{itemize}

  \item High fidelity free field seismic motions on regional scale


\vspace*{4mm}
  \item Knowledge of geology (deep and shallow) needed


\vspace*{4mm}
  \item High Performance Computing using SW4 on CORI (LBNL)


\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}

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

% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Regional Geophysical  Models}
% 
%  \begin{figure}[!htb]
%  \begin{center}
%   \includegraphics[width=8truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/San_Francisco_Model_Geology_Base_and_Stoch.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 Simulations using SW4}
% - 
% -  \begin{figure}[!htb]
% -  \begin{center}
% -   \includegraphics[width=8truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/CPU_scaling_CORI.png}
% -  \end{center}
% - % \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
% -  \end{figure}
% - \vspace*{-2mm} 
% - 
% - Rodgers and Petersson
% - 
% - 
% - \end{frame}
% - 
% - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - \begin{frame}
% - \frametitle{HPC on CORI (LBNL/NERSC)}
% - 
% -  \begin{figure}[!htb]
% -  \begin{center}
% -   \includegraphics[width=8truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/CORI_picture.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}

 \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*{-2mm}
\begin{center}
\hspace*{-15mm}
%
\movie[label=show3,width=8.0cm,poster,autostart,showcontrols]
  {\includegraphics[width=60mm]{BJicon.png}}{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/M6.5_s500_BASIN+STOCHASTIC.mag.SLOW.mpg}
\hspace*{-15mm}
%
\end{center}


\end{frame}

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


 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Seismic Motions: SW4 to MS-ESSI}

 \begin{figure}[!htb]
 \begin{center}
  \includegraphics[width=11truecm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_08June2017/pic/SW42DRM.pdf}
 \end{center}
% \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
 \end{figure}
 
\end{frame}

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
























































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

\subsection{Stress Test Motions} 
  

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



\begin{itemize}

\item Excite SSI system with a suite of  seismic motions

%\vspace*{2mm}
  \item  Simple  sources, variation in strike and dip, 
  P and S waves,  surface waves (Rayleigh, Love, etc.)

%\vspace*{2mm}
  \item Stress test soil-structure system 
%  system
%   for a variety of body and surface waves/motions   


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


%\vspace*{3mm}
%\item 

\end{itemize}

\vspace*{-2mm}
\begin{figure}[!htb]
\begin{center}
\includegraphics[width=6.5cm]{/home/jeremic/tex/works/Conferences/2015/CNSC_July/Present/Stress_test_NPP_idea.jpg}
\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}


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
























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



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

\begin{frame}
  \frametitle{Layered and Dyke/Sill Models}


\vspace*{5mm}

\begin{itemize}

%   \item Uniform soil/rock, to show surface waves
   
\vspace*{1mm}
   \item  (a)  Horizontal layers
   \item  (b)  Dyke/Sill  intrusion  
\vspace*{-12mm}
\begin{figure}[!hbpt]
\begin{flushright}
%
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/models.png}
%
\end{flushright}
\end{figure}
%\vspace*{10mm}



   \item Source locations matrix (point sources)
   
   \item Source strike and dip variation 
      
   \item Magnitude variations

   \item Range of frequencies

\end{itemize}

%\vspace*{-5mm}


\begin{figure}[!hbpt]
\begin{center}
%
%\hspace*{-5mm}
\includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/geom.png}
%
\end{center}
\end{figure}


\end{frame}



% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}
%   \frametitle{Layered System, Variable Source Depth}
% 
% \vspace*{2mm}
% 
% \begin{itemize}
% 
%    \item Epicenter is  $2500$m away from the location of interest
% 
%    \item Source depth $850$m (softer layers) and  $2500$m  (hard rock)
%    
%    \item Different wave propagation path to the point of interest
%    
%    \item Surface waves quite pronounced 
% 
% \end{itemize}
% 
% 
% \vspace*{-5mm}
% 
% \begin{figure}[!hbpt]
% \begin{center}
% %
% \hspace*{-5mm}
% %\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_no/bh_x_output_z850_dip45_gaussx4750.png}
% \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_no/borehole_ux_gauss_x5000.png}
% \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_no/borehole_uz_gauss_x5000.png}
% %\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_no/bh_x_output_z850_dip45_gaussx5250.png}
% %
% \end{center}
% \end{figure}
% 
% \end{frame}
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}
  \frametitle{Layered System, Displacement Traces}


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

   \item Epicenter is  $2500$m away from the location of interest

   \item Source depth $850$m (left) and  $2500$m  (right)
   
   \item Different wave propagation path to the point of interest
   
   \item Surface waves quite pronounced 

%   \item Surface waves present 
   \item Layered geology did not filter out surface waves 
%   \item Mildly incoherent motions
   
\end{itemize}

\vspace*{-7mm}

\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-5mm}
\includegraphics[width=5.8truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_no/cut_output_z850_dip45_gauss.png}
\includegraphics[width=5.8truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_no/cut_output_z2500_dip45_gauss.png}
%\hspace*{-4mm}
%
\end{center}
\end{figure}

\end{frame}

                  


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Layered System, Variable Source Depth}

%   
% \begin{center}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_3d.mp4}
%   {\includegraphics[width=50mm]{movie_ff_3d_mp4_icon.jpeg}}
% %
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_1d.mp4}
%   {\includegraphics[width=50mm]{movie_ff_1d_mp4_icon.jpeg}}
% \end{center}
% 

%\vspace*{-2mm}
\begin{center}
\hspace*{-15mm}
%
\movie[label=show3,width=6.0cm,poster,autostart,showcontrols]
  {\includegraphics[width=50mm]{BJicon.png}}{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/movie01.mp4}
%
\movie[label=show3,width=6.0cm,poster,autostart,showcontrols]
  {\includegraphics[width=50mm]{BJicon.png}}{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/movie04.mp4}
\hspace*{-15mm}
%
\end{center}


% \begin{flushleft}
% \vspace*{-15mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_3d.mp4}
% %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
%   {\tiny (MP4)}
% \end{flushleft}
% %


\end{frame}



% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%   \frametitle{Dyke/Sill Intrusion, Variable Source Depth}
% 
% \begin{itemize}
% 
%    \item Lower amplitudes than with layered only model!
%    
%    \item Difference in body and surface wave arrivals
%    
%    \item Surface waves present
% 
% \end{itemize}
% 
% 
% 
% \begin{figure}[!hbpt]
% \begin{center}
% %
% \hspace*{-5mm}
% %\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_right/bh_x_output_z850_dip45_gaussx4750.png}
% \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_right/borehole_ux_gauss_x5000.png}
% \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_right/borehole_uz_gauss_x5000.png}
% %\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_right/bh_x_output_z850_dip45_gaussx5250.png}
% %
% \end{center}
% \end{figure}
% 
% \end{frame}
% 


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

\begin{frame}
  \frametitle{Dyke/Sill Intrusion, Variable Source Depth}


\vspace*{5mm}

\begin{itemize}


   \item Lower amplitudes than with layered only model!
   
   \item Difference in body and surface wave arrivals
   
   \item Surface waves present, more complicated wave field

%   \item Incoherent motion field 
%
%   \item Note incoherence is in 2D (and really in 3D, it is reduced, for this model) 
   
   
\end{itemize}
\vspace*{-5mm}



\begin{figure}[!hbpt]
\begin{center}
%
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_right/cut_output_z850_dip45_gauss.png}
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_right/cut_output_z2500_dip45_gauss.png}
%
\end{center}
\end{figure}

\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Dyke/Sill Intrusion, Variable Source Depth}

%   
% \begin{center}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_3d.mp4}
%   {\includegraphics[width=50mm]{movie_ff_3d_mp4_icon.jpeg}}
% %
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_1d.mp4}
%   {\includegraphics[width=50mm]{movie_ff_1d_mp4_icon.jpeg}}
% \end{center}
% 

%\vspace*{-2mm}
\begin{center}
\hspace*{-15mm}
%
\movie[label=show3,width=6.0cm,poster,autostart,showcontrols]
  {\includegraphics[width=50mm]{BJicon.png}}{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/movie02.mp4}
%
\movie[label=show3,width=6.0cm,poster,autostart,showcontrols]
  {\includegraphics[width=50mm]{BJicon.png}}{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/movie03.mp4}
\hspace*{-15mm}
%
\end{center}


% \begin{flushleft}
% \vspace*{-15mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_3d.mp4}
% %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
%   {\tiny (MP4)}
% \end{flushleft}
% %


\end{frame}




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

\begin{frame}
  \frametitle{Dyke/Sill as Seismic Energy Sink}

\vspace*{2mm}

\begin{itemize}

   \item  Dyke/Sill (right Fig),  made  of  stiff  rock,  is  an  energy  sink, as well as energy
   reflector

   \item  Variable  wave  lengths behave differently, depending on dyke/sill geometry
   and location
   
   
\end{itemize}

\vspace*{-5mm}


\begin{figure}[!hbpt]
\begin{center}
%
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_no/cut_output_z2500_dip45_gauss.png}
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_right/cut_output_z2500_dip45_gauss.png}
%
\end{center}
\end{figure}

\end{frame}


% 

 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Plane Wave Stress Test Motions}

\begin{itemize}



%\vspace*{2mm}
  \item Plane wave stress test motions: 3D-6C (Haskel's solution for plane harmonic waves) 
  and/or 3D-3$\times$1C and/or 3D-1C and or 1D-1C motions





\vspace*{4mm}
  \item Knowledge of geology and  the site is important





\end{itemize}
 
\end{frame}





% 
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{Example Structure, a Small Modular Reactor (SMR)}
%  
%  
%  
%  %\vspace*{-4mm}  
%  \begin{figure}[!htb]
%  \begin{center}
%  %\hspace*{-5mm}
%  \includegraphics[width=5.2cm]{/home/jeremic/tex/works/Reports/2012/DOE-LLNL-SSI/SMR_generic_LLNL_01.jpg}
%  \end{center}
%  \end{figure}
%  
%  
%   
%  \end{frame}
%  
%  


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


%\vspace*{-10mm}  

\begin{itemize}

\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{flushleft}
\hspace*{-5mm}
\includegraphics[width=8.5cm]{/home/jeremic/tex/works/Conferences/2018/BestPSHANI/Presentation/stress_test_Best_SHANI_May2018.jpg}
\end{flushleft}
\end{figure}



\vspace*{-45mm}  
\begin{figure}[!htb]
\begin{flushright}
\includegraphics[width=3cm]{/home/jeremic/tex/works/Conferences/2015/CNSC_July/Present/Stress_test_NPP_idea.jpg}
\hspace*{-5mm}
\end{flushright}
\end{figure}


\vspace*{-5mm}  
\begin{figure}[!htb]
\begin{flushright}
\includegraphics[width=3cm]{/home/jeremic/tex/works/consulting/2017/IAEA/TECDOC/Version_14Mar2017/1Dvs3x1Dvs3D_waves_02.pdf}
\hspace*{-5mm}
\end{flushright}
\end{figure}




\end{frame}










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

\frametitle{Free Field, Variation in Input Wave Angle,  $f = 5$Hz}

% 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_angle.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/free_field_inclination.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_inclination.mp4}
  {\tiny (MP4)}
\end{flushleft}
% online  
   

\end{frame}

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


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

\frametitle{SMR ESSI, Variation in Input Wave Angle,  $f = 5$Hz}

% 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/SMR_animations_May2018/SMR_ESSI_4_inclinations.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR_ESSI_4_inclindations.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/SMR_animations_May2018/SMR_ESSI_4_inclindations.mp4}
  {\tiny (MP4)}
\end{flushleft}
% online  
   

\end{frame}

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



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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)}
\end{flushleft}
% online  
   

\end{frame}

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



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

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

% 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/SMR_animations_May2018/SMR-ESSI_real_time_four_freq.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/SMR_animations_May2018/SMR-ESSI_real_time_four_freq.mp4}
  {\tiny (MP4)}
\end{flushleft}
% online  
   

\end{frame}

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



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

\frametitle{3D wave effects - different frequencies}


\begin{textblock*}{8cm}(1.0cm,2.5cm) % {block width} (coords) 
   \scriptsize Acceleration response - Surface center point A
\end{textblock*}
\begin{textblock*}{2cm}(0.2cm,4cm) % {block width} (coords) 
   \tiny X direction
\end{textblock*}
\begin{textblock*}{2cm}(0.2cm,6.3cm) % {block width} (coords) 
   \tiny Z direction
\end{textblock*}
\begin{textblock*}{3cm}(2.4cm,7.6cm) % {block width} (coords) 
   \tiny  (a) $f=1Hz \ \ \theta=60^{o}$
\end{textblock*}
\begin{textblock*}{3cm}(5.6cm,7.6cm) % {block width} (coords) 
   \tiny  (b) $f=5Hz \ \ \theta=60^{o}$
\end{textblock*}
\begin{textblock*}{3cm}(8.8cm,7.6cm) % {block width} (coords) 
   \tiny  (c) $f=10Hz \ \ \theta=60^{o}$
\end{textblock*}

\vspace*{-30mm}
  \begin{figure}[!H]
    \centering
     % \begin{flushleft}
       \includegraphics[width=3.3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/1Hz_center_ax.pdf}
       \includegraphics[width=3.3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/5Hz_center_ax.pdf}
       \includegraphics[width=3.3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/10Hz_center_ax.pdf}
      \\
       \includegraphics[width=3.3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/1Hz_center_az.pdf}
       \includegraphics[width=3.3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/5Hz_center_az.pdf}
       \includegraphics[width=3.3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/10Hz_center_az.pdf}
    % \end{flushleft}
  \end{figure}
\vspace*{-75mm}
  \begin{figure}[!H]
     \begin{flushright}
     \hspace*{30mm}
       \includegraphics[width=2.5cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/Points_configuration.pdf}
     \hspace*{-10mm}
    \end{flushright}
  \end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%






%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  
%  \frametitle{SMR, Free Field vs  ESSI, $f=2.5$Hz, $\theta = 60^{o}$}
%  
%  % Elastoplastic soil with contact elements
%  %% Both solid and contact elements dissipate energy
%  
%       
%  % \vspace*{-5mm}
%  \begin{flushleft}
%  \hspace*{-7mm}
%  %\movie[label=show3,width=54mm,poster,autostart,showcontrols]
%  \movie[label=show3,width=54mm,poster,showcontrols]
%  {\includegraphics[width=54mm]                                                                                       
%  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR_FreeField_f2_5_theta_60.jpg}
%  }
%  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR_free_field_2frequency.mp4}
%  \end{flushleft}
%  % online   
%  %\vspace*{-12mm}
%  \begin{flushleft}
%  \hspace*{-4mm}
%  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR_free_field_2frequency.mp4}
%    {\tiny (MP4)}
%  \end{flushleft}
%  % online  
%  
%  
%  
%  
%  % \vspace*{-5mm}
%  \vspace*{-49mm}
%  \begin{flushright}
%  % \hspace*{-15mm}
%  %\movie[label=show3,width=58mm,poster,autostart,showcontrols]
%  \movie[label=show3,width=58mm,poster,showcontrols]
%  {\includegraphics[width=58mm]
%  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR_ESSI_f2_5_theta_60.jpg}
%  }
%  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR_2frequency.mp4}
%  \end{flushright}
%  \hspace*{-7mm}
%  % online   
%  %\vspace*{-12mm}
%  \begin{flushright}
%  %\hspace*{-4mm}
%  \vspace*{-9mm}
%  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR_2frequency.mp4}
%    {\tiny (MP4)}
%  \hspace*{-4mm}
%  \end{flushright}
%  % online  
%  
%  
%  
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  
%  \frametitle{SMR, Free Field vs  ESSI, $f=10$Hz, $\theta = 60^{o}$}
%  
%  % Elastoplastic soil with contact elements
%  %% Both solid and contact elements dissipate energy
%  
%       
%  % \vspace*{-5mm}
%  \begin{flushleft}
%  \hspace*{-7mm}
%  %\movie[label=show3,width=54mm,poster,autostart,showcontrols]
%  \movie[label=show3,width=54mm,poster,showcontrols]
%  {\includegraphics[width=54mm]
%  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR_FreeField_f10_theta60.jpg}
%  }
%  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR_free_field_10frequency.mp4}
%  \end{flushleft}
%  % online   
%  %\vspace*{-12mm}
%  \begin{flushleft}
%  \hspace*{-4mm}
%  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR_free_field_10frequency.mp4}
%    {\tiny (MP4)}
%  \end{flushleft}
%  % online  
%  
%  
%  
%  
%  % \vspace*{-5mm}
%  \vspace*{-48mm}
%  \begin{flushright}
%  % \hspace*{-15mm}
%  %\movie[label=show3,width=58mm,poster,autostart,showcontrols]
%  \movie[label=show3,width=58mm,poster,showcontrols]
%  {\includegraphics[width=58mm]
%  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR_ESSI_f10_theta60.jpg}
%  }
%  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR_10frequency.mp4}
%  \end{flushright}
%  \hspace*{-7mm}
%  % online   
%  %\vspace*{-12mm}
%  \begin{flushright}
%  %\hspace*{-4mm}
%  \vspace*{-9mm}
%  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR_10frequency.mp4}
%    {\tiny (MP4)}
%  \hspace*{-4mm}
%  \end{flushright}
%  % online  
%  
%  
%  
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  



% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame} 
%  \frametitle{Free Field Motion Verification}
% 
% 
%   \vspace*{-3mm}
% 
%  \begin{figure}[!H] 
%     \begin{center}
%   \hspace*{-8mm}
%       \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/free_field_ux_time_series.pdf} 
%   \hspace*{-1mm}
%       \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/free_field_uy_time_series.pdf} 
%   \hspace*{-1mm}
%       \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/free_field_uz_time_series.pdf} \\
%   \hspace*{-3mm}
% %
% \\
%   \hspace*{-8mm}
%       \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/free_field_ax_time_series.pdf} 
%   \hspace*{-1mm}
%       \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/free_field_ay_time_series.pdf} 
%   \hspace*{-1mm}
%       \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/free_field_az_time_series.pdf}  
%   \hspace*{-3mm}
%    \end{center}
%  \end{figure}
% \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}
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


 

% 
%  
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Regional Scale Model (Rodgers et al, LLNL)}
% 
%  \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}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%








































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\section{Inelasticity and Energy Dissipation}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Energy Dissipation}



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

\begin{itemize}

\vspace*{1mm}
     \item[] Seismic energy input, through a closed boundary


\vspace*{4mm}
     \item[] Mechanical dissipation outside SSI domain:
       \begin{itemize}
         \item[] Reflected wave radiation
         \item[] SSI system oscillation radiation
       \end{itemize}
%\vspace*{1mm}
     \item[] Mechanical dissipation/conversion inside SSI domain:
       \begin{itemize}
         \item[] Inelasticity of soil and contact zone
         \item[] Inelasticity/damage of structure and foundation
         \item[] Viscous coupling of fluids and  soils and structure
% %         \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{Incremental Plastic Work: $d W_p = \sigma_{ij} \, d\epsilon_{ij}^{pl}$}
 
\begin{itemize}
\item Negative incremental energy dissipation
\item Plastic work is NOT plastic dissipation
\end{itemize}
 
\begin{figure}[!H]
\begin{center}
\includegraphics[height=5.2cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Negative_Dissipation_Problem.png}
\end{center}
\end{figure}
 
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  
% \frametitle{Negative incremental energy dissipation!}
%  
% \begin{itemize}
% \item Direct violation of the second law of thermodynamics
% \item Where is the problem?
% \item[]
% \item[]
% \end{itemize}
%  
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  
% \frametitle{Negative incremental energy dissipation!}
%  
% \begin{itemize}
% \item Direct violation of the second law of thermodynamics
% \item Where is the problem?
% \item One important form of energy is missing!
% \item \textbf{Plastic Free Energy}
% \end{itemize}
%  
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% % 
% % \subsection{Thermodynamics-Based Theory and Formulation}
% % 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  
% \frametitle{Plastic Free Energy}
%  
% \begin{itemize}
% \item Direct violation of the second law of thermodynamics
% % \item Where is the problem?
% \item Missing is the plastic free energy
% 
% 
% \item Multi-scale effect of particle interlocking/rearrangement
% \item Strain energy on particle level
% \end{itemize}
%  
% \begin{figure}[!h]
% \begin{center}
% \includegraphics[width=7truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Plastic_Free_Energy.png}
% \end{center}
% \end{figure}
%  
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%f%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  
% \frametitle{Energy Transformation in Elastic-Plastic Material}
%  
% \begin{figure}[!H]
% \begin{center}
% \includegraphics[height=6cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Energy_Transformation.png}
% \end{center}
% \end{figure}
%  
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  
% \frametitle{Traditional Energy Components}
%  
% \begin{itemize}
% \item Kinetic Energy Density: 
% \begin{equation*}
%   d E_K({x},t) = \rho({x}) \, v_i({x}, t) \, d v_i({x}, t)
% \end{equation*}
%   
% \item Strain Energy Density: 
% \begin{equation*}
%   d E_S({x},t) = \sigma_{ij}({x},t) \, d \epsilon_{ij}^{el}({x}, t)
% \end{equation*}
%   
% \vspace*{1mm}
%   
% \item Plastic Work Density: 
% \begin{equation*}
%   d W_P(x,t) = \sigma_{ij}(x,t) \, d \epsilon_{ij}^{pl}(x, t)
% \end{equation*}
% \end{itemize}
%   
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  
% \frametitle{Plastic Free Energy and Dissipation}
%  
% \begin{itemize}
% \item Free Energy
% \begin{itemize}
% \item Based on the second law of thermodynamics
% \item Decomposed into elastic and plastic components
% \end{itemize}
%   
% \item Plastic Free Energy
% \begin{itemize}
% \item Decomposed into isotropic and kinematic components
% \item Related to hardening laws in classic plasticity theory
% \item Related to material state variables (back stress etc.)
% \end{itemize}
% \begin{equation*}
%   d\Psi_{pl}^{iso} = \frac{1}{\kappa_1} k \, dk; \quad d\Psi_{pl}^{kin} = \frac{1}{a_1} \alpha_{ij} \, d \alpha_{ij}
% \end{equation*}
%   
% \item Energy Dissipation due to Plasticity
% \begin{itemize}
% \item Incremental dissipation should always be nonnegative
% \end{itemize}
% \begin{equation*}
%   d D_P = d W_P - d\Psi_{pl} = \sigma_{ij} \, d \epsilon^{pl}_{ij} - d\Psi_{pl} \ge 0
% \end{equation*}
% \end{itemize}
%  
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  
% \frametitle{Use Incremental Equation: $d\Phi = \sigma_{ij} \, d\epsilon_{ij}^{pl}$}
%  
% \begin{itemize}
% \item \textbf{Plastic Work} vs. \textbf{Energy Dissipation due to Plasticity}
% \end{itemize}
%  
% \begin{figure}[!H]
% \begin{center}
% \includegraphics[height=5.5cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Negative_Dissipation_Problem2.png}
% \end{center}
% \end{figure}
%  
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% 
% 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %\begin{frame}
% % % 
% % %\frametitle{Area of Hysteresis Loop}
% % % 
% % %\begin{figure}[!H]
% % %\begin{center}
% % %\includegraphics[height=6cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Stress-Strain.png}
% % %\end{center}
% % %\end{figure}
% % % 
% % %\end{frame}
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %\begin{frame}
% % % 
% % %\frametitle{Area of Hysteresis Loop}
% % % 
% % %\begin{figure}[!H]
% % %\begin{center}
% % %\includegraphics[height=6cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Stress-Strain-Dissipation.png}
% % %\end{center}
% % %\end{figure}
% % % 
% % %\end{frame}
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %\begin{frame}
% % % 
% % %\frametitle{Area of the Stress-Strain Loop}
% % % 
% % %\begin{itemize}
% % %\item[] Evolving loop? Monotonic loading?
% % %\end{itemize}
% % % 
% % %\begin{figure}[!H]
% % %\begin{center}
% % %\includegraphics[height=5.5cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Stress-Strain-Monotonic.png}
% % %\end{center}
% % %\end{figure}
% % % 
% % %\end{frame}
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %\begin{frame}
% % 
% %\frametitle{Use Incremental Equation: $\sigma_{ij} \, d\epsilon_{ij}^{pl}$}
% % 
% %\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% %  
% % \frametitle{Use Incremental Equation: $d\Phi = \sigma_{ij} \, d\epsilon_{ij}^{pl}$}
% % 
% %  
% % \end{frame}
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% %  
% % \frametitle{Use Incremental Equation: $d\Phi = \sigma_{ij} \, d\epsilon_{ij}^{pl}$}
% %  
% % \begin{itemize}
% % \item[] Notice any problem?
% % \end{itemize}
% %  
% % \begin{figure}[!H]
% % \begin{center}
% % \includegraphics[height=5.5cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Negative_Dissipation.png}
% % \end{center}
% % \end{figure}
% %  
% % \end{frame}
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  
% \frametitle{Incremental Equation: $d W = \sigma_{ij} \, d\epsilon_{ij}^{pl}$}
%  
% \begin{itemize}
% \item[] PROBLEM: negative incremental energy dissipation!
% \item[] 600 papers since 1990 (!?!): \\
%       
% \end{itemize}
%  
% \begin{figure}[!H]
% \begin{center}
% \includegraphics[height=5cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Negative_Dissipation_Problem2.png}
% \end{center}
% \end{figure}
%  
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% %  
% % \frametitle{Negative incremental energy dissipation!}
% %  
% % \begin{itemize}
% % \item[] Direct violation of the second law of thermodynamics
% % \item[] Where is the problem?
% % \item[]
% % \item[]
% % \end{itemize}
% %  
% % \end{frame}
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 
\frametitle{Negative Incremental Energy Dissipation!}
 
\begin{itemize}

\item[] Direct violation of the second law of thermodynamics

\vspace*{2mm}
\item[] 600 papers use Uang and Bertero (1990) and repeat their error

\vspace*{2mm}
\item[] Important form of energy missing: {Plastic Free Energy}

\vspace*{2mm}
\item[]  Observed  by  Farren  and  Taylor  (1925)   and explained by Taylor and
Quinney (1934)

\vspace*{2 mm}
\item[] Plastic Work vs. {Plastic Energy Dissipation}


%\vspace*{4mm}
%\item[] However it seems to be forgotten

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


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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 dissipation
\item[] Plastic work can decrease, dissipation always increases
\end{itemize}
 
\vspace*{-7mm}
\begin{figure}[!hbpt]
\begin{center}
\hspace*{-5mm}
\includegraphics[width=12.0truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Dissipation_Material.png}
\end{center}
\end{figure}
  
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 
\frametitle{Plastic Free Energy}
 
\begin{itemize}
% \item Direct violation of the second law of thermodynamics
% % \item Where is the problem?
% \item Missing is the plastic free energy


\item Multi-scale effect of particle interlocking/rearrangement
\item Strain energy on particle level
\end{itemize}
 
\begin{figure}[!h]
\begin{center}
\includegraphics[width=7truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Plastic_Free_Energy.png}
\end{center}
\end{figure}
 
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%f%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 
\frametitle{Energy Transformation in Elastic-Plastic Material}
 
\begin{figure}[!H]
\begin{center}
\includegraphics[height=6cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Energy_Transformation.png}
\end{center}
\end{figure}
 
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


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

\frametitle{Energy Dissipation in Large-Scale Model (NPP)}

% 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}


\end{frame}

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



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

\frametitle{Energy Dissipation in Large-Scale Model (SMR)}

% 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/Nonlinear_Analysis_of_ESSI_for_SMR/SMR_Energy_Dissipation_screen_grab.jpg}}
{/home/jeremic/tex/works/Thesis/HanYang/Files_16Aug2017/SMR_Energy_Dissipation.mp4}
\end{center}


\end{frame}

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





% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  
% \frametitle{Energy Dissipation in Small-Scale Model}
% 
%  Short cantilever under shear/bending loading
%  
% \vspace*{-5mm}
% \begin{figure}[!hbpt]
% \begin{center}
% \hspace*{-10mm}
% \includegraphics[width=4.2truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Rectangular_Block1.png}
% \hspace*{-2mm}
% \includegraphics[width=4.2truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Rectangular_Block2.png}
% \hspace*{-2mm}
% \includegraphics[width=4.2truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Rectangular_Block3.png}
% \end{center}
% \end{figure}
%  
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  
% \frametitle{Energy Dissipation in Small-Scale Model}
% 
%  Irregular-shaped block under surface shear loading
%  
% \vspace*{-5mm}
% \begin{figure}[!hbpt]
% \begin{center}
% \hspace*{-10mm}
% \includegraphics[width=4.3truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Cornered_Block1.png}
% \hspace*{-3mm}
% \includegraphics[width=4.3truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Cornered_Block2.png}
% \hspace*{-3mm}
% \includegraphics[width=4.3truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Cornered_Block3.png}
% \end{center}
% \end{figure}
%  
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  
% \frametitle{Energy Dissipation in Contact Zone}
% 
%  Elasto-plastic brick elements coupled with contact elements.
%  
% \vspace*{-6mm}
% \begin{figure}[!hbpt]
% \begin{center}
% \hspace*{-7mm}
% \includegraphics[width=4truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/DEMO_Dissipation1.png}
% \includegraphics[width=4truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/DEMO_Dissipation2.png}
% \includegraphics[width=4truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/DEMO_Dissipation3.png}
% \\
% \hspace*{-7mm}
% \includegraphics[width=4truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/DEMO_Dissipation4.png}
% \includegraphics[width=4truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/DEMO_Dissipation5.png}
% \includegraphics[width=4truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/DEMO_Dissipation6.png}
% \end{center}
% \end{figure}
%  
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  
% \frametitle{Energy Dissipation in a Large-Scale Model (NPP)}
% 
% % 
% % Some notes:
% % Energy density curves at the corner of the structure (as indicated in the picture of NPP model).
% % Can see large amount of energy dissipated in both soil and contact elements.
% % An arc-shaped area of "elastic zone" formed beneath the structure, where soil strength can be better utilized.
% % 
% 
% %\vspace*{-2mm}
% \begin{figure}[!hbpt]
% \begin{center}
% % \hspace*{-7mm}
% \includegraphics[width=9truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/NPP_Energy_Dissipation_Curve.pdf}
% \end{center}
% \end{figure}
%  
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% % 
% % \frametitle{Energy Dissipation in a  Large-Scale Model (NPP)}
% % 
% %  Elastic soil with contact elements
% %  % Only contact elements dissipate energy
% % 
% % % \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_with_Contact_Elastic.mp4}
% % \end{center}
% % 
% % 
% % \end{frame}
% % 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
% \frametitle{Energy Dissipation in Large-Scale Model (NPP)}
% 
%  Elastoplastic soil without contact elements
%  % Only solid elements dissipate energy
% 
% % \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}
% \end{center}
% 
% 
% \end{frame}
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
% \frametitle{Energy Dissipation in Large-Scale Model (NPP)}
% 
%  Elastoplastic soil with contact elements
% % Both solid and contact elements dissipate energy
% 
% % \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_with_Contact_vonMises.mp4}
% \end{center}
% 
% 
% \end{frame}
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  
% \frametitle{Energy Dissipation in Large-Scale Model (SMR)}
% 
% % 
% % Some notes:
% % Energy density curves at the corner of the structure (as indicated in the picture of NPP model).
% % Can see large amount of energy dissipated in both soil and contact elements.
% % An arc-shaped area of "elastic zone" formed beneath the structure, where soil strength can be better utilized.
% % 
% 
% \vspace*{-2mm}
% \begin{figure}[!hbpt]
% \begin{center}
% % \hspace*{-7mm}
% \includegraphics[width=8truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/SMR_Energy_Dissipation_Curve.pdf}
% \end{center}
% \end{figure}
%  
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
% \frametitle{Energy Dissipation in Large-Scale Model (SMR)}
% 
%  Elastoplastic soil without contact elements
%  % Only solid elements dissipate energy
% 
% % \vspace*{-5mm}
% \begin{center}
% % \hspace*{-15mm}
% \movie[label=show3,width=9cm,poster,autostart,showcontrols]
% {\includegraphics[width=9cm]
% {/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/SMR_Plastic_Dissipation_Density.png}}
% {/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/SMR_without_Contact_vonMises.mp4}
% \end{center}
% 
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




    
% 
% - 
% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -\begin{frame}
% -\frametitle{Quality Assurance}
% -
% -\begin{itemize}
% -
% -\item[] Full verification suit for each element, model, algorithm
% -
% -\vspace*{4mm}
% -\item[] Certification process in progress for NQA-1 and ISO-90003-2014
% -
% -%\vspace*{3mm}
% -%\item[] Verification examples given below
% -
% -\end{itemize}
% -
% -
% -
% -
% -\end{frame}
% -
% -  
% -
% -%-------------------------------------------------------
% -\begin{frame}{High Fidelity (Parametric, Geometric and Algorithmic)}
% -
% -\begin{figure}
% -\includegraphics[width=0.95\textwidth]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_06June2017/latex_slides/Figure-files/verification/asymptotic_converge.png}
% -\end{figure}
% -\end{frame}
% -
% -% \begin{frame}{One of Verification Techniques}
% -% Richardson Extrapolation
% -% \begin{itemize}
% -%   \item[] Stress solution with the strain increment size as:
% -%         \begin{equation}
% -%           \sigma(d\epsilon) = \sigma^* + C d\epsilon^{\beta} + O(d\epsilon^{\beta+1})
% -%         \end{equation}
% -%         where $\sigma^*$ is the accurate result.
% -% 
% -%   \item[] Richardson extrapolation is defined as 
% -%         \begin{equation}
% -%           \begin{aligned}
% -%             R(d\epsilon, k) & = \frac{k^{\beta}\sigma(d\epsilon) - \sigma(k d\epsilon) } { k^{\beta} - 1} \\ 
% -%                   & = \frac{k^{\beta} 
% -%                         \left(\sigma^* + C d\epsilon^{\beta} + O(d\epsilon^{\beta+1}) \right) } 
% -%                         { k^{\beta} - 1}
% -%                        - 
% -%                         \frac{\sigma^* + C k^{\beta} d\epsilon^{\beta} + O(d\epsilon^{\beta+1}) } 
% -%                         { k^{\beta} - 1} \\
% -%                   & = \sigma^* + O (d\epsilon^{\beta + 1})
% -%           \end{aligned}  
% -%         \end{equation}
% -% %        The higher order error is cancelled out. 
% -% \end{itemize}
% -% \end{frame}
% -% 
% -% 
% -% 
% -% 
% -% 
% -
% -
% -
% -
% -%-------------------------------------------------------
% -\begin{frame}{Verification of Elastoplastic Algorithms}
% -Comparison between forward and backward Euler algorithms.
% -\begin{figure}
% -\includegraphics[width=0.5\textwidth]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_06June2017/latex_slides/Figure-files/verification/NonAssociate.pdf}
% -\includegraphics[width=0.5\textwidth]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_06June2017/latex_slides/Figure-files/verification/verification_example.png}
% -\end{figure}
% -\end{frame}
% -
% -
% -
% -
% -
% -
% -
% -
% -
% -
% -
% -
% -
% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -\subsection{Inelastic Response}
% -
% -
% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -\begin{frame}
% -\frametitle{Soil Inelastic Response}
% -
% -
% -A number of new models have been implemented and verified:
% -
% -
% -\begin{itemize}
% -
% -
% -\item[] Nested Surface Models (von Mises, Drucker-Prager, rounded Mohr-Coulomb)
% -
% -\vspace*{2mm}                                                               
% -\item[] PM4 model (2D/3D)
% -
% -\vspace*{2mm}
% -\item[] Bounding Surface Liquefaction (Tsinghua) Model
% -
% -\vspace*{2mm}
% -\item[] Concrete01 and Concrete02 fiber models (for nonlinear fiber beam and wall element)
% -
% -\vspace*{2mm}
% -\item[] Steel01 and Steel02 fiber models (for nonlinear fiber beam and wall element)
% -
% -
% -\end{itemize}
% -
% -\end{frame}
% -
% -
% -
% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -\begin{frame}
% -\frametitle{Partially Saturated Soil Modeling: Verification}
% -
% -%\vspace*{-5mm}
% -\begin{figure}[!hbpt]
% -\begin{center}
% -%\hspace*{-10mm}
% -\includegraphics[width=11truecm]{/home/jeremic/tex/works/Conferences/2017/DOE_Project_Review_Meeting_LBNL_09June2017/Present/upU_unsatruated_verification.jpg}
% -\end{center}
% -\end{figure}
% -
% -
% -\end{frame}
% -
% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -\begin{frame}
% -\frametitle{Partially Saturated Soil Modeling: Validation}
% -
% -%\vspace*{-5mm}
% -\begin{figure}[!hbpt]
% -\begin{center}
% -%\hspace*{-10mm}
% -\includegraphics[width=11truecm]{/home/jeremic/tex/works/Conferences/2017/DOE_Project_Review_Meeting_LBNL_09June2017/Present/upU_unsatruated_validation.jpg}
% -\end{center}
% -\end{figure}
% -
% -
% -\end{frame}
% -
% -
% -
% -% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -% \begin{frame}
% -% \frametitle{Structural Inelastic Response}
% -% 
% -% 
% -% 
% -% \end{frame}
% -
% -
% -% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -% %\begin{frame}
% -% %\frametitle{Dry Contact (Soil-Structure) Inelastic Response}
% -% %
% -% %
% -% %
% -% %\end{frame}
% -% %
% -
% -% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -% \begin{frame}
% -% \frametitle{Contact Modeling}
% -% 
% -% 
% -% \begin{itemize}
% -% 
% -%   \item[] Soft contact,  concrete to soil
% -%   
% -% \hspace*{3mm}
% -%   \item[] Hard contact, concrete to rock/concrete
% -% 
% -% \hspace*{3mm}
% -%   \item[] Dry contact, 
% -% 
% -% 
% -% \hspace*{3mm}
% -%   \item[] Saturated contacts, effective contact force/stress
% -% 
% -% 
% -% \hspace*{3mm}
% -%   \item[] Buoyant force (dynamic) modeling
% -% 
% -% 
% -% \end{itemize}
% -% 
% -% 
% -% \end{frame}
% -% %
% -
% -
% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -
% -
% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -\begin{frame}
% -\frametitle{Saturated Contact}
% -
% -
% -%\vspace*{-5mm}
% -\begin{figure}[!hbpt]
% -\begin{center}
% -%\hspace*{-10mm}
% -\includegraphics[width=9truecm]{/home/jeremic/tex/works/Conferences/2017/DOE_Project_Review_Meeting_LBNL_09June2017/Present/coupled_contact_schematics.jpg}
% -\end{center}
% -\end{figure}
% -
% -
% -
% -\end{frame}
% -
% -
% -
% -
% -
% -
% -
% -



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\subsection{Probabilistic Inelastic Modeling}





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% 
%          
%  \subsection{FPK Formulations}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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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 What if all (any) 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}




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



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\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}
%-- 
%--  


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\end{frame}






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\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}



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



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

\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}
{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 f-ion
%$E(x,t,\theta) = \sum_{i=0}^{P_d} r_i(x,t) * \Phi_i[\{\xi_1, ..., \xi_m\}]$

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

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

%\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}












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


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

\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}
{SEPFEM_Animation_Elastic.mp4}
\end{center}

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




\end{frame}



% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}
% \frametitle{SEPFEM: Example in 3D}
%  
%  
% 
% %\vspace*{-5mm}
% \begin{center}
% % \hspace*{-15mm}
% \movie[label=show3,width=11cm,poster,autostart,showcontrols]
% {\includegraphics[width=11cm]
% {/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/SFEM_3D.png}}
% % /home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_PEP_25.pdf
% {SFEM_Animation_3D.mp4}
% \end{center}
% 
% %  \includegraphics[width = 12cm]{./img/SFEM_3D.pdf}
% 
% 
% \end{frame}
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}{Application of SEPFEM to Practical Problems}
%  
% 
% Obtain accurate fragility curves (CDFs) for each soil structure system location 
% for stress, strain, displacements, etc.
% 
% 
% 
% 
%  
% \begin{figure}[!htbp] 
% \begin{center}
% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/Conferences/2017/SEECMM_2017_Kragujevac/present/Brana_3D_01.jpg}
% %
% \includegraphics[width=4.0cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
% %
% \includegraphics[width=4.0cm]{/home/jeremic/tex/works/Conferences/2017/SEECMM_2017_Kragujevac/present/NPP01.jpg}
% 
% %\includegraphics[width=5.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Slope_Stability_in_2D_and_3D/3D_final04.jpg}
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\section{Summary}

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%     \item[]   The MS-ESSI Simulator (inelastic, deterministic and probabilistic,
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  \frametitle{Summary}

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    \item[]   Importance   of   using  proper  models  correctly  (verification,
    validation)
    
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    \item[]   Availability of different  levels of sophistication of modeling is
    important for reduction of modeling uncertainty



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    \item[]     Development     of    the    MS-ESSI    Simulator    system
    \url{http://ms-essi.info}



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   \item[]     Collaborators:    Feng,  Abell,  Han,  Sinha,  Wang, Lacour, 
   Pisan{\'o}, Kova{\v c}evi{\' c}, McCallen, McKenna, Petrone, Rodgers
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  \item[]  Funding  from  and  collaboration  with  the US-DOE, US-NRC, US-NSF, 
  CNSC-CCSN, UN-IAEA, and Shimizu Corp. is greatly appreciated,


      

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