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

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


\title[Nonlinear ESSI Analysis]
        {Time Domain Nonlinear \\
Earthquake Soil Structure Interaction Analysis }


%\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.
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\pgfdeclareimage[height=0.7cm]{lbnl-logo}{/home/jeremic/BG/amblemi/lbnl-logo}


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


%\institute[Computational Geomechanics Group \hspace*{0.3truecm}
%\institute[\pgfuseimage{university-logo}\hspace*{0.1truecm}\pgfuseimage{lbnl-logo}] % (optional, but mostly needed)
\institute[\pgfuseimage{university-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 ASCE-4 Seminar, \\
         07Dec2021}

\subject{}
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% If you have a file called "university-logo-filename.xxx", where xxx
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%\logo{\pgfuseimage{university-logo}}

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




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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}
\subsection{\ }



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

\begin{itemize}



    


\vspace*{3mm}
  \item[]  Improve  modeling  and  simulation  for  infrastructure objects


% \vspace*{2mm}
%  \item[]  Expert numerical modeling and simulation tool
%
% \vspace*{1mm}
%   \item[]      Use of numerical models to
%   analyze statics and dynamics of soil/rock-structure systems
%

\vspace*{1mm}
  \item[]  Control modeling, epistemic uncertainty

%\vspace*{3mm}
%  \item[]  Choice of analysis level of sophistication

\vspace*{1mm}
  \item[] Propagate parametric, aleatory  uncertainty



%\vspace*{1mm}
%  \item[] Goal: predict and inform

\vspace*{1mm}
  \item[] Predict and inform, Engineer needs to know!


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


\vspace*{1mm}
  \item[] Design, build and maintain sustainable objects


\begin{figure}[!hbpt]
\begin{center}
%
%\hspace*{-7mm}
%\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Conferences/2021/CU-Boulder-GEGM-seminar-series-02Apr2021/present/Saint_Sophia_Constantinopolis.jpg}
\includegraphics[height=2.3truecm]{/home/jeremic/tex/works/Conferences/2021/ASCE-4_Kennedy_Lecture/present/Aya-Sofia_03_1990.jpg}
%\hspace*{2mm}
\includegraphics[height=2.3truecm]{/home/jeremic/tex/works/Conferences/2021/ASCE-4_Kennedy_Lecture/present/Four_Water_Wheels_Hama_Syria.jpg}
%\hspace*{2mm}
\includegraphics[height=2.3truecm]{/home/jeremic/tex/works/Conferences/2021/ASCE-4_Kennedy_Lecture/present/ZhaozhouBridge.jpg}
%
%\vspace*{3mm}
\end{center}
\end{figure}
%\vspace*{3mm}




%
%
%
%  \vspace*{1mm}
%    \item[]  Follow  the  flow, input and dissipation,  of seismic  energy,

%  \vspace*{2mm}
%    \item[]
%  %System  for
%   {\bf Real}istic modeling and simulation of
%    {\bf E}arthquakes and/or
%    {\bf S}oils and/or
%    {\bf S}tructures    and    their
%    {\bf I}nteraction:\\
%     Real-ESSI
%   \hspace*{5mm}
%    \url{http://real-essi.us/}
%  % % %  \hspace*{25mm}
%  %     \url{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
%  % %    \href{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}{{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
%  % %  % \url{http://ms-essi.us/}
%  % %
%




\end{itemize}
\end{frame}
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\begin{frame}
 \frametitle{Dedication}


% Thick fbox lines 
\setlength{\fboxrule}{1.8pt} 
 
    
%\noindent \rule[.1mm]{\textwidth}{.1mm}
%

\vspace*{5mm}

\noindent
\framebox{Robert P. Kennedy, 1939-2018}

\vspace*{3mm}
\noindent
"Response of a soil structure system 
 is nonlinear, and I would really 
 like to know what that response is!"

\vspace*{1mm}
\noindent
"There are engineers and then there are Engineers!"

%\vspace*{-40mm}
%%\begin{figure}[!htbp]
%\begin{flushright}
%\includegraphics[width=30mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Dedication_Photos/Robert_P_Kennedy/Robert_P_Kennedy_07Dec2018.jpg}
%% \par
%% {Robert P. Kennedy}
%% % {Robert P. Kennedy, 07Dec2018}
%% % %\caption2{Robert P. Kennedy, 07Dec2018.}
%% % %\label{Robert_P_Kennedy_07Dec2018}
%\end{flushright}
%%\end{figure}


%\vspace*{10mm}

\begin{center}
%\includegraphics[width=15mm]{/home/jeremic/tex/works/Conferences/2021/ASCE-4_Kennedy_Lecture/present/Kennedy_07Dec2018.jpg}
%\includegraphics[height=22mm]{/home/jeremic/tex/works/Conferences/2021/ASCE-4_Kennedy_Lecture/present/Kennedy_Oct2015.jpg}
\includegraphics[height=32mm]{/home/jeremic/tex/works/Conferences/2021/ASCE-4_Kennedy_Lecture/present/Kennedy_alone_Oct2015.jpg}
%\includegraphics[height=22mm]{/home/jeremic/tex/works/Conferences/2021/ASCE-4_Kennedy_Lecture/present/IMG_Budnitz_and_Kennedy_at_Reno.jpg}
\includegraphics[height=32mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Dedication_Photos/Robert_P_Kennedy/Robert_P_Kennedy_07Dec2018.jpg}
%\includegraphics[width=20mm]{/home/jeremic/public_html/NaseSlike/2018/Decembar/na_planini_i_u_Renou_06-08Dec2018/IMG_7529.JPG}
%\includegraphics[width=20mm]{/home/jeremic/public_html/NaseSlike/2018/Decembar/na_planini_i_u_Renou_06-08Dec2018/IMG_7572.JPG}
%\includegraphics[width=20mm]{/home/jeremic/public_html/NaseSlike/2018/Decembar/na_planini_i_u_Renou_06-08Dec2018/IMG_7579.JPG}
%\includegraphics[width=20mm]{/home/jeremic/public_html/NaseSlike/2018/Decembar/na_planini_i_u_Renou_06-08Dec2018/IMG_7593.JPG}
\end{center}




\end{frame}
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\begin{frame}
% Thick fbox lines 
 \frametitle{Dedication}


% Thick fbox lines 
\setlength{\fboxrule}{1.8pt} 
 
    
%\noindent \rule[.1mm]{\textwidth}{.1mm}
%

\vspace*{-5mm}


\noindent
\fbox{Neboj{\v s}a Orbovi{\' c},  1962-2021}

\vspace*{5mm}

\noindent
"As an engineer, I have to know, \\
with good accuracy, what will happen \\
to the structure during loading, \\
hence numerical analysis and \\
verification and validation for \\
numerical analysis is really important"

\vspace*{2mm}
\noindent
"As an engineer, I have to know  what are response sensitivities 
 to modeling parameters."

\vspace*{-46mm}
%\begin{figure}[!htbp]
\begin{flushright}
\includegraphics[width=30mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Dedication_Photos/Nebojsa_Orbovic/Nebojsa_Orbovic_26Feb2016.jpg}
% \par
% {Neboj{\v s}a Orbovi{\'c}}
% % {Neboj{\v s}a Orbovi{\'c}, 26Feb20216}
% % %\caption2{Neboj{\v s}a Orbovi{\'c}, 26Feb20216.}
\end{flushright}
%\end{figure}


% back to standard fbox lines 
 \setlength{\fboxrule}{0.2pt} 



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






%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Engineer Needs to Know!}

\begin{itemize}



    


%\vspace*{2mm}
  \item[] Engineer needs versatile, quality assured analysis tool

  \begin{itemize}
  \item[-] Explore different design options

\vspace*{1mm}
  \item[-] Assess object performance

  \end{itemize}


\vspace*{4mm}
  \item[]  Choice of analysis/modeling level of sophistication

\vspace*{4mm}
  \item[] Predict and Inform






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



                       

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Numerical Prediction under Uncertainty}


\begin{itemize}




%\vspace*{1mm}
  \item    {Modeling, Epistemic Uncertainty}
    \begin{itemize}

%\vspace*{1mm}
      \item[-] Modeling simplifications

%\vspace*{1mm}
      \item[-] Model sophistication 
%      for confidence in  results 

%\vspace*{1mm}
      \item[-] Verification and Validation 

%\vspace*{1mm}
      \item[-] Elastic design does NOT guaranty \\
      safe structure!
\begin{flushright}
 \vspace*{-25mm}
{\includegraphics[width=3cm]{/home/jeremic/tex/works/Conferences/2021/ASCE-4_Kennedy_Lecture/present/Kaatsiz_and_Sucuoglu_unsafe_elastic_design.jpg}}
\end{flushright}



%
%\vspace*{2mm}
%      \item[] Choice of sophistication level for confidence in  results

    \end{itemize}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\vspace*{2mm}
  
  \item   {Parametric, Aleatory    Uncertainty}

  \begin{itemize}


%\vspace*{1mm}
    \item[-]  ${M}  \ddot{u_i}  +  {C}  \dot{u_i} + {K}^{ep} {u_i} = {F(t)}$, 

%\vspace*{1mm}
    \item[-] Uncertain: mass $M$, viscous damping  $C$ and stiffness $K^{ep}$


%\vspace*{1mm}
    \item[-] Uncertain  loads, $F(t)$


%\vspace*{1mm}
    \item[-] Results are PDFs   and   CDFs  for  $\sigma_{ij}$,  $\epsilon_{ij}$,  $u_i$,  $\dot{u}_i$,  $\ddot{u}_i$

  \end{itemize}




\end{itemize}



% 
% 
% %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)



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% 
% 
% 
%   \item[-]  Important (?!)  features are simplified, 1C vs 3C, inelasticity
% 
% %\vspace*{4mm}
% %     \item   Unrealistic   and   unnecessary  modeling simplifications
% 
% \vspace*{1mm}
%      \item[-]  Modeling  simplifications   are  justifiable  if  one  or  two 
%      level higher sophistication model demonstrates that features being
%      simplified out are less or not important
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% % %  \movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
% % %    {\includegraphics[width=90mm]{movie_2_npps_mp4_icon.jpeg}}{movie_2_npps.mp4}
% % %  \end{center}
% % 
% % 
% % % online
% % \vspace*{-12mm}
% % \begin{flushleft}
% % %\vspace*{-15mm}
% % \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_2_npps.mp4}
% %   {\tiny (MP4)}
% % \end{flushleft}
% % % online
% % 
% % 
% % 
% 
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% \end{frame}
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%     
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Parametric, Aleatory Uncertainty}
% 
% 
% 
% \vspace*{2mm}
% %\vspace*{-5mm}
% \begin{figure}[!hbpt]
% \begin{center}
% %
% \hspace*{-7mm}
% \includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01-Ed.pdf}
% \hspace*{-3mm}
% % \hfill
% \includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_Histogram_Normal_01-Ed.pdf}
% %
% \end{center}
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% 
% 
% \vspace*{-5mm}
% %\vspace*{-1.8cm}
% %\hspace*{-3.3cm}
% \begin{flushright}
% {\tiny
% (cf. Phoon and Kulhawy (1999B))\\
% ~}
% \end{flushright}
% %
% 
% 
% 
% 
% 
%    
% 
% \vspace*{-9mm}
% \begin{figure}[!hbpt]
% \begin{center}
% %
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% \includegraphics[width=5.00truecm]{/home/jeremic/tex/works/Thesis/HexiangWang/time_series_motionsn_06ug2019_SMIRT/Acc_realization_200.pdf}
% %\hspace*{-3mm}
% %\includegraphics[width=2cm]{/home/jeremic/tex/works/Papers/2019/Hexiang/1D_risk/version2/Figures/Acc_time_series_realiztion70.pdf}
% %\includegraphics[width=2cm]{/home/jeremic/tex/works/Papers/2019/Hexiang/1D_risk/version2/Figures/Acc_time_series_realiztion100.pdf}
% %% \includegraphics[width=0.31\textwidth]{Figures/Acc_time_series_realiztion350.pdf}
% %\includegraphics[width=2cm]{/home/jeremic/tex/works/Papers/2019/Hexiang/1D_risk/version2/Figures/Acc_time_series_realiztion367.pdf}
% \includegraphics[width=4cm]{/home/jeremic/tex/works/Papers/2019/1D_risk/version2/Figures/SA_GMPE_verification_std_08_no_smooth.pdf}
% %
% \end{center}
% \end{figure}
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% 
% \vspace*{-7mm}
% \begin{flushright}
% {\tiny
% (cf. Wang et al. (2019))\\
% ~}
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% \end{frame}
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% 











%                        
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% % \frametitle{Sensitivity Analysis}
%  \frametitle{Engineer Needs to Know!}
% 
% 
% \begin{itemize}
% 
% 
% 
%   \item[-]    Forward    propagation    of   uncertainty,   full   probabilistic,
%   nonlinear/inelastic  Earthquake-Soil-Structure-Interaction, ESSI response in
%   time domain (Jeremic et al 2011, Wang et al 2019)
% % %\vspace*{1mm}
% %   \item[]      \underline{Sensitivity Analysis} quantifies the relative importance
% %   of  input  uncertain  parameters  and their contributions to the probabilistic
% %   system response
% % 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \vspace*{4mm}
% %   \item[]    \underline{Local sensitivity analysis} focuses on the local impact of
% %   input  uncertain  parameters  on model response, quantified by the gradient of
% %   system response with respect to the variation of input parameters
% % 
% 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \vspace*{4mm}
% %   \item[]    \underline{Global sensitivity analysis} studies the
% % respective
% \vspace*{4mm}
%   \item[-] Backward propagation, sensitivity analysis, quantifies the relative importance
%  of  input  uncertain  parameters on the variance of the probabilistic system
%   response  
% (Sobol 2001, Sudret 2008, Jeremic et al 2021)
% %Sobol, {\cyss Sobol{p1}} indices (Sobol 2001), Sudret (2008)
% % encoding for soft b is {p1}, see
% 
% 
% 
% \end{itemize}
% 
% 
% 
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 


% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Parametric Uncertainty: Soil Stiffness and Strength}
% 
% 
% \vspace*{2mm}
% %\vspace*{-3mm}
% \begin{figure}[!hbpt]
% \begin{center}
% %
% \hspace*{-7mm}
% \includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01-Ed.pdf}
% \hspace*{-3mm}
% % \hfill
% \includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_Histogram_Normal_01-Ed.pdf}
% %
% \end{center}
% \end{figure}
% 
% \vspace*{-5mm}
% \begin{figure}[!hbpt]
% \begin{center}
% %
% \hspace*{-7mm}
% \includegraphics[width=5.00truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_RawData_and_MeanTrend-Mod.pdf}
% \hspace*{-3mm}
% % \hfill
% \includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_Histogram_PearsonIV-FineTuned-Mod.pdf}
% %
% \end{center}
% \end{figure}
% 
% %\vspace*{-5mm}
% %\vspace*{-1.8cm}
% %\hspace*{-3.3cm}
% \begin{flushright}
% {\tiny
% (cf. Phoon and Kulhawy (1999B))\\
% ~}
% \end{flushright}
% %
% 
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Parametric Uncertainty: Material Properties}
% 
%           
% 
% \vspace*{5mm}
% \begin{figure}[!hbpt]
% \begin{center}
% % %
% \hspace*{-3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldPhiPdf.pdf}
% \hspace*{-3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldPhiCdf.pdf}
% \hspace*{3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldSuPdf.pdf}
% \hspace*{-3mm}
% \includegraphics[width=2.5truecm]{/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*{10mm}
% \hspace*{-3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabPhiPdf.pdf}
% \hspace*{-3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabPhiCdf.pdf}
% \hspace*{3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabSuPdf.pdf}
% \hspace*{-3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabSuCdf.pdf}
% \\
% %\vspace*{-8mm}
% \hspace*{-2.5cm} \mbox{\tiny Lab $\phi$} \hspace*{3.5cm} \mbox{\tiny Lab $c_u$}
% \end{center}
% \end{figure}
% 
% 
% 
% \end{frame}
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% 
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame} 
%  
%  \frametitle{Real-ESSI Simulator System}
%  
%  % 
%  
%  \vspace*{2mm}
%  The  Real-ESSI,
%  {\underline {\bf Real}}istic  
%  %{\underline {\bf M}}odeling  and  
%  %{\underline {\bf S}}imulation  of  
%  {M}odeling  and  
%  {S}imulation  of  
%  {\underline {\bf E}}arthquakes,  
%  {\underline {\bf S}}oils,
%  {\underline {\bf S}}tructures  and  their  
%  {\underline {\bf I}}nteraction.  Simulator  is  a  software,  hardware  and
%  documentation   system   for   time  domain,
%  linear  and  nonlinear,  inelastic,  deterministic  or probabilistic, 3D, 
%  modeling and simulation of:
%  
%  \vspace*{-1mm}
%      \begin{itemize}
%  %\vspace*{1mm}
%        \item[-] statics and dynamics of soil,
%  % %\vspace*{1mm}
%  %       \item[-]    statics and dynamics of rock,
%  %\vspace*{1mm}
%        \item[-]    statics and dynamics of structures,
%  %\vspace*{1mm}
%        \item[-]    statics of soil-structure systems, and
%  %\vspace*{1mm}
%        \item[-]    dynamics of earthquake-soil-structure system interaction
%      \end{itemize}
%  
%  
%  
%  Used for:
%  \begin{itemize}
%  %\vspace*{1mm}
%    \item[-] Design: linear elastic, load combinations, dimensioning
%  
%  
%  %\vspace*{1mm}
%    \item[-] Assessment: nonlinear/inelastic, risk, safety margins
%  \end{itemize}
%  
%  
%  
%  
%  \end{frame}
%  
%  
%  
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame} 
% 
% \frametitle{Real-ESSI Simulator System}
% 
%  
% \begin{itemize}
% 
% 
%   \item Real-ESSI System Components
%     \begin{itemize} 
%      \item[-] Real-ESSI Pre-processor (gmsh/gmESSI, X2ESSI) 
%      \item[-] Real-ESSI Program (local, remote, cloud)
%      \item[-] Real-ESSI Post-Processor (Paraview/pvESSI, Python)
% 
%     \end{itemize} 
% 
% \vspace*{1mm}
%   \item Real-ESSI System availability:                   
%     \begin{itemize}
% %\vspace*{1mm}
%      \item[-] Educational  Institutions: AWS, Linux Image, free 
%      \item[-] Government Agencies, National Labs: AWS GovCloud
%      \item[-] Professional  Practice: AWS, commercial
% %\vspace*{1mm}
% %%\vspace*{1mm}
% %      \item Sources available to collaborators
%     \end{itemize}
% 
% 
% 
% \vspace*{1mm}
%   \item Real-ESSI education and training: theory and applications
% 
% 
% 
% \vspace*{1mm}
%   \item Real-ESSI documentation and program available at  
% \url{http://real-essi.us/}    
% %\url{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
% %
% %\url{http://real-essi.us/}
% %
% 
% 
% % \vspace*{2mm}
% %   \item
% % 
% 
% 
% \end{itemize}
% 
% 
% \end{frame}
% 
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\section{Real-ESSI Simulator}

      
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%\subsection*{Real-ESSI Simulator System}
% \subsection{Real ESSI Components}
\subsection{Real-ESSI }



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

\frametitle{Real-ESSI Simulator System}

The  Real-ESSI, 
{\underline {\bf Real}}istic  
%{\underline {\bf M}}odeling  and  
%{\underline {\bf S}}imulation  of  
{M}odeling  and  
{S}imulation  of  
{\underline {\bf E}}arthquakes,  
{\underline {\bf S}}oils,
{\underline {\bf S}}tructures  and  their  
{\underline {\bf I}}nteraction  Simulator  is  a  software,  hardware  and
documentation   system   for   time  domain,
linear and  nonlinear,  
elastic and inelastic,  
deterministic  or probabilistic,
3D, 
modeling and simulation of:

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



Used for:
\begin{itemize}
%\vspace*{1mm}
  \item[-] Design, linear elastic, load combinations, dimensioning


%\vspace*{1mm}
  \item[-] Assessment, nonlinear/inelastic, safety margins
\end{itemize}




\end{frame}



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

\frametitle{Real-ESSI Simulator System}

 
\begin{itemize}


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

    \end{itemize} 

\vspace*{1mm}
  \item[] Availability, free executable downloads:
    \begin{itemize} 
%     \item[-] Docker Container Images for
%       \begin{itemize} 
%      \vspace*{-1mm}
         \item[-] MS-Windows 
         \item[-] MacOS 
         \item[-] Linux 
%       \end{itemize} 

%     \item[-] Linux Executables                                           
     \item[-] Amazon Web Services                                          

    \end{itemize} 
  
  
  
   
   
   
%     \begin{itemize}
% %\vspace*{1mm}
%      \item[-] Educational  Institutions: AWS and Linux Executables, free 
%      \item[-] Government Agencies, National Labs: AWS GovCloud, free
%      \item[-] Professional  Practice: AWS and Linux Executables, commercial
% %\vspace*{1mm}
% %%\vspace*{1mm}
% %      \item Sources available to collaborators
%     \end{itemize}


%  
%  \vspace*{3mm}
%    \item Real-ESSI education and training: theory and applications
%  


\vspace*{1mm}
  \item[] Real-ESSI program, documentation, examples:
\url{http://real-essi.us/}    
%\url{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
%
%\url{http://real-essi.us/}
%


% \vspace*{2mm}
%   \item
% 


\end{itemize}


\end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Real-ESSI Simulator Quality Assurance}

\begin{itemize}

\item[-] Verification available for each element, model, algorithm, ...

\vspace*{10mm}
\item[-] Validation partially available, working with UCSD, TJU...

% \vspace*{5mm}
% \item Certification process
% 
%  \begin{itemize}
% 
% \vspace*{2mm}
%     \item[-] ASME  NQA-1
%  
% \vspace*{2mm}
%     \item[-] ISO-90003-2014
% 
%  \end{itemize}

%\vspace*{3mm}
%\item[] Verification examples given below

\end{itemize}




\end{frame}
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Real-ESSI Modeling Features}

\begin{itemize}



%\vspace*{2mm}
  \item[-] Solids: dry, saturated/liquefaction, elastic, elastic-plastic

%\vspace*{1mm}
  \item[-] Structural elements: beams (B,T), shells, elastic, inelastic 

%\vspace*{1mm}
  \item[-] Contact/interface/joint elements: gapping, frictional
%   (EPP, EPH,
%EPS); Gap/Normal; linear, nonlinear, dry, coupled/saturated,
%  Bonded, Shear/Frictional (EPP, EPH,
%  EPS); Gap/Normal; linear, nonlinear, dry, coupled/saturated,

%\vspace*{1mm}
  \item[-] Super element: stiffness and mass matrices

%\vspace*{1mm}
  \item[-] Material models: soil, rock, concrete, steel... 
  
%\vspace*{1mm}
  \item[-] Seismic input: 1C and 3C, deterministic or probabilistic

%\vspace*{1mm}
  \item[-] Energy calculations: input, el-pl, viscous, algorithmic

%\vspace*{1mm}
  \item[-] Solid/Structure-Fluid interaction, full coupling, OpenFOAM

%\vspace*{1mm}
  \item[-] Forward probabilistic inelastic modeling

%\vspace*{1mm}
  \item[-] Backward probabilistic inelastic modeling: Sensitivities

%\vspace*{1mm}
  \item[-] Input: Domain Specific Language

%
%\vspace*{1mm}
%  \item Modeling features listed at
%  \hspace*{5mm}
%  \href{http://real-essi.us/}{http://real-essi.us/} 
%%  \hspace*{5mm} 
%%  and 
%%  \hspace*{5mm} 
%%  \href{http://real-essi.us/}{http://real-essi.us/}


\end{itemize}
 
\end{frame}


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Real-ESSI Simulation Features}
% 
% 
% 
% %\vspace*{-10mm}
% 
% \begin{itemize}
% 
%   \item[-] Static loading stages
% 
% \vspace*{1mm}
%   \item[-] Dynamic loading stages
% 
% \vspace*{1mm}
%   \item[-] Restart, simulation tree
% 
% \vspace*{1mm}
%   \item[-] Solution advancement methods/algorithms, \\
%         on global and constitutive levels, \\
%         with and without enforcing equilibrium
% 
% %\vspace*{1mm}
% %  \item Load combinations, elastic, for design
% 
% \vspace*{1mm}
%   \item[-] High Performance Computing (HPC): \\
%            Sequential and Parallel
% %  %  clusters, cloud, supercomputers 
% %      \begin{itemize}
% %  %\vspace*{1mm}
% %        \item[.] Fine grained, template mataprograms, small matrix library
% %  %\vspace*{1mm}
% %        \item[.] Coarse grained, distributed memory parallel 
% %      \end{itemize}
% 
% 
% % \vspace*{1mm}
% %   \item All  Simulation Features are listed at  
% %   \hspace*{5mm}
% %   \href{http://real-essi.us/}{http://real-essi.us/} 
% % %  \hspace*{5mm} 
% % %  and 
% % %  \hspace*{5mm} 
% % %  \href{http://real-essi.us/}{http://real-essi.us/}
% 
% 
% 
% \end{itemize}
% 
% 
%  
% \vspace*{-60mm}
% %\begin{figure}[!hbpt]
% \begin{flushright}
% \includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Theory_Introduction/tex_works_psfigures_loading_stage-increments-iterations.pdf}
% \end{flushright}
% %\vspace*{-0.5cm}
% %\end{figure}
% %
% 
% 
% 
% 
%  
% \end{frame}
% 
% 
% 
%   
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Real ESSI Simulator: Domain Specific Language, DSL}
% 
%  \begin{itemize}
%    \item Domain Specific Language (DSL), Yacc \& Lex
% \vspace*{3mm}
%    \item English like modeling and simulation language
% \vspace*{3mm}
%    \item Parser and compiler, can define functions, models, etc.
% \vspace*{3mm}
%    \item Can extend models and methods
% \vspace*{3mm}
%    \item Requires units!
%  \end{itemize}
% %
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% 
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}[fragile]
%   \frametitle{DSL: English Language Binding Modeling Parser}
%  {\footnotesize
%  \begin{lstlisting}
%  // Defining variables
%  x = 7; // x is double-valued variable with adimenisional units.
%  y = 3.972e+2; // Decimal and scientific notation is supported.
%  // Operations: All standard arithmetic operations (Unites!)
%  a = x + y;  // Addition
%  b = x - y;  // Subtraction
%  c = x*y;  // Product
%  d = x/y;  // Quotient
%  e = y%x;  // Modulus (how many times x fits in y)
%  // Predefined variables. For example, the variable 'm' defines 'meter'.
%  L1 = 1*m;
%  L2 = 40*mm;    // Defines L2 to be 40 millimiters.
%  L3 = 3.14*cm;
%  L4 = 3.14;
%  A5 = 3.14*cm^2;
%  \end{lstlisting}
%  }
%  \end{frame}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}[fragile]
%   \frametitle{DSL: English Language Modeling Parser}
%  {\footnotesize
%  \begin{lstlisting}
%  F1 = 10*kN; // Define few forces.
%  F2 = 300*N;
%  F3 = 4*kg*g; // Here g is the predefined acceleration
%               // due to gravity.
%  // Operations are sensitive to units. For example,
%  foo = L1 + F1; // Produces an error because units are
%                 // not compatible. However,
%  L4 = L1 + L2 + L3;  // is OK.
%  // Multiplication (division and modulus) always work
%  // because the result produces a quantity with new units
%  // (except when the adimensional quantity is involved).
%  A = L1*L2;
%  pressure = F1 / A;
%  // All numbers are converted to SI units (kg - m - s)
%  // and internally stored in that system.
%  \end{lstlisting}
%  }
%  \end{frame}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{DSL: ESSI Input Language, Basics}
%  
%  
%  \begin{itemize}
%  
%  \item Angle  brackets  \lstinline|<>| denotes  user input
%  
%  \item Expected   unit (dimension)  is  given (example: 
%  \lstinline|<L>|, for length unit)
%  
%  \item Symbol \lstinline|<.>| represents the adimensional quantity.
%  
%  \item Vertical  bar  \lstinline+|+ (``OR'' sign)) is used to separate two or more keyword
%  options,   i.e.   \lstinline+[a|b|c]+   is   used   indicate   keyword   options
%  \lstinline+a+ or \lstinline+b+ or \lstinline+c+.
%  
%  \item The  symbol  \lstinline+|...|+  is  used  to  denote  where several long options
%  exist  and  are  explained elsewhere (an example of this is available below in a
%  material model definitions).
%  
%  \end{itemize}
%  
%  \end{frame}
%  
%  
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{DSL: ESSI Input Language, Units}
%  
%  
%  All    commands  require  unit  consistency.  Base units, SI  or  other (British
%  Imperial)  can be used
%  \begin{itemize}
%    \item  length, symbol  $L$, units [m, in, ft]
%    \item  mass, symbol    $M$, units [kg, lb],
%    \item  time, symbol    $T$, units [s]
%  \end{itemize}
%  
%  Derived units can also be used:
%  
%  \begin{itemize}
%    \item angle, symbol rad (radian), unit [$dimensionless, L/L$]
%    \item force, symbol N (Newton), units [$N, kN, MN, M*L/T^2$],
%    \item stress, symbol Pa (Pascal), units [$Pa, kPa, MPa, N/L^2, M/L/T^2$]
%    \item strain, symbol (no symbol), units [$L/L$]
%    \item mass density, symbol (no symbol), units [$M/L^3$]
%    \item force density, symbol (no symbol), units [$M/L^2/T^2$]
%  \end{itemize}
%  
%  \end{frame}
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{DSL: ESSI Input Language, Loading Stages}
%  
%  
%  Start         a    new    loading    stage  with
%  
%  \lstinline|new loading stage "loading_stage_name";|
%  
%  \vspace*{0.5cm}
%  Example,  starting a new loading stage called {\it "self weight load"}
%  
%  \lstinline|new loading stage "self weight load";|
%  
%  
%  
%  
%  
%  
%  \end{frame}
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  
%  
%  % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}[fragile]
%   \frametitle{DSL: Beam Example, Model}
%  
%  
%  
%  \begin{figure}[!h]
%  \begin{center}
%  \includegraphics[width=10cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Cantilever_Beam.pdf}
%  %\caption{8 node brick element}
%  %\label{fig:8node_command}
%  \end{center}
%  \end{figure}
%  
%  
%  %}
%  \end{frame}
%  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}[fragile]
%  \frametitle{Real ESSI DSL Example}
% 
% 
% \vspace*{-8mm}
% \begin{figure}[!h]
% \begin{flushright}
% \includegraphics[width=4cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Cantilever_Beam.pdf}
% %\caption{8 node brick element}
% %\label{fig:8node_command}
% \end{flushright}
% \end{figure}
% 
% 
% \vspace*{-4mm}
% 
% \begin{lstlisting}
% model name "SmallTestModel";
% new loading stage "First_static";
% // Nodal  Coordinates
% add node # 1 at (0*m, 0*m, 0*m) with 6 dofs;
% add node # 2 at (0*m, 0*in, 1000*mm) with 6 dofs;
% add element # 1 type beam_elastic with
%   nodes (1, 2) cross_section=1.0*m^2
%   elastic_modulus=1.0e5*KN/m^2
%   shear_modulus=2.0e4*KN/m^2
%   torsion_Jx=2*0.083*m^4
%   bending_Iy=0.083*m^4 bending_Iz=0.083*m^4
%   mass_density=2500.0*kg/m^3
%   xz_plane_vector = (0, -1, 0)
%   joint_1_offset = (0.0*m, 0.0*m, 0.0*m)
%   joint_2_offset = (0.0*m, 0.0*m, 0.0*m);
% \end{lstlisting}
% 
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}[fragile]
%  \frametitle{Real ESSI DSL Example}
% 
% 
% \begin{lstlisting}
% fix node No 1 dofs all;
% add load # 1 to node # 2 type linear Fy=-9*kN;
% define load factor increment 0.01;
% 
% define solver UMFPack;
% 
% define convergence test
%   Norm_Displacement_Increment
%   tolerance = 1e-5
%   maximum_iterations = 20
%   verbose_level = 4;
% 
% define algorithm Newton;
% 
% simulate 100 steps using static algorithm;
% 
% bye;
% \end{lstlisting}
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Real-ESSI Model Development}
% 
% \begin{itemize}
% 
%     \item[-] Pre-Processing, model development gmsh/gmESSI
% 
% \vspace*{1mm}
%     \item[-] Existing model translation, SASSI$\rightarrow$Real-ESSI
% 
% 
% \vspace*{1mm}
%     \item[-] Self documenting input language
% 
% \vspace*{1mm}
%     \item[-] Units required for all input variables
% 
% \vspace*{1mm}
%     \item[-] All variables and constants need to be defined by user
% 
% 
% 
% \vspace*{1mm}
%     \item[-] Sophistication level of choice
% 
% %\vspace*{1mm}
% %     \item[-] Reduce modeling uncertainty
% 
% \vspace*{1mm}
%     \item[-] Model developed in phases
% 
% \vspace*{1mm}
%     \item[-] Verify model components
% 
% 
% \vspace*{1mm}
%     \item[-]  Build confidence in inelastic modeling
% 
% \end{itemize}
%  
% \end{frame}
% 
% 


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



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



\end{frame}



% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Real-ESSI Results Post Processing}
% 
% \begin{itemize}
% 
% 
%       \item[-] All output is saved (stress, strain, displacement, energy...)
% 
% \vspace*{5mm}
%       \item[-] Scripts to plot or extract time histories
% 
% \vspace*{5mm}
%       \item[-] 3D visualization, Paraview with pvESSI plugin
% 
% 
% 
% \end{itemize}
%  
% \end{frame}
% 
% 












%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Real-ESSI Core Functionality}

\begin{itemize}



%\vspace*{2mm}
  \item [-] Inelastic, nonlinear analysis for professional practice 

% 
%  % \vspace*{3mm}
%    \item Usable models for professional practice
%  
%  %\vspace*{2mm}
%   \item  Core  functionality  needed  for  nonlinear  modeling  in professional
%   practice
%  % 
%  


%  %\vspace*{0.3cm}
%  %\vspace*{2mm}
%    \item Hierarchy of modeling capabilities, 
%    
%       \begin{itemize}
%  
%  %\vspace*{1mm}
%          \item Linear elastic models, elastic constants, viscous damping
%  
%  %\vspace*{1mm}
%          \item    Nonlinear  models,  core  functionality,  does not require much
%          material data however, sensitivity study is advised
%    
%  %\vspace*{1mm}
%          \item High sophistication  nonlinear models, require material data
%       
%       
%       \end{itemize}
%  


\vspace*{3mm}
  \item[-]  Low/medium/high sophistication models for ESSI analysis


\vspace*{3mm}
  \item[-]  Set of suggested modeling and simulation parameters

\vspace*{3mm}
  \item[-]  Investigate  sensitivity  of  response  to model sophistication

\vspace*{3mm}
  \item[-]  Investigate  sensitivity  of response  to model parameters

% 
% \vspace*{1mm}
%   \item[]  Accurately   follow  the  flow   of  seismic  energy  in  a
%   soil structure system
% 
% \vspace*{1mm}
%   \item[]   The  goal is to create methodology and numerical tool that is used to 
%   predict and inform and not to fit
% 
% 
% 
% %\vspace*{1mm}
% %  \item[]   Directing,   in   space   and   time,   seismic  energy  flow  in  the
% %  soil structure system
% 


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






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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Real-ESSI Core Functionality Components}

\begin{itemize}


   \item[-] Structural elements: Truss, Beam, Shell, Super-Element

\vspace*{2mm}
   \item[-] Soil, solids:  elastic, $G/G_{max}$
        
\vspace*{2mm}
%   \item[-] Contacts/interfaces/joints: Bonded, Frictional (EPP, EPH, EPS), Gap
   \item[-] Contacts/interfaces/joints: Bonded, Frictional, Gap
   open/close


\vspace*{2mm}
   \item[-] Loads: Static, Dynamic, Earthquake  1C/3$\times$1C/3C, Restart   

\vspace*{2mm}
   \item[-] Simulation: explicit/no-equilibrium, Implicit/equilibrium

\vspace*{2mm}
   \item[-] Core Functionality Application programs: APs
% 


\end{itemize}


\end{frame}











%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Real-ESSI Education and Training}

\vspace*{1mm}
\begin{itemize}


%  \item[] Real-ESSI Eduction 
%    \begin{itemize}
%\vspace*{1mm}
      \item[-] In-person and online courses
%\vspace*{1mm}
%      \item[-] Educational short videos
% \vspace*{1mm}
%      \item[-] Professional practice 
%   \vspace*{1mm}
%        \item Developers 

%\vspace*{1mm}
%     \item[-] Practical examples available
%      in lecture notes, and documentation
\vspace*{2mm}
     \item[-] Lecture Notes/Book:
       \begin{itemize}
             \item[(I)] Theory and Computational Formulation,
             \item[(II)] Software and Hardware System,
             \item[(III)] Verification and Validation,
             \item[(IV)] Modeling and Simulation Examples,
             \item[(V)] Application to Practical Engineering Problems.
       \end{itemize}

%    \end{itemize}

%\vspace{1mm}
%  \item Documentation, extensive

\vspace*{2mm}
  \item[-] Nonlinear SSI workshop at SMiRT26

\vspace*{2mm}
  \item[-] Nonlinear SSI short course at SMiRT26

\vspace{2mm}
  \item[-] Documentation and Program at \url{http://real-essi.us/}    
  

\end{itemize}
 
\end{frame}








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\subsection{Verification  and Validation}

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Verification and Validation}
\begin{itemize}
    
    



     \item[-]  {{  Verification:}  provides  evidence  that  the  model is solved
     correctly.} Mathematics issue.  Well developed 
     for the Real ESSI Simulator.

\vspace*{4mm}
     \item[-]  {{  Validation:}  provides  evidence  that  the  correct  model is
     solved.} Physics issue. Work in progress (UCSD, TJU, ...)
        
\vspace*{4mm}
   \item[-] {  Prediction:}  use  of  computational  model
   to  foretell  the  state  of  a  physical  system  under  consideration under
   conditions for which the computational model has not been validated.
  
%   \item {  Prediction under Uncertainty}:  use  of  computational  model
%   to  predict  the  state  of SSI system under
%   conditions for which the computational model has not been validated.
% 
% 
%   
% \vspace*{1mm}
%    \item  Modeling  and  parametric uncertainties are always present, need to be
%    addressed 
% 
% %\vspace*{1mm}
% %   \item Predictive capabilities with {low Kolmogorov Complexity}
% %
% 
% \vspace*{1mm}
%      \item Goal: Predict and Inform and rather than (force) Fit
% 
% 



\end{itemize}
\end{frame}




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



\begin{itemize}


%\vspace*{0.5cm}
\vspace*{2mm}
\item[-] How much can  we trust  model implementations?
%(verification)?

%\vspace*{0.5cm}
\vspace*{2mm}
\item[-] How much can  we trust numerical simulations? 
%(validation)?

%\vspace*{0.5cm}
\vspace*{2mm}
\item[-] How good are our numerical predictions?

%\vspace*{0.5cm}
\vspace*{2mm}
\item[-]    Can      simulation  tools  be used for improving safety and economy?

%   \vspace*{2.0truecm}
\vspace*{2mm}
   \item[-]  V  \&  V  procedures  are  the  primary means of assessing accuracy
   and  building  confidence  and  credibility  in  modeling  and  computational
   simulations


%  %   \vspace*{1.0truecm}
%  \vspace*{1mm}
%     \item[-]  V  \&  V  procedures  are the tools with which we build confidence and
%     credibility in modeling and computational simulations




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




\end{itemize}




\end{frame}



   
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\begin{frame}
  \frametitle{Fundamentals of Verification and Validation}



%--


\begin{figure}[!h]
% \vspace*{-0.5cm}
\hspace*{-8mm}
%\begin{center}
%{\includegraphics[width=11cm]{/home/jeremic/tex/works/Conferences/2005/OpenSeesWorkshopAugust/DeveloperSymposium/VerifValidFund01.pdf}}
{\includegraphics[width=10cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present06_figs/VerifValidFund01.pdf}}
%\end{center}
\end{figure}


\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Role of Verification and Validation}
%  
%  
%  
%  \begin{figure}[!h]
%  \begin{center}
%  %\hspace*{-2cm}
%  %{\includegraphics[width=5.0cm]{/home/jeremic/tex/works/Conferences/2012/ASME_V_and_V_symposium/presentetation/RoleVV_NEW_knowledge.pdf}}
%  %{\includegraphics[width=4.5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present06_figs/RoleVV_NEW_knowledge.pdf}}
%  %\hfill
%  %{\includegraphics[width=6.5cm]{/home/jeremic/tex/works/Conferences/2011/USNCCM11_Minneapolis/Coupled/Present/VandV_ODEN.jpg}}
%  {\includegraphics[width=8.0cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present06_figs/VandV_ODEN.jpg}}
%  % \hspace*{-2cm}
%  \end{center}
%  \end{figure}
%  
%  %{Oberkampf et al. 
%  \hspace*{4cm}  
%  Oden et al.
%  %}
%  %{Oden et al.}
%  %
%  %\item Models available (some now, some later)
%  %\vspace*{-2.0cm}
%  
%  %
%  %\item Models available (some now, some later)
%  %\vspace*{-2.0cm}
%  \end{frame}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{V \& V Important Documents}



\begin{itemize}




%\item {\it  Short Course on Verification and Validation in
%Computational Mechanics}, by {\sc Dr. William Oberkampf}, Sandia National Laboratories
%July 27th, 2003, Albuquerque, New Mexico.
% 
% \item
% {\sc WL Oberkampf, TG Trucano, and C Hirsch.}
% Verification, validation and predictive capability in computational
%   engineering and physics.
% {
% %Proceedings of the Foundations for Verification and
% %  Validation on the 21st Century Workshop}, pages 1--74, Laurel, Maryland,
% % October 22-23 2002. 
%  2002. 
%   Johns Hopkins University / Applied Physics Laboratory.
% %{\href{http://sokocalo.engr.ucdavis.edu/~jeremic/UsefulReadings/Oberkampf-Trucano-Hirsch.pdf
% }
% %{PDF available here}}



\item[-]
{\sc PJ Roache.}
 {Verification and Validation in Computational Science and
  Engineering}.
Hermosa publishers, (1998).
%ISBN 0-913478-08-3.
%


% \item Material from {\it Verification and Validation in Computational Mechanics}
% web site \texttt{http://www.usacm.org/vnvcsm/} at the USACM.

\vspace*{2mm}
 \item[-]  WL Oberkampf and CJ Roy. Verification and Validation
 in Scientific Computing. Cambridge University Press, (2010).


\vspace*{2mm}
 \item[-] ASME-VV-10, 
% 
%  Standard for verification and validation in computational
%solid mechanics, V&V 10 - 2019. Technical report, American Society of
%Mechanical Engineers, 2019. ISBN: 9780791873168.
 ASME-VV-20, (2019).
% ,
% Standard for verification and validation in computational
%fluid dynamics and heat transfer V&V 20 - 2009(r2016). Technical report,
%American Society of Mechanical Engineers, 2009. ISBN: 9780791832097.
%  ASME-VV-40. 
% % Assessing credibility of computational modeling through
% %verification and validation: Application to medical devices V&V 40 - 2018.
% %Technical report, American Society of Mechanical Engineers, 2018. ISBN:
% %9780791872048.

 
\vspace*{2mm}
 \item[-]   ISO-90003. ISO/IEC/IEEE 90003, (2018)
% software engineering ? guidelines for
%the application of ISO 9001:2015 to computer software. Technical Report
%ISO/IEC/IEEE 90003:2018(E), ISO, 2018.


\vspace*{2mm}
 \item[-]  SASSI Verification Project, (2015)

\end{itemize}




\end{frame}


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












% 
% 
% 
% 




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
  \frametitle{Verification and Validation Summary}

  \vspace*{5mm}
    \begin{itemize}
       
      \item[-]  V\&V most important for providing confidence in results

\vspace*{3mm}
      \item[-] FEM analysis model verification is essential too!

\vspace*{3mm}
      \item[-] Numerical analysis should not be used without V\&V


%\vspace*{3mm}
%      \item  Real  ESSI  Simulator has an extensive Verification database, and a
%      smaller Validation database

% 
%       \item    Education  is  the  key  to successful use of realistic nonlinear
%       Earthquake Soil Structure Interaction modeling and simulation
% 
%     \item     Development     of    the    Real    ESSI    Simulator    system
%     \href{http://real-essi.us}{http://real-essi.us}

%     \item Importance of using proper models correctly (verification, validation, level of sophistication)
%    

\end{itemize}



%  \vspace*{5mm}
\begin{center}
\begin{figure}
 \includegraphics[width=3.00cm]{/home/jeremic/tex/works/Conferences/2021/ASCE-4_Kennedy_Lecture/present/VandV_under_the_hood_from-Oberkampf_NAFEMS_talk.jpg}
\end{figure}
\end{center}


\end{frame}
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%  \begin{frame}
%  
%  \frametitle{NPP, Inelastic Response, Energy Dissipation}
%  
%  % Elastoplastic soil with contact elements
%  %% Both solid and contact elements dissipate energy
%  
%  
%  % \vspace*{-5mm}
%  \begin{center}
%  % \hspace*{-15mm}
%  \movie[label=show3,width=10cm,poster,autostart,showcontrols]
%  {\includegraphics[width=10cm]
%  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/NPP_Plastic_Dissipation_grab.jpg}}
%  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/NPP_Plastic_Dissipation.mp4}
%  \end{center}
%  
%  
%  \begin{flushleft}
%  \vspace*{-15mm}
%  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animation/NPP_Plastic_Dissipation.mp4}
%  %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
%    {\tiny (MP4)}
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\section{ESSI Analysis}



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\subsection{Seismic Motions}



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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{ESSI: 6C or 1C Seismic Motions}
% 
% 
% \begin{itemize}
% 
% 
% \item Assume that a full 6C (3C) motions at the surface are only recorded in one
% horizontal direction
% 
% 
% \item  From such recorded motions one can develop a vertically propagating shear
% wave (1C) in 1D
% 
% \item  Apply  such  vertically propagating shear wave to same soil-structure
% system
% 
% \end{itemize}
% 
% \vspace*{-3mm}
% \begin{figure}[!H]
% \begin{center}
%  \includegraphics[width=6.5cm]{/home/jeremic/tex/works/Conferences/2015/CompDyn/Present/6D_to_1D_01.jpg}
% \end{center}
% \end{figure}
% 
% 
% 
%  \end{frame}
% 
% 
% 
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\begin{frame}
 \frametitle{Realistic Ground Motions}

%\begin{itemize}
%
%  \item Free field seismic motion models
%
%\end{itemize}

% local
% local
% local
\vspace*{2mm}
\begin{center}
%\movie[label=show3,width=8.5cm,poster,autostart,showcontrols,loop]
%\hspace*{-12mm}
% %\movie[label=show3,width=6.0cm,autostart,showcontrols]
% \movie[label=show3,width=6.0cm,poster]
%   {\includegraphics[width=60mm]{movie_input_mp4_icon.jpeg}}{movie_input.mp4}
% \hspace*{-2mm}
% %\hfill
\hspace*{-5mm}
\movie[label=show3,width=100mm,poster,autostart,showcontrols]
%\movie[label=show3,width=90mm,poster]
  {\includegraphics[width=90mm]{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input_mp4_icon.jpeg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input.mp4}
\hspace*{-12mm}
\end{center}
% local
% local
% local
%


\end{frame}




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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Development of Realistic Motions}
% 
% \begin{itemize}
% 
%   \item Sources will send both P and S waves
% 
% \end{itemize}
% 
% % online
% % online  \begin{center}
% % online  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input.mp4}
% % online    {\includegraphics[width=55mm]{movie_input_mp4_icon.jpeg}}
% % online  %
% % online  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input_closeup.mp4}
% % online    {\includegraphics[width=50mm]{movie_input_closeup_mp4_icon.jpeg}}
% % online  \end{center}
% % online
% 
% % local
% % local
% % local
% \vspace*{-2mm}
% \begin{center}
% %\movie[label=show3,width=8.5cm,poster,autostart,showcontrols,loop]
% \hspace*{-12mm}
% % %\movie[label=show3,width=6.0cm,autostart,showcontrols]
% % \movie[label=show3,width=6.0cm,poster]
% %   {\includegraphics[width=60mm]{movie_input_mp4_icon.jpeg}}{movie_input.mp4}
% % \hspace*{-2mm}
% % %\hfill
% % %\hspace*{-7mm}
% % %\movie[label=show3,width=5.3cm,poster,autostart,showcontrols]
% \movie[label=show3,width=80mm,poster, showcontrols]
%   {\includegraphics[width=80mm]{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input_closeup.jpg}}
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input_closeup.mp4}
% \hspace*{-12mm}
% \end{center}
% % local
% % local
% % local
% %
% 
% 
% \end{frame}
% 
% 
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% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
\frametitle{1C vs 6C Free Field Motions}



 
\begin{itemize}

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

  \item[-]  Excellent fit, wrong dynamics
%  (goal is to predict and inform and not (force) fit)


\end{itemize}




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


% online
\begin{center}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_3d.mp4}
{\tiny (MP4)}
%
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_1d.mp4}
 {\tiny (MP4)}
\end{center}
% online






% out      
% out  % local
% out  %\vspace*{-2mm}
% out  \begin{center}
% out  \hspace*{-16mm}
% out  %\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
% out  \movie[label=show3,width=61mm,poster, showcontrols]
% out    {\includegraphics[width=60mm]{movie_ff_3d_mp4_icon.jpeg}}{movie_ff_3d.mp4}
% out  % \hspace*{-16mm}
% out  % \end{center}
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% out  \movie[label=show3,width=61mm,poster, showcontrols]
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% out  \hspace*{-16mm}
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% out  \begin{flushleft}
% out  %\vspace*{-15mm}
% out  \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}
% out  %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
% out    {\tiny (MP4)}
% out  %
% out  \hspace*{55mm}
% out  \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}
% out  %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
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% out  % 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}
% out  % online    {\includegraphics[width=50mm]{movie_ff_3d_mp4_icon.jpeg}}
% out  % online  %
% out  % 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}
% out  % online    {\includegraphics[width=50mm]{movie_ff_1d_mp4_icon.jpeg}}
% out  % online  \end{center}
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\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]
  {/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_2_npps_mp4_icon.jpeg}}
  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_2_npps.mp4}
\end{center}
% local
%  \vspace*{-2mm}
%  \begin{center}
%  \hspace*{-7mm}
%  \movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
%    {\includegraphics[width=90mm]{movie_2_npps_mp4_icon.jpeg}}{movie_2_npps.mp4}
%  \end{center}


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



% out 
% out  \vspace*{-2mm}
% out  \begin{center}
% out  \hspace*{-7mm}
% out  \movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
% out    {\includegraphics[width=69mm]{BJicon.png}}
% out    {movie_2_npps.mp4}
% out  \end{center}
% out  
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% out  \begin{flushleft}
% out  \vspace*{-15mm}
% out  \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}
% out    {\tiny (MP4)}
% out  \end{flushleft}
% out  %
% out  


 \end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{1C vs 3$\times$1C vs 3C Seismic Motions}
% 
% 
% \begin{itemize}
% 
% \vspace{2mm}
%  \item 1C is required by the code
% 
% \vspace{4mm}
%  \item 3$\times$1C can be used depending on frequency/wave length of interest, 
% 
% \vspace{4mm}
%  \item 3C is more realistic, however it is challenging to define motions in full 3C
% 
% \end{itemize}
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{When to  use  3C and/or 3$\times$1C}


\begin{figure}[!hbpt]
\begin{center}
%
%\includegraphics[width=4.5truecm]{/home/jeremic/tex/works/Papers/2016/3D_vs_3_x_1D_motions/version_04Jan2017/NearFieldESSINPPs/results/3d_vs_1d_6/node_733_acce.pdf}
%\includegraphics[width=4.5truecm]{/home/jeremic/tex/works/Papers/2016/3D_vs_3_x_1D_motions/version_04Jan2017/NearFieldESSINPPs/results/6/node_733_acce.pdf}
% %
% \\
% \includegraphics[width=9.5truecm]{/home/jeremic/tex/works/Papers/2016/3D_vs_3_x_1D_motions/version_04Jan2017/NearFieldESSINPPs/results/3d_vs_1d_6/node_733_fft.pdf}
% \\
\includegraphics[width=11truecm]{/home/jeremic/tex/works/consulting/2017/IAEA/TECDOC/Version_14Mar2017/1Dvs3x1Dvs3D_waves.pdf}
\end{center}
\end{figure}

\end{frame}









% 

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



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

\frametitle{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}

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

%\frametitle{SMR ESSI, Variation in Input Frequency, $\theta = 60^{o}$}
\frametitle{SMR ESSI, 3C vs 3$\times$1C}

% 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_May2018/3Dvs1D_deconvolution.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/3Dvs1D_deconvolution.ogv}
\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_May2018/3Dvs1D_deconvolution.ogv}
  {\tiny (OGV)}
\end{flushleft}
% online  
   

\end{frame}

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% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
% %\frametitle{SMR ESSI, Variation in Input Frequency, $\theta = 60^{o}$}
% \frametitle{Incoherent Seismic Motions}
% 
% Primer ATC-144
% 
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 




  

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%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
% \frametitle{Free Field vs ESSI - 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}
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%        \includegraphics[width=3.3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/1Hz_center_az.pdf}
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%\subsection{Plastic Energy Dissipation}
\subsection{Inelasticity}



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

\begin{itemize}

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


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



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


\end{itemize}

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



% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 
\frametitle{Plastic Energy Dissipation}


\vspace*{2mm}
 
 Single elastic-plastic element under cyclic shear loading
 
\begin{itemize}
\item[] Difference between plastic work and plastic dissipation
\item[] Plastic work can decrease
\item[] Plastic dissipation always increases
\end{itemize}
 
%\vspace*{-7mm}
\begin{figure}[!hbpt]
\begin{center}
\hspace*{-5mm}
\includegraphics[width=11.0truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Dissipation_Material.png}
\end{center}
\end{figure}
  
\end{frame}
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%  \begin{frame}
%  
%  frametitle{Energy Dissipation Control Mechanisms}
%  
%  \begin{figure}[!H]
%  \hspace*{-10mm}
%      \includegraphics[width=3.4cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_plasticity.pdf}
%      \includegraphics[width=3.4cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_Rayleigh.pdf}
%      \includegraphics[width=3.4cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_Newmark.pdf}
%  \end{figure}
%  
%  
%   \hspace*{10mm} Numerical  \hspace*{20mm}  Viscous  \hspace*{20mm} Plasticity 
%  \hspace*{10mm} Plasticity \hspace*{20mm}  Viscous  \hspace*{20mm} Numerical
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\begin{frame}

\frametitle{Energy Dissipation Control}

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




\end{frame}

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\begin{frame}
 \frametitle{Inelastic Modeling of Soil Structure Systems}

\begin{itemize}

%\vspace*{1mm}
     \item Soil, inelastic, elastic-plastic
       \begin{itemize}
         \item[] Dry, single phase
         \item[] Unsaturated, partially saturated
         \item[] Fully saturated
       \end{itemize}


%\vspace*{1mm}
     \item Contact/interface/joint, inelastic, soil/rock -- foundation
       \begin{itemize}
         \item[]  Dry,  single  phase,  
           \begin{itemize}
             \item[]  Normal, hard  and  soft, gap open/close
             \item[]  Friction, nonlinear
           \end{itemize}
         \item[] Fully saturated, suction, excess pressure, buoyant force
       \end{itemize}


%\vspace*{1mm}
     \item Structure, inelastic, damage, cracks
       \begin{itemize}
         \item[] Nonlinear/inelastic reinforced concrete fiber beam
         \item[] Nonlinear/inelastic reinforced concrete solid element
         \item[] Alcali Silica Reaction concrete modeling
       \end{itemize}


%%\vspace*{1mm}
%     \item Fluid-Solid interaction (open surface)



\end{itemize}

%
\end{frame}


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
%  \frametitle{NPP Model }
% 
%   \begin{figure}[!h]
%   \begin{center}
%    \includegraphics[width=8.5cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/NPP_With_Shallow_Foundation.pdf}
%   \end{center}
% %  \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
%   \end{figure}
% 
% 
% % \begin{tikzpicture}[remember picture,overlay]
% %     \node[xshift=3.5cm,yshift=-0.6cm] at (current page.center) {\includegraphics[width=0.5\textwidth]{images/Contact_In_Industry}};
% % \end{tikzpicture}
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% \end{frame}
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% \begin{frame}
% 
%  \frametitle{Structure Model}
% 
%  The nuclear power plant structure comprise of
%  \begin{itemize}
%   \item Auxiliary building, $f^{aux}_{1}= 8Hz$
%   \item Containment/Shield building, $f^{cont}_{1}= 4Hz$
%   \item Concrete raft foundation: $3.5m$ thick
%  \end{itemize}
%   \begin{figure}[!h]
%   \begin{center}
%    \includegraphics[width=0.8\textwidth]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/NPP_Model_Auxiliary_And_Containment_Building.pdf}
%   \end{center}
%   \caption{\label{Fig:NPP_Structure_Model_In_Real_ESSI} Auxiliary and Containment Building }
%   \end{figure}
% 
% \end{frame}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  \begin{frame}
%  
%   \frametitle{Inelastic Soil and Inelastic Contact/Interface/Joint}
%  
%   \begin{itemize}
%    \item Shear velocity of soil $V_s=500m/s$
%    \item Undrained shear strength (Dickenson 1994) $V_s [m/s] = 23 (S_u [kPa])^{0.475}$
%    \item For $V_s=500m/s$ Undrained Strength $S_u=650kPa$ and Young's Modulus of $E=1.3GPa$
%    \item von Mises, Armstrong Frederick kinematic hardening
%    ($S_u=650kPa$ at $\gamma=0.01\%$; $h_a = 30MPa$, $c_r = 25$)
%    \item Soft contact (concrete-soil), gaping and nonlinear shear
%    \end{itemize}
%  
%   \begin{figure}[!h]
%   \begin{center}
%    \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Von_Mies_non_Linear_Hardening.pdf}
%    \includegraphics[width=3.5cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/SoftContact.pdf}
%   \end{center}
%    \end{figure}
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% \begin{frame}
% 
%  \frametitle{Acc. Response, Top of Containment Building}
% 
%  \begin{figure}[!h]
%  \begin{center}
% \hspace*{-8mm}
%   \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/D_Acceleration_X.pdf}
%   \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/D_Acceleration_Y.pdf}
%   \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/D_Acceleration_Z.pdf}
% \\
% \hspace*{-8mm}
%   \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/FFT_D_Acceleration_X.pdf}
%   \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/FFT_D_Acceleration_Y.pdf}
%   \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/FFT_D_Acceleration_Z.pdf}
% % \caption{\label{Fig:Response_of_Top_of_Containment_Building} Seismic Response at Top of Containment Building}
%  \end{center}
% \end{figure}
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}

 \frametitle{Acceleration Traces, Elastic vs Inelastic }

\vspace*{5mm}

\hspace*{-35mm}
  \begin{figure}[!h]
  \vspace*{-2mm}
  \begin{center}
  \hspace*{-15mm}
   \includegraphics[width=7.0cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Acceleration_Elastic_Without_Contact_SMIRT_2017.pdf}
  \hspace*{-20mm}
   \includegraphics[width=7.0cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Acceleration_Inelastic_With_Contact_SMIRT_2017.pdf}
  \hspace*{-25mm}
  \end{center}
 \end{figure}
\hspace*{-35mm}

\vspace*{-5mm}
\hspace*{10mm} Elastic  \hspace*{40mm} Inelastic \hspace*{40mm} 

\end{frame}

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

 
 \frametitle{Displacement Traces, Elastic vs Inelastic}
 
\vspace*{5mm}

\hspace*{-35mm}
  \begin{figure}[!h]
  \vspace*{-2mm}
  \begin{center}
  \hspace*{-15mm}
   \includegraphics[width=7.0cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Elastic_Without_Contact_SMIRT_2017.pdf}
  \hspace*{-20mm}
   \includegraphics[width=7.0cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Inelastic_With_Contact_SMIRT_2017.pdf}
  \hspace*{-25mm}
  \end{center}
 \end{figure}
\hspace*{-35mm}

\vspace*{-5mm}
\hspace*{10mm} Elastic  \hspace*{40mm} Inelastic \hspace*{40mm} 

\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}
%  
%  
%  
%  \begin{flushleft}
%  \vspace*{-15mm}
%  \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}
%  %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
%    {\tiny (MP4)}
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\begin{frame}

\frametitle{NPP: Plastic Energy Dissipation}

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

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




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



\end{frame}

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%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Deeply Embedded Structures}
%   \begin{columns}[T]
%    \begin{column}{.5\textwidth}
%     \vspace{-0.5cm}
%     \begin{figure}[!H]
%        \begin{center}
%          \includegraphics[width=\textwidth]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/Points_configuration.pdf}
%       \end{center}
%     \end{figure}
%    \end{column}
%    \begin{column}{.5\textwidth}
%    \vspace{0.6cm}
%    \centerline{\scriptsize Location of points}
%    \vspace{-0.6cm}
%     \begin{figure}[!H]
%        \begin{center}
%          \includegraphics[width=\textwidth]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/representative_points.pdf}
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%       \begin{flushleft}
%         \includegraphics[width=3.2cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_point1_ax_time_series.pdf}
%         \includegraphics[width=3.2cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_point1_ay_time_series.pdf}
%         \includegraphics[width=3.2cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_point1_az_time_series.pdf}
%        \\
%         \includegraphics[width=3.2cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_Point1_ax_fft.pdf}
%         \includegraphics[width=3.2cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_Point1_ay_fft.pdf}
%         \includegraphics[width=3.2cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_Point1_az_fft.pdf}
%      \end{flushleft}
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%         \includegraphics[width=2cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/Points_configuration.pdf}
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%  % \vspace*{-30mm}
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%  %   \scriptsize \hspace*{20mm} Point 3 \hspace*{25mm} Point 4   \hspace*{20mm}  Point 5
%  %   \begin{figure}[!H]
%  %      \begin{flushleft}
%  %        \includegraphics[width=3.6cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_point3_ax_time_series.pdf}
%  %        \includegraphics[width=3.6cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_point4_ax_time_series.pdf}
%  %        \includegraphics[width=3.6cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_point5_ax_time_series.pdf}
%  % \\
%  %        \includegraphics[width=3.6cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_Point3_ax_fft.pdf}
%  %        \includegraphics[width=3.6cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_Point4_ax_fft.pdf}
%  %        \includegraphics[width=3.6cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_Point5_ax_fft.pdf}
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%  %        \includegraphics[width=2cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/Points_configuration.pdf}
%  %      \hspace*{-10mm}
%  %     \end{flushright}
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%  % %    \vspace{-0.6cm}
%  % %    \scriptsize \quad \quad \quad \quad Point 3\quad \quad \quad \quad \quad \quad \quad Point 4\quad \quad \quad \quad \quad \quad Point 5
%  % %    \vspace{-0.3cm}
%  % %    \begin{figure}[!H]
%  % %       \begin{center}
%  % %         \includegraphics[width=0.3\textwidth]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_point3_ax_time_series.pdf}
%  % %         \includegraphics[width=0.3\textwidth]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_point4_ax_time_series.pdf}
%  % %         \includegraphics[width=0.3\textwidth]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_point5_ax_time_series.pdf} \\
%  % %         \includegraphics[width=0.3\textwidth]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_Point3_ax_fft.pdf}
%  % %         \includegraphics[width=0.3\textwidth]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_Point4_ax_fft.pdf}
%  % %         \includegraphics[width=0.3\textwidth]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_Point5_ax_fft.pdf}
%  % %      \end{center}
%  % %    \end{figure}
%  % %    \vspace{-0.3cm}
%  % %    \begin{itemize}
%  % %     \item Nonlinear effects attenuate along the depth
%  % %    \end{itemize}
%  % %   \end{column}
%  % %   \begin{column}{0.3\textwidth}
%  % %    \begin{figure}[!H]
%  % %       \begin{center}
%  % %         \includegraphics[width=\textwidth]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/Points_configuration.pdf}
%  % %      \end{center}
%  % %    \end{figure}
%  % %   \end{column}
%  % %   \end{columns}
%  %
%  %
%  %
%  % \end{frame}
%  %
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{SMR: ESSI Effects, Material Modeling}
%   \begin{columns}[T]
%   \begin{column}{0.6\textwidth}
%    \scriptsize \quad \quad \quad \quad  \quad Material A\quad \quad \quad \quad \quad \quad \quad Material B
%    \vspace{-3mm}
%    \begin{figure}[!H]
%       \begin{center}
%         \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_point1_ax_time_series.pdf}
%         \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/bilinear_point1_ax_time_series.pdf} \\
%         \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_Point1_ax_fft.pdf}
%         \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/bilinear_Point1_ax_fft.pdf}
%      \end{center}
%    \end{figure}
%    \vspace{-0.3cm}
%    % \begin{itemize}
%    %  \item
%    % \end{itemize}
%   \end{column}
%   \hspace{-0.3cm}
%   \begin{column}{0.3\textwidth}
%   \vspace{-0.35cm}
%    \begin{figure}[!H]
%       \begin{center}
%         \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/ha=30Mpa.png} \\
%         \tiny \quad Material A: nonlinear, vM - AF\\
%         \vspace{0.2cm}
%         \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/material_stress_strain_behavior.pdf} \\
%         \tiny \quad Material B: Bilinear\\
%      \end{center}
%    \end{figure}
%   \end{column}
%   \end{columns}
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{SMR: Accelerations Along Depth}
%  
%   \vspace{-0.6cm}
%  
%   \begin{columns}[T]
%  
%   \hspace{-0.6cm}
%  
%   \begin{column}{1.1\textwidth}
%  
%    \begin{figure}[!H]
%       \begin{center}
%         \includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/free_field_acceleration_depth_variation.pdf}\hspace{-0.7cm}
%         \includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/free_field_a_depth_variation_AF.pdf}
%      \end{center}
%    \end{figure}
%  
%    \vspace{-1.1cm}
%  
%    \begin{figure}[!H]
%       \begin{center}
%         \includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/SMR_acceleration_depth_variation_elastic.pdf}\hspace{-0.7cm}
%         \includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/SMR_acceleration_depth_variation.pdf}
%      \end{center}
%    \end{figure}
%   \end{column}
%  
%  
%   \hspace{-0.7cm}
%   \begin{column}{0.15\textwidth}
%   \vspace{1.5cm}
%   Nonlinear site effects\\
%   \vspace{2.5cm}
%   SSI effects
%   \end{column}
%   \end{columns}
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\begin{frame}

\frametitle{SMR: Plastic Energy Dissipation}

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


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


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





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% \begin{frame}
%  \frametitle{SMR: Depth variation - PGA \& PGD}
%  \vspace{-0.9cm}
%   \begin{figure}[!H]
%      \begin{center}
%      \hspace*{-10mm}
%        \includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/depth_variation_peak_AH_annotation.pdf}
%        \includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/depth_variation_peak_UH_annotation.pdf}
%      \hspace*{-5mm}
%     \end{center}
%   \end{figure}
% %  \vspace{-0.5cm}
%   \begin{itemize}
%    \item[-]  The PGA \& PGD of SSI systems are (very) different from free field motions
%    \item[-]  Material nonlinearity has significant effect on 
% %   \item \scriptsize Deconvolution methodology for analysis of embedded structure is inaccurate and even dangerous.
%   \end{itemize}
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
% \frametitle{Energy Dissipation for a SMR}
% 
% % Elastoplastic soil with contact elements
% %% Both solid and contact elements dissipate energy
% 
%      
% % \vspace*{-5mm}
% \begin{center}
% % \hspace*{-15mm}
% %\movie[label=show3,width=9cm,poster,autostart,showcontrols]
% \movie[label=show3,width=10cm,poster,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/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation.mpg}
% %{/home/jeremic/tex/works/Thesis/HanYang/Files_16Aug2017/SMR_Energy_Dissipation.mp4}
% \end{center}
% 
%  
% \begin{flushleft}
% \vspace*{-15mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation.mp4}
% %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
%   {\tiny (MP4)}
% \end{flushleft}
% %
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% 
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% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Liquefaction as Base Isolation, Model}
% 
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=4.5truecm]{/home/jeremic/tex/works/Conferences/2017/Slovenia_IAEA_short_course/present/SSI-Site_Response_Analysis/Liquefaction_04.jpg}
% \end{center}
% \end{figure}
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Liquefaction, Wave Propagation}
% 
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Conferences/2017/Slovenia_IAEA_short_course/present/SSI-Site_Response_Analysis/Liquefaction_01.jpg}
% \end{center}
% \end{figure}
% 
% \hspace*{40mm} Dry  \hspace*{10mm} Liquefied \hspace*{40mm} 
% 
% \end{frame}
% 
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Liquefaction, Stress-Strain Response}
% 
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Conferences/2017/Slovenia_IAEA_short_course/present/SSI-Site_Response_Analysis/Liquefaction_03.jpg}
% \end{center}
% \end{figure}
% 
% \hspace*{40mm} Dry  \hspace*{10mm} Liquefied \hspace*{40mm} 
% 
% \end{frame}
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% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Energy Dissipation for Design}
% 
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=10.0truecm]{/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/2D_Frame_Model.pdf}
% \end{center}
% \end{figure}
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% 
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% \begin{frame}
% \frametitle{Design Alternatives}
% 
% 
% % local
% %\vspace*{-2mm}
% \begin{center}
% \hspace*{-16mm}
% %\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
% \movie[label=show3,width=61mm,poster, showcontrols]
%   {\includegraphics[width=60mm]{/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/Individual_Foundation_screen_grab.jpg}}
%   {/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/Individual_Foundation.mp4}
% %\hspace*{-2mm}
% %\hfill
% %\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
% \movie[label=show3,width=61mm,poster, showcontrols]
%   {\includegraphics[width=61mm]{/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/Continuous_Foundation_screen_grab.jpg}}
%   {/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/Continuous_Foundation.mp4}
% \hspace*{-16mm}
% \end{center}
% % local
% 
% 
% % online
% \begin{center}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Energy_dissipation_frames/Individual_Foundation.mp4}
% {\tiny (MP4)}
% %
% \hspace*{40mm}
% %
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Energy_dissipation_frames/Continuous_Foundation.mp4}
%  {\tiny (MP4)}
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% % online
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Liquefaction as Base Isolation, Model}
% 
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=4.5truecm]{/home/jeremic/tex/works/Conferences/2017/Slovenia_IAEA_short_course/present/SSI-Site_Response_Analysis/Liquefaction_04.jpg}
% \end{center}
% \end{figure}
% 
% \end{frame}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Liquefaction, Wave Propagation}
% 
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Conferences/2017/Slovenia_IAEA_short_course/present/SSI-Site_Response_Analysis/Liquefaction_01.jpg}
% \end{center}
% \end{figure}
% 
% \end{frame}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Liquefaction, Stress-Strain Response}
% 
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Conferences/2017/Slovenia_IAEA_short_course/present/SSI-Site_Response_Analysis/Liquefaction_03.jpg}
% \end{center}
% \end{figure}
% 
% \end{frame}
% 
% 
% 
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%  \begin{frame}
%  \frametitle{Pile in Liquefiable Soil, Model}
%  
%  \begin{figure}[!hbpt]
%  \begin{center}
%  \includegraphics[width=2.7truecm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Cyclic_Mobility_and_Liquefaction/tex_works_Papers_2008_Pile_in_liquefied_soil_upU_final_FEmesh3D.pdf}
%  \hfill
%  \includegraphics[width=3.5truecm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Cyclic_Mobility_and_Liquefaction/tex_works_Papers_2008_Pile_in_liquefied_soil_upU_final_FEmeshPileBeam.pdf}
%  %\hfill
%  \includegraphics[width=4truecm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Cyclic_Mobility_and_Liquefaction/tex_works_Papers_2008_Pile_in_liquefied_soil_upU_final_SFSIModelSetup_upU_01.pdf}
%  \end{center}
%  \end{figure}
%  
%  
%  \end{frame}
%  
%  
%  
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%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{Pile in Liquefiable Soil}
%  
%  \begin{figure}[!hbpt]
%  \begin{center}
%  \includegraphics[width=6truecm]{/home/jeremic/tex/works/Conferences/2018/Oersted-DONG-Energy/present/Pile_in_liquefied_soil.jpg}
%  \end{center}
%  \end{figure}
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\begin{frame}
\frametitle{Energy Dissipation for Design}

\begin{figure}[!hbpt]
\begin{center}
\includegraphics[width=10.0truecm]{/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/2D_Frame_Model.pdf}
\end{center}
\end{figure}


\end{frame}






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\begin{frame}
\frametitle{Design Alternatives}


% local
%\vspace*{-2mm}
\begin{center}
\hspace*{-16mm}
%\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
\movie[label=show3,width=61mm,poster, showcontrols]
  {\includegraphics[width=60mm]{/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/Individual_Foundation_screen_grab.jpg}}
  {/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/Individual_Foundation.mp4}
%\hspace*{-2mm}
%\hfill
%\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
\movie[label=show3,width=61mm,poster, showcontrols]
  {\includegraphics[width=61mm]{/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/Continuous_Foundation_screen_grab.jpg}}
  {/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/Continuous_Foundation.mp4}
\hspace*{-16mm}
\end{center}
% local


% online
\begin{center}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Energy_dissipation_frames/Individual_Foundation.mp4}
{\tiny (MP4)}
%
\hspace*{40mm}
%
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Energy_dissipation_frames/Continuous_Foundation.mp4}
 {\tiny (MP4)}
\end{center}
% online





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\begin{frame}
 \frametitle{Regular and ASR Concrete}
 
   \begin{figure}[!h]
    \begin{center}
\hspace*{-15mm}
     \includegraphics[width=2truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/Rebar_Plan.pdf}
     \includegraphics[width=4truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/3D_mesh.pdf}
\includegraphics[width=2.8truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/Reg_A_Force_Displacement.pdf}
\includegraphics[width=2.8truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/ASR_A1_Force_Displacement.pdf}
\hspace*{-15mm}
    \end{center}
\end{figure}


\vspace{-2mm}
\begin{figure}[!htbp]
\begin{center}
\includegraphics[width=10.0truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_Natural_Hazartd_Oct2018/Present/OECD_wall_damage_3_stages.jpg}
\end{center}
\end{figure}



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

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\begin{frame}
 \frametitle{Building on Liquefiable Soil}



\vspace*{16mm}

\noindent
Plastic Strain \hspace*{40mm} Pore Fluid Pressures

\vspace*{-1mm}
% local
%\vspace*{-2mm}
\begin{center}
\hspace*{-16mm}
%\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
\movie[label=show3,width=61mm, showcontrols]
  {\includegraphics[width=60mm]
  {/home/jeremic/tex/works/Thesis/HanYang/Liquefaction_models_Nov-Dec2021/Plastic_Strain.jpg}}
  {/home/jeremic/tex/works/Thesis/HanYang/Liquefaction_models_Nov-Dec2021/Plastic_Strain.mp4}
%\hspace*{-2mm}
%\hfill
%\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
\movie[label=show3,width=61mm, showcontrols]
  {\includegraphics[width=60mm]
  {/home/jeremic/tex/works/Thesis/HanYang/Liquefaction_models_Nov-Dec2021/Pore_Presure.jpg}}
  {/home/jeremic/tex/works/Thesis/HanYang/Liquefaction_models_Nov-Dec2021/Pore_Presure.mp4}
\hspace*{-16mm}
\end{center}
% local

\vspace*{-1mm}

% online
\begin{center}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/building_on_liquefiable_soil_ETH_model/Plastic_Strain.mp4}
{\tiny (MP4)}
%
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/building_on_liquefiable_soil_ETH_model/Pore_Presure.mp4}
 {\tiny (MP4)}
\end{center}
% online

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%  \begin{frame}
%  
%  \frametitle{Buoyant Force Simulation}
%  
%  \begin{figure}[!H]
%  \hspace*{-20mm}
%       \includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/upU_element_type_annotation.pdf}
%       \includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/bouyant_displacement.pdf}
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%  % -  % \end{tikzpicture}
%  % -
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%\vspace*{-5mm}
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% \hspace*{-15mm}
\movie[label=show3,width=9cm,poster,autostart,showcontrols]
{\includegraphics[width=8.5cm]
{/home/jeremic/tex/works/Conferences/2017/DOE_Project_Review_Meeting_LBNL_09June2017/Present/Solid-Fluid-Interaction.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Fluid_Solid_interaction/Solid_Fluid_Interaction_NEW.mpeg}
\end{center}


\begin{flushleft}
\vspace*{-15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Fluid_Solid_interaction/Solid_Fluid_Interaction.mp4}
%  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
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%\subsection{Stochastic Modeling}
\subsection{Probabilistic Modeling}



 
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% \frametitle{Probabilistic Elastic-Plastic Response}
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% \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}
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\frametitle{{El-Pl, Cam Clay  with  Random $G$, $M$ and $p_0$}}


\begin{figure}[!hbpt]
\begin{center}
\hspace*{-15mm}
\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Conferences/2006/KallolsPresentationGaTech/ContourLowOCR_RandomG_RandomM_Randomp0-m.pdf}
%\hspace*{-2mm}
\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Conferences/2006/KallolsPresentationGaTech/ContourHighOCR_RandomG_RandomM-m.pdf}
\hspace*{-15mm}
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\begin{frame}
\frametitle{Probabilistic Cyclic Elastic-Plastic Response}


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

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


 

\begin{flushleft}
\vspace*{-15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Probabilistic_Elasto_Plasticity_and_Stochastic_Elastic_Plastic_Finite_Element_Method/PEP_Animation.mp4}
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% \includegraphics[width = 12cm]{./img/figure_PEP_25.pdf}


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\begin{frame}

\frametitle{Stochastic Ground Motion Modeling}

% \vspace{-0.4cm}

\begin{itemize}



%\item[-] \normalsize Shift from modeling specific IM to fundamental characteristics of ground motions
\item[-]   \normalsize   Shift   from   modeling   specific  Intensity Measures
(IMs) to fundamental characteristics of ground motions

\vspace*{-1mm}
\begin{itemize}

\item[-] \normalsize Uncertain Fourier amplitude spectra (FAS)  

\item[-] \normalsize Uncertain Fourier phase spectra (FPS)

\end{itemize}



\vspace*{1mm}
  \item[-] No need to define Intensity Measures!

% \item \scriptsize Mean behavior of stochastic FAS  

% \begin{itemize}

% \item[--] \scriptsize $w^2$ source radiation spectrum by \textit{Brune(1970)}

% \item[--] \scriptsize Systematic studies by \textit{ \textbf{Boore}(1983, \textbf{2003}, 2015)}.  

% \end{itemize}


%\item[-] \normalsize Recent GMPE study of FAS,
%(FAS marginal median \& variability GMPEs by \textit{{Bora et al.
%(2018)}} and {\textit{Bayless \& Abrahamson (2019)}} ; 
%FAS Inter-frequency correlation GMPE by \textit{Stafford(2017)} and
%{\textit{Bayless \& Abrahamson (2018)}})


\vspace*{1mm}
\item[-] \normalsize GMPE studies of FAS,
(
\textit{{Bora et al. (2018)}},
\textit{Bayless \& Abrahamson (2018,2019)}, 
\textit{Stafford(2017)}, 
%{\textit{Bayless \& Abrahamson (2018)}
)

% \begin{itemize}
% 
% \item[-] \scriptsize FAS marginal median \& variability GMPEs by \textit{\textbf{Bora et al. (2018)}} and \textbf{\textit{Bayless \& Abrahamson (2019)}}
% 
% %\vspace{0.1cm}
% 
% \item[-] \scriptsize FAS Inter-frequency correlation GMPE by \textit{Stafford(2017)} and \textbf{\textit{Bayless \& Abrahamson (2018)}}.  
% 
% \end{itemize}


%\vspace{0.05cm}

%\item[-] \normalsize Stochastic FPS by phase derivative (Boore,2005)
%(Logistic phase derivative model by {\textit{Baglio \& Abrahamson (2017)}})
\vspace*{1mm}
\item[-] \normalsize Stochastic FPS by phase derivative (Boore,2005)
(Logistic phase derivative model by {\textit{Baglio \& Abrahamson (2017)}})

\vspace*{1mm}
\item[-] \normalsize Near future change from \textbf{ $\boldsymbol{Sa(T_0)}$} to \textbf{FAS} 
%next five years
% as envisioned by Abrahamson (2018)

\end{itemize}

\end{frame}
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% 
% \begin{frame}{Time Domain Stochastic Galerkin Method}
% 
% 
% \vspace*{2mm}
% Dynamic Finite Elements 
% $
% { M} \ddot{ u_i} +
% { C} \dot{ u_i} +
% { K}^{ep} { u_i} =
% { F(t)}$
% 
% 
% \begin{itemize}
% \vspace*{2mm}
% \item[-] Input random field/process{\normalsize{(non-Gaussian, heterogeneous/ non-stationary)}}:
%           Multi-dimensional Hermite Polynomial Chaos (PC) with {known coefficients}
% %\vspace{0.05in}
% \vspace*{2mm}
% \item[-] Output response process: Multi-dimensional Hermite PC with {unknown coefficients}
% % \vspace{0.05in}
% \vspace*{2mm}
%  \item[-] Galerkin projection: minimize the error to compute unknown coefficients of response process
% % %\vspace{0.05in}
% % \vspace*{2mm}
% %  \item[-] Time integration using Newmark's method
% % % : Update coefficients following
% % % an elastic-plastic constitutive law at each time step
%  
% \end{itemize}
% 
% %\scriptsize 
% %Note: PC = Polynomial Chaos
% 
% \end{frame}
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\begingroup

\setbeamertemplate{footline}{}

\begin{frame}

%\frametitle{TDNIPSRA Framework}
\frametitle{Application: Seismic Hazard}

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\begin{textblock}{15}(0, 4.0)
\includegraphics[width=0.35\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/UCERF3.pdf}
\end{textblock}

\begin{textblock}{15}(0.3, 3.5)
\scriptsize{Seismic source characterization}
\end{textblock}

\begin{textblock}{15}(2.9, 5.2)
\tiny{UCERF3 (2014)}
\end{textblock}

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\begin{textblock}{15}(5.1, 6.5)
%$\Rightarrow$
{\Large $\rightarrow$}
\end{textblock}
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\begin{textblock}{15}(5.8, 3.9)
\vspace*{1mm}
\includegraphics[width=0.27\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/SMSIM.pdf}
\end{textblock}


\begin{textblock}{15}(7.1, 6.2)
\scalebox{.9}{\tiny{Fourier spectra}}
\\
\vspace*{-0.2cm}
\scalebox{.9}{\tiny{\hspace{0.14cm} Boore(2003)}}
\end{textblock}

\begin{textblock}{15}(6.1, 3.5)
\scriptsize{Stochastic ground motion}
\end{textblock}

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\begin{textblock}{15}(9.9, 6.5)
%{\bf $\Rightarrow$}
{\Large $\rightarrow$}
\end{textblock}
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\begin{textblock}{15}(10.5, 4.2)
% \includegraphics[width=0.35\linewidth]{pic/KL_exact_dis_correlation_from_dis.pdf}
\includegraphics[width=0.35\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/Acc_realization_200.pdf}
\end{textblock}

\begin{textblock}{15}(11.1, 9.6)
\scriptsize{Uncertainty characterization \\
\hspace{0.1cm} Hermite polynomial chaos}
\end{textblock}


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\begin{textblock}{15}(10.2, 13.2)
{\Large $\leftarrow$}
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\begin{textblock}{15}(11, 11.2)
\includegraphics[width=0.35\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/structural_uncertainty.pdf}
\end{textblock}

\begin{textblock}{15}(5.3, 10.75)
\includegraphics[width=0.33\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/probabilsitc_evolution.png}
\end{textblock}

\begin{textblock}{15}(5.4, 9.6)
\scriptsize{\quad \quad Uncertainty propagation \\ 
\quad \quad \quad \quad SEPFEM}
\end{textblock}

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\begin{textblock}{15}(4.6, 13.2)
%$\Leftarrow$
{\Large $\leftarrow$}
\end{textblock}
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\begin{textblock}{15}(0.3, 11.0)
\includegraphics[width=0.29\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/seismic_risk_result_framework.png}
\end{textblock}

\begin{tikzpicture}[remember picture, overlay]
\draw[line width=1pt, draw=black, rounded corners=4pt, fill=gray!20, fill opacity=1]
([xshift=-25pt,yshift=-55pt]$(pic cs:a) + (0pt,8pt)$) rectangle ([xshift=95pt,yshift=-18pt]$(pic cs:b)+(0pt,-2pt)$);
\end{tikzpicture}


\begin{textblock}{15}(-0.1, 9.3)
\scriptsize
\quad \quad \quad \quad $\lambda(EDP>z)=$

$\quad \sum N_i(M_i, R_i) P(EDP>z|M_i, R_i)$
\end{textblock}

\begin{textblock}{15}(1.6, 10.7)
\scriptsize{EDP hazard/risk}
\end{textblock}

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% %\subsection{Illustrative Example}
% %
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\begin{frame} 
%\frametitle{TDNIPSRA Example Object}
\frametitle{Example Soil-Structure/Location}

\begin{textblock}{15}(0.5, 4.0)
\includegraphics[width=0.47\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/Lec4/faults_configuration_new.pdf}
\end{textblock}

\begin{textblock}{15}(7.5, 3.5)
\includegraphics[width=0.55\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/SSC_legend.pdf}
\end{textblock}

\begin{textblock}{15}(0.8, 11.6)
\scriptsize
\begin{itemize}
\item Fault 1: San Gregorio fault 
\item Fault 2: Calaveras fault
\item Uncertainty: Segmentation, \\ slip rate, rupture geometry, etc.
\end{itemize} 
\end{textblock}

\begin{textblock}{15}(8.5, 11.6)
\scriptsize
\begin{itemize}
\item 371 total seismic scenarios 
\item $M \ 5 \sim 5.5$ and $6.5 \sim 7.0$
\item $R_{jb} \ 20km \sim 40km$
\end{itemize}
\end{textblock}

\end{frame}
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% \begin{frame}
% 
% \frametitle{Stochastic Ground Motion Modeling}
% 
% 
% \begin{textblock}{15}(1.0, 3.7)
% \small Realizations of simulated uncertain motions for scenario $M=7$, $R=15km$: 
% \end{textblock}
% 
% \begin{textblock}{15}(0.5, 4.0)
% \includegraphics[width=0.35\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/Acc_time_series100.pdf}
% \end{textblock}
% 
% \begin{textblock}{15}(5.5, 4.0)
% \includegraphics[width=0.35\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/Acc_time_series343.pdf} \enspace
% \end{textblock}
% 
% \begin{textblock}{15}(10.5, 4.0)
% \includegraphics[width=0.35\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/Acc_time_series439.pdf}
% \end{textblock}
% 
% \begin{textblock}{15}(1.0, 9.2)
% \small Verification with GMPE: 
% \end{textblock}
% 
% \begin{textblock}{15}(0.3, 9.5)
% \includegraphics[width=0.36\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/SA_GMPE_verification_std_08_no_smooth.pdf}
% \end{textblock}
% 
% \begin{textblock}{15}(5.6, 9.5)
% \includegraphics[width=0.36\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/Goodness_fit_std_08_no_smooth.pdf}
% \end{textblock}
% 
% \begin{textblock}{15}(10.8, 9.5)
% \includegraphics[width=0.36\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/Lec4/Standard_deviation_std_08_no_smooth_new.pdf}
% \end{textblock}
% 
% % \begin{textblock}{15}(0.5, 11.0)
% % \begin{itemize}
% % \item $\Delta \sigma= 84bar$, $\kappa=0.03s$ with total $\sigma=0.8ln$. 
% % \item Simulated median is not biased. 
% % \item Consistent total uncertainties with GMPE.  
% % \end{itemize}
% % \end{textblock}
% 
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 


% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame} 
% \frametitle{Stochastic Ground Motion Characterization}
% 
% {\begin{textblock}{15}(-0.1, 3.62)
% \scriptsize
% \includegraphics[width=0.3\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/KL_mean_acc_from_acc.pdf}
% 
% \quad \quad \quad Acc. marginal mean
% \end{textblock}
% 
% \begin{textblock}{15}(3.7, 3.62)
% \scriptsize
% \includegraphics[width=0.3\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/KL_var_acc_from_acc.pdf}
% 
% \quad \quad \quad Acc. marginal S.D. 
% \end{textblock}
% 
% \begin{textblock}{15}(7.6, 3.8)
% \scriptsize
% \includegraphics[width=0.3\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/KL_exact_acc_correlation_from_acc.pdf}
% 
% \quad \quad \quad Acc. realization Cov.
% \end{textblock}
% 
% \begin{textblock}{15}(11.8, 3.9)
% \scriptsize
% \includegraphics[width=0.3\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/KL_simulated_acc_correlation_from_acc.pdf}
% 
% \quad \quad Acc. synthesized Cov.
% \end{textblock}}
% 
% \begin{textblock}{15}(-0.1, 9.3)
% \scriptsize
% \includegraphics[width=0.31\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/KL_mean_dis_from_dis.pdf}
% \end{textblock}
% 
% \begin{textblock}{15}(0.9, 13.75)
% \scriptsize
% Dis. marginal mean
% \end{textblock}
% 
% \begin{textblock}{15}(4.2, 9.4)
% \scriptsize
% \includegraphics[width=0.3\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/KL_var_dis_from_dis.pdf}
% \end{textblock}
% 
% \begin{textblock}{15}(5.1, 13.75)
% \scriptsize
% Dis. marginal S.D. 
% \end{textblock}
% 
% \begin{textblock}{15}(8.2, 9.5)
% \scriptsize
% \includegraphics[width=0.27\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/KL_exact_dis_correlation_from_dis.pdf}
% 
% \quad \quad Dis. realization Cov.
% \end{textblock}
% 
% \begin{textblock}{15}(12.2, 9.6)
% \scriptsize
% \includegraphics[width=0.27\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/KL_simulated_dis_correlation_from_dis.pdf}
% 
% \quad Dis. synthesized Cov.
% \end{textblock}
% \end{frame}
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% 
% 
% 
% % 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
% \frametitle{Stochastic Material Modeling}
% 
% %Uncertain 1D shear response 
% 
% 
% 
% \begin{figure}[!htbp]
% \centering
% %\subfloat[Uncertain $H_a$]{
% %\hspace{-0.8cm}
% %\includegraphics[width=0.53\textwidth]{/home/jeremic/tex/works/Papers/2019/Hexiang/1D_risk/version6/Figures/constitutive_relation_uncertainHa_certainCr_MC_verification.pdf}}
% %\subfloat[Uncertain $H_a$ and $C_r$]{
% %\hspace{-0.2cm}
% %\includegraphics[width=0.53\textwidth]{/home/jeremic/tex/works/Papers/2019/Hexiang/1D_risk/version6/Figures/constitutive_relation_uncertainHa_uncertainCr_MC_verification.pdf}}
% %\vspace{-2mm}
% %\caption{\label{figure_probabilisitc_constitutive_relation} Intrusive probabilistic modeling of Armstrong-Frederick hysteretic behavior and  verification  with Monte Carlo simulation: (a) Gaussian distributed  $Ha$  with  mean 1.76 $\times 10^{7} \ N/m$ and 15\% coefficient of variation (COV), $C_r = 17.6$. (b) Gaussian distributed  $Ha$  with  mean 1.76 $\times 10^{7} \ N/m$ and 15\% coefficient of variation (COV), Gaussian distributed $C_r$ with mean 17.6 and 15\% COV.}
% \subfloat[Frame]{
% \hspace{-0.8cm}
% \includegraphics[width=2.5cm]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/Shear-Frame-8-levels.jpg}}
% \subfloat[Interstory response]{
% \hspace{10mm}
% \includegraphics[width=6cm]{/home/jeremic/tex/works/Papers/2019/1D_risk/version6/Figures/constitutive_relation_uncertainHa_uncertainCr_MC_verification.pdf}}
% %\vspace{-2mm}
% %\caption{\label{figure_probabilisitc_constitutive_relation} Intrusive probabilistic modeling of Armstrong-Frederick hysteretic behavior and  verification  with Monte Carlo simulation: (a) Gaussian distributed  $Ha$  with  mean 1.76 $\times 10^{7} \ N/m$ and 15\% coefficient of variation (COV), $C_r = 17.6$. (b) Gaussian distributed  $Ha$  with  mean 1.76 $\times 10^{7} \ N/m$ and 15\% coefficient of variation (COV), Gaussian distributed $C_r$ with mean 17.6 and 15\% COV.}
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% \scriptsize
% \includegraphics[width=0.46\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/Lec4/shear_frame_illustration_update.pdf}
% \end{textblock}
% 
% \begin{textblock}{15}(0.2, 10.8)
% \begin{itemize}
% \scriptsize \item Coefficient of variation 15$\%$ for $H_a$ and $C_r$
% %\scriptsize \item Exponential correlation with correlation  \\
% %length $l_c = 10$ floors 
% \scriptsize \item Time domain stochastic \\
%                   El-Pl FEM analysis (SEPFEM)
% % : uncertain \\ structure with uncertain excitations
% \end{itemize}
% \end{textblock}
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% \begin{textblock}{15}(7.7, 5)
% \scriptsize
% \includegraphics[width=0.52\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/Probabilistic_Response_Node_1_new.pdf}
% \end{textblock}
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% \begin{textblock}{15}(8.3, 4.2)
% \scriptsize Probabilistic response of top floor from SFEM
% \end{textblock}
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% \begingroup
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% \frametitle{Seismic Risk Analysis}
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% \scriptsize
% \includegraphics[width=0.42\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/Lec4/MIDR_PDF_evolution.pdf}
% \includegraphics[width=0.42\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/Lec4/PDF_MIDR_combine.pdf}
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% \scriptsize
% \includegraphics[width=0.42\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/Lec4/MIDR_distribution_different_floors.pdf}
% \includegraphics[width=0.42\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/Lec4/Risk_MIDR.pdf}
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% \scriptsize Engineering demand parameter (EDP): Maximum inter-story drift ratio (MIDR) 
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% \scriptsize
% \includegraphics[width=0.42\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/Lec4/PFA_distribution.pdf}
% \includegraphics[width=0.42\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/Lec4/Risk_PFA.pdf}
% \end{textblock}
% 
% \begin{textblock}{15}(1.9,9.3)
% \scriptsize
% \includegraphics[width=0.41\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/Lec4/2D_EDP_PDF_1e5.pdf}
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% \scriptsize
% \includegraphics[width=0.40\linewidth]{/home/jeremic/tex/works/Conferences/2020/Natural_Phenomena_Hazard_Oct2020/present/from_Hexiang_17Oct2020/pic/Lec4/2D_EDP_PDF_downview_1e5.pdf}
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% \scriptsize Engineering demand parameter (EDP): Peak floor acceleration (PFA) 
% \end{textblock}
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\begin{frame} 

\frametitle{Seismic Risk Analysis, Forward Propagation}

%\vspace{-0.5cm}
\vspace*{2mm}

\begin{itemize}

  \item[-] No need to define Intensity Measures!

%  \item[-] \small Damage measure (DM) defined on multiple EDPs: 
%  \item[-] \small Damage measure (DM) defined on single EDP:
\vspace{2mm}
  \item[-] Damage measure defined on single EDP:

\vspace*{-3mm}

%\begin{textblock}{15}(0.7,8.9)
\begin{table}[!htbp]
\small
\resizebox{0.98\hsize}{!}{
\begin{tabular}{ccccccc}
%\hline
\textbf{DM} & MIDR\textgreater{}0.5\% & \textbf{MIDR\textgreater{}1\%} & MIDR\textgreater{}2\% & PFA\textgreater{}0.5${\rm m/s^2}$ & \textbf{PFA\textgreater{}1\boldsymbol{${\rm m/s^2}$}} & PFA\textgreater{}1.5${\rm m/s^2}$ \\ 
\hline
\textbf{Risk [/yr]} & 6.66$\times 10^{-3}$                    & \textbf{3.83\boldsymbol{$\times 10^{-3}$}}                  & 9.97$\times 10^{-5}$                   & 6.65$\times 10^{-3}$                 & \textbf{1.92 \boldsymbol{$\times 10^{-3}$}}               & 9.45$\times 10^{-5}$                 \\ 
%\hline
\end{tabular}}
\end{table}
%\end{textblock}


\vspace{2mm}
  \item[-] Damage measure (DM) defined on multiple EDPs: 

%    \vspace{2mm}
    {\scriptsize $DM: \{\text{MIDR}>1\%\,  \cup \,\text{PFA}>1{\rm m/s^2} \}$, seismic risk is \boldsymbol{$4.2 \times 10^{-3}/yr$} }

    \vspace{1mm}
    {\scriptsize $DM: \{\text{MIDR}>1\%\,  \cap \,\text{PFA}>1{\rm m/s^2} \}$, seismic risk is \boldsymbol{$1.71 \times 10^{-3}/yr$}}

    \vspace{3mm}


%\vspace{20mm}

\vspace{2mm}
\item[-] \small Seismic risk for DM defined on multiple EDPs can be quite
different from that defined on single EDP.

\end{itemize}
\end{frame}
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%  %  
%      \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}
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%  %
%  \begin{equation}
%  { M} \ddot{ u_i} +
%  { C} \dot{ u_i} +
%  { K}^{ep} { u_i} =
%  { F(t)}
%      \nonumber
%  \end{equation}
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%  Dynamic Finite Elements 
%  $
%  { M} \ddot{ u_i} +
%  { C} \dot{ u_i} +
%  { K}^{ep} { u_i} =
%  { F(t)}$
%  
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%  \begin{itemize}
%  \vspace*{2mm}
%  \item[-] Input random field/process{\normalsize{(non-Gaussian, heterogeneous/ non-stationary)}}:
%            Multi-dimensional Hermite Polynomial Chaos (PC) with {known coefficients}
%  %\vspace{0.05in}
%  \vspace*{2mm}
%  \item[-] Output response process: Multi-dimensional Hermite PC with {unknown coefficients}
%  % \vspace{0.05in}
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%   \item[-] Galerkin projection: minimize the error to compute unknown coefficients of response process
%  % %\vspace{0.05in}
%  % \vspace*{2mm}
%  %  \item[-] Time integration using Newmark's method
%  % % : Update coefficients following
%  % % an elastic-plastic constitutive law at each time step
%   
%  \end{itemize}
%  
%  %\scriptsize 
%  %Note: PC = Polynomial Chaos
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%  % \begin{frame}{Discretization of Input Random Process/Field $\beta(x,\theta)$}
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%  % \includegraphics[scale=0.35]{/home/jeremic/tex/works/Thesis/FangboWang/slides_13Mar2019/Fangbo_slides/figs/PC_KL_explanation.PNG} \\
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%  % \footnotesize{Note: $\beta(x,\theta)$ is an input random process with any
%  % marginal distribution,  \\ \hspace{21mm} with any covariance structure;} \\
%  % \footnotesize{\hspace{8mm} $\gamma(x,\theta)$ is a zero-mean unit-variance Gaussian random process.} \\
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%  \begin{frame}{Polynomial Chaos Representation}
%  
%  %\scriptsize{
%  Material random field: \\
%  %\vspace{-0.3cm}
%  %\begin{equation*} 
%  $D(x, \theta)= \sum_{i=1}^{P1} a_i(x) \Psi_i(\left\{\xi_r(\theta)\right\})$      
%  %\end{equation*}
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%  Seismic loads/motions random process: \\
%  %\vspace{-0.3cm}
%  %\begin{equation*} 
%  $f_m(t, \theta)=\sum_{j=1}^{P_2} f_{mj}(t) \Psi_j(\{\xi_k(\theta)\})$         
%  %\end{equation*}
%  
%  \vspace{4mm}
%  
%  Displacement response:  \\
%  %\vspace{-0.3cm}
%  %\begin{equation*} 
%  $u_n(t, \theta)=\sum_{k=1}^{P_3} d_{nk}(t) \Psi_k(\{\xi_l(\theta)\})$         
%  %\end{equation*}
%  
%  \vspace{3mm}
%  
%  %Acceleration response:
%  %%\vspace{-0.3cm}
%  %%\begin{equation*} 
%  %$\ddot u_n(t, \theta)=\sum_{k=1}^{P_3} \ddot d_{nk}(t) \Psi_k(\{\xi_l(\theta)\})$         
%  %%\end{equation*}
%  
%  %\vspace{3mm}
%  \vspace{5mm}
%  
%  where $a_i(x), f_{mj}(t)$ are {known PC coefficients}, while $d_{nk}(t)$
%  are {unknown PC coefficients}.
%  %}
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%  % \subsection{Direct Solution for Probabilistic Stiffness and Stress in 1D}
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%  % \begin{itemize}
%  %  
%  %  \vspace{0.5cm}
%  % 
%  % \item<1-> Probabilistic constitutive modeling : \vspace{0.5cm}
%  
%  \begin{itemize}
%  
%  
%  \vspace*{4mm}
%  \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*{4mm}
%  \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 $
%  
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%  \vspace*{4mm}
%  \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$
%  % - 
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%   
%   \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]
%  $
%  
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%  \vspace*{2mm}
%  \item[-] Stiffness: each Polynomial Chaos component is updated incrementally
%  % at each Gauss Point via stochastic Galerkin projection
%  
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%    \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{$E_{t_P}^{n+1}  =  \frac{1}{<\Phi_1\Phi_P> }\{\sum_{i=1}^{P_h} \ h_i   <\Phi_i \Phi_P> \pm \sum_{j=1}^{P_c} \sum_{l=1}^{P_{\sigma}} \ c_j  \sigma_l^{n+1} <\Phi_j  \Phi_l \Phi_P>\}$}
%    
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%  \vspace*{2mm}
%  \item[-] Total stiffness is : 
%    
%    $ E_{t}^{n+1} = \sum_{l=1}^{P_{E}} E_{t_i}^{n+1} \Phi_i $
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%  \begin{frame}{Direct 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*{2mm}
%  \item[-] Incremental stress: each  Polynomial  Chaos  component  is updated
%  incrementally 
%  % via stochastic Galerkin projection
%  
%  
%   
%   
%    {$\Delta\sigma_1^{n+1}  = \frac{1}{<\Phi_1\Phi_1> }\{\sum_{i=1}^{P_h} \sum_{k=1}^{P_e}\ h_i  \Delta \epsilon_k^n <\Phi_i \Phi_k \Phi_1>- \sum_{j=1}^{P_g} \sum_{k=1}^{P_e}\sum_{l=1}^{P_{\sigma}} \ c_j \Delta \epsilon_k^n \sigma_l^n <\Phi_j \Phi_k \Phi_l \Phi_1>\}$}
%  \\
%  . . . 
%  \\
%  % ${\vdots}$ 
%  {$\Delta\sigma_P^{n+1}  = \frac{1}{<\Phi_P\Phi_P> }\{\sum_{i=1}^{P_h} \sum_{k=1}^{P_e}\ h_i  \Delta \epsilon_k^n <\Phi_i \Phi_k \Phi_P>- \sum_{j=1}^{P_g} \sum_{k=1}^{P_e}\sum_{l=1}^{P_{\sigma}} \ c_j \Delta \epsilon_k^n \sigma_l^n <\Phi_j \Phi_k \Phi_l \Phi_P>\}$}
%  
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%  \vspace*{2mm}
%  \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$
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%  %$f(x,t,\theta) = \sum_{i=0}^{P_f} f_i(x,t) * \zeta_i[\{\xi_{m+1}, ..., \xi_f]$
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%  \item[-] Displacement expanded into stochastic shape funcs.
%  %$u(x,t,\theta) = \sum_{i=0}^{P_u} u_i(x,t) * \Psi_i[\{\xi_1, ..., \xi_m, \xi_{m+1}, ..., \xi_f\}]$
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%  \item[-] Jeremi{\'c} et al. 2011
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%      \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 \\
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%      \vdots \\
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%     \sum_{i=0}^{P_f} f_i    <\Psi_2\zeta_i> \\
%      \vdots \\
%       \sum_{i=0}^{P_f} f_i  <\Psi_{P_u}\zeta_i>\\
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%  %   \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 $10^{11}$\\  
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%     ...  & ... & ... & ...\\   
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\frametitle{Sensitivity Analysis, Backward Propagation}

%  

\begin{itemize}

\item[-] Sensitivity of forward uncertain response to input
uncertainties
%, analytic development

\vspace*{1mm}
\item[-] Analytic sensitivity analysis development

%\begin{itemize}
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%
% \vspace*{2mm}
\vspace*{1mm}
\item[-] Total variance in PGA, \underline{in this case}, dominated by uncertain ground motions
    \begin{itemize}
\vspace*{1mm}
      \item[] $49$\% from uncertain rock motions at depth
\vspace*{1mm}
      \item[] $2$\% from uncertain soil
\vspace*{1mm}
      \item[] $49$\% from interaction of uncertain rock motions and  uncertain soil 


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\section{Summary}



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\begin{frame}
  \frametitle{Summary}

  \begin{itemize}

%    \item Importance   of   using  proper  models  correctly  (verification,
%    validation, level of sophistication)
%     
 
%    \item Reduction of modeling uncertainty 
%

%  \vspace*{2mm}
%      \item[-] Analysis of uncertainties and sensitivities
%  
%\vspace*{1mm}
    \item[-] Predict and Inform, Engineer Needs to Know!

   
%\vspace*{1mm}
   \item[-]     Teacher, Motivator, Supporter: {Robert P Kennedy} 

% %\vspace*{1mm}
%    \item[-]     Supporter, Motivators: {Neboj{\v s}a Orbovi{\'c}}, 

%\vspace*{1mm}
   \item[-]     Collaborators: Yang, Feng,  
                Behbehani, Sinha, Wang, Wang, Pisan{\'o}, Abell, Tafazzoli, Jie,
                Preisig,  Tasiopoulou,  Watanabe,  Luo,  Cheng,  Yang, Lizundia,
                Rangelow, V{\"o}geli, Salamon, Altinyollar, ...
   
   

%\vspace*{1mm}
  \item[-]       Much appreciated is collaboration with and  funding  from  the 
                 USDOE, USNRC,  USNSF, USFEMA,      USBR,  ETHZ,    CNSC/CCSN,     
                 UN-IAEA, CH-ENSI/IFSN, Basler\&Hofmann and Shimizu Corp.


%
%\vspace*{1mm}
%  \item[-]    Funding    from  and  collaboration  with the ATC/US-FEMA, US-DOE,
%  US-NRC, US-NSF, CNSC-CCSN, CH-ENSI, UN-IAEA, and Shimizu Corp. is greatly appreciated,

 
%\vspace*{1mm}
  \item[-]  
    \url{http://real-essi.us/}
      
%
%\vspace*{1mm}
%    \item[-] Sensitivity analysis


%\vspace*{1mm}
%   \item[-]     Collaborators:    Feng,  Yang, Wang,  Yang.
   
   

% 
%\vspace*{1mm}
%  \item[-]  
%    \url{http://sokocalo.engr.ucdavis.edu/~jeremic}
%      

\end{itemize}



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%   \frametitle{Dedication}
% 
%  RIP:  Neboj{\v s}a Orbovi{\' c}  (1962-2021) \\
% %  who pushed hard for sensitivity analysis \\
% \vspace*{5mm}
% \hspace*{30mm}
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%   \includegraphics[width=4cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Dedication_Photos/Nebojsa_Orbovic/Nebojsa_Orbovic_26Feb2016.jpg}
% % \end{center}
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% %    \url{http://sokocalo.engr.ucdavis.edu/~jeremic}
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