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% %% Jose Antonio Abell Mena provided this for DSL descriptions
% % (used in a file _Chapter_SoftwareHardware_Domain_Specific_Language_English.tex
% % This is added for listing FEI DSL
% % since he customized it, it needs to be changed (linked to
% % /usr/share/texmf/tex/latex/misc)
% %\usepackage{myListings}
% \input{essi_listings_options.tex}
\usepackage{threeparttable}
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\usepackage{wasysym}%
\usepackage{multirow}
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\usepackage{subfig}
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% for inclusion of other PDF pages, in this case Frank's presentation
\usepackage{pdfpages}
%This is a macro to convert eps to pdf files on the fly.
% make sure figure syntax uses graphicx syntax NOT epsfig syntax
%from http://mailman.mit.edu/pipermail/macpartners/2005January/000780.html
%
% \ifx\pdfoutput\undefined
% % we are running LaTeX, not pdflatex
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% % we are running pdflatex, so convert .pdf files to .pdf
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% \fi
% %*****************************************
%% ovo je za cirilicu
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% \usetheme{Marburg} % ima naslov i sadrzaj sa desne strane
% \usetheme{Hannover} % ima naslov i sadrzaj sa leve strane
% \usetheme{Singapore} % ima sadrzaj i tackice gore
% \usetheme{Antibes} % ima sadrzaj gore i kao graf ...
% \usetheme{Berkeley} % ima sadrzaj desno
% \usetheme{Berlin} % ima sadrzaj gore i tackice
% \usetheme{Goettingen} % ima sadrzxaj za desne strane
% \usetheme{Montpellier} % ima graf sadrzaj gore
% \usetheme{Warsaw}
% \usetheme{Warsaw}
\usetheme{Dresden}
\usecolortheme[RGB={20,0,128}]{structure}
% or ...
\setbeamercovered{transparent}
% \setbeamercovered{transparent}
% or whatever (possibly just delete it)
% \usecolortheme{albatross} % teget sa svetlim slovima
% \usecolortheme{beetle} % siva pozadina (vrh plav)
\usecolortheme{seagull} % sivo
%%%%%%%
% \usecolortheme{BorisJeremic}
%%%%%%%
% \usecolortheme{rose}
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% \usefonttheme{structuresmallcapsserif}
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\usepackage{amsmath}
\usepackage{mathrsfs}
\usepackage{amsfonts}
\newcommand{\ud}{{\rm d}}
\usepackage{array}
%%%% HYPERREF HYPERREF HYPERREF HYPERREF HYPERREF
%%%% HYPERREF HYPERREF HYPERREF HYPERREF HYPERREF
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\definecolor{webblue}{rgb}{0, 0, 0.50} % less intense blue
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pdfmenubar=true,
pdftoolbar=true,
pdfpagemode={None}
colorlinks=true,
linkcolor=webblue,
citecolor=webblue,
urlcolor=webblue,
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% \usepackage[pdfauthor={Boris Jeremic},
% colorlinks=true,
% linkcolor=webblue,
% citecolor=webblue,
% urlcolor=webblue,
% linktocpage,
% pdftex]{hyperref}
\usepackage{pause}
% or whatever
%\usepackage{html}
%\usepackage{url}
\usepackage[latin1]{inputenc}
% or whatever
\usepackage{times}
\usepackage[T1]{fontenc}
% Or whatever. Note that the encoding and the font should match. If T1
% does not look nice, try deleting the line with the fontenc.
% Site Specific Dynamics of Structures:
%From Seismic Source to
%the Safety of Occupants and Content
\title[RealESSI]
{ Modeling and Simulation \\
Earthquake Soil Structure Interaction}
%\subtitle
%{Include Only If Paper Has a Subtitle}
%\author[Author, Another] % (optional, use only with lots of authors)
%{F.~Author\inst{1} \and S.~Another\inst{2}}
%  Give the names in the same order as the appear in the paper.
%  Use the \inst{?} command only if the authors have different
% affiliation.
\pgfdeclareimage[height=0.2cm]{universitylogo}{/home/jeremic/BG/amblemi/ucdavis_logo_blue_sm}
\pgfdeclareimage[height=0.7cm]{lbnllogo}{/home/jeremic/BG/amblemi/lbnllogo}
\author[Jeremi{\'c} et al.] % (optional, use only with lots of authors)
%{Boris~Jeremi{\'c}}
{Boris Jeremi{\'c}
}
%\institute[Computational Geomechanics Group \hspace*{0.3truecm}
\institute[\pgfuseimage{universitylogo}\hspace*{0.1truecm}\pgfuseimage{lbnllogo}] % (optional, but mostly needed)
%{ Professor, University of California, Davis\\
{ University of California, Davis, CA\\
% and\\
% Faculty Scientist, Lawrence Berkeley National Laboratory, Berkeley }
Lawrence Berkeley National Laboratory, Berkeley, CA}
%  Use the \inst command only if there are several affiliations.
%  Keep it simple, no one is interested in your street address.
\date[] % (optional, should be abbreviation of conference name)
{\small United States Society on Dams\\
Chicago, April 2019}
\subject{}
% This is only inserted into the PDF information catalog. Can be left
% out.
% If you have a file called "universitylogofilename.xxx", where xxx
% is a graphic format that can be processed by latex or pdflatex,
% resp., then you can add a logo as follows:
%\pgfdeclareimage[height=0.2cm]{universitylogo}{/home/jeremic/BG/amblemi/ucdavis_logo_gold_lrg}
%\logo{\pgfuseimage{universitylogo}}
% \pgfdeclareimage[height=0.5cm]{universitylogo}{universitylogofilename}
% \logo{\pgfuseimage{universitylogo}}
% Delete this, if you do not want the table of contents to pop up at
% the beginning of each subsection:
% \AtBeginSubsection[]
\setcounter{tocdepth}{3}
\AtBeginSubsection[]
% \AtBeginSection[]
{
\begin{scriptsize}
\begin{frame}
\frametitle{Outline}
\tableofcontents[currentsection,currentsubsection]
% \tableofcontents[currentsection]
\end{frame}
\end{scriptsize}
}
% If you wish to uncover everything in a stepwise fashion, uncomment
% the following command:
\begin{document}
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\begin{frame}
\titlepage
\end{frame}
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\begin{frame}
\frametitle{Outline}
\begin{scriptsize}
\tableofcontents
% You might wish to add the option [pausesections]
\end{scriptsize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Structuring a talk is a difficult task and the following structure
% may not be suitable. Here are some rules that apply for this
% solution:
%  Exactly two or three sections (other than the summary).
%  At *most* three subsections per section.
%  Talk about 30s to 2min per frame. So there should be between about
% 15 and 30 frames, all told.
%  A conference audience is likely to know very little of what you
% are going to talk about. So *simplify*!
%  In a 20min talk, getting the main ideas across is hard
% enough. Leave out details, even if it means being less precise than
% you think necessary.
%  If you omit details that are vital to the proof/implementation,
% just say so once. Everybody will be happy with that.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Introduction}
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\subsection{Motivation}
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\begin{frame}
\frametitle{Motivation}
\begin{itemize}
%\vspace*{0.3cm}
\item[] Improve modeling and simulation for infrastructure objects
% \vspace*{2mm}
% \item[] Expert numerical modeling and simulation tool
\vspace*{1mm}
\item[] Use select fidelity (high $\leftrightarrow$ low) numerical models to
analyze static and dynamic behavior of soil/rock structure fluid systems
\vspace*{1mm}
\item[] Reduction of modeling uncertainty, ability to perform desired level
of sophistication modeling and simulation
\vspace*{1mm}
\item[] Accurately follow the flow of input and dissipation of energy
in a soil structure system
\vspace*{1mm}
\item[] Development of an expert system for modeling and simulation of
Earthquakes, Soils, Structures and their Interaction, RealESSI:
\hspace*{5mm} \href{http://realessi.info/}{http://realessi.info/}
% \vspace*{1mm}
% \item[] The goal is to create methodology and numerical tool that is used to
% predict and inform and not to fit
%
%\vspace*{1mm}
% \item[] Directing, in space and time, seismic energy flow in the
% soil structure system
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Hypothesis}
%
% \begin{itemize}
%
%
%
% %\vspace*{0.5cm}
% \item Interplay dynamic characteristics of the Dynamic Forcing /
% Earthquake, Soil/Rock and Structure in time domain, plays a decisive role in
% successes and failures
%
%
% \vspace*{3mm}
% \item Timing and spatial location of energy dissipation determines location
% and amount of damage
%
% \vspace*{3mm}
% \item If timing and spatial location of the energy dissipation
% can be controlled (directed),
% we could optimize soil structure system for
% \begin{itemize}
% \item Safety and
% \item Economy
% \end{itemize}
%
% \end{itemize}
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% % \frametitle{Seismic Energy Dissipation for \underline{Soil}FoundationStructure Systems}
% \frametitle{Energy Dissipation in SSI System}
% % \frametitle{Seismic Energy Dissipation for
% % \underline{Soil}FoundationStructure Systems}
%
%
% \begin{itemize}
%
%
% \vspace*{0.2cm}
% \item Mechanical dissipation outside of SSI domain:
% \begin{itemize}
% \item SSI system oscillation radiation
% \item reflected wave radiation
% \end{itemize}
% \vspace*{0.2cm}
% \item Mechanical dissipation/conversion inside SSI domain:
% \begin{itemize}
% \item plasticity of soil subdomain
% \item plasticity/damage of the parts of structure/foundation
% \item viscous coupling of porous solid (soil) with pore fluid (air, water)
% \item viscous coupling of structure/foundation with fluids
% % \item potential and kinetic energy
% % \item potential $\leftarrow \! \! \! \! \! \! \rightarrow$ kinetic energy
% \end{itemize}
%
%
%
% \vspace*{0.2cm}
% % \item Numerical energy dissipation (numerical damping/production and period errors)
% % \item Numerical energy dissipation (damping/production)
% \item Numerical energy dissipation/production
%
%
% \end{itemize}
%
% %
% \end{frame}
% % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Predictive Capabilities}
% \frametitle{High Fidelity Modeling of SFS System:
% Verification, Validation and Prediction}
\begin{itemize}
\item { Prediction under Uncertainty}: use of computational model
to predict the state of SSI system under
conditions for which the computational model has not been validated.
\vspace*{1mm}
\item {{ Verification} provides evidence that the model is solved
correctly.} Mathematics issue.
\vspace*{1mm}
\item {{ Validation} provides evidence that the correct model is
solved.} Physics issue.
\vspace*{1mm}
\item Modeling and parametric uncertainties are always present, need to be
addressed
% \vspace*{1mm}
% \item Predictive capabilities with {low Kolmogorov Complexity}
%
\vspace*{1mm}
\item Goal: Predict and Inform rather than (force) Fit
\vspace*{1mm}
\item Engineer needs to know!
\end{itemize}
\end{frame}
%
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%\subsection*{Uncertainties}
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\begin{frame}
\frametitle{Motivation: Modeling Uncertainty}
\begin{itemize}
\item Simplified modeling: Features (important ?) are neglected (3C, 6C
ground motions, inelasticity)
\vspace*{4mm}
\item Modeling Uncertainty: unrealistic and unnecessary modeling
simplifications
\vspace*{4mm}
\item Modeling simplifications are justifiable if one or two level higher
sophistication model shows that features being simplified out are not
important
%\vspace*{3mm}
% \item Chief Engineer in my old company: "I would really love to know what
% would a realistic response this object be"
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Parametric Uncertainty: Soil Stiffness}
\vspace*{10mm}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{7mm}
\includegraphics[width=6.2truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01Ed.pdf}
% \hfill
\includegraphics[width=4.8truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/YoungModulus_Histogram_Normal_01Ed.pdf}
%
\end{center}
\end{figure}
%\vspace*{1.8cm}
%\hspace*{3.3cm}
\begin{flushright}
{\small
%Transformation of SPT $N$value:
%1D Young's modulus, $E$
cf. Phoon and Kulhawy (1999B)
~}
\end{flushright}
\end{frame}
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\begin{frame}
\frametitle{Modeling Uncertainty, 6C vs 1C Motions}
% local
\vspace*{2mm}
\begin{center}
\hspace*{7mm}
%\movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
\movie[label=show3,width=8.8cm,poster, showcontrols]
{\includegraphics[width=92mm]
{/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_2_npps_mp4_icon.jpeg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_2_npps.mp4}
\end{center}
% local
% \vspace*{2mm}
% \begin{center}
% \hspace*{7mm}
% \movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
% {\includegraphics[width=90mm]{movie_2_npps_mp4_icon.jpeg}}{movie_2_npps.mp4}
% \end{center}
% online
\vspace*{12mm}
\begin{flushleft}
%\vspace*{15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_2_npps.mp4}
{\tiny (MP4)}
\end{flushleft}
% online
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %\subsection{Personal Experience with Dam Engineering}
% %
%
% \begin{frame}
% \frametitle{Spillway Dynamic Analysis, '88'89}
%
%
%
% % % \begin{itemize}
% % %
% % % \item {\cyr Diplomski pre skoro 18 godina}
% % %
% % % \vspace*{0.10cm}
% % % \item {\cyr relativno mali model}
% % %
% % % \vspace*{0.10cm}
% % % \item {\cyr linearno elastichan materijal}
% % %
% % % \vspace*{0.10cm}
% % % \item {\cyr aksisimetrichni elementi sa \\
% % % razvojem pomeranja u \\
% % % trigonometrijske redove}
% % %
% % %
% % % \vspace*{0.10cm}
% % % \item {\cyr uprosh\cj{}eno zemljtresno \\
% % % optere\cj{}enje}
% % %
% % % \vspace*{0.10cm}
% % % \item {\cyr vrlo korisna analiza \\
% % % interakcije zemljotresa, \\
% % % tla i konstrukcije }
% % % %
% % % % \item {\cyr }
% % %
% % %
% % % \end{itemize}
% % %
% % %
% % \vspace*{6.2cm}
% % %
% \begin{center}
% \begin{figure}[!htbp]
% \includegraphics[width=6.2cm]{/home/jeremic/tex/works/Conferences/2018/USBR_22Aug2018/present/Monticelo_dam_glory_hole_spillway_01.jpg}
% \hfill
% \includegraphics[width=4.2cm]{/home/jeremic/tex/works/Conferences/2018/USBR_22Aug2018/present/DiplomskiModel.pdf}
% \end{figure}
% \end{center}
% %\vspace*{2.0cm}
%
%
%
% \end{frame}
%
%
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Behkme Dam Project, Iraq, '89'90}
%
%
%
% \begin{center}
% \begin{figure}[!htbp]
% %\includegraphics[width=4cm]{/home/jeremic/public_html/Bekhme/Bekhme_panorama_pogled_na_istok_jug_zapad_April_1990.jpg}
% %\\
% %\includegraphics[width=4cm]{/home/jeremic/public_html/Bekhme/Bekhme_panorama_pogled_na_tunele_jug_zapad_April_1990.jpg}
% %\\
% %\includegraphics[width=4cm]{/home/jeremic/public_html/Bekhme/Bekhme_panorama_pogled_na_levu_obalu_istok_April_1990.jpg}
% %
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/Bekhme/Bekhme_panorama_pogled_na_istok_jug_zapad_April_1990.jpg}
% {\includegraphics[width=7cm]{/home/jeremic/tex/works/Conferences/2018/USBR_22Aug2018/present/Bekhme_panorama_pogled_na_istok_jug_zapad_April_1990_SMALL.jpg}}
% \\
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/Bekhme/Bekhme_panorama_pogled_na_tunele_jug_zapad_April_1990.jpg}
% {\includegraphics[width=7cm]{/home/jeremic/tex/works/Conferences/2018/USBR_22Aug2018/present/Bekhme_panorama_pogled_na_tunele_jug_zapad_April_1990_SMALL.jpg}}
% \\
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/Bekhme/Bekhme_panorama_pogled_na_levu_obalu_istok_April_1990.jpg}
% {\includegraphics[width=7cm]{/home/jeremic/tex/works/Conferences/2018/USBR_22Aug2018/present/Bekhme_panorama_pogled_na_levu_obalu_istok_April_1990_SMALL.jpg}}
% %
% \end{figure}
% \end{center}
% %\vspace*{2.0cm}
%
%
% \end{frame}
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Wolf Creek Dam, '09'10}
%
% %
% \begin{figure}[!htbp]
% \begin{center}
% \includegraphics[width=3.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WolfCreekDam_SateliteView01.jpg}
% \hfill
% \includegraphics[width=2.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WolfCreekDam_SatelliteView_with_slope01.jpg}
% \hfill
% \includegraphics[width=2.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/img0188.jpg}
% \hfill
% \includegraphics[width=2.6cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WolfCreekDam_Q261_621_Embankment_Sep_30_48.jpg}
% \\
% \includegraphics[width=3.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WolfCreekDam_PerpendicularSection.jpg}
% \hfill
% \includegraphics[width=2.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/3D_final02.jpg}
% \hfill
% \includegraphics[width=2.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/3D_final04.jpg}
% \hfill
% \includegraphics[width=2.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/3D_final05.jpg}
% %\hfill
% %\includegraphics[width=2.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/3D_final_Top.jpg}
% \\
% \includegraphics[width=2.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/UndrainedSu440VectorPlan_snapshot.jpg}
% \hfill
% \includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Undrained_L680_E680_Su800_Alluvium_Su1500_FS250.jpg}
% \hfill
% \includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Undrained_L680_E680_Su900_Alluvium_Su1000_FS222.jpg}
% \hfill
% \includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Undrained_L680_E720_Su1300_FS154.jpg}
%
% %\hspace*{0.9cm}
% %bridge.}
% \end{center}
% \end{figure}
% %
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% \end{frame}
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\subsection{Modeling and Simulation of ESSI}
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\begin{frame}
\frametitle{Energy Input and Dissipation}
\begin{itemize}
\vspace*{1mm}
\item[] Energy input, dynamic forcing
\vspace*{4mm}
\item[] Energy dissipation outside SSI domain:
\begin{itemize}
\item[] SSI system oscillation radiation
\item[] Reflected wave radiation
\end{itemize}
%\vspace*{1mm}
\item[] Energy dissipation/conversion inside SSI domain:
\begin{itemize}
\item[] Inelasticity of soil, contact zone, structure, foundation, dissipators
\item[] Viscous coupling with internal/pore fluids, and external fluids
% % \item[] potential and kinetic energy
% \item[] potential $\leftarrow \! \! \! \! \! \! \rightarrow$ kinetic energy
\end{itemize}
%\vspace*{1mm}
% \item[] Numerical energy dissipation (numerical damping/production and period errors)
% \item[] Numerical energy dissipation (damping/production)
\item[] Numerical energy dissipation/production
\end{itemize}
%
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
\frametitle{Fully Coupled Formulation, upU}
%
%
\begin{small}
\begin{eqnarray}
\hspace*{13mm}
\left[ \begin{array}{ccc}
(M_s)_{KijL} & 0 & 0 \\
0 & 0 & 0 \\
0 & 0 & (M_f)_{KijL}
\end{array} \right]
\left[ \begin{array}{c}
\ddot{\overline{u}}_{Lj} \\
\ddot{\overline{p}}_N \\
\ddot{\overline{U}}_{Lj}
\end{array} \right]
+
\left[ \begin{array}{ccc}
(C_1)_{KijL} & 0 & (C_2)_{KijL} \\
0 & 0 & 0 \\
(C_2)_{LjiK} & 0 & (C_3)_{KijL} \\
\end{array} \right]
\left[ \begin{array}{c}
\dot{\overline{u}}_{Lj} \\
\dot{\overline{p}}_N \\
\dot{\overline{U}}_{Lj}
\end{array} \right]
\nonumber
\\
+
\left[ \begin{array}{ccc}
(K^{EP})_{KijL} & (G_1)_{KiM} & 0 \\
(G_1)_{LjM} & P_{MN} & (G_2)_{LjM} \\
0 & (G_2)_{KiL} & 0
\end{array} \right]
\left[ \begin{array}{c}
\overline{u}_{Lj} \\
\overline{p}_M \\
\overline{U}_{Lj}
\end{array} \right]
=
\left[ \begin{array}{c}
\overline{f}_{Ki}^{solid} \\
0 \\
\overline{f}_{Ki}^{fluid}
\end{array} \right] \nonumber
%\\
%\label{68}
\end{eqnarray}
\end{small}
%
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%
\end{frame}
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\begin{frame}
\frametitle{Fully Coupled Formulation, upU}
%
%
%
%
%
\begin{eqnarray}
\hspace*{10mm} (M_s)_{KijL}&=&\int_{\Omega} H_K^u (1n) \rho_s \delta_{ij} H_L^u d\Omega
\hspace*{5mm} (M_f)_{KijL}=\int_{\Omega} H_K^U n \rho_f \delta_{ij} H_L^U d\Omega \nonumber\\
\hspace*{10mm} (C_1)_{KijL}&=&\int_{\Omega} H_K^u n^2 k_{ij}^{1} H_L^u d\Omega
\hspace*{5mm} (C_2)_{KijL}=\int_{\Omega} H_K^u n^2 k_{ij}^{1} H_L^U d\Omega \nonumber\\
\hspace*{10mm} (C_3)_{KijL}&=&\int_{\Omega} H_K^U n^2 k_{ij}^{1} H_L^U d\Omega
\hspace*{5mm} (K^{EP})_{KijL}=\int_{\Omega} H_{K,m}^u D_{imjn} H_{L,n}^u d\Omega \nonumber\\
\hspace*{10mm} (G_1)_{KiM}&=&\int_{\Omega} H_{K,i}^u (\alphan) H_M^p d\Omega
\hspace*{5mm} (G_2)_{KiM}=\int_{\Omega} n H_{K,i}^U H_M^p d\Omega \nonumber\\
\hspace*{10mm} P_{NM}&=&\int_{\Omega} H_N^p \frac{1}{Q} H_M^p d\Omega \nonumber
\end{eqnarray}
%
%
%
%
%\newpage
% \begin{eqnarray}
% \overline{f}_{Ki}^{solid}&=&(f_1^u)_{Ki}(f_4^u)_{Ki}+(f_5^u)_{Ki} \nonumber\\
% \overline{f}_{Ki}^{fluid}&=&(f_1^U)_{Ki}+(f_2^U)_{Ki} \nonumber\\
% (f_1^u)_{Ki}&=&\int_{\Gamma_t} H_K^u n_j \sigma_{ij}^{''} d\Gamma \nonumber\\
% (f_4^u)_{Ki}&=&\int_{\Gamma_p} H_K^u (\alphan) n_i p d\Gamma \nonumber\\
% (f_5^u)_{Ki}&=&\int_{\Omega} H_K^u (1n) \rho_s b_i d\Omega \nonumber\\
% (f_1^U)_{Ki}&=&\int_{\Gamma_p} n H_K^U n_i p d\Gamma \nonumber\\
% (f_2^U)_{Ki}&=&\int_{\Omega} n H_K^U \rho_f b_i d\Omega
% \label{69}
% \end{eqnarray}
%
%
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
\frametitle{Energy Dissipation Control Mechanisms}
\begin{figure}[!H]
%\hspace*{10mm}
\includegraphics[width=3.4cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_plasticity.pdf}
\includegraphics[width=3.4cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_Rayleigh.pdf}
\includegraphics[width=3.4cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_Newmark.pdf}
\end{figure}
% \hspace*{10mm} Numerical \hspace*{20mm} Viscous \hspace*{20mm} Plasticity
\hspace*{10mm} Plasticity \hspace*{20mm} Viscous \hspace*{20mm} Numerical
\end{frame}
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\begin{frame}
\frametitle{Energy Dissipation Control}
\begin{figure}[!H]
%\hspace*{10mm}
% \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_a.pdf}
% \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_b.pdf}
\includegraphics[width=9cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_g.pdf}
% \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_e.pdf}
\end{figure}
\end{frame}
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\begin{frame}
\frametitle{Energy Dissipation on Material Level}
\vspace*{2mm}
Single elasticplastic element under cyclic shear loading
\begin{itemize}
\item[] Difference between plastic work and plastic dissipation
\item[] Plastic work can decrease
\item[] Plastic dissipation always increases
\end{itemize}
%\vspace*{7mm}
\begin{figure}[!hbpt]
\begin{center}
\hspace*{5mm}
\includegraphics[width=11.0truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Dissipation_Material.png}
\end{center}
\end{figure}
\end{frame}
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Liquefaction as Base Isolation, Model}
%
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=4.5truecm]{/home/jeremic/tex/works/Conferences/2017/Slovenia_IAEA_short_course/present/SSISite_Response_Analysis/Liquefaction_04.jpg}
% \end{center}
% \end{figure}
%
% \end{frame}
%
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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/SSISite_Response_Analysis/Liquefaction_01.jpg}
% \end{center}
% \end{figure}
%
% \end{frame}
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Liquefaction, StressStrain Response}
%
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Conferences/2017/Slovenia_IAEA_short_course/present/SSISite_Response_Analysis/Liquefaction_03.jpg}
% \end{center}
% \end{figure}
%
% \end{frame}
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%
% \begin{frame}
%
% \frametitle{Buoyant Force Simulation}
%
% \begin{figure}[!H]
% \hspace*{10mm}
% \includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/upU_element_type_annotation.pdf}
% \includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/bouyant_displacement.pdf}
% \end{figure}
%
% %  %
% %  % \begin{tikzpicture}[remember picture,overlay]
% %  % \node[anchor=south west,inner sep=0pt] at ($(current page.south west)+(7.5cm,2.5cm)$) {
% %  % \includegraphics[width=0.4\textwidth]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/bouyant_displacement.pdf}};
% %  % \end{tikzpicture}
% % 
% %  % \vspace{1.4cm}
% % \begin{itemize}
% % \item \scriptsize Upward structural displacement under buoyant force
% % \end{itemize}
% \end{frame}
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% \begin{frame}
% \frametitle{Solid/StructureFluid Interaction, Example}
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% \movie[label=show3,width=9cm,poster,autostart,showcontrols]
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% {/home/jeremic/tex/works/Conferences/2017/DOE_Project_Review_Meeting_LBNL_09June2017/Present/SolidFluidInteraction.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}
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% \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}
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\section{Seismic Motions, Inelasticity and Uncertainty}
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\subsection{Six Component Seismic Motions}
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\begin{frame}
\frametitle{3C, 6C Seismic Motions}
\vspace*{2mm}
\begin{itemize}
\item All (most) measured motions are full 3C, 6C
\item One example of an almost 2C motion (LSST07, LSST12)
\vspace*{2mm}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{5mm}
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Lotung_LSST07_FA25.jpeg}
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Lotung_LSST12_FA25.jpeg}
\hspace*{5mm}
%
\end{center}
\end{figure}
%
% \item 1D (?): M 6.9 San Pablo, Guatemala EQ, 14Jun2017
%
\end{itemize}
\end{frame}
% %
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Regional Geophysical Models}
%
% \begin{itemize}
%
% \item Free Field seismic motions on regional scale
%
%
% \vspace*{4mm}
% \item Knowledge of geology (deep and shallow) needed
%
%
% \vspace*{4mm}
% \item Developed using SW4 and/or RealESSI
%
%
% \vspace*{4mm}
% \item Collaboration with LLNL: Dr.~Rodgers, Dr.~Pitarka and Dr.~Petersson
%
%
%
%
% \end{itemize}
%
% \end{frame}
%
%
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Regional Geophysical Models}
%
% \begin{figure}[!htb]
% \begin{center}
% \includegraphics[width=5truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/San_Francisco__Regional_Model_BIG.jpg}
% \includegraphics[width=5.2truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/San_Francisco__Regional_Model.jpg}
% \end{center}
% % \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
% \end{figure}
%
% Rodgers and Pitarka
%
% \end{frame}
%
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% \begin{frame}
% \frametitle{Regional Geophysical Models}
%
% \begin{figure}[!htb]
% \begin{center}
% \includegraphics[width=10truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/USGBay_Area_Model_CC_det2_sm.jpg}
% \end{center}
% % \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
% \end{figure}
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% USGS
%
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% % \begin{frame}
% % \frametitle{Example Regional Model}
% %
% % \begin{figure}[!htb]
% % \begin{center}
% % \includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/Vs_at_top.jpg}
% % % \includegraphics[width=5truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/Horizontal_Velocity_at_12s.jpg}
% % \includegraphics[width=5truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/Peak_Velocity.jpg}
% % \end{center}
% % % \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
% % \end{figure}
% %
% % \end{frame}
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% \begin{frame}
% \frametitle{Example Regional Model (Rodgers)}
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% {\includegraphics[width=80mm]{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/NPP_animations_August2017/M6_5_s500_BASIN_STOCHASTIC_mag_SLOW.jpg}}
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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 soilstructure
system
\end{itemize}
\vspace*{3mm}
\begin{figure}[!H]
\begin{center}
\includegraphics[width=6.5cm]{/home/jeremic/tex/works/Conferences/2015/CompDyn/Present/6D_to_1D_01.jpg}
\end{center}
\end{figure}
\end{frame}
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\begin{frame}
\frametitle{6C Free Field Motions (closeup)}
%\vspace*{2mm}
\begin{center}
\movie[label=show3,width=80mm,poster,showcontrols]
{\includegraphics[width=80mm]{/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_input_closeup_mp4_icon.jpeg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input_closeup.mp4}
\end{center}
\begin{flushleft}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input_closeup.mp4}
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\begin{frame}
\frametitle{1C vs 6C Free Field Motions}
\begin{itemize}
\item One component of motions, 1C from 6C
% or 3$\times$1D (it is done all the time!)
\item Excellent fit
% (goal is to predict and inform and not (force) fit)
\end{itemize}
% local
%\vspace*{2mm}
\begin{center}
\hspace*{16mm}
%\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
\movie[label=show3,width=61mm,poster, showcontrols]
{\includegraphics[width=60mm]{/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_ff_3d_mp4_icon.jpeg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_ff_3d.mp4}
%\hspace*{2mm}
%\hfill
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{\includegraphics[width=60mm]
{/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_ff_1d_mp4_icon.jpeg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_ff_1d.mp4}
\hspace*{16mm}
\end{center}
% local
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\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_3d.mp4}
{\tiny (MP4)}
%
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_1d.mp4}
{\tiny (MP4)}
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% \frametitle{1D vs 3$\times$1C vs 3C Seismic Motions}
%
%
% \begin{itemize}
%
% \vspace{2mm}
% \item 1D is required by the code
%
% \vspace{4mm}
% \item 3$\times$1D can be used depending on frequency/wave length of interest,
%
% \vspace{4mm}
% \item 3C is more realistic, however it is challenging to define motions in full 3C
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% \frametitle{When to use 3C and/or 3$\times$1C}
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% %
% %\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}
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\frametitle{6C vs 1C NPP ESSI Response Comparison}
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\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}
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% online
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%\vspace*{15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_2_npps.mp4}
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\begin{frame}
\frametitle{Stress Testing SSI Systems}
\begin{itemize}
\item Excite SSI system with a suite of seismic motions
\item Waves: P, SV, SH, Surface (Rayleigh, Love, etc.)
\item Variation in inclination, frequency, energy and duration
\item Try to "break" the system, shakeout strong and weak links
\end{itemize}
\vspace*{4mm}
\begin{figure}[!htb]
\begin{center}
\hspace*{5mm}
\includegraphics[width=6.5cm]{/home/jeremic/tex/works/Conferences/2018/BestPSHANI/Presentation/stress_test_Best_SHANI_May2018.jpg}
\end{center}
\end{figure}
\vspace*{5mm}
\begin{figure}[!htb]
\begin{center}
\hspace*{5mm}
%\includegraphics[width=4cm]{/home/jeremic/tex/works/consulting/2017/IAEA/TECDOC/Version_14Mar2017/1Dvs3x1Dvs3D_waves_02.pdf}
\includegraphics[width=7.5cm]{/home/jeremic/tex/works/Conferences/2018/WCCM2018/Present/1Dvs3x1Dvs3D_waves_03.pdf}
\hspace*{4mm}
\includegraphics[width=3.6cm]{/home/jeremic/tex/works/Conferences/2018/WCCM2018/Present/1Dvs3x1Dvs3D_waves_02.pdf}
\hspace*{5mm}
\end{center}
\end{figure}
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\frametitle{Stress Test Source Signals}
\begin{itemize}
% \item Gauss
% \begin{figure}[!hbpt]
% \begin{flushright}
% \vspace*{0.5cm}
% \includegraphics[width=7.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/gauss.png}
% \end{flushright}
% \end{figure}
\item Ricker
\begin{figure}[!hbpt]
\begin{flushright}
\vspace*{1cm}
\includegraphics[width=4.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ricker2nd.pdf}
\includegraphics[width=4.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ricker2nd_FFT.pdf}
\hspace*{0.7cm}
\end{flushright}
\end{figure}
\item Ormsby
\begin{figure}[!hbpt]
\begin{flushright}
\vspace*{1cm}
\includegraphics[width=4.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ormsby.pdf}
\includegraphics[width=4.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ormsby_FFT.pdf}
\hspace*{0.7cm}
\end{flushright}
\end{figure}
\end{itemize}
% \begin{figure}[!hbpt]
% \begin{center}
% %
% \includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/gauss.png}
% %
% \includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ricker2nd.pdf}
% \includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ricker2nd_FFT.pdf}
% %
% \includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ormsby.pdf}
% \includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ormsby_FFT.pdf}
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%\subsection{Local Geology Effects}
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\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)}
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% online
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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}
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\subsection{Inelasticity, Plastic Energy Dissipation and Uncertainty}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Energy Input and Dissipation}
\begin{itemize}
\vspace*{1mm}
\item[] Energy input, static and dynamic forcing
\vspace*{4mm}
\item[] Energy dissipation outside SSI domain:
\begin{itemize}
\item SSI system oscillation radiation
\item Reflected wave radiation
\end{itemize}
\vspace*{1mm}
\item[] Energy dissipation/conversion inside SSI domain:
\begin{itemize}
\item Inelasticity of soil, contact zone, structure, foundation, dissipators
\item Viscous coupling with internal/pore fluids, and external fluids
% % \item[] potential and kinetic energy
% \item[] potential $\leftarrow \! \! \! \! \! \! \rightarrow$ kinetic energy
\end{itemize}
%\vspace*{1mm}
% \item[] Numerical energy dissipation (numerical damping/production and period errors)
% \item[] Numerical energy dissipation (damping/production)
%\vspace*{4mm}
\item[] Numerical energy dissipation/production
\end{itemize}
%
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Energy Dissipation in NPP Model}
% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy
% \vspace*{5mm}
\begin{center}
% \hspace*{15mm}
\movie[label=show3,width=10cm,poster,autostart,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/tex/works/Conferences/2017/SMiRT_24/present/3D_Nonlinear_Modeling_and_it_Effects/NPP_Plastic_Dissipation_grab.jpg}}
{/home/jeremic/tex/works/Thesis/HanYang/Files_10Aug2017/NPP_Plastic_Dissipation.mp4}
\end{center}
\begin{flushleft}
\vspace*{15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/NPP_Plastic_Dissipation.mp4}
% \href{./homo_50mmesh_45degree_Ormsby.mp4}
{\tiny (MP4)}
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\begin{frame}
\frametitle{Energy Dissipation for an SMR Model}
% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy
% \vspace*{5mm}
\begin{center}
% \hspace*{15mm}
\movie[label=show3,width=10cm,poster,autostart,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation_screen_grab.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation.mp4}
\end{center}
\begin{flushleft}
\vspace*{15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation.mp4}
% \href{./homo_50mmesh_45degree_Ormsby.mp4}
{\tiny (MP4)}
\end{flushleft}
%
% \vspace*{5mm}
\end{frame}
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\begin{frame}
\frametitle{Wall, Regular and ASR Concrete}
\vspace{1mm}
\begin{figure}[!h]
\begin{center}
\includegraphics[width=4truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/Rebar_Plan.pdf}
\includegraphics[width=6truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/3D_mesh.pdf}
\end{center}
\end{figure}
\begin{figure}[!h]
\begin{center}
\includegraphics[width=2.7truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/Reg_A_Force_Displacement.pdf}
\includegraphics[width=2.7truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/ASR_A1_Force_Displacement.pdf}
%
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_Natural_Hazartd_Oct2018/Present/OECD_wall_damage_3_stages.jpg}
\end{center}
\end{figure}
\vspace{4mm}
%
%\vspace{2mm}
%\begin{figure}[!htbp]
%\begin{center}
%\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_Natural_Hazartd_Oct2018/Present/OECD_wall_damage_3_stages.jpg}
%\end{center}
%\end{figure}
\vspace{2mm}
% \vspace{20mm}
% \begin{figure}[!htbp]
% \hspace*{10mm}
% \begin{center}
% \includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/Damage_3000.pdf}
% \hspace*{5mm}
% \includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/Damage_5000.pdf}
% \hspace*{5mm}
% \includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/Damage_10000.pdf}
% \end{center}
% \end{figure}
%
%
% \vspace*{5mm}
% \hspace*{12mm}
% \begin{footnotesize}
% $u_y$ = 1.4 mm
% \hspace{12mm}
% $u_y$ = 1.8 mm
% \hspace{12mm}
% $u_y$ = 3.0 mm
% \end{footnotesize}
\end{frame}
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%
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\begin{frame}
\frametitle{RealESSI 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/Figurefiles/nonlinear_analysis_steps/soilstructure/overview.png}
\vspace*{1mm}
\\
\includegraphics[width = 0.35cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figurefiles/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/Figurefiles/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/Figurefiles/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/Figurefiles/nonlinear_analysis_steps/soilfoundation/soil_foundation.png}
% \includegraphics[width = 3cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figurefiles/nonlinear_analysis_steps/soilfoundation/slice.png}
\includegraphics[width = 2.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figurefiles/nonlinear_analysis_steps/soilfoundation/foundation_results.png}
% \includegraphics[width = 3cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figurefiles/nonlinear_analysis_steps/soilstructure/overview.png}
\\
\vspace*{3mm}
\includegraphics[width = 1.0cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figurefiles/nonlinear_analysis_steps/structure/eigen/structureonly.png}
\hfill
\includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figurefiles/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/Figurefiles/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/Figurefiles/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/Figurefiles/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/Figurefiles/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/Figurefiles/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/Figurefiles/nonlinear_analysis_steps/structure/imposed_motion/structureonly.png}
%\hfill
\includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figurefiles/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/Figurefiles/nonlinear_analysis_steps/soilstructure/overview.png}
\\
\vspace*{1mm}
\includegraphics[width = 6cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figurefiles/nonlinear_analysis_steps/soilstructure/DRM3D_motion3D_structure.png}
\end{center}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Uncertainty Propagation through
Inelastic System}
%
\begin{itemize}
\item Incremental elpl constitutive equation
%
\begin{eqnarray}
\nonumber
\Delta \sigma_{ij}
=
% E^{EP}_{ijkl}
E^{EP}_{ijkl} \; \Delta \epsilon_{kl}
=
\left[
E^{el}_{ijkl}

\frac{\displaystyle E^{el}_{ijmn} m_{mn} n_{pq} E^{el}_{pqkl}}
{\displaystyle n_{rs} E^{el}_{rstu} m_{tu}  \xi_* h_*}
\right]
\Delta \epsilon_{kl}
\end{eqnarray}
\vspace*{2mm}
\item Dynamic Finite Elements
%
\begin{equation}
{ M} \ddot{ u_i} +
{ C} \dot{ u_i} +
{ K}^{ep} { u_i} =
{ F(t)}
\nonumber
\end{equation}
\vspace*{2mm}
\item Material and load parameters are uncertain
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Probabilistic ElasticPlastic Response}
\begin{figure}[!hbpt]
\begin{center}
%\includegraphics[width=8cm]{/home/jeremic/tex/works/Papers/2007/ProbabilisticYielding/figures/vonMises_G_and_cu_very_uncertain/Contour_PDFedited.pdf}
\includegraphics[width=8cm]{/home/jeremic/tex/works/Conferences/2012/DOELLNLworkshop2728Feb2012/ProbabilisticYielding_vonMises_G_and_cu_very_uncertain_Contour_PDFedited.pdf}
\end{center}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{Previous Work}
%
%
%
% \begin{itemize}
%
% \item
% Linear algebraic or differential equations:
%
% \begin{itemize}
% \item Variable Transf. Method (Montgomery and Runger 2003)
% \item Cumulant Expansion Method (Gardiner 2004)
% \end{itemize}
%
% \item
% Nonlinear differential equations:
%
% \begin{itemize}
%
% \item Monte Carlo Simulation (Schueller 1997, De Lima et al 2001, Mellah
% et al. 2000, Griffiths et al. 2005...) \\ $\rightarrow$ can be accurate, very costly
%
% \item Perturbation Method (Anders and Hori 2000, Kleiber and Hien 1992,
% Matthies et al. 1997) \\ $\rightarrow$ first and second order Taylor series
% expansion about mean  limited to problems with small C.O.V. and inherits
% "closure problem"
%
% \item SFEM (Matthies et al, 2004, 2005, 2014...)
%
%
% \end{itemize}
%
% %
% % \item
% % Monte Carlo method: accurate, very costly
% %
% % \item
% % Perturbation method:
%
% \end{itemize}
%
%
%
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \end{frame}
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame} \frametitle{{3D FPK Equation}}
%
% \begin{footnotesize}
%
% \begin{eqnarray}
% \nonumber
% \lefteqn{\displaystyle \frac{\partial P(\sigma_{ij}(x_t,t), t)}{\partial t} = \displaystyle \frac{\partial}{\partial \sigma_{mn}}
% \left[ \left\{\left< \vphantom{\int_{0}^{t}} \eta_{mn}(\sigma_{mn}(x_t,t), D_{mnrs}(x_t), \epsilon_{rs}(x_t,t))\right> \right. \right.} \\
% \nonumber
% &+& \left. \left. \int_{0}^{t} d\tau Cov_0 \left[\displaystyle \frac{\partial \eta_{mn}(\sigma_{mn}(x_t,t), D_{mnrs}(x_t),
% \epsilon_{rs}(x_t,t))} {\partial \sigma_{ab}}; \right. \right. \right. \\
% \nonumber
% & & \left. \left. \left. \eta_{ab} (\sigma_{ab}(x_{t\tau}, t\tau), D_{abcd}(x_{t\tau}), \epsilon_{cd}(x_{t\tau}, t\tau)
% \vphantom{\int_{0}^{t}} \right] \right \} P(\sigma_{ij}(x_t,t),t) \right] \\
% \nonumber
% &+& \displaystyle \frac{\partial^2}{\partial \sigma_{mn} \partial \sigma_{ab}} \left[ \left\{ \int_{0}^{t} d\tau Cov_0 \left[
% \vphantom{\int_{0}^{t}} \eta_{mn}(\sigma_{mn}(x_t,t), D_{mnrs}(x_t), \epsilon_{rs}(x_t,t)); \right. \right. \right. \\
% \nonumber
% & & \left. \left. \left. \eta_{ab} (\sigma_{ab}(x_{t\tau}, t\tau), D_{abcd}(x_{t\tau}), \epsilon_{cd}(x_{t\tau}, t\tau))
% \vphantom{\int_{0}^{t}} \right] \vphantom{\int_{0}^{t}} \right\} P(\sigma_{ij}(x_t,t),t) \right]
% \end{eqnarray}
%
%
% \end{footnotesize}
%
%
%
% % \begin{itemize}
% %
% %
% %
% % \item 6 equations
% %
% % \item Complete description of 3D probabilistic stressstrain response
% %
% % \end{itemize}
% %
% %
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \end{frame}
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{FPK Equation}
%
%
%
% \begin{itemize}
%
% \item Advectiondiffusion equation
% %
% \begin{equation}
% \nonumber
% \frac{\partial P(\sigma,t)}{\partial t} = \frac{\partial}{\partial \sigma}\left[N_{(1)}P(\sigma,t)\frac{\partial}{\partial \sigma}
% \left\{N_{(2)} P(\sigma,t)\right\} \right]
% \end{equation}
%
% %
%
% \item Complete probabilistic description of response
%
%
% \item Solution PDF is secondorder exact to covariance of time (exact mean and variance)
%
%
% \item It is deterministic equation in probability density space
%
% \item It is linear PDE in probability density space
% $\rightarrow$ simplifies the numerical solution process
%
% %\vspace*{0.2truecm}
%
% \end{itemize}
%
% %
% % \vspace*{0.5cm}
% % {%
% % \begin{beamercolorbox}{section in head/foot}
% % \usebeamerfont{framesubtitle}\tiny{B. Jeremi\'{c}, K. Sett, and M. L. Kavvas, "Probabilistic
% % ElastoPlasticity: Formulation in 1D", \textit{Acta Geotechnica}, Vol. 2, No. 3, 2007, In press (published
% % online in the \textit{Online First} section)}
% % %\vskip2pt\insertnavigation{\paperwidth}\vskip2pt
% % \end{beamercolorbox}%
% % }
%
%
%
% \end{frame}
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
%
%
% \frametitle{Template Solution of FPK Equation}
%
%
%
% \begin{itemize}
%
%
%
%
% \item FPK diffusionadvection equation is applicable to any material model $\rightarrow$
% only the coefficients $N_{(1)}$ and $N_{(2)}$ are different for different material models
% % %
% % %
% % %
% % %\begin{normalsize}
% % \begin{equation}
% % \nonumber
% % \frac{\partial P(\sigma,t)}{\partial t} = \frac{\partial}{\partial \sigma}\left[N_{(1)}P(\sigma,t)\frac{\partial}{\partial \sigma}
% % \left\{N_{(2)} P(\sigma,t)\right\} \right]
% % %\nonumber
% % = \frac{\partial \zeta}{\partial \sigma}
% % \end{equation}
% % %\end{normalsize}
%
% %
%
% \item Initial condition
%
% \begin{itemize}
%
% \item Deterministic $\rightarrow$ Dirac delta function $\rightarrow$ $ P(\sigma,0)=\delta(\sigma) $
%
% \item Random $\rightarrow$ Any given distribution
%
% \end{itemize}
%
% \item Boundary condition: Reflecting BC $\rightarrow$ conserves probability mass
% $\zeta(\sigma,t)_{At \ Boundaries}=0$
%
% \item Solve using finite differences and/or finite elements
%
%
% \item However (!!) it is a stress solution and probabilistic stiffness is an
% approximation!
%
% \end{itemize}
%
%
% \end{frame}
%
%
%
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Direct Solution for Probabilistic Stiffness and Stress in 1D}
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%% BEGGINING PEP %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
% \begin{frame}{Direct Probabilistic Constitutive Modeling in 1D}
%
%
% % \begin{itemize}
% %
% % \vspace{0.5cm}
% %
% % \item<1> Probabilistic constitutive modeling : \vspace{0.5cm}
%
% \begin{itemize}
%
%
% \item Zero elastic region elastoplasticity with stochastic ArmstrongFrederick
% kinematic hardening
%
% $ \Delta\sigma =\ H_a \Delta \epsilon  c_r \sigma \Delta \epsilon ;
% \hspace{0.5cm}
% E_t = {d\sigma}/{d\epsilon} = H_a \pm c_r \sigma $
%
% \vspace*{2mm}
% \item Uncertain:
% init. stiff. $H_a$,
% shear strength $H_a/c_r$,
% strain $\Delta \epsilon$:
%
% $ H_a = \Sigma h_i \Phi_i; \;\;\;
% C_r = \Sigma c_i \Phi_i; \;\;\;
% \Delta\epsilon = \Sigma \Delta\epsilon_i \Phi_i $
%
%
%
% \vspace*{2mm}
% \item Resulting stress and stiffness are also uncertain
%
% % 
% %  $ \sum_{l=1}^{P_{\sigma}} \Delta\sigma_i \Phi_i = \sum_{i=1}^{P_h} \sum_{k=1}^{P_e}\ h_i \Delta \epsilon_k \Phi_i \Phi_k  \sum_{j=1}^{P_g} \sum_{k=1}^{P_e}\sum_{l=1}^{P_{\sigma}} \ c_i \Delta \epsilon_k \sigma_l \Phi_j \Phi_k \Phi_l$
% % 
% %  $ \sum_{l=1}^{P_{E_t}} \Delta E_{t_i} \Phi_i = \sum_{i=1}^{P_h} h_i \Phi_i \pm \sum_{i=1}^{P_c} \sum_{l=1}^{P_{\sigma}} \ c_i \sigma_l \Phi_i \Phi_l$
% % 
%
%
% \end{itemize}
%
%
% % \vspace{0.5cm}
%
%
%
% % \vspace{1cm}
%
% %\item<1> Time integration is done via Newmark algorithm
%
% %
% % \end{itemize}
% %
% \end{frame}
%
%
% % % % % % % % % % % % % % % % %
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}{Probabilistic Stiffness Solution}
%
% \begin{itemize}
%
%
% \item Analytic product for all the components,
%
% $ E^{EP}_{ijkl}
% =
% \left[
% E^{el}_{ijkl}
% 
% \frac{\displaystyle E^{el}_{ijmn} m_{mn} n_{pq} E^{el}_{pqkl}}
% {\displaystyle n_{rs} E^{el}_{rstu} m_{tu}  \xi_* h_*}
% \right]
% $
%
%
%
%
% \item Stiffness: each Polynomial Chaos component is updated incrementally
% % at each Gauss Point via stochastic Galerkin projection
%
%
%
% \small{$E_{t_1}^{n+1} = \frac{1}{<\Phi_1\Phi_1> }\{\sum_{i=1}^{P_h} \ h_i <\Phi_i \Phi_1> \pm \sum_{j=1}^{P_c} \sum_{l=1}^{P_{\sigma}} \ c_j \sigma_l^{n+1} <\Phi_j \Phi_l \Phi_1>\}$}
%
% $\large{\vdots}$
%
% \small{$E_{t_P}^{n+1} = \frac{1}{<\Phi_1\Phi_P> }\{\sum_{i=1}^{P_h} \ h_i <\Phi_i \Phi_P> \pm \sum_{j=1}^{P_c} \sum_{l=1}^{P_{\sigma}} \ c_j \sigma_l^{n+1} <\Phi_j \Phi_l \Phi_P>\}$}
%
%
% \item Total stiffness is :
%
% $ E_{t}^{n+1} = \sum_{l=1}^{P_{E}} E_{t_i}^{n+1} \Phi_i $
%
%
%
%
% \end{itemize}
%
%
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}{Probabilistic Stress Solution}
%
% \begin{itemize}
%
%
%
% \item Analytic product, for each stress component,
%
% $ \Delta \sigma_{ij} = E^{EP}_{ijkl} \; \Delta \epsilon_{kl} $
% % =
% % \left[
% % E^{el}_{ijkl}
% % 
% % \frac{\displaystyle E^{el}_{ijmn} m_{mn} n_{pq} E^{el}_{pqkl}}
% % {\displaystyle n_{rs} E^{el}_{rstu} m_{tu}  \xi_* h_*}
% % \right]
% % \Delta \epsilon_{kl}
% %
%
%
% \vspace*{1mm}
% \item Incremental stress: each Polynomial Chaos component is updated
% incrementally
% % via stochastic Galerkin projection
%
%
%
%
% {$\Delta\sigma_1^{n+1} = \frac{1}{<\Phi_1\Phi_1> }\{\sum_{i=1}^{P_h} \sum_{k=1}^{P_e}\ h_i \Delta \epsilon_k^n <\Phi_i \Phi_k \Phi_1> \sum_{j=1}^{P_g} \sum_{k=1}^{P_e}\sum_{l=1}^{P_{\sigma}} \ c_j \Delta \epsilon_k^n \sigma_l^n <\Phi_j \Phi_k \Phi_l \Phi_1>\}$}
%
% ${\vdots}$
%
% {$\Delta\sigma_P^{n+1} = \frac{1}{<\Phi_P\Phi_P> }\{\sum_{i=1}^{P_h} \sum_{k=1}^{P_e}\ h_i \Delta \epsilon_k^n <\Phi_i \Phi_k \Phi_P> \sum_{j=1}^{P_g} \sum_{k=1}^{P_e}\sum_{l=1}^{P_{\sigma}} \ c_j \Delta \epsilon_k^n \sigma_l^n <\Phi_j \Phi_k \Phi_l \Phi_P>\}$}
%
%
% \vspace*{1mm}
% \item Stress update:
%
% $ \sum_{l=1}^{P_{\sigma}} \sigma_i^{n+1} \Phi_i = \sum_{l=1}^{P_{\sigma}} \sigma_i^{n} \Phi_i + \sum_{l=1}^{P_{\sigma}} \Delta\sigma_i^{n+1} \Phi_i$
%
%
%
% \end{itemize}
%
% \end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Probabilistic ElasticPlastic Modeling}
% % \vspace*{5mm}
% \begin{center}
% % \hspace*{15mm}
% \movie[label=show3,width=7cm,poster,autostart,showcontrols]
% {\includegraphics[width=7cm]
% {/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/NPP_Plastic_Dissipation_Density.png}}
% %{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/NPP_without_Contact_vonMises.mp4}
% {NPP_without_Contact_vonMises.mp4}
% \end{center}
%\vspace*{5mm}
\begin{center}
% \hspace*{15mm}
\movie[label=show3,width=9cm,poster,autostart,showcontrols]
{\includegraphics[width=9cm]
{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_PEP_25.png}}
% /home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_PEP_25.pdf
%{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Animations/PEP_Animation.mp4}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Probabilistic_Elasto_Plasticity_and_Stochastic_Elastic_Plastic_Finite_Element_Method/PEP_Animation.mp4}
\end{center}
%
% \includegraphics[width = 12cm]{./img/figure_PEP_25.pdf}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Stochastic ElasticPlastic Finite Element Method}
\begin{itemize}
\item Material uncertainty expanded into stochastic shape funcs.
%$E(x,t,\theta) = \sum_{i=0}^{P_d} r_i(x,t) * \Phi_i[\{\xi_1, ..., \xi_m\}]$
\vspace*{1mm}
\item Loading uncertainty expanded into stochastic shape funcs.
%$f(x,t,\theta) = \sum_{i=0}^{P_f} f_i(x,t) * \zeta_i[\{\xi_{m+1}, ..., \xi_f]$
\vspace*{1mm}
\item Displacement expanded into stochastic shape funcs.
%$u(x,t,\theta) = \sum_{i=0}^{P_u} u_i(x,t) * \Psi_i[\{\xi_1, ..., \xi_m, \xi_{m+1}, ..., \xi_f\}]$
%\item
%Stochastic system of equation resulting from Galerkin approach (static example):
%
%\item Time domain integration using Newmark and/or HHT, in probabilistic spaces
\end{itemize}
\begin{tiny}
\[
%$
\begin{bmatrix}
\sum_{k=0}^{P_d} <\Phi_k \Psi_0 \Psi_0> K^{(k)} & \dots & \sum_{k=0}^{P_d} <\Phi_k \Psi_P \Psi_0> K^{(k)}\\
\sum_{k=0}^{P_d} <\Phi_k \Psi_0 \Psi_1> K^{(k)} & \dots & \sum_{k=0}^{P_d} <\Phi_k \Psi_P \Psi_1> K^{(k)}\\ \\
\vdots & \vdots & \vdots & \vdots\\
\sum_{k=0}^{P_d} <\Phi_k \Psi_0 \Psi_P> K^{(k)} & \dots & \sum_{k=0}^{M} <\Phi_k \Psi_P \Psi_P> K^{(k)}
\end{bmatrix}
\begin{bmatrix}
\Delta u_{10} \\
\vdots \\
\Delta u_{N0}\\
\vdots \\
\Delta u_{1P_u}\\
\vdots \\
\Delta u_{NP_u}
\end{bmatrix}
=
%\]
%\[
\begin{bmatrix}
\sum_{i=0}^{P_f} f_i <\Psi_0\zeta_i> \\
\sum_{i=0}^{P_f} f_i <\Psi_1\zeta_i> \\
\sum_{i=0}^{P_f} f_i <\Psi_2\zeta_i> \\
\vdots \\
\sum_{i=0}^{P_f} f_i <\Psi_{P_u}\zeta_i>\\
\end{bmatrix}
%$
\]
\end{tiny}
\end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \begin{frame}
% \frametitle{SEPFEM: System Size}
%
% \begin{itemize}
%
% \item SEPFEM offers a complete solution (single step)
%
% \item It is NOT based on Monte Carlo approach
%
% \item System of equations does grow (!)
%
% \end{itemize}
%
%
% % \normalsize{Typical number of terms required for a SEPFEM problem} \vspace{1cm}\\
% \scalebox{0.7}{
% \begin{tabular}{ c c c c}
% \# KL terms material & \# KL terms load & PC order displacement& Total \# terms per DoF\\ \hline
% 4 & 4 & 10 & 43758 \\
% 4 & 4 & 20 & 3 108 105 \\
% 4 & 4 & 30 & 48 903 492 \\
% 6 & 6 & 10 & 646 646 \\
% 6 & 6 & 20 & 225 792 840 \\
% 6 & 6 & 30 & 1.1058 $10^{10}$ \\
% 8 & 8 & 10 & 5 311 735 \\
% 8 & 8 & 20 & 7.3079 $10^{9}$ \\
% 8 & 8 & 30 & 9.9149 $10^{11}$\\
%
% ... & ... & ... & ...\\
% % \hline
% \end{tabular}}
%
%
% \end{frame}
%
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{SEPFEM: Example in 1D}
\vspace*{2mm}
\begin{center}
% \hspace*{15mm}
\movie[label=show3,width=9cm,poster,autostart,showcontrols]
{\includegraphics[width=9cm]{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_elastic_900.png}}
% /home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_PEP_25.pdf
%{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Animations/SEPFEM_Animation_Elastic.mp4}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Probabilistic_Elasto_Plasticity_and_Stochastic_Elastic_Plastic_Finite_Element_Method/SEPFEM_Animation_Elastic.mp4}
\end{center}
% \includegraphics[width = 12cm]{./img/figure_elastic_900.pdf}
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{Energy Dissipation}
%
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\section{Pine Flat Dam}
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\subsection{Pine Flat Dam Test Model}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Repeat of Simulations}
%
% \begin{itemize}
%
% \vspace*{1mm}
% \item[]
%
%
%
% \end{itemize}
%
% %
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Pine Flats Dam, Model}
\begin{itemize}
%\vspace*{1mm}
\item Material properties provided
\item Motions applied through DRM, from bottom
\item Energy dissipation, Viscous, Numerical, Radiation
\item Load cases as provided
% \item
\end{itemize}
\vspace*{5mm}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{8mm}
\includegraphics[width=12.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Model_Mesh_No_Reservior.pdf}
%
\end{center}
\end{figure}
%
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Pine Flats Dam, Static, Displacements}
\begin{itemize}
%\vspace*{1mm}
\item Self weight
\item Water pressure, on dam side and lake bottom
\end{itemize}
\begin{small}
%
\begin{table}[!htb]
\centering
\begin{tabular}{cccccc}
%\hline
& & \multicolumn{3}{c}{Disp. [m]} & Disp. [in] \\ \hline
& & Top & Heel & Rel. & Rel. \\ \hline
Mat. Prop. I & Hor. & 0.0121 & 0.0031 & 0.00900 & 0.354 \\ \cline{26}
(Soft Found.) & Vert. & 0.0095 & 0.0059 & 0.00348 & 0.137 \\ \hline
Mat. Prop, II & Hor. & 0.0101 & 0.0011 & 0.00904 & 0.356 \\ \cline{26}
(Stiff Found.) & Vert. & 0.0048 & 0.0019 & 0.00298 & 0.117 \\
%\hline
\end{tabular}
\end{table}
\end{small}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Static, Displacements and \huge{$\sigma_v$}}
% \begin{itemize}
% %\vspace*{1mm}
% \item Displacements
% \item Vertical stress distribution
% \end{itemize}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{7mm}
\includegraphics[width=12.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Case_A_Vertical_Stress.png}
%
\end{center}
\end{figure}
%
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Mesh Refinement Effects}
%\begin{itemize}
%%\vspace*{1mm}
% \item Material properties provided
%\end{itemize}
%
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{5mm}
\includegraphics[width=11.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Model_Refined_Mesh.pdf}
%
\end{center}
\end{figure}
%
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Mesh Refinement Effects}
%\begin{itemize}
%%\vspace*{1mm}
% \item Meshing effects are small
%\end{itemize}
%
% \begin{figure}[!hbpt]
% \begin{center}
% %
% %\hspace*{5mm}
% \includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/}
% %
% \end{center}
% \end{figure}
%
\begin{table}[!htb]
\centering
\begin{tabular}{ccccc}
%\hline
& & \multicolumn{3}{c}{Displacements [m]} \\
%\hline
& & Original & Refined & Difference \\ \hline
\multirow{2}{*}{Dam Top} & Horizontal & 0.012121 & 0.012201 & 0.66\% \\ \cline{25}
& Vertical & 0.009463 & 0.009794 & 3.51\% \\ \hline
\multirow{2}{*}{Dam Heel} & Horizontal & 0.003124 & 0.003287 & 5.21\% \\ \cline{25}
& Vertical & 0.005981 & 0.006953 & 16.25\% \\ \hline
\multirow{2}{*}{Relative} & Horizontal & 0.008996 & 0.009064 & 0.76\% \\ \cline{25}
& Vertical & 0.003481 & 0.003489 & 0.23\% \\
% \hline
\end{tabular}
\end{table}
%
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Eigen Analysis, Dry}
\begin{itemize}
%\vspace*{1mm}
\item Eigen frequencies: \\
(a) 2.46945~Hz,
(b) 3.82403~Hz,
(c) 4.48795~Hz, \\
(d) 5.25455~Hz,
(e) 5.32023~Hz,
(f) 5.60061~Hz,
\end{itemize}
% \begin{table}[!htb]
% \centering
% \begin{tabular}{cc}
% %\hline
% Mode & Natural Frequency (Hz) \\ \hline
% 1 & 2.46945 \\ \hline
% 2 & 3.82403 \\ \hline
% 3 & 4.48795 \\ \hline
% 4 & 5.25455 \\ \hline
% 5 & 5.32023 \\ \hline
% 6 & 5.60061 \\
% %\hline
% \end{tabular}
% \end{table}
%
%
\begin{figure}[!htbp]
\centering
\subfloat[]{\includegraphics[width=3.5cm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/mode1.pdf}}
\subfloat[]{\includegraphics[width=3.5cm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/mode2.pdf}}
\subfloat[]{\includegraphics[width=3.5cm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/mode3.pdf}}
\\
\subfloat[]{\includegraphics[width=3.5cm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/mode4.pdf}}
\subfloat[]{\includegraphics[width=3.5cm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/mode5.pdf}}
\subfloat[]{\includegraphics[width=3.5cm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/mode6.pdf}}
%\caption{\label{figure_case_d1_modal_shapes}
%Modal shapes: (a) First mode; (b) Second mode; (c) Third mode; (d) Fourth mode; (e) Fifth mode; (f) Sixth mode.}
\end{figure}
%
% \begin{figure}[!hbpt]
% \begin{center}
% %
% %\hspace*{5mm}
% \includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/}
% %
% \end{center}
% \end{figure}
%
%
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Taft Earthquake, Time History of \huge{$\sigma_v$}}
\begin{itemize}
%\vspace*{1mm}
\item Vertical stress at dam heel, there is a tension!
\end{itemize}
\begin{figure}[!hbpt]
\begin{center}
%
%\hspace*{5mm}
\includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Heel_Vertical_Stress_IU.pdf}
%
\end{center}
\end{figure}
%
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Taft Earthquake, {\huge $\sigma_v$} Distribution at
{\huge $\sigma_{min}$} and {\huge $\sigma_{max}$}}
%\begin{itemize}
%%\vspace*{1mm}
% \item Vertical stress at max tension and max compression
%\end{itemize}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{5mm}
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Max_IU.pdf}
\hfill
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Min_IU.pdf}
\hspace*{5mm}
%\\
%\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Max_US.pdf}
%\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Min_US.pdf}
%
\end{center}
\end{figure}
%
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{D2, Taft Earthquake, Dam and the Reservoir}
\begin{itemize}
%\vspace*{1mm}
\item Pressures: total at the heel, total at the upstream face, hydrodynamic at the upstream face
\end{itemize}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{5mm}
\includegraphics[width=3.4truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Pressure_heel_time_series.pdf}
%\hfill
\includegraphics[width=3.4truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Pressure_distribution_upstream_surface.pdf}
%\hfill
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Pressure_dynamic_distribution_upstream_surface.pdf}
\hspace*{5mm}
%\\
%\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Max_US.pdf}
%\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Min_US.pdf}
%
%
\end{center}
\end{figure}
%
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{D2, Tafts Earthquake, Dam and the Reservoir}
\begin{itemize}
%\vspace*{1mm}
\item Vertical stress: heel time series, along base for max stress at the heel, for min stress at the heel
\end{itemize}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{5mm}
\includegraphics[width=3.5truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Heel_Vertical_Stress_US_D2_taft.pdf}
\hfill
\includegraphics[width=3.5truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Max_IU_D2_taft.pdf}
\hfill
\includegraphics[width=3.5truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Min_IU_D2_taft.pdf}
\hspace*{5mm}
%\\
%\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Max_US.pdf}
%\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Min_US.pdf}
%
\end{center}
\end{figure}
%
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{D2, ETAF Earthquake, Dam and the Reservoir}
\begin{itemize}
%\vspace*{1mm}
\item Pressures: total at the heel, total at the upstream face, hydrodynamic at the upstream face
\end{itemize}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{5mm}
\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Pressure_heel_time_series_ETAF.pdf}
\hfill
\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Pressure_distribution_upstream_surface_ETAF.pdf}
\hfill
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Pressure_dynamic_distribution_upstream_surface_ETAF.pdf}
\hspace*{5mm}
%\\
%\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Max_US.pdf}
%\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Min_US.pdf}
%
\end{center}
\end{figure}
%
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{D2, ETAF Earthquake, Dam and the Reservoir}
\begin{itemize}
%\vspace*{1mm}
\item Vertical stress: heel time series, along base for max stress at the heel, for min stress at the heel
\end{itemize}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{5mm}
\includegraphics[width=3.5truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Heel_Vertical_Stress_US_D2_ETAF.pdf}
\hfill
\includegraphics[width=3.5truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Max_IU_D2_ETAF.pdf}
\hfill
\includegraphics[width=3.5truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Min_IU_D2_ETAF.pdf}
\hspace*{5mm}
%\\
%\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Max_US.pdf}
%\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Min_US.pdf}
%
\end{center}
\end{figure}
%
\end{frame}
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\subsection{Pine Flat Dam, Additional Modeling and Simulation}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Numerical Damping Effects, Elastic
{\Large $\ddot{u}_{hor}^{top}$},
{\Large ${\sigma}_{v}^{heel}$}}
%\begin{itemize}
%%\vspace*{1mm}
% \item Vertical stress at max tension and max compression
%\end{itemize}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{5mm}
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Top_Horizontal_Acceleration_IU.pdf}
\hfill
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Different_NP_Heel_Vertical_Stress_IU.pdf}
\hspace*{5mm}
%\\
%\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Max_US.pdf}
%\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Min_US.pdf}
%
\end{center}
\end{figure}
%
\end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Numerical Damping Effects, Inelastic
{\Large $\ddot{u}_{hor}^{top}$},
{\Large ${\sigma}_{v}^{heel}$}}
%\begin{itemize}
%%\vspace*{1mm}
% \item Vertical stress at max tension and max compression
%\end{itemize}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{5mm}
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Case_D3_Different_NP_Top_Horizontal_Acceleration_IU.pdf}
\hfill
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Case_D3_Different_NP_Heel_Vertical_Stress_IU.pdf}
\hspace*{5mm}
%\\
%\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Max_US.pdf}
%\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Min_US.pdf}
%
\end{center}
\end{figure}
%
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Pine Flat Dam, Dynamic Response with Reservoir}
%\vspace*{5mm}
\begin{center}
% \hspace*{15mm}
\movie[label=show3,width=9cm,poster,autostart,showcontrols]
{\includegraphics[width=8cm]
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/soil_fluid_interaction_dam.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/soil_fluid_interaction_dam.mp4}
\end{center}
\begin{flushleft}
\vspace*{15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/soil_fluid_interaction_dam.mp4}
% \href{./homo_50mmesh_45degree_Ormsby.mp4}
{\tiny (MP4)}
\end{flushleft}
%
\end{frame}
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\begin{frame}
\frametitle{Pine Flat Dam, Hydrodynamic Pressure}
%\vspace*{5mm}
\begin{center}
% \hspace*{15mm}
\movie[label=show3,width=10cm,poster,autostart,showcontrols]
{\includegraphics[width=10.0cm]
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/dynamic_pressure.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/dynamic_pressure.mp4}
\end{center}
\begin{flushleft}
\vspace*{15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/dynamic_pressure.mp4}
% \href{./homo_50mmesh_45degree_Ormsby.mp4}
{\tiny (MP4)}
\end{flushleft}
%
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Pine Flat Dam, Inelastic Interface, Hydrostatic}
%\vspace*{5mm}
\begin{center}
% \hspace*{15mm}
\movie[label=show3,width=10cm,poster,autostart,showcontrols]
{\includegraphics[width=10.0cm]
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/Case_D3_Gap_Open_more.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/Case_D3_Gap_Open_more.mp4}
\end{center}
\begin{flushleft}
\vspace*{15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/Case_D3_Gap_Open_more.mp4}
% \href{./homo_50mmesh_45degree_Ormsby.mp4}
{\tiny (MP4)}
\end{flushleft}
%
\end{frame}
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\begin{frame}
\frametitle{Pine Flat Dam, Dynamic Response, Inclined Plane Waves}
%\vspace*{5mm}
\begin{center}
% \hspace*{15mm}
\movie[label=show3,width=10cm,poster,autostart,showcontrols]
{\includegraphics[width=10.0cm]
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/dynamic_response_inclination.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/dynamic_response_inclination.mp4}
\end{center}
\begin{flushleft}
\vspace*{15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/dynamic_response_inclination.mp4}
% \href{./homo_50mmesh_45degree_Ormsby.mp4}
{\tiny (MP4)}
\end{flushleft}
%
\end{frame}
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\section{Conclusion}
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\subsection{RealESSI Simulator System}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{RealESSI Simulator System}
The RealESSI, Realistic
{\underline {\bf M}}odeling and
{\underline {\bf S}}imulation of
{\underline {\bf E}}arthquakes,
{\underline {\bf S}}oils,
{\underline {\bf S}}tructures and their
{\underline {\bf I}}nteraction. Simulator is a software, hardware and
documentation system for high fidelity, high performance, time domain,
nonlinear/inelastic, deterministic or probabilistic, 3D, finite element modeling
and simulation of:
\begin{itemize}
%\vspace*{1mm}
\item statics and dynamics of soil,
\vspace*{1mm}
\item statics and dynamics of rock,
\vspace*{1mm}
\item statics and dynamics of structures,
\vspace*{1mm}
\item statics of soilstructure systems, and
\vspace*{1mm}
\item dynamics of earthquakesoilstructure system interaction
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{RealESSI Simulator System}
\begin{itemize}
\item RealESSI System Components
\begin{itemize}
\item RealESSI Preprocessor (gmsh/gmESSI, X2ESSI)
\item RealESSI Program (local, remote, cloud)
\item RealESSI PostProcessor (Paraview, Python, Matlab)
\end{itemize}
\vspace*{1mm}
\item RealESSI System availability:
\begin{itemize}
%\vspace*{1mm}
\item Educational Institutions: Amazon Web Services (AWS), free
\item Government Agencies, National Labs: AWS GovCloud
\item Professional Practice: AWS, commercial
%\vspace*{1mm}
%%\vspace*{1mm}
% \item Sources available to collaborators
\end{itemize}
\vspace*{1mm}
\item Quality Management System, ASMENQA1, ISO90032018, Certification in progress
\vspace*{1mm}
\item RealESSI Short Courses (online, this Fall)
\vspace*{1mm}
\item System description and documentation at \url{http://realessi.info/}
% \vspace*{2mm}
% \item
%
\end{itemize}
\end{frame}
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%\subsection*{Summary}
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%
%
% \begin{frame}
%
% \frametitle{Science Quotes}
%
% \begin{itemize}
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% \item Max Planck:
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% \item Fran{\c c}oisMarie Arouet, Voltaire:
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% \item Niklaus Wirth:
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\begin{frame}
\frametitle{Summary}
\begin{itemize}
% \item Importance of using proper models correctly (verification,
% validation, level of sophistication)
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% \item Reduction of modeling uncertainty
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\item Numerical modeling to predict and inform, rather than fit
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% \item Change of demand due to inelastic effects
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% \item Reduction of dynamic motions
% \item Increase in deformations
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\item Sophisticated inelastic/nonlinear modeling and simulations need to be
done carefully and in phases
\vspace*{1mm}
\item Education and Training is the key!
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\item Collaborators: Feng, Yang, Behbehani, Sinha, Wang,
Pisan{\'o}, Abell, Tafazzoli, Jie, Preisig, Tasiopoulou, Watanabe, Cheng, Yang...
\vspace*{1mm}
\item Funding from and collaboration with the USDOE, USNRC, USNSF,
CNSCCCSN, UNIAEA, and Shimizu Corp. is greatly appreciated,
\vspace*{1mm}
\item {\large \url{http://realessi.info/}}
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