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\title[Modeling and Simulation Uncertainty]
{Modelling and Simulation Uncertainty}
%\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}}
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\author[Jeremi{\'c}] % (optional, use only with lots of authors)
%{Boris~Jeremi{\'c}}
{Boris Jeremi{\'c}}
%\institute[Computational Geomechanics Group \hspace*{0.3truecm}
\institute[\pgfuseimage{universitylogo}\hspace*{0.1truecm}\pgfuseimage{lbnllogo}] % (optional, but mostly needed)
%{ Professor, University of California, Davis\\
{ University of California, Davis\\
% and\\
% Faculty Scientist, Lawrence Berkeley National Laboratory, Berkeley }
Lawrence Berkeley National Laboratory, Berkeley }
%  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 Computational Mechanics Working Group \\
UC Davis, February 2016}
\subject{}
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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 seismic design of soil structure systems
\vspace*{1mm}
\item {E}arthquake {S}oil {S}tructure {I}nteraction
({ESSI}) in time and space, plays a major role in successes and failures
%\vspace*{0.1cm}
\vspace*{1mm}
\item Accurate following and directing (!) the flow of seismic energy in
ESSI system to optimize for
\begin{itemize}
\item Safety and
\item Economy
\end{itemize}
%\vspace*{0.1cm}
\vspace*{1mm}
\item Development of high fidelity numerical modeling and simulation tools
to analyze realistic ESSI behavior: \\
{Real ESSI} simulator
% ({\small aka}: {\cyrssDvanaest Stvarno Lako},
% { Muy F{\'a}cil},
% {Molto Facile},
% \raisebox{1.2mm}{\includegraphics[height=5mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/Real_ESSI_in_different_langauges/Real_ESSI_Chinese.jpeg}},
% \raisebox{1.2mm}{\includegraphics[height=5mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/Real_ESSI_in_different_langauges/Real_ESSI_Japanese.jpg}},
% {\greektext{Pragmatik'a E'ukolo}},
% \raisebox{1.2mm}{\includegraphics[height=5mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/Real_ESSI_in_different_langauges/Real_ESSI_Farsi.jpg}},
% {Tr{\`e}s Facile},
% {\cyrssDvanaest Vistinski Lesno}
% %{Wirklich Einfach}
% )
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{Predictive Capabilities}
% \frametitle{High Fidelity Modeling of SFS System:
% Verification, Validation and Prediction}
\begin{itemize}
\item {{ Verification} provides evidence that the model is solved
correctly.} Mathematics issue.
%\vspace*{0.1cm}
\vspace*{1mm}
\item {{ Validation} provides evidence that the correct model is
solved.} Physics issue.
%\vspace*{0.1cm}
\vspace*{1mm}
\item { Prediction under Uncertainty (!)}: use of computational model
to predict the state of SSI system under
conditions for which the computational model has not been validated.
\vspace*{1mm}
\item Modeling and Parametric Uncertainties
\vspace*{1mm}
\item Predictive capabilities with {low Kolmogorov Complexity}
\vspace*{1mm}
\item Modeling and simulation goal: \\
predict and inform, rather than (force) fit
%
\end{itemize}
\end{frame}
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\subsection{Uncertainties}
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\begin{frame}
\frametitle{Modeling Uncertainty}
\begin{itemize}
\item Simplified modeling: Features (important ?) are neglected (6D
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
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Parametric Uncertainty: Material Stiffness}
%\vspace*{3mm}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{7mm}
\includegraphics[width=7.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01Ed.pdf}
% \hfill
\includegraphics[width=5.0truecm]{/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}
% {\tiny
% Transformation of SPT $N$value: \\
% 1D Young's modulus, $E$ \\
% (cf. Phoon and Kulhawy (1999B))\\
% ~}
% \end{flushright}
%
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Parametric Uncertainty: Material Strength}
%
%
% \begin{figure}[!hbpt]
% \begin{center}
% %
% \hspace*{7mm}
% \includegraphics[width=6.50truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/ShearStrength_RawData_and_MeanTrendMod.pdf}
% \hspace*{7mm}
% % \hfill
% \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/ShearStrength_Histogram_PearsonIVFineTunedMod.pdf}
% %
% \end{center}
% \end{figure}
%
% % \vspace*{1.8cm}
% % %\hspace*{3.3cm}
% % \begin{flushright}
% % {\tiny
% % 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{Parametric Uncertainty: Material Properties}
\begin{figure}[!hbpt]
\begin{center}
% %
\hspace*{3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldPhiPdf.pdf}
\hspace*{3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldPhiCdf.pdf}
\hspace*{3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldSuPdf.pdf}
\hspace*{3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldSuCdf.pdf}
\\
%\vspace*{2mm}
\hspace*{2.5cm} \mbox{\tiny Field $\phi$} \hspace*{3.5cm} \mbox{\tiny Field $c_u$}
%\vspace*{45mm}
\hspace*{3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabPhiPdf.pdf}
\hspace*{3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabPhiCdf.pdf}
\hspace*{3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabSuPdf.pdf}
\hspace*{3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabSuCdf.pdf}
\\
%\vspace*{8mm}
\hspace*{2.5cm} \mbox{\tiny Lab $\phi$} \hspace*{3.5cm} \mbox{\tiny Lab $c_u$}
\end{center}
\end{figure}
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Realistic ESSI Modeling (Uncertainties)}
%
%
% \begin{itemize}
%
%
% \item Seismic Motions: 6D, inclined, body and surface waves
% (translations, rotations)
% %; Incoherency
%
% %\vspace*{3mm}
% \vspace*{1mm}
% \item Inelastic material: soil (dry, saturated), rock, concrete, steel
%
% \vspace*{1mm}
% \item Inelastic contact: foundationsoil, dry, saturated, slipgap
%
% \vspace*{1mm}
% \item Nonlinear buoyant forces
%
% \vspace*{1mm}
% \item Base Isolators, Dissipators
%
% \vspace*{1mm}
% \item Uncertain loading and material
%
% \vspace*{1mm}
% \item Verification and Validation $\Rightarrow$ Predictions
%
%
% \end{itemize}
%
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
%
%
%
%
%
%
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\subsection{Real ESSI Simulator}
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\begin{frame}
\frametitle{Real ESSI Simulator System}
\begin{itemize}
\item {\bf The Real ESSIProgram} is a 3D, nonlinear, time domain,
parallel finite element program specifically developed for
HiFi modeling and simulation of Earthquake Soil/Rock Structure
Interaction problems for NPPs (infrastructure objects) on ESSIComputers. \
%The NRC ESSI Program is based on
%a number of public domain numerical libraries developed at UCD as well as those
%available on the web, that are compiled and linked together to form the
%executable program (NRCESSIProgram). Significant effort is devoted to development
%of verification and validation procedures, as well as on development of
%extensive documentation. NRCESSIProgram is in public domain and is licensed
%through the Lesser GPL.
%\vspace*{0.3cm}
\vspace*{1mm}
\item {\bf The Real ESSIComputer} is a distributed memory
parallel computer, a cluster of clusters with multiple performance
processors and multiple performance networks.
%Compute nodes are Shared Memory Parallel
%(SMP) computers, that are connected, using high speed network(s), into a
%Distributed Memory Parallel (DMP) computer.
%\vspace*{0.3cm}
\vspace*{1mm}
\item {\bf The Real ESSINotes} represent a hypertext
documentation system
(Theory and Formulation, Software and Hardware, Verification and Validation, and
Case Studies and Practical Examples)
detailing modeling and simulation of ESSI
problems.
%
%the
%NRCESSIProgram code API (application Programming Interface) and DSLs (Domain
%Specific Language).
%%NRCESSINotes, developed by Boris Jeremic and collaborators, are in public
%domain
%%and are licensed under a Creative Commons AttributionShareAlike 3.0 Unported
%%License.
%
%\vspace*{0.3cm}
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Real ESSI Simulator System}
\begin{itemize}
\item Developed with funding from USNRC, USNSF, CNSCCCSN, and USDOE
\vspace*{2mm}
\item The Real ESSI simulator system is designed based on premise of high
fidelity modeling and simulation
\vspace*{2mm}
\item Reduction of modeling uncertainty and propagation of parametric uncertainty
\vspace*{2mm}
\item
Real ESSI simulator, also known as
{\small{\cyrssDvanaest Vrlo Prosto},
\raisebox{1.2mm}{\includegraphics[height=4mm] {/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/Real_ESSI_in_different_langauges/Real_ESSI_Chinese.jpeg}},
\raisebox{1.2mm}{\includegraphics[height=4mm] {/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/Real_ESSI_in_different_langauges/Real_ESSI_Bengali.pdf}},
{ Muy F{\'a}cil},
{Molto Facile},
\raisebox{1.2mm}{\includegraphics[height=4.2mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/Real_ESSI_in_different_langauges/Real_ESSI_Japanese.jpg}},
{\greektext{Pragmatik'a E'ukolo}},
\raisebox{1.6mm}{\includegraphics[height=5mm] {/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/Real_ESSI_in_different_langauges/Real_ESSI_Hindi.jpg}},
\raisebox{1.2mm}{\includegraphics[height=5mm] {/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/Real_ESSI_in_different_langauges/Real_ESSI_Farsi.jpg}},
{Tr{\`e}s Facile},
{\cyrssJedanaest Vistinski Lesno},
{Wirklich Einfach},
\raisebox{1.6mm}{\includegraphics[height=5mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/Real_ESSI_in_different_langauges/Real_ESSI_Arabic.jpg}}.
%\raisebox{1.2mm}{\includegraphics[height=4.5mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/Real_ESSI_in_different_langauges/Real_ESSI_Chinese.jpeg}},
%{ Muy F{\'a}cil},
%{Molto Facile},
%\raisebox{1.2mm}{\includegraphics[height=4mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/Real_ESSI_in_different_langauges/Real_ESSI_Japanese.jpg}},
%{\greektext{Pragmatik'a E'ukolo}},
%\raisebox{1.2mm}{\includegraphics[height=4.5mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/Real_ESSI_in_different_langauges/Real_ESSI_Hindi.jpg}},
%\raisebox{1.2mm}{\includegraphics[height=4mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/Real_ESSI_in_different_langauges/Real_ESSI_Farsi.jpg}},
%{Tr{\`e}s Facile},
%{\cyrssDvanaest Vistinski Lesno},
%{Wirklich Einfach},
%\raisebox{0.80mm}{\includegraphics[height=5.2mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/Real_ESSI_in_different_langauges/Real_ESSI_Arabic.jpg}}.
}
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Real ESSI Modelling}
\vspace*{4mm}
\begin{figure}[!hbpt]
\begin{center}
\includegraphics[width=3.2cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Theory_Introduction/tex_works_psfigures_loading_stageincrementsiterations.pdf}
%\caption{\label{loading_stagesincrements_iterations} }
\end{center}
%\vspace*{0.5cm}
\end{figure}
%
\end{frame}
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\begin{frame}
\frametitle{Verification and Validation for High Fidelity Predictive Capabilities}
% \frametitle{High Fidelity Modeling of SFS System:
% Verification, Validation and Prediction}
\begin{itemize}
% \vspace*{0.2cm}
% \item {\bf Prediction}: use of computational model to foretell the state
% of a physical system under consideration under conditions for which the
% computational model has not been validated.
\vspace*{3mm}
\item {{Verification} provides evidence that the
model is solved correctly.} Mathematics issue.
\vspace*{3mm}
\item {{Validation} provides
evidence that the correct model is solved.} Physics issue.
\vspace*{3mm}
\item Goal: predictive capabilities with low information (Kolmogorov) Complexity
% %% % \vspace*{0.2cm}
% % \item {\bf The Finite Element
% % Interpreter \FEI{}} might be one such
% % predictive tool (application program)
\end{itemize}
\end{frame}
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\section{Modeling and Parametric Uncertainty}
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\subsection{Modeling Uncertainty: 3D Dam/Slope Model, Expert Opinion}
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\begin{frame}
\frametitle{3D Dam  Slope Stability}
\begin{itemize}
\item 3D earth slope part of a concrete, earth dam
% \vspace*{3mm}
\item Movements recorded during lowering of reservoir
% \vspace*{3mm}
\item 3D slope unstable (?), no one could tell, all commercial software
does 2D slope stability
% \vspace*{3mm}
\item 2D vs 3D slope stability
% \vspace*{3mm}
\item Shear strength (?) as the only material parameter
\item (")Expert(") increased value of measured shear strength
\item Load cases: lowering and raising reservoir, slow and fast
\item Dam build using untreated alluvium
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{Dam, Satellite Photo}
%
\begin{figure}[!htbp]
\begin{center}
\includegraphics[width=10.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WolfCreekDam_SateliteView01.jpg}
%\hspace*{0.9cm}
%bridge.}
\end{center}
\end{figure}
%
\end{frame}
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\begin{frame}
\frametitle{Dam, 3D Slope, Satellite Photo}
%
\begin{figure}[!htbp]
\begin{center}
\includegraphics[width=10.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WolfCreekDam_SateliteView02.jpg}
%\hspace*{0.9cm}
%bridge.}
\end{center}
\end{figure}
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\end{frame}
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\begin{frame}
\frametitle{3D Slope}
%
\begin{figure}[!htbp]
\begin{center}
\includegraphics[width=10.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WolfCreekDam_SatelliteView_with_slope01.jpg}
%\hspace*{0.9cm}
%bridge.}
\end{center}
\end{figure}
%
\end{frame}
%
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\begin{frame}
\frametitle{3D Slope, Ground Photo}
%
\begin{figure}[!htbp]
\begin{center}
\includegraphics[width=9.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/img0188.jpg}
%\hspace*{0.9cm}
%bridge.}
\end{center}
\end{figure}
%
\end{frame}
%
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\begin{frame}
\frametitle{Dam, Construction Photo}
%
\begin{figure}[!htbp]
\begin{center}
\includegraphics[width=10.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WolfCreekDam_Q261_621_Embankment_Sep_30_48.jpg}
%\hspace*{0.9cm}
%bridge.}
\end{center}
\end{figure}
%
\end{frame}
%
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\begin{frame}
\frametitle{Dam, Section}
%
\begin{figure}[!htbp]
\begin{center}
\includegraphics[width=10.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WolfCreekDam_PerpendicularSection.jpg}
%\hspace*{0.9cm}
%bridge.}
\end{center}
\end{figure}
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\end{frame}
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\begin{frame}
\frametitle{Dam, Model}
%
\begin{figure}[!htbp]
\begin{center}
\includegraphics[width=5.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/3D_final02.jpg}
\includegraphics[width=5.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/3D_final04.jpg}
//
\includegraphics[width=5.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/3D_final05.jpg}
\includegraphics[width=5.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/3D_final_Top.jpg}
%\hspace*{0.9cm}
%bridge.}
\end{center}
\end{figure}
%
\end{frame}
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\begin{frame}
\frametitle{Dam Slope, Failure Modes}
\vspace*{5mm}
\begin{itemize}
\item 3D failure pattern
\item 3D has lower FS than 2D
\item Original $S_u$ FS barely enough,
\item With "increased" $S_u$ a bit higher
\end{itemize}
\vspace*{40mm}
\begin{figure}[!htbp]
\begin{flushright}
\includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/UndrainedSu440VectorPlan_snapshot.jpg}
\end{flushright}
\end{figure}
\vspace*{10mm}
%
\begin{figure}[!htbp]
\begin{center}
% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Drained_3D_AbsVal_L680_E680_Phi18_FS178.jpg}
% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Drained_3D_Vector_L680_E680_Phi18_FS178.jpg}
% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_drained_case_40_FS_1_89_displacement_vectors_factor_42_39.jpg}
% \\
% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Drained_L680_E680_Phi17_FS189.jpg}
% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_undrained_case_41_FS_1_43__displacement_vectors_factor_1_80.jpg}
% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Undrained_L680_E680_Su1200_FS167.jpg}
% \\
\includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Undrained_L680_E680_Su800_Alluvium_Su1500_FS250.jpg}
\includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Undrained_L680_E680_Su900_Alluvium_Su1000_FS222.jpg}
\includegraphics[width=3.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/WCD_Undrained_L680_E720_Su1300_FS154.jpg}
%\hspace*{0.9cm}
%bridge.}
\end{center}
\end{figure}
%
\end{frame}
%
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Modeling Uncertainty: Bridge Model}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \begin{frame}
% \frametitle{Detailed 3D Bridge Model}
%
% %
% \begin{figure}[!htbp]
% \begin{center}
% \includegraphics[width=8.0cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
% %\hspace*{0.9cm}
% %bridge.}
% \end{center}
% \end{figure}
% %
% \end{frame}
% %
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% % \begin{frame}
% % \frametitle{Model Components}
% %
% % %
% % \begin{itemize}
% % \item Soils: elasticplastic solids (yield land potential surface
% % DruckerPrager, kinematic hardening ArmstrongFrederick) (UCD: Jie and Jeremi{\'c})
% % \vspace*{0.2cm}
% % \item Structure nonlinear beamcolumn elements (fiber element)
% % (UCB: Fenves, UW: Eberhardt)
% %
% % \vspace*{0.2cm}
% % \item Piles: nonlinear beamcolumn elements (fiber element) (UCD: Jie and Jeremi{\'c})
% %
% %
% % \vspace*{0.2cm}
% % \item Two types of soil: stiff soil (UT, UCD), soft soil (Bay Mud)
% %
% % \vspace*{0.2cm}
% % \item Use of the Domain Reduction Method (DRM) (Bielak et al.) for seismic
% % input into FEM model
% %
% %
% % \end{itemize}
% %
% % \end{frame}
% % %
% %
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Modeling Issues}
%
% \begin{itemize}
%
% \vspace*{0.2cm}
% \item Construction process
%
% \vspace*{0.2cm}
% \item Deconvolution of given surface ground motions
%
% \vspace*{0.2cm}
% \item No artificial damping (only mat. dissipation, radiation)
%
% \vspace*{0.2cm}
% \item Element size issues (filtering of frequencies)
%
% \vspace*{0.4cm}
% \begin{table}[!htbp]
% %\caption{ }
% \begin{center}
% \begin{tabular}{rcccc}
% \hline
% elem. \# & elem. size & $f_{cutoff}$ & min. $G^{ep}/Gmax$ & $\gamma$ \\
% \hline
% %
% %
% % 100cm element model, f_cuttof=10HZ, G/Gmax=1.0, 12K elements, Gmax model
% 12K & 1.00~m & 10~Hz & 1.0 & <0.5~\% \\
% %
% %
% %~90cm element model, f_cutoff ~= 3Hz, G/Gmax~=0.08, for epsilon ~= 1%, 15K
% %elements, now running...
% 15K & 0.90~m & >3~Hz & 0.08 & <1.0~\% \\
% %
% %
% %27.6cm element model, f_cutoff= 10HZ, G/Gmax=0.08, for epsilon = 1%, 150K
% %elements, finest model
% 150K & 0.30~m & 10~Hz & 0.08 & <1.0~\% \\
% 500K & 0.15~m & 10~Hz & 0.02 & <5.0~\% \\
% % 27.6cm element model, f_cutoff= 10HZ, G/Gmax=0.08, for epsilon = 1%, 150K
% %elements, finest model
% \hline
% \end{tabular}
% \end{center}
% \end{table}
%
% \end{itemize}
%
%
% \end{frame}
% %
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %\begin{frame}
% % \frametitle{FEM Mesh (one of)}
% %
% %%
% %\begin{figure}[!htbp]
% %\begin{center}
% %\includegraphics[width=8cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
% %%\caption{\label{BridgeSFSI01} FEM model for seismic response of a three bend
% %%bridge.}
% %\end{center}
% %\end{figure}
% %%
% %\end{frame}
% %
%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% % \frametitle{Northridge and Kocaeli Input Motions}
% %
% %
% % \begin{figure}[!htbp]
% % \begin{center}
% % \hspace*{1cm}
% % \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/InputMotion_Northridge.pdf}
% % \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/LongMotion/InputMotion_Kocaeli.pdf}
% % \hspace*{1cm}
% % \\
% % \hspace*{1cm}
% % \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/InputMotion_Northridge_Spectrum.pdf}
% % \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/LongMotion/InputMotion_Kocaeli_Spectrum.pdf}
% % \hspace*{1cm}
% % %bridge.}
% % \end{center}
% % \end{figure}
% % %
% %
% % \end{frame}
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% % \begin{frame}
% % \frametitle{Simulation Results}
% %
% %
% % \vspace*{0.5cm}
% % %\begin{landscape}
% % \begin{figure}[!htbp]
% % \begin{center}
% % \hspace*{1cm}
% % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispSoilBlock1.pdf}
% % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispBent1.pdf}
% % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispSoilBlock2.pdf}
% % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispBent2.pdf}
% % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispSoilBlock3.pdf}
% % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispBent3.pdf}
% % \hspace*{1cm}
% % \\
% % \hspace*{1cm}
% % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelSoilBlock1.pdf}
% % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelBent1.pdf}
% % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelSoilBlock2.pdf}
% % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelBent2.pdf}
% % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelSoilBlock3.pdf}
% % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelBent3.pdf}
% % \hspace*{1cm}
% % \\
% % \hspace*{1cm}
% % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispSoilBlock1_Spectrum.pdf}
% % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispBent1_Spectrum.pdf}
% % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispSoilBlock2_Spectrum.pdf}
% % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispBent2_Spectrum.pdf}
% % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispSoilBlock3_Spectrum.pdf}
% % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispBent3_Spectrum.pdf}
% % \hspace*{1cm}
% % \\
% % \hspace*{1cm}
% % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelSoilBlock1_Spectrum.pdf}
% % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelBent1_Spectrum.pdf}
% % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelSoilBlock2_Spectrum.pdf}
% % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelBent2_Spectrum.pdf}
% % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelSoilBlock3_Spectrum.pdf}
% % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelBent3_Spectrum.pdf}
% % \hspace*{1cm}
% % \\
% % \hspace*{1cm}
% % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/MomentBent1Pile1.pdf}
% % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/MomentBent1Pile2.pdf}
% % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/MomentBent2Pile1.pdf}
% % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/MomentBent2Pile2.pdf}
% % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/MomentBent3Pile1.pdf}
% % \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/MomentBent3Pile2.pdf}
% % \hspace*{1cm}
% % \end{center}
% % \end{figure}
% %
% % \vspace*{0.8cm}
% % \begin{figure}[!htbp]
% % \begin{center}
% % \includegraphics[width=3.2cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
% % %bridge.}
% % \end{center}
% % \end{figure}
% % \vspace*{2cm}
% %
% %
% % \clearpage
% %
% %
% %
% %
% % \end{frame}
% %
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%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Short Period (Northridge) Input Motions}
%
%
% \vspace*{0.7cm}
% \begin{figure}[!htbp]
% \begin{center}
% \hspace*{1cm}
% \includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/InputMotion_Northridge.pdf}
% \hspace*{1cm}
% \\
% \hspace*{1cm}
% \includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/InputMotion_Northridge_Spectrum.pdf}
% \hspace*{1cm}
% %bridge.}
% \end{center}
% \end{figure}
% \vspace*{1.0cm}
% %
%
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Short Period Eq.: Left Bent, Displacements}
%
%
%
%
% \vspace*{1cm}
% \begin{figure}[!htbp]
% \begin{center}
% \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispBent1.pdf}
% %\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispBent1.pdf}
% \\
% \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispSoilBlock1.pdf}
% %\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispSoilBlock1.pdf}
% %bridge.}
% \end{center}
% \end{figure}
%
%
% \vspace*{2.9cm}
% \hspace*{0.2cm}
% \begin{figure}[!htbp]
% \begin{flushright}
% \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
% %bridge.}
% \end{flushright}
% \end{figure}
% \hspace*{0.5cm}
% \vspace*{2.0cm}
%
%
%
% \end{frame}
% %
%
%
%
%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% % \frametitle{Short Period E.: Left Bent, Structure and Soil, Acc.}
% %
% %
% %
% %
% % \vspace*{1cm}
% % \begin{figure}[!htbp]
% % \begin{center}
% % \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelBent1.pdf}
% % \\
% % \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelSoilBlock1.pdf}
% % %bridge.}
% % \end{center}
% % \end{figure}
% %
% %
% % \vspace*{2.9cm}
% % \hspace*{0.2cm}
% % \begin{figure}[!htbp]
% % \begin{flushright}
% % \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
% % %bridge.}
% % \end{flushright}
% % \end{figure}
% % \hspace*{0.5cm}
% % \vspace*{2.0cm}
% %
% % \end{frame}
% % %
% %
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% % \frametitle{Short Period E.: Left Bent, Structure and Soil, Acc.Sp.}
% %
% %
% %
% %
% % \vspace*{1cm}
% % \begin{figure}[!htbp]
% % \begin{center}
% % \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelBent1_Spectrum.pdf}
% % \\
% % \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelSoilBlock1_Spectrum.pdf}
% % %bridge.}
% % \end{center}
% % \end{figure}
% %
% %
% % \vspace*{2.9cm}
% % \hspace*{0.2cm}
% % \begin{figure}[!htbp]
% % \begin{flushright}
% % \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
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% \begin{center}
% \includegraphics[width=11cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/MomentBent1Pile1_25s_SC.pdf}
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% \frametitle{Short Period E.: Left Bent, Free Field vs Real Disp.}
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% \begin{figure}[!htbp]
% \begin{center}
% \includegraphics[width=11cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispSoilBlock1_15cm_25s_SC.pdf}
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% %bridge.}
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% \begin{frame}
% \frametitle{Long Period (Kocaeli) Input Motions}
%
%
% \vspace*{0.7cm}
% \begin{figure}[!htbp]
% \begin{center}
% \hspace*{1cm}
% \includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/LongMotion/InputMotion_Kocaeli.pdf}
% \hspace*{1cm}
% \\
% \hspace*{1cm}
% \includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/LongMotion/InputMotion_Kocaeli_Spectrum.pdf}
% \hspace*{1cm}
% %bridge.}
% \end{center}
% \end{figure}
% %
% \vspace*{1cm}
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% \begin{frame}
% \frametitle{Long Period E.: Left Bent, Bending Moments.}
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% %\vspace*{1cm}
% \begin{figure}[!htbp]
% \begin{center}
% %\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/MomentBent1Pile1.pdf}
% %\\
% \includegraphics[width=11cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/MomentBent1Pile2.pdf}
% %bridge.}
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% \end{figure}
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% \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
% %bridge.}
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% % \begin{frame}
% % \frametitle{Long Period E.: Left Bent, Structure and Soil, Disp.}
% %
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% %
% % \vspace*{1cm}
% % \begin{figure}[!htbp]
% % \begin{center}
% % \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/DispBent1.pdf}
% % \\
% % \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/DispSoilBlock1.pdf}
% % %bridge.}
% % \end{center}
% % \end{figure}
% %
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% % \vspace*{2.9cm}
% % \hspace*{0.2cm}
% % \begin{figure}[!htbp]
% % \begin{flushright}
% % \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
% % %bridge.}
% % \end{flushright}
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% % \hspace*{0.5cm}
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\subsection{Modeling Uncertainty: Seismic Behavior of Nuclear Power Plants}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Modeling and Simulation of Nuclear Power Plants}
\begin{itemize}
\item Nuclear Power Plants (NPPs) design based on a number of simplified assumptions!
\vspace*{1mm}
\item Linear elastic material behavior
\vspace*{1mm}
\item Seismic Motions: $1$D or $3 \times 1$D, or real 3D (6D)
\vspace*{1mm}
\item Savings in construction cost possible with more accurate modeling of
NPPs
\vspace*{1mm}
\item Improvements in safety of NPPs also possible, even with higher seismic
motions, as inelastic effects "eat up" (dissipate) seismic energy
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Nuclear Power Plants: 6D or 1D Seismic Motions}
\begin{itemize}
\item Assume that a full 6D (3D) motions at the surface are only recorded in one
horizontal direction
\item From such recorded motions one can develop a vertically propagating shear
wave in 1D
\item Apply such vertically propagating shear wave to the same 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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Synthetic Test Motions}
\begin{itemize}
\item Develop free field models with sources within
\item Sources are simple, point (mostly), line and surface
\item Sources will send both P and S waves
\item Variation in strike and dip
\item Simulation programs, Real ESSI Simulator and SW4
\end{itemize}
\vspace*{2mm}
\begin{center}
\hspace*{7mm}
\movie[label=show3,width=5.0cm,poster,autostart,showcontrols]
{\includegraphics[width=40mm]{BJicon.png}}{movie_input_closeup.mp4}
\movie[label=show3,width=5.0cm,poster,autostart,showcontrols]
{\includegraphics[width=40mm]{BJicon.png}}{movie_ff_3d.mp4}
\end{center}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Synthetic Test Motions, 6D vs 1D}
\begin{itemize}
\item Danger of picking one component of motions for 1D or 3$\times$1D (it is done all the time!)
\item Excellent (forced) fit, but not a prediction and information is lost
(goal is to predict and inform and not (force) fit)
\end{itemize}
\vspace*{2mm}
\begin{center}
\hspace*{7mm}
\movie[label=show3,width=5.0cm,poster,autostart,showcontrols]
{\includegraphics[width=40mm]{BJicon.png}}{movie_ff_3d.mp4}
\movie[label=show3,width=5.0cm,poster,autostart,showcontrols]
{\includegraphics[width=40mm]{BJicon.png}}{movie_ff_1d.mp4}
\end{center}
\end{frame}
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{6D Free Field Motions}
%
%
% \vspace*{2mm}
% \begin{center}
% %\movie[label=show3,width=8.5cm,poster,autostart,showcontrols,loop]
% \hspace*{7mm}
% \movie[label=show3,width=8.8cm,autostart,showcontrols]
% {\includegraphics[width=70mm]{BJicon.png}}{movie_input.mp4}
% \end{center}
%
% \begin{flushleft}
% \vspace*{15mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_01AApr2015/movie_input.mp4}
% % \href{./homo_50mmesh_45degree_Ormsby.mp4}
% {\tiny (MP4)}
% %
% \end{flushleft}
%
%
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{6D Free Field Motions (closeup)}
%
%
% \vspace*{2mm}
% \begin{center}
% \hspace*{7mm}
% \movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
% {\includegraphics[width=70mm]{BJicon.png}}{movie_input_closeup.mp4}
% \end{center}
%
% \begin{flushleft}
% \vspace*{15mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_01AApr2015/movie_input_closeup.mp4}
% % \href{./homo_50mmesh_45degree_Ormsby.mp4}
% {\tiny (MP4)}
% \end{flushleft}
% %
%
%
% \end{frame}
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{6D Free Field at Location}
%
%
% \vspace*{2mm}
% \begin{center}
% \hspace*{7mm}
% \movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
% {\includegraphics[width=69mm]{BJicon.png}}{movie_ff_3d.mp4}
% \end{center}
%
%
% \begin{flushleft}
% \vspace*{15mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_3d.mp4}
% % \href{./homo_50mmesh_45degree_Ormsby.mp4}
% {\tiny (MP4)}
% \end{flushleft}
% %
%
%
% \end{frame}
%
%
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%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{6D Earthquake Soil Structure Interaction}
%
% \vspace*{2mm}
% \begin{center}
% \hspace*{7mm}
% \movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
% {\includegraphics[width=70mm]{BJicon.png}}
% {movie_npp_3d.mp4}
% \end{center}
%
% \begin{flushleft}
% \vspace*{15mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_npp_3d.mp4}
% {\tiny (MP4)}
% \end{flushleft}
% %
%
% \end{frame}
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{1D Free Field at Location}
%
%
% \vspace*{2mm}
% \begin{center}
% \hspace*{7mm}
% \movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
% {\includegraphics[width=70mm]{BJicon.png}}
% {movie_ff_1d.mp4}
% \end{center}
%
% \begin{flushleft}
% \vspace*{15mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_1d.mp4}
% {\tiny (MP4)}
% \end{flushleft}
% %
%
%
% \end{frame}
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{1D ESSI of NPP}
%
%
% \vspace*{2mm}
% \begin{center}
% \hspace*{7mm}
% \movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
% {\includegraphics[width=70mm]{BJicon.png}}
% {movie_npp_1d.mp4}
% \end{center}
%
% \begin{flushleft}
% \vspace*{15mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_npp_1d.mp4}
% {\tiny (MP4)}
% \end{flushleft}
% %
%
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% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{6D vs 1D NPP ESSI Response Comparison}
\vspace*{2mm}
\begin{center}
\hspace*{7mm}
\movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
{\includegraphics[width=69mm]{BJicon.png}}
{movie_2_npps.mp4}
\end{center}
\begin{flushleft}
\vspace*{15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_2_npps.mp4}
{\tiny (MP4)}
\end{flushleft}
%
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{6D vs 1D: Containment Displacement Response}
%
%
% \begin{figure}[!hp]
% \begin{center}
% \hspace*{13mm}
% \includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/NPP_movies_19May2015/01_displacements_Containment_building_bottom.pdf}
% \hspace*{6mm}
% \includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/NPP_movies_19May2015/02_displacements_Containment_building_top.pdf}
% \hspace*{10mm}
% \end{center}
% \end{figure}
%
%
%
% \end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{6D vs 1D: Containment Acceleration Response}
\begin{figure}[!hp]
\begin{center}
\hspace*{13mm}
\includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/NPP_movies_19May2015/01_accelerations_Containment_building_bottom.pdf}
\hspace*{6mm}
\includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/NPP_movies_19May2015/02_accelerations_Containment_building_top.pdf}
\hspace*{10mm}
\end{center}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection{Parametric Uncertainty: Probabilistic Inelasticity}
\subsection{Parametric Uncertainty: Wave Propagation}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Uncertain Material Parameters and Loads}
\begin{itemize}
\item Decide on modeling complexity
\vspace*{3mm}
\item Determine model/material parameters
\vspace*{3mm}
\item Model/material parameters are uncertain!
\begin{itemize}
\item Measurements
\item Transformation
\item Spatial variability
\end {itemize}
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{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*{5mm}
\item Dynamic Finite Elements
%
\begin{equation}
{\bf M} \ddot{\bf u} +
{\bf C} \dot{\bf u} +
{\bf K}^{ep} {\bf u} =
{\bf F}
\nonumber
\end{equation}
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Critique of our Previous Work, PEP and SEPFEM}
%
% \begin{itemize}
%
% \item Constitutive weighted coefficients $N_1$ and $N_2$ do not work well for
% stress solution!
%
% \vspace{1mm}
% \item We suggested that $\sigma(t)$ be considered a $\delta$correlated, and
% based on that simplified stiffness equations. Both the assumption and the
% resulting equation were not right.
%
%
% \vspace{1mm}
% \item On a SEPFEM level, stiffness needs update basis functions and KL
% coefficients in each step. We updated the eigenvalues
% $\lambda_i$ and kept the same structure (KarhunenLoeve) in the approximation
% of the stiffness, which is not physical
%
% \vspace{1mm}
% \item Implicitly assumed that the stiffness remains Gaussian, which is
% not the case
%
%
% \end{itemize}
%
%
%
%
%
%
%
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Gradient Flow Theory of Probabilistic ElastoPlasticity}
%
%
% Decomposition of an elastoplastic random process:
% % into
% %the following general form:
% %
% \begin{eqnarray}
% \begin{array}{c c c c c}
% \bigg( \displaystyle{\pder[]{t}}  \mathcal{L}_{rev} \bigg) P(\boldsymbol{\sigma},t) &=& 0& \qquad &\text{if }
% \boldsymbol{\sigma} \in \Omega^{el}
% \\
% ~
% \\
% \bigg( \displaystyle{\pder[]{t}}  \mathcal{L}_{irr} \bigg) P(\boldsymbol{\sigma},t) &=& 0& \qquad &\text{if }
% \boldsymbol{\sigma} \in \Omega^{el} \cup \Omega^{pl}
% \end{array}
% \nonumber
% \end{eqnarray}
%
% %
% \begin{itemize}
%
% \item Reversible ($\mathcal{L}_{rev} $) and Irreversible ($\mathcal{L}_{irr} $) operators
% %
%
% \vspace*{2mm}
% \item Yield PDF is an attractor, similar to plastic corrector
%
% \vspace*{2mm}
% \item Ergodicity of the elasticplastic process can be proven!
%
% \end{itemize}
%
%
%
%
%
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
% \begin{frame}
% \frametitle{Gradient Flow Theory of Probabilistic ElastoPlasticity}
%
% \begin{itemize}
%
% \item
% Elastic, reversible process, FokkerPlanck (forward Kolmogorov) equation
% %
% \begin{equation}
% \pder[P (\boldsymbol{\sigma},t)]{t}
% = \nabla \cdot (\langle \boldsymbol{E} \dot{\boldsymbol{\epsilon}} \rangle P(\boldsymbol{\sigma},t))
% + t ~\text{Var}[\boldsymbol{E}\dot{\boldsymbol{\epsilon}}] \Delta P(\boldsymbol{\sigma},t)
% \nonumber
% \end{equation}
% %
% \begin{equation}
% \mathcal{L}_{rev} = \nabla \cdot (t \,\text{Var}[\boldsymbol{C}\dot{\boldsymbol{\epsilon}}] \nabla 
% \langle \boldsymbol{C} \dot{\boldsymbol{\epsilon}} \rangle)
% \nonumber
% \end{equation}
%
% \item
% Plastic, irreversible process, FokkerPlanck (forward Kolmogorov) equation
% %
% \begin{equation}
% \pder[P(\boldsymbol{\sigma},t)]{t} = \nabla \cdot (\nabla \Psi(\boldsymbol{\sigma})
% P(\boldsymbol{\sigma},t)) + D \Delta P(\boldsymbol{\sigma},t)
% \nonumber
% \end{equation}
% %
% \begin{equation}
% \mathcal{L}_{irr} = D \nabla \cdot \bigg(\nabla  \frac{\nabla P_y(\boldsymbol{\sigma})}{P_y(\boldsymbol{\sigma})}\bigg)
% \nonumber
% \end{equation}
% %
%
% \end{itemize}
%
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Gradient Flow Theory of Probabilistic ElastoPlasticity}
%
% \begin{itemize}
%
% \item Limiting (final) distribution
% is considered to be known
% %(given as a material parameter) and
%
% \vspace*{2mm}
% \item Underlying potential leading to this distribution is sought
%
% \vspace*{2mm}
% \item Transition from uncertain elastic to uncertain plastic response
%
%
% \vspace*{2mm}
% \item Only in a 1D elastoplastic problem does one end up with a stationary
% distribution
%
% \vspace*{2mm}
% \item In higher dimensional problems this yield stress distribution is
% only "marginally" stationary along one or a combination of the stress
% components.
%
% \end{itemize}
%
%
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Probabilistic ElastoPlasticity: von Mises Surface}
% An example of a Mises probabilistic yield surface is given in Fig.~\ref{ProbCylinder}.
\begin{figure}[H]
\centering
\vspace*{5mm}
%\hspace*{30mm}
\includegraphics
% [scale = 0.8, trim = 0.6in 0.4in 0.6in 0.4in, clip=true]
[width=12cm]
{/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Probabilistic_von_Mises_Surface.jpg}
% \caption{An example of a probabilistic von Mises yield surface.}
\label{ProbCylinder}
\end{figure}
\end{frame}
% %
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Gradient Theory of Probabilistic ElastoPlasticity: Numerical Solution}
%
%
% \begin{itemize}
%
% \item Using radial basis functions (a meshless method) for solving
% FokkerPlanck equations for uncertain elasticplastic response
%
%
% \vspace*{6mm}
% \item Details in a talk by Mr. Karapiperis later this afternoon (room 2, MS6,
% 17:0019:00, last talk)
%
%
% \end{itemize}
% % %
%
%
% \end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Gradient Theory of Probabilistic ElastoPlasticity:
Verification, ElasticPerfectly Plastic}
%\vspace*{3mm}
\begin{figure}[H]
\centering
\includegraphics
% [scale = 0.55, trim = 0.0in 0.0in 0.0in 0.0in, clip=true]
[width=8cm]
{/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/M+SD_1D_Perf_Cyclic.pdf}
% \caption{Combining the above plots to get the evolution of mean $\pm$ std.
% deviation of stress.}
\label{MSD_12}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection{SEPFEM}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \begin{frame}{Stochastic ElasticPlastic FEM (SEPFEM)}
%
% \begin{itemize}
% \item<1> KLPC expansion of material random fields (stiffness, etc)
% %
% % \begin{equation*}
% $
% \mathbb{D}(\bold{x}, \theta) = \sum_{i=0}^{M} r_{i}(\bold{x}) \Phi_i[\{\xi_r(\theta)\}]
% \label{nonGaussian1}
% $
% %\end{equation*}
%
% \item<1> PC expansion of displacement field
% %
% \begin{eqnarray*}
% u(\bold{x},\theta) = \sum_{i=0}^p d_i(\bold{x}) \psi_i[\{\xi_r(\theta)\}]
% \label{PC1}
% \end{eqnarray*}
%
% \item<1> Stochastic Galerkin
%
% \begin{eqnarray*}
% \sum_{n = 1} ^ N K'_{mn} d_{ni} + \sum_{n=1}^N \sum_{j=0}^P d_{nj} \sum_{k=1}^M b_{ijk} K''_{mnk} =
% \Phi_{m}\langle\psi_i[\{\xi_r\}]\rangle
% \label{Lognormal6}
% \end{eqnarray*}
%
% \end{itemize}
%
%
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \begin{frame}{SEPFEM Statistical linearization}
%
% Update the FE stiffness in the elastoplastic regime:
%
% \begin{itemize}
% \item Solve elastoplastic FPE for each integration point
% %
% \begin{eqnarray*}
% \pder[P^{nl}(\sigma,t)]{t}
% &=& \pder[]{\sigma} \bigg(\bigg\langle D^k (1  P[\Sigma_y \leq \sigma]) \frac{\Delta
% \epsilon}{\Delta t} \bigg\rangle P\bigg) \nonumber \\
% & & + \pder[^2]{\sigma^2} \bigg( t Var\bigg[ D^k (1  P[\Sigma_y \leq \sigma]) \frac{\Delta
% \epsilon}{\Delta t} \bigg] P\bigg)
% \label{SEPFEMLinearization1}
% \end{eqnarray*}
%
% \item Consider an equivalent linear FPE
% %
% \begin{eqnarray*}
% \pder[P^{lin}(\sigma,t)]{t}
% &=& N_{(1)}^{eq} \pder[P]{\sigma} + N_{(2)}^{eq} \pder[^2 P]{\sigma^2}
% \label{SEPFEMLinearization2}
% \end{eqnarray*}
%
% \item Linearization of the PC coeff. as an optimization problem
% %
% \begin{equation*}
% \pder[P^{lin}(\sigma,t)]{t}
% = \pder[P^{nl}(\sigma,t)]{t}
% \end{equation*}
%
%
% \end{itemize}
%
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \begin{frame}{Dynamic, Time Domain, SEPFEM}
%
% \begin{itemize}
% \item Gaussian formulation inadequate due to occurrence of "probabilistic softening" modes
% $\Rightarrow$ Need for positive definite kernel
%
% \vspace*{2mm}
% \item Stochastic forcing (e.g. uncertain earthquake)
%
% \vspace*{2mm}
% \item Stability of time marching algorithm (Newmark, Rosenbrock, Cubic Hermitian ) analyzed using
% amplification matrix
%
% \vspace*{2mm}
% \item Longintegration error and higher order statistics phase shift
% \end{itemize}
%
% % \begin{figure}[H]
% % \centering
% % \includegraphics[scale = 0.4, trim = 0.1in 0.0in 0.0in 0.0in, clip=true]{/home/jeremic/tex/Classes/2015/spring/ECI280A/SEPFEM/odKonstantinosa/figures/Sendai_1Sine_PCk2PCd8.pdf}
% % \label{Sendai_1Sine_PCk2PCd8.pdf}
% % \end{figure}
% %
%
%
% \end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Wave Propagation Through Uncertain Soil}
\vspace{2mm}
\begin{figure}[H]
\centering
\includegraphics
% [scale = 0.56, trim = 0.0in 0.15in 0.2in 0.16in, clip=true]
[width=7cm]
{/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_profile.png}
%
%
\includegraphics
%[scale = 0.56, trim = 0.0in 0.0in 0.0in 0.0in, clip=true]
[width=1.5cm]
{/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/meshes.png}
% \caption{Simplified profile and properties for the 1dimensional profile considered.}
\label{Sendai_profile}
\end{figure}
\vspace{5mm}
\begin{figure}[htbp]
\centering
%\hspace{0.2in}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\includegraphics
% [scale = 0.37, trim = 0.0in 0.0in 0.0in 0.0in,clip=true]
[width=3.5cm]
{/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/ShearModulusStats.pdf}
\hfill
\includegraphics
% [scale = 0.37, trim = 0.0in 0.0in 0.0in 0.0in, clip=true]
[width=3.5cm]
{/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/ShearStrengthStats.pdf}
%\caption{Shear modulus and shear strength statistics in the middle of the soil column.}
\hfill
\includegraphics
% [scale = 0.62, trim = 0in 0.15in 0in 0.22in, clip=true]
[width=3.5cm]
{/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_1Sine_PCk2PC2_elastic_COV45_BaseInput.pdf}
% \caption{Single sine pulse excitation of the soil column at its base.}
% \label{Sendai_1Sine_PCk2PC2_elastic_COV45_BaseInput}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Uncertain Elastic Response at the Surface {\tiny(COV = 120\%)} }
\vspace*{2mm}
\begin{figure}[H]
\centering
\includegraphics
% [scale = 0.62, trim = 0in 0.16in 0in 0.26in, clip=true]
[width=9.3cm]
{/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_1Sine_PCk2PC2_elastic_COV120.pdf}
% \caption{Mean $\pm$ std. deviation of the elastic response at the top of the
% soil column for the conservative COV case (COV = 120\%).}
% \label{Sendai_1Sine_PCk2PC2_elastic_COV120}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Displacement PDFs at the Surface {\tiny(COV = 120\%)} }
%\vspace*{20mm}
%\hspace*{30mm}
\begin{figure}[H]
\centering
\includegraphics
%[scale = 0.62, trim = 0in 0.16in 0in 0.26in, clip=true]
[width=10cm]
{/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_1Sine_PCk2PC2_elastic_COV120_FullPdf.jpg}
% \caption{Mean $\pm$ std. deviation of the elastic response at the top of the
% soil column for the conservative COV case (COV = 120\%).}
% \label{Sendai_1Sine_PCk2PC2_elastic_COV120}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Displacement CDFs (Fragilities) at the Surface {\tiny(COV = 120\%)} }
\vspace*{3mm}
\begin{figure}[H]
\centering
\includegraphics
% [scale = 0.62, trim = 0in 0.16in 0in 0.26in, clip=true]
[width=11cm]
{/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_1Sine_PCk2PC2_elastic_COV120_FullCdf.jpg}
% \caption{Mean $\pm$ std. deviation of the elastic response at the top of the
% soil column for the conservative COV case (COV = 120\%).}
% \label{Sendai_1Sine_PCk2PC2_elastic_COV120}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Probability of Exceedance, $disp=0.1m$ {\tiny(COV = 120\%)} }
\begin{figure}[H]
\centering
\includegraphics
% [scale = 0.62, trim = 0in 0.16in 0in 0.26in, clip=true]
[width=9cm]
{/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_1Sine_PCk2PC2_elastic_COV120_ProbExc.pdf}
% \caption{Mean $\pm$ std. deviation of the elastic response at the top of the
% soil column for the conservative COV case (COV = 120\%).}
% \label{Sendai_1Sine_PCk2PC2_elastic_COV120}
\end{figure}
\end{frame}
%
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\section{Summary}
\subsection*{Summary}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Concluding Remarks}
\begin{itemize}
%\vspace*{2mm}
\item Modeling and simulation of infrastructure object requires high sophistication
\vspace*{3mm}
\item Uncertainties (modeling and parametric) influences results
\vspace*{3mm}
\item Those uncertainties need to be addressed and propagated to results and
used in decision making
\vspace*{3mm}
\item Goal is to {predict} and {inform}, and not force fit
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Acknowledgement}
\begin{itemize}
\vspace*{2mm}
\item Funding from and collaboration with the USNRC, USDOE, USNSF, CNSC,
AREVA NP GmbH, and Shimizu Corp. is greatly appreciated,
\vspace*{2mm}
\item Collaborators:
% Dr. Budnitz (LBNL),
Prof. Yang,
Dr Cheng, Dr. Jie, Dr. Tafazzoli,
Prof. Pisan{\`o},
Mr. Watanabe,
Mr. Vlaski,
Mr. Orbovi{\'c},
and
UCD students:
Mr. Abell,
Mr. Karapiperis,
Mr. Feng,
Mr. Sinha,
Mr. Luo,
Mr. Lacour,
Mr. Yang,
Ms. Behbehani
%
%
\vspace*{2mm}
\item Real ESSI Simulator:
\url{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%
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\section*[]{Real ESSI Simulator}
% invisible section trick
%\subsection*{Summary}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Real ESSI Modelling and Simulation Process}
%
% \begin{itemize}
%
% %\vspace*{4mm}
% \item Mesh development: gmsh (UL), gmESSI, FeConv (Vlaski)
%
% \vspace*{2mm}
% \item Model Development: sublime text editor
%
% \vspace*{2mm}
% \item Model Simulation:
% \begin{itemize}
% \item Domain Specific Language (DSL) for input
% \item Real ESSI
% \item output in HDF5 (NCSA...)
% \end{itemize}
%
% \vspace*{2mm}
% \item Result Visualization: VisIt (LLNL), visitESSI plugin (all
% displacements, stress, strain)
%
% \end{itemize}
% %
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Source Code Development and Management}
%
% \begin{itemize}
%
% %\vspace*{4mm}
% \item Real ESSI sources (finite element, material models, algorithms, DSL
% interpreter, \&c.) in a private online repository with version control
%
%
% \vspace*{4mm}
% \item Real ESSI dependencies (external libraries: solvers, MPI, BLAS, LAPACK,
% \&c.)
%
%
% % %\vspace*{1mm}
% % \item Sequential performance optimization (templates, global linking
% % optimization, pipeline parallel, \&c.)
% %
% % %\vspace*{1mm}
% % \item Parallel performance optimization (Plastic Domain Decomposition)
% % for local clusters as well as large national parallel computers.
% %
% \end{itemize}
% %
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Real ESSI Developers}
%
% \begin{itemize}
% \item UC Davis:
% Core system architecture (sequential and
% parallel), finite elements, material models,
% constitutive integration, deterministic and stochastic elastic plastic
% finite elements
%
% \vspace*{2mm}
%
% \item LBNL: Nonlinear/inelastic beam, Nonlinear/inelastic shell (plate
% and wall, deterministic)
%
% \vspace*{2mm}
% \item TU Delft: Material Models (deterministic)
% \end{itemize}
%
% %
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Real ESSI Users}
%
%
% \begin{itemize}
% \item DOE Project Team:
% \begin{itemize}
% \item UC Davis: verification, system modeling, \&c.
%
% \item LBNL: verification, validation, validation system design, system modeling)
%
% \item UN Reno: validation system design, validation
% \end{itemize}
%
% \vspace*{2mm}
% \item National Labs
%
% \vspace*{2mm}
% \item Companies: AREVA, Shimizu Corp., Rizzo and Assoc.
%
% \vspace*{2mm}
% \item Universities: TU Delft, NTUA, UCB
%
% \end{itemize}
%
% %
% \end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\subsection{Real ESSI Simulator: Program}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Real ESSI: Finite Elements}
%\vspace*{3mm}
\begin{itemize}
%\vspace*{1mm}
\item Dry/single phase solids (8, 20, 27, 827 node bricks), elastic and/or
inelastic
%\vspace*{1mm}
\item Saturated/two phase solids (8 and 27 node bricks, liquefaction
modeling), elastic and/or inelastic
%\vspace*{1mm}
\item Truss, elastic
%\vspace*{1mm}
\item Beams (six and variable DOFs per node), elastic, inelastic
%\vspace*{1mm}
\item Shell (ANDES) with 6DOF per node, linear elastic, inelastic shell soon
%\vspace*{1mm}
\item Contacts (dry and/or saturated soil/rock  concrete, gap
openingclosing, frictional slip), inelastic
%\vspace*{1mm}
\item Base isolators (elastomeric, frictional pendulum), inelastic
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Real ESSI: Material Models}
%\vspace*{2mm}
\begin{itemize}
\item Linear and nonlinear, isotropic and anisotropic elastic
\vspace*{3mm}
\item ElasticPlastic (von Mises, Drucker Prager, Rounded MohrCoulomb,
Leon Parabolic, CamClay, SaniSand, SaniClay,
Pisan{\` o}...). All elasticplastic models can be used as perfectly
plastic, isotropic hardening/softening and kinematic hardening
models.
\vspace*{3mm}
\item Viscous damping solids, Rayleigh and Caughey damping
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Real ESSI: Solution Advancement Algorithms}
\begin{itemize}
%\vspace*{10mm}
\item Constitutive
\begin{itemize}
%\vspace*{1mm}
\item Explicit, Implicit, Subincrementation, Line Search
\end{itemize}
\item Nonlinear Static FEM
\begin{itemize}
%\vspace*{1mm}
\item No equilibrium iteration
\item Equilibrium Iterations (full Newton, modified N, Initial Stiff.)
\item Hyperspherical constraint (arch length, displacement control, load
control)
\item Line Search
\item Convergence criteria:
displacement, load, energy
\end{itemize}
\item Nonlinear Dynamic FEM
\begin{itemize}
%\vspace*{1mm}
\item No equilibrium iteration
\item Equilibrium Iterations (full Newton, modified N, Initial Stiff.)
\item Constant or variable time stepping
\item Convergence criteria: displacement, load, energy
\end{itemize}
\end{itemize}
%\vspace*{60mm}
%%\begin{figure}[!hbpt]
%\begin{flushright}
%\hspace*{50mm}
%\includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Theory_Introduction/tex_works_psfigures_loading_stageincrementsiterations.pdf}
%%\caption{\label{loading_stagesincrements_iterations} }
%\end{flushright}
%%\vspace*{0.5cm}
%%\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Real ESSI: Seismic Input}
\begin{itemize}
%\vspace*{1.5mm}
\vspace*{4mm}
\item Analytic input of seismic motions (both body (P, S) and surface
(Rayleigh, Love, etc., waves), including analytic radiation damping using Domain
Reduction Method (Bielak et al.)
\end{itemize}
%
%\begin{figure}[!hbpt]
\begin{center}
\includegraphics[width=8cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/tex_works_psfigures_DRM_NPP_idea01.pdf}
%\caption{\label{DRMidea01} Large physical domain with the source of load $P_e(t)$
%and the local feature (in this case a soilstructure system.}
\end{center}
%\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Real ESSI Simulator Program: Parallel, HPC}
\begin{itemize}
\item High Performance Parallel Computing:
both parallel and sequential version available, however, for high fidelity
modeling, parallel is really the only option. Parallel Real ESSI Simulator
runs on clusters of PCs and on large supercomputers (Distributed Memory
Parallel machines, all top national supercomputers). Plastic Domain
Decomposition Method (PDD, dynamic computational load balancing) for
elasticplastic computations with multiple types of finite elements and on
variable speed CPUs (and networks)
% Parallel algorithm uses our
% original Plastic Domain Decomposition method (featuring dynamic computational
% load balancing) that is efficient for elasticplastic finite element problems
% where elasticplastic (slow) and elastic (fast) domains change dynamically
% during run time.
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Real ESSI Simulator Program: Probabilistic/Stochastic}
%\vspace*{2mm}
\begin{itemize}
%\vspace*{2.5mm}
\item Constitutive: EulerLagrange form of FokkerPlanck (forward
Kolmogorov) equation for probabilistic elastoplasticity (PEP)
%\vspace*{1.5mm}
\item Spatial: stochastic elastic plastic finite element method (SEPFEM)
\end{itemize}
Uncertainties in material and load are analytically taken into account.
Resulting displacements, stress and strain are obtained as very accurate
(second order accurate for stress) Probability Density Functions.
PEP and SEPFEM are not based on a Monte Carlo method, rather they expand
uncertain input variables and uncertain degrees of freedom (unknowns) into
spectral probabilistic spaces and solve for PDFs of
resulting displacement, stress and strain in a single run.
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \begin{frame}
% \frametitle{Real ESSI Simulator Program: Design and Users}
%
% \begin{itemize}
%
% %\vspace*{0.2cm}
% \item Based on a Collection of Useful Libraries (portable)
%
% \vspace*{0.1cm}
% \item Library centric software design
%
% \vspace*{0.1cm}
% \item Sequential (learning) and Parallel (production modeling and simulation)
%
% \vspace*{0.1cm}
% \item Distributed Memory Parallel (DMP) paradigm, scales well to large supercomputers
%
%
%
% \vspace*{0.1cm}
% \item Various public domain licenses (GPL, LGPL, BSD, CC)
%
% %\vspace*{0.3cm}
% \vspace*{0.1cm}
% \item Verification (extensive) and Validation (not much)
%
%
% \vspace*{0.1cm}
% \item Target users: USDOE, USNRC, CNSC, IAEA, Collaborators (AREVA, Shimizu,
% Rizzo...), others
%
% \vspace*{0.1cm}
% \item Limited use Expert Modeling and Simulation System, and not a public domain
% program
%
%
% \end{itemize}
%
% \end{frame}
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}[fragile]
% \frametitle{ESSI Simulator Computer(s)}
%
% A distributed memory parallel (DMP) computer
% designed for high performance,
% parallel finite element simulations
%
% \begin{itemize}
% %\vspace*{0.1cm}
% \item Multiple performance CPUs \\
% and Networks
% %\vspace*{0.1cm}
% \item Most costperformance \\
% effective
% %\vspace*{0.1cm}
% \item Source compatibility with \\
% any DMP supercomputer
% %\vspace*{0.1cm}
% \item Current systems:
% \begin{itemize}
% \item 208CPUs,
% \item 40CPUs (8+32)
% \item 160CPUs (8x5+2x16+24+64)
% \item 32CPUs (multiple machines like this)
% \end{itemize}
%
% \end{itemize}
%
%
% \vspace*{4.5cm}
% \hspace*{0.5cm}
% \begin{flushright}
% \includegraphics[width=4.0cm]{/home/jeremic/public_html/NRC_ESSI_Simulator/NRC_ESSI_Computer/photos/IMG_2607.JPG}
% %\includegraphics[width=6.0cm]{/home/jeremic/public_html/NRC_ESSI_Simulator/NRC_ESSI_Computer/photos/IMG_2609.JPG}
% %\includegraphics[width=8.0cm]{/home/jeremic/public_html/NRC_ESSI_Simulator/NRC_ESSI_Computer/photos/IMG_2611.JPG}
% \end{flushright}
%
%
%
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Near Future Plan}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Real ESSI: Verification and Validation}
% \begin{itemize}
% %\vspace*{2mm}
% \item Verification:
% each element, model, algorithm and procedure has been extensively verified
% (math issue)
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% \item Validation: limited
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\begin{frame}
\frametitle{Verification}
\begin{itemize}
\vspace*{1mm}
\item Code Verification (code coverage, memory leaks and pointer
assignment testing, static argument list testing, \&c.)
\vspace*{1mm}
\item Solution verification (finite elements, constitutive integration,
material models, algorithms, seismic input, \&c.) based on analytic, closed form solutions
\vspace*{1mm}
\item Method of manufactured solutions for elastoplastic verification
\vspace*{1mm}
\item Parameter bounds (finite elements, material models, algorithms, \&c.)
\vspace*{1mm}
\item Develop error plots for elements, models, algorithms over a range of parameter
\end{itemize}
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\begin{frame}
\frametitle{Validation}
\begin{itemize}
\item {Traditional Experiments}
\begin{itemize}
\item Improve the fundamental understanding of physics involved
\item Improve the mathematical models for physical phenomena
\item Assess component performance
\end{itemize}
\vspace*{2mm}
\item {Validation Experiments}
\begin{itemize}
\item Model validation experiments
\item Designed and executed to quantitatively estimate mathematical
model's ability to simulate well defined physical behavior
\item The simulation tool (Real ESSI Simulator) (conceptual model, computational model,
computational solution) is the customer
\item New USDOE project to validate
inelastic seismic wave propagation and soilstructure interaction
\end{itemize}
\end{itemize}
\end{frame}
\end{document}
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