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\title[ESSI Modeling and Simulation]
{Earthquake Soil Structure Interaction \\
(ESSI) \\
Modeling and Simulation }
%\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.
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% affiliation.
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\pgfdeclareimage[height=0.7cm]{lbnl-logo}{/home/jeremic/BG/amblemi/lbnl-logo}
\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{JEC-logo}\hspace{1mm}\pgfuseimage{university-logo}\hspace{1mm}\pgfuseimage{lbnl-logo}] % (optional, but mostly needed)
%{ Professor, University of California, Davis\\
{Consulting Engineer, Jeremic Engineering Consultants \\
%
Professor, University of California, Davis\\
% and\\
% Faculty Scientist, Lawrence Berkeley National Laboratory, Berkeley }
Faculty Scientist, 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 INL Steering Committee Meeting \\
December 2013}
\subject{}
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% may not be suitable. Here are some rules that apply for this
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% - 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
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% - In a 20min talk, getting the main ideas across is hard
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% 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{Intro}
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\subsection{Motivation}
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\begin{frame}
\frametitle{Motivation}
\begin{itemize}
%\vspace*{0.3cm}
\item Improving seismic design for Nuclear Power Plants (NPPs)
\vspace*{0.5cm}
\item Use of high fidelity numerical models for analyzing seismic behavior
of NPP soil structure interaction (SSI) system
\vspace*{0.5cm}
\item Accurately follow, and direct (!), in space and time, flow of
seismic energy through the NPP SSI system
%\vspace*{0.3cm}
% \item Direct in space and time, flow of seismic energy through the
% NPP SSI system
\end{itemize}
\end{frame}
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%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{The Very First Published Work on ESSI}
%
% \begin{itemize}
% \item Professor Kyoji Suyehiro
% \item Ship engineer (Professor of Naval Arch. at U. of Tokyo),
% \item Witnessed Great Kant{\= o} earthquake
% (Tokyo, 01Sept1923
% 11:58am(7.5),
% 12:01pm(7.3),
% 12.03pm(7.2),
% shaking until 12:08pm)
% \item Saw earthquake surface waves travel and buildings sway
% \item Became founding Director of the
% Earthquake Engineering Research
% Institute at the Univ. of Tokyo,
% \item His published records (ASCE 1932) show
% four times more damage to soft
% wooden buildings on soft ground
% then same buildings on stiff soil
% \end{itemize}
%
% \end{frame}
%
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\begin{frame}
\frametitle{Hypothesis}
\begin{itemize}
%\vspace*{0.5cm}
\item Interplay of an Earthquake with
Soil/Rock and Structure, in time domain, plays a major
role in seismic response successes and failures.
\vspace*{0.2cm}
\item Timing and spatial location of energy dissipation determines location
and amount of damage.
\vspace*{0.2cm}
\item If timing and spatial location of energy dissipation
can be controlled (directed, designed),
NPP soil structure systems can be optimized for
\begin{itemize}
\item Safety and
\item Economy
\end{itemize}
\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 {{\bf Verification} provides evidence that the
model is solved correctly.} Mathematics issue.
\vspace*{1mm}
\item {{\bf Validation} provides
evidence that the correct model is solved.} Physics issue.
\vspace*{1mm}
\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*{1mm}
\item Goal: physics based predictive capabilities
with {\bf low Kolmogorov Complexity}
\vspace*{1mm}
\item High Fidelity, {\bf hierarchical}, predictive capabilities, aim for
higher modeling sophistication then needed
\end{itemize}
\end{frame}
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\subsection{Flow of Seismic Energy}
% %-
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{NPP SSI System: Seismic Energy Input}
%
% \begin{itemize}
%
% \vspace*{-1.5cm}
% \item Kinetic energy flux through closed surface $\Gamma$ includes both incoming
% and outgoing waves (using Domain Reduction Method by Bielak et al.)
% \begin{eqnarray*}
% E_{flux} =
% \left[0 ; -M^{\Omega+}_{be} \ddot{u}^0_e-K^{\Omega+}_{be}u^0_e ;
% M^{\Omega+}_{eb}\ddot{u}^0_b+K^{\Omega+}_{eb}u^0_b \right]_i
% %
% % \left[
% % \begin{array}{c}
% % 0 \\
% % -M^{\Omega+}_{be} \ddot{u}^0_e-K^{\Omega+}_{be}u^0_e \\
% % M^{\Omega+}_{eb}\ddot{u}^0_b+K^{\Omega+}_{eb}u^0_b
% % \end{array}
% % \right]^{T}
% \times u_i
% %\left[
% %\begin{array}{c}
% %0 \\
% %{u}_b\\
% %{u}_e
% %\end{array}
% %\right]
% \end{eqnarray*}
%
% \item Alternatively, $E_{flux} = \rho A c \int_0^t \dot{u}_i^2 dt$
%
% \item Outgoing kinetic energy \\
% is obtained from outgoing \\
% wave field ($w_i$, in DRM)
%
% \item Incoming kinetic energy \\
% is then the difference.
%
%
% \end{itemize}
%
%
% \vspace*{-7.0cm}
% % \begin{figure}[!hbpt]
% %\begin{flushright}
% \hfill \includegraphics[width=5.5cm]{/home/jeremic/tex/works/psfigures/DRMidea03.pdf}
% %\end{flushright}
% %\end{figure}
% \vspace*{-2cm}
%
%
% \end{frame}
% %-
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
% \frametitle{Seismic Energy Dissipation for \underline{Soil}-Foundation-Structure Systems}
\frametitle{Seismic Energy Input and Dissipation}
% \frametitle{Seismic Energy Dissipation for
% \underline{Soil}-Foundation-Structure Systems}
\begin{itemize}
\item Seismic energy influx through closed boundary
% $E_{flux} = \rho A c \int_0^t \dot{u}_i^2 dt$
\vspace*{2mm}
\item Mechanical dissipation outside of NPP SSI domain:
\begin{itemize}
\item reflected wave radiation
\item NPP SSI system oscillation radiation
\end{itemize}
\vspace*{2mm}
\item Mechanical dissipation inside NPP SSI domain:
\begin{itemize}
\item plasticity of soil subdomains
\item viscous coupling of porous solid with pore fluid (air, water)
\item plasticity/damage of the parts of structure/foundation
\item viscous coupling of structure/foundation with fluids
% \item potential and kinetic energy
\item potential $\leftarrow \! \! \! \! \! \! \rightarrow$ kinetic energy
\end{itemize}
\vspace*{2mm}
% \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{Energy Dissipation by Soil Plasticity}
\vspace*{2mm}
Energy dissipation (plastic work) capacity for different soils
%
% \begin{itemize}
%
% % \item Plastic work ($W = \int_{0}^{t} \sigma_{ij} d \epsilon_{ij}^{pl}$)
% \item Plastic work
% % ($W = \int \sigma_{ij} d \epsilon_{ij}^{pl}$)
%
% \item Energy dissipation capacity for different soils
%
%
% \end{itemize}
%\vspace*{-1.0cm}
\begin{center}
\vspace*{-0.9cm}
\includegraphics[width=8.5cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/Energy-Capacity2.pdf}
\hspace*{-0.2cm}
%\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/Energy-Capacity10.pdf}
\vspace*{-1.0cm}
\end{center}
\end{frame}
%-
%- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%- \begin{frame}
%- \frametitle{Plasticity Energy Dissipation}
%-
%- \begin{itemize}
%-
%- \item
%-
%- \end{itemize}
%-
%-
%- \end{frame}
%- %-
%- %- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%- \begin{frame}
%- \frametitle{Energy Dissipation by Soil Viscous Coupling}
%-
%-
%- \begin{itemize}
%-
%- \item Viscous coupling of porous solid and fluid
%- \item Energy loss per unit volume is $E_{vc}= n^2 k^{-1} (\dot{U}_i - \dot{u}_i)^2$
%- \item Natural in $u-p-U$ formulation:
%-
%- \end{itemize}
%- %\vspace*{-0.4cm}
%-
%-
%-
%-
%- \begin{footnotesize}
%- %\begin{tiny}
%- \begin{eqnarray*}
%- %& &\left[ \begin{array}{ccc}
%- \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}
%- \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{tiny}
%- \end{footnotesize}
%-
%- \vspace*{-1cm}
%-
%- \begin{footnotesize}
%- \begin{eqnarray*}
%- %%%%%%%%
%- (C_{(1,2,3)})_{KijL}
%- =
%- \int_{\Omega} N_K^{(u,u,U)}
%- n^2 k_{ij}^{-1}
%- N_L^{(u,U,U)} d\Omega
%- % (C_1)_{KijL} =\int_{\Omega} N_K^u n^2 k_{ij}^{-1} N_L^u d\Omega
%- % \;\; \mbox{;} \;\;
%- % (C_2)_{KijL} =\int_{\Omega} N_K^u n^2 k_{ij}^{-1} N_L^U d\Omega
%- % %%%%%%%%
%- % %\;\; \mbox{;}\;\;
%- % \\
%- % %%%%%%%%
%- % (C_3)_{KijL} =\int_{\Omega} N_K^U n^2 k_{ij}^{-1} N_L^U d\Omega
%- \end{eqnarray*}
%- \end{footnotesize}
%- %
%- %
%- %
%- %
%- %\newpage
%-
%-
%-
%-
%- \end{frame}
%- %-
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%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Numerical Energy Dissipation}
%
% \begin{itemize}
%
% \item Newmark and Hilber-Hughes-Taylor integration algorithms can be
% made non-dissipative for
% elastic system $\alpha=0.0, \beta = 0.25 ; \gamma = 0.5,$
%
% \item Or dissipative (for elastic) for higher frequencies
% %Newmark ($\gamma \ge 0.5, \;\;\; \beta = 0.25(\gamma+0.5)^2$ ),
% %Hilber-Hughes-Taylor ($-0.3\dot{3}\le\alpha \le0, \;\;\;\gamma =
% %0.5(1-2\alpha), \;\;\; \beta = 0.25(1-\alpha)^2$)
% \begin{itemize}
% \item N: $\gamma \ge 0.5, \;\;\; \beta = 0.25(\gamma+0.5)^2$,
% \item HHT: $-0.3\dot{3}\le\alpha \le0, \;\;\;\gamma =
% 0.5(1-2\alpha), \;\;\; \beta = 0.25(1-\alpha)^2$
% \end{itemize}
%
% \item For nonlinear problems,
% energy cannot be maintained
% \begin{itemize}
% \item Energy dissipation for steps with reduction of stiffness
% \item Energy production for steps with increase of stiffness
%
% \hspace{1cm}
% \includegraphics[width=1.80cm, angle=-90]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/EnergyDissipationReducationStiffness.pdf}
% \hspace{1cm}
% \includegraphics[width=1.80cm, angle=-90]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/EnergyProductionIncreaseStiffness.pdf}
% \hspace{1cm}
%
%
%
% \end{itemize}
%
%
% \end{itemize}
%
%
% \end{frame}
% %-
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Modeling Uncertainty}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Modeling Uncertainty}
\begin{itemize}
%\vspace*{0.3cm}
\item Simplified (or inadequate/wrong) modeling: important features are
missed (seismic ground motions, etc.)
\vspace*{0.2cm}
\item Introduction of uncertainty and (unknown) lack of accuracy in results due
to use of un-verified simulation tools (software quality, etc.)
\vspace*{0.2cm}
\item Introduction of uncertainty and (unknown) lack of accuracy in results due
to use of un-validated models (due to lack of quality validation experiments)
% (still missing data, experiments under
% uncertainty, for more see below)
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Complexity of and Uncertainty in Ground Motions}
\begin{itemize}
%\vspace*{0.3cm}
\item 6D (3 translations, 3 rotations)
\vspace*{0.3cm}
\item Vertical motions usually neglected
\vspace*{0.3cm}
\item Rotational components usually not measured and neglected
\vspace*{0.3cm}
\item Lack of models for such 6D motions (from measured data))
\vspace*{0.3cm}
\item Sources of uncertainties in ground motions (Source, Path (rock), soil (rock))
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Complexity of and Uncertainty in Material Modeling}
\begin{itemize}
%\vspace*{0.3cm}
\item All engineering materials experience inelastic deformations for working loads
\vspace*{0.1cm}
\item This is even more so for hazard loads (earthquakes)
\vspace*{0.1cm}
\item Pressure sensitive materials (soil, rock , concrete, etc) can have very
complex constitutive response, tying together nonlinear stress-strain with volume response
\vspace*{0.1cm}
\item Simplistic material modeling (elastic, $G/G_{max}$, etc.) introduce
(significant) uncertainties in response results
\vspace*{0.1cm}
\item In addition, man-made and natural materials are spatially variable and
their material modeling parameters are uncertain
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{Material Behavior Inherently Uncertain}
%\begin{itemize}
%\vspace*{0.5cm}
%\item
%Material behavior is inherently uncertain (concrete, metals, soil, rock,
%bone, foam, powder etc.)
\begin{itemize}
\vspace*{0.5cm}
\item Spatial \\
variability
\vspace*{0.5cm}
\item Point-wise \\
uncertainty, \\
testing \\
error, \\
transformation \\
error
\end{itemize}
% \vspace*{0.5cm}
% \item Failure mechanisms related to spatial variability (strain localization and
% bifurcation of response)
%
% \vspace*{0.5cm}
% \item Inverse problems
%
% \begin{itemize}
%
% \item New material design, ({\it point-wise})
%
% \item Solid and/or structure design (or retrofits), ({\it spatial})
%
% \end{itemize}
%\end{itemize}
\vspace*{-5cm}
\begin{figure}[!hbpt]
%\nonumber
%\begin{center}
\begin{flushright}
%\includegraphics[height=5.0cm]{/home/jeremic/tex/works/Conferences/2006/KragujevacSEECCM06/Presentation/MGMuzorak01.jpg}
\includegraphics[height=5.5cm]{/home/jeremic/tex/works/Conferences/2006/KallolsPresentationGaTech/FrictionAngleProfile.jpg}
\\
\mbox{(Mayne et al. (2000) }
\end{flushright}
%\end{center}
%\end{center}
\end{figure}
\end{frame}
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\begin{frame}
\frametitle{SPT Based Determination of Shear Strength}
\begin{figure}[!hbpt]
\begin{center}
%
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_RawData_and_MeanTrend-Mod.pdf}
\hfill
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_Histogram_PearsonIV-FineTuned-Mod.pdf}
%
\end{center}
\end{figure}
\vspace*{-0.3cm}
Transformation of SPT $N$-value $\rightarrow$ un-drained shear
strength, $s_u$ (cf. Phoon and Kulhawy (1999B)
Histogram of the residual
(w.r.t the deterministic transformation
equation) un-drained strength,
along with fitted probability density function
(Pearson IV)
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{SPT Based Determination of Young's Modulus}
\begin{figure}[!hbpt]
\begin{center}
%
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01-Ed.pdf}
\hfill
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_Histogram_Normal_01-Ed.pdf}
%
\end{center}
\end{figure}
\vspace*{-0.3cm}
Transformation of SPT $N$-value $\rightarrow$ 1-D Young's modulus, $E$ (cf. Phoon and Kulhawy (1999B))
Histogram of the residual (w.r.t the deterministic transformation equation) Young's modulus, along with fitted probability density function
\end{frame}
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Verification and Validation}
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Verification \& Validation (V\&V) Definition}
%
%
% \begin{itemize}
%
% % \vspace*{1.0truecm}
% \item {\bf Verification}: The process of determining that a model
% implementation accurately represents the developer's conceptual description
% and specification. Mathematics issue. {\it Verification provides evidence that the
% model is solved correctly.}
%
% \vspace*{0.5truecm}
% \item {\bf Validation}: The process of determining the degree to which a
% model is accurate representation of the real world from the perspective of
% the intended uses of the model. Physics issue. {\it Validation provides
% evidence that the correct model is solved.}
%
%
%
% \end{itemize}
%
%
% \end{frame}
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Importance of V\&V}
%
%
% \begin{itemize}
%
% % \vspace*{2.0truecm}
% \item V \& V procedures are the primary means of assessing accuracy in
% modeling and computational simulations
%
% \vspace*{0.5truecm}
% \item V \& V procedures are the tools with which we build confidence and
% credibility in modeling and computational simulations
%
%
% \end{itemize}
%
%
% \end{frame}
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Role of Verification and Validation}
%
%
% \begin{figure}[!h]
% \begin{center}
% \hspace*{-2cm}
% %{\includegraphics[width=5.0cm]{/home/jeremic/tex/works/Conferences/2012/ASME_V_and_V_symposium/presentetation/RoleVV_NEW_knowledge.pdf}}
% {\includegraphics[width=8.5cm]{/home/jeremic/tex/works/Conferences/2011/USNCCM11_Minneapolis/Coupled/Present/VandV_ODEN.jpg}}
% \hspace*{-2cm}
% \end{center}
% \end{figure}
%
% {Oden et al.}
% %{Oberkampf et al. \hspace*{4cm} Oden et al.}
% forCaltrans %
% %\item Models available (some now, some later)
% %\vspace*{-2.0cm}
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Types of Physical Experiments}
%
%
% \begin{itemize}
%
% % \vspace*{1.0truecm}
% \item {\bf 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*{0.2truecm}
% \item {\bf 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 (SimTool) (conceptual model, computational model,
% computational solution) is the customer
% \item Experimental uncertainty analysis!
% \end{itemize}
%
%
% \end{itemize}
%
%
%
% \end{frame}
%
%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% % \frametitle{Validation Experiments}
% %
% %
% % \begin{itemize}
% %
% % \vspace*{0.0truecm}
% % \item Jointly designed and executed by
% % experimentalist and computationalist
% % %
% % \item Designed to capture the relevant physics
% %
% % \item Use any possible synergism between
% % experiment and computational approaches
% %
% % \item Maintain independence between computational and experimental results
% %
% % \item Validate experiments on unit level problems, hierarchy of experimental
% % measurements should be made which present an increasing range of
% % computational difficulty
% %
% % \item Develop experimental uncertainty analysis
% %
% % \end{itemize}
% %
% %
% %
% % \end{frame}
% %
%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Validation and Application Domains -- No Overlap}
%
%
% %\vspace*{0.3cm}
%
% \begin{figure}[!h]
% \begin{center}
% %\vspace*{-2.5cm}
% {\includegraphics[width=4.0cm]{/home/jeremic/tex/works/Presentation/2004/VandV/VPI03.pdf}}
% %\vspace*{-5.0cm}
% \end{center}
% \end{figure}
%
% %\vspace*{-0.5cm}
%
% \begin{itemize}
% \item Inference $\Rightarrow$ probabilistic modeling and numerical
% simulation (deterministic is a special case)
% % % \item Validation domain is actually an aggregation of tests and thus might not
% % % be convex (bifurcation of behavior)
% % \item Current experiments $\Rightarrow$ non--overlapping validation and
% % application domains
% % % \item We have to rely on {\bf Modeling} and {\bf Numerical Simulation}
% \end{itemize}
%
% \end{frame}
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Prediction}
%
%
% \begin{itemize}
%
% \vspace*{0.0truecm}
% \item Prediction: use of computational model to foretell the state of a
% physical system under consideration under conditions for which the
% computational model has not been validated
%
% \vspace*{0.3truecm}
% \item Validation does not directly make a claim about the accuracy of a prediction
% \begin{itemize}
% \item Computational models are easily misused (unintentionally or intentionally)
% \item How closely related are the conditions of the prediction and
% specific cases in validation database
% \item How well is physics of the problem understood
%
% \end{itemize}
%
%
% \end{itemize}
%
%
%
% \end{frame}
%
%
%
%
% %
%
%
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{ESSI System}
%
\subsection{ESSI Program}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \begin{frame}
% \frametitle{Desirable Modeling and Simulation Capabilities}
%
%
% \begin{itemize}
%
% \item Body (SH, SV, P) and Surface (Rayleigh, Love, etc) seismic motions modeling
% and their input into finite element models
%
% \item Elastic-plastic modeling of dry and saturated soil/rock behavior beneath
% foundations
%
% \item Elastic-plastic modeling of soil/rock (limited data)
%
% \item Soil/rock - foundation contact zone modeling (for dry and saturated
% conditions)
%
% \item Verification and Validation suite
%
% \item High performance, parallel simulation using dynamic domain
% decomposition (Plastic Domain Decomposition) for elastic-plastic simulations
%
% \item Probabilistic elasto-plasticity and stochastic elastic-plastic finite
% element methods
%
%
% \end{itemize}
%
% \end{frame}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{ESSI Simulator System}
\begin{itemize}
\item {\bf ESSI-Program} is a 3D, nonlinear, time domain,
parallel finite element program specifically developed for
Hi-Fi modeling and simulation of Earthquake Soil/Rock Structure
Interaction of NPPs on ESSI-Computer. \
%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 (NRC-ESSI-Program). Significant effort is devoted to development
%of verification and validation procedures, as well as on development of
%extensive documentation. NRC-ESSI-Program is in public domain and is licensed
%through the Lesser GPL.
%\vspace*{0.3cm}
\vspace*{0.1cm}
\item {\bf ESSI-Computer} 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*{0.1cm}
\item {\bf ESSI-Notes} are 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
%NRC-ESSI-Program code API (application Programming Interface) and DSLs (Domain
%Specific Language).
%%NRC-ESSI-Notes, developed by Boris Jeremic and collaborators, are in public
%domain
%%and are licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported
%%License.
%
%\vspace*{0.3cm}
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{ESSI Program: Finite Elements}
%\vspace*{-3mm}
\begin{itemize}
\vspace*{1mm}
\item Dry/single phase solids (8, 20, 27 8-27 node bricks)
\vspace*{1mm}
\item Saturated/two phase solids (8 and 27 node bricks, liquefaction modeling, buoyant forces)
\vspace*{1mm}
\item Quad (ANDES) Shell (6DOFs per node)
\vspace*{1mm}
\item Beams (6DOFs and variable DOFs per node)
\vspace*{1mm}
\item Truss
\vspace*{1mm}
\item Contacts (dry or saturated soil/rock - concrete, gap
opening-closing, frictional slip)
\vspace*{1mm}
\item Base isolators (elastomeric, frictional pendulum)
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{ESSI Program: Material Models}
%\vspace*{-2mm}
\begin{itemize}
\item Linear and nonlinear, isotropic and anisotropic elastic
\vspace*{3.5mm}
\item Elastic-Plastic (von Mises, Drucker Prager, Rounded Mohr-Coulomb,
Parabolic Leon, Cam-Clay, SaniSand (Dafalias-Manzari), SaniClay,
Pisan{\`o}...)
\vspace*{3.5mm}
\item All elastic-plastic models can be used as perfectly
plastic, isotropic hardening/softening and kinematic hardening
models
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{ESSI Program: Seismic Input}
\begin{itemize}
\item Analytic input of seismic motions
\begin{itemize}
\item Body waves (P, SH, SV)
\item Surface waves (Rayleigh, Love, etc.)
\item Analytic radiation damping
\end{itemize}
\vspace*{3.5mm}
\item Domain Reduction Method (Bielak et al.)
\vspace*{3.5mm}
\item Synthetic and realistic seismic motions (Hisada, fk, FEM, etc.)
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{ESSI Program: Verification and Validation}
\begin{itemize}
\vspace*{2mm}
\item Detailed Verification (math issue)
\begin{itemize}
\item Finite elements
\item Material model
\item Solution algorithms
\item Analysis procedure
\item Code
documented in detail in ESSI Notes.
\end{itemize}
\vspace*{2mm}
\item (Not so) Detailed Validation (physics issue) (lack of high quality experimental data)
\vspace*{2mm}
\item Detailed V\&V documentation in ESSI Notes
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{ESSI Program: High Performance Computing, Parallel}
\begin{itemize}
\vspace*{2mm}
\item Sequential computing: available for all models, however
\vspace*{2mm}
\item High Performance Parallel Computing: for high fidelity
modeling, parallel is really the only option.
Parallel ESSI Program available on
\begin{itemize}
\item Single, multi-core/multi-CPU PCs,
\item Clusters of (multi-core/multi-CPU) PCs,
\item Distributed memory parallel (DMP) supercomputers (all top national
supercomputers).
\end{itemize}
\vspace*{2mm}
\item Template metaprograms for local, element and material model level high
performance computing
% Parallel algorithm uses our
% original Plastic Domain Decomposition method (featuring dynamic computational
% load balancing) that is efficient for elastic-plastic finite element problems
% where elastic-plastic (slow) and elastic (fast) domains change dynamically
% during run time.
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{ESSI Program: Probabilistic/Stochastic}
%\vspace*{-2mm}
\begin{itemize}
%\vspace*{-2.5mm}
\item Constitutive:
% Euler-Lagrange form of
%
Fokker-Planck-Kolmogorov equation for probabilistic elasto-plasticity (PEP)
%\vspace*{-1.5mm}
\item Spatial: stochastic elastic plastic finite element method (SEPFEM)
\item Uncertain: material (LHS) and loads (RHS):
$M_{AacB} \; \ddot{\bar{u}}_{Bc} +
C_{AacB} \; \dot{\bar{u}}_{Bc} +
K^{EP}_{AacB} \; \bar{u}_{Bc}
=
F_{Aa}$
%
%
% $M \ddot{\bf u} + C \dot{\bf u} + K^{ep} {\bf u} = F$
%
%
\item Results ($u_{i}, \sigma_{ij}, \epsilon{ij}$) are very accurate
(second order accurate for stress) Probability Density Functions (PDFs)
\item PEP and SEPFEM are {\bf not} based on a Monte Carlo method,
\item Uncertain input variables and uncertain DOFs are expanded into
spectral probabilistic spaces, single run solution
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Probabilistic Modeling}
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
%
% \frametitle{Recent State-of-the-Art}
%
% \begin{itemize}
%
% %\vspace*{-0.5cm}
% \item Governing equation
%
% % \vspace*{-0.5cm}
% \begin{itemize}
%
% \item Dynamic problems $\rightarrow$ $ M \ddot u + C \ddot u + K u = F $
%
% \item Static problems $\rightarrow$ $ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ K u = F $
%
% \end{itemize}
%
% %\vspace{-0.4cm}
% \item Existing solution methods
%
% % \vspace*{-0.5cm}
% \begin{itemize}
%
% \item \textbf{Random r.h.s} (external force random)
%
% \begin{itemize}
%
% \item FPK equation approach
%
% \item Use of fragility curves with deterministic FEM (DFEM)
%
% \end{itemize}
%
% % \vspace*{0.2cm}
% \item \textbf{Random l.h.s} (material properties random)
%
% \begin{itemize}
%
% \item Monte Carlo approach with DFEM $\rightarrow$ CPU expensive
%
% % \item Stochastic finite element method (e.g. Perturbation method
% % $\rightarrow$ a linearized expansion! Error increases as a function
% % of COV; Spectral method
% % $\rightarrow$ developed for elastic materials so far)
%
% \item Perturbation method
% $\rightarrow$ a linearized expansion! Error increases as a function
% of COV
%
% \item Spectral method
% $\rightarrow$ developed for elastic materials so far
%
% % \begin{itemize}
% %
% % \item Perturbation method $\rightarrow$ fails if COVs of soil $>$ 20\%
% %
% % \item Spectral method $\rightarrow$ only for elastic material
% %
% % \end{itemize}
%
% \end{itemize}
%
% \end{itemize}
%
% \item Original development of {\bf Probabilistic Elasto--Plasticity}
%
%
% \end{itemize}
%
% \end{frame}
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{Eulerian--Lagrangian FPK Equation and (SEP)FEM}
%
%
%
% \begin{itemize}
%
% \item Constitutive: Advection-diffusion equation
% %
% \begin{equation}
% \nonumber
% \frac{\partial P(\sigma_{ij},t)}{\partial t}
% =
% -\frac{\partial}{\partial\sigma_{ab}}
% \left[N_{ab}^{(1)}P(\sigma_{ij},t)
% -
% \frac{\partial}{\partial \sigma_{cd}}
% \left\{N_{abcd}^{(2)} P(\sigma_{ij},t)\right\} \right]
% \end{equation}
%
% %
%
% \vspace*{0.1cm}
% \item {\bf Complete} probabilistic description of stress-strain response
%
%
% \vspace*{0.1cm}
% \item {\bf Second-order exact} to covariance of time (exact mean and variance)
%
% % -
% % - \item Deterministic equation in probability density space
% % -
% % - \item Linear PDE in probability density space
% % - $\rightarrow$ simplifies the numerical solution process
% % -
%
% %\item Applicable to any elastic-plastic-damage material model (only coefficients $N_{ab}^{(1)}$
% %and $N_{abcd}^{(2)}$ differ)
%
%
% \vspace*{0.1cm}
% \item Any uncertain FEM problem
% (${\bf M} \ddot{\bf u}
% +
% {\bf C} \dot{\bf u}
% +
% {\bf K} {\bf u}
% =
% {\bf F}
% $)
% with
% \begin{itemize}
% \item uncertain material parameters (stiffness matrix ${\bf K}$),
% \item uncertain loading (load vector ${\bf F}$)
% \end{itemize}
% can be analyzed using PEP and SEPFEM to obtain PDFs of DOFs,
% stress, strain...
%
% % - %\vspace*{0.2cm}
% % - \item PEP solution is second order accurate (exact mean and standard deviation)
% % -
% % - %\vspace*{0.2cm}
% % - \item SEPFEM solution (PDFs) can be made as accurate as need be
% % -
% % -
% % - \item Tails of PDFs can than be used to develop accurate risk
% % -
% % -
% % - \item Application to a realistic case of seismic wave propagation
%
%
% %\vspace*{0.2truecm}
%
% \end{itemize}
%
%
% \end{frame}
%
%
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Probabilistic Elastic-Plastic Response}
\begin{figure}[!hbpt]
\begin{center}
%\includegraphics[height=6.0cm]{/home/jeremic/tex/works/Conferences/2011/ICASP11_Zurich/Present/PDF_Plot-Ed.pdf}
\includegraphics[width=9.5cm]{/home/jeremic/tex/works/Conferences/2012/DOE-LLNL-workshop-27-28-Feb-2012/ProbabilisticYielding_vonMises_G_and_cu_very_uncertain_PDF-edited.pdf}
\end{center}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Probabilistic Elastic-Plastic Response}
\begin{figure}[!hbpt]
\begin{center}
%\includegraphics[width=8cm]{/home/jeremic/tex/works/Papers/2007/ProbabilisticYielding/figures/vonMises_G_and_cu_very_uncertain/Contour_PDF-edited.pdf}
\includegraphics[width=8cm]{/home/jeremic/tex/works/Conferences/2012/DOE-LLNL-workshop-27-28-Feb-2012/ProbabilisticYielding_vonMises_G_and_cu_very_uncertain_Contour_PDF-edited.pdf}
\end{center}
\end{figure}
\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
%
%
% \frametitle{SPT Based Determination of Shear Strength}
%
%
%
%
% \begin{figure}[!hbpt]
% \begin{center}
% %
% \includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_RawData_and_MeanTrend-Mod.pdf}
% \hfill
% \includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_Histogram_PearsonIV-FineTuned-Mod.pdf}
% %
% \end{center}
% \end{figure}
%
% \vspace*{-0.3cm}
% Transformation of SPT $N$-value $\rightarrow$ undrained shear
% strength, $s_u$ (cf. Phoon and Kulhawy (1999B)
%
% Histogram of the residual
% (w.r.t the deterministic transformation
% equation) undrained strength,
% along with fitted probability density function
% (Pearson IV)
% \end{frame}
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
%
%
% \frametitle{SPT Based Determination of Young's Modulus}
%
%
% \begin{figure}[!hbpt]
% \begin{center}
% %
% \includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01-Ed.pdf}
% \hfill
% \includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_Histogram_Normal_01-Ed.pdf}
% %
% \end{center}
% \end{figure}
%
% \vspace*{-0.3cm}
% Transformation of SPT $N$-value $\rightarrow$ 1-D Young's modulus, $E$ (cf. Phoon and Kulhawy (1999B))
%
% Histogram of the residual (w.r.t the deterministic transformation equation) Young's modulus, along with fitted probability density function
%
% \end{frame}
%
%
%
%
%
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{ESSI Examples}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{3D, Inclined, Body and Surface}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Earthquake Ground Motions}
Realistic earthquake ground motions
\begin{itemize}
\vspace*{0.1cm}
\item Body waves: P and S waves
\vspace*{0.1cm}
\item Inclined waves
\vspace*{0.1cm}
\item 3D (6D!) waves
\vspace*{0.1cm}
\item Surface waves: Rayleigh, Love waves, etc.
\vspace*{0.1cm}
\item Surface waves carry most seismic energy of interest
\vspace*{0.1cm}
\item Lack of correlation (incoherence)
%\vspace*{0.1cm}
% \item Earthquake energy dissipation
\end{itemize}
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Body (P, S) and Surface (Rayleigh, Love) Waves}
%
%
% \vspace*{-0.3cm}
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=2.5cm, angle=45]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Presentation/P_body_wave.jpeg}
% \includegraphics[width=2.5cm, angle=45]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Presentation/S_body_wave.jpeg}
% \vspace*{-0.7cm}
% \\
% \includegraphics[width=3cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Presentation/Rayleigh_surface_wave.jpeg}
% \includegraphics[width=3cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Presentation/Love_surface_wave.jpeg}
% %\caption{\label{Love_surface_wave} Visualization of propagation of a Love
% %surface seismic wave (illustrations are from MTU web site).}
% \end{center}
% \end{figure}
%
% \end{frame}
%
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Spatial Variability (Incoherence, Lack of Correlation)}
%
% Incoherence $\rightarrow$ frequency domain
%
% \vspace*{0.2cm}
%
% Lack of Correlation $\rightarrow$ time domain
%
%
% \vspace*{0.5cm}
%
% \begin{itemize}
% \item Wave passage effects
% \item Attenuation effects
% \item Extended source effects
% \item Scattering effects
% % \item Variable seismic energy dissipation
% \end{itemize}
%
% %\begin{figure}[!htb]
% %\begin{center}
% \vspace*{-3.5cm}
% \hspace*{5.5cm}
% \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2011/NRC_Staff_Capacity_Building_25May2011/Lack_of_Correlation_5_points.pdf}
% %\caption{\label{LC} Four main sources contributing to the lack of correlation of
% %seismic waves as measured at two observation points.}
% %\end{center}
% %\end{figure}
% %
% %A number of models available (Abrahamson...)
% %
% \end{frame}
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Seismic Input}
%
%
% %\begin{itemize}
%
% % \item
% The Domain Reduction Method \\
% (Bielak et al.): \\
% The effective force $P^{eff}$ \\
% is a dynamically consistent \\
% replacement for the dynamic \\
% source forces $P_{e}$
%
% % \end{itemize}
%
% \begin{eqnarray}
% P^{eff} = \left\{\begin{array}{c} P^{eff}_i \\ P^{eff}_b \\ P^{eff}_e \end{array}\right\}
% = \left\{\begin{array}{c} 0 \\ -M^{\Omega+}_{be} \ddot{u}^0_e-K^{\Omega+}_{be}u^0_e
% \\ M^{\Omega+}_{eb}\ddot{u}^0_b+K^{\Omega+}_{eb}u^0_b\end{array}\right\}
% \nonumber
% \label{DRMeq09}
% \end{eqnarray}
% %
%
% \begin{figure}[!h]
% \begin{flushright}
% %\vspace*{-0.50cm}
% %\begin{center}
% %\hspace*{1cm}
% \vspace*{-6.90cm}
% {\includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2010/NRC-LBL-ProjectReviewMeeting_21_22_Sept_2010/DRM05NPP.pdf}}
% %\vspace*{-5.50cm}
% %\hspace*{1cm}
% %\vspace*{-2.50cm}
% %\end{center}
% %\vspace*{-0.3cm}
% \end{flushright}
% \end{figure}
%
%
%
%
% \end{frame}
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{DRM}
%
%
%
%
%
% \begin{itemize}
% %\vspace*{-0.2cm}
% \item Seismic forces $P_e$ replaced by $P^{eff}$
%
% %\vspace*{-0.2cm}
% \item $P^{eff}$ applied only to a single \\
% layer of elements next to $\Gamma$.
% %\vspace*{-0.2cm}
% \item The only outgoing waves are \\
% from dynamics of the NPP
% %\vspace*{-0.2cm}
% \item Material inside $\Omega$ \\
% can be elastic-plastic
%
% \item All types of seismic waves\\
% (body, surface...) are \\
% properly modeled
%
%
% % \item The only input wave field is the one for the nodes of this layer of elements.
% \end{itemize}
%
% \begin{figure}[!h]
% \begin{flushright}
% %\vspace*{-0.50cm}
% %\begin{center}
% %\hspace*{1cm}
% \vspace*{-4.50cm}
% {\includegraphics[width=5.8cm]{/home/jeremic/tex/works/Conferences/2010/NRC-LBL-ProjectReviewMeeting_21_22_Sept_2010/DRM05NPP.pdf}}
% %\vspace*{-5.50cm}
% \hspace*{-0.8cm}
% %\vspace*{-2.50cm}
% %\end{center}
% %\vspace*{-0.3cm}
% \end{flushright}
% \end{figure}
%
%
% \end{frame}
%
%
%
%
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%
%\subsection{3D Synthetic Seismic Motions}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{3D Synthetic Seismic Motions}
\begin{itemize}
\item Development of analytic and numerical 3D, inclined, uncorrelated
seismic motions for verification, stress testing of NPPs, etc.
\vspace*{0.2cm}
\item Large scale model
\vspace*{0.2cm}
\item Point shear source
\vspace*{0.2cm}
\item Stress drop:
\begin{itemize}
\item Wavelet (Ricker, \\
Ormsby, etc)
\item Analytic
\end{itemize}
\vspace*{0.2cm}
\item Seismic input using DRM (Bielak et al (2003))
\end{itemize}
\vspace*{-5.3cm}
\begin{flushright}
\hspace*{5mm}
\includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/wave_propagation/figs/FaultSlipModel2km.pdf}
\hspace*{-5mm}
\end{flushright}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Plane Wave Model}
\vspace*{-1cm}
\begin{figure}[!h]
\begin{flushright}
\includegraphics[width=4cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_wave_propagation_figs_DRMModel.pdf}
\label{fig:DRMModel}
\end{flushright}
\end{figure}
\vspace*{-1.5cm}
\begin{figure}[H]
\begin{center}
\includegraphics[width=8cm]{/home/jeremic/tex/works/Conferences/2011/NRC_LBNL_Review_Panel_Sept2011/2D_faul_slip_model.pdf}
\end{center}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Seismic Source Mechanics}
\vspace*{0.5cm}
Stress drop, Ormsby wavelet \\
controlled frequency range
\vspace*{-1.5cm}
\begin{figure}[H]
\begin{flushright}
\includegraphics[width=2cm]{/home/jeremic/tex/works/Conferences/2011/NRC_LBNL_Review_Panel_Sept2011/Seismic_source_moment_couple.pdf}
\end{flushright}
\end{figure}
\vspace*{-1.9cm}
\hspace*{-1cm}
\begin{figure}[H]
\begin{center}
\hspace*{-0.4cm}
\includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FaultModel_7seconds/xz_TimeHistory/3000_3000_x_displacement.pdf}
\hspace*{-0.4cm}
\includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FaultModel_7seconds/xz_FFT/3000_3000_x_displacement_FFT.pdf}
\end{center}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Middle (NPP Location) Plane,\\ Top 2km}
\vspace*{-2.0cm}
\begin{figure}[H]
\begin{flushright}
\includegraphics[width=4cm]{/home/jeremic/tex/works/Conferences/2011/NRC_LBNL_Review_Panel_Sept2011/2D_faul_slip_model_MIDDLE.pdf}
\end{flushright}
\end{figure}
\vspace*{-2.0cm}
\begin{figure}[H]
\begin{center}
\hspace*{-1.0cm}
\includegraphics[width=6.5cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FreeFieldInclinedMotionModels/Ormsby/middle_top2000/middle_acceleration_x.pdf}
\hspace*{-0.5cm}
\includegraphics[width=6.5cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FreeFieldInclinedMotionModels/Ormsby/middle_top2000/middle_acceleration_z.pdf}
\hspace*{-0.5cm}
\end{center}
\end{figure}
\vspace*{-0.90cm}
{horizontal accelerations \hfill vertical accelerations}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Verification: Displacements, Top Middle Point }
% \begin{itemize}
% \item
% \end{itemize}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[!htbp]
\begin{center}
\begin{tabular}{ccc}
%\hline
(X)
&
(Z)
\\
\includegraphics[width=5.0cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/wave_propagation/figs/ricker_2km/top_middle_comparison_disp_x.pdf}
&
\includegraphics[width=5.0cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/wave_propagation/figs/ricker_2km/top_middle_comparison_disp_z.pdf}
&
\end{tabular}
%\caption{Comparison of displacements for top middle point using Ricker wave $(f=1Hz)$ as an input motion}
%\label{fig:ricker_acc}
\end{center}
\end{figure}
\end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Verification: Accelerations, Top Middle Point }
% % \begin{itemize}
% % \item
% % \end{itemize}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{figure}[!htbp]
% \begin{center}
% \begin{tabular}{ccc}
% %\hline
% (X)
% &
% (Z)
% \\
% \includegraphics[width=5.0cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/wave_propagation/figs/ricker_2km/top_middle_comparison_accel_x.pdf}
% &
% \includegraphics[width=5.0cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/wave_propagation/figs/ricker_2km/top_middle_comparison_accel_z.pdf}
% &
% \end{tabular}
% %\caption{Comparison of accelerations for top middle point using Ricker wave $(f=1Hz)$ as an input motion}
% %\label{fig:ricker_acc}
% \end{center}
% \end{figure}
%
%
%
%
% \end{frame}
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Verification: Disp. and Acc., Out of DRM }
% \begin{itemize}
% \item
% \end{itemize}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[!htbp]
\begin{center}
\begin{tabular}{ccc}
%\hline
Displacement
&
Acceleration
\\
\includegraphics[width=5.0cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/wave_propagation/figs/ricker_2km/10_40_disp_x.pdf}
&
\includegraphics[width=5.0cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/wave_propagation/figs/ricker_2km/10_40_accel_x.pdf}
&
\end{tabular}
%\caption{Displacement and acceleration time history for a point outside of DRM layer in (x) direction}
%\label{fig:out_ricker_disp}
\end{center}
\end{figure}
\end{frame}
%
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\subsection{Model Verification, Mesh Size Effects}
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\begin{frame}
\frametitle{Motion Filtering: Mesh Size Effects}
\begin{itemize}
\item Finite element mesh "filters out" \\
high frequencies
%\vspace*{0.2cm}
\item Usual rule of thumb: 10-12 elements \\
needed per wave length
% (SASSI recommends only 5 ?!)
%
% \item Maximum grid spacing should not exceed
% $\Delta h \;\le\; {\lambda}/{10}\;=\;{v}/({10\,f_{max}})$
% where $v$ is the lowest wave velocity (shear, elastic-plastic ?)
%
% \item Tests without and with numerical damping, for different element sizes
%
\item 1D wave propagation model
%\vspace*{0.2cm}
\item 3D finite elements (same in 3D)
%\vspace*{0.2cm}
\item Motions applied as displacements at the bottom
\item Linear elastic and elastic -- linear hardening plastic material
\end{itemize}
%\begin{figure}[H]
\vspace*{-4.0cm}
\begin{flushright}
\includegraphics[width=0.7cm]{/home/jeremic/tex/works/Conferences/2011/NRC_Staff_Capacity_Building_21Nov2011/model01.pdf}
\end{flushright}
%\end{figure}
\vspace*{-0.4cm}
\begin{small}
\begin{table}[!htbp]
\centering
% \begin{tabular}{|c|c|c|c|c|}
\begin{tabular}{|r|m{2.6cm}|m{1.5cm}|m{1.8cm}|m{2.3cm}|}
\hline
case & model height [m] & $V_s$ [m/s] & El.size [m] & $f_{max}$ (10el) [Hz]\\
\hline
%\hline
3 & 1000 & 1000 & 10 & 10\\
%\hline
4 & 1000 & 1000 & 20 & 5\\
%\hline
6 & 1000 & 1000 & 50 & 2\\
\hline
% \begin{tabular}{|m{1.5cm}c|m{2.8cm}c|m{2.8cm}c|m{3.0cm}c|m{4.0cm}c|}
% \begin{tabularx}{\linewidth}{|c|c|c|c|c|}
% \begin{tabular*}{0.75\textwidth}{@{\extracolsep{\fill}}|c|c|c|c|c|}
\end{tabular}
% \end{tabularx}
\end{table}
\end{small}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Ormsby Wavelet Input Motions}
\begin{figure}[H]
\begin{center}
\includegraphics[width=9cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/MeshSize/figs/3_4_6/Input_Displacement.pdf}
\end{center}
\end{figure}
\end{frame}
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\begin{frame}
\frametitle{Linear Elastic Material: Surface Motions}
\begin{figure}[H]
\begin{center}
\includegraphics[width=9cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/MeshSize/figs/3_4_6/displacement.pdf}
\end{center}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Linear Elastic Material, FFT of Input and Surface Motions}
\begin{figure}[H]
\begin{center}
\includegraphics[width=9cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/MeshSize/figs/3_4_6/FFT.pdf}
\end{center}
\end{figure}
\end{frame}
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\begin{frame}
\frametitle{Elastic Plastic Material, Stress-Strain Response}
\begin{figure}[H]
\begin{center}
\vspace*{-1cm}
\includegraphics[width=6cm]{/home/jeremic/tex/works/Conferences/2013/INL-SteeringCommittee_Dec2013/elm180-H0_1-ss-2-A0_1m-H0_1E.pdf}
\end{center}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Elastic Plastic Material, Surface Response}
\begin{figure}[H]
\begin{center}
\vspace*{-1.5cm}
\includegraphics[width=9cm]{/home/jeremic/tex/works/Conferences/2013/INL-SteeringCommittee_Dec2013/H0_1E-A0_1m_TimeDomain.pdf}
\vspace*{-1.5cm}
\\
\vspace*{-1.5cm}
\includegraphics[width=9cm]{/home/jeremic/tex/works/Conferences/2013/INL-SteeringCommittee_Dec2013/H0_1E-A0_1m_FrequencyDomain.pdf}
\vspace*{-1.5cm}
\end{center}
\end{figure}
\end{frame}
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\subsection{Seismic Wave Propagation Through Uncertain Soils}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
%
% \frametitle{Applications}
%
%
%
%
% \begin{itemize}
%
% \vspace*{0.3cm}
% \item Stochastic elastic--plastic simulations of soils and structures
%
% \vspace*{0.3cm}
% \item Probabilistic inverse problems
%
% \vspace*{0.3cm}
% \item Geotechnical site characterization design
%
% \vspace*{0.3cm}
% \item Optimal material design
%
%
% \end{itemize}
%
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% - +
% - + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - +
% - + \begin{frame}
% - +
% - +
% - + \frametitle{Random Field Modeling of Uncertain Soil Properties}
% - +
% - + \begin{itemize}
% - +
% - + \item Finite scale model
% - +
% - + \begin{itemize}
% - +
% - + \item Short memory, finite correlation length
% - +
% - + \item Common autocovariance model $\rightarrow$ exponential, spherical, triangular, linear--exponential
% - +
% - + \end{itemize}
% - +
% - + \item Fractal model
% - +
% - + \begin{itemize}
% - +
% - + \item long memory, infinite correlation length $\rightarrow$ more realistic for modeling horizontal
% - + spatial uncertainty
% - +
% - + \item 1/f-type noise process with power spectral density, $P(\omega)~=~P_0~\omega^{-\gamma}$, with
% - + upper and/or lower frequency cut-off.
% - +
% - + \end{itemize}
% - +
% - + \end{itemize}
% - +
% - + \end{frame}
% - +
% - + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
%
% \frametitle{Seismic Wave Propagation through Stochastic Soil}
%
%
% \begin{itemize}
%
% %\item maximizing the log--likelihood of observing the spatial data under assumed joined distribution (for finite
% %scale model) or maximizing the log--likelihood of observing the periodogram estimates (for fractal model)
%
% \item Maximum likelihood estimates
%
% \vspace*{0.3truecm}
%
% %\begin{figure}
% \begin{flushleft}
% \hspace*{-1.7cm}
% \includegraphics[height=4.0cm]{/home/jeremic/tex/works/Thesis/KallolSett/Dissertation/figures/CPT_DataAnalysis_Plots/SamplingPlan-Edited.jpg}
% \hspace*{0.0cm}
% \includegraphics[height=4.0cm]{/home/jeremic/tex/works/Thesis/KallolSett/Dissertation/figures/CPT_DataAnalysis_Plots/TypicalDataPlotBH1-Edited.jpg} \\
% \small{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Typical CPT $q_T$}
% \end{flushleft}
% %\end{figure}
%
% \vspace*{-4.9truecm}
%
% %\begin{figure}
% \begin{flushright}
% \includegraphics[width=4.0cm]{/home/jeremic/tex/works/Thesis/KallolSett/Dissertation/figures/CPT_DataAnalysis_Plots/TypicalAutoCovariancePlotBH1_FiniteScale-Edited.jpg} \\
% \vspace*{0.01truecm}
% \small{Finite Scale}
% \end{flushright}
% %\end{figure}
%
% \vspace*{0.02truecm}
%
% %\begin{figure}
% \begin{flushright}
% \includegraphics[width=4.0cm]{/home/jeremic/tex/works/Thesis/KallolSett/Dissertation/figures/CPT_DataAnalysis_Plots/TypicalAutoCovariancePlotBH1_Fractal-Edited.jpg} \\
% \small{Fractal}
% \end{flushright}
% %\end{figure}
%
% \end{itemize}
%
%
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
\frametitle{"Uniform" CPT Site Data}
\vspace*{-0.7cm}
%\begin{figure}
\begin{center}
\includegraphics[height=6.7cm]{/home/jeremic/tex/works/Thesis/KallolSett/Dissertation/figures/CPT_DataAnalysis_Plots/EastWestProfile-Edited.pdf}
\end{center}
%\end{figure}
\end{frame}
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\begin{frame}
\frametitle{Random Field Parameters from Site Data}
%\begin{flushleft}
%\includegraphics[height=5.0cm]{PEER2007_3.jpg}
%\end{flushleft}
%\vspace*{-0.5truecm}
\begin{itemize}
\item Soil as 12.5 m deep 1--D soil column (von Mises Material)
\begin{itemize}
\item Properties (including testing uncertainty) obtained through random field modeling of CPT $q_T$
%
$\left = 4.99 ~MPa;~~Var[q_T] = 25.67 ~MPa^2; $\\
Cor. ~Length $[q_T] = 0.61 ~m; $ Testing~Error $= 2.78 ~MPa^2$
\end{itemize}
\vspace*{0.2cm}
\item $q_T$ was transformed to obtain $G$: ~~$G/(1-\nu)~=~2.9q_T$
\begin{itemize}
\item Assumed transformation uncertainty = 5\%
%
$\left = 11.57MPa; Var[G] = 142.32 MPa^2$ \\
Cor.~Length $[G] = 0.61 m$
\end{itemize}
%\begin{center}
%\hspace*{-1.7cm}
%\includegraphics[height=3.5cm]{Chapter9_Schematic.jpg}
%\hspace*{0.0cm}
%\includegraphics[height=3.5cm]{Chapter9_BaseDisplacement.jpg} \\
%\small{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Base Displacement}
%\end{center}
\vspace*{0.2cm}
\item Input motions: modified 1938 Imperial Valley
% \vspace*{-0.2cm}
% \begin{center}
% \includegraphics[height=2.0cm]{Chapter9_BaseDisplacement.jpg}
% \end{center}
\end{itemize}
\end{frame}
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%-- \begin{frame}
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%-- \frametitle{Seismic Wave Propagation through Stochastic Soil}
%--
%--
%--
%-- \begin{figure}
%-- \begin{center}
%-- \hspace*{-0.75cm}
%-- \includegraphics[width=9.0cm]{/home/jeremic/tex/works/Thesis/KallolSett/Dissertation/figures/Chapter9Plots/Chapter9_ElasticPlasticResponse-New.pdf}
%-- %\includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2007/USC_seminar/Application_figs/Mean_and_SDElasticPlastic_ps.pdf}
%-- \end{center}
%-- \end{figure}
%--
%-- Mean$\pm$ Standard Deviation
%--
%--
%--
%-- %\begin{flushleft}
%-- %\includegraphics[height=5.0cm]{PEER2007_3.jpg}
%-- %\end{flushleft}
%--
%-- % \hspace*{-1.0cm} \noindent Statistics of Top Node Displacement:
%-- %
%-- % \vspace*{-0.5truecm}
%-- %
%-- % \begin{figure}
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\begin{frame}
\frametitle{Decision About Site (Material) Characterization}
\begin{itemize}
\item Do nothing about site characterization (rely on experience): conservative
{\bf guess} of soil data, $COV = 225$\%, correlation length $= 12$m.
\vspace*{0.3cm}
\item Do better than standard site characterization: $COV = 103$\%, correlation
length $= 0.61$m)
\vspace*{0.3cm}
\item Improve site (material) characterization if probabilities of exceedance are unacceptable!
\end{itemize}
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\begin{frame}
\frametitle{Full PDFs of all DOFs (and $\sigma_{ij}$, $\epsilon_{ij}$, etc.)}
%\frametitle{Full PDFs for Real Data Case}
\begin{itemize}
\vspace*{0.7cm}
\item Stochastic Elastic-Plastic\\
Finite Element Method \\
(SEPFEM) \\
\vspace*{0.5cm}
\item Dynamic case
\vspace*{0.5cm}
\item Full PDF at \\
each time step $\Delta t$
\end{itemize}
\vspace*{-4.60cm}
\begin{flushright}
\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/Plots_with_Labels/EvolutionaryPDF_Actual-Edited.pdf}
%\vspace*{-0.75cm}
%\includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2007/USC_seminar/Application_figs/Mean_and_SDElasticPlastic_ps.pdf}
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\begin{frame}
\frametitle{PDF at each $\Delta t$ (say at $6$ s)}
\begin{figure}
\begin{center}
\hspace*{1.75cm}
\includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/Plots_with_Labels/PDFs_at6sec_Actual_vs_NoData-Edited.pdf}
\vspace*{-0.75cm}
%\includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2007/USC_seminar/Application_figs/Mean_and_SDElasticPlastic_ps.pdf}
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\begin{frame}
\frametitle{PDF $\rightarrow$ CDF (Fragility) at $6$ s}
\begin{figure}
\begin{center}
%\hspace*{-0.75cm}
\includegraphics[width=8.0cm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/Plots_with_Labels/CDFs_at6sec_Actual_vs_NoData-Edited.pdf}
\vspace*{-0.75cm}
%\hspace*{-0.75cm}
%\includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2007/USC_seminar/Application_figs/Mean_and_SDElasticPlastic_ps.pdf}
\end{center}
\end{figure}
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% \frametitle{Probability of Exceedance of $20$cm}
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% \begin{figure}
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% \includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/Plots_with_Labels/ProbabilityOfExceedance20cm_Actual_vs_NoData-Edited.pdf}
% \vspace*{-0.75cm}
% %\hspace*{-0.75cm}
% %\includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2007/USC_seminar/Application_figs/Mean_and_SDElasticPlastic_ps.pdf}
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% \frametitle{Probability of Exceedance of $50$cm}
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% \begin{figure}
% \begin{center}
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% \includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/Plots_with_Labels/ProbabilityOfExceedance50cm_Actual_vs_NoData-Edited.pdf}
% \vspace*{-0.75cm}
% %\hspace*{-0.75cm}
% %\includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2007/USC_seminar/Application_figs/Mean_and_SDElasticPlastic_ps.pdf}
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% \frametitle{Probabilities of Exceedance vs. Displacements}
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%
%
% \begin{figure}
% \begin{center}
% %\hspace*{-0.75cm}
% \includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/Plots_with_Labels/ProbabilityOfExceedance_vs_Displacement_Actual_vs_NoData-Edited.pdf}
% \vspace*{-0.75cm}
% %\hspace*{-0.75cm}
% %\includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2007/USC_seminar/Application_figs/Mean_and_SDElasticPlastic_ps.pdf}
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% \frametitle{Probabilities of Unacceptable Deformation}
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% \begin{figure}
% \begin{center}
% \vspace*{-0.3cm}
% \includegraphics[width=10.5cm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/NewPlots/with_legends_and_labels/Exceedance20cm_LomaPrieta-Edited_ps.pdf}
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% %\hspace*{-0.75cm}
% %\includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2007/USC_seminar/Application_figs/Mean_and_SDElasticPlastic_ps.pdf}
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% \frametitle{Probability of Unacceptable Deformation ($50$cm)}
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% %\hspace*{-0.75cm}
% %\includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2007/USC_seminar/Application_figs/Mean_and_SDElasticPlastic_ps.pdf}
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% \frametitle{Risk Informed Decision Process}
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% %\hspace*{-0.75cm}
% %\includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2007/USC_seminar/Application_figs/Mean_and_SDElasticPlastic_ps.pdf}
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\section{Summary}
\subsection*{Summary}
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\begin{frame}
\frametitle{Current NPP Model(s)}
%
% \vspace*{-0.5cm}
% \begin{figure}[!hbpt]
% \begin{center}
% %\hspace*{-0.5cm}
% \includegraphics[width=6cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/03_cropped.jpg}
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% %\vspace*{-0.5cm}
% \includegraphics[width=3cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/02_cropped.jpg}
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% %\vspace*{-1.5cm}
% \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/04_cropped.jpg}
% %\hspace*{-0.5cm}
% \end{center}
% \end{figure}
% %
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\vspace*{-1.0cm}
\begin{figure}[!hbpt]
\begin{center}
\raisebox{0.9cm}{\includegraphics[width=1.5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/04_cropped.jpg}}
\raisebox{1.2cm}{\includegraphics[width=3cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/02_cropped.jpg}}
\raisebox{-0.5cm}{\includegraphics[width=6cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/03_cropped.jpg}}
\end{center}
\end{figure}
\vspace*{-1.6cm}
\begin{itemize}
% \item Modular models
%\vspace*{-0.1cm}
\item General 3D seismic waves
%\vspace*{-0.1cm}
\item Foundation slip -- gap
%\vspace*{-0.1cm}
\item Isolators, dissipators
%\vspace*{-0.1cm}
\item Uncorrelated (incoherent) motions
%\vspace*{-0.1cm}
\item Saturated dense vs loose soil with buoyant forces
%\vspace*{-0.1cm}
\item Piles and pile groups
%\vspace*{-0.1cm}
\item Uncertain material (LHS) and seismic motions (RHS)
\end{itemize}
\end{frame}
%
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\begin{frame}
\frametitle{Summary}
\begin{itemize}
\item {\bf Interplay} of
{\bf uncertain}
{\bf earthquake},
{\bf uncertain}
{\bf soil},
and {\bf uncertain}
{\bf structure}, in time domain,
{\bf probably}
plays a
decisive role in seismic performance of NPPs
\vspace*{5mm}
\item Improve {\bf
risk informed
decision making} ({\bf design $\Rightarrow$ safety} and {\bf economy})
through
{\bf high fidelity},
% {\bf Deterministic} and
% {\bf Stochastic Elastic-Plastic Finite Element}
modeling and simulation
({\bf ESSI Simulator System})
% \vspace*{0.1cm}
% \item {\bf ESSI Simulator System}, extensively {\bf Verified} and
% {\bf Validated} is used for modeling, simulations, design and regulatory
% decision making
%
\vspace*{5mm}
\item {\bf Education} and {\bf training} of users (designers, regulators,
owners) will prove essential
\end{itemize}
\end{frame}
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{UCD/LBNL ESSI Group Current Work}
%
% \begin{itemize}
%
%
%
% %\vspace*{0.5cm}
% \item ESSI Simulator System: continued development
% (US-NRC, US-DOE, CNSC, and INL, AREVA, Shimizu Corp., IAEA, ...)
%
% \vspace*{0.2cm}
% \item Small Modular Reactor: ESSI modeling
% and simulation, 3D
% elastic-plastic soil models for professional practice (DOE, LLNL)
%
% \vspace*{0.2cm}
% \item Stochastic ESSI Modeling: uncertain source, path,
% site and SSI (NSF, US NRC, AREVA)
%
% \vspace*{0.2cm}
% \item ESSI of base isolated NPPs (US NRC, IAEA)
%
% \vspace*{0.2cm}
% \item Verification and Validation: (US NRC, DOE, AREVA)
%
% \vspace*{0.2cm}
% \item Education (US NRC, AREVA, Shimizu Corp., etc.)
%
% \end{itemize}
%
%
% \end{frame}
% %
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\begin{frame}
\frametitle{Acknowledgement}
\begin{itemize}
% \item High fidelity
% modeling and simulations for performance assessment of infrastructure systems
\vspace*{0.1cm}
\item Funding from and collaboration with the US-NRC,
US-NSF, US-DOE, CNSC, LLNL, INL,
AREVA NP GmbH, Shimizu Corp., and EDF is greatly appreciated,
\vspace*{0.5cm}
\item Collaborators, students:
Mr. Abell, Mr. Jeong, Mr. Aldridge. Mr. Kamranimoghadam, Mr. Karapiperis,
Mr. Watanabe, Mr. Chao,
Dr. Tafazzoli, Dr. Pisan{\`o}, Dr. Martinelli,
Dr. Preisig, Dr. Chang,
Prof. Sett (U. Bufallo), Prof. Taiebat (U. British Columbia), Prof. Yang (U. Alaska)
\end{itemize}
\end{frame}
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