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%\title{NRC Staff Capacity Building: \\
% Micromechanical Origins of Elasto-Plasticity }
\title{Challenges and Tools for \\
Non-Linear SSI Analysis }
%\subtitle
%{Include Only If Paper Has a Subtitle}
%\author[Author, Another] % (optional, use only with lots of authors)
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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}}
%\institute[Computational Geomechanics Group \hspace*{0.3truecm}
\institute[\pgfuseimage{university-logo}\hspace*{0.1truecm}\pgfuseimage{lbnl-logo}] % (optional, but mostly needed)
%{ Professor, University of California, Davis\\
{ University of California, Davis\\
% 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 UCB SSI Meeting, January 2013}
\subject{}
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\begin{frame}
\titlepage
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\begin{frame}
\frametitle{Presentation Goals}
\begin{itemize}
\item Briefly overview of most important current challenges
for SSI modeling and simulation (personal view )
\vspace*{0.3cm}
\item Briefly overview select current work that aims to address some of those
challenges
\vspace*{0.3cm}
\item Hope for a discussion/information about validation experiments
(we are done with the verification for the most part)
\end{itemize}
\end{frame}
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\section{Current Challenges}
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% \frametitle{}
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\subsection{Modeling Uncertainty}
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\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}
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\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}
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\begin{frame}
\frametitle{Errors in Scientific Software: The T Experiments}
\begin{itemize}
% \vspace*{0.2truecm}
\item Les Hatton, Kingston University (formerly of Oakwood Comp. Assoc.)
\vspace*{0.1truecm}
\item "Extensive tests showed that many software codes widely used in science
and engineering are not as accurate as we would like to think."
\vspace*{0.1truecm}
\item "Better software engineering practices would help solve this problem,"
\vspace*{0.1truecm}
\item "Realizing that the problem exists is an important first step."
\vspace*{0.1truecm}
\item Large experiment over 4 years measuring faults (T1) and failures (T2)
of scientific and engineering codes
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{The T2 Experiments}
\begin{itemize}
\item Specific application area: seismic data processing (inverse analysis)
\vspace*{0.2truecm}
\item Echo sounding of underground and reconstructing "images" of
subsurface geological structure
\vspace*{0.2truecm}
\item Nine mature packages, using same algorithms, on a same data set!
\vspace*{0.2truecm}
\item 14 primary calibration points for results check
\vspace*{0.2truecm}
\item Results "fascinating and disturbing"
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{T2: Disagreement at Calibration Points}
\begin{figure}[!h]
\begin{center}
\hspace*{-1.5cm}
%\vspace*{-2.5cm}
{\includegraphics[width=8.0cm]{/home/jeremic/tex/works/Conferences/2009/GheoMat/VandV_01/T2_01.jpg}}
\hspace*{-1.5cm}
%\vspace*{-5.0cm}
\end{center}
\end{figure}
% \begin{itemize}
%
%
%
% \end{itemize}
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% \begin{frame}
% \frametitle{T2: Stage 14, Interpretation of Data }
%
%
%
%
% \begin{figure}[!h]
% \begin{center}
% %\vspace*{-2.5cm}
% \vspace*{-1.0cm}
% \hspace*{-1.5cm}
% {\includegraphics[width=8.0cm]{/home/jeremic/tex/works/Conferences/2009/GheoMat/VandV_01/T2_02.jpg}}
% \hspace*{-1.5cm}
% \vspace*{-1.5cm}
% %\vspace*{-5.0cm}
% \end{center}
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\subsection{Uncertainty in Material Behavior/Properties}
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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}
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\begin{frame}
\frametitle{Soil Uncertainties and Quantification}
\begin{itemize}
%
%\vspace*{0.5cm}
\item Natural variability of soil deposit (Fenton 1999)
\begin{itemize}
\item Function of soil formation process
\end{itemize}
%
\vspace*{0.2cm}
\item Testing error (Stokoe et al. 2004)
\begin{itemize}
\item Imperfection of instruments
\item Error in methods to register quantities
\end{itemize}
%
\vspace*{0.2cm}
\item Transformation error (Phoon and Kulhawy 1999)
\begin{itemize}
\item Correlation by empirical data fitting (e.g. CPT data $\rightarrow$ friction angle etc.)
\end{itemize}
\end{itemize}
\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}
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\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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\subsection{Verification and Validation}
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\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.}
%
%\item Models available (some now, some later)
%\vspace*{-2.0cm}
\end{frame}
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\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}
%
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\section{Brief Overview of Select Modeling and Simulations Tools}
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\subsection{NRC ESSI Simulator System}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{NRC ESSI Simulator System}
\begin{itemize}
\item {\bf The NRC-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 (ESSI) problems for NPPs on NRC-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 The NRC-ESSI-Computer} is a distributed memory parallel computer,
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 The NRC-ESSI-Notes} is a hypertext documentation system detailing
modeling and simulation of NPP 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}
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\begin{frame}
\frametitle{NRC ESSI Simulator Program}
\begin{itemize}
%\vspace*{0.2cm}
\item Based on a Collection of Useful Libraries (library centric software
design, modular, portable)
\vspace*{0.3cm}
\item A number of models, elements and algorithms available
\vspace*{0.3cm}
\item Detailed V\&V (actually, good validation experiments are rare!)
\vspace*{0.3cm}
\item Current users, testers, collaborators: US-NRC, UCD students,
National Laboratories, Foreign Nuclear Regulatory Agencies,
Nuclear Power Companies
%\vspace*{0.3cm}
%\item Future target user space: a very limited number of experts
\end{itemize}
\end{frame}
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\begin{frame}[fragile]
\frametitle{NRC ESSI Simulator Computer}
A distributed memory parallel (DMP) computer
designed for high performance,
parallel finite element simulations
\begin{itemize}
\vspace*{0.2cm}
\item Multiple performance CPUs
and Networks
\vspace*{0.2cm}
\item Most cost-performance
effective
\vspace*{0.2cm}
\item Source compatibility with
any DMP supercomputers
\vspace*{0.2cm}
\item Current system: 208 CPUs (near future: 784 CPUs)
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{NRC ESSI Simulator Notes}
A hypertext documentation system describing in detail modeling and
simulations of NPP ESSI problems
\begin{itemize}
\vspace*{0.3cm}
\item[] {\bf Part I}: Theoretical and Computational Formulations
\vspace*{0.3cm}
\item[] {\bf Part II}: Software and Hardware Platform Design
\vspace*{0.3cm}
\item[] {\bf Part III}: Verification and Validation
\vspace*{0.3cm}
\item[] {\bf Part IV}: Application to Practical Nuclear Power Plant Earthquake
Soil/Rock Structure Interaction Problems
\end{itemize}
\end{frame}
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\subsection{Pisan{\` o} Material Model}
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\begin{frame}
\frametitle{Pisan{\` o} Material Model: Brief Description}
\begin{itemize}
%\vspace*{0.2cm}
\item Primary modeling objective: calibration of a 3D elastic-plastic model
from $G/G_{max}$ and damping curves
\vspace*{0.2cm}
\item 3D elastic-plastic material model, with vanishing elastic region,
rotational kinematic hardening, bounding surface, and stress split into
frictional and viscous components
\vspace*{0.2cm}
\item No volume change data (since it is missing in $G/G_{max}$ and damping
curve data), however, volume modeling can be calibrated as well if data is
available
\end{itemize}
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Triaxial Response}
%
%
% \begin{figure} [!htb]
% \centering
% \includegraphics [width=6cm] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res1a.pdf}
% \\
% \includegraphics [width=6cm] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res1b.pdf}
% % \caption{Predicted triaxial responses for different dilatancy surfaces (
% % $p_0$=100 kPa, $G_{max}$ = 4 MPa, $\nu$=0.25, $M$=1.2, $\xi$=1,
% % $h$=$G$/(1.5$p_0$), $m$=1)}
% \label{fig:res1}
% \end{figure}
%
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% \end{frame}
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\begin{frame}
\frametitle{Pure Shear Cyclic}
\begin{figure} [!htb]
\centering
\includegraphics [width=6cm] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res2a.pdf}
\\
\includegraphics [width=6cm] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res2b.pdf}
% \hfill
% \caption{Predicted pure shear response at two different shear strain amplitudes ($p_0$=100 kPa, $T$=2$\pi$ s, $\zeta_0$ = 0.003,
%$G_{max}$= 4 MPa, $\nu$=0.25, $M$=1.2, $k_d$=$\xi$=0, $h$=$G$/(1.5$p_0$), $m$=1)}
% \label{fig:res2}
\end{figure}
\end{frame}
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\begin{frame}
\frametitle{Calibration for $G/G_{max}$ and Damping}
\begin{figure} [!htb]
\centering
\includegraphics [width=0.8\textwidth] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res4.pdf}
% \hfill
\caption{Comparison between experimental and simulated $G/G_{max}$
and damping curves ($p_0$=100 kPa, T=2$\pi$ s, $\zeta$ = 0.003, $G_{max}$ = 4
MPa, $\nu$=0.25, $M$=1.2, $k_d$=$\xi$=0, $h$=$G_{max}$/(15$p_0$), $m$=1)}
\label{fig:res4}
\end{figure}
\end{frame}
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\begin{frame}
\frametitle{Variation in Viscous Damping}
\begin{figure} [!htb]
\centering
\includegraphics [width=0.4\textwidth] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res9.pdf}
% \hfill
\caption{Damping curves simulated at varying $\zeta_0$ ($p_0$=100 kPa,
$T$=2$\pi$ s, $G_{max}$ = 4 MPa, $\nu$=0.25, $M$=1.2, $k_d$=$\xi$=0,
$h$=$G_{max}$/(15$p_0$), $m$=1)}
\label{fig:res9}
\end{figure}
\end{frame}
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\subsection{Fragility Curve Simulations}
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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{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{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}
\item Use of {\bf Probabilistic Elasto-Plasticity} and {\bf Stochastic Elastic-Plastic Finite
Element Method}
\end{itemize}
\end{frame}
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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}
%
% \end{frame}
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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}
\end{flushright}
%
\end{frame}
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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}
\end{center}
\end{figure}
%
\end{frame}
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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}
%
\end{frame}
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\begin{frame}
\frametitle{Probability of Unacceptable Deformation (say $50$cm)}
\begin{figure}
\begin{center}
\vspace*{-0.3cm}
%\hspace*{-0.75cm}
\includegraphics[width=10.50cm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/NewPlots/with_legends_and_labels/Exceedance50cm_LomaPrieta-Edited_ps.pdf}
\vspace*{-0.5cm}
%\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}
\end{frame}
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%
% \frametitle{Risk Informed Decision Process}
%
% \begin{figure}
% \begin{center}
% %\hspace*{-0.75cm}
% \includegraphics[width=8.0cm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/NewPlots/with_legends_and_labels/Summary_LomaPrieta-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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\section{Summary and Credits}
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\begin{frame}
\frametitle{Summary and Credits}
\begin{itemize}
%\vspace*{0.1cm}
\item {\bf Interplay} of {\bf uncertain} {\bf earthquake}, {\bf uncertain}
{\bf soil/rock}, and {\bf uncertain} {\bf structure} in time domain, {\bf
probably} plays a decisive role in seismic performance of NPPs
\vspace*{0.1cm}
\item Improve {risk informed decision making} through {\bf high
fidelity} { deterministic} and { stochastic elastic-plastic finite
element} modeling and simulation
\vspace*{0.1cm}
\item {\bf Education} and {\bf Training} are essential!
%\vspace*{0.1cm}
% \item {\bf Education and training} will prove essential
\vspace*{0.1cm}
\item { Post-Docs and Students:} Tafazzoli, Pisan{\`o}, Martinelli,
Kamrani, Abell, Jeong, Aldridge, Anderson
\vspace*{0.1cm}
\item { Acknowledgement:} funding from and collaboration with the
US-NRC, CNSC
%AREVA and Shimizu
and funding from NSF and DOE is much appreciated
\end{itemize}
\end{frame}
%
\end{document}