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\title{ Time Domain Nonlinear \\
Earthquake Soil/Rock Structure Interaction \\
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]{lbnllogo}{/home/jeremic/BG/amblemi/lbnllogo}
\author[Jeremi{\'c}] % (optional, use only with lots of authors)
{Boris~Jeremi{\'c} \\
%{\small with
% Dr. Tafazzoli,
% Mr. Abell,
% Mr. Jeong,
% Dr. Pisan{\`o},
% Prof. Sett (UA),
% Prof. Taiebat (UBC),
% Prof. Yang (UAA),
% Dr. Cheng (Itasca)}
}
%{Boris~Jeremi{\'c}, Nima Tafazzoli, Babak Kamrani, Panagiota Tasiopoulou and
%ChangGyun Jeong}
%  Give the names in the same order as the appear in the paper.
%  Use the \inst{?} command only if the authors have different
% affiliation.
%\institute[Computational Geomechanics Group \hspace*{0.3truecm}
\institute[\pgfuseimage{universitylogo}\hspace*{0.1truecm}\pgfuseimage{lbnllogo}] % (optional, but mostly needed)
{ Professor, University of California, Davis, CA\\
% and\\
Faculty Scientist, Lawrence Berkeley National Laboratory, Berkeley, CA }
%  Use the \inst command only if there are several affiliations.
%  Keep it simple, no one is interested in your street address.
\date[] % (optional, should be abbreviation of conference name)
{\small ASCE4 Meeting \\ April 2013}
\subject{}
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\titlepage
\end{frame}
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\begin{frame}
\frametitle{Outline}
\tableofcontents
% You might wish to add the option [pausesections]
\end{frame}
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\section{Introduction}
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\subsection{The Problem}
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\begin{frame}
\frametitle{The Problem}
\begin{itemize}
\item Earthquake Soil/Rock Structure Interaction (ESSI) response of Nuclear
Power Plants
\vspace*{0.1cm}
\item 3D, inclined, body and surface seismic waves
\vspace*{0.1cm}
\item Nonlinear behavior (elastic, damage, plastic behavior of materials:
soil, rock, concrete, steel, rubber, etc.)
\vspace*{0.1cm}
\item Full coupling of pore fluids with soil/rock skeleton
\vspace*{0.1cm}
\item Contact and buoyancy effects
\vspace*{0.1cm}
\item Uncertainty in seismic sources, path, soil/rock response and structural
response
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{Solution (?)}
\begin{itemize}
%\vspace*{0.3cm}
\item {\bf Physics based modeling and simulation} of
seismic behavior of NPP soil/rock  structure systems
\vspace*{0.1cm}
\item Development and use of {\bf high fidelity} time domain,
nonlinear numerical models, in {\bf deterministic} and {\bf probabilistic}
spaces
\vspace*{0.1cm}
\item Accurate following of the {\bf flow of seismic
energy} (input and dissipation) within soilstructure NPP system
\vspace*{0.1cm}
\item {\bf Directing}, in space and time, with {\bf high (known)
confidence}, seismic energy flow in the soilfoundationstructure system
%\vspace*{0.1cm}
% \item {\bf Education} for researchers, professional practice.
\end{itemize}
\end{frame}
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\subsection{Uncertainties}
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\begin{frame}
\frametitle{Modeling, Material and Loading Uncertainty}
\begin{itemize}
%\vspace*{0.3cm}
\item Simplified (or inadequate/wrong) modeling: important features are
missed (seismic ground motions, etc.)
\vspace*{0.1cm}
\item Introduction of uncertainty and (unknown) lack of accuracy in results due
to use of unverified simulation tools (software quality, etc.)
\vspace*{0.1cm}
\item Introduction of uncertainty and (unknown) lack of accuracy in results due
to use of unvalidated models (due to lack of quality validation experiments)
% (still missing data, experiments under
% uncertainty, for more see below)
\vspace*{0.1cm}
\item Material (left hand side) and load (right hand side) uncertainties
affect (probabilities of) overall response
\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), SSI
(soil,rock))
\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 Pointwise \\
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 pointwise})
%
% \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 Young's Modulus}
\begin{figure}[!hbpt]
\begin{center}
%
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01Ed.pdf}
\hfill
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/YoungModulus_Histogram_Normal_01Ed.pdf}
%
\end{center}
\end{figure}
\vspace*{0.3cm}
Transformation of SPT $N$value $\rightarrow$ 1D 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}
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\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}
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\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{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}
\end{frame}
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\section{Modeling and Simulation Issues}
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\subsection{High Fidelity Modeling}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
% \frametitle{Seismic Energy Dissipation for \underline{Soil}FoundationStructure Systems}
\frametitle{High Fidelity Modeling}
% \frametitle{Seismic Energy Dissipation for
% \underline{Soil}FoundationStructure Systems}
\begin{itemize}
\item Energy influx:
\begin{itemize}
\item \underline{Seismic body and surface waves, 3D, inclined}
\end{itemize}
% $E_{flux} = \rho A c \int_0^t \dot{u}_i^2 dt$ (Aki \& Richards)
\vspace*{0.1cm}
\item Mechanical dissipation outside of SSI domain:
\begin{itemize}
\item \underline{Radiation} of reflected waves
\item \underline{Radiation} of oscillating SSI system
\end{itemize}
\vspace*{0.1cm}
\item Mechanical dissipation inside SSI domain:
\begin{itemize}
\item \underline{Plasticity} of soil/rock subdomain
\item \underline{Plasticity} of foundation  soil/rock interface
\item \underline{Viscous coupling} of porous solid with pore fluid (air,
water)
\item Plasticity/damage of the structure
\item Viscous coupling of structure/foundation with fluids
% \item potential and kinetic energy
% \item[] potential $\leftarrow \! \! \! \! \! \! \rightarrow$ kinetic energy
\end{itemize}
\vspace*{0.1cm}
% \item Numerical energy dissipation (numerical damping/production and period errors)
% \item Numerical energy dissipation (damping/production)
\item Numerical energy dissipation/production
\end{itemize}
%
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%
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\begin{frame}
\frametitle{Earthquake Ground Motions}
\vspace*{1cm}
%\vspace*{0.5cm}
\begin{itemize}
\item Body: P and S waves
\item Surface: Rayleigh,\\
Love waves, etc.
\item Lack of correlation \\
(incoherence)
\item Inclined waves
\item 3D waves
\end{itemize}
\vspace*{5.3cm}
\begin{figure}[!hbpt]
\begin{flushright}
\includegraphics[width=2.0cm, angle=45]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Presentation/P_body_wave.jpeg}
\includegraphics[width=2.0cm, angle=45]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Presentation/S_body_wave.jpeg}
\vspace*{0.5cm}
\\
\includegraphics[width=2.5cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Presentation/Rayleigh_surface_wave.jpeg}
\includegraphics[width=2.5cm]{/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{flushright}
\end{figure}
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
\frametitle{Seismic Input: The Domain Reduction Method}
%\begin{itemize}
% \item
The DRM (Bielak et al.): \\
The effective force $P^{eff}$ \\
is a dynamically consistent \\
replacement 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_eK^{\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*{6.50cm}
{\includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2010/NRCLBLProjectReviewMeeting_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}
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\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 (easy to damp out)
%\vspace*{0.2cm}
\item Material inside $\Omega$ \\
can be elasticplastic
\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*{5.50cm}
{\includegraphics[width=5.8cm]{/home/jeremic/tex/works/Conferences/2010/NRCLBLProjectReviewMeeting_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{Verification and Validation}
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\begin{frame}
\frametitle{V \& V for ESSI Modeling and Simulations}
\begin{itemize}
\vspace*{0.3cm}
\item Material modeling and simulation (elastic, elasticplastic...)
\vspace*{0.3cm}
\item Finite elements (solids, structural, special elements...)
\vspace*{0.3cm}
\item Solution advancement algorithms (static, dynamic...)
\vspace*{0.3cm}
\item Seismic input and radiation
\vspace*{0.3cm}
\item Finite element model verification!
\end{itemize}
\end{frame}
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%
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\begin{frame}
\frametitle{Mesh Size Effects on Seismic Wave Propagation Modeling}
\begin{itemize}
\item Finite element mesh "filters out" \\
high frequencies
%\vspace*{0.2cm}
\item Usual rule of thumb: 1012 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, elasticplastic ?)
%
% \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
\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}{ccccc}
\begin{tabular}{rm{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}cm{2.8cm}cm{2.8cm}cm{3.0cm}cm{4.0cm}c}
% \begin{tabularx}{\linewidth}{ccccc}
% \begin{tabular*}{0.75\textwidth}{@{\extracolsep{\fill}}ccccc}
\end{tabular}
% \end{tabularx}
\end{table}
\end{small}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Cases 3, 4, and 6, Ormsby Wavelet Input Motions}
\vspace*{7mm}
\begin{figure}[H]
\begin{center}
\includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/MeshSize/figs/3_4_6/Input_Displacement.pdf}
\end{center}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Cases 3, 4, and 6, Surface Motions}
\vspace*{7mm}
\begin{figure}[H]
\begin{center}
\includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/MeshSize/figs/3_4_6/displacement.pdf}
\end{center}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Cases 3, 4, and 6, Input and Surface Motions, FFT}
\vspace*{7mm}
\begin{figure}[H]
\begin{center}
\includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/MeshSize/figs/3_4_6/FFT.pdf}
\end{center}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection{3D Inclined Body and Surface Seismic Wave Fields}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Free Field, Inclined, 3D Body and Surface Waves}
\begin{itemize}
\item Development of analytic and numerical 3D, inclined, uncorrelated
seismic motions for verification
\vspace*{0.2cm}
\item Large scale models
\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
\end{itemize}
\vspace*{4.6cm}
\begin{flushright}
\includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/wave_propagation/figs/FaultSlipModel2km.pdf}
\end{flushright}
\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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{ElasticPlastic Material Modeling}
%\subsection{Material Modeling: $G/G_{max}$ and Damping Curves}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Modulus Reduction ($G/G_{max}$ ) and Damping Curves}
\begin{itemize}
%\vspace*{5mm}
\item Idriss and Seed 1970
\vspace*{3mm}
\item Much work gone into development of curves for different types of soils
\vspace*{3mm}
\item However, it is still a linear elastic (secant) approach with some energy
dissipation taken into account
\vspace*{3mm}
\item Not good for any case where soil volume change makes a difference or where 2D
or 3D behavior is important
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{$G/G_{max}$ and Damping Curves}
\vspace*{5mm}
\begin{figure}[!htb]
\centering
\includegraphics[width=11.5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Staff_Capacity_Building_28Jan2013/Figure_Stiffness_Damping.pdf}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Commonly used $G/G_{max}$ and Damping Curves: \\
Vu{\v c}eti{\' c} and Dobry (1991)}
\begin{figure}[!hbpt]
\begin{center}
%
\includegraphics[width=5truecm]{/home/jeremic/tex/works/Conferences/2013/NRC_Staff_Capacity_Building_28Jan2013/Vucetic_and_Dobry_01.jpeg}
\hspace*{5mm}
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Conferences/2013/NRC_Staff_Capacity_Building_28Jan2013/Vucetic_and_Dobry_02.jpeg}
%
\end{center}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Pisan{\`o} 3D Elastic Plastic Material Model}
\begin{itemize}
\item Split stress into frictional and viscous components
$\sigma_{ij}=\sigma_{ij}^{f} + \sigma_{ij}^{v}$
\item Elasticity: classic, linear (can be nonlinear)
\item Yield surface, DruckerPrager cone, collapsed (limit analysis, vanishing elastic
regions) to cylinder (von Mises), with conical bounding surface
\item Plastic flow and rotational kinematic hardening, borrowed from
ManzariDafalias model (1997)
\item Yield (loadingunloading) condition established using stress projection
\item Special (unique) developments of a stiffness tensor (used for FEM)
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Pisan{\`o} Model: Triaxial and Pure Shear Response}
\begin{figure} [!htb]
\centering
\includegraphics [width=5.5cm] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res1a.pdf}
\includegraphics [width=5.8cm] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res1b.pdf}
\\
\includegraphics [width=5.5cm] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res2a.pdf}
\includegraphics [width=5.5cm] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res2b.pdf}
\label{fig:res1}
\end{figure}
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Pisan{\`o} Model: 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/res3.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, $h$=$G$/(112$p_0$), $m$=1.38)}
% \label{fig:res3}
% \end{figure}
%
%
% \end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Pisan{\`o} Model: 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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Pisan{\`o} Model: Variation in Confining Pressure}
\begin{figure}[!htb]
\centering
\includegraphics [width=0.8\textwidth] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res7.pdf}
% \hfill
\caption{Simulated $G/G_{max}$ and damping curves at varying
confining pressure (T=2$\pi$ s, $G_{max}$ = 4 MPa, $\nu$=0.25, $M$=1.2,
$k_d$=$\xi$=0, $h$=$G$/(15$p_0$), $m$=1)}
\label{fig:res5}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Soil Volume Response}
\begin{itemize}
\item Soil behavior is very much a function of volumetric response
\vspace*{2mm}
\item Dilative soils: increase volume due to shearing
\vspace*{2mm}
\item Compressive soils: decrease volume due to shearing
\vspace*{2mm}
\item Modulus reduction and damping curves do not provide volumetric data
\vspace*{2mm}
\item Soil volume change will affect response due to volume constraints
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{No Volume Change Soil (at Critical State?)}
\begin{figure}[!h]
\begin{center}
\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/FedericoPisano/Pisano_model/Issue_of_dilatancy/sine1Hz4.pdf}
\end{center}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Compressive Soil}
\begin{figure}[!h]
\begin{center}
\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/FedericoPisano/Pisano_model/Issue_of_dilatancy/sine1Hz_comp4.pdf}
\end{center}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Dilative Soil}
\begin{figure}[!h]
\begin{center}
\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/FedericoPisano/Pisano_model/Issue_of_dilatancy/sine1Hz_dil4.pdf}
\end{center}
\end{figure}
\end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Northridge, No Volume Change Soil}
\vspace*{0.6cm}
\begin{figure}[!h]
\begin{center}
\includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/FedericoPisano/Pisano_model/Issue_of_dilatancy/Northridge12.pdf}
\end{center}
\end{figure}
\end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Northridge, Dilatant Soil}
\vspace*{0.6cm}
\begin{figure}[!h]
\begin{center}
\includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/FedericoPisano/Pisano_model/Issue_of_dilatancy/Northridge13.pdf}
\end{center}
\end{figure}
\end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Northridge, No Volume Change and Dilative Soils}
\vspace*{0.6cm}
\begin{figure}[!h]
\begin{center}
\includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/FedericoPisano/Pisano_model/Issue_of_dilatancy/Northridge14.pdf}
\end{center}
\end{figure}
\end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Northridge, No Volume Change and Dilative Soils}
\vspace*{0.6cm}
\begin{figure}[!h]
\begin{center}
\includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/FedericoPisano/Pisano_model/Issue_of_dilatancy/Northridge15.pdf}
\end{center}
\end{figure}
\end{frame}
%
%
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Examples}
% %
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Few Illustrative Examples}
%
% \begin{itemize}
% \item Slip between foundation slab and the soil/rock
% underneath
%
% \vspace*{0.2cm}
% \item Passive seismic isolation by liquefaction
%
% \vspace*{0.2cm}
% \item Structural response in liquefied soil
%
%
% \end{itemize}
%
% \end{frame}
%
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Nuclear Power Plant with Base Slip}
%
% \begin{itemize}
%
% \item Low friction zone between \\
% concrete foundation and soil/rock
%
% \item Inclined, 3D, body and surface, \\
% seismic wave field (wavelets: \\
% Ricker, Ormsby; real seismic, etc.)
%
%
% \end{itemize}
%
%
%
% \vspace*{4.0cm}
% \begin{figure}[!h]
% \begin{flushright}
% \includegraphics[width=2.50cm]{/home/jeremic/tex/works/Conferences/2011/NRC_LBNL_Review_Panel_Sept2011/2D_faul_slip_model_top_200m.pdf}
% %{\includegraphics[width=4.0cm]{/home/jeremic/tex/works/Conferences/2011/NRC_LBNL_Review_Panel_Feb2011/Case_study_model/visit0002.jpeg}}
% \end{flushright}
% \end{figure}
%
% \vspace*{0.9cm}
% \begin{figure}[!h]
% \begin{flushright}
% {\includegraphics[width=4.0cm]{/home/jeremic/tex/works/Conferences/2011/NRC_LBNL_Review_Panel_Feb2011/Case_study_model/visit0002.jpeg}}
% \end{flushright}
% \end{figure}
%
%
%
%
% \vspace*{3.6cm}
% \begin{figure}[H]
% \begin{center}
% %\vspace*{0.5cm}
% %\includegraphics[width=2.0cm]{/home/jeremic/tex/works/Conferences/2011/NRC_LBNL_Review_Panel_Sept2011/2D_faul_slip_model_top_200m.pdf}
% %\hspace*{0.5cm}
% %\vspace*{0.2cm}
% \includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FreeFieldInclinedMotionModels/FaultSlip_Ormsby/figs/surface_200m/middle_acceleration_x.pdf}
% \hspace*{0.5cm}
% \includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FreeFieldInclinedMotionModels/FaultSlip_Ormsby/figs/surface_200m/middle_acceleration_z.pdf}
% %
% \vspace*{0.5cm}
% \hspace*{0.8cm}
% \mbox{horizontal}
% \hspace*{4cm}
% \mbox{vertical}
% \hspace*{3cm}
% \end{center}
% \end{figure}
% \vspace*{1.0cm}
% %
% % %\vspace*{3.5cm}
% % \begin{figure}[H]
% % \begin{center}
% % \includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FreeFieldInclinedMotionModels/FaultSlip_Ormsby/figs/surface_200m/middle_acceleration_x.pdf}
% % \hspace*{0.5cm}
% % \includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FreeFieldInclinedMotionModels/FaultSlip_Ormsby/figs/surface_200m/middle_acceleration_z.pdf}
% % \end{center}
% % \end{figure}
% %
% % %\vspace*{3.5cm}
% % \begin{figure}[H]
% % \begin{center}
% % \includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FaultModel_7seconds/xz_TimeHistory/5000_5000_x_acceleration.pdf}
% % \hspace*{0.5cm}
% % \includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FaultModel_7seconds/xz_TimeHistory/5000_5000_z_acceleration.pdf}
% % \end{center}
% % \end{figure}
% %
% % \vspace*{0.90cm}
% % {horizontal accelerations \hfill vertical accelerations}
% %
% %
% %
%
%
% \end{frame}
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Acc. Response for a Full 3D (at $45^\circ$) Ricker Wavelet}
%
% \begin{figure}[H]
% \begin{center}
% \begin{tabular}{rr}
% %\hline
% \mbox{\tiny top X}\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/91_97/top_structure_x_acceleration.pdf}
% &
% \mbox{\tiny top Z}\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/91_97/top_structure_z_acceleration.pdf}
% \\
% \mbox{\tiny bottom X}\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/91_97/bottom_structure_x_acceleration.pdf}
% &
% \mbox{\tiny bottom Z}\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/91_97/bottom_structure_z_acceleration.pdf}
% \end{tabular}
% %\caption{Comparison of acceleration time histories of the structure between
% %slipping and noslipping models for Ricker wave}
% \label{fig:3d_ricker_acc_1000}
% \end{center}
% \end{figure}
%
%
%
% \end{frame}
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{FFT Response for a Full 3D (at $45^\circ$) Ricker Wavelet}
%
% \begin{figure}[H]
% \begin{center}
% \begin{tabular}{rr}
% \mbox{\tiny top X}\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/91_97/top_structure_x_acceleration_FFT.pdf}
% &
% \mbox{\tiny top Z}\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/91_97/top_structure_z_acceleration_FFT.pdf}
% \\
% \mbox{\tiny bottom X}\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/91_97/bottom_structure_x_acceleration_FFT.pdf}
% &
% \mbox{\tiny bottom Z}\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/91_97/bottom_structure_z_acceleration_FFT.pdf}
% \end{tabular}
% %\caption{Comparison of FFT of the acceleration of the structure between
% %slipping and noslipping models for Ricker wave}
% \label{fig:3d_ricker_fft_1000}
% \end{center}
% \end{figure}
%
%
% \end{frame}
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Gaping Response ($45^\circ$ Ricker Wavelet)}
%
% \vspace*{0.1cm}
% \begin{tiny}
% \begin{figure}[H]
% \begin{center}
% \begin{tabular}{ccc}
% %\hline
% $4.5s$
% &
% $4.6s$
% &
% $4.7s$
% \\
% \includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/gap450.pdf}
% &
% \includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/gap460.pdf}
% &
% \includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/gap470.pdf}
% \\
% $4.8s$
% &
% $4.9s$
% &
% $5.0s$
% \\
% \includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/gap480.pdf}
% &
% \includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/gap490.pdf}
% &
% \includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/gap500.pdf}
% \\
% $5.1s$
% &
% $5.2s$
% &
% $5.3s$
% \\
% \includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/gap510.pdf}
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\section{Current Work}
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\subsection{NRC ESSI Simulator System}
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\begin{frame}
\frametitle{NRC ESSI Simulator System}
\begin{itemize}
\item {\bf The NRCESSIProgram} is a 3D, nonlinear, time domain,
parallel finite element program specifically developed for
HiFi modeling and simulation of Earthquake Soil/Rock Structure
Interaction problems for NPPs on NRCESSIComputer. \
%The NRC ESSI Program is based on
%a number of public domain numerical libraries developed at UCD as well as those
%available on the web, that are compiled and linked together to form the
%executable program (NRCESSIProgram). Significant effort is devoted to development
%of verification and validation procedures, as well as on development of
%extensive documentation. NRCESSIProgram is in public domain and is licensed
%through the Lesser GPL.
%\vspace*{0.3cm}
%\vspace*{0.1cm}
\item {\bf The NRCESSIComputer} 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 The NRCESSINotes} represent a hypertext
documentation system
%(Theory and Formulation, Software and Hardware, Verification and Validation, and
%Case Studies and Practical Examples)
detailing modeling and simulation of NPP ESSI
problems.
%
%the
%NRCESSIProgram code API (application Programming Interface) and DSLs (Domain
%Specific Language).
%%NRCESSINotes, developed by Boris Jeremic and collaborators, are in public
%domain
%%and are licensed under a Creative Commons AttributionShareAlike 3.0 Unported
%%License.
%
%\vspace*{0.3cm}
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{NRC ESSI Simulator Program}
\begin{itemize}
%\vspace*{0.2cm}
\item Collection of Useful Libraries (modular, portable)
\vspace*{0.1cm}
\item Library centric software design
\vspace*{0.1cm}
\item Various open source licenses (GPL, LGPL, BSD, CC)
%\vspace*{0.3cm}
\vspace*{0.1cm}
\item Extensive verification and (not so much) validation
\vspace*{0.1cm}
\item Detailed program documentation (part of NRC ESSI Notes)
\vspace*{0.1cm}
\item Target users: U.S.NRC, other domestic (DOE) and international
agencies (CNSC, IAEA), National Labs, Testers, eventually external users
%\item Sources will be available through
%{\bf
%\url{http://nrcessisimulator.info}}
\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*{0.1cm}
\item Multiple performance CPUs \\
and Networks
%\vspace*{0.1cm}
\item Most costperformance \\
effective
%\vspace*{0.1cm}
\item Source compatibility with \\
any DMP supercomputers
%\vspace*{0.1cm}
\item Current system: 208 CPUs
%\vspace*{0.1cm}
\item Near future: 784 CPUs
\end{itemize}
\vspace*{4.5cm}
\begin{flushright}
%\hspace*{0.5cm}
\includegraphics[width=5.0cm]{/home/jeremic/public_html/NRC_ESSI_Simulator/NRC_ESSI_Computer/photos/IMG_2607.JPG}
%\includegraphics[width=6.0cm]{/home/jeremic/public_html/NRC_ESSI_Simulator/NRC_ESSI_Computer/photos/IMG_2609.JPG}
%\includegraphics[width=8.0cm]{/home/jeremic/public_html/NRC_ESSI_Simulator/NRC_ESSI_Computer/photos/IMG_2611.JPG}
\end{flushright}
\end{frame}
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\begin{frame}
\frametitle{NRC ESSI Simulator Notes}
A hypertext documentation system describing in detail
modeling and simulations of NPP ESSI
problems
\begin{itemize}
\vspace*{0.1cm}
\item Theoretical and Computational Formulations
\vspace*{0.1cm}
\item Software and Hardware Platform Design
\vspace*{0.1cm}
\item Verification and Validation
\vspace*{0.1cm}
\item Application Example
\end{itemize}
\end{frame}
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\subsection{Features in Development}
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\begin{frame}
\frametitle{Features in Development}
\begin{itemize}
\item Buoyancy effects for foundations
\vspace*{2mm}
\item Piles
\vspace*{2mm}
\item Isolators
%\vspace*{2mm}
%\item Liquefiable soil
\vspace*{2mm}
\item Saturated contact (dry is already in)
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{Models in Development \#1}
\begin{figure}[!h]
\begin{center}
\includegraphics[width=5.5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Project_Review_LBNL_2323Feb2013/Roche_NRC_model/FixedBase_Shell_LSDYNA_001.png}
\hspace*{1mm}
\includegraphics[width=5.5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Project_Review_LBNL_2323Feb2013/Roche_NRC_model/FixedBase_Shell_LSDYNA_002.png}
\\
\vspace*{1mm}
\includegraphics[width=5.5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Project_Review_LBNL_2323Feb2013/Roche_NRC_model/FixedBase_Shell_LSDYNA_003.png}
\hspace*{1mm}
\includegraphics[width=5.5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Project_Review_LBNL_2323Feb2013/Roche_NRC_model/FixedBase_Shell_LSDYNA_004.png}
\end{center}
\end{figure}
\end{frame}
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\begin{frame}
\frametitle{Models in Development \#2}
\vspace*{0.50cm}
\begin{itemize}
\item Body and surface seismic waves
\item Seismic wave frequencies \\
up to $50$Hz
\item Elasticplastic soil/rock and \\
structural components,
\item Inelastic contact/gap
\item Seismic isolator effects
\item Buoyant effects for deep foundation embedment
\item High Fidelity Model: soil block: $230m \times 230m \times100m$, foundation
$90m \times 90m$, Containment Structure: $40m \times 50m$, 2.1 Million DOFs,
700,000 elements,
\end{itemize}
\vspace*{6.0cm}
\begin{flushright}
\hspace*{1cm}
\includegraphics[width=5.0cm]{/home/jeremic/tex/works/Conferences/2012/Seismic_research_issues_for_NPPs/Large_NPP_model_01A.jpg}
\end{flushright}
\end{frame}
\subsection{Uncertainty Propagation}
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\begin{frame}
\frametitle{EulerianLagrangian FPK Equation and (SEP)FEM}
\begin{itemize}
\item Advectiondiffusion 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 response
\vspace*{0.1cm}
\item {\bf Secondorder 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 elasticplasticdamage 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}
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\begin{frame}
\frametitle{Probabilistic ElasticPlastic Response}
\begin{figure}[!hbpt]
\begin{center}
%\includegraphics[width=8cm]{/home/jeremic/tex/works/Papers/2007/ProbabilisticYielding/figures/vonMises_G_and_cu_very_uncertain/Contour_PDFedited.pdf}
\includegraphics[width=8cm]{/home/jeremic/tex/works/Conferences/2012/DOELLNLworkshop2728Feb2012/ProbabilisticYielding_vonMises_G_and_cu_very_uncertain_Contour_PDFedited.pdf}
\end{center}
\end{figure}
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\begin{frame}
\frametitle{Probabilistic ElasticPlastic Response}
\begin{figure}[!hbpt]
\begin{center}
%\includegraphics[height=6.0cm]{/home/jeremic/tex/works/Conferences/2011/ICASP11_Zurich/Present/PDF_PlotEd.pdf}
\includegraphics[width=9.5cm]{/home/jeremic/tex/works/Conferences/2012/DOELLNLworkshop2728Feb2012/ProbabilisticYielding_vonMises_G_and_cu_very_uncertain_PDFedited.pdf}
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\frametitle{Stochastic Finite Element Formulation}
\begin{itemize}
\item Input random field material properties ($E$) $\rightarrow$
KarhunenLo{\`e}ve (KL) expansion, optimal expansion, error minimizing property
\item Unknown solution random field ($u$) $\rightarrow$ Polynomial Chaos (PC)
expansion
\end{itemize}
%
%
% Minimizing norm of error of finite representation using Galerkin
%technique (Ghanem and Spanos 2003):
\vspace*{0.6truecm}
\begin{flushright}
\begin{equation}
\nonumber
\sum_{n = 1}^N K_{mn}^{ep} d_{ni} + \sum_{n = 1}^N \sum_{j = 0}^P d_{nj} \sum_{k = 1}^M C_{ijk} K_{mnk}^{'ep} = \left< F_m \psi_i[\{\xi_r\}] \right >
\end{equation}
\end{flushright}
% \begin{itemize}
%
% \vspace*{0.5cm}
% \item Final eqn.:
%
% \vspace*{0.4cm}
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% \begin{normalsize}
% \begin{equation}
% \nonumber
% \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sum_{n = 1}^N K_{mn} d_{ni} + \sum_{n = 1}^N \sum_{j = 0}^P d_{nj} \sum_{k = 1}^M C_{ijk} K'_{mnk} = \left< F_m \psi_i[\{\zeta_r\}] \right >
% \end{equation}
% \end{normalsize}
% \end{flushright}
\vspace*{0.5cm}
\begin{equation}
\nonumber
K_{mn}^{ep} = \int_D B_n \textcolor{mycolor}{E}^{ep} B_m dV
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
K_{mnk}^{'ep} = \int_D B_n {\sqrt \lambda_k h_k} B_m dV
\end{equation}
\vspace*{1.0cm}
\begin{equation}
\nonumber
C_{ijk} = \left < \xi_k(\theta) \psi_i[\{\xi_r\}] \psi_j[\{\xi_r\}] \right >
\ \ \ \ \ \ \ \ \ \ \ \
F_m = \int_D \phi N_m dV \ \ \ \ \ \ \ \ \ \ \ \
\end{equation}
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\begin{frame}
\frametitle{Seismic Wave Propagation through Stochastic Soil}
Uniform CPT site data
%\begin{figure}
\begin{flushleft}
%\hspace*{1.7cm}
\includegraphics[height=2.0cm]{/home/jeremic/tex/works/Thesis/KallolSett/Dissertation/figures/CPT_DataAnalysis_Plots/SamplingPlanEdited.jpg}
\end{flushleft}
\vspace*{2.7cm}
%\begin{figure}
\begin{flushright}
\includegraphics[height=4.7cm]{/home/jeremic/tex/works/Thesis/KallolSett/Dissertation/figures/CPT_DataAnalysis_Plots/EastWestProfileEdited.pdf}
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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 1D 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}
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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 ElasticPlastic\\
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/UNIONUnivBGD/Present/Plots_with_Labels/EvolutionaryPDF_ActualEdited.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}
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% \frametitle{Evolution of Mean $\pm$ SD for Guess Case}
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% \begin{figure}
% \begin{center}
% \hspace*{0.75cm}
% \includegraphics[width=10.0cm]{/home/jeremic/tex/works/Conferences/2009/UNIONUnivBGD/Present/Plots_with_Labels/Evolutionary_Mean_pm_SD_NoDataEdited.pdf}
% \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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\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/UNIONUnivBGD/Present/Plots_with_Labels/PDFs_at6sec_Actual_vs_NoDataEdited.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}
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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/UNIONUnivBGD/Present/Plots_with_Labels/CDFs_at6sec_Actual_vs_NoDataEdited.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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\begin{frame}
\frametitle{Probability of Unacceptable Deformation ($50$cm)}
\begin{figure}
\begin{center}
\vspace*{0.3cm}
%\hspace*{0.75cm}
\includegraphics[width=10.50cm]{/home/jeremic/tex/works/Conferences/2009/UNIONUnivBGD/Present/NewPlots/with_legends_and_labels/Exceedance50cm_LomaPrietaEdited_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}
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\section{Summary}
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\begin{frame}
\frametitle{Summary}
\begin{itemize}
% \item High fidelity
% modeling and simulations for performance assessment of infrastructure systems
%\vspace*{0.5cm}
\item {\bf Interplay} of {\bf Uncertain} {\bf Earthquake}, {\bf Uncertain}
{\bf Soil/Rock},
% {Foundation}
and {\bf Uncertain} {\bf Structure} in time domain {\bf probably} plays a
decisive role in seismic performance of NPPs
%\vspace*{0.1cm}
\item Improve {\bf risk informed decision making} through high fidelity
(Verified and Validated) Time Domain. {\bf Deterministic} and {\bf
Stochastic} ElasticPlastic Finite Element modeling and simulation
%\vspace*{0.1cm}
% \item {\bf Education and training} of users will prove essential
%\vspace*{0.1cm}
\item {\bf Acknowledgement:} funding and collaboration with the USNRC,
CNSC, NSF, DOE, AREVA, Shimizu. \\
Drs. and students:
Nima Tafazzoli, Federico Pisan{\`o}, Mario Martinelli, Jos{\'e} Abell
Mena, Kohei Watanabe, Babak Kamrani, ChangGyun Jeong...
\end{itemize}
\end{frame}
%
\end{document}