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\title[High Fidelity Modeling and Simulation of \\
SFS Interaction: \\
Energy Dissipation by Design]
% (optional, use only with long paper titles)
{High Fidelity Modeling and Simulation of \\
SFS Interaction: \\
Energy Dissipation by Design}
%\subtitle
%{{\tiny full set of slides available at:}\\
%%\verb{http://sokocalo.engr.ucdavis.edu/~jeremic/}
%}
\pgfdeclareimage[height=0.2cm]{university-logo}{/home/jeremic/BG/amblemi/ucdavis_logo_blue_sm}
%\author[Boris Jeremi{\'c}, CompGeoMech \includegraphics[width=8cm]{/home/jeremic/BG/amblemi/ucdavis_logo_gold_lrg}] % (optional, use only with lots of authors)
\author[Boris Jeremi{\'c}] % (optional, use only with lots of authors)
{Boris~Jeremi{\'c} \\ {\tiny with contributions by} \\
{\small Nima Tafazzoli (UCD), Guanzhou Jie (Wachovia Corp.), Mahdi Taiebat (UBC), Zhao
Cheng (EarthMechanics Inc.)}}
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{
CompGeoMech group, CEE Dept. UCD}
% Department of Civil and Environmental Engineering\\
% University of California, Davis}
% - Use the \inst command only if there are several affiliations.
% - Keep it simple, no one is interested in your street address.
\date[SFSI Auckland, NZ] % (optional, should be abbreviation of conference name)
{SFSI Auckland, NZ}
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% may not be suitable. Here are some rules that apply for this
% solution:
% - Exactly two or three sections (other than the summary).
% - At *most* three subsections per section.
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\section{Motivation}
\subsection*{Motivation}
%\subsection*{}
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\begin{frame}
\frametitle{Motivation}
\begin{itemize}
%\vspace*{0.3cm}
\item Improving seismic design for infrastructure objects
\vspace*{0.3cm}
\item Use of high fidelity numerical models in analyzing seismic behavior
of soil-foundation-structure systems
\vspace*{0.3cm}
\item Accurate following of the flow of seismic energy in the
soil-foundation-structure
system
\vspace*{0.3cm}
\item Directing, in space and time, seismic energy flow in the
soil-foundation-structure system
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{The Very First Published Work on SFSI}
\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 the Earthquake with the
Soil, Foundation and Structure in time domain plays major
role in failures (and successes).
\vspace*{0.5cm}
\item Timing and spatial location of energy dissipation determines location
and amount of damage.
\vspace*{0.5cm}
\item If timing and spatial location of energy dissipation
can be controlled (directed, designed),
we could optimize soil-foundation-structure system for
\begin{itemize}
\item Safety and
\item Economy
\end{itemize}
\end{itemize}
\end{frame}
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% \subsection{Predictive Capabilities}
%
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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*{0.2cm}
\item {{\bf Validation} provides
evidence that the correct model is solved.} Physics issue.
%\vspace*{0.2cm}
\item {\bf Prediction}: use of computational model to foretell the state of a
physical system under consideration under conditions for which the
computational model has not been validated.
% \vspace*{0.2cm}
\item Goal: predictive capabilities
with {\bf low Kolmogorov Complexity}
% \vspace*{0.2cm}
\item {\bf The Finite Element
Interpreter \FEI{}} might be one such
predictive tool (application program)
\end{itemize}
%literature: \cite{Roach1998}, \cite{Oberkampf2002}.
%Verification, validation and predictive capability in computational
% engineering and physics.
%In {\em Proceedings of the Foundations for Verification and
% Validation on the 21st Century Workshop}, pages 1-74, Laurel, Maryland,
% October 22-23 2002. Johns Hopkins University / Applied Physics Laboratory.
%%{\href{http://sokocalo.engr.ucdavis.edu/~jeremic/UsefulReadings/Oberkampf-Trucano-Hirsch.pdf}
%%{PDF available here}}
%
%
%\item
%{\sc P.~J. Roache.}
% {\em Verification and Validation in Computational Science and
% Engineering}.
%Hermosa publishers, 1998.
%ISBN 0-913478-08-3.
%%
%\item Material from {\it Verification and Validation in Computational Mechanics}
%web site \texttt{http://www.usacm.org/vnvcsm/} at the USACM.
%
%
%\item Models available (some now, some later)
%\vspace*{-2.0cm}
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%\section{Modeling and Simulation of Soil Structure Systems}
\section{Seismic Energy Flow}
%\section{High Fidelity Modeling and
% Simulation of Seismic Energy Flow}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Distribution of Seismic Energy in Soil-Structure Systems}
%
%
% \begin{itemize}
%
% \item Input: seismic waves from the source
%
% \item Output: various dissipation mechanisms:
% \begin{itemize}
% \item wave reflection and radiation
% \item soil structure system oscilation radiation
% \item plasticity of soil (different subdomains)
% \item viscous coupling of porous solid with pore fluid (air, water)
% \item plasticity/damage of the structure (different parts)
% \item viscous coupling of structure with surounding fluid (air, water)
% \item potential energy
% \item kinetic energy
% \end{itemize}
%
%
% \item Preserving energy in numerical models (numerical damping and period
% errors)
%
%
% \end{itemize}
%
% %
% %\item Models available (some now, some later)
% %\vspace*{-2.0cm}
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Input}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Seismic Energy Source}
\begin{itemize}
%\vspace*{0.2cm}
\item Large energy releases,
\begin{itemize}
\item Northridge, 1994, $M_{Richter} = 6.7$, $E_r = 6.8 \times 10^{16}J$
% \item Loma Prieta, 1989, $M_{Richter} = 6.9$, $E_r =1.1 \times 10^{17}J$
% \item LARGE JAPANESE EQ.
% \item LARGE NEW ZEALAND EQ.
\item Sumatra-Andaman, 2004, $M_{Richter} = 9.3$, $E_r =4.8 \times 10^{20}J$
\item Valdivia, Chile, 1960, $M_{Richter} = 9.5$, $E_r =7.5 \times 10^{20}J$
% \item Rhodes, 2008, $M_{Richter} = 6.5$, $E_r =2.4 \times 10^{16}J$
\end{itemize}
\vspace*{0.5cm}
\item Part that energy is radiated as mechanical waves ($\approx 1.6 \times 10^{-5}$)
and makes it to the surface
%\vspace*{0.2cm}
% \item For comparison, specific energy of TNT is $4.2\times 10^6 J/kg$.
%%\vspace*{0.2cm}
%% \item Rhodes earthquake was $\approx 0.1 kt$.
\end{itemize}
\end{frame}
%-
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\begin{frame}
\frametitle{Seismic Energy Input Into the SFS System}
\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}
%-
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\subsection{Dissipation}
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\begin{frame}
% \frametitle{Seismic Energy Dissipation for \underline{Soil}-Foundation-Structure Systems}
\frametitle{Seismic Energy Dissipation for
\underline{\bf S}FS System}
% \frametitle{Seismic Energy Dissipation for
% \underline{Soil}-Foundation-Structure Systems}
\begin{itemize}
\vspace*{0.2cm}
\item Mechanical dissipation outside of SFS domain:
\begin{itemize}
\item reflected wave radiation
\item SFS system oscillation radiation
\end{itemize}
\vspace*{0.2cm}
\item Mechanical dissipation/conversion inside SFS 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*{0.2cm}
% \item Numerical energy dissipation (numerical damping/production and period errors)
% \item Numerical energy dissipation (damping/production)
\item Numerical energy dissipation/production
\end{itemize}
%
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
\frametitle{Energy Dissipation by Soil Plasticity}
\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}
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%- \begin{frame}
%- \frametitle{Plasticity Energy Disipation}
%-
%- \begin{itemize}
%-
%- \item
%-
%- \end{itemize}
%-
%-
%- \end{frame}
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\begin{frame}
\frametitle{Energy Disipation 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 can be made non-dissipative for
elastic system $\alpha=0.0, \beta = 0.25 ; \gamma = 0.5,$
\item Or dissipative (for elastic) for higher frequency modes:
%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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\section{Energy Dissipation Examples}
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\subsection{Soft Soil}
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\begin{frame}
\frametitle{Earthquake-Soil-Bridge
System}
%
\begin{itemize}
\item Inelastic soils (el-pl,
Armstrong-Frederick, stiff and soft),
inelastic structure (columns),
inelastic piles, DRM for seismic input,
%\vspace*{0.3cm}
\item Construction process
% %
% \item Deconvolution of surface ground motions
%\vspace*{0.3cm}
\item No artificial damping, \\
only plastic dissipation \\
and radiation
%\vspace*{0.3cm}
\item Plastic Domain \\
Decomposition Method \\
for parallel computing
% \item Element size issues (filtering of frequencies)
%\vspace*{0.3cm}
\item 1.6 M DOFs \\
(15cm element size)
\end{itemize}
\vspace*{-5.2cm}
%\hfill
\hspace*{4.8cm}
\includegraphics[width=6.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
% %
% \begin{figure}[!htbp]
% \begin{center}
% \includegraphics[width=4.0cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
% %\hspace*{-0.9cm}
% %bridge.}
% \end{center}
% \end{figure}
%
%
\end{frame}
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\begin{frame}
\frametitle{Northridge and Kocaeli Input Motions}
\vspace*{-0.7cm}
\begin{figure}[!htbp]
\begin{center}
\hspace*{-1cm}
\includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/InputMotion_Northridge.pdf}
\hspace*{-1cm}
%\\
%\hspace*{-1cm}
%\includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/InputMotion_Northridge_Spectrum.pdf}
%\hspace*{-1cm}
%%\caption{\label{BridgeSFSI01} FEM model for seismic response of a three bend
%%bridge.}
\end{center}
\end{figure}
%\vspace*{-1.0cm}
%
\vspace*{-0.7cm}
\begin{figure}[!htbp]
\begin{center}
\hspace*{-1cm}
\includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/InputMotion_Kocaeli.pdf}
\hspace*{-1cm}
%\\
%\hspace*{-1cm}
%\includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/InputMotion_Kocaeli_Spectrum.pdf}
%\hspace*{-1cm}
%%\caption{\label{BridgeSFSI01} FEM model for seismic response of a three bend
%bridge.}
\end{center}
\end{figure}
%
\vspace*{-1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Northridge Energy: Strain (dissipated) and Kinetic}
\vspace*{-0.1cm}
\begin{figure}[!htbp]
\begin{center}
\includegraphics[width=9cm,height=3.5cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/MomentBent1Pile1_25s_SC.pdf}
%\caption{\label{BridgeSFSI01} FEM model for seismic response of a three bend
%bridge.}
\end{center}
\end{figure}
% \vspace*{-2.9cm}
% \hspace*{0.2cm}
% \begin{figure}[!htbp]
% \begin{flushright}
% \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
% %\caption{\label{BridgeSFSI01} FEM model for seismic response of a three bend
% %bridge.}
% \end{flushright}
% \end{figure}
% \hspace*{-0.5cm}
% \vspace*{-2.0cm}
%
\vspace*{-1.2cm}
\begin{figure}[!htbp]
\begin{center}
%\includegraphics[width=11cm,height=7.0cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/Northridge-Bent.pdf}
\includegraphics[width=11cm,height=7.0cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/Northridge-Diff-Comp.pdf}
%\caption{\label{BridgeSFSI01} FEM model for seismic response of a three bend
%bridge.}
\end{center}
\end{figure}
% %
% \vspace*{2.0cm}
% {%
% \begin{beamercolorbox}{section in head/foot}
% \usebeamerfont{framesubtitle}\tiny{B. Jeremi\'{c}, G. Jie,
% M. Preisig and N. Tafazzoli.} "Soil-Foundation-Structure Interaction
% in non-Uniform Soils", \textit{Earthquake Engineering and Structural Dynamics},
% 38, 5 pp 699-718, 2009.
% %\vskip2pt\insertnavigation{\paperwidth}\vskip2pt
% \end{beamercolorbox}%
% }
%
\end{frame}
%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Kocaeli Energy: Strain (dissipated) and Kinetic}
\vspace*{-0.1cm}
\begin{figure}[!htbp]
\begin{center}
\includegraphics[width=9cm,height=3.5cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/MomentBent1Pile1.pdf}
%\\
%\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/MomentBent1Pile2.pdf}
%\caption{\label{BridgeSFSI01} FEM model for seismic response of a three bend
%bridge.}
\end{center}
\end{figure}
\vspace*{-0.8cm}
\begin{figure}[!htbp]
\begin{flushleft}
\hspace*{0.4cm}
%\includegraphics[width=7.85cm,height=7.0cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/Kocaeli-Bent.pdf}
\includegraphics[width=7.85cm,height=7.0cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/Kocaeli-Diff-Comp.pdf}
%\caption{\label{BridgeSFSI01} FEM model for seismic response of a three bend
%bridge.}
\end{flushleft}
\end{figure}
%
% \vspace*{-2.9cm}
% \hspace*{0.2cm}
% \begin{figure}[!htbp]
% \begin{flushright}
% \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
% %\caption{\label{BridgeSFSI01} FEM model for seismic response of a three bend
% %bridge.}
% \end{flushright}
% \end{figure}
% \hspace*{-0.5cm}
% \vspace*{-2.0cm}
%
\end{frame}
%
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\subsection{Liquefaction}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Uniform and Layered Soils}
\vspace*{-0.5cm}
\begin{figure}[!htbp]
\begin{center}
\includegraphics[width=7cm,angle=90]{/home/jeremic/tex/works/Papers/2009/SeismicIsolationLiquefaction/Mesh-Isolation.pdf}
%\\
%\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/MomentBent1Pile2.pdf}
%\caption{\label{BridgeSFSI01} FEM model for seismic response of a three bend
%bridge.}
\end{center}
\end{figure}
\vspace*{-1cm}
\end{frame}
%
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\begin{frame}
\frametitle{Acceleration Time History}
\vspace*{-0.1cm}
\begin{figure}[!htbp]
%\begin{center}
\includegraphics[width=6cm]{/home/jeremic/tex/works/Papers/2009/SeismicIsolationLiquefaction/time-history-acc.jpg} \\
%\end{center}
\end{figure}
%\vspace*{-0.3cm}
%\hspace*{2.3cm} EPPR \hspace{1.5cm} $\gamma$ \hspace{1.7cm} $u_{hor}$
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Excess Pore Pressure Ratio}
%
% \vspace*{-0.1cm}
% \begin{figure}[!htbp]
% \begin{center}
% \hspace*{-0.7cm}
% \includegraphics[width=10cm]{/home/jeremic/tex/works/Papers/2009/SeismicIsolationLiquefaction/contours-exc-pore-press-ratio.jpg} \\
% \hspace*{-1.0cm}
% \end{center}
% \end{figure}
% %\vspace*{-0.3cm}
% %\hspace*{2.3cm} EPPR \hspace{1.5cm} $\gamma$ \hspace{1.7cm} $u_{hor}$
%
%
%
% \vspace*{-0.9cm}
% \begin{center}
% %\begin{center}
% \includegraphics[width=4cm]{/home/jeremic/tex/works/Conferences/2009/GheoMat/Coupled-behavior_04/Niigata-Earthquake-tilted-buildings.jpg} \\
% %\end{center}
% \end{center}
% %\vspace*{-0.3cm}
% %\hspace*{2.3cm} EPPR \hspace{1.5cm} $\gamma$ \hspace{1.7cm} $u_{hor}$
%
%
%
% \end{frame}
%
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\begin{frame}
\frametitle{Kinetic Energy at the Soil Surface}
%\vspace*{-0.3cm}
\begin{figure}[h]
\begin{center}
\includegraphics[width=10cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/StackElements-Compare.pdf}
%\hspace*{-0.1cm}
\end{center}
\vspace*{-4.3cm}
\end{figure}
%\vspace*{-5.3cm}
%\hspace*{2.3cm} EPPR \hspace{1.5cm} $\gamma$ \hspace{1.7cm} $u_{hor}$
%
\begin{itemize}
\item Liquefaction base isolates seismic motions
\item Energy dissipated by plasticity and
viscous coupling
% \item
\end{itemize}
\end{frame}
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% \frametitle{SPT: Shear Strength and Young's Modulus}
%
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% \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=4.50truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_Histogram_PearsonIV-FineTuned-Mod.pdf}
% %
% \end{center}
% \end{figure}
%
% \vspace*{-0.3cm}
% \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=4.50truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_Histogram_Normal_01-Ed.pdf}
% %
% \end{center}
% \end{figure}
%
%
% \vspace*{-0.2cm}
% Phoon and Kulhawy (1999B)
%
% \end{frame}
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% \subsection{Probabilistic Elasto-Plasticity}
%
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% % \begin{frame}
% %
% % \frametitle{Bi-Linear von Mises Response}
% %
% %
% % \begin{figure}[!hbpt]
% % \begin{center}
% % \includegraphics[width=9cm]{/home/jeremic/tex/works/Papers/2007/ProbabilisticYielding/figures/vonMises_G_and_cu_very_uncertain/Contour_PDF-edited.pdf}
% % \end{center}
% % \end{figure}
% %
% % %\vspace*{-0.3cm}
% % %linear elastic - linear hardening plastic von Mises
% %
% %
% % \end{frame}
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%
% \frametitle{Cyclic Response of Such Uncertain Material}
%
%
% \begin{figure}[!hbpt]
% \begin{center}
% %
% \includegraphics[width=5.15truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/meanStressStrainPlot_1Point026-Mod.pdf}
% \hfill
% \includegraphics[width=4.35truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/sdStressStrainPlot_1Point026-Mod.pdf}
% %
% \end{center}
% \end{figure}
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% \vspace*{-0.3cm}
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% \frametitle{$G/G_{max}$ and Damping Responses}
%
%
% \begin{figure}[!hbpt]
% \begin{center}
% %
% \hspace*{-1cm}
% \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/GoverGmax-Mod.pdf}
% \hspace*{-0.5cm}
% \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/Damping-Mod.pdf}
% \hspace*{-1cm}
% %
% \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 the { Earthquake}, the { Soil},
{Foundation} and {Structure} in {\bf time domain} plays a decisive role in
catastrophic failures and great successes
\vspace*{0.2cm}
\item {\bf Improve design through high fidelity
simulations}: direct the flow of seismic energy in the SFS systems
%\vspace*{0.2cm}
% \item {\bf Ability to direct} seismic energy flow, in space and time,
% for a complete SFS system will lead to an increase in safety and economy
\vspace*{0.2cm}
\item {\bf Uncertainty} (point-wise and spatial) is very important
\vspace*{0.2cm}
\item {\bf Predictive tools}, will prove essential:
\begin{itemize}
\item The Finite Element Interpreter (\FEI{})
\item {\url{www.OpenHazards.com}}
\end{itemize}
\end{itemize}
\end{frame}
%
\end{document}