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\title[Directing Energy Dissipation in Earthquake-Soil-Structure Systems]
% (optional, use only with long paper titles)
{Directing Energy Dissipation in Earthquake-Soil-Structure Systems}
%\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},\\
Nima Tafazzoli, Mahdi Taiebat, Guanzhou Jie}
% - Give the names in the same order as the appear in the paper.
% - Use the \inst{?} command only if the authors have different
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%\institute[Computational Geomechanics Group
\institute[Computational Geomechanics Group
\pgfuseimage{university-logo} \hspace*{-0.3truecm}] % (optional, but mostly needed)
{ \vspace*{1cm} \\
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[CompDyn09] % (optional, should be abbreviation of conference name)
{CompDyn09}
% - Either use conference name or its abbreviation.
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\begin{frame}
\frametitle{Outline}
\tableofcontents
% You might wish to add the option [pausesections]
\end{frame}
% Structuring a talk is a difficult task and the following structure
% 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.
% - Talk about 30s to 2min per frame. So there should be between about
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% just say so once. Everybody will be happy with that.
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\section{Motivation}
\subsection*{Motivation}
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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--structure systems
\vspace*{0.3cm}
\item Accurately (high fidelity modeling and simulations)
following the flow of seismic energy in the soil--structure system
\vspace*{0.3cm}
\item Directing, in space and time, seismic energy flow in the soil--structure system
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{Hypothesis}
\begin{itemize}
\vspace*{0.5cm}
\item Interplay of Earthquake with Soil and Structure plays major
role in (catastrophic) 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,
we could optimize soil--structure systems for
\begin{itemize}
\item Safety and
\item Economy
\end{itemize}
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{First Published Work on Soil--Structure Interaction}
\begin{itemize}
\item Professor Kyoji Suyehiro
\item Ship engineer (Professor of Naval Arch. at U. of Tokyo),
\item Was in Tokyo during Great Kant{\= o} earthquake
(11:58am(7.5), 12:01pm(7.3), 12.03pm(7.2) (shaking until
12:08pm), 1st. Sept. 1923)
\item Saw earthquake surface waves travel and buildings sway
\item Founding Director of the Earthquake Engineering Research Institute Univ. of Tokyo),
\item Records shows $4 \times$ (four) more damage to soft
wooden buildings on soft ground
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{Northridge Example}
\begin{figure}[ht]
\begin{center}
\vspace*{-0.7cm}
\includegraphics[width=8.7cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Paper/SanFernando_spatial_distribution_of_damage.jpg}
%\includegraphics[width=7cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Paper/LosAngeles-SantaMonica_spatial_distribution_of_damage.jpg}
\end{center}
\end{figure}
\vspace*{-0.9cm}
\hfill {\tiny [Trifunac and Todorovska 1998]}
\vspace*{-0.4cm}
\end{frame}
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%
%
%
%
% \item Slow and Fast earthquakes
%
% \item Uncertainty and variability (source, material...)
%
%
% \end{itemize}
% \end{frame}
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% \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{High Fidelity Modeling of Soil--Foundation--Structure System}
%
%
%
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%
%
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% \begin{frame}
% \frametitle{Verification, Validation and Prediction}
%
%
% \begin{itemize}
%
% \item {Verification provides evidence that the
% model is solved correctly.} Mathematics issue.
%
% \item {Validation provides
% evidence that the correct model is solved.} Physics issue.
%
% \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
%
% \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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%
%
% % \vspace*{1.5truecm}
%
% \begin{figure}[!h]
% \begin{center}
% {\includegraphics[width=8.0cm]{/home/jeremic/tex/works/Presentation/2003/Verif_and_Valid/RoleVV.pdf}}
% \end{center}
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% % \frametitle{Application Domain Complete or Partial Overlap}
% %
% %
% %
% %
% %
% % %\vspace*{0.3cm}
% %
% % \begin{figure}[!h]
% % \begin{center}
% % \hspace*{1.5cm}
% % {\includegraphics[width=2.50cm]{/home/jeremic/tex/works/Presentation/2004/VandV/VPI01.pdf}}
% % \hfill
% % {\includegraphics[width=2.50cm]{/home/jeremic/tex/works/Presentation/2004/VandV/VPI02.pdf}}
% % \hspace*{1.5cm}
% % %\vspace*{-5.0cm}
% % \end{center}
% % \end{figure}
% %
% % \vspace*{-0.3cm}
% %
% % \begin{itemize}
% % \item Rarely applicable to infrastructure objects
% % %( bridges, buildings, port facilities, dams...
% % \item Environmental influences (generalized loads, conditions, wear and tare) are hard to predict
% % \item Human factors (I-35 bridge failure, {\bf forgot} to multiply loads with safety factor...)
% % \end{itemize}
% %
% %
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% \begin{center}
% %\vspace*{-2.5cm}
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% %\vspace*{-5.0cm}
% \end{center}
% \end{figure}
%
% \vspace*{-0.2cm}
%
% \begin{itemize}
% \item Inference $\Rightarrow$ Based on {\bf physics} or {\bf statistics} (or
% both)
% \item Validation domain is actually an aggregation of tests and thus might not
% be convex (bifurcation of behavior)
% \item Validation domain for infrastructure objects (bridges, dams,
% buildings, ports...) is exclusively non--overlapping with the application
% domain.
% \end{itemize}
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%\section{Modeling and Simulation of Soil Structure Systems}
\section{Modeling and Simulation}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Seismic Energy Input}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Seismic Energy at the 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 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*{0.2cm}
\item Part that energy is radiated as 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}
%-
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Seismic Energy and 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}
%-
%- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%-
%- \begin{frame}
%- \frametitle{Simulation of the Incomming SFS Energy}
%-
%- \begin{itemize}
%-
%- \item Domain Reduction Method
%-
%- \end{itemize}
%-
%-
%- \end{frame}
%- %-
%-
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\subsection{Seismic Energy Dissipation}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
% \frametitle{Seismic Energy Dissipation for \underline{Soil}--Foundation--Structure Systems}
\frametitle{Seismic Energy Dissipation for \underline{Soil}--Structure Systems}
\begin{itemize}
\vspace*{0.2cm}
\item Mechanical dissipation outside of SFS domain:
\begin{itemize}
\item wave reflection
\item SFS system oscillation radiation
\end{itemize}
\vspace*{0.2cm}
\item Mechanical dissipation/conversion inside SFS domain:
\begin{itemize}
\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 surrounding 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}
%
%\item Models available (some now, some later)
%\vspace*{-2.0cm}
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Energy Losses (Disipation)}
%
% \begin{itemize}
%
% \item Losses outside of SFS domain
% \item Losses within SFS domain
% \item Numerical algorithm losses
%
% \end{itemize}
%
%
% \end{frame}
% %-
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Energy Dissipation by 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}
%-
%- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%- \begin{frame}
%- \frametitle{Plasticity Energy Disipation}
%-
%- \begin{itemize}
%-
%- \item
%-
%- \end{itemize}
%-
%-
%- \end{frame}
%- %-
%- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Energy Disipation by 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{Examples of Energy Dissipation}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Use of Soft Soil}
% - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - \begin{frame}
% - \frametitle{Detailed 3D FEM Model (one of)}
% -
% - %
% - \begin{figure}[!htbp]
% - \begin{center}
% - \includegraphics[width=8.0cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
% - %\hspace*{-0.9cm}
% - %bridge.}
% - \end{center}
% - \end{figure}
% - %
% - \end{frame}
% - %-
% - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -
% - \begin{frame}
% - \frametitle{Model Components}
% -
% - %
% - \begin{itemize}
% - \item Soils: elastic--plastic solids (yield potential surface
% - Drucker-Prager, kinematic hardening Armstrong-Frederick) (UCD: Jie and Jeremi{\'c})
% - \vspace*{0.2cm}
% - \item Structure: non--linear beam--column elements (fiber element)
% - (UCB: Fenves, UW: Eberhardt)
% -
% - \vspace*{0.2cm}
% - \item Piles: non--linear beam--column elements (fiber element) (UCD: Jie and Jeremi{\'c})
% -
% -
% - \vspace*{0.2cm}
% - \item Two types of soil: stiff soil (UT, UCD), soft soil (Bay Mud)
% -
% - \vspace*{0.2cm}
% - \item Use of the Domain Reduction Method (DRM) (Bielak et al.) for seismic
% - input into FEM model
% -
% -
% - \end{itemize}
% -
% - \end{frame}
% - %-
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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 osurface ground motions
%\vspace*{0.3cm}
\item No artificial damping, \\
only plastic dissipation \\
and radiation
%\vspace*{0.3cm}
\item Plastic Domain \\
Decompisition 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*{-4cm}
\hfill \includegraphics[width=5.5cm]{/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{Modeling Issues}
%
% \begin{itemize}
%
% \vspace*{0.2cm}
% \item Construction process
%
% \vspace*{0.2cm}
% \item Deconvolution of given surface ground motions
%
% \vspace*{0.2cm}
% \item No artificial damping (only mat. dissipation, radiation)
%
% \vspace*{0.2cm}
% \item Element size issues (filtering of frequencies)
%
% \vspace*{-0.4cm}
% \begin{table}[!htbp]
% %\caption{ }
% \begin{center}
% \begin{tabular}{|r|c|c|c|c|}
% \hline
% elem. \# & elem. size & $f_{cutoff}$ & min. $G^{ep}/Gmax$ & $\gamma$ \\
% \hline
% %
% %
% % 100cm element model, f_cuttof=10HZ, G/Gmax=1.0, 12K elements, Gmax model
% 12K & 1.00~m & 10~Hz & 1.0 & <0.5~\% \\
% %
% %
% %~90cm element model, f_cutoff ~= 3Hz, G/Gmax~=0.08, for epsilon ~= 1%, 15K
% %elements, now running...
% 15K & 0.90~m & >3~Hz & 0.08 & <1.0~\% \\
% %
% %
% %27.6cm element model, f_cutoff= 10HZ, G/Gmax=0.08, for epsilon = 1%, 150K
% %elements, finest model
% 150K & 0.30~m & 10~Hz & 0.08 & <1.0~\% \\
% 500K & 0.15~m & 10~Hz & 0.02 & <5.0~\% \\
% % 27.6cm element model, f_cutoff= 10HZ, G/Gmax=0.08, for epsilon = 1%, 150K
% %elements, finest model
% \hline
% \end{tabular}
% \end{center}
% \end{table}
%
% \end{itemize}
%
%
% \end{frame}
% %-
% %-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%-
%- \begin{frame}
%- \frametitle{Parametric Simulation Results}
%-
%-
%- \vspace*{-0.5cm}
%- %\begin{landscape}
%- \begin{figure}[!htbp]
%- \begin{center}
%- \hspace*{-1cm}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispSoilBlock1.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispBent1.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispSoilBlock2.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispBent2.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispSoilBlock3.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispBent3.pdf}
%- \hspace*{-1cm}
%- \\
%- \hspace*{-1cm}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelSoilBlock1.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelBent1.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelSoilBlock2.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelBent2.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelSoilBlock3.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelBent3.pdf}
%- \hspace*{-1cm}
%- \\
%- \hspace*{-1cm}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispSoilBlock1_Spectrum.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispBent1_Spectrum.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispSoilBlock2_Spectrum.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispBent2_Spectrum.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispSoilBlock3_Spectrum.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispBent3_Spectrum.pdf}
%- \hspace*{-1cm}
%- \\
%- \hspace*{-1cm}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelSoilBlock1_Spectrum.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelBent1_Spectrum.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelSoilBlock2_Spectrum.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelBent2_Spectrum.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelSoilBlock3_Spectrum.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelBent3_Spectrum.pdf}
%- \hspace*{-1cm}
%- \\
%- \hspace*{-1cm}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/MomentBent1Pile1.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/MomentBent1Pile2.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/MomentBent2Pile1.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/MomentBent2Pile2.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/MomentBent3Pile1.pdf}
%- \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/MomentBent3Pile2.pdf}
%- \hspace*{-1cm}
%- \end{center}
%- \end{figure}
%-
%- \vspace*{-0.8cm}
%- \begin{figure}[!htbp]
%- \begin{center}
%- \includegraphics[width=3.2cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
%- %\caption{\label{BridgeSFSI01} FEM model for seismic response of a three bend
%- %bridge.}
%- \end{center}
%- \end{figure}
%- \vspace*{-2cm}
%-
%-
%- \clearpage
%-
%-
%-
%-
%- \end{frame}
%-
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%- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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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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% - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - %\begin{frame}
% - % \frametitle{Short Period E.: Left Bent, Structure and Soil, Disp.}
% - %
% - %
% - %
% - %
% - %\vspace*{-1cm}
% - %\begin{figure}[!htbp]
% - %\begin{center}
% - %\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispBent1.pdf}
% - %%\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispBent1.pdf}
% - %\\
% - %\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispSoilBlock1.pdf}
% - %%\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispSoilBlock1.pdf}
% - %%\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}
% - %
% - %
% - %
% - %\end{frame}
% - %%--
% - %%--
% - %%--
% - %%--
%--
%-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%-- \begin{frame}
%-- \frametitle{Short Period E.: Left Bent, Structure and Soil, Acc.}
%--
%--
%--
%--
%-- \vspace*{-1cm}
%-- \begin{figure}[!htbp]
%-- \begin{center}
%-- \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelBent1.pdf}
%-- \\
%-- \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelSoilBlock1.pdf}
%-- %\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}
%--
%-- \end{frame}
%-- %--
%--
%--
%--
%-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - %\begin{frame}
% - % \frametitle{Short Period E.: Left Bent, Structure and Soil, Acc.Sp.}
% - %
% - %
% - %
% - %
% - %\vspace*{-1cm}
% - %\begin{figure}[!htbp]
% - %\begin{center}
% - %\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelBent1_Spectrum.pdf}
% - %\\
% - %\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/AccelSoilBlock1_Spectrum.pdf}
% - %%\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}
% - %
% - %
% - %\end{frame}
% - %%--
% - %
% - %
% - %
% - %%-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - %%-- \begin{frame}
%-- \frametitle{Short Period E.: Left Bent, Structure and Soil, M.}
%--
%--
%--
%--
%-- \vspace*{-1cm}
%-- \begin{figure}[!htbp]
%-- \begin{center}
%-- \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/MomentBent1Pile1.pdf}
%-- \\
%-- \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/MomentBent1Pile2.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}
%--
%--
%-- \end{frame}
%-- %--
%--
%-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}
%--
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%-- \begin{frame}
%-- \frametitle{Short Period E.: Left Bent, Free Field vs Real Disp.}
%--
%--
%--
%--
%-- \vspace*{-1cm}
%-- \begin{figure}[!htbp]
%-- \begin{center}
%-- \includegraphics[width=11cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/DispSoilBlock1_15cm_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}
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%-- \frametitle{Kocaeli Input Motions}
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%-- \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}
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%-- \frametitle{Long Period E.: Left Bent, Structure and Soil, Disp.}
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%-- \begin{figure}[!htbp]
%-- \begin{center}
%-- \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/DispBent1.pdf}
%-- \\
%-- \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/DispSoilBlock1.pdf}
%-- %\caption{\label{BridgeSFSI01} FEM model for seismic response of a three bend
%-- %bridge.}
%-- \end{center}
%-- \end{figure}
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%-- \vspace*{-2.9cm}
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%-- \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}
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%-- \frametitle{Long Period E.: Left Bent, Structure and Soil, Acc.}
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%-- \begin{figure}[!htbp]
%-- \begin{center}
%-- \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/AccelBent1.pdf}
%-- \\
%-- \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/AccelSoilBlock1.pdf}
%-- %\caption{\label{BridgeSFSI01} FEM model for seismic response of a three bend
%-- %bridge.}
%-- \end{center}
%-- \end{figure}
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%-- \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}
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%-- \frametitle{Long Period E.: Left Bent, Structure and Soil, Acc.Sp.}
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%-- \vspace*{-1cm}
%-- \begin{figure}[!htbp]
%-- \begin{center}
%-- \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/AccelBent1_Spectrum.pdf}
%-- \\
%-- \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/AccelSoilBlock1_Spectrum.pdf}
%-- %\caption{\label{BridgeSFSI01} FEM model for seismic response of a three bend
%-- %bridge.}
%-- \end{center}
%-- \end{figure}
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%--
%-- \vspace*{-2.9cm}
%-- \hspace*{0.2cm}
%-- \begin{figure}[!htbp]
%-- \begin{flushright}
%-- \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
%-- %\caption{\label{BridgeSFSI01} FEM model for seismic response of a three bend
%-- %bridge.}
%-- \end{flushright}
%-- \end{figure}
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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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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Soft Soils: Left Bent, Structure and Soil, Moments}
%
%
%
%
% \vspace*{-1cm}
% \begin{figure}[!htbp]
% \begin{center}
% \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/MomentBent1Pile1_25s_SC.pdf}
% %\caption{\label{BridgeSFSI01} FEM model for seismic response of a three bend
% %bridge.}
% \end{center}
% \end{figure}
% \vspace*{-2cm}
%
%
% \end{frame}
% %--
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Soft Soils: Left Bent, Free Field vs Real Displacements}
%
%
%
%
% \vspace*{-1cm}
% \begin{figure}[!htbp]
% \begin{center}
% \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/DispSoilBlock1_15cm_25s_SC.pdf}
% %\caption{\label{BridgeSFSI01} FEM model for seismic response of a three bend
% %bridge.}
% \end{center}
% \end{figure}
% \vspace*{-2cm}
%
%
% \end{frame}
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\subsection{Use of Liquefaction}
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\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}
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%-- \vspace*{-0.1cm}
%-- \begin{figure}[!htbp]
%-- %\begin{center}
%-- \includegraphics[width=6cm]{/home/jeremic/tex/works/Papers/2009/SeismicIsolationLiquefaction/variation-sigmaxz-sigmaz.jpg} \\
%-- %\end{center}
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%-- \begin{frame}
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%-- \vspace*{-0.1cm}
%-- \begin{figure}[!htbp]
%-- %\begin{center}
%-- \includegraphics[width=6cm]{/home/jeremic/tex/works/Papers/2009/SeismicIsolationLiquefaction/variation-sigmaxz-gamma.jpg} \\
%-- %\end{center}
%-- \end{figure}
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%-- %\hspace*{2.3cm} EPPR \hspace{1.5cm} $\gamma$ \hspace{1.7cm} $u_{hor}$
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% \begin{frame}
% \frametitle{Excess Pore Pressure}
%
%
% \vspace*{-0.3cm}
% \begin{figure}[!htbp]
% %\begin{center}
% \includegraphics[width=10cm]{/home/jeremic/tex/works/Papers/2009/SeismicIsolationLiquefaction/contours-exc-pore-press.jpg} \\
% %\end{center}
% \end{figure}
% %\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{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{Plastic Energy Dissipation in Uniform Soils}
\vspace*{-1cm}
\begin{figure}[!htbp]
\begin{center}
\includegraphics[width=10cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/Uniform.pdf}
%\includegraphics[width=4cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/Layered.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{Plastic Energy Dissipation in Layered Soils}
\vspace*{-1cm}
\begin{figure}[!htbp]
\begin{center}
%\includegraphics[width=10cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/Uniform.pdf}
\includegraphics[width=10cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/Layered.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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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
\frametitle{Kinetic Energy at the Top}
%\vspace*{-0.3cm}
\begin{figure}[h]
\begin{center}
\hspace*{-1.3cm}
\includegraphics[width=13cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/StackElements-Compare.pdf}
\hspace*{-0.1cm}
\end{center}
\end{figure}
%\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{Void Ratio Variation (Potential Energy)}
\vspace*{-0.1cm}
\begin{figure}[!htbp]
%\begin{center}
\includegraphics[width=6cm]{/home/jeremic/tex/works/Papers/2009/SeismicIsolationLiquefaction/variation-e-t.jpg} \\
%\end{center}
\end{figure}
%\vspace*{-0.3cm}
%\hspace*{2.3cm} EPPR \hspace{1.5cm} $\gamma$ \hspace{1.7cm} $u_{hor}$
\end{frame}
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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 Earthquake}, {\bf Soil} and {\bf
Structure} plays a major role in catastrophic failures
and great successes
\vspace*{0.5cm}
\item {\bf Opportunity to improve design}: following the
flow of seismic energy in the soil--structure systems
\vspace*{0.5cm}
\item {\bf Directing} in space and time, seismic
energy flow in the soil--structure system might/will lead to increase in safety and
economy
%
% \item {\bf Matching Triad}:
% \underline{Earthquake},
% \underline{Soil} and
% \underline{Structure}
% ({\bf ESS}) interaction determines
% possible benefits or detriments of SFSI
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{Colossus of Rhodes: What if?}
\includegraphics[height=5cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/rhodes.jpg}
\includegraphics[height=5cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/colossus_final.jpg}
\includegraphics[height=5cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/rhodes_tilted.jpg}
\end{frame}
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%-- \frametitle{References}
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\end{document}