% $Header: /cvsroot/latex-beamer/latex-beamer/solutions/conference-talks/conference-ornate-20min.en.tex,v 1.6 2004/10/07 20:53:08 tantau Exp $

\documentclass{beamer}

% This file is a solution template for:

% - Talk at a conference/colloquium.
% - Talk length is about 20min.
% - Style is ornate.



% Copyright 2004 by Till Tantau <tantau@users.sourceforge.net>.
%
% In principle, this file can be redistributed and/or modified under
% the terms of the GNU Public License, version 2.
%
% However, this file is supposed to be a template to be modified
% for your own needs. For this reason, if you use this file as a
% template and not specifically distribute it as part of a another
% package/program, I grant the extra permission to freely copy and
% modify this file as you see fit and even to delete this copyright
% notice. 

\setbeamertemplate{navigation symbols}{}
\mode<presentation>
{
%  \usetheme{CambridgeUS}
  \usetheme{Dresden}
  \usecolortheme[RGB={20,0,128}]{structure}
  % or ...

  \setbeamercovered{transparent}
  % or whatever (possibly just delete it)
}


\usepackage[english]{babel}
% or whatever

\usepackage[latin1]{inputenc}
% or whatever

\usepackage{times}
\usepackage[T1]{fontenc}
% Or whatever. Note that the encoding and the font should match. If T1
% does not look nice, try deleting the line with the fontenc.


%\title[Short Paper Title] % (optional, use only with long paper titles)
%{Title As It Is In the Proceedings}

\title[Modeling and Simulations of Liquefied Soils]
% (optional, use only with long paper titles)
{Modeling and Simulations of Liquefied Soils}

%\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[Jeremi{\'c}, Cheng, Taiebat, Dafalias] % (optional, use only with lots of authors)
{Boris~Jeremi{\'c}, Zhao Cheng, \\ Mahdi Taiebat, and Yannis Dafalias}
% - 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
\pgfuseimage{university-logo} \hspace*{-0.3truecm}] % (optional, but mostly needed)
{
%  Department of Civil and Environmental Engineering\\
  University of California, Davis \\ and \\
  EarthMechanics Inc. Fountain Valley \\ and \\
  National Technical University, Athens, Greece}
% - 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 Funding: NSF--EEC--9701568, NSF--CMS--0201231, NSF--CMS--0324661}
% - Either use conference name or its abbreviation.
% - Not really informative to the audience, more for people (including
%   yourself) who are reading the slides online

\subject{}
% This is only inserted into the PDF information catalog. Can be left
% out. 



% If you have a file called "university-logo-filename.xxx", where xxx
% is a graphic format that can be processed by latex or pdflatex,
% resp., then you can add a logo as follows:

% \pgfdeclareimage[height=0.5cm]{university-logo}{university-logo-filename}
% \logo{\pgfuseimage{university-logo}}



%% Delete this, if you do not want the table of contents to pop up at
%% the beginning of each subsection:
% \AtBeginSubsection[]
% {
%   \begin{frame}<beamer>
%     \frametitle{Outline}
%     \tableofcontents[currentsection,currentsubsection]
%%    \tableofcontents[currentsection]
%   \end{frame}
% }


% If you wish to uncover everything in a step-wise fashion, uncomment
% the following command: 

%\beamerdefaultoverlayspecification{<+->}


\begin{document}

\begin{frame}
  \titlepage
\end{frame}

\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
%   15 and 30 frames, all told.

% - A conference audience is likely to know very little of what you
%   are going to talk about. So *simplify*!
% - In a 20min talk, getting the main ideas across is hard
%   enough. Leave out details, even if it means being less precise than
%   you think necessary.
% - If you omit details that are vital to the proof/implementation,
%   just say so once. Everybody will be happy with that.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Modeling}


\subsection{Fully Coupled Formulation}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Fully Coupled $u-p-U$ Formulation}

\begin{itemize}
  \item Formulation: fully coupled by Zienkiewicz and Shiomi 1984),
  nonlinear dynamics  by Argyris and Mlejnek (1991) 
\vspace*{0.3cm}
  \item  Physical,  velocity  proportional  damping from solid--fluid interaction
  (not using Raleigh damping)
\vspace*{0.3cm}
  \item Accelerations of pore fluid not neglected 
    \begin{itemize}
      \item important for SFSI
      \item inertial forces of fluid allow liquefaction modeling
    \end{itemize}
\vspace*{0.3cm}
  \item Stable formulation for near incompressible pore fluid
%  \item  Formulation and implementation verified on a number of available closed
%  form solutions

\end{itemize}
%\vspace*{-2.0cm}
\end{frame}



\subsection{Dafalias Manzari Material Model}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\begin{frame}
\frametitle{Dafalias Manzari Material Model}

\begin{itemize}
%\item Constitutive model is the necessary component of any rational numerical analysis.

\item  Dafalias  \&  Manzari  (2004):  critical  state compatible elasto-plastic
constitutive model for sands.

\vspace*{0.3cm}
\item Systematic and relatively simple calibration process.

\vspace*{0.3cm}
\item Capable of simulating different feature of sand response such as
\begin{itemize}
 \item hardening 
 \item softening
 \item consolidation
 \item dilation 
\end{itemize}

\vspace*{0.3cm}
\item Single set of parameters for all stages of loading (self weight, cycling...)
\end{itemize}

%\vspace*{-2.0cm}

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%--
%-- 
%-- \begin{frame}
%-- \frametitle{Dafalias Manzari Material Model}
%-- 
%-- Model Formulation in Triaxial Space%
%-- \[
%-- \left\{
%-- \begin{array}
%-- [c]{l}%
%-- \dot{\varepsilon}_{q}^{{}}=\dot{\varepsilon}_{q}^{e}+\dot{\varepsilon}_{q}%
%-- ^{p}\\
%-- \dot{\varepsilon}_{v}^{{}}=\dot{\varepsilon}_{v}^{e}+\dot{\varepsilon}_{v}^{p}%
%-- \end{array}
%-- \right.  \ \ \ ;\ \ \ \eta=\dfrac{q}{p}\ \ \ \ ;\ \ \ \
%-- %TCIMACRO{\TeXButton{darkgreen}{\color{darkgreen}}}%
%-- %BeginExpansion
%-- %\color{darkgreen}%
%-- %EndExpansion
%-- f=\left\vert \eta-\alpha\right\vert -m=0
%-- \]
%-- 
%-- 
%-- \vspace*{-0.9cm}%
%-- 
%-- %TCIMACRO{\TeXButton{B}{\begin{figure}[htbp] \centering}}%
%-- %BeginExpansion
%-- \begin{figure}[htbp] \centering
%-- %EndExpansion%
%-- %TCIMACRO{\FRAME{itbpF}{2.2364in}{1.6855in}{0in}{}{}%
%-- %{triaxial_model_surfaces.eps}{\special{ language "Scientific Word";
%-- %type "GRAPHIC";  maintain-aspect-ratio TRUE;  display "USEDEF";
%-- %valid_file "F";  width 2.2364in;  height 1.6855in;  depth 0in;
%-- %original-width 5.8219in;  original-height 4.3708in;  cropleft "0.0500";
%-- %croptop "0.9333";  cropright "0.9499";  cropbottom "0.0333";
%-- %filename 'triaxial_model_surfaces.eps';file-properties "XNPEU";}}}%
%-- %BeginExpansion
%-- {\includegraphics[
%-- trim=0.291095in 0.145548in 0.291677in 0.291532in,
%-- %height=1.6855in,
%-- width=2.2364in
%-- ]%
%-- {Mahdi/triaxial_model_surfaces.pdf}%
%-- }%
%-- %EndExpansion%
%-- %TCIMACRO{\FRAME{itbpF}{2.2364in}{1.6855in}{0in}{}{}{csl.pdf}%
%-- %{\special{ language "Scientific Word";  type "GRAPHIC";
%-- %maintain-aspect-ratio TRUE;  display "USEDEF";  valid_file "F";
%-- %width 2.2364in;  height 1.6855in;  depth 0in;  original-width 5.8219in;
%-- %original-height 4.3708in;  cropleft "0.0499";  croptop "0.9333";
%-- %cropright "0.9498";  cropbottom "0.0332";
%-- %filename 'CSL.pdf';file-properties "XNPEU";}}}%
%-- %BeginExpansion
%-- {\includegraphics[
%-- trim=0.290513in 0.145111in 0.292259in 0.291532in,
%-- %height=1.6855in,
%-- width=2.2364in
%-- ]%
%-- {Mahdi/CSL.pdf}%
%-- }%
%-- %EndExpansion
%-- %\caption{}\label{Key}%
%-- %TCIMACRO{\TeXButton{E}{\end{figure}}}%
%-- %BeginExpansion
%-- \end{figure}%
%-- %EndExpansion
%-- 
%-- 
%-- \vspace*{-1cm}%
%-- \begin{align*}
%-- \dot{\varepsilon}_{q}^{p}  &  =\dfrac{\dot{\eta}}{h%
%-- %TCIMACRO{\TeXButton{blue}{\color{blue}}}%
%-- %BeginExpansion
%-- %\color{blue}%
%-- %EndExpansion
%-- b}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
%-- %TCIMACRO{\TeXButton{blue}{\color{blue}}}%
%-- %BeginExpansion
%-- %\color{blue}%
%-- %EndExpansion
%-- b=(M_{{}}^{b}-\eta)\\
%-- \dot{\varepsilon}_{v}^{p}  &  =A_{d}%
%-- %TCIMACRO{\TeXButton{red}{\color{red}}}%
%-- %BeginExpansion
%-- %\color{red}%
%-- %EndExpansion
%-- d%
%-- %TCIMACRO{\TeXButton{black}{\color{black}}}%
%-- %BeginExpansion
%-- %\color{black}%
%-- %EndExpansion
%-- \left\vert \dot{\varepsilon}_{q}^{p}\right\vert \ \ \ \ \ \ \ \
%-- %TCIMACRO{\TeXButton{red}{\color{red}}}%
%-- %BeginExpansion
%-- %\color{red}%
%-- %EndExpansion
%-- d=(M_{{}}^{d}-\eta)
%-- \end{align*}
%-- 
%-- 
%-- %\vspace*{-2.0cm}
%-- 
%-- \end{frame}
%-- 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



\begin{frame}
\frametitle{Multiaxial Representation}

\vspace*{-2.5cm}

%TCIMACRO{\TeXButton{B}{\begin{figure}[htbp] \centering}}%
%BeginExpansion
\begin{figure}[htbp] \centering
%EndExpansion%
%TCIMACRO{\FRAME{itbpF}{2.2364in}{1.6855in}{0in}{}{}%
%{triaxial_model_surfaces.pdf}{\special{ language "Scientific Word";
%type "GRAPHIC";  maintain-aspect-ratio TRUE;  display "USEDEF";
%valid_file "F";  width 2.2364in;  height 1.6855in;  depth 0in;
%original-width 5.8219in;  original-height 4.3708in;  cropleft "0.0500";
%croptop "0.9333";  cropright "0.9499";  cropbottom "0.0333";
%filename 'triaxial_model_surfaces.pdf';file-properties "XNPEU";}}}%
%BeginExpansion
\hspace*{-1cm}
{\includegraphics[
trim=0.291095in 0.145548in 0.291677in 0.291532in,
%height=1.6855in,
width=7cm
]%
{Mahdi/triaxial_model_surfaces.pdf}%
}%
\hspace*{-1cm}
%EndExpansion%
%TCIMACRO{\FRAME{itbpF}{2.2364in}{1.7781in}{0in}{}{}{pi-plane.pdf}%
%{\special{ language "Scientific Word";  type "GRAPHIC";
%maintain-aspect-ratio TRUE;  display "USEDEF";  valid_file "F";
%width 2.2364in;  height 1.7781in;  depth 0in;  original-width 5.8219in;
%original-height 4.3708in;  cropleft "0.1166";  croptop "0.9776";
%cropright "0.9166";  cropbottom "0.1329";
%filename 'pi-plane.pdf';file-properties "XNPEU";}}}%
%BeginExpansion
{\includegraphics[
trim=0.678834in 0.580879in 0.485547in 0.097906in,
%height=1.7781in,
width=7cm
]%
{Mahdi/pi-plane.pdf}%
}%
\hspace*{-1cm}
%EndExpansion
%\caption{}\label{Key}%
%TCIMACRO{\TeXButton{E}{\end{figure}}}%
%BeginExpansion
\end{figure}%
%EndExpansion


\vspace*{1cm}

%\vspace*{-2.0cm}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\begin{frame}
\frametitle{Dafalias Manzari Material Model}

Fabric Dilatancy Tensor%
\begin{align*}
\dot{\varepsilon}_{v}^{p}  &  =A_{d}d\left\vert \dot{\varepsilon}_{q}%
^{p}\right\vert \\
A_{d}  &  =A_{0}\left(  1+\langle\mathbf{z}\mathbf{:}\mathbf{n}\rangle\right)
\text{ \ \ \ ; \ \ \ }\mathbf{\dot{z}}=-c_{z}\langle-\dot{\varepsilon}_{v}%
^{p}\rangle\left(  z_{max}\mathbf{n}+\mathbf{z}\right)
\end{align*}%
%TCIMACRO{\FRAME{ftbpF}{2.8383in}{2.188in}{0pt}{}{}{fabric_effect.pdf}%
%{\special{ language "Scientific Word";  type "GRAPHIC";
%maintain-aspect-ratio TRUE;  display "USEDEF";  valid_file "F";
%width 2.8383in;  height 2.188in;  depth 0pt;  original-width 5.8219in;
%original-height 4.3708in;  cropleft "0";  croptop "0.9554";
%cropright "0.9333";  cropbottom "0";
%filename 'fabric_effect.pdf';file-properties "XNPEU";}}}%
%BeginExpansion
\vspace*{-3cm}
\begin{figure}
[ptb]
\begin{center}
\includegraphics[
trim=0.000000in 0.000000in 0.388321in 0.194938in,
%height=2.188in,
width=2.8383in
]%
{Mahdi/fabric_effect.pdf}%
\end{center}
\end{figure}
%EndExpansion


%\vspace*{-2.0cm}

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%









%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Verification, Validation and Prediction}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Verification, Validation and Prediction}


\begin{itemize}

     \item 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.}

     \item 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.}

   \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}

%
%\item Models available (some now, some later) 
%\vspace*{-2.0cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Formulation Verification}



Using closed form solutions (consolidation, injection of
     fluid  into  reservoir,  cylindrical  cavity    expansion, spherical cavity
     expansion.

\vspace*{-2.5cm}
\hspace*{-0.5cm}
\begin{figure}[!hbpt]
\hspace*{-1.9cm}
%\begin{center}
\includegraphics[width=6.9cm]{/home/jeremic/tex/works/Thesis/QingLiu/thesis/fig/InjectionPressure.pdf}
\hspace*{-1cm}
\includegraphics[width=6.9cm]{/home/jeremic/tex/works/Thesis/QingLiu/thesis/fig/InjectionDisplacement.pdf}
\hspace*{-1.5cm}
%\end{center}
\end{figure}

%
%\item Models available (some now, some later) 
%\vspace*{-2.0cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Material Model Validation}



\begin{figure}[!htbp]
\hspace*{-0.4cm}
%\begin{center}
\includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2007/GeoDenver/Coupled/Present/DMvalidation01a.jpg}
\hspace*{0.5cm}
\includegraphics[width=5.2cm]{/home/jeremic/tex/works/Conferences/2007/GeoDenver/Coupled/Present/DMvalidation02a.jpg}
\hspace*{-0.4cm}
%\end{center}
\end{figure}
%--   
%--   

%
%\item Models available (some now, some later) 
%\vspace*{-2.0cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Prediction Examples}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Seismic Behavior of Horizontal Grounds}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Level Ground, Dense Sand}


\vspace*{-0.7cm}
\begin{figure}[!htbp]
\begin{center}
  \includegraphics[width=11cm]{/home/jeremic/tex/works/Conferences/2007/PEERAnnualMeeting/Liquefaction/DenseLevelGround.jpg} \\
\end{center}
\end{figure}



\end{frame}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Medium Sand}
% 
% 
% 
% 
% \end{frame}
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Level Ground, Loose Sand}


\vspace*{-0.7cm}
\begin{figure}[!htbp]
\begin{center}
  \includegraphics[width=11cm]{/home/jeremic/tex/works/Conferences/2007/PEERAnnualMeeting/Liquefaction/LooseLevelGround.jpg} \\
\end{center}
\end{figure}




\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Seismic Behavior of Sloping  Grounds}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Sloping Ground, Dense Sand}

\vspace*{-0.0cm}
\begin{figure}[!htbp]
\begin{center}
  \includegraphics[width=10.5cm]{/home/jeremic/tex/works/Conferences/2007/PEERAnnualMeeting/Liquefaction/DenseSlopingGround.jpg} \\
\end{center}
\end{figure}


% 

\end{frame}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Medium Sand}
% 
% 
% 
% 
% \end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Sloping Ground, Loose Sand}

\vspace*{-0.0cm}
\begin{figure}[!htbp]
\begin{center}
  \includegraphics[width=10.5cm]{/home/jeremic/tex/works/Conferences/2007/PEERAnnualMeeting/Liquefaction/LooseSlopingGround.jpg} \\
\end{center}
\end{figure}




\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%







%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Piles in Liquefying Soils}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Bridge Pier--Pile Model}


\vspace*{-0.2cm}
\begin{figure}[!htbp]
\begin{center}
  \includegraphics[width=6cm]{/home/jeremic/tex/works/Conferences/2007/PEERAnnualMeeting/Liquefaction/PileBridgeModel01.jpg} \\
  \includegraphics[width=7cm]{/home/jeremic/tex/works/Conferences/2007/PEERAnnualMeeting/Liquefaction/PileBridgeModel02.jpg} \\
\end{center}
\end{figure}





\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Bridge Pier in Level Ground}

\vspace*{-0.3cm}
\begin{figure}[!htbp]
%\begin{center}
\hspace*{-1.0cm}
  \includegraphics[width=13cm]{/home/jeremic/tex/works/Conferences/2007/PEERAnnualMeeting/Liquefaction/PileBridgeLevelGroundEPP.jpg} \\
%\end{center}
\end{figure}





\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Bridge Pier in Sloping Ground}

\vspace*{-0.3cm}
\begin{figure}[!htbp]
%\begin{center}
\hspace*{-1.0cm}
\includegraphics[width=13cm]{/home/jeremic/tex/works/Conferences/2007/PEERAnnualMeeting/Liquefaction/PileBridgeSlopingGroundEPP.jpg} \\
%\end{center}
\end{figure}





\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%








%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section*{Summary}
\subsection*{Summary}

\begin{frame}
 \frametitle{Summary}

\begin{itemize}


\vspace*{0.5cm}
     \item Importance of consistent formulation, material modeling and implementation

\vspace*{0.5cm}
     \item Verified, validate models and simulations tools used for prediction of behavior

\vspace*{0.5cm}
     \item Program and examples available in public domain (Author's web site)

%
%\item Models available (some now, some later) 

%\vspace*{0.5cm}
\end{itemize}



\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\end{document}


