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\title[Verification and Validation in Computational Geomechanics]
% (optional, use only with long paper titles)
{Verification and Validation in Computational Geomechanics}

%\subtitle
%{{\tiny full set of slides available at:}\\
%%\verb{http://sokocalo.engr.ucdavis.edu/~jeremic/}
%}

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%\author[Boris Jeremi{\'c}, CompGeoMech \includegraphics[width=8cm]{/home/jeremic/BG/amblemi/ucdavis_logo_gold_lrg}] % (optional, use only with lots of authors)
\author[Jeremi{\'c}] % (optional, use only with lots of authors)
{Boris~Jeremi{\'c}  \\  Mahdi  Taiebat (UBC), Nima Tafazzoli, Panagiota Tasiopoulou }
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\pgfuseimage{university-logo} \hspace*{-0.3truecm}] % (optional, but mostly needed)
{
%  \texttt{http://geomechanics.ucdavis.edu} \\
  Department of Civil and Environmental Engineering\\
  University of California, Davis}
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\date[GheoMat] % (optional, should be abbreviation of conference name)
{GheoMat \\
 {\small Masseria Salamina  \\
 Italy, June 2009} }
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% \begin{frame}
%  \frametitle{Motivation}
%
% \begin{itemize}
%
%   \item Designers needs the best available tools for performance assessment
%
%   \item Steady progress of numerical simulations over last 4 decades
%
%   \item Steady progress of computer hardware
%
%   \item Use of software and hardware tools for detailed (as needed) performance assessment
%
%   \item In other words: simulation tools are available
%
%   \item Need to convince practice (you) that these tools are useful,
%         robust, verified, validated, and ready to be used
%
%
% \end{itemize}
% \end{frame}






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\section{Before We Start}


\subsection*{Before We Start}
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\begin{frame}
\frametitle{Important Sources}



\begin{itemize}




%\item {\it  Short Course on Verification and Validation in
%Computational Mechanics}, by {\sc Dr. William Oberkampf}, Sandia National Laboratories
%July 27th, 2003, Albuquerque, New Mexico.

\item
{\sc W.~L. Oberkampf, T.~G. Trucano, and C. Hirsch.}
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.


\end{itemize}




\end{frame}



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\begin{frame}
\frametitle{Motivation}



\begin{itemize}


\vspace*{0.5cm}
\item How much can (should) we trust  model implementations (verification)?

\vspace*{0.5cm}
\item How much can (should) we trust numerical simulations (validation)?

\vspace*{0.5cm}
\item How good are our numerical predictions?

\vspace*{0.5cm}
\item    Can      simulation  tools  (SimTool) be used for assessing {\bf public
safety}?


%\vspace*{2.5cm}
%\item How do we  use experimental simulations   to improve models




\end{itemize}




\end{frame}


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\begin{frame}
 \frametitle{Verification}


\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.}

\end{itemize}

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


\begin{itemize}

     \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.}

\end{itemize}

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


\begin{itemize}

   \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}
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\begin{frame}
 \frametitle{Role of Verification and Validation}


    
%   \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}
\end{figure}


%
%\item Models available (some now, some later)
%\vspace*{-2.0cm}
\end{frame}
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \section{Verification and Validation}
%
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection*{Fundamentals}



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\section{Why Do You Trust a Simulation?}


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\subsection{Verification, Validation}


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\begin{frame}
\frametitle{Importance of V \& V}


\begin{itemize}

%   \vspace*{2.0truecm}
   \item  V  \&  V  procedures  are  the  primary means of assessing accuracy in
   modeling and computational simulations

   \vspace*{1.0truecm}
   \item  V  \&  V  procedures  are the tools with which we build confidence and
   credibility in modeling and computational simulations


\end{itemize}



\end{frame}

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\begin{frame}
\frametitle{Maturity of Computational Simulations}



\noindent
National Research Council committee (1986) identified five stages of maturity in
computational fluid dynamics




\begin{itemize}

%   \vspace*{0.5truecm}
   \item {\bf Stage 1:} Developing enabling technologies (scientific papers published)
%   \pause

%   \vspace*{0.5truecm}
   \item {\bf Stage   2:}  Demonstration of and Confidence in technologies and tools
   (capabilities and limitations of technology understood)
%   \pause


%   \vspace*{0.5truecm}
   \item {\bf Stage 3:} Compilation of technologies and tools
   (capabilities and limitations of technology understood)
%      \pause
%
%   \item[] {\tiny \it UCD's CompGeoMech Group is about here}
%  \pause

%   \vspace*{0.5truecm}
   \item {\bf Stage  4:}  Spreading  of  the  effective  use  (changes the engineering
   process, value exceeds expectations)
%   \pause

%   \vspace*{0.5truecm}
   \item {\bf Stage  5:}  Mature capabilities (fully dependable, cost effective design
   applications)
%   \pause

\end{itemize}



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\frametitle{Alternative V \& V Definitions}



\noindent
IEEE V \& V definitions (1984):


\begin{itemize}

   \vspace*{0.0truecm}
   \item  {\bf Verification:} The process of determining whether the products of a
   given  phase  of  the  software  development  cycle  fulfill the requirements
   established during the previous phase

   \vspace*{0.0truecm}
   \item  {\bf Validation:} The process of evaluating software at the end of the
   software development process to ensure compliance with software requirements.

   \vspace*{0.0truecm}
   \item Other organization have similar definitions:
      \begin{itemize}
         \item Software quality assurance community
         \item  American  Nuclear Society (safety analysis of commercial nuclear
         reactors)
         \item International Organization for Standardization (ISO)
      \end{itemize}


\end{itemize}



\end{frame}

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\begin{frame}
\frametitle{Certification and Accreditation}


\begin{itemize}

   \vspace*{0.0truecm}
   \item  {\bf  Certification:}  A  written guarantee that a system or component
   complies  with  its  specified requirements and is acceptable for operational
   use (IEEE (1990)).
     \begin{itemize}
       \item  Written  guarantee  can  be issued by anyone (code developer, code
       user, independent code evaluator)
       \item Code certification is more formal than validation documentation
     \end{itemize}

   \vspace*{0.0truecm}
   \item    {\bf  Accreditation:}  The  official  certification  that a model or
   simulation is acceptable for use for a specific purpose (DOD/DMSO (1994))
      \begin{itemize}
         \item Only officially designated entities can accredit
         \item  Normally  appointed  by the customers/users of the code or legal
         authority
         \item Appropriate for major liability or public safety applications
      \end{itemize}



\end{itemize}



\end{frame}

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% \begin{frame}
% \frametitle{Certification and Accreditation}
% 
% 
% \begin{itemize}
% 
%    \vspace*{1.0truecm}
%    \item  Certification:  a  written  guarantee  that  a  simulation  system or
%    component  complies  with  a  specified  requirements  and is acceptable for
%    operational use (certification is more formal than validation documentation)
% 
%    \vspace*{1.0truecm}
%    \item   Accreditation:   The  official  certification  that  a  model  and/or
%    simulation  system  is  acceptable for use for a specific purpose (officially
%    designated  entities  can  accredit, appropriate for major liability and {\it
%    public safety applications})
% 
% 
% \end{itemize}
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\begin{frame}
\frametitle{Independence of Computational Confidence Assessment}


\begin{enumerate}

   \vspace*{0.3truecm}
   \item V\&V conducted by the computational tool developer,  {\it No Independence}

   \vspace*{0.3truecm}
   \item V\&V conducted by a user from same organization

   \vspace*{0.3truecm}
   \item V\&V conducted by a computational tool evaluator contracted by developer's organization

   \vspace*{0.3truecm}
   \item V\&V conducted by  a computational tool evaluator contracted by the customer

   \vspace*{0.3truecm}
   \item V\&V conducted by  a computational tool evaluator contracted by the a legal authority  {\it High Independence}


\end{enumerate}



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  \frametitle{Fundamentals of Verification and Validation}



%--


\begin{figure}[!h]
\vspace*{-0.5cm}
\hspace*{-0.5cm}
%\begin{center}
{\includegraphics[width=11cm]{/home/jeremic/tex/works/Conferences/2005/OpenSeesWorkshopAugust/DeveloperSymposium/VerifValidFund01.pdf}}
%\end{center}
\end{figure}


\end{frame}


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\begin{frame}
  \frametitle{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.}

\begin{figure}[!h]
\begin{center}
{\includegraphics[width=8.0cm]{/home/jeremic/tex/works/Conferences/2005/OpenSeesWorkshopAugust/DeveloperSymposium/VerifValidFund02.pdf}}
\end{center}
\end{figure}


% % 
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% \begin{figure}[!htbp] 
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\begin{frame}
  \frametitle{Verification}

   Mathematics issue. {\it Verification provides evidence that the
  model is solved correctly.}

\vspace*{0.3cm}
   \begin{itemize}
     \item Identify and remove errors in computer coding
       \begin{itemize}
         \item Numerical algorithm verification
         \item Software quality  assurance practice
       \end{itemize}

\vspace*{0.3cm}
     \item Quantification of the  numerical errors in  computed solution
   \end{itemize}



\end{frame}

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\begin{frame}
  \frametitle{Verification}


   \begin{itemize}
\vspace*{0.3cm}
     \item Improving software quality through development process 

\vspace*{0.3cm}
     \item  Application  Programming  Interface  (API) defines software services
     developed by {\bf Developers} that are used by {\bf Users}
               
                 
       \begin{itemize}
%\vspace*{0.3cm}
         \item Public API is forever (asset, liability)
%\vspace*{0.5cm}
%\vspace*{0.3cm}
         \item Realistically, API evolves
%\vspace*{0.3cm}
         \item API design is tough (perfection unachievable, try anyway)
                    
         \item Literate programming for API

       \end{itemize}



\vspace*{0.3cm}
     \item  Two sided software platform connect Developers AND users through
     positive feedback (through API)

       \end{itemize}

\end{frame}

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% \begin{frame}
%   \frametitle{Verification for Computational Geomechanics}
% 
% 
%    \begin{itemize}
%          \item Elasto--Plasticity
% 
% 
%          \item Coupled Systems
%                   
%  1) INJECTION OF FLUID (Coussy, 2004) 
%   
%      a) Point injection of fluid mass and its progressive diffusion 
%       
%      b) Line Injection of fluid mass and its progressive diffusion 
%  
%  2) CONSOLIDATION OF SOIL LAYER (Coussy, 2004) 
%   
%  3) DRILLING OF A BOREHOLE (Coussy, 2004) 
%  
%  4) TRANSIENT  RESPONSE  OF  SATURATED  LINEAR  ELASTIC  POROUS  MEDIA 
%     (Gajo \& Mongiovi, 1995b) 
%   
%      a) One Dimensional Propagation of Longitudinal Waves in any Range 
%         of  Viscous Coupling 
%       
%      b) One Dimensional Propagation of Rotational Waves in any Range of  
%         Viscous Coupling 
%  
%  5) ANALYSIS  OF  ONE­DIMENSIONAL  WAVE  PROPAGATION  IN  A  FLUID­
%     SATURATED FINITE SOIL COLUMN (Hiremath et al., 1988) 
%   
%  6) SOME  BASIC  STRESS  DIFFUSION  SOLUTIONS  FOR  FLUID­SATURATED 
%     ELASTIC  POROUS  MEDIA  WITH  COMPRESSIBLE  CONSTITUENTS  (Rice  \& 
%     Cleary, 1976) 
%  
%  7) STRESSES IN FLUID­SATURATED POROUS HALF­SPACE DUE TO NORMAL \& 
%     TANGENTIAL LOADINGS (Dey \& De, 1984) 
%  
%   
%  8) NONLINEAR  ANALYTICAL  SOLUTION  FOR  1D  CONSOLIDATION  OF  SOFT 
%     SOIL UNDER CYCLIC LOADING (Xie et al., 2006) 
%   
%  9) ANALYTICAL SOLUTION FOR 2D DYNAMIC CONSOLIDATION IN FREQUENCY 
%     DOMAIN (Valliappan et al., 1995) 
%  
%   
%  10) ON NUMERICAL AND ANALYTICAL SOLUTIONS OF SOIL CONSOLIDATION 
%     PROBLEMS AT VARIOUS BOUNDARY CONDITIONS  (Glagovsky, 2000) 
%   
%  11) CRYER?S PROBLEM (Cryer, 1963) 
%  
% 
%          \item Numerics
% 
% 
%     \end{itemize}
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\begin{frame}
  \frametitle{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.}

\begin{figure}[!h]
%\vspace*{-4.3cm}
%\hspace*{5.5cm}
\begin{center}
{\includegraphics[width=6.5cm]{/home/jeremic/tex/works/Conferences/2005/OpenSeesWorkshopAugust/DeveloperSymposium/VerifValidFund03.pdf}}
\end{center}
\end{figure}



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%   \frametitle{Validation}
% 
% 
% %   Physics issue. {\it Validation provides
% %   evidence that the correct model is solved.}
% 
%    \begin{itemize}
% %\vspace*{0.3cm}
%      \item Physics issue. {\it Validation provides evidence that the correct model is solved.}
% \vspace*{0.3cm}
%      \item    Tactical  goal: Identification  and  minimization of uncertainties
%      and errors in the computational model
% \vspace*{0.3cm}
%      \item    Strategic    goal:  Increase    confidence    in  the quantitative
%      predictive capability of the computational model
%    \end{itemize}
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%  %\vspace*{-5.0cm}
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\begin{frame}
\frametitle{Validation}



Quantification  of  uncertainties  and errors in the computational model and the
experimental measurements



\begin{itemize}

 \item Goals on validation
   \begin{itemize}
     \item  Tactical  goal:  Identification  and minimization of uncertainties and
     errors in the computational model
     \item  Strategic  goal:  Increase  confidence  in the quantitative predictive
     capability of the computational model
   \end{itemize}

 \item Strategy  is to reduce as much as possible the following:
   \begin{itemize}
     \item Computational model uncertainties and errors
     \item Random (precision) errors and bias (systematic) errors in the experiments
     \item Incomplete physical characterization of the experiment
  \end{itemize}

\end{itemize}






\end{frame}

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\begin{frame}
\frametitle{Validation Procedure Uncertainty}



\begin{itemize}

%\vspace*{1cm}
 \item  Aleatory uncertainty $\rightarrow$ inherent variation associated with the
 physical  system (variation in external excitation, material
 properties...). AKA irreducible uncertainty, variability and
 stochastic uncertainty.


%\vspace*{0.5cm}
 \item  Epistemic uncertainty $\rightarrow$ potential deficiency in any phase of
 the  modeling  process  that is due to lack of knowledge (poor understanding of
 mechanics...). AKA reducible uncertainty, model form uncertainty and
 subjective uncertainty.


\end{itemize}

%\vspace*{1cm}
\begin{figure}[!h]
\begin{center}
\vspace*{-1.0cm}
\includegraphics[height=4cm,angle=-90]{/home/jeremic/tex/works/Conferences/2007/USC_seminar/Present/uncertain03.pdf}
%{\includegraphics[width=4.0cm]{/home/jeremic/tex/works/Presentation/2004/UCLA/uncertain01.pdf}}
%\vspace*{-5.0cm}
\end{center}
\end{figure}






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\begin{frame}
\frametitle{Use of Physical Experiments for Validation}


\begin{itemize}

%   \vspace*{1.0truecm}
   \item {\bf Traditional Experiments}
     \begin{itemize}
       \item Improve the fundamental understanding of physics involved
       \item Improve the mathematical models for physical phenomena
       \item Assess component performance
     \end{itemize}

%   \vspace*{1.0truecm}
   \item {\bf Validation Experiments}
     \begin{itemize}
       \item Model validation experiments
       \item  Designed  and  executed  to  quantitatively estimate mathematical
       model's ability to simulate well defined physical behavior
       \item   The  simulation  tool (SimTool) (conceptual  model,  computational  model,
       computational solution) is the customer
     \end{itemize}


\end{itemize}


\end{frame}

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\begin{frame}
\frametitle{Validation Experiments }


\begin{itemize}

   \vspace*{0.0truecm}
   \item  A  validation  experiment  should be jointly designed and executed by
   experimentalist and computationalist
     \begin{itemize}
       \item Need for close working relationship from inception to documentation
       \item Elimination of typical competition between each
       \item  Complete  honesty  concerning  strengths  and  weaknesses  of both
       experimental and computational simulations
     \end{itemize}


   \vspace*{0.0truecm}
   \item A validation experiment should be designed to capture the relevant physics
     \begin{itemize}
       \item Measure all important modeling data in the experiment
       \item  Characteristics  and  imperfections  of  the experimental facility
       should be included in the model
     \end{itemize}


\end{itemize}



\end{frame}

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\begin{frame}
\frametitle{Validation Experiments (contd)}


\begin{itemize}

   \vspace*{0.0truecm}
   \item  A  validation  experiment  should  use any possible synergism between
   experiment and computational approaches
     \begin{itemize}
       \item Offset strength and weaknesses of computations and experiments
       \item  Use high confidence simulations for simple physics to calibrate of
       improve the characterization of the experimental facility
       \item    Conduct  experiments  with a  hierarchy of physics complexity  to
       determine where the computational simulation breaks (remember, SimTool is
       the customer!)
     \end{itemize}


   \vspace*{0.0truecm}
   \item  Maintain independence  between computational and experimental results
     \begin{itemize}
       \item Blind comparison, the computational simulations should be predictions
       \item Neither side is allowed to use fudge factors, parameters
     \end{itemize}


\end{itemize}



\end{frame}

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% %%%%
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\begin{frame}
\frametitle{Validation Experiments (contd)}


\begin{itemize}

   \vspace*{0.0truecm}
   \item  Validate experiments on unit level problems, hierarchy of experimental
   measurements   should   be   made   which  present  an  increasing  range  of
   computational difficulty
     \begin{itemize}
       \item Use of qualitative data (e.g. visualization) and quantitative data
       \item  Computational  data  should be processed to match the experimental
       measurement techniques
     \end{itemize}

   \vspace*{0.0truecm}
   \item Experimental uncertainty analysis should be developed and employed
     \begin{itemize}
       \item Distinguish and quantify random and correlated bias errors
       \item   Use  symmetry  arguments  and  statistical  methods  to  identify
       correlated bias errors
       \item Make uncertainty estimates on input quantities needed by the SimTool
     \end{itemize}






\end{itemize}


\end{frame}

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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Validation Experiments }
% 
% 
% \begin{itemize}
% 
%    \vspace*{0.0truecm}
% 
%    \item  Jointly designed and executed by
%    experimentalist and computationalist
% 
%    \vspace*{0.0truecm}
%    \item Designed to capture the relevant physics
% 
%    \vspace*{0.0truecm}
%    \item  Use any possible synergism between
%    experiment and computational approaches
% 
%    \vspace*{0.0truecm}
%    \item  Maintain independence  between computational and experimental results
% 
%    \vspace*{0.0truecm}
%    \item  Validate experiments on unit level problems, hierarchy of experimental
%    measurements   should   be   made   which  present  an  increasing  range  of
%    computational difficulty
% 
%    \vspace*{0.0truecm}
%    \item Experimental uncertainty analysis should be developed and employed
% 
% \end{itemize}
% 
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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\subsection{Prediction}

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\begin{frame}
\frametitle{Prediction}


\begin{itemize}

   \vspace*{0.0truecm}
   \item  Prediction:  use  of  computational  model  to foretell the state of a
   physical   system   under  consideration  under  conditions  for  which  the
   computational model has not been validated

   \vspace*{0.5truecm}
   \item Validation does not directly make a claim about the accuracy of a prediction
     \begin{itemize}
       \item Computational models are easily misused (unintentionally or intentionally)
       \item  How  closely  related  are  the  conditions  of the prediction and
       specific cases in validation database
       \item How well is physics of the problem understood

     \end{itemize}


\end{itemize}



\end{frame}

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\begin{frame}
\frametitle{Relation Between Verification, Validation and Prediction}



Quantification of confidence in a prediction:

\begin{itemize}

   \vspace*{0.2truecm}
   \item  How do I quantify verification and its inference value in a prediction?

   \vspace*{0.2truecm}
   \item How do I quantify validation and its inference value in a predictions?

   \vspace*{0.2truecm}
   \item  How  far are individual validation experiments from physical system of interest?

%   \item

\end{itemize}



\end{frame}

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\begin{frame}
\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}




\end{frame}

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\begin{frame}
\frametitle{Application Domain --  No Overlap}





%\vspace*{0.3cm}

\begin{figure}[!h]
\begin{center}
%\vspace*{-2.5cm}
{\includegraphics[width=3.0cm]{/home/jeremic/tex/works/Presentation/2004/VandV/VPI03.pdf}}
%\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}





\end{frame}

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\begin{frame}
\frametitle{Importance of Models and Numerical Simulations}

%   \vspace*{0.6truecm}


\begin{itemize}

   \vspace*{0.2truecm}
   \item Verified and Validated models can be used for assessing behavior of
     \begin{itemize}
       \item components or
       \item complete systems,
     \end{itemize}

   \vspace*{0.2truecm}
   \item with the understanding that the environmental influences cannot all be taken into the account prior to operation

   \vspace*{0.2truecm}
   \item  but  with  a  good  model,  their influence on system behavior  can be
   assessed as need be (before or after the event)


\end{itemize}



\end{frame}

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\begin{frame}
\frametitle{Prediction under Uncertainty}


\begin{itemize}

   \vspace*{0.2truecm}
   \item Ever present uncertainty needs to be estimated for predictions

   \vspace*{0.2truecm}
   \item  Identify  all  relevant sources of uncertainty (see next lecture on uncertain soils)

   \vspace*{0.2truecm}
   \item Create mathematical representation of individual sources

   \vspace*{0.2truecm}
   \item Propagate representation of sources through modeling and simulation process




\end{itemize}



\end{frame}

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\section{Verification and Validation}







%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{The T Experiments}





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\begin{frame}
 \frametitle{Errors in Scientific Software}


\begin{itemize}

%   \vspace*{0.2truecm}
   \item Les Hatton, Oakwood Computing

   \vspace*{0.2truecm}
   \item "Extensive tests showed that many software codes widely used in science
   and engineering are not as accurate as we would like to think."

   \vspace*{0.2truecm}
   \item "Better software engineering practices wold help solve this problem,"

   \vspace*{0.2truecm}
   \item "Realizing that the problem exists is an important first step."
   
   
   \vspace*{0.2truecm}
   \item Large experiment over 4 years measuring faults (T1) and failures (T2) of scientific and engineering codes
   
   
   
    

\end{itemize}





\end{frame}


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\begin{frame}
 \frametitle{The T1 Experiments}


\begin{itemize}

%   \vspace*{0.2truecm}
   \item  Measured defects without running the code, measuring
   formal consistency of 3,305,628 lines f77 and 1,928,011 lines of C 

%   \vspace*{0.2truecm}
   \item 100 codes, 40 application areas:
   graphics, nuc. mech.  chem. aero. civil engineering, 
   comms, DBs, med. systems


%   \vspace*{0.2truecm}
   \item Safety--critical and 
   non--safety--critical applications

%   \vspace*{0.2truecm}
   \item Applications with and without internationally
   standardized systems of quality control

%   \vspace*{0.2truecm}
   \item Mature codes (1 - 20 years old), in regular
   use

   \item    Errors    (select),    arguments   sequence   in   function   calls,
   misunderstanding of finite precision arithmetic, code complexity

%   \item Results indicate 



    

\end{itemize}





\end{frame}


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\begin{frame}
 \frametitle{T1: C Sources}




\begin{figure}[!h]
\begin{center}
\hspace*{-1.5cm}
{\includegraphics[width=12.0cm]{/home/jeremic/tex/works/Conferences/2009/GheoMat/VandV_01/T1_01.jpg}}
\hspace*{-1.5cm}
%\vspace*{-5.0cm}
\end{center}
\end{figure}


% \begin{itemize}
% 
%     
% 
% \end{itemize}

\end{frame}


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\begin{frame}
 \frametitle{T1: f77 Sources}




\begin{figure}[!h]
\begin{center}
%\vspace*{-2.5cm}
\hspace*{-1.5cm}
{\includegraphics[width=10.0cm]{/home/jeremic/tex/works/Conferences/2009/GheoMat/VandV_01/T1_02.jpg}}
\hspace*{-1.5cm}
%\vspace*{-5.0cm}
\end{center}
\end{figure}


% \begin{itemize}
% 
%     
% 
% \end{itemize}

\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{The T2 Experiments}






\begin{itemize}

\item Specific application area: seismic data processing (inverse analysis)

\item Echo sounding of underground and reconstructing "images" of 
subsurface geological structure

\item Nine mature packages, using same algorithms were used on a same data set!

\item 14 primary calibration points for results check
\item Results "fascinating and disturbing"

    

\end{itemize}

\end{frame}


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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{T2: Disagreement at Calibration Points}




\begin{figure}[!h]
\begin{center}
\hspace*{-1.5cm}
%\vspace*{-2.5cm}
{\includegraphics[width=8.0cm]{/home/jeremic/tex/works/Conferences/2009/GheoMat/VandV_01/T2_01.jpg}}
\hspace*{-1.5cm}
%\vspace*{-5.0cm}
\end{center}
\end{figure}


% \begin{itemize}
% 
%     
% 
% \end{itemize}

\end{frame}


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\begin{frame}
 \frametitle{T2: Stage 14, Interpretation of Data  }




\begin{figure}[!h]
\begin{center}
%\vspace*{-2.5cm}
\vspace*{-1.0cm}
\hspace*{-1.5cm}
{\includegraphics[width=8.0cm]{/home/jeremic/tex/works/Conferences/2009/GheoMat/VandV_01/T2_02.jpg}}
\hspace*{-1.5cm}
\vspace*{-1.5cm}
%\vspace*{-5.0cm}
\end{center}
\end{figure}


% \begin{itemize}
% 
%     
% 
% \end{itemize}

\end{frame}


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\subsection{Select V and V Examples}





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\begin{frame}
 \frametitle{Constitutive Integration Error Maps}

Normalized     error:     $     \delta^r    =    {\sqrt{(\sigma_{ij}    -
\sigma^{\ast}_{ij})(\sigma_{ij} - \sigma^{\ast}_{ij})}}/
{\sqrt{\sigma^{0}_{pq}\sigma^{0}_{pq}}}$



von Mises, linear isotropic hardening:
\begin{figure}[!hbpt]
\begin{center}
\includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/ZhaoCheng/thesis/file/NewTemplate3Dep/ErrorMap/VM_LinearIsotropic/errMap_normalized_VM.pdf}
\end{center}
\end{figure}  




\end{frame}


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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Constitutive Integration Error Maps}


von Mises, non--linear kinematic hardening  (Armstrong-Frederick):
%%%
\begin{figure}[!hbpt]
\begin{center}
\includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/ZhaoCheng/thesis/file/NewTemplate3Dep/ErrorMap/VM_AF/errMap_normalized_VM.pdf}
\end{center}
\end{figure}  



\end{frame}


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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Constitutive Integration Error Maps}


Dafalias-Manzari, rotational kinematic hardening, bounding surface:
%%%
\begin{figure}[!hbpt]
\begin{center}
\includegraphics[width = 10cm]{/home/jeremic/tex/works/Thesis/ZhaoCheng/thesis/file/NewTemplate3Dep/ErrorMap/DM_ConstantE/errMap_normalized_DM.pdf}
\end{center}
\end{figure}  

\end{frame}


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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Single Pile in Layered Soils: Model}
% 
% 
% \begin{figure}[!htbp]
% \begin{center}
% \includegraphics[width=4.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/SinglePile_CS_color.pdf}
% \hfill
% \includegraphics[width=4.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/spUFmesh.pdf}
% \end{center}
% %\vspace*{-0.3cm}
% \end{figure}
% 
% \end{frame}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Available Data for Prototype}
% 
% 
%  \begin{itemize}
%    \item Sand:
%     \begin{itemize}
%      \item friction angle $\phi$ of  $37.1^{o}$,
%      \item Shear  modulus  at  a depth of 13.7 m of 8960 kPa ($E_o$ = 17400 kPa),
%      \item Poisson ratio  of  0.35   
%      \item Unit  weight  of  14.50  kN/$m^3$. 
%      \item Dilation angle   $0^{o}$
%     \end{itemize}
%    \item Clay (made up)
%      \begin{itemize}
%        \item Shear strength $21.7$~kPa
%        \item Young's modulus $11000$~kPa
%        \item Poisson ratio $0.45$
%        \item Unit weight $13.7~{\rm kN/m^3}$
%      \end{itemize}
% 
%  \end{itemize}
% 
% 
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Single Pile in Sand: M, Q, p}
% \begin{figure}[!htbp]
% \begin{center}
% \includegraphics[width=7.5cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/MQP_dsand_UFmid2hdp0.jpg}
% \end{center}
% \end{figure}
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% %  \frametitle{Single Pile in Clay: M, Q, p}
% % \begin{figure}[!htbp]
% % \begin{center}
% % \includegraphics[width=7.5cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/MQP_sfclay_UF2hdp0.jpg}
% % \end{center}
% % \end{figure}
% % \end{frame}
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Single Pile in Sand with Clay Layer: M, Q, p}
% \begin{figure}[!htbp]
% \begin{center}
% \includegraphics[width=7.5cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/MQP_sand_wsfclay_UFmid2hdp0.jpg}
% \end{center}
% \end{figure}
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% %  \frametitle{Single Pile in Clay with Sand Layer: M, Q, p}
% % \begin{figure}[!htbp]
% % \begin{center}
% % \includegraphics[width=7.5cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/MQP_sfclay_sand_UF2hdp0.jpg}
% % \end{center}
% % \end{figure}
% % \end{frame}
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % 
% % 
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Single Pile in Sand: $p-y$ Response}
% \begin{figure}[!htbp]
% \begin{center}
% \includegraphics[width=6.5cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/p_y_dsand_UFmid2hdp0.jpg}
% \includegraphics[width=4.0cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/MQP_dsand_UFmid2hdp0.jpg}
% \hspace*{-1cm}
% \end{center}
% \end{figure}
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% %  \frametitle{Single Pile in Clay: $p-y$ Response}
% % \begin{figure}[!htbp]
% % \begin{center}
% % \includegraphics[width=7.5cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/p_y_sfclay_UF2hdp0.jpg}
% % \includegraphics[width=3.5cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/MQP_sfclay_UF2hdp0.jpg}
% % \hspace*{-1cm}
% % \end{center}
% % \end{figure}
% % \end{frame}
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Single Pile in Sand with Clay Layer: $p-y$ Response}
% \begin{figure}[!htbp]
% \begin{center}
% \includegraphics[width=7.5cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/p_y_sand_sfclay_UFmid2hdp0.jpg}
% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/MQP_sand_wsfclay_UFmid2hdp0.jpg}
% \hspace*{-1cm}
% \end{center}
% \end{figure}
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% %  \frametitle{Single Pile in Clay with Sand Layer: $p-y$ Response}
% % \begin{figure}[!htbp]
% % \begin{center}
% % \includegraphics[width=7.5cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/p_y_sfclay_sand_UF2hdp0.jpg}
% % \includegraphics[width=3.5cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/MQP_sfclay_sand_UF2hdp0.jpg}
% % \hspace*{-1cm}
% % \end{center}
% % \end{figure}
% % \end{frame}
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{$p-y$ Pressure Ratio Reduction for Layered Soils}
% \begin{figure}[!htbp]
% \begin{center}
% \includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/P_ReductionRatio_sand3casesdp0_065.jpg}
% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/MQP_sand_wsfclay_UFmid2hdp0.jpg}
% \hspace*{-1cm}
% \end{center}
% \end{figure}
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
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% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \subsection{Pile Groups}
% % 
% % 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% %  \frametitle{Pile Group Simulations}
% % 
% % \begin{figure}[!hbpt]
% % \vspace*{-1.0cm}
% % \begin{center}
% % \hspace*{-1.0cm}
% % \includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/PileGroups/p4X3_Joey_iso.pdf}
% % \includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/PileGroups/Plastified_3X3pg_skewCOLOR.pdf}
% % \end{center}
% % \end{figure}
% % 
% % \end{frame}
% % 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% %  \frametitle{Bending Moments}
% % 
% % \begin{figure}[!hbpt]
% % %\vspace*{-0.3cm}
% % \begin{center}
% % \includegraphics[width=7.5cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/PileGroups/4x3PileGroupBendingMoments.jpg}
% % \end{center}
% % \end{figure}
% % %\vspace*{-1.0cm}
% % 
% % \end{frame}
% % 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% %  \frametitle{Out of Plane Effects}
% % 
% % \begin{figure}[!hbpt]
% % \vspace*{-0.3cm}
% % \begin{center}
% % \includegraphics[width=4.5cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/PileGroups/Mx_4x3_4piles_com_dense.jpg}
% % \includegraphics[width=2cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/PileGroups/p4X3_deformedPile_Y.jpg}
% % \end{center}
% % \end{figure}
% % \vspace*{-1.0cm}
% % 
% % \end{frame}
% % 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% %  \frametitle{Load Distribution per Pile}
% % 
% % \begin{figure}[!h]
% % \vspace*{-6.3cm}
% % \begin{center}
% % \includegraphics[width=9cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/PileGroups/LoadRatio_per_pile_Dense_pg4x3.pdf}
% % \end{center}
% % \end{figure}
% % \vspace*{-8.3cm}
% % 
% % \end{frame}
% % 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% %  \frametitle{Piles Interaction at -2.0m ($p-y$)}
% % 
% % 
% % 
% % 
% % %\vspace*{-1.3cm}
% % %\vspace*{-1.3cm}
% % \begin{figure}[!hbpt]
% % \begin{center}
% % \includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/PileGroups/pg4x3_p_y_allpiles_20.jpg}
% % \end{center}
% % \end{figure}
% % 
% % %\begin{large}
% % %\begin{itemize}
% % %\item  Note the difference in response curves (cannot scale single pile response
% % %for multiple piles)
% % %\end{itemize}
% % %\end{large}
% % 
% % 
% % \end{frame}
% % 
% % 
% % 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% 
% \subsection{Liquefying Soils}
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection{Single Element and Soil Column Liquefaction}

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Coupled Formulation and Implementation}



%\begin{flushright}
\begin{figure}[!htbp]
%\vspace*{-3.5cm}
%\hspace*{3cm}
\begin{center}
\includegraphics[width=10cm]{/home/jeremic/tex/works/Conferences/2009/GheoMat/VandV_01/u-p-U_VandV_01.jpg}
\end{center}
\end{figure}
%\end{flushright}
%--   
%--   

\hfill (after Gajo 1995)
%
%\item Models available (some now, some later) 
%\vspace*{-2.0cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Coupled Formulation and Implementation}


%\begin{flushright}
\begin{figure}[!htbp]
%\vspace*{-3.5cm}
\begin{center}
\hspace*{-1cm}
\includegraphics[width=12cm]{/home/jeremic/tex/works/Conferences/2009/GheoMat/VandV_01/u-p-U_VandV_02.jpg}
\hspace*{-1cm}
\end{center}
\end{figure}
%\end{flushright}
%--   
%--   

%
%\item Models available (some now, some later) 
%\vspace*{-2.0cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Coupled Formulation and Implementation}
%  
%  
%  
%  %\begin{flushright}
%  \begin{figure}[!htbp]
%  %\vspace*{-3.5cm}
%  %\hspace*{3cm}
%  \begin{center}
%  \includegraphics[width=10cm]{/home/jeremic/tex/works/Conferences/2009/GheoMat/VandV_01/u-p-U_VandV_03.jpg}
%  %\includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2009/GheoMat/VandV_01/u-p-U_VandV_04.jpg}
%  \end{center}
%  \end{figure}
%  %\end{flushright}
%  
%  %
%  %\item Models available (some now, some later) 
%  %\vspace*{-2.0cm}
%  \end{frame}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Material Model Validation (Dafalias-Manzari)}


\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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Loose Sand, Level Ground}
% 
% 
% \begin{figure}[!htbp]
% \vspace*{-1.8cm}
% %\begin{center}
% \includegraphics[width=11cm]{/home/jeremic/tex/works/Papers/2006/upU1D/e85L.pdf}
% %\hspace*{-0.4cm}
% %\end{center}
% \end{figure}
% %--   
% %--   
% 
% %
% %\item Models available (some now, some later) 
% %\vspace*{-2.0cm}
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Loose Sand, Sloping Ground}
% 
% 
% \begin{figure}[!htbp]
% \vspace*{-0.3cm}
% %\begin{center}
% \includegraphics[width=9cm]{/home/jeremic/tex/works/Papers/2006/upU1D/e85s.pdf}
% %\hspace*{-0.4cm}
% %\end{center}
% \end{figure}
% %--   
% %--   
% 
% %
% %\item Models available (some now, some later) 
% %\vspace*{-2.0cm}
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \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}
% % 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \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}
% % 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% %  \frametitle{Case IV: Sloping Ground}
% % 
% % \begin{figure}[!htbp]
% % %\begin{center}
% % \hspace*{-1.0cm}
% % \includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/ZhaoCheng/thesis/file/upU/SinglePile/SP_Slope_FixAngle/EPP_CaseIV.jpg} 
% % %\end{center}
% % \end{figure}
% % 
% % \end{frame}
% % 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% %  \frametitle{Case V: Pile in Sloping Ground, Free Top}
% % 
% % \begin{figure}[!htbp]
% % %\begin{center}
% % \hspace*{-1.0cm}
% % \includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/ZhaoCheng/thesis/file/upU/SinglePile/SP_Slope_FixAngle/EPP_CaseV.jpg} 
% % %\end{center}
% % \end{figure}
% % 
% % \end{frame}
% % 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% %  \frametitle{Case VI: Pile in Sloping Ground, Fixed Top Rotation}
% % 
% % \begin{figure}[!htbp]
% % %\begin{center}
% % \hspace*{-1.0cm}
% % \includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/ZhaoCheng/thesis/file/upU/SinglePile/SP_Slope_FixAngle/EPP_CaseVI.jpg} 
% % %\end{center}
% % \end{figure}
% % 
% % \end{frame}
% % 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% %  \frametitle{Comparing Cases IV, V, and VI}
% % 
% % \begin{figure}[!htbp]
% % %\begin{center}
% % \hspace*{-1.0cm}
% % \vspace*{-0.5cm}
% % 
% % \begin{flushleft}
% % \includegraphics[width=4.8cm]{/home/jeremic/tex/works/Thesis/ZhaoCheng/thesis/file/upU/SinglePile/SP_Slope_FixAngle/Ru_Case456.jpg} 
% % \end{flushleft}
% % %
% % \vspace*{-7cm}
% % \begin{flushright}
% % \includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/ZhaoCheng/thesis/file/upU/SinglePile/SP_Slope_FixAngle/HorizontalDisp_Case456.jpg}
% % \\ 
% % \includegraphics[width=2.5cm]{/home/jeremic/tex/works/Thesis/ZhaoCheng/thesis/file/upU/SinglePile/SP_Slope_FixAngle/maxMoment_Case56.jpg} 
% % \end{flushright}
% % %\end{center}
% % \end{figure}
% % 
% % \end{frame}
% % 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% 
% \subsection{ESS Simulations}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %\subsection{High Fidelity, 3D Models}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% \begin{frame}
%  \frametitle{Detailed 3D, FEM model}
% 
%    \begin{itemize}
% 
%   \item Construction process
% 
%   \item Two types of soil: stiff soil (UT, UCD), soft soil (Bay Mud)
% 
%   \item Deconvolution of given surface ground motions
% 
%   \item Use of the DRM  (Bielak et al.) for seismic input
% 
% 
%   \item Soil:
%     \begin{itemize}
%        \item Sand (single monotonic triax test from UT...)
%        \item Clay (made up, bay mud, total stress)
%     \end{itemize}
%   \item Piles $\rightarrow$ beam-column elements in soil holes
% 
%   \item Structural model: collaboration UCD, UCB and UW
% 
%   \item No artificial damping (only mat. dissipation, radiation)
% 
% 
% 
% 
%   \end{itemize}
% 
% 
% \end{frame}
% %- 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% \begin{frame}
%  \frametitle{Element Size Issue}
% 
% Filtering  of  frequencies depending on element size (want at least 10 nodes per
% full wave form)
% 
% \vspace*{-0.3cm}
% \begin{table}[!htbp]
% %\caption{ }
% \begin{center}
% \begin{tabular}{|c|c|c|c|r|} 
% \hline
% model  size (el) &  el.  size  &  $f_{cutoff}$  & min. $G/Gmax$ & $\gamma$  \\
% \hline
% %
% %
% % 100cm element model, f_cuttof=10HZ, G/Gmax=1.0, 12K elements, Gmax model
% 12K         &  1.0~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         &  0.9~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        &  0.3~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{frame}
% %- 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}
%  \frametitle{FEM Mesh (one of)}
% 
% %
% \begin{figure}[!htbp] 
% \begin{center}
% \includegraphics[width=8cm]{/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}
% %
% \end{frame}
% %- 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % 
% % \begin{frame}
% %   \frametitle{Northridge and Kocaeli Input Motions}
% % 
% % 
% % \begin{figure}[!htbp] 
% % \begin{center}
% % \hspace*{-1cm}
% % \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/InputMotion_Northridge.pdf}
% % \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/LongMotion/InputMotion_Kocaeli.pdf}
% % \hspace*{-1cm}
% % \\
% % \hspace*{-1cm}
% % \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/InputMotion_Northridge_Spectrum.pdf}
% % \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/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}
% % %
% % 
% % \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}
%   \frametitle{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/version_OKT/Images/DispSoilBlock1.pdf}
% \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispBent1.pdf}
% \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispSoilBlock2.pdf}
% \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispBent2.pdf}
% \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispSoilBlock3.pdf}
% \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispBent3.pdf}
% \hspace*{-1cm}
% \\
% \hspace*{-1cm}
% \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelSoilBlock1.pdf}
% \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelBent1.pdf}
% \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelSoilBlock2.pdf}
% \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelBent2.pdf}
% \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelSoilBlock3.pdf}
% \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelBent3.pdf}
% \hspace*{-1cm}
% \\
% \hspace*{-1cm}
% \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispSoilBlock1_Spectrum.pdf}
% \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispBent1_Spectrum.pdf}
% \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispSoilBlock2_Spectrum.pdf}
% \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispBent2_Spectrum.pdf}
% \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispSoilBlock3_Spectrum.pdf}
% \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/DispBent3_Spectrum.pdf}
% \hspace*{-1cm}
% \\
% \hspace*{-1cm}
% \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelSoilBlock1_Spectrum.pdf}
% \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelBent1_Spectrum.pdf}
% \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelSoilBlock2_Spectrum.pdf}
% \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelBent2_Spectrum.pdf}
% \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelSoilBlock3_Spectrum.pdf}
% \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/AccelBent3_Spectrum.pdf}
% \hspace*{-1cm}
% \\
% \hspace*{-1cm}
% \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/MomentBent1Pile1.pdf}
% \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/MomentBent1Pile2.pdf}
% \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/MomentBent2Pile1.pdf}
% \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/MomentBent2Pile2.pdf}
% \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/MomentBent3Pile1.pdf}
% \includegraphics[width=1.8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/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}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% 
% %\subsection{Behavior for Short and Long Period Motions}
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% 
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% \begin{frame}
%   \frametitle{Northridge Input Motions}
% 
% 
% \vspace*{-0.7cm}
% \begin{figure}[!htbp] 
% \begin{center}
% \hspace*{-1cm}
% \includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/Images/InputMotion_Northridge.pdf}
% \hspace*{-1cm}
% \\
% \hspace*{-1cm}
% \includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/version_OKT/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}
% %
% 
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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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{Short Period E.: Left Bent, Structure and Soil, M.}
% %   
% % 
% % 
% % 
% % \vspace*{-1cm}
% % \begin{figure}[!htbp] 
% % \begin{center}
% % \includegraphics[width=11cm]{/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}
% % 
% % 
% % \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}
% \end{figure}
% \hspace*{-0.5cm}
% \vspace*{-2.0cm}
% 
% 
% \end{frame}
% %-- 
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\section{Summary}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
  \frametitle{Summary}

  \begin{itemize}


%\vspace*{0.3cm}
    \item    Importance    of proper  verification  and validation for numerical
    predictions used in design of     infrastructure objects 
    
\vspace*{0.3cm}
    \item Public (yours and mine) safety issue!


\vspace*{0.3cm}
    \item Would  you trust (design using) numerical simulations if 
    SimTool did not follow (extensive) Verification and 
    Validation procedures?



  \end{itemize}



\end{frame}
%--

\end{document}


