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\title[On Computational Simulations and Predictions]
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{On Computational Simulations and Predictions}

%\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}}
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%  \texttt{http://geomechanics.ucdavis.edu} \\
  Department of Civil and Environmental Engineering\\
  University of California, Davis}
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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
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% \begin{itemize}
%   
%   \item UCD Computational Geomechanics libraries: 
%     \begin{itemize}
%      \item nDarray (tensor, matrix and vector manipulations)
%      \item FEMtools (dry and saturated  elements)
%      \item Template3DEP (elastic--plastic computations)
%      \item Plastic--Domain--Decomposition (PDD, for parallel runs)
%     \end{itemize}
% 
%   \item Pre--processors (mesh generators) (ABAQUS, Matlab (UCD), ...)
% 
%   \item Post--processors (visualizers) (VEES (UCSC--UCD), Joey3D (UCD), Matlab, ...)
% 
%   \item Solvers (PETSc, UMFpack, ColSol (UCD)...)
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%   
%   \item Linux and Windows PCs 
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%   \item  Any other UNIX (Apple) based computer
% 
%   \item  BeoWulf class parallel computers (clusters)
% 
%   \item Simulations possible on desktops and on large national parallel supercomputers! 
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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}




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\begin{frame}
\frametitle{Motivation}



\begin{itemize}


%\vspace*{1.5cm}
\item How do we  use experiments   to develop and improve models?

\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 predictions?
                                                                      

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




\end{itemize}




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\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}
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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}



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\frametitle{Maturity of Computational Simulations}



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

\begin{itemize}


%   \vspace*{0.5truecm}
   \item {\bf Stage 1:} Developing enabling technologies (scientific papers published)
   
%   \vspace*{0.5truecm}
   \item {\bf Stage   2:}  Demonstration of and Confidence in technologies and tools
   (capabilities and limitations of technology understood)
   
%   \vspace*{0.5truecm}
   \item {\bf Stage 3:} Compilation of technologies and tools 
   (capabilities and limitations of technology understood)
   
%   \vspace*{0.5truecm}
   \item {\bf Stage  4:}  Spreading  of  the  effective  use  (changes the engineering
   process, value exceeds expectations)
   
%   \vspace*{0.5truecm}
   \item {\bf Stage  5:}  Mature capabilities (fully dependable, cost effective design
   applications)
   


\end{itemize}



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\frametitle{Role of Verification and Validation}



%   \vspace*{1.5truecm}

\begin{figure}[!h]
\begin{center}
{\includegraphics[width=6.5cm]{/home/jeremic/tex/works/Presentation/2003/Verif_and_Valid/RoleVV.pdf}}
\end{center}
\end{figure}



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% 
% \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}
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% \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}
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% 
% 
% \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})
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% 
% \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}                                                                     
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%-- 


\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}
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\begin{frame}
  \frametitle{Verification: Model is solved correctly (Mathematics)}

   {\bf  Verification}:  The  process  of  determining  that    a  model
   implementation  accurately  represents the developer's conceptual description
   and specification. 
%   Mathematics issue. {\it Verification provides evidence that the
%   model is solved correctly.}

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

     \item Quantification of the \\ numerical errors in \\ computed solution
   \end{itemize}


\begin{figure}[!h]
\vspace*{-4cm}
\hspace*{4.5cm}
%\begin{flushright}
{\includegraphics[width=6.5cm]{/home/jeremic/tex/works/Conferences/2005/OpenSeesWorkshopAugust/DeveloperSymposium/VerifValidFund02.pdf}}
%\end{flushright}
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  \frametitle{Validation: Correct model is solved (Physics)}


  {\bf  Validation}:  The process of determining the degree to which a
   model  is  accurate  representation of the real world from the perspective of
   the  intended  uses  of  the  model.  
%   Physics issue. {\it Validation provides
%   evidence that the correct model is solved.}

   \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}

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



\begin{itemize}

%\vspace*{1cm}
 \item  Aleatory uncertainty $\rightarrow$ inherent variation associated with the
 physical  system  of  the environment (variation in external excitation, material
 properties...).  Also  know  known  as 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...).  Also known as reducible uncertainty, model form uncertainty and
 subjective uncertainty
 

\end{itemize}
% 
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\frametitle{Types of Physical Experiments}


\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}


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% \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
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% 
% \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}
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%        \item Neither side is allowed to use fudge factors, parameters
%      \end{itemize}
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% 
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% \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}
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% \end{itemize}
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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

   \vspace*{0.0truecm}
   \item A validation Experiment should be designed to capture the relevant physics

   \vspace*{0.0truecm}
   \item  A  validation  experiment  should  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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\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*{0.0truecm}
   \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}



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



Quantification of confidence in a prediction: 

\begin{itemize}

   \vspace*{0.5truecm}
   \item  How do I quantify verification and its inference value in a prediction?

   \vspace*{0.5truecm}
   \item How do I quantify validation and its inference value in a predictions?

   \vspace*{0.5truecm}
   \item  How  far are individual experiments in my validation database from my
   physical system of interest?

%   \item 

\end{itemize}



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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 engineering systems, certainly not for 
       bridges, buildings, port facilities, dams...
 \item Even if the engineering system is small, environmental influences 
       (generalized loads, conditions, wear and tare)  are hard to predict
 \item  Human  factors (Mars rover example: memory overflow, operator
 {\bf  forgot} to flush the memory...)
\end{itemize}




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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 Experimental facilities provide for validation domain 
 that are  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}



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\frametitle{Prediction under Uncertainty}


\begin{itemize}

   \vspace*{0.5truecm}
   \item Ever present uncertainty needs to be estimated for predictions

   \vspace*{0.5truecm}
   \item Identify all relevant sources of uncertainty
   
   \vspace*{0.5truecm}
   \item Create mathematical representation of individual sources
   
   \vspace*{0.5truecm}
   \item Propagate representation of sources through modeling and simulation process 
    
   


\end{itemize}



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%  \section{System Components}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Simulation Framework}
%  
%  
%  \begin{itemize}
%    \item Parts of OpenSees framework used
%      \begin{itemize}
%        \item  FEM  Classes  (Node, Element, Constraint, Load and Domain) 
%        \item Analysis (sequential) class drives the global level analysis,
%        \item Matric and Vector class for some tasks,
%      \end{itemize}
%  %
%     \item  PDD drives parallel finite element computations
%  
%     \item  Template3Dep  and  NewTemplate3Dep  (const. comp., mat. models)
%  
%     \item nDarray for tensor, matrix and vector manipulations,
%  
%     \item Elements  (solids (u, u-p, u-p-U), beam-column (u, f)
%  
%     \item Graph partitioning using parMETIS
%  
%     \item System solvers (uMfPACK, PETSc
%  
%     \item Preprocessing (Abaqus, matlab, cubit), postprocessing (VEES, matlab)
%  
%  
%  \end{itemize}
%  %\vspace*{-2.0cm}
%  \end{frame}
%  
%  
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \subsection*{Material Models}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Elastic Material Models}
%  
%  \begin{itemize}
%    \item Small deformation elasticity 
%      \begin{itemize}
%       \item linear isotropic
%       \item nonlinear isotropic
%       \item cross anisotropic
%      \end{itemize}
%  
%  
%  \vspace*{1cm}
%    \item  Large  deformation  hyperelasticity 
%      \begin{itemize} 
%        \item Neo--Hookean
%        \item Ogden
%        \item Logarithmic
%        \item  Mooney--Rivlin
%        \item Simo--Pister
%      \end{itemize} 
%  
%  \end{itemize}
%  %\vspace*{-2.0cm}
%  \end{frame}
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % \subsection*{Elastic--Plastic Continuum Models}
%  
%  \begin{frame}
%   \frametitle{Elastic--Plastic Continuum Models: Small Deformations}
%  
%      \begin{itemize} 
%        \item Yield surfaces:   
%          \begin{itemize}
%            \item von Mises
%            \item Drucker--Prager
%            \item Cam--Clay
%            \item Rounded Mohr--Coulomb
%            \item Parabolic Leon
%          \end{itemize}
%          
%         \item  Plastic  flow  directions (plastic potential functions): 
%          \begin{itemize}
%            \item von Mises
%            \item Drucker--Prager
%            \item Cam--Clay
%            \item Rounded Mohr--Coulomb
%            \item Parabolic Leon
%            \item Dafalias Manzari
%          \end{itemize}
%  
%  %      \item  Evolution  Laws (hardening and/or softening laws):  
%  %        \begin{itemize}
%  %          \item linear  scalar,  
%  %          \item nonlinear  scalar  (Cam--Clay type), 
%  %          \item linear tensorial (kinematic hardening/softening: translational  
%  %          and/or   rotational)
%  %          \item nonlinear tensorial (kinematic hardening/softening: translational  
%  %          and/or   rotational)
%  %            \begin{itemize}
%  %              \item Armstrong Frederick hardening 
%  %              \item bounding surface hardening/softening
%  %            \end{itemize}
%  %        \end{itemize}
%      \end{itemize}
%  
%  %\vspace*{-2.0cm}
%  \end{frame}
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %\subsection{Elastic--Plastic Continuum Models}
%  
%  \begin{frame}
%   \frametitle{Elastic--Plastic Continuum Models: Small Deformations (continued)}
%  
%      \begin{itemize} 
%  %      \item Yield surfaces:   
%  %        \begin{itemize}
%  %          \item von Mises
%  %          \item Drucker--Prager
%  %          \item Cam--Clay
%  %          \item Rounded Mohr--Coulomb
%  %          \item Parabolic Leon
%  %        \end{itemize}
%  %        
%  %       \item  Plastic  flow  directions (plastic potential functions): 
%  %        \begin{itemize}
%  %          \item von Mises
%  %          \item Drucker--Prager
%  %          \item Cam--Clay
%  %          \item Rounded Mohr--Coulomb
%  %          \item Parabolic Leon
%  %          \item Dafalias Manzari
%  %        \end{itemize}
%  %
%        \item  Evolution  Laws (hardening and/or softening laws):  
%          \begin{itemize}
%            \item linear  scalar,  
%            \item nonlinear  scalar  (Cam--Clay type), 
%            \item linear tensorial (kinematic hardening/softening: translational  
%            and/or   rotational)
%            \item nonlinear tensorial (kinematic hardening/softening: translational  
%            and/or   rotational)
%              \begin{itemize}
%                \item Armstrong--Frederick hardening 
%                \item bounding surface hardening/softening
%              \end{itemize}
%          \end{itemize}
%      \end{itemize}
%  
%  %\vspace*{-2.0cm}
%  \end{frame}
%  
%  
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%  %\subsection{Small Deformation Elastic--Plastic Continuum}
%  
%  \begin{frame}
%   \frametitle{Hyperelastic--Plastic Continuum Models: Large Deformations}
%  
%      \begin{itemize} 
%        \item Yield surfaces
%          \begin{itemize}
%            \item von Mises, 
%            \item Drucker--Prager...
%          \end{itemize}
%        \item  Plastic  flow  directions (plastic potential functions):  
%          \begin{itemize}
%            \item Drucker--Prager, 
%            \item von Mises, 
%          \end{itemize}
%        \item  Evolution  Laws:  
%          \begin{itemize}
%            \item linear and nonlinear scalar,  
%            \item nonlinear  scalar 
%            \item linear and nonlinear (AF) tensorial (kinematic hardening/softening: translational  
%            and/or   rotational)
%          \end{itemize}
%      \end{itemize}
%  %\vspace*{-2.0cm}
%  \end{frame}
%  
%  
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%  \subsection*{Elements}
%  
%  \begin{frame}
%   \frametitle{Single Phase FE Formulations}
%  
%  \begin{itemize}
%    \item Small deformation solid elements, bricks (8, 20, 21, 27, 8-20 variable node bricks)
%    \item Large deformation (total Lagrangian) solid elements, bricks (20 node brick)
%  \end{itemize}
%  %\vspace*{-2.0cm}
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%  % \subsection*{Multi Phase FE, Coupled}
%  
%  \begin{frame}
%   \frametitle{Multi Phase Formulations}
%  
%  \begin{itemize}
%    \item Fully coupled, u--p--U elements (3D) for small deformations
%    \item Fully coupled, u--p  (3D) elements for small deformations
%    \item Fully coupled u--p (3D) elements for large deformations
%  \end{itemize}
%  
%  Degrees of freedom (DOFs)  are:
%  
%  \begin{itemize}
%    \item   $u  \rightarrow$  solid displacements, 
%    \item $p \rightarrow$ pore fluid pressures, 
%    \item $U \rightarrow$ pore fluid displacements
%  \end{itemize}
%  
%  %\vspace*{-2.0cm}
%  \end{frame}
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%  \subsection*{Computational  Procedures}
%  
%  \begin{frame}
%   \frametitle{Computational Procedures}
%  
%   \begin{itemize}
%     \item Hyperspherical arc--length solution control
%     \item Domain reduction method (Bielak et al.)
%     \item Plastic Domain Decomposition (PDD) parallel simulations 
%   \end{itemize}
%  \end{frame}
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%  
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%  % \subsection*{HPC Simulations: PDD}
%  
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % \begin{frame}
%  %  \frametitle{PDD Method: Design Goals}
%  % 
%  %    \begin{itemize}
%  % 
%  %   \item Graph partitioning $\rightarrow$
%  %   balance   multiple   phases   simultaneously,   while  also  minimizing  the
%  %   inter-processor communications costs
%  % 
%  % 
%  %   \item  It is a multi-objective optimization
%  %   problem (minimize  both  the  inter-processor communications, the data
%  %   redistribution  costs  and  create balanced  partitions)
%  % 
%  % 
%  % 
%  % 
%  % %\vspace*{0.5cm}
%  %   \item Take into the account (deterministic or probabilistic):
%  % 
%  %     \begin{itemize}
%  %       \item heterogeneous element loads that change in each iteration
%  % 
%  %       \item heterogeneous processor performance (multiple generations nodes)
%  % 
%  %       \item inter-processor communications (LAN or WAN)
%  % 
%  %       \item data redistribution costs    
%  % 
%  % 
%  %     \end{itemize}
%  %   
%  % 
%  %   \end{itemize}
%  % 
%  % 
%  % 
%  % \end{frame}
%  % %- 
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % \begin{frame}
%  %  \frametitle{PDD Method: Implementation}
%  % 
%  %      \begin{itemize}
%  % 
%  %   
%  % %\vspace*{0.4cm}
%  %       \item  Perform  global  optimization for both  internal state determination
%  %       and  system of equatons solution phases
%  % 
%  % 
%  % \vspace*{0.4cm}
%  %       \item Adaptive partitioning done using ParMETIS
%  %   
%  % \vspace*{0.4cm}
%  %       \item Iterative system of equations solver PETSC
%  %   
%  % \vspace*{0.4cm}
%  %       \item OpenSees: standard interface and framework
%  %   
%  % 
%  % %  \item Improves methods from the standard interface (Buffered sendSelf and RecvSelf), 
%  % 
%  % \vspace*{0.4cm}
%  %   \item Works on SMPs, local DMPs, grids of computers
%  % 
%  %      
%  %  \item
%  % 
%  % \end{itemize}
%  % 
%  % 
%  % 
%  % \end{frame}
%  % %-           
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % % \subsection*{PDD: Current Status}
%  % 
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % \begin{frame}
%  %    \frametitle{Features}
%  %    \begin{itemize}
%  %  
%  % %\vspace*{0.4cm}
%  %      \item Initial domain partitioning
%  % %\vspace*{0.4cm}
%  %      \item Adaptive domain repartitioning depending on CPU imbalance, LAN and/or WAN performance
%  %\vspace*{0.4cm}
%  %      \item  Repartitioning  works  with  loads,  constraints...,  all  necessary
%  %      movable objects
%  % %\vspace*{0.4cm}
%  %       \item  Available  for  all  elements  (solid, structural) that provide the
%  %       standard OpenSees interface (sendSelf, RecvSelf, timer or CL weight estimate)
%  % 
%  % %\vspace*{0.4cm}
%  %      \item Scalable to a large number of CPUs
%  % %     \item   Optimized   for  the  constitutive  and  element  level  CPU  loads
%  % %     (iterations),
%  % %%\vspace*{0.4cm}
%  % %    \item Using implicit, iterative solver (PETSC)
%  % 
%  % 
%  % %    \item Global optimization for ISD and system of equations solver CPU load is in works 
%  % %\vspace*{0.4cm}
%  %     \item Performance tuning (local cluster GeoWulf, SDSC, TACC)
%  % 
%  %    \end{itemize}
%  % 
%  % 
%  % 
%  % 
%  % \end{frame}
%  % 
%  % 
%  % 
%  % 
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % \begin{frame}
%  %   \frametitle{Speedup Overview}
%  %   
%  % 
%  % 
%  % 
%  % %
%  % \begin{figure}[!htbp] 
%  % \begin{center}
%  % \includegraphics[width=8truecm]{/home/jeremic/tex/works/Conferences/2006/NEES-annual-mmeting-WashingtonDC/PDD/Speedup01.pdf}
%  % %\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
%  % %bridge.}
%  % \end{center}
%  % \end{figure}
%  % %
%  % 
%  % 
%  % 
%  % 
%  % \end{frame}
%  % %-- 
%  % 
%  % 
%  % %-- 
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%  %\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
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\section{Examples}








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\subsection{Piles in Layered Soils}



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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}


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\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}
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\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}
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\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}
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 



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\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}
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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\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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\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}
% 
% 
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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}



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%\subsection{Single Element and Soil Column Liquefaction}

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\begin{frame}
 \frametitle{Verification}


Number of \\
closed form \\
solutions used \\
(elastic, coupled, \\
static and dynamic)


%\begin{flushright}
\begin{figure}[!htbp]
\vspace*{-3.5cm}
\hspace*{3cm}
%\begin{center}
\includegraphics[width=5.5cm]{/home/jeremic/tex/works/Conferences/2007/GeoTechSeminarUCDavis/Figure-compareMethod-a.pdf}
%\end{center}
\end{figure}
%\end{flushright}
%--   
%--   

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






% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}
%-- 

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



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%   \frametitle{Kocaeli 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/LongMotion/InputMotion_Kocaeli.pdf}
% \hspace*{-1cm}
% \\
% \hspace*{-1cm}
% \includegraphics[width=8.0truecm]{/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}
% %
% \vspace*{-1cm}
% 
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%   \frametitle{Long 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/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}
% 
% 
% \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{Long 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/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}
% 
% 
% 
% \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{Long 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/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}
% 
% 
% \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{Long 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/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*{-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{Soft Soils: Left Bent, Structure and Soil, Moments}
% %   
% % 
% % 
% % 
% % \vspace*{-1cm}
% % \begin{figure}[!htbp] 
% % \begin{center}
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\section{Summary}



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  \frametitle{Summary}
  
  \begin{itemize}


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    \item  Importance  of  verification  and validation for numerical prediction
    (simulations)


\vspace*{0.3cm}
    \item   Detailed treatment in new courses: 
      \begin{itemize}
        \item Spring '08 ECI280A, Nonlinear Finite Elements
        \item Spring '09 ECI280B, Nonlinear Dynamic Finite Elements
      \end{itemize}

\vspace*{0.3cm}
    \item  Would  you  (and  others)  trust  simulations if you followed V and V
    procedures?


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%    \item It might take a bit of learning
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%     \item Sources and examples forthcoming as we publish 
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%     \item Executables will be available soon on the net.


  \end{itemize}



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\end{document}


