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%  \usetheme{Singapore} % ima sadrzaj i tackice gore
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%\title{NRC Staff Capacity Building: \\
%       Micromechanical Origins of Elasto-Plasticity }
\title{On Earthquake Soil Structure Interaction \\
       Modeling and Simulation}


%\subtitle
%{Include Only If Paper Has a Subtitle}

%\author[Author, Another] % (optional, use only with lots of authors)
%{F.~Author\inst{1} \and S.~Another\inst{2}}
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\pgfdeclareimage[height=0.7cm]{lbnl-logo}{/home/jeremic/BG/amblemi/lbnl-logo}

\author[Jeremi{\'c} et al.] % (optional, use only with lots of authors)
{N.~Tafazzoli, P.~Tasiopoulou, J.A.~Abell~Mena, B.~Kamrani, 
C.-G.~Jeong, K.~Watanabe, B.~Aldridge, J.~Anderson, F.~Pisan{\`o}, M.~Martinelli, 
K.~Sett, \\ ~ \\
B.~Jeremi{\'c}}
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{ Professor, University of California, Davis\\
%  and\\ 
  Faculty Scientist, Lawrence Berkeley National Laboratory, Berkeley }
% - Use the \inst command only if there are several affiliations.
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{\small NTUA Seminar, June 12th, 2013}

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%   just say so once. Everybody will be happy with that.














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\section{Motivation}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{}
% 
% \begin{itemize}
% %\vspace*{0.3cm}
%   \item   
% 
%   \item   
% \end{itemize}
% \end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Problem -- Solution}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{The Problem}

\begin{itemize}
  

  \item Seismic response of Soil/Rock -- Structure systems


\vspace*{0.1cm}
  \item  3D, inclined seismic motions, body and surface waves

\vspace*{0.1cm}
  \item      Inelastic  (elastic,  damage, plastic) behavior of materials: soil,
  rock, concrete, steel, rubber, etc.)

\vspace*{0.1cm}
  \item  Full coupling of pore fluids (in soil, rock, concrete, etc.) 
  with porous material skeleton

\vspace*{0.1cm}
  \item  Buoyant effects (foundations below water table)

\vspace*{0.1cm}
  \item    Uncertainty  in  seismic  sources, path, soil/rock response and structural
  response
  

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Solution}

\begin{itemize}
  


%\vspace*{0.3cm}
  \item    {\bf Physics based  modeling  and  simulation} of seismic behavior of
  Soil/Rock -- Structure systems 

\vspace*{0.1cm}
  \item             Development  and  use  of  {\bf high  fidelity} time domain,
  nonlinear numerical  models,
  in {\bf deterministic} and  {\bf probabilistic} spaces


\vspace*{0.1cm}
  \item   Accurate following of  the  {\bf flow  of  seismic 
  energy}    (input  and  dissipation)   within Soil/Rock -- Structure  system

\vspace*{0.1cm}
  \item  {\bf  Directing},      in   space   and   time,  with {\bf high (known)
  confidence}, seismic energy flow in the soil-foundation-structure system

%\vspace*{0.1cm}
%  \item  {\bf Education} for researchers, professional practice.
  

\end{itemize}
\end{frame}










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\section{Challenges}



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\subsection{Uncertainty in Modeling Ground Motions}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Modeling Uncertainty}

\begin{itemize}

%\vspace*{0.3cm}
  \item  Simplified (or inadequate/wrong) modeling:  important  features    are 
  missed (seismic ground motions, etc.)

\vspace*{0.2cm}
  \item  Introduction of uncertainty and  (unknown) lack of accuracy in results due
  to  use  of  un-verified  simulation tools (software quality, etc.)

\vspace*{0.2cm}
  \item  Introduction of uncertainty and  (unknown) lack of accuracy in results due
  to    use  of  un-validated  models  (due to lack of quality validation experiments)
%    (still    missing  data, experiments under
%  uncertainty, for more see below)


\end{itemize}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Complexity of and Uncertainty in Ground Motions}

\begin{itemize}
%\vspace*{0.3cm}
  \item 6D (3 translations, 3 rotations)

\vspace*{0.3cm}
  \item Vertical motions usually neglected
 
\vspace*{0.3cm}
  \item Rotational components usually not measured and neglected 
 
\vspace*{0.3cm}
  \item Lack of models for such 6D motions (from measured data))
  
\vspace*{0.3cm}
  \item Sources of uncertainties in ground motions (Source, Path (rock), soil (rock))  
\end{itemize}



\end{frame}









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\subsection{Uncertainty in  Modeling Material}


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\begin{frame} 

\frametitle{Material Behavior Inherently Uncertain}


%\begin{itemize}

%\vspace*{0.5cm}
%\item  
%Material  behavior  is  inherently uncertain  (concrete,  metals,  soil,  rock, 
%bone, foam, powder etc.)

        \begin{itemize}

\vspace*{0.5cm}
        \item (a) Spatial \\ 
              variability

\vspace*{0.5cm}
        \item Point-wise \\ 
              uncertainty:   \\
              (b) testing \\
              error, \\
              (c) transformation \\
              error

        \end{itemize}

% \vspace*{0.5cm}
% \item  Failure mechanisms related to spatial variability (strain localization and
%        bifurcation of response)
% 
% \vspace*{0.5cm}
% \item Inverse problems
% 
%       \begin{itemize}
%       
%       \item New material design, ({\it point-wise})
% 
%       \item Solid and/or structure design (or retrofits),  ({\it spatial})
% 
%       \end{itemize}
                                  
%\end{itemize}

\vspace*{-5cm}
\begin{figure}[!hbpt]
%\nonumber
%\begin{center}
\begin{flushright}
%\includegraphics[height=5.0cm]{/home/jeremic/tex/works/Conferences/2006/KragujevacSEECCM06/Presentation/MGMuzorak01.jpg}
\includegraphics[height=5.5cm]{/home/jeremic/tex/works/Conferences/2006/KallolsPresentationGaTech/FrictionAngleProfile.jpg}
\\
\mbox{(Mayne et al. (2000) }
\end{flushright}
%\end{center}
%\end{center}
\end{figure}

\end{frame}

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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame} 
% \frametitle{Soil Uncertainties and Quantification}
% 
% \begin{itemize}
% %
% %\vspace*{0.5cm}
% \item Natural variability of soil deposit  (Fenton 1999) 
% 
%   \begin{itemize}
% 
%     \item Function of soil formation process 
%  
%   \end{itemize}
% 
% 
% %
% \vspace*{0.2cm}
% \item Testing error (Stokoe et al. 2004)
% 
%   \begin{itemize}
% 
%     \item Imperfection of instruments 
%  
%     \item Error in methods to register quantities
% 
%   \end{itemize}
% 
% %
% \vspace*{0.2cm}
% \item Transformation error (Phoon and Kulhawy 1999)
% 
%   \begin{itemize}
% 
%     \item Correlation by empirical data fitting (e.g. CPT data $\rightarrow$ friction angle etc.)
% 
%   \end{itemize}
% 
% \end{itemize}
% 
% 
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}



\frametitle{SPT Based Determination of Shear Strength}




\begin{figure}[!hbpt]
\begin{center}
% 
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_RawData_and_MeanTrend-Mod.pdf}
\hfill
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_Histogram_PearsonIV-FineTuned-Mod.pdf}
%
\end{center}
\end{figure}                                                          

\vspace*{-0.3cm}
Transformation of SPT $N$-value $\rightarrow$ undrained shear
strength, $s_u$ (cf. Phoon and Kulhawy (1999B)

Histogram  of  the  residual  
(w.r.t  the  deterministic transformation
equation) undrained strength, 
along with fitted probability density function 
(Pearson IV)
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}



\frametitle{SPT Based Determination of Young's Modulus}


\begin{figure}[!hbpt]
\begin{center}
%
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01-Ed.pdf} 
\hfill
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_Histogram_Normal_01-Ed.pdf}
%
\end{center}
\end{figure}                                                          

\vspace*{-0.3cm}
 Transformation of SPT $N$-value $\rightarrow$ 1-D Young's modulus, $E$ (cf. Phoon and Kulhawy (1999B))

 Histogram of the residual (w.r.t the deterministic transformation equation) Young's modulus, along with fitted probability density function

\end{frame}































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\subsection{Errors in Scientific Software}


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\begin{frame}
 \frametitle{Errors in Scientific Software: The T Experiments}


\begin{itemize}

%   \vspace*{0.2truecm}
   \item Les Hatton, Kingston University (formerly of Oakwood Comp. Assoc.)

   \vspace*{0.1truecm}
   \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*{0.1truecm}
   \item "Better software engineering practices would help solve this problem,"

   \vspace*{0.1truecm}
   \item "Realizing that the problem exists is an important first step."
   
   
   \vspace*{0.1truecm}
   \item  Large  experiment over 4 years measuring faults (T1) and failures (T2)
   of scientific and engineering codes
   
   
   
    

\end{itemize}





\end{frame}


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






\begin{itemize}

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

\vspace*{0.2truecm}
\item Echo sounding of underground and reconstructing "images" of 
subsurface geological structure

\vspace*{0.2truecm}
\item Nine mature packages, using {\bf same algorithms}, on a {\bf same data set}!

\vspace*{0.2truecm}
\item 14 primary calibration points for results check

\vspace*{0.2truecm}
\item Results "fascinating and disturbing"

    

\end{itemize}

\end{frame}


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

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


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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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\section{ESSI Simulator System}


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\subsection{ESSI Simulator System}


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

\begin{frame}
\frametitle{ESSI Simulator System}

\begin{itemize}

\item {\bf The ESSI-Program} is a 3D, nonlinear, time domain, 
parallel finite element program specifically developed for
Hi-Fi modeling  and  simulation  of  Earthquake  Soil/Rock  Structure
Interaction problems on ESSI-Computer. \
%The NRC ESSI Program is based on
%a  number of public domain numerical libraries developed at UCD as well as those
%available  on  the  web,  that  are  compiled  and  linked  together to form the
%executable  program (NRC-ESSI-Program). Significant effort is devoted to development
%of  verification  and  validation  procedures,  as  well  as  on  development of
%extensive  documentation.  NRC-ESSI-Program  is  in  public  domain  and is licensed
%through the Lesser GPL.

%\vspace*{0.3cm}
\vspace*{0.1cm}
\item {\bf The ESSI-Computer} is a distributed memory 
parallel computer, a cluster of clusters with multiple performance  
processors and multiple performance networks.  
%Compute  nodes are Shared Memory Parallel
%(SMP)  computers,  that  are  connected,  using  high  speed  network(s), into a
%Distributed Memory Parallel (DMP) computer.

%\vspace*{0.3cm}
\vspace*{0.1cm}
\item    {\bf        The    ESSI-Notes} represent a hypertext 
documentation system
%(Theory and Formulation, Software and Hardware, Verification and Validation, and
%Case  Studies  and  Practical  Examples)   
detailing modeling and simulation of ESSI
problems.
%
%the
%NRC-ESSI-Program  code  API (application Programming Interface) and DSLs (Domain
%Specific Language).
%%NRC-ESSI-Notes,    developed  by Boris Jeremic and collaborators, are in public
%domain
%%and  are  licensed  under a Creative Commons Attribution-ShareAlike 3.0 Unported
%%License.
%
%\vspace*{0.3cm}
\end{itemize}

\end{frame}



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

\begin{frame}
\frametitle{ESSI Simulator Program}

\begin{itemize}

%\vspace*{0.2cm}
\item  Based  on  a  Collection  of Useful Libraries  (modular, portable)

\vspace*{0.1cm}
\item Library centric software design

\vspace*{0.1cm}
\item Various public domain licenses (GPL, LGPL, BSD, CC)

%\vspace*{0.3cm}
\vspace*{0.1cm}
\item Verification (extensive) and Validation (not much)


\vspace*{0.1cm}
\item  Program documentation  (part of ESSI Notes)
    
\vspace*{0.1cm}
\item      Target    users:   US-NRC  staff,  CNSC  staff, IAEA, LBNL, INL, DOE,
Professional Practice and Academia collaborators, expert users
    
%\item Sources will be available through
%{\bf 
%\url{http://nrc-essi-simulator.info}}


\end{itemize}

\end{frame}




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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Collection of Useful Libraries (Modeling Part)}

\begin{itemize}


\vspace*{0.2cm}
\item  Template3D-EP  libraries   for  elastic  and elastic-plastic
computations (UCD,  CC) 

\vspace*{0.2cm}
\item    FEMTools  finite    element  libraries provide 
finite elements (solids,
beams, shells, contacts/isolators, seismic input) (UCD, CC)


\vspace*{0.2cm}
\item  Loading, staged, self weight, service loads, seismic loads 
(the  Domain  Reduction  Method,  analytic  input
(incoming/outgoing) of 3D, inclined, un-correlated seismic motions)
(UCD, CC)

\vspace*{0.2cm}
\item    Domain Specific Language for input (UCD, CC)

     

\end{itemize}

\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Collection of Useful Libraries (Simulation Part)}

\begin{itemize}


     


\vspace*{0.12cm}
\item Plastic Domain Decomposition (PDD) for parallel computing  (UCD, CC) 


\vspace*{0.12cm}
\item  PETSc (ANL, GPL-like), UMFPACK (UF, GPL), ProfileSPD (LBNL, GPL) solvers


\vspace*{0.12cm}
\item Modified OpenSees Services (MOSS) for managing the finite 
element domain (UCD, CC;  UCB, GPL?) 

\vspace*{0.12cm}
\item nDarray (UCD, CC), LTensor (CIMEC, GPL), 
BLAS (UTK, GPL) for lower level
computational tasks,

\vspace*{0.12cm}
\item Message Passing Interface (MPI, openMPI, new BSD license)

\end{itemize}

\end{frame}








%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[fragile]
 \frametitle{ESSI Simulator Computer}

  A distributed memory parallel (DMP) computer
   designed for high performance,  
   parallel finite element simulations

 \begin{itemize}
%\vspace*{0.1cm}
   \item Multiple performance CPUs \\
         and Networks
%\vspace*{0.1cm}
   \item Most cost-performance \\
         effective 
%\vspace*{0.1cm}
   \item Source compatibility with \\
         any DMP supercomputers
%\vspace*{0.1cm}
   \item Current systems: 208CPUs, \\
         and 40CPUs (8+32) and \\ 
         160CPUs (8x5+2x16+24+64)...

%%\vspace*{0.1cm}
%   \item Near future: 784 CPUs

 \end{itemize}

  
\vspace*{-4.5cm}
\begin{flushright}
%\hspace*{-0.5cm}
\includegraphics[width=5.0cm]{/home/jeremic/public_html/NRC_ESSI_Simulator/NRC_ESSI_Computer/photos/IMG_2607.JPG}
%\includegraphics[width=6.0cm]{/home/jeremic/public_html/NRC_ESSI_Simulator/NRC_ESSI_Computer/photos/IMG_2609.JPG}
%\includegraphics[width=8.0cm]{/home/jeremic/public_html/NRC_ESSI_Simulator/NRC_ESSI_Computer/photos/IMG_2611.JPG}
\end{flushright}



\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %\begin{frame}[fragile]
% % \frametitle{NRC ESSI Simulator Version December 2010}
% %
% %
% %\begin{itemize}
% %\item Operating System: Linux Fedora Core 14.
% %
% %\item Kernel: \verb|2.6.35.10-74.fc14.x86_64| 
% %
% %\item Compute Nodes (two):
% %
% %    \begin{itemize}
% %      \item  CPU:  2  $\times$  Intel  Xeon  E5620 
% %      Westmere 2.4 GHz Quad Core (8 threads) 
% %
% %      \item  RAM:    6 $\times$ 4GB DDR3 1333 MHz ECC/Registered Memory (24GB
% %      Total Memory)
% %
% %      \item  Disk:  8  $\times$  500  GB  Seagate Constellation ES 3.5" SATA/300
% %      (Linux Software RAID10)
% %
% %    \end{itemize}
% %
% %\item Network: single GigaBit
% %\end{itemize}
% %
% %
% %\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[fragile]
 \frametitle{ESSI Computer Version April 2012}


Operating System:  Ubuntu

Kernel: 3.2

{\bf Controller:} 1 node + {\bf Compute:} 8 Nodes
    \begin{itemize}
      \item    CPU:  2 x 12 cores Opteron 6234  = 24 cores
 
      \item  RAM: 32GB (8 x 4GB) 

  
      \item NICs: 
      \begin{itemize}
        \item GigaBit: Intel 82576 (Controller)
        \item InfiniBand: ConnectX-2 QDR IB 40Gb/s (Controller+Compute)
      \end{itemize}

      \item Disk: 8 $\times$  2TB Toshiba MK2002TSKB (Controller)
      \item  Disk:   1TB Toshiba MK1002TSKB (Compute)

    \end{itemize}

Network (dual): 
\begin{itemize}

  \item GigaBit: HP ProCurve Switch 1810-48G 48 Port


  \item  InfiniBand::  Mellanox  MIS5030Q-1SFCA 36-port QDR 


\end{itemize}


\end{frame}





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


\begin{frame}
\frametitle{ESSI Simulator Notes}

\begin{itemize}


\item  A  hypertext  documentation  system    describing  in detail modeling and
simulations of ESSI problems

  \begin{itemize}

    \item  Theoretical  and  Computational  Formulations    (FEM,  EL-PL, Static
    and Dynamic solution, Parallel Computing)
    
    \item    Software  and  Hardware Platform Design (OO Design, Library centric
    design, API, DSL, Software Build Process, Hardware Platform)
    
    \item      Verification  and  Validation  (code  V, Components V, Static and
    Dynamic V, Wave Propagation V)
    
    \item      Application    to   Practical   Earthquake 
    Soil/Rock   Structure   Interaction   Problems   (ESSI  with  3D,  inclined,
    uncorrelated   seismic   waves,   ESSI   with  foundation  slip,  isolators.
    liquefaction)

  \end{itemize}


\end{itemize}

\end{frame}

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

%



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection{Modeling and Simulation}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
% \frametitle{Seismic Energy Dissipation for \underline{Soil}-Foundation-Structure Systems}
 \frametitle{ESSI: High Fidelity Modeling}
% \frametitle{Seismic Energy Dissipation for 
%             \underline{Soil}-Foundation-Structure Systems}


\begin{itemize}

  \item   Seismic energy  influx,  {body  and  surface waves, 3D, inclined} 
%  $E_{flux} = \rho A c \int_0^t \dot{u}_i^2 dt$ (Aki \& Richards)

\vspace*{0.1cm}
     \item Mechanical dissipation outside of SSI domain:
       \begin{itemize}
         \item {Radiation} of reflected waves
         \item {Radiation} of oscillating SSI system
       \end{itemize}
\vspace*{0.1cm}
     \item Mechanical dissipation inside SSI domain:
       \begin{itemize}
         \item {Plasticity} of soil/rock subdomain
         \item {Viscous coupling} of porous solid with pore fluid (air,
         water)
         \item {Plasticity} and viscosity of foundation -- soil/rock contact
         \item Plasticity/damage of the structure
         \item Viscous coupling of structure/foundation with fluids 
%         \item potential and kinetic energy
%         \item[] potential $\leftarrow \! \! \! \! \! \! \rightarrow$ kinetic energy
       \end{itemize}                           



\vspace*{0.1cm}
%   \item Numerical energy dissipation (numerical damping/production and period  errors)
%   \item Numerical energy dissipation (damping/production)
   \item Numerical energy dissipation/production


\end{itemize}

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




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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{ESSI: High Performance, Parallel Computing}

\begin{itemize}

\item The ESSI Program can be used in both sequential and 
parallel modes

\vspace*{0.2cm}
\item For high fidelity models, parallel is really the only option

\vspace*{0.2cm}
\item  High  performance, parallel computing using 
Plastic Domain Decomposition
Method

\vspace*{0.2cm}
\item    Developed  for  multiple/variable capability CPUs and 
networks (DMP and
SMPs)

\end{itemize}

\end{frame}







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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{ESSI: Finite Elements}
\begin{itemize}

\item Linear and nonlinear truss element

\item Linear and nonlinear beam (disp. based), variable BC el.

\item Linear shell Triangle and Quad with drilling DOFs

%\item Linear and nonlinear thick  shell (bricks)

  \item  Single  phase  solid  bricks    (8, 20, 27, 8-20, 8-27 nodes)

  \item  Two phase (fully coupled, porous solid, pore fluid) 
	 solid bricks (8, 20 and 27 node: $u-p-U$, $u-p$)

\item Dry friction slip and gap element 

\item Saturated gap and slip element 

\item  Seismic  isolator  (latex rubber, neoprene rubber, rubber with lead core,
friction pendulum) 

\end{itemize}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{ESSI: Material Models for Solids and Structures}

    \begin{itemize}
      \item Small deformation elastic: linear, nonlinear isotropic, cross anisotropic
      
\vspace*{0.3cm}
      \item    Small  deformation        elastic-Plastic:        von     Mises, 
      Drucker--Prager,   Cam--Clay,   Rounded   Mohr--Coulomb,  Parabolic  Leon,
      SaniSand2004,  SaniSand2008, SaniClay, Pisan{\`o}; Gens normal contact and
      Coulomb shear contact model; 1D concrete and steel models
      
%\vspace*{0.3cm}
%      \item Isotropic and kinematic (translational and rotational) hardening


\vspace*{0.3cm}
      \item   Large deformation elastic and elastic-plastic: Ogden, neo-Hookean,
      Mooney-Rivlin, Logarithmic, Simo-Pister, von Mises, Drucker-Prager

    \end{itemize}

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





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{ESSI: Earthquake Ground Motions}



 Realistic earthquake ground motions 
   \begin{itemize}
%\vspace*{0.1cm}
     \item Body: P and S waves
%\vspace*{0.1cm}
     \item Surface: Rayleigh, Love waves, etc.
%\vspace*{0.1cm}
     \item Lack of correlation (incoherence)
%\vspace*{0.1cm}
     \item Inclined waves
%\vspace*{0.1cm}
     \item 3D waves

     \item Seismic input: Domain Reduction Method (Bielak et al.)

        \begin{itemize}
          \item Dynamically consistent replacement seismic source
          \item The only outgoing waves are from dynamics of the structure
          \item Material can be elastic-plastic
        
          \item All types of seismic waves (body, surface...) are properly modeled 
        \end{itemize}
        
%\vspace*{0.1cm}
%     \item Earthquake energy  dissipation

   \end{itemize}






\end{frame}



% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Body (P, S) and Surface (Rayleigh, Love) Waves}
% 
%  
% \vspace*{-0.3cm}
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=2.5cm, angle=45]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Presentation/P_body_wave.jpeg}
% \includegraphics[width=2.5cm, angle=45]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Presentation/S_body_wave.jpeg}
% \vspace*{-0.7cm}
% \\
% \includegraphics[width=3cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Presentation/Rayleigh_surface_wave.jpeg}
% \includegraphics[width=3cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Presentation/Love_surface_wave.jpeg}
% %\caption{\label{Love_surface_wave}   Visualization  of  propagation  of  a  Love
% %surface seismic wave (illustrations are from MTU web site).}
% \end{center}
% \end{figure}
% 
% \end{frame}
% 
% 
% 
% 
% - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - \begin{frame} 
% - \frametitle{Spatial Variability (Incoherence, Lack of Correlation)}
% - 
% - Incoherence $\rightarrow$ frequency domain
% - 
% - \vspace*{0.2cm}
% - 
% - Lack of Correlation $\rightarrow$ time domain
% - 
% - 
% - \vspace*{0.5cm}
% - 
% - \begin{itemize}
% -   \item Attenuation effects
% -   \item Wave passage effects
% -   \item Extended source effects
% -   \item Scattering effects
% -   \item Variable seismic energy dissipation
% - \end{itemize}
% - 
% - %\begin{figure}[!htb]
% - %\begin{center}
% - \vspace*{-3.5cm}
% - \hspace*{5.5cm}
% - \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2011/NRC_Staff_Capacity_Building_25May2011/Lack_of_Correlation_5_points.pdf}
% - %\caption{\label{LC} Four main sources contributing to the lack of correlation of
% - %seismic waves as measured at two observation points.}
% - %\end{center}
% - %\end{figure}
% - %
% - %A number of models available (Abrahamson...)
% - %
% - \end{frame}
% - 
% - 
% - % out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - % out \begin{frame} 
% out \frametitle{Attenuation Effects}
% out 
% out 
% out Responsible for change in amplitude and phase of seismic motions
% out due to the distance between observation points and losses (damping, energy dissipation) that
% out seismic wave experiences along that distance. This is a significant source of lack of correlation
% out for long structures (bridges), however for NPPs it is not of much significance.
% out 
% out 
% out %\begin{figure}[!htb]
% out \begin{center}
% out %\vspace*{-2cm}
% out %\hspace*{5.5cm}
% out \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2011/NRC_Staff_Capacity_Building_25May2011/Lack_of_Correlation_5_points.pdf}
% out %\caption{\label{LC} Four main sources contributing to the lack of correlation of
% out %seismic waves as measured at two observation points.}
% out \end{center}
% out %\end{figure}
% out 
% out 
% out 
% out \end{frame}
% out 
% out 
% out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out \begin{frame}
% out \frametitle{Wave Passage Effects}
% out 
% out  Contribute  to  lack of correlation due to difference in
% out  recorded  wave  field  at  two  location  points as the (surface) wave travels,
% out  propagates from the first to second point.
% out 
% out \begin{center}
% out %\hspace*{5.5cm}
% out \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2011/NRC_Staff_Capacity_Building_25May2011/Lack_of_Correlation_5_points.pdf}
% out \end{center}
% out 
% out 
% out \end{frame}
% out 
% out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out \begin{frame}
% out \frametitle{Extended Source Effects}
% out 
% out Contribute to lack of correlation by creating a complex wave source
% out field, as the fault ruptures, rupture propagates and generate seismic sources along the fault.
% out Seismic energy is thus emitted from different points (along the rupturing fault) and will have
% out different travel path and timing as it makes it observation points.
% out 
% out 
% out \begin{center}
% out %\hspace*{5.5cm}
% out \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2011/NRC_Staff_Capacity_Building_25May2011/Lack_of_Correlation_5_points.pdf}
% out \end{center}
% out 
% out \end{frame}
% out 
% out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out 
% out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out \begin{frame}
% out \frametitle{Scattering Effects}
% out 
% out  Responsible  to  lack  of  correlation  by creating a
% out  scattered wave field.
% out Scattering  is due to (unknown or not known enough) subsurface geologic features
% out that contribute to (elastic) modification of the wave field.
% out 
% out 
% out \begin{center}
% out %\hspace*{5.5cm}
% out \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2011/NRC_Staff_Capacity_Building_25May2011/Lack_of_Correlation_5_points.pdf}
% out \end{center}
% out 
% out 
% out 
% out \end{frame}
% out 
% out 
% out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out 
% out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out \begin{frame}
% out \frametitle{Variable Seismic Energy Dissipation}
% out 
% out Contribute  to  variability  of seismic motions by bending seismic waves as they
% out pass through inelastic soil/rock.
% out Variable  seismic  energy  dissipation  is  due to (unknown or not known enough)
% out subsurface   geologic  features  that contribute to (inelastic, elastic-plastic)
% out modification of the wave field.
% out 
% out 
% out \begin{center}
% out %\hspace*{5.5cm}
% out \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2011/NRC_Staff_Capacity_Building_25May2011/Lack_of_Correlation_5_points.pdf}
% out \end{center}
% out 
% out 
% out 
% out 
% out \end{frame}
% out 
% out 
% out %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% out \begin{frame}
% out \frametitle{Modeling Lack of Correlation (Incoherence)}
% out 
% out \begin{itemize}
% out 
% out \item A number of models available (Abrahamson...)
% out 
% out \item Most of the models (all) are based on a (very) limited data set from Lotung, Pinyon Flat...
% out 
% out \item Most of the models (all) are based on hard rock data ($V_s > 2600$m/s)
% out 
% out \item  Most  of the models (all) can produce statistically significant number of
% out motions, yet only few are used (destroying the model statistical assumptions)
% out 
% out 
% out \item  Ergodic  assumption  must  be  made  in order to extrapolate those models
% out (data) to other parts of the USA (world)
% out 
% out %\item Extrapolations can be  (are) dangerous
% out 
% out 
% out \end{itemize}
% out 
% out 
% out \end{frame}
% out 
% out 
% out 
% out 
% out 
% out 



% - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - \begin{frame} 
% - \frametitle{Seismic Input}
% - 
% - 
% - %\begin{itemize}
% - 
% - %  \item 
% -   The Domain Reduction Method \\
% -   (Bielak et al.): \\
% -   The effective force  $P^{eff}$ \\
% -   is a dynamically consistent \\
% -   replacement for the dynamic \\
% -   source forces  $P_{e}$
% - 
% - % \end{itemize}
% - 
% -   \begin{eqnarray}
% - P^{eff} = \left\{\begin{array}{c} P^{eff}_i \\ P^{eff}_b \\ P^{eff}_e \end{array}\right\}
% - = \left\{\begin{array}{c} 0 \\ -M^{\Omega+}_{be} \ddot{u}^0_e-K^{\Omega+}_{be}u^0_e
% -    \\ M^{\Omega+}_{eb}\ddot{u}^0_b+K^{\Omega+}_{eb}u^0_b\end{array}\right\}
% - \nonumber
% - \label{DRMeq09}
% - \end{eqnarray}
% - %
% - 
% - \begin{figure}[!h]
% - \begin{flushright}
% - %\vspace*{-0.50cm}
% - %\begin{center}
% - %\hspace*{1cm}
% - \vspace*{-6.90cm}
% - {\includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2010/NRC-LBL-ProjectReviewMeeting_21_22_Sept_2010/DRM05NPP.pdf}}
% - %\vspace*{-5.50cm}
% - %\hspace*{1cm}
% - %\vspace*{-2.50cm}
% - %\end{center}
% - %\vspace*{-0.3cm}
% - \end{flushright}
% - \end{figure}
% - 
% - 
% - 
% - 
% - \end{frame}
% - 
% - 
% - 
% - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame} 
% \frametitle{DRM}
% 
% 
% 
% 
% 
% \begin{itemize}
% %\vspace*{-0.2cm}
%   \item  Seismic forces $P_e$  replaced by $P^{eff}$
% 
% %\vspace*{-0.2cm}
%   \item $P^{eff}$ applied only to a  single \\
%         layer of elements next to  $\Gamma$.
% %\vspace*{-0.2cm}
%   \item The only outgoing waves are \\
%         from dynamics of the NPP
% %\vspace*{-0.2cm}
%   \item Material inside $\Omega$ \\
%         can be elastic-plastic
% 
%   \item All types of seismic waves\\
%         (body, surface...) are \\
%         properly modeled 
% 
% 
% % \item  The only input wave field is the one for the nodes of this layer of elements.
% \end{itemize}
% 
% \begin{figure}[!h]
% \begin{flushright}
% %\vspace*{-0.50cm}
% %\begin{center}
% %\hspace*{1cm}
% \vspace*{-4.50cm}
% {\includegraphics[width=5.8cm]{/home/jeremic/tex/works/Conferences/2010/NRC-LBL-ProjectReviewMeeting_21_22_Sept_2010/DRM05NPP.pdf}}
% %\vspace*{-5.50cm}
% \hspace*{-0.8cm}
% %\vspace*{-2.50cm}
% %\end{center}
% %\vspace*{-0.3cm}
% \end{flushright}
% \end{figure}
% 
% 
% \end{frame}
% 
% 
% 
% 
% 
% 
% 
% 
% 
% 
% 
% 
% 
% 
% 










%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Verification and  Validation Suite}


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


\begin{itemize}

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

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

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

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


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


\begin{figure}[!h]
\begin{center}
\hspace*{-2cm}
{\includegraphics[width=5.0cm]{/home/jeremic/tex/works/Conferences/2012/ASME_V_and_V_symposium/presentetation/RoleVV_NEW_knowledge.pdf}}
{\includegraphics[width=6.5cm]{/home/jeremic/tex/works/Conferences/2011/USNCCM11_Minneapolis/Coupled/Present/VandV_ODEN.jpg}}
\hspace*{-2cm}
\end{center}
\end{figure}

{Oberkampf et al. \hspace*{4cm}  Oden et al.}
%
%\item Models available (some now, some later)
%\vspace*{-2.0cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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*{0.5truecm}
   \item  V  \&  V  procedures  are the tools with which we build confidence and
   credibility in modeling and computational simulations


\end{itemize}


\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{V \& V for ESSI Modeling and Simulations}


\begin{itemize}

   \vspace*{0.3cm}
   \item Material modeling and simulation (elastic, elastic-plastic...)


   \vspace*{0.3cm}
   \item Finite elements (solids, structural, special...)


   \vspace*{0.3cm}
   \item Solution advancement algorithms (static, dynamic...)


   \vspace*{0.3cm}
   \item Seismic input and radiation 


   \vspace*{0.3cm}
   \item Finite element model verification


\end{itemize}



\end{frame}

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

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Mesh Size Effects on Seismic Wave Propagation Modeling}

\begin{itemize}

  \item Finite element mesh "filters out" \\
       high frequencies

%\vspace*{0.2cm}
  \item Usual rule of thumb: 10-12 elements \\
        needed per wave length
%  (SASSI recommends only 5 ?!)

% 
%    \item  Maximum grid spacing should not exceed 
%    $\Delta h \;\le\; {\lambda}/{10}\;=\;{v}/({10\,f_{max}})$
%  where $v$ is the lowest wave velocity  (shear, elastic-plastic ?)
%  
%    \item  Tests  without and with numerical damping, for different element sizes 
%  

\item 1D wave propagation model
%\vspace*{0.2cm}
\item 3D finite elements (same in 3D)
%\vspace*{0.2cm}
\item Motions applied as displacements at the bottom


\end{itemize}

%\begin{figure}[H]
\vspace*{-4.0cm}
\begin{flushright}
\includegraphics[width=0.7cm]{/home/jeremic/tex/works/Conferences/2011/NRC_Staff_Capacity_Building_21Nov2011/model01.pdf}
\end{flushright}
%\end{figure}

\vspace*{-0.4cm}
\begin{small}
\begin{table}[!htbp]
\centering
% \begin{tabular}{|c|c|c|c|c|}
\begin{tabular}{|r|m{2.6cm}|m{1.5cm}|m{1.8cm}|m{2.3cm}|}
\hline
case  &  model  height  [m]  &  $V_s$ [m/s] & El.size [m] & $f_{max}$ (10el) [Hz]\\
\hline
%\hline
3 & 1000 & 1000 & 10 & 10\\
%\hline
4 & 1000 & 1000 & 20 & 5\\
%\hline
6 & 1000 & 1000 & 50 & 2\\
\hline
% \begin{tabular}{|m{1.5cm}c|m{2.8cm}c|m{2.8cm}c|m{3.0cm}c|m{4.0cm}c|}
% \begin{tabularx}{\linewidth}{|c|c|c|c|c|}
% \begin{tabular*}{0.75\textwidth}{@{\extracolsep{\fill}}|c|c|c|c|c|}
\end{tabular}
% \end{tabularx}
\end{table}
\end{small}




\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Cases 3, 4, and 6, Ormsby Wavelet Input Motions}

 
\begin{figure}[H]
\begin{center}
\includegraphics[width=9cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/MeshSize/figs/3_4_6/Input_Displacement.pdf}
\end{center}
\end{figure}


 
\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Cases 3, 4, and 6, Surface Motions}

 
\begin{figure}[H]
\begin{center}
\includegraphics[width=9cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/MeshSize/figs/3_4_6/displacement.pdf}
\end{center}
\end{figure}


 
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Cases 3, 4, and 6, Input and Surface Motions, FFT}

 
\begin{figure}[H]
\begin{center}
\includegraphics[width=9cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/MeshSize/figs/3_4_6/FFT.pdf}
\end{center}
\end{figure}


 
\end{frame}


 











%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Seismic Body and Surface Waves}

\begin{itemize}

  \item Both body (P, SV and SH) and surface (Rayleigh, Love, etc.) waves
  are present

\vspace*{1mm}
  \item Surface waves carry most seismic energy

\vspace*{1mm}
  \item            Analytic  (Aki and Richards, Trifunac and Lee, Hisada et
  al.,  fk,  etc.)  and  numerically  generated,  3D,  inclined (plane) body and
  surface waves are used in tests

\vspace*{1mm}
  \item  Seismic moment from a point source at $2$km depth used

\vspace*{1mm}
  \item Stress drop at the source: Ricker and/or Ormsby wavelets

\end{itemize}

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Plane Wave Model}
	 
\vspace*{-1cm}
\begin{figure}[!h]
\begin{flushright}
\includegraphics[width=4cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_wave_propagation_figs_DRMModel.pdf}
\label{fig:DRMModel}
\end{flushright}
\end{figure}


\vspace*{-1.5cm}
\begin{figure}[H]
\begin{center}
\includegraphics[width=8cm]{/home/jeremic/tex/works/Conferences/2011/NRC_LBNL_Review_Panel_Sept2011/2D_faul_slip_model.pdf}
\end{center}
\end{figure}

%
% \begin{figure}[H]
% \begin{center}
% \includegraphics[width=10cm]{/home/jeremic/tex/works/Conferences/2011/NRC_LBNL_Review_Panel_Sept2011/2D_faul_slip_model.pdf}
% \end{center}
% \end{figure}

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Seismic Source Mechanics}

\vspace*{0.5cm}
Stress drop, Ormsby wavelet

\vspace*{-1cm}
\begin{figure}[H]
\begin{flushright}
\includegraphics[width=2cm]{/home/jeremic/tex/works/Conferences/2011/NRC_LBNL_Review_Panel_Sept2011/Seismic_source_moment_couple.pdf}
\end{flushright}
\end{figure}

\vspace*{-1.9cm}
\hspace*{-1cm}
\begin{figure}[H]
\begin{center}
\hspace*{-0.4cm}
\includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FaultModel_7seconds/xz_TimeHistory/3000_3000_x_displacement.pdf}
\hspace*{-0.4cm}
\includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FaultModel_7seconds/xz_FFT/3000_3000_x_displacement_FFT.pdf}
\end{center}
\end{figure}

\end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Middle (Structure Location) Plane, Top 2km}

\vspace*{-0.4cm}
\begin{figure}[H]
\begin{flushright}
\includegraphics[width=3cm]{/home/jeremic/tex/works/Conferences/2011/NRC_LBNL_Review_Panel_Sept2011/2D_faul_slip_model_MIDDLE.pdf}
\end{flushright}
\end{figure}

\vspace*{-2.0cm}
\begin{figure}[H]
\begin{center}
\includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FreeFieldInclinedMotionModels/Ormsby/middle_top2000/middle_acceleration_x.pdf}
\hspace*{-0.5cm}
\includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FreeFieldInclinedMotionModels/Ormsby/middle_top2000/middle_acceleration_z.pdf}
\end{center}
\end{figure}

\vspace*{-0.90cm}
{horizontal accelerations   \hfill vertical accelerations}


\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Verification: Displacements, Top Middle Point }
%  \begin{itemize}
%   \item 
%  \end{itemize}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[!htbp] 
\begin{center}
\begin{tabular}{ccc} 
%\hline 
(X)
&
(Z)
\\
\includegraphics[width=5.0cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/wave_propagation/figs/ricker_2km/top_middle_comparison_disp_x.pdf}
&
\includegraphics[width=5.0cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/wave_propagation/figs/ricker_2km/top_middle_comparison_disp_z.pdf}
&
\end{tabular}
%\caption{Comparison of displacements for top middle point using Ricker wave $(f=1Hz)$ as an input motion}
%\label{fig:ricker_acc}
\end{center}
\end{figure}



\end{frame}


% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Verification: Accelerations, Top Middle Point }
% %  \begin{itemize}
% %    \item 
% %  \end{itemize}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{figure}[!htbp] 
% \begin{center}
% \begin{tabular}{ccc} 
% %\hline 
% (X)
% &
% (Z)
% \\
% \includegraphics[width=5.0cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/wave_propagation/figs/ricker_2km/top_middle_comparison_accel_x.pdf}
% &
% \includegraphics[width=5.0cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/wave_propagation/figs/ricker_2km/top_middle_comparison_accel_z.pdf}
% &
% \end{tabular}
% %\caption{Comparison of accelerations for top middle point using Ricker wave $(f=1Hz)$ as an input motion}
% %\label{fig:ricker_acc}
% \end{center}
% \end{figure}
% 
% 
% 
% 
% \end{frame}
% 
% 
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Verification: Disp. and Acc., Out of DRM }
%  \begin{itemize}
%    \item 
%  \end{itemize}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[!htbp] 
\begin{center}
\begin{tabular}{ccc} 
%\hline 
Displacement
&
Acceleration
\\
\includegraphics[width=5.0cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/wave_propagation/figs/ricker_2km/10_40_disp_x.pdf}
&
\includegraphics[width=5.0cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/wave_propagation/figs/ricker_2km/10_40_accel_x.pdf}
&
\end{tabular}
%\caption{Displacement and acceleration time history for a point outside of DRM layer in (x) direction}
%\label{fig:out_ricker_disp}
\end{center}
\end{figure}



\end{frame}


















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% \section{Probabilistic Modeling}



 

\subsection{Uncertain (Geo) Materials}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame} 

\frametitle{Uncertainty Propagation through Constitutive Eq.}

% 

\begin{itemize}

 


\item Incremental el--pl constitutive equation  
     $\displaystyle \Delta \sigma_{ij} = D_{ijkl} \displaystyle \Delta \epsilon_{kl}$

 
  
%\begin{normalsize}

%    
%    \begin{equation}
%    \nonumber
%    \frac{d\sigma_{ij}}{dt} = D_{ijkl} \frac{d\epsilon_{kl}}{dt}
%    \end{equation}
    
    
    \begin{eqnarray}
    \nonumber
     D_{ijkl} = \left\{\begin{array}{ll}
%
     D^{el}_{ijkl}
%
%
        \;\;\; & \mbox{\large{~for elastic}} \\
%
           \\
%
           D^{el}_{ijkl}
           -
           \frac{\displaystyle  D^{el}_{ijmn} m_{mn} n_{pq} D^{el}_{pqkl}}
           {\displaystyle n_{rs} D^{el}_{rstu} m_{tu} - \xi_* r_*}

           \;\;\; & \mbox{\large{~for elastic--plastic}}
%
           \end{array} \right.
           \end{eqnarray}

%\end{normalsize}

 



%\vspace{0.5cm}
% \item Non--linear coupling in the El--Pl modulus


\item What if all (any) material parameters are uncertain

\item PEP and SEPFEM methods for spatially variable and point uncertain material 


%-  \item Focus on 1-D $\rightarrow$ a nonlinear ODE with random coefficient and random forcing
%-  
%-  
%- 
%-  \begin{eqnarray}
%-  \nonumber
%-  \frac{d\sigma(x,t)}{dt} &=& \beta(\sigma(x,t),D^{el}(x),q(x),r(x);x,t) \frac{d\epsilon(x,t)}{dt} \\
%-  \nonumber
%-  &=& \eta(\sigma,D^{el},q,r,\epsilon; x,t)  \mbox{\ \ \ \ with an I.C. $\sigma(0)=\sigma_0$}
%-  \end{eqnarray}
%- 
 

\end{itemize}

% 


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


\end{frame}






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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} 

\frametitle{Probabilistic Stress Solution: \\ Eulerian--Lagrangian form of FPK Equation}

%

%\begin{itemize}
% 3D
\begin{footnotesize}

\begin{eqnarray}
\nonumber
\lefteqn{\displaystyle \frac{\partial P(\sigma_{ij}(x_t,t), t)}{\partial t} = \displaystyle \frac{\partial}{\partial \sigma_{mn}} 
\left[ \left\{\left< \vphantom{\int_{0}^{t}} \eta_{mn}(\sigma_{mn}(x_t,t), E_{mnrs}(x_t), \epsilon_{rs}(x_t,t))\right> \right. \right.} \\
\nonumber
&+&  \left.  \left.  \int_{0}^{t} d\tau Cov_0 \left[\displaystyle \frac{\partial
\eta_{mn}(\sigma_{mn}(x_t,t), E_{mnrs}(x_t),
\epsilon_{rs}(x_t,t))} {\partial \sigma_{ab}}; \right.  \right. \right. \\
\nonumber
& & \left. \left. \left. \eta_{ab} (\sigma_{ab}(x_{t-\tau}, t-\tau), E_{abcd}(x_{t-\tau}), \epsilon_{cd}(x_{t-\tau}, t-\tau) 
\vphantom{\int_{0}^{t}} \right] \right \} P(\sigma_{ij}(x_t,t),t) \right] \\
\nonumber
&+& \displaystyle \frac{\partial^2}{\partial \sigma_{mn} \partial \sigma_{ab}} \left[ \left\{ \int_{0}^{t} d\tau Cov_0 \left[ 
\vphantom{\int_{0}^{t}} \eta_{mn}(\sigma_{mn}(x_t,t), E_{mnrs}(x_t), \epsilon_{rs}(x_t,t)); \right. \right. \right. \\
\nonumber
& & \left. \left. \left. \eta_{ab} (\sigma_{ab}(x_{t-\tau}, t-\tau), E_{abcd}(x_{t-\tau}), \epsilon_{cd}(x_{t-\tau}, t-\tau)) 
\vphantom{\int_{0}^{t}} \right] \vphantom{\int_{0}^{t}} \right\} P(\sigma_{ij}(x_t,t),t) \right]
\end{eqnarray}

 
\end{footnotesize}




% 1D % 1D
% 1D \begin{footnotesize}
% 1D \begin{eqnarray}
% 1D \nonumber
% 1D &&\displaystyle \frac{\partial P(\sigma(x_t,t), t)}{\partial t}=
% 1D - \displaystyle \frac{\partial}{\partial \sigma} \left[ \left\{\left< \vphantom{\int_{0}^{t} d\tau} \eta(\sigma(x_t,t), D^{el}(x_t),
% 1D q(x_t), r(x_t), \epsilon(x_t,t)) \right> \right. \right. \\
% 1D \nonumber
% 1D &+& \left. \left. \int_{0}^{t} d\tau Cov_0 \left[ \displaystyle \frac{\partial \eta(\sigma(x_t,t), D^{el}(x_t), q(x_t), r(x_t),
% 1D \epsilon(x_t,t))}{\partial \sigma}; \right. \right. \right. \\
% 1D \nonumber
% 1D & & \left. \left. \left. \eta(\sigma(x_{t-\tau},t-\tau), D^{el}(x_{t-\tau}), q(x_{t-\tau}), r(x_{t-\tau}),
% 1D \epsilon(x_{t-\tau},t-\tau) \vphantom{\int_{0}^{t} d\tau} \right] \right \} P(\sigma(x_t,t),t) \right] \\
% 1D \nonumber
% 1D &+& \displaystyle \frac{\partial^2}{\partial \sigma^2} \left[ \left\{ \int_{0}^{t} d\tau Cov_0 \left[ \vphantom{\int_{0}^{t}}
% 1D \eta(\sigma(x_t,t), D^{el}(x_t), q(x_t), r(x_t), \epsilon(x_t,t)); \right. \right. \right. \\
% 1D \nonumber
% 1D & & \left. \left. \left. \eta (\sigma(x_{t-\tau},t-\tau), D^{el}(x_{t-\tau}), q(x_{t-\tau}), r(x_{t-\tau}),
% 1D \epsilon(x_{t-\tau},t-\tau)) \vphantom{\int_{0}^{t}} \right] \vphantom{\int_{0}^{t}} \right\} P(\sigma (x_t,t),t) \right] \\
% 1D \nonumber
% 1D \end{eqnarray}
% 1D 
% 1D \end{footnotesize}





\end{frame}







%-- 
%-- \item 6 equations
%-- 
%-- \item Complete description of 3-D probabilistic stress-strain response
%-- 
%-- \end{itemize}
%-- 
%--  


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} 

\frametitle{Eulerian--Lagrangian FPK Equation and (SEP)FEM}

 

\begin{itemize}

\item Advection-diffusion equation 
%
\begin{equation}                
\nonumber
\frac{\partial P(\sigma_{ij},t)}{\partial t} 
= 
-\frac{\partial}{\partial\sigma_{ab}}
\left[N_{ab}^{(1)}P(\sigma_{ij},t)
-
\frac{\partial}{\partial \sigma_{cd}}
\left\{N_{abcd}^{(2)} P(\sigma_{ij},t)\right\} \right]
\end{equation}

%

\vspace*{0.1cm}
\item {\bf  Complete} probabilistic description of response 


\vspace*{0.1cm}
\item {\bf Second-order  exact} to covariance of time (exact mean and variance)

% - 
% -  \item Deterministic equation in probability density space
% -  
% -  \item Linear PDE in probability density space 
% -  $\rightarrow$ simplifies the numerical solution process
% -  

%\item  Applicable  to any elastic-plastic-damage material model (only coefficients $N_{ab}^{(1)}$
%and $N_{abcd}^{(2)}$ differ)


\vspace*{0.1cm}
\item  Any uncertain FEM problem
(${\bf M} \ddot{\bf u}
+
{\bf C} \dot{\bf u}
+
{\bf K} {\bf u}
=
{\bf F}
$)  
with
  \begin{itemize}
    \item uncertain material parameters (stiffness matrix ${\bf K}$),
    \item uncertain loading (load vector ${\bf F}$)
  \end{itemize}
 can  be  analyzed using PEP and SEPFEM to obtain PDFs of DOFs,
 stress, strain...

% -  %\vspace*{0.2cm}
% -  \item PEP solution is second order accurate (exact mean and standard deviation)
% -  
% -  %\vspace*{0.2cm}
% -  \item SEPFEM solution (PDFs) can be made as accurate as need be
% -  
% -  
% -  \item Tails of PDFs can than be used to develop accurate risk
% -  
% -  
% -  \item Application to a realistic case of seismic wave propagation


%\vspace*{0.2truecm}

\end{itemize}


\end{frame}






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\begin{frame} 

\frametitle{Probabilistic Elastic-Plastic Response}


\begin{figure}[!hbpt]
\begin{center}
%\includegraphics[width=8cm]{/home/jeremic/tex/works/Papers/2007/ProbabilisticYielding/figures/vonMises_G_and_cu_very_uncertain/Contour_PDF-edited.pdf}
\includegraphics[width=8cm]{/home/jeremic/tex/works/Conferences/2012/DOE-LLNL-workshop-27-28-Feb-2012/ProbabilisticYielding_vonMises_G_and_cu_very_uncertain_Contour_PDF-edited.pdf}
\end{center}
\end{figure}

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} 

\frametitle{Probabilistic Elastic-Plastic Response}


\begin{figure}[!hbpt]
\begin{center}
%\includegraphics[height=6.0cm]{/home/jeremic/tex/works/Conferences/2011/ICASP11_Zurich/Present/PDF_Plot-Ed.pdf}
\includegraphics[width=9.5cm]{/home/jeremic/tex/works/Conferences/2012/DOE-LLNL-workshop-27-28-Feb-2012/ProbabilisticYielding_vonMises_G_and_cu_very_uncertain_PDF-edited.pdf}
\end{center}
\end{figure}

\end{frame}




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\begin{frame}
\frametitle{Spectral Stochastic Elastic--Plastic FEM}

\begin{itemize}

\item  Minimizing    norm  of  error  of  finite  representation  using Galerkin
technique (Ghanem and Spanos 2003):

      \vspace*{-0.6truecm}
      \begin{flushright}
      \begin{equation}
      \nonumber
      \sum_{n = 1}^N K_{mn}^{ep} d_{ni} + \sum_{n = 1}^N \sum_{j = 0}^P d_{nj} \sum_{k = 1}^M C_{ijk} K_{mnk}^{'ep}  = \left< F_m \psi_i[\{\xi_r\}] \right >
      \end{equation}
      \end{flushright}

%      \begin{itemize}
%
%      \vspace*{0.5cm}
%      \item Final eqn.:
%      
%      \vspace*{-0.4cm}
%      \begin{flushright}
%      \begin{normalsize}
%      \begin{equation}
%      \nonumber
%      \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sum_{n = 1}^N K_{mn} d_{ni} + \sum_{n = 1}^N \sum_{j = 0}^P d_{nj} \sum_{k = 1}^M C_{ijk} K'_{mnk}  = \left< F_m \psi_i[\{\zeta_r\}] \right >
%      \end{equation}
%      \end{normalsize}
%      \end{flushright}

      \vspace*{-0.5cm}
      \begin{equation}
      \nonumber
      K_{mn}^{ep} = \int_D B_n \textcolor{mycolor}{E}^{ep}  B_m dV    
      \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 
      K_{mnk}^{'ep} = \int_D B_n {\sqrt \lambda_k h_k} B_m dV
      \end{equation}
      
      \vspace*{-1.0cm}
      \begin{equation}
      \nonumber
      C_{ijk} = \left < \xi_k(\theta) \psi_i[\{\xi_r\}] \psi_j[\{\xi_r\}] \right >  
      \ \ \ \ \ \ \ \ \ \ \ \  
      F_m = \int_D \phi N_m dV  \ \ \ \ \ \ \ \ \ \ \ \
      \end{equation}

%\item Fokker--Planck--Kolmogorov approach based probabilistic constitutive integration
%      at Gauss integration points


\end{itemize}

%  \noindent Salient Features:
       
%      \begin{itemize}
%
%      \item Efficient representation of input random fields into finite number of random
%            variables using KL-expansion
%      
%      \item Representation of (unknown) solution random variables using polynomial chaos of
%            (known) input random variables
%
%      \item Fokker--Planck--Kolmogorov approach based probabilistic constitutive integration
%      at Gauss integration points
%
%      \end{itemize}
%      
%%   \end{itemize}
%
\end{frame}

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%\subsection{Seismic Wave Propagation Through Uncertain Soils}


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

\begin{frame}
\frametitle{"Uniform" CPT  Site Data}


%\vspace*{-0.7cm}
%\begin{figure}
\begin{center}
\includegraphics[height=6.0cm]{/home/jeremic/tex/works/Thesis/KallolSett/Dissertation/figures/CPT_DataAnalysis_Plots/EastWestProfile-Edited.pdf}
\end{center}
%\end{figure}


\end{frame}


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\begin{frame}


\frametitle{Full PDFs of all DOFs (and $\sigma_{ij}$, $\epsilon_{ij}$, etc.)}
%\frametitle{Full PDFs for Real Data Case}


\begin{itemize}
\vspace*{0.7cm}
  \item Stochastic Elastic-Plastic\\
        Finite Element Method \\
        (SEPFEM)  \\    
\vspace*{0.5cm}
  \item Dynamic case
\vspace*{0.5cm}
  \item Full PDF at \\
        each time step $\Delta t$
\end{itemize}


\vspace*{-4.60cm}
\begin{flushright}
\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/Plots_with_Labels/EvolutionaryPDF_Actual-Edited.pdf}
%\vspace*{-0.75cm}
%\includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2007/USC_seminar/Application_figs/Mean_and_SDElasticPlastic_ps.pdf}
\end{flushright}

% 
\end{frame}

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

\begin{frame}


\frametitle{PDF at each $\Delta t$ (say at $6$ s)}



\begin{figure}
\begin{center}
\hspace*{1.75cm}
\includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/Plots_with_Labels/PDFs_at6sec_Actual_vs_NoData-Edited.pdf}
\vspace*{-0.75cm}
%\includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2007/USC_seminar/Application_figs/Mean_and_SDElasticPlastic_ps.pdf}
\end{center}
\end{figure}

% 
\end{frame}

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

\begin{frame}


\frametitle{PDF $\rightarrow$ CDF (Fragility) at $6$ s}



\begin{figure}
\begin{center}
%\hspace*{-0.75cm}                                                                                               
\includegraphics[width=8.0cm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/Plots_with_Labels/CDFs_at6sec_Actual_vs_NoData-Edited.pdf}
\vspace*{-0.75cm}
%\hspace*{-0.75cm}
%\includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2007/USC_seminar/Application_figs/Mean_and_SDElasticPlastic_ps.pdf}
\end{center}
\end{figure}

% 
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\begin{frame}

\frametitle{Probability of Unacceptable Deformation ($50$cm)}

\begin{figure}
\begin{center}
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\includegraphics[width=10.50cm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/NewPlots/with_legends_and_labels/Exceedance50cm_LomaPrieta-Edited_ps.pdf}
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%\includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2007/USC_seminar/Application_figs/Mean_and_SDElasticPlastic_ps.pdf}
\end{center}
\end{figure}
 
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\section{Summary}
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\begin{frame}
\frametitle{Summary}

\begin{itemize}



\item   High   fidelity,  time  domain,  nonlinear,  earthquake  soil  structure
interaction (ESSI) modeling and simulations (deterministic and probabilistic)

\vspace*{0.1cm}  
\item The ESSI Simulator System (Program, Computer, Lecture Notes)


\vspace*{0.1cm}  
\item      Educational  effort is essential (US-NRC, CNSC, IAEA, UCD, LBNL, INL,
companies), seminars, short courses

%\vspace*{0.1cm}  
%\item Information Portal:\\
%{\large \bf 
%\url{http://nrc-essi-simulator.info}}

\vspace*{0.1cm}  
\item Funding from the US-NRC, DOE, NSF, and CNSC  is much appreciated



\end{itemize}

\end{frame}

\end{document}


