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\title[ESSI Modeling and Simulation]
        {Earthquake Soil Structure Interaction \\
        (ESSI) \\
        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}}
% - Give the names in the same order as the appear in the paper.
% - Use the \inst{?} command only if the authors have different
%   affiliation.
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\pgfdeclareimage[height=0.7cm]{lbnl-logo}{/home/jeremic/BG/amblemi/lbnl-logo}


\author[Jeremi{\'c}] % (optional, use only with lots of authors)
%{Boris~Jeremi{\'c}}
{Boris Jeremi{\'c}}

%\institute[Computational Geomechanics Group \hspace*{0.3truecm}
\institute[\pgfuseimage{JEC-logo}\hspace{1mm}\pgfuseimage{university-logo}\hspace{1mm}\pgfuseimage{lbnl-logo}] % (optional, but mostly needed)
%{ Professor, University of California, Davis\\
{Consulting Engineer, Jeremic Engineering Consultants  \\
%
Professor, University of California, Davis\\
%  and\\ 
%  Faculty Scientist, Lawrence Berkeley National Laboratory, Berkeley }
Faculty Scientist,  Lawrence Berkeley National Laboratory, Berkeley }
% - Use the \inst command only if there are several affiliations.
% - Keep it simple, no one is interested in your street address.


\date[] % (optional, should be abbreviation of conference name)
{\small INL Steering Committee Meeting \\
 December 2013}

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\section{Intro}




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\subsection{Motivation}



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\begin{frame}
 \frametitle{Motivation}

\begin{itemize}
  


%\vspace*{0.3cm}
  \item Improving seismic design for Nuclear Power Plants (NPPs)

\vspace*{0.5cm}
  \item  Use of high fidelity numerical models for analyzing seismic behavior
  of NPP  soil structure interaction (SSI) system


\vspace*{0.5cm}
  \item        Accurately      follow, and direct (!), in space and time,  flow  of 
  seismic energy through the NPP SSI system

%\vspace*{0.3cm}
%  \item   Direct   in   space   and   time,  flow of  seismic  energy  through  the
%  NPP SSI system

  

\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{The Very First Published Work on ESSI}
% 
%   \begin{itemize}
%          \item Professor Kyoji Suyehiro 
%          \item Ship engineer (Professor of Naval Arch. at U. of Tokyo),
%          \item Witnessed Great Kant{\= o} earthquake 
%                (Tokyo, 01Sept1923
%                 11:58am(7.5),    
%                 12:01pm(7.3),    
%                 12.03pm(7.2),   
%                 shaking until 12:08pm)
%          \item Saw earthquake surface waves travel and buildings sway 
%          \item  Became  founding Director of the 
%                 Earthquake Engineering Research
%                 Institute at the Univ. of Tokyo,
%          \item  His published records (ASCE 1932) show 
%                 four times more damage to soft
%                 wooden buildings on soft ground 
%                 then same buildings on stiff soil
%   \end{itemize}
% 
% \end{frame}
% 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
 \frametitle{Hypothesis}

\begin{itemize}
  


%\vspace*{0.5cm}
  \item    Interplay   of  an Earthquake  with    
  Soil/Rock  and  Structure, in time domain, plays a  major
  role in seismic response successes and failures.


\vspace*{0.2cm}
  \item   Timing  and spatial location of energy dissipation determines location
  and amount of damage.

\vspace*{0.2cm}
  \item  If timing and spatial location of energy dissipation 
         can be controlled (directed, designed),
         NPP soil structure systems can be optimized for
    \begin{itemize}
      \item Safety and
      \item Economy
    \end{itemize}

\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
 \frametitle{Predictive Capabilities}
% \frametitle{High Fidelity Modeling of SFS System:
% Verification, Validation and Prediction}


\begin{itemize}


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

\vspace*{1mm}
     \item {{\bf Validation} provides
   evidence that the correct model is solved.} Physics issue. 

\vspace*{1mm}
   \item {\bf 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*{1mm}
   \item Goal: physics based predictive capabilities 
   with {\bf low Kolmogorov Complexity}

\vspace*{1mm}
   \item    High  Fidelity, {\bf hierarchical},  predictive capabilities, aim for
   higher modeling sophistication then needed

\end{itemize}


\end{frame}






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\subsection{Flow of Seismic Energy}



% %- 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{NPP SSI System: Seismic Energy Input}
% 
%    \begin{itemize}
% 
% \vspace*{-1.5cm}
%      \item Kinetic  energy  flux  through closed surface $\Gamma$ includes both incoming
%      and outgoing waves (using Domain Reduction Method by Bielak et al.)
% \begin{eqnarray*}
% E_{flux} = 
% \left[0 ; -M^{\Omega+}_{be} \ddot{u}^0_e-K^{\Omega+}_{be}u^0_e ;
% M^{\Omega+}_{eb}\ddot{u}^0_b+K^{\Omega+}_{eb}u^0_b \right]_i
% %
% % \left[
% % \begin{array}{c} 
% % 0 \\ 
% % -M^{\Omega+}_{be} \ddot{u}^0_e-K^{\Omega+}_{be}u^0_e \\ 
% % M^{\Omega+}_{eb}\ddot{u}^0_b+K^{\Omega+}_{eb}u^0_b
% % \end{array}
% % \right]^{T}
% \times u_i
% %\left[
% %\begin{array}{c} 
% %0 \\ 
% %{u}_b\\ 
% %{u}_e
% %\end{array}
% %\right]
% \end{eqnarray*}
% 
%   \item Alternatively, $E_{flux} = \rho A c \int_0^t \dot{u}_i^2 dt$
% 
%   \item  Outgoing kinetic  energy  \\
%          is obtained from outgoing \\
%          wave field ($w_i$, in DRM)
% 
%   \item Incoming kinetic energy \\
%         is then the difference.
% 
% 
%    \end{itemize}
% 
% 
% \vspace*{-7.0cm}
% % \begin{figure}[!hbpt]
% %\begin{flushright}
% \hfill \includegraphics[width=5.5cm]{/home/jeremic/tex/works/psfigures/DRMidea03.pdf}
% %\end{flushright}
% %\end{figure}
% \vspace*{-2cm}
% 
% 
% \end{frame}
% %- 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
% \frametitle{Seismic Energy Dissipation for \underline{Soil}-Foundation-Structure Systems}
 \frametitle{Seismic Energy Input and Dissipation}
% \frametitle{Seismic Energy Dissipation for 
%             \underline{Soil}-Foundation-Structure Systems}


\begin{itemize}

     \item Seismic  energy  influx  through closed boundary 
%     $E_{flux} = \rho A c \int_0^t \dot{u}_i^2 dt$ 

\vspace*{2mm}
     \item Mechanical dissipation outside of NPP SSI domain:
       \begin{itemize}
         \item reflected wave radiation
         \item NPP SSI system oscillation radiation
       \end{itemize}


\vspace*{2mm}
     \item Mechanical dissipation inside NPP SSI domain:
       \begin{itemize}
         \item plasticity of soil subdomains
         \item viscous coupling of porous solid with pore fluid (air, water)
         \item plasticity/damage of the parts of structure/foundation
         \item viscous coupling of structure/foundation with fluids 
%         \item potential and kinetic energy
         \item potential $\leftarrow \! \! \! \! \! \! \rightarrow$ kinetic energy
       \end{itemize}                           



\vspace*{2mm}
%   \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{Energy Dissipation by Soil Plasticity}


\vspace*{2mm}
 Energy dissipation (plastic work) capacity for different soils 
% 
%    \begin{itemize}
% 
% %     \item Plastic work ($W = \int_{0}^{t} \sigma_{ij} d \epsilon_{ij}^{pl}$)
%      \item Plastic work 
% %     ($W = \int \sigma_{ij} d \epsilon_{ij}^{pl}$)
% 
%      \item Energy dissipation capacity for different soils
% 
% 
%   \end{itemize}

%\vspace*{-1.0cm}
\begin{center}
\vspace*{-0.9cm}
\includegraphics[width=8.5cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/Energy-Capacity2.pdf}
\hspace*{-0.2cm}
%\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/Energy-Capacity10.pdf}
\vspace*{-1.0cm}
\end{center}


\end{frame}
%- 
%- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%- \begin{frame}
%-  \frametitle{Plasticity Energy Dissipation}
%- 
%-    \begin{itemize}
%- 
%-      \item
%- 
%-   \end{itemize}
%- 
%- 
%- \end{frame}
%- %- 
%- %- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%- \begin{frame}
%-  \frametitle{Energy Dissipation by Soil Viscous Coupling}
%- 
%- 
%-    \begin{itemize}
%- 
%-      \item Viscous coupling of porous solid and fluid
%-      \item Energy loss per unit volume is  $E_{vc}= n^2 k^{-1} (\dot{U}_i - \dot{u}_i)^2$ 
%-      \item Natural in $u-p-U$ formulation:
%- 
%-   \end{itemize}
%- %\vspace*{-0.4cm}
%- 
%- 
%- 
%- 
%- \begin{footnotesize}
%- %\begin{tiny}
%- \begin{eqnarray*}
%- %& &\left[ \begin{array}{ccc}
%- \left[ \begin{array}{ccc}
%- (M_s)_{KijL} & 0 & 0 \\
%-  0  & 0 & 0 \\
%-  0  & 0 & (M_f)_{KijL}
%- \end{array} \right]
%- \left[ \begin{array}{c}
%- \ddot{\overline{u}}_{Lj} \\
%- \ddot{\overline{p}}_N \\
%- \ddot{\overline{U}}_{Lj}
%- \end{array} \right]
%- +
%- \left[ \begin{array}{ccc}
%- (C_1)_{KijL} & 0 & -(C_2)_{KijL} \\
%-  0  & 0 &   0  \\
%- -(C_2)_{LjiK} & 0 & (C_3)_{KijL} \\
%- \end{array} \right]
%- \left[ \begin{array}{c}
%- \dot{\overline{u}}_{Lj} \\
%- \dot{\overline{p}}_N \\
%- \dot{\overline{U}}_{Lj}
%- \end{array} \right]   
%- \nonumber\\
%- +
%- %& &\left[ \begin{array}{ccc}
%- \left[ \begin{array}{ccc}
%- (K^{EP})_{KijL} & -(G_1)_{KiM} & 0 \\
%- -(G_1)_{LjM}  & -P_{MN} & -(G_2)_{LjM} \\
%-  0  & -(G_2)_{KiL} & 0
%- \end{array} \right]
%- \left[ \begin{array}{c}
%- \overline{u}_{Lj} \\
%- \overline{p}_M \\
%- \overline{U}_{Lj}
%- \end{array} \right]
%- =
%- \left[ \begin{array}{c}
%- \overline{f}_{Ki}^{solid} \\
%- 0  \\
%- \overline{f}_{Ki}^{fluid}
%- \end{array} \right] \nonumber\\
%- \label{68}
%- \end{eqnarray*}
%- %\end{tiny}
%- \end{footnotesize}
%- 
%- \vspace*{-1cm}
%- 
%- \begin{footnotesize}
%- \begin{eqnarray*}
%- %%%%%%%%
%- (C_{(1,2,3)})_{KijL}   
%- =
%- \int_{\Omega} N_K^{(u,u,U)} 
%- n^2 k_{ij}^{-1} 
%- N_L^{(u,U,U)} d\Omega
%- % (C_1)_{KijL}   =\int_{\Omega} N_K^u n^2 k_{ij}^{-1} N_L^u d\Omega
%- % \;\; \mbox{;} \;\;
%- % (C_2)_{KijL}   =\int_{\Omega} N_K^u n^2 k_{ij}^{-1} N_L^U d\Omega 
%- % %%%%%%%%
%- % %\;\; \mbox{;}\;\;
%- % \\
%- % %%%%%%%%
%- % (C_3)_{KijL}   =\int_{\Omega} N_K^U n^2 k_{ij}^{-1} N_L^U d\Omega
%- \end{eqnarray*}
%- \end{footnotesize}
%- %
%- %
%- %
%- %
%- %\newpage
%- 
%- 
%- 
%- 
%- \end{frame}
%- %- 
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% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Numerical Energy Dissipation}
% 
%    \begin{itemize}
% 
%      \item    Newmark    and  Hilber-Hughes-Taylor integration algorithms can be
%      made non-dissipative for
%      elastic system $\alpha=0.0, \beta = 0.25 ; \gamma  = 0.5,$
% 
%      \item Or dissipative (for elastic) for higher frequencies 
% %Newmark ($\gamma     \ge     0.5,     \;\;\;    \beta    = 0.25(\gamma+0.5)^2$ ),
% %Hilber-Hughes-Taylor   ($-0.3\dot{3}\le\alpha        \le0,        \;\;\;\gamma    =  
% %0.5(1-2\alpha), \;\;\; \beta = 0.25(1-\alpha)^2$)
%       \begin{itemize}
%         \item N: $\gamma     \ge     0.5,     \;\;\;    \beta    = 0.25(\gamma+0.5)^2$,
%         \item HHT: $-0.3\dot{3}\le\alpha        \le0,        \;\;\;\gamma    =  
% 0.5(1-2\alpha), \;\;\; \beta = 0.25(1-\alpha)^2$
%       \end{itemize}
% 
%      \item  For nonlinear problems, 
%             energy cannot be maintained
%        \begin{itemize}
%            \item Energy dissipation for steps with reduction of stiffness
%            \item Energy production for steps with increase of stiffness
% 
% \hspace{1cm}
% \includegraphics[width=1.80cm, angle=-90]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/EnergyDissipationReducationStiffness.pdf}
% \hspace{1cm}
% \includegraphics[width=1.80cm, angle=-90]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/EnergyProductionIncreaseStiffness.pdf}
% \hspace{1cm}
% 
% 
% 
%        \end{itemize}
%      
% 
%   \end{itemize}
% 
% 
% \end{frame}
% %- 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%






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\subsection{Modeling Uncertainty}




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




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Complexity of and Uncertainty in Material Modeling}

\begin{itemize}
%\vspace*{0.3cm}
  \item All engineering materials experience inelastic deformations for working loads

\vspace*{0.1cm}
  \item This is even more so for hazard loads (earthquakes)
 
\vspace*{0.1cm}
  \item  Pressure sensitive materials (soil, rock , concrete, etc) can have very
  complex constitutive response, tying together nonlinear stress-strain with volume response
 
\vspace*{0.1cm}
  \item  Simplistic  material  modeling  (elastic,  $G/G_{max}$, etc.) introduce
  (significant) uncertainties in response results
  
\vspace*{0.1cm}
  \item  In  addition, man-made and natural materials are spatially variable and
  their material modeling parameters are uncertain


\end{itemize}

\end{frame}











%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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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 Spatial \\ 
              variability

\vspace*{0.5cm}
        \item Point-wise \\ 
              uncertainty, \\
              testing \\
              error, \\
              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}

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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 $\rightarrow$ un-drained shear
strength, $s_u$ (cf. Phoon and Kulhawy (1999B)

Histogram  of  the  residual  
(w.r.t  the  deterministic transformation
equation) un-drained 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{Verification and Validation}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Verification \& Validation (V\&V) Definition}
% 
% 
% \begin{itemize}
% 
% %   \vspace*{1.0truecm}
%    \item   {\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.}
% 
%    \vspace*{0.5truecm}
%    \item    {\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.}
%    
% 
% 
% \end{itemize}
% 
% 
% \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{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=8.5cm]{/home/jeremic/tex/works/Conferences/2011/USNCCM11_Minneapolis/Coupled/Present/VandV_ODEN.jpg}}
% \hspace*{-2cm}
% \end{center}
% \end{figure}
% 
% {Oden et al.}
% %{Oberkampf et al. \hspace*{4cm}  Oden et al.}
% forCaltrans %
% %\item Models available (some now, some later)
% %\vspace*{-2.0cm}
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \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*{0.2truecm}
%    \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
%       \item Experimental uncertainty analysis!
%      \end{itemize}
% 
% 
% \end{itemize}
% 
% 
% 
% \end{frame}
% 
% 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% %  \frametitle{Validation Experiments}
% % 
% % 
% %  \begin{itemize}
% % 
% %    \vspace*{0.0truecm}
% %    \item  Jointly designed and executed by
% %    experimentalist and computationalist
% % % 
% %    \item Designed to capture the relevant physics
% % 
% %    \item  Use any possible synergism between
% %    experiment and computational approaches
% % 
% %    \item  Maintain independence  between computational and experimental results
% % 
% %    \item  Validate experiments on unit level problems, hierarchy of experimental
% %    measurements   should   be   made   which  present  an  increasing  range  of
% %    computational difficulty
% % 
% %    \item Develop experimental uncertainty analysis
% % 
% % \end{itemize}
% % 
% % 
% % 
% % \end{frame}
% % 
% 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Validation and Application Domains --  No Overlap}
% 
%      
% %\vspace*{0.3cm}
% 
% \begin{figure}[!h]
% \begin{center}
% %\vspace*{-2.5cm}
% {\includegraphics[width=4.0cm]{/home/jeremic/tex/works/Presentation/2004/VandV/VPI03.pdf}}
% %\vspace*{-5.0cm}
% \end{center}
% \end{figure}
% 
% %\vspace*{-0.5cm}
% 
% \begin{itemize}
%  \item  Inference  $\Rightarrow$ probabilistic modeling and numerical
%  simulation (deterministic is a special case)
% %  %  \item  Validation domain is actually an aggregation of tests and thus might not
% %  %  be convex (bifurcation of behavior)
% %   \item Current experiments $\Rightarrow$ non--overlapping validation and
% %   application domains
% %  % \item We have to rely on {\bf Modeling} and {\bf Numerical Simulation}
% \end{itemize}
% 
% \end{frame}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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*{0.3truecm}
%    \item Validation does not directly make a claim about the accuracy of a prediction
%      \begin{itemize}
%        \item Computational models are easily misused (unintentionally or intentionally)
%        \item  How  closely  related  are  the  conditions  of the prediction and
%        specific cases in validation database
%        \item How well is physics of the problem understood
% 
%      \end{itemize}
% 
% 
% \end{itemize}
% 
% 
% 
% \end{frame}
% 
% 
% 
% 
% % 
% 
% 
% 
% 
% 
% 



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\section{ESSI System}
%




\subsection{ESSI Program}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \begin{frame}
% \frametitle{Desirable Modeling and Simulation Capabilities}
% 
% 
% \begin{itemize}
% 
% \item   Body (SH, SV, P) and Surface (Rayleigh, Love, etc) seismic motions modeling
%    and their input into finite element models
%  
%  \item   Elastic-plastic modeling of dry and saturated soil/rock behavior beneath
%    foundations
%  
%  \item   Elastic-plastic modeling of soil/rock (limited data)
%  
%  \item  Soil/rock - foundation contact zone modeling (for dry and saturated
%    conditions)
%  
%  \item   Verification and Validation suite
%  
%  \item         High   performance,  parallel  simulation  using  dynamic  domain
%  decomposition (Plastic Domain Decomposition) for elastic-plastic simulations
%  
%  \item     Probabilistic elasto-plasticity and stochastic elastic-plastic finite
%  element methods
% 
% 
% \end{itemize}
% 
% \end{frame}
% 
% 

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


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

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

\begin{itemize}

\item {\bf 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 of NPPs 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 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  ESSI-Notes} are    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 Program: Finite Elements}


%\vspace*{-3mm} 
   \begin{itemize}
\vspace*{1mm} 
    \item Dry/single phase solids (8, 20, 27 8-27 node bricks) 
\vspace*{1mm} 
    \item Saturated/two phase solids (8 and 27 node bricks, liquefaction modeling, buoyant forces)
\vspace*{1mm} 
    \item Quad (ANDES) Shell (6DOFs per node) 
\vspace*{1mm} 
    \item Beams (6DOFs and variable DOFs per node)
\vspace*{1mm} 
    \item Truss 
\vspace*{1mm} 
    \item   Contacts      (dry   or   saturated   soil/rock   -  concrete,  gap
    opening-closing, frictional slip)
\vspace*{1mm} 
    \item Base isolators (elastomeric, frictional pendulum)
   \end{itemize}

\end{frame}

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

\begin{frame}
\frametitle{ESSI Program: Material Models}

%\vspace*{-2mm} 
   \begin{itemize}
      \item Linear and nonlinear, isotropic and anisotropic  elastic
\vspace*{3.5mm} 
       \item  Elastic-Plastic  (von Mises, Drucker Prager, Rounded Mohr-Coulomb,
       Parabolic   Leon,   Cam-Clay,   SaniSand   (Dafalias-Manzari),  SaniClay,
       Pisan{\`o}...)
\vspace*{3.5mm} 
       \item  All  elastic-plastic  models can be used as perfectly
              plastic,  isotropic  hardening/softening  and  kinematic hardening
              models
   \end{itemize}

\end{frame}

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

\begin{frame}
\frametitle{ESSI Program: Seismic Input}

\begin{itemize}

 \item    Analytic    input    of  seismic motions 
   \begin{itemize}
     \item Body waves (P, SH, SV) 
     \item Surface waves  (Rayleigh, Love, etc.)
     \item Analytic radiation damping
   \end{itemize}

\vspace*{3.5mm} 
 \item  Domain Reduction Method (Bielak et al.)

\vspace*{3.5mm} 
 \item  Synthetic and realistic seismic motions (Hisada, fk, FEM, etc.)


\end{itemize}

\end{frame}

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

\begin{frame}
\frametitle{ESSI Program: Verification and Validation}

\begin{itemize}



\vspace*{2mm} 
\item Detailed Verification (math issue)
 \begin{itemize}
   \item Finite elements 
   \item Material model
   \item Solution algorithms
   \item Analysis procedure
   \item Code 
  documented in detail in ESSI Notes.
 \end{itemize}


\vspace*{2mm} 
\item (Not so) Detailed Validation (physics issue) (lack of high quality experimental data)


\vspace*{2mm} 
\item Detailed V\&V documentation in ESSI Notes






\end{itemize}

\end{frame}

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

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

\begin{itemize}


\vspace*{2mm} 
\item Sequential computing: available for all models, however


\vspace*{2mm} 
\item High Performance Parallel Computing: for high fidelity
  modeling,  parallel is really the only option. 
  Parallel ESSI Program available on

   \begin{itemize}
     \item Single, multi-core/multi-CPU PCs,
     \item Clusters  of (multi-core/multi-CPU) PCs,
     \item Distributed memory parallel  (DMP) supercomputers (all  top  national
     supercomputers).
   \end{itemize}


\vspace*{2mm} 
\item  Template  metaprograms  for  local, element and material model level high
performance computing


%  Parallel  algorithm  uses our
%  original  Plastic Domain Decomposition method (featuring dynamic computational
%  load  balancing) that is efficient for elastic-plastic finite element problems
%  where  elastic-plastic  (slow)  and  elastic (fast) domains change dynamically
%  during run time.


\end{itemize}

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
\frametitle{ESSI Program: Probabilistic/Stochastic}
%\vspace*{-2mm} 


   \begin{itemize}
%\vspace*{-2.5mm} 
     \item         Constitutive:      
%        Euler-Lagrange         form        of
%          
     Fokker-Planck-Kolmogorov equation for probabilistic elasto-plasticity (PEP)

%\vspace*{-1.5mm} 
     \item Spatial: stochastic elastic plastic finite element method (SEPFEM)

     \item Uncertain: material  (LHS) and loads  (RHS):
     $M_{AacB} \; \ddot{\bar{u}}_{Bc} +
     C_{AacB} \; \dot{\bar{u}}_{Bc} +
     K^{EP}_{AacB}   \; \bar{u}_{Bc}   
     = 
     F_{Aa}$

%
% 
%      $M \ddot{\bf u} + C \dot{\bf u} +  K^{ep} {\bf u} = F$
% 
% 
     \item Results ($u_{i}, \sigma_{ij}, \epsilon{ij}$)   are very accurate
  (second  order accurate for stress) Probability Density Functions (PDFs)

    \item PEP  and  SEPFEM  are  {\bf not}  based  on a Monte Carlo method, 
    
    \item Uncertain  input  variables  and  uncertain DOFs are expanded into
  spectral  probabilistic  spaces, single run solution

   \end{itemize}

\end{frame}




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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Probabilistic Modeling}
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
% 
% \frametitle{Recent State-of-the-Art}
% 
% \begin{itemize}
% 
% %\vspace*{-0.5cm}
% \item Governing equation
% 
% %       \vspace*{-0.5cm}
%        \begin{itemize}
% 
%        \item Dynamic problems  $\rightarrow$ $ M \ddot u + C \ddot u + K u = F $
% 
%        \item Static problems  $\rightarrow$   $ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \   K u = F $
% 
%        \end{itemize}
% 
% %\vspace{-0.4cm}
% \item Existing solution methods
% 
% %       \vspace*{-0.5cm}
%        \begin{itemize}
% 
%        \item \textbf{Random r.h.s} (external force random)
% 
%              \begin{itemize}
% 
%       \item FPK equation approach 
% 
%       \item Use of fragility curves with deterministic FEM (DFEM)
% 
%       \end{itemize}
% 
% %       \vspace*{0.2cm}
%        \item \textbf{Random l.h.s} (material properties random)
% 
%              \begin{itemize}
% 
%       \item Monte Carlo approach with DFEM $\rightarrow$ CPU expensive
% 
% %      \item Stochastic finite element method (e.g. Perturbation method  
% %             $\rightarrow$ a linearized expansion! Error increases as a function
% %      of COV; Spectral method 
% %             $\rightarrow$ developed for elastic materials so far)
% 
%       \item Perturbation method 
%              $\rightarrow$ a linearized expansion! Error increases as a function
%       of COV 
%       
%       \item Spectral method 
%              $\rightarrow$ developed for elastic materials so far
% 
% %             \begin{itemize}
% %
% %             \item Perturbation method  $\rightarrow$ fails if COVs of soil $>$ 20\%
% %
% %      \item Spectral method $\rightarrow$ only for elastic material
% %
% %             \end{itemize}
% 
%       \end{itemize}
%              
%        \end{itemize}      
% 
% \item  Original development of  {\bf Probabilistic Elasto--Plasticity}
% 
% 
% \end{itemize}
% 
% \end{frame}
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame} 
% 
% \frametitle{Eulerian--Lagrangian FPK Equation and (SEP)FEM}
% 
%  
% 
% \begin{itemize}
% 
% \item Constitutive: 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 stress-strain 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}
% 
% 
% 
% 
% 
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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{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}

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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}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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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\section{ESSI Examples}








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\subsection{3D, Inclined, Body and Surface}




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\begin{frame}
\frametitle{Earthquake Ground Motions}



 Realistic earthquake ground motions 
   \begin{itemize}
\vspace*{0.1cm}
     \item Body waves: P and S waves
\vspace*{0.1cm}
     \item Inclined waves
\vspace*{0.1cm}
     \item 3D (6D!) waves
\vspace*{0.1cm}
     \item Surface waves: Rayleigh, Love waves, etc.
\vspace*{0.1cm}
  \item Surface waves carry most seismic energy of interest 
\vspace*{0.1cm}
     \item Lack of correlation (incoherence)
%\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 Wave passage effects
%   \item Attenuation 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}
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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{3D Synthetic Seismic Motions}
%

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\begin{frame}
\frametitle{3D Synthetic Seismic Motions}

  \begin{itemize}
    
    \item  Development  of  analytic  and  numerical  3D, inclined, uncorrelated
    seismic motions for verification, stress testing of NPPs, etc.

   \vspace*{0.2cm}
    \item Large scale model

   \vspace*{0.2cm}
    \item Point shear source 

   \vspace*{0.2cm}
    \item Stress drop:
         \begin{itemize}

           \item Wavelet (Ricker, \\
           Ormsby, etc)
  
           \item Analytic 


         \end{itemize}

   \vspace*{0.2cm}
    \item Seismic input using DRM (Bielak et al (2003))

  \end{itemize}



 
   \vspace*{-5.3cm}
\begin{flushright}
\hspace*{5mm}
\includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/wave_propagation/figs/FaultSlipModel2km.pdf}
\hspace*{-5mm}
\end{flushright}



\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}

\end{frame}

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

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

\vspace*{-1.5cm}
\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 (NPP Location) Plane,\\ Top 2km}

\vspace*{-2.0cm}
\begin{figure}[H]
\begin{flushright}
\includegraphics[width=4cm]{/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}
\hspace*{-1.0cm}
\includegraphics[width=6.5cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FreeFieldInclinedMotionModels/Ormsby/middle_top2000/middle_acceleration_x.pdf}
\hspace*{-0.5cm}
\includegraphics[width=6.5cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FreeFieldInclinedMotionModels/Ormsby/middle_top2000/middle_acceleration_z.pdf}
\hspace*{-0.5cm}
\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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\subsection{Model Verification, Mesh Size Effects}




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\begin{frame}
\frametitle{Motion Filtering: Mesh Size Effects}

\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

\item Linear elastic and elastic -- linear hardening plastic material


\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{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{Linear Elastic Material: 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{Linear Elastic Material, FFT of Input and Surface Motions}

 
\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{Elastic Plastic Material, Stress-Strain Response}

 
\begin{figure}[H]
\begin{center}
\vspace*{-1cm}
\includegraphics[width=6cm]{/home/jeremic/tex/works/Conferences/2013/INL-SteeringCommittee_Dec2013/elm180-H0_1-ss-2-A0_1m-H0_1E.pdf}
\end{center}
\end{figure}


 
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Elastic Plastic Material, Surface Response}

 
\begin{figure}[H]
\begin{center}
\vspace*{-1.5cm}
\includegraphics[width=9cm]{/home/jeremic/tex/works/Conferences/2013/INL-SteeringCommittee_Dec2013/H0_1E-A0_1m_TimeDomain.pdf}
\vspace*{-1.5cm}
\\
\vspace*{-1.5cm}
\includegraphics[width=9cm]{/home/jeremic/tex/works/Conferences/2013/INL-SteeringCommittee_Dec2013/H0_1E-A0_1m_FrequencyDomain.pdf}
\vspace*{-1.5cm}
\end{center}
\end{figure}


 
\end{frame}








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\subsection{Seismic Wave Propagation Through Uncertain Soils}


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
% 
% \frametitle{Applications}
% 
% 
% 
% 
% \begin{itemize}
% 
% \vspace*{0.3cm}
% \item Stochastic elastic--plastic simulations of soils and structures
% 
% \vspace*{0.3cm}
% \item Probabilistic inverse problems
% 
% \vspace*{0.3cm}
% \item Geotechnical site characterization design
% 
% \vspace*{0.3cm}
% \item Optimal material design
% 
% 
% \end{itemize}
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% - +
% - + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - + 
% - + \begin{frame}
% - + 
% - + 
% - + \frametitle{Random Field Modeling of Uncertain Soil Properties}
% - + 
% - + \begin{itemize}
% - + 
% - + \item Finite scale model 
% - + 
% - + \begin{itemize}
% - + 
% - + \item Short memory, finite correlation length
% - + 
% - + \item Common autocovariance model $\rightarrow$ exponential, spherical, triangular, linear--exponential
% - + 
% - + \end{itemize}
% - + 
% - + \item Fractal model 
% - + 
% - + \begin{itemize}
% - + 
% - + \item long memory, infinite correlation length $\rightarrow$ more realistic for modeling horizontal 
% - + spatial uncertainty
% - + 
% - + \item 1/f-type noise process with power spectral density, $P(\omega)~=~P_0~\omega^{-\gamma}$, with
% - + upper and/or lower frequency cut-off.
% - + 
% - + \end{itemize}
% - + 
% - + \end{itemize}
% - + 
% - + \end{frame}
% - + 
% - + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
% 
% \frametitle{Seismic Wave Propagation through Stochastic Soil}
% 
% 
% \begin{itemize}
% 
% %\item maximizing the log--likelihood of observing the spatial data under assumed joined distribution (for finite 
% %scale model) or maximizing the log--likelihood of observing the periodogram estimates (for fractal model)
% 
% \item Maximum likelihood estimates
% 
% \vspace*{0.3truecm}
% 
% %\begin{figure}
% \begin{flushleft}
% \hspace*{-1.7cm}
% \includegraphics[height=4.0cm]{/home/jeremic/tex/works/Thesis/KallolSett/Dissertation/figures/CPT_DataAnalysis_Plots/SamplingPlan-Edited.jpg}
% \hspace*{0.0cm}
% \includegraphics[height=4.0cm]{/home/jeremic/tex/works/Thesis/KallolSett/Dissertation/figures/CPT_DataAnalysis_Plots/TypicalDataPlotBH1-Edited.jpg} \\
% \small{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Typical CPT $q_T$}
% \end{flushleft}
% %\end{figure}
% 
% \vspace*{-4.9truecm}
% 
% %\begin{figure}
% \begin{flushright}
% \includegraphics[width=4.0cm]{/home/jeremic/tex/works/Thesis/KallolSett/Dissertation/figures/CPT_DataAnalysis_Plots/TypicalAutoCovariancePlotBH1_FiniteScale-Edited.jpg} \\
% \vspace*{0.01truecm}
% \small{Finite Scale}
% \end{flushright}
% %\end{figure}
% 
% \vspace*{0.02truecm}
% 
% %\begin{figure}
% \begin{flushright}
% \includegraphics[width=4.0cm]{/home/jeremic/tex/works/Thesis/KallolSett/Dissertation/figures/CPT_DataAnalysis_Plots/TypicalAutoCovariancePlotBH1_Fractal-Edited.jpg} \\
% \small{Fractal}
% \end{flushright}
% %\end{figure}
% 
% \end{itemize}
% 
% 
% \end{frame}
% 
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\begin{frame}




\frametitle{"Uniform" CPT  Site Data}


\vspace*{-0.7cm}
%\begin{figure}
\begin{center}
\includegraphics[height=6.7cm]{/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{Random Field Parameters from Site Data}


%\begin{flushleft}
%\includegraphics[height=5.0cm]{PEER2007_3.jpg}
%\end{flushleft}
%\vspace*{-0.5truecm}

\begin{itemize}

\item Soil as 12.5 m deep 1--D soil column (von Mises Material) 

\begin{itemize}

\item Properties (including testing uncertainty) obtained through random field modeling of CPT $q_T$
%
$\left<q_T\right> = 4.99 ~MPa;~~Var[q_T] = 25.67 ~MPa^2; $\\
Cor. ~Length $[q_T] = 0.61 ~m; $ Testing~Error $= 2.78 ~MPa^2$

\end{itemize}

\vspace*{0.2cm}
\item $q_T$ was transformed to obtain $G$: ~~$G/(1-\nu)~=~2.9q_T$ 

\begin{itemize}
\item Assumed transformation uncertainty = 5\%
%
$\left<G\right> = 11.57MPa; Var[G] = 142.32 MPa^2$ \\
Cor.~Length $[G] = 0.61 m$

\end{itemize}


%\begin{center}
%\hspace*{-1.7cm}
%\includegraphics[height=3.5cm]{Chapter9_Schematic.jpg}
%\hspace*{0.0cm}
%\includegraphics[height=3.5cm]{Chapter9_BaseDisplacement.jpg} \\
%\small{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Base Displacement}
%\end{center}

\vspace*{0.2cm}
\item Input motions: modified 1938 Imperial Valley

% \vspace*{-0.2cm}
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% \includegraphics[height=2.0cm]{Chapter9_BaseDisplacement.jpg} 
% \end{center}

\end{itemize}
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%--  % \hspace*{-1.0cm} \tiny{~~~~~~~~~~~~~~~~~~~~~~~~~~~~Mean~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Standard Deviation}
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%--  % \hspace*{-0.5cm} \tiny{~~~~~~~Mean$\pm$ Standard Deviation~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~COV}
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\begin{frame}


\frametitle{Decision About Site (Material) Characterization}




\begin{itemize}

\item  Do nothing about site characterization (rely on experience): conservative
{\bf guess}  of  soil  data, $COV  = 225$\%, correlation length $= 12$m.


\vspace*{0.3cm}
\item  Do better than standard site characterization: $COV = 103$\%, correlation
length $= 0.61$m)


\vspace*{0.3cm}
\item Improve site (material) characterization if  probabilities of exceedance are unacceptable!


\end{itemize}

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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}
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\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}

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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}
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% %\hspace*{-0.75cm}                                                                                               
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% \frametitle{Probability of Exceedance of $50$cm}
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% %\hspace*{-0.75cm}                                                                                               
% \includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/Plots_with_Labels/ProbabilityOfExceedance50cm_Actual_vs_NoData-Edited.pdf}
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% %\includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2007/USC_seminar/Application_figs/Mean_and_SDElasticPlastic_ps.pdf}
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% \frametitle{Probabilities of Exceedance vs. Displacements}
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% %\hspace*{-0.75cm}                                                                                               
% \includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/Plots_with_Labels/ProbabilityOfExceedance_vs_Displacement_Actual_vs_NoData-Edited.pdf}
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% %\includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2007/USC_seminar/Application_figs/Mean_and_SDElasticPlastic_ps.pdf}
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% \vspace*{-0.3cm}                                                                                               
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% %\hspace*{-0.75cm}                                                                                               
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% %\hspace*{-0.75cm}                                                                                               
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\section{Summary}


\subsection*{Summary}









       
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\begin{frame}
\frametitle{Current NPP Model(s)}

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% \begin{figure}[!hbpt]
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% \includegraphics[width=3cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/02_cropped.jpg}
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% \includegraphics[width=1.5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/04_cropped.jpg}
% %\hspace*{-0.5cm}
% \end{center}                              
% \end{figure}
% %
% 
% 

\vspace*{-1.0cm}
\begin{figure}[!hbpt]
\begin{center}
\raisebox{0.9cm}{\includegraphics[width=1.5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/04_cropped.jpg}}
\raisebox{1.2cm}{\includegraphics[width=3cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/02_cropped.jpg}}
\raisebox{-0.5cm}{\includegraphics[width=6cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/03_cropped.jpg}}
\end{center}                              
\end{figure}

\vspace*{-1.6cm}
\begin{itemize}
% \item Modular models
%\vspace*{-0.1cm}
 \item General 3D seismic waves
%\vspace*{-0.1cm}
 \item Foundation slip -- gap 
%\vspace*{-0.1cm}
 \item Isolators, dissipators
%\vspace*{-0.1cm}
 \item Uncorrelated (incoherent) motions
%\vspace*{-0.1cm}
 \item Saturated dense vs loose soil with buoyant forces
%\vspace*{-0.1cm}
 \item Piles and pile groups 
%\vspace*{-0.1cm}
 \item Uncertain material (LHS) and seismic motions (RHS)

\end{itemize}

\end{frame}



% 








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\begin{frame}
  \frametitle{Summary}
  
  \begin{itemize}


  \item              {\bf    Interplay}        of     
 {\bf uncertain} 
{\bf   earthquake}, 
 {\bf uncertain}  
{\bf soil},
  and    {\bf  uncertain}   
{\bf structure}, in  time domain, 
{\bf probably} 
plays a
  decisive role in seismic performance of NPPs

\vspace*{5mm}
  \item           Improve {\bf 
 risk informed 
 decision making} ({\bf design $\Rightarrow$ safety} and {\bf economy}) 
   through  
  {\bf high fidelity}, 
%  {\bf  Deterministic}  and  
%  {\bf  Stochastic Elastic-Plastic  Finite Element} 
  modeling and simulation 
  ({\bf    ESSI  Simulator  System})

% \vspace*{0.1cm}
%   \item  {\bf    ESSI  Simulator  System},  extensively  {\bf Verified} and 
%   {\bf    Validated}  is  used for modeling, simulations, design  and regulatory
%   decision making
% 

 
\vspace*{5mm}
  \item      {\bf  Education}  and  {\bf training}  of  users  (designers, regulators,
  owners) will prove essential
  
  
\end{itemize}


\end{frame}
%




% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%   \frametitle{UCD/LBNL ESSI Group Current Work}
%   
%   \begin{itemize}
% 
% 
% 
% %\vspace*{0.5cm}
%   \item  ESSI Simulator System: continued development 
%         (US-NRC, US-DOE, CNSC, and INL, AREVA, Shimizu Corp.,  IAEA, ...)
% 
% \vspace*{0.2cm}
%   \item         Small    Modular  Reactor:  ESSI  modeling  
%   and  simulation,  3D
%   elastic-plastic soil models for professional practice (DOE, LLNL)
% 
% \vspace*{0.2cm}
%   \item Stochastic ESSI Modeling: uncertain source, path, 
%   site and SSI (NSF, US NRC, AREVA)
% 
% \vspace*{0.2cm}
%   \item ESSI of base isolated NPPs (US NRC, IAEA)
% 
% \vspace*{0.2cm}
%   \item  Verification and Validation: (US NRC, DOE, AREVA)
% 
% \vspace*{0.2cm}
%   \item Education (US NRC, AREVA, Shimizu Corp., etc.)
% 
% \end{itemize}
% 
% 
% \end{frame}
% %


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\begin{frame}
  \frametitle{Acknowledgement}
  
  \begin{itemize}


%  \item  High fidelity
%  modeling and simulations for performance assessment of infrastructure systems


\vspace*{0.1cm}
  \item Funding from and collaboration with the US-NRC,
  US-NSF,  US-DOE, CNSC, LLNL, INL, 
  AREVA NP GmbH, Shimizu Corp., and EDF is greatly appreciated,
  
\vspace*{0.5cm}
  \item  Collaborators, students:      
  Mr.  Abell,  Mr.  Jeong, Mr. Aldridge. Mr.   Kamranimoghadam, Mr. Karapiperis,
  Mr. Watanabe, Mr. Chao,
  Dr.  Tafazzoli,   Dr.  Pisan{\`o}, Dr. Martinelli,  
  Dr.  Preisig, Dr. Chang, 
  Prof. Sett (U. Bufallo), Prof. Taiebat (U. British Columbia), Prof. Yang (U. Alaska)

  
\end{itemize}


\end{frame}
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