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\title[ESSI Modeling and Simulation]
        {Earthquake Soil Structure Interaction \\
        (ESSI) \\
        Modeling and Simulation }


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

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%{ Professor, University of California, Davis\\
{ University of California, Davis\\
%  and\\ 
%  Faculty Scientist, Lawrence Berkeley National Laboratory, Berkeley }
  Lawrence Berkeley National Laboratory, Berkeley }
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{\small Caltrans Seminar \\
 December 2013}

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\section{Introduction}




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\subsection{Motivation}



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\begin{frame}
 \frametitle{Motivation}

\begin{itemize}
  


%\vspace*{0.3cm}
  \item Improving seismic design for infrastructure objects

\vspace*{0.3cm}
  \item  Use of high fidelity numerical models in analyzing seismic behavior
  of soil/rock-foundation-structure systems


\vspace*{0.3cm}
  \item      Accurate     following  of  the  flow  of  seismic  energy  in  the
  soil/rock-foundation-structure
  system

\vspace*{0.3cm}
  \item   Directing,   in   space   and   time,   seismic  energy  flow  in  the
  soil/rock-foundation-structure 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  the  Earthquake  with the   
  Soil/Rock, Foundation  and  Structure in time domain plays  major
  role in  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),
         we could  optimize soil-foundation-structure system 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*{0.2cm}
     \item {{\bf Validation} provides
   evidence that the correct model is solved.} Physics issue. 

\vspace*{0.2cm}
   \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*{0.2cm}
%   \item Goal: predictive capabilities 
%   with {\bf low Kolmogorov Complexity}



% %% % \vspace*{0.2cm}
% %   \item {\bf The Finite Element 
% %   Interpreter  \FEI{}} might be one such 
% %   predictive tool (application program)
   


\end{itemize}


\end{frame}






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\subsection{Flow of Seismic Energy}



%- 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Seismic Energy Input for the SSI System}

   \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 Dissipation for  the SSI System}
% \frametitle{Seismic Energy Dissipation for 
%             \underline{Soil}-Foundation-Structure Systems}


\begin{itemize}


\vspace*{0.2cm}
     \item Mechanical dissipation outside of SSI domain:
       \begin{itemize}
         \item reflected wave radiation
         \item SSI system oscillation radiation
       \end{itemize}
\vspace*{0.2cm}
     \item Mechanical dissipation/conversion inside 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*{0.2cm}
%   \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}


   \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 can be made non-dissipative for
     elastic system $\alpha=0.0, \beta = 0.25 ; \gamma  = 0.5,$

     \item Or dissipative (for elastic) for higher frequency modes: 
%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}

\end{frame}

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\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}


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






























% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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 Modeling}








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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 Surface waves: Rayleigh, Love waves, etc.
\vspace*{0.1cm}
  \item Surface waves carry most seismic energy
\vspace*{0.1cm}
     \item Lack of correlation (incoherence)
\vspace*{0.1cm}
     \item Inclined waves
\vspace*{0.1cm}
     \item 3D waves
%\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}



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


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Free Field, Inclined, 3D Body and Surface Waves}

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

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

   \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*{-4.6cm}
\begin{flushright}
\includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/wave_propagation/figs/FaultSlipModel2km.pdf}
\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}

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


%  
























%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Model Verification: 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


\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}


 







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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Realistic 3D Seismic Motions}





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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Northridge 3D FE Model}
\vspace*{-3.5cm}
\begin{figure}
% \includegraphics[scale=0.35]{Present06_figs/3DModel.pdf}
 \includegraphics[scale=0.35]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Jose_fix/presentation/Present06_figs/3DModel.pdf}
\end{figure}
\end{frame}


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{FE Model}
% \begin{figure}
% % \includegraphics[scale=0.4]{Present06_figs/3DModelxzPlane.pdf}
%  \includegraphics[scale=0.4]{Present06_figs/3DModelxzPlane.pdf}
% \end{figure}
% \end{frame}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Northridge 3D Model Properties}
\begin{itemize}
 \item Model Properties
 \begin{itemize}
  \item 90 m $\times$ 90 m $\times$ 90 m dimension
  \item Vs1 = 300 m/s, Vs2 = 400 m/s
  \item Poisson's ratio1 = 0.25, Poisson's ratio2 = 0.25
%  \item Density1 = 940 kg/m$^3$, Density2 = 990 kg/m$^3$
 \end{itemize}
 \vspace{2mm}
 \item Input Wave Properties
 \begin{itemize}
  \item Northridge earthquake source properties
  \item Generated using fk program
 \end{itemize}
\end{itemize}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{FEM Results, EW Component}
\vspace*{-3.5cm}
\begin{figure}
% \includegraphics[scale=0.5]{Present06_figs/90m_Northridge_EW.pdf}
 \includegraphics[scale=0.5]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Jose_fix/presentation/Present06_figs/90m_Northridge_EW.pdf}
\end{figure}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{FEM Results, NS Component}
\vspace*{-3.5cm}
\begin{figure}
% \includegraphics[scale=0.5]{Present06_figs/90m_Northridge_NS.pdf}
 \includegraphics[scale=0.5]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Jose_fix/presentation/Present06_figs/90m_Northridge_NS.pdf}
\end{figure}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{FEM Results, UD Component}
\vspace*{-3.5cm}
\begin{figure}
% \includegraphics[scale=0.5]{Present06_figs/90m_Northridge_UD.pdf}
 \includegraphics[scale=0.5]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Jose_fix/presentation/Present06_figs/90m_Northridge_UD.pdf}
\end{figure}
\end{frame}












%


%  
%  
%  

















%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \subsection{Material Modeling, $G/G_{max}$ and Damping Curves}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Modulus Reduction ($G/G_{max}$ ) and Damping Curves}
%  
%  \begin{itemize}
%  
%  %\vspace*{5mm}
%  \item Idriss and Seed 1970
%  
%  \vspace*{3mm}
%  \item Much work gone into development of curves for different types of soils
%  
%  \vspace*{3mm}
%  \item  However,  it is still a linear elastic (secant) approach with some energy
%  dissipation taken into account
%  
%  \vspace*{3mm}
%  \item   Not good for any case where soil volume change makes a difference or where 2D
%  or 3D behavior is important
%  
%     
%  \end{itemize}
%  \end{frame}
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{$G/G_{max}$ and Damping Curves}
%  
%  \vspace*{-5mm}
%  \begin{figure}[!htb]
%   \centering
%   \includegraphics[width=11.5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Staff_Capacity_Building_28Jan2013/Figure_Stiffness_Damping.pdf}
%  \end{figure}
%  
%  
%  \end{frame}
%  
%  
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %  \frametitle{Commonly used $G/G_{max}$ and Damping Curves: \\
%  %  Vu{\v c}eti{\' c} and  Dobry (1991)}
%  % 
%  % \begin{figure}[!hbpt]
%  % \begin{center}
%  % % 
%  % \includegraphics[width=5truecm]{/home/jeremic/tex/works/Conferences/2013/NRC_Staff_Capacity_Building_28Jan2013/Vucetic_and_Dobry_01.jpeg}
%  % \hspace*{5mm}
%  % \includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Conferences/2013/NRC_Staff_Capacity_Building_28Jan2013/Vucetic_and_Dobry_02.jpeg}
%  % %
%  % \end{center}
%  % \end{figure}                                                          
%  % 
%  % 
%  % 
%  % \end{frame}
%  
%  
%  
%  
%  
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Pisan{\`o} Elastic Plastic Material Model}
%  
%  \begin{itemize}
%  
%    \item    Split    stress    into    frictional    and    viscous    components
%    $\sigma_{ij}=\sigma_{ij}^{f} + \sigma_{ij}^{v}$
%  
%    \item Elasticity: classic, linear (can be nonlinear)
%  
%    \item  Yield  surface, Drucker-Prager cone,  collapsed  (limit  analysis,  vanishing elastic
%    regions) to cylinder (von Mises), with conical bounding surface
%  
%    \item   Plastic   flow  and  rotational  kinematic  hardening,  borrowed  from
%    Manzari-Dafalias model (1997)
%  
%    \item Yield (loading-unloading) condition established using stress projection
%    
%    \item Special (unique) developments of a stiffness tensor (used for FEM)
%  
%  
%  
%     
%  \end{itemize}
%  
%  \end{frame}
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Pisan{\`o} Model: Triaxial  and Pure Shear Response}
%  
%  
%  \begin{figure}  [!htb]
%   \centering
%  \includegraphics [width=5.5cm] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res1a.pdf}
%  \includegraphics [width=5.8cm] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res1b.pdf}
%  \\
%  \includegraphics [width=5.5cm] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res2a.pdf}
%  \includegraphics [width=5.5cm] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res2b.pdf}
%   \label{fig:res1}
%  \end{figure}
%  
%  
%      
%  
%  \end{frame}
%  
%  
%  
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % \begin{frame}
%  %  \frametitle{Pisan{\`o} Model: Calibration for $G/G_{max}$ and Damping}
%  % 
%  % 
%  %   
%  %      
%  % \begin{figure}  [!htb]
%  %  \centering
%  % \includegraphics [width=0.8\textwidth] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res3.pdf}
%  %  \hfill
%  %  \caption{Comparison  between  experimental and simulated $G/G_{max}$
%  %  and  damping  curves ($p_0$=100 kPa, T=2$\pi$ s, $\zeta$ = 0.003, $G_{max}$ = 4
%  %  MPa, $\nu$=0.25, $M$=1.2, $k_d$=$\xi$=0, $h$=$G$/(112$p_0$), $m$=1.38)}
%  %  \label{fig:res3}
%  % \end{figure}
%  %     
%  % 
%  % \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Pisan{\`o} Model: Calibration for $G/G_{max}$ and Damping}
%  
%          
%  \begin{figure}  [!htb]
%   \centering
%  \includegraphics [width=0.8\textwidth] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res4.pdf}
%   \hfill
%   \caption{Comparison  between  experimental and simulated $G/G_{max}$
%   and  damping  curves ($p_0$=100 kPa, T=2$\pi$ s, $\zeta$ = 0.003, $G_{max}$ = 4
%   MPa, $\nu$=0.25, $M$=1.2, $k_d$=$\xi$=0, $h$=$G_{max}$/(15$p_0$), $m$=1)}
%   \label{fig:res4}
%  \end{figure}
%  
%     
%  
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % \begin{frame}
%  %  \frametitle{Pisan{\`o} Model: Variation in Confining Pressure}
%  % 
%  % 
%  %  
%  % \begin{figure}  [!htb]
%  %  \centering
%  % \includegraphics [width=0.8\textwidth] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res7.pdf}
%  %  \hfill
%  %  \caption{Simulated  $G/G_{max}$  and  damping  curves  at  varying
%  %  confining  pressure  (T=2$\pi$  s,  $G_{max}$  =  4  MPa,  $\nu$=0.25, $M$=1.2,
%  %  $k_d$=$\xi$=0, $h$=$G$/(15$p_0$), $m$=1)}
%  %  \label{fig:res5}
%  % \end{figure}
%  % 
%  % 
%  %     
%  % 
%  % \end{frame}
%  % 
%  %%%%%%%%%%%%%%%%%%%%
%  
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % \begin{frame}
%  %  \frametitle{Pisan{\`o} Model: Variation in Hardening Parameter $h$}
%  % 
%  % 
%  %  
%  % \begin{figure}  [!htb]
%  %  \centering
%  % \includegraphics [width=0.8\textwidth] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res5.pdf}
%  %  \hfill
%  %  \caption{Simulated  $G/G_{max}$ and  damping  curves  at  varying h
%  %  ($p_0$=100   kPa,  $T$=2$\pi$  s,  $G_{max}$  =  4  MPa,  $\nu$=0.25,  $M$=1.2,
%  %  $k_d$=$\xi$=0, $m$=1)}
%  %  \label{fig:res6}
%  % \end{figure}
%  % 
%  % 
%  %     
%  % 
%  % \end{frame}
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % \begin{frame}
%  %  \frametitle{Pisan{\`o} Model: Variation in Hardening Parameter $m$}
%  % 
%  % 
%  %          
%  % \begin{figure}  [!htb]
%  %  \centering
%  % \includegraphics [width=0.8\textwidth] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res6.pdf}
%  %  \hfill
%  %  \caption{Simulated  $G/G_{max}$  and  damping  curves  at  varying m
%  %  ($p_0$=100   kPa,  $T$=2$\pi$  s,  $G_{max}$  =  4  MPa,  $\nu$=0.25,  $M$=1.2,
%  %  $k_d$=$\xi$=0, $h$=$G_{max}$/(15$p_0$))}
%  %  \label{fig:res7}
%  % \end{figure}
%  % 
%  % 
%  %     
%  % 
%  % \end{frame}
%  % 
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % \begin{frame}
%  %  \frametitle{Pisan{\`o} Model: Variation in Viscous Damping}
%  % 
%  % 
%  %          
%  %     
%  % \begin{figure}  [!htb]
%  %  \centering
%  % \includegraphics [width=0.4\textwidth] {/home/jeremic/tex/works/Papers/2012/Bounding_Surface_Frictional_Model/Figures/res9.pdf}
%  % % \hfill
%  %  \caption{Damping   curves   simulated  at  varying  $\zeta_0$  ($p_0$=100  kPa,
%  %  $T$=2$\pi$   s,   $G_{max}$   =  4  MPa,  $\nu$=0.25,  $M$=1.2,  $k_d$=$\xi$=0,
%  %  $h$=$G_{max}$/(15$p_0$), $m$=1)}
%  %  \label{fig:res9}
%  % \end{figure}
%  % 
%  % 
%  %     
%  % 
%  % \end{frame}
%  % 
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % 
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Soil Volume Response}
%  
%  \begin{itemize}
%    \item Soil behavior is very much a function of volumetric response
%  
%    \item Dilative soils: increase  volume due to shearing
%    \item Compressive soils: decrease  volume due to shearing
%  
%  
%    \item Modulus reduction and damping curves do not provide volumetric data
%  
%    \item Soil volume change will affect response due to volume constraints
%  
%  \end{itemize}
%  
%      
%  
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{No Volume Change Soil (at Critical State?)}
%  
%  \begin{figure}[!h]
%  \begin{center}
%    \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/FedericoPisano/Pisano_model/Issue_of_dilatancy/sine1Hz-4.pdf}
%  \end{center}
%  \end{figure}
%  
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Compressive Soil}
%  
%  \begin{figure}[!h]
%  \begin{center}
%    \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/FedericoPisano/Pisano_model/Issue_of_dilatancy/sine1Hz_comp-4.pdf}
%  \end{center}
%  \end{figure}
%  
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Dilative Soil}
%  
%  \begin{figure}[!h]
%  \begin{center}
%    \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/FedericoPisano/Pisano_model/Issue_of_dilatancy/sine1Hz_dil-4.pdf}
%  \end{center}
%  \end{figure}
%  
%  \end{frame}
%  
%  % % 
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % \begin{frame}
%  %  \frametitle{Northridge, No Volume Change Soil}
%  % 
%  % \vspace*{-0.6cm}
%  % \begin{figure}[!h]
%  % \begin{center}
%  %   \includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/FedericoPisano/Pisano_model/Issue_of_dilatancy/Northridge1-2.pdf}
%  % \end{center}
%  % \end{figure}
%  % 
%  % \end{frame}
%  % 
%  % 
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % \begin{frame}
%  %  \frametitle{Northridge, Dilatant Soil}
%  % 
%  % \vspace*{-0.6cm}
%  % \begin{figure}[!h]
%  % \begin{center}
%  %   \includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/FedericoPisano/Pisano_model/Issue_of_dilatancy/Northridge1-3.pdf}
%  % \end{center}
%  % \end{figure}
%  % 
%  % \end{frame}
%  % 
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Northridge, No Volume Change and Dilative Soils}
%  
%  \vspace*{-0.6cm}
%  \begin{figure}[!h]
%  \begin{center}
%    \includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/FedericoPisano/Pisano_model/Issue_of_dilatancy/Northridge1-4.pdf}
%  \end{center}
%  \end{figure}
%  
%  \end{frame}
%  % % 
%  
%  
%  
%  
%  
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{ESSI System and Examples}
%




\subsection{ESSI System}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \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 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 for infrastructure objects 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: Finite Elements}


%\vspace*{-3mm} 
   \begin{itemize}
%\vspace*{-1.5mm} 
     \item Dry/single phase solids (8, 20, 27 8-27 node bricks), 
%\vspace*{-1.5mm} 
     \item Saturated/two phase solids (8 and 27 node bricks, liquefaction modeling),
%\vspace*{-1.5mm} 
     \item Shell with 6DOF per node, 
%\vspace*{-1.5mm} 
     \item Beams (six and variable DOFs per node), 
%\vspace*{-1.5mm} 
     \item Truss, 
%\vspace*{-1.5mm} 
     \item   Contacts      (dry   or   saturated   soil/rock   -  concrete,  gap
     opening-closing, frictional slip),
%\vspace*{-1.5mm} 
     \item Base isolators (elastomeric, frictional pendulum)
   \end{itemize}

\end{frame}

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

\begin{frame}
\frametitle{ESSI Simulator Program: Material Models and Seismic Input}

\begin{itemize}

\item Material Models
%\vspace*{-2mm} 
   \begin{itemize}
%\vspace*{-1.5mm} 
      \item Linear and nonlinear, isotropic and anisotropic  elastic
%\vspace*{-1.5mm} 
       \item  Elastic-Plastic  (von Mises, Drucker Prager, Rounded Mohr-Coulomb,
              Leon      Parabolic,      Cam-Clay,      SaniSand,     SaniClay,  
              Pisan{\` o}...).  All  elastic-plastic  models can be used as perfectly
              plastic,  isotropic  hardening/softening  and  kinematic hardening
              models.
   \end{itemize}

%\vspace*{-4mm} 
 \item    Analytic    input    of  seismic motions (both body (P, S) and surface
 (Rayleigh, Love, etc., waves), including analytic radiation damping.

\end{itemize}

\end{frame}

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

\begin{frame}
\frametitle{ESSI Simulator Program: V\&V, Parallel}

\begin{itemize}

%\vspace*{-2mm} 
\item Verification and Validation:
  each element, model, algorithm and procedure has been extensively verified
  (math  issue)  and  validated  (physics issue). Verification and Validation is
  documented in detail in ESSI Notes.

%%\vspace*{-2mm} 
%\item  Documentation: available in great detail through ESSI Notes, consisting
%of four parts: Theory/Formulation Background, Software and Hardware description,
%Verification and Validation, Examples and Case Studies.

%\vspace*{-2mm} 
\item High Performance Parallel Computing:
  both  parallel  and  sequential  version available, however, for high fidelity
  modeling,  parallel is really the only option. Parallel ESSI Simulator runs on
  clusters  of  PCs  and  on  large  supercomputers (Distributed Memory Parallel
  machines,  all  top  national  supercomputers).  
%  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}

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

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


   \begin{itemize}
%\vspace*{-2.5mm} 
     \item   Constitutive:   Euler-Lagrange   form   of  Fokker-Planck  (forward
     Kolmogorov) equation for probabilistic elasto-plasticity (PEP)
%\vspace*{-1.5mm} 
     \item Spatial: stochastic elastic plastic finite element method (SEPFEM)
   \end{itemize}


  Uncertainties  in  material  and  load  are  analytically  taken into account.
  Resulting  displacements,  stress  and  strain  are  obtained as very accurate
  (second  order accurate for stress) Probability Density Functions.
  PEP  and  SEPFEM  are  not  based  on a Monte Carlo method, rather they expand
  uncertain  input  variables  and  uncertain degrees of freedom (unknowns) into
  spectral  probabilistic  spaces  and  solve  for  PDFs  of
  resulting displacement, stress and strain in a single run.


\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 Solids (dry, saturated), beams, shells, contacts, elastic or elastic-plastic
% 
% \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 collaborators, expert users
%     
% %\item Sources will be available through
% %{\bf 
% %\url{http://nrc-essi-simulator.info}}
% 
% 
% \end{itemize}
% 
% \end{frame}
% 
% 
% 
% 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \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, UCB, CU, 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) and UMFPACK (UF, 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 supercomputer
% %\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 NPP 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  Nuclear  Power  Plant  Earthquake 
%     Soil/Rock   Structure   Interaction   Problems   (ESSI  with  3D,  inclined,
%     uncorrelated seismic waves, ESSI with foundation slip, Isolators)
% 
%   \end{itemize}
% 
% 
% \end{itemize}
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%



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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Illustrative Examples}
%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Few Illustrative Examples}

\begin{itemize}
\item Slip between foundation slab and the soil/rock
underneath

\vspace*{0.2cm}
\item Passive seismic isolation by liquefaction

\vspace*{0.2cm}
\item Structural response in liquefied soil


\end{itemize}

\end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Nuclear Power Plant with Base Slip}

\begin{itemize}

  \item Low friction zone between \\
        concrete foundation and soil/rock

  \item Inclined, 3D, body and surface, \\
        seismic wave field (wavelets: \\
        Ricker, Ormsby; real seismic, etc.)


\end{itemize}



\vspace*{-4.0cm}
\begin{figure}[!h]
\begin{flushright}
\includegraphics[width=2.50cm]{/home/jeremic/tex/works/Conferences/2011/NRC_LBNL_Review_Panel_Sept2011/2D_faul_slip_model_top_200m.pdf}
%{\includegraphics[width=4.0cm]{/home/jeremic/tex/works/Conferences/2011/NRC_LBNL_Review_Panel_Feb2011/Case_study_model/visit0002.jpeg}}
\end{flushright}
\end{figure}

\vspace*{-0.9cm}
\begin{figure}[!h]
\begin{flushright}
{\includegraphics[width=4.0cm]{/home/jeremic/tex/works/Conferences/2011/NRC_LBNL_Review_Panel_Feb2011/Case_study_model/visit0002.jpeg}}
\end{flushright}
\end{figure}




\vspace*{-3.6cm}
\begin{figure}[H]
\begin{center}
%\vspace*{-0.5cm}
%\includegraphics[width=2.0cm]{/home/jeremic/tex/works/Conferences/2011/NRC_LBNL_Review_Panel_Sept2011/2D_faul_slip_model_top_200m.pdf}
%\hspace*{0.5cm}
%\vspace*{0.2cm}
\includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FreeFieldInclinedMotionModels/FaultSlip_Ormsby/figs/surface_200m/middle_acceleration_x.pdf}
\hspace*{-0.5cm}
\includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FreeFieldInclinedMotionModels/FaultSlip_Ormsby/figs/surface_200m/middle_acceleration_z.pdf}
%
\vspace*{-0.5cm} 
\hspace*{0.8cm} 
\mbox{horizontal}
\hspace*{4cm} 
\mbox{vertical}
\hspace*{3cm} 
\end{center}
\end{figure}
\vspace*{-1.0cm} 
% 
%  %\vspace*{-3.5cm}
%  \begin{figure}[H]
%  \begin{center}
%  \includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FreeFieldInclinedMotionModels/FaultSlip_Ormsby/figs/surface_200m/middle_acceleration_x.pdf}
%  \hspace*{-0.5cm}
%  \includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FreeFieldInclinedMotionModels/FaultSlip_Ormsby/figs/surface_200m/middle_acceleration_z.pdf}
%  \end{center}
%  \end{figure}
%  
%  %\vspace*{-3.5cm}
%  \begin{figure}[H]
%  \begin{center}
%  \includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FaultModel_7seconds/xz_TimeHistory/5000_5000_x_acceleration.pdf}
%  \hspace*{-0.5cm}
%  \includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/FaultModel_7seconds/xz_TimeHistory/5000_5000_z_acceleration.pdf}
%  \end{center}
%  \end{figure}
%  
%  \vspace*{-0.90cm}
%  {horizontal accelerations   \hfill vertical accelerations}
%  
%  
%  


\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Acc. Response for a Full 3D (at $45^\circ$) Ricker Wavelet}

\begin{figure}[H]
\begin{center}
\begin{tabular}{rr} 
%\hline 
\mbox{\tiny top X}\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/91_97/top_structure_x_acceleration.pdf}
&
\mbox{\tiny top Z}\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/91_97/top_structure_z_acceleration.pdf}
\\
\mbox{\tiny bottom X}\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/91_97/bottom_structure_x_acceleration.pdf}
&
\mbox{\tiny bottom Z}\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/91_97/bottom_structure_z_acceleration.pdf}
\end{tabular}
%\caption{Comparison of acceleration time histories of the structure between 
%slipping and no-slipping models for Ricker wave}
\label{fig:3d_ricker_acc_1000}
\end{center}
\end{figure}



\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{FFT Response for a Full 3D (at $45^\circ$) Ricker Wavelet}

\begin{figure}[H]
\begin{center}
\begin{tabular}{rr} 
\mbox{\tiny top X}\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/91_97/top_structure_x_acceleration_FFT.pdf}
&
\mbox{\tiny top Z}\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/91_97/top_structure_z_acceleration_FFT.pdf}
\\
\mbox{\tiny bottom X}\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/91_97/bottom_structure_x_acceleration_FFT.pdf}
&
\mbox{\tiny bottom Z}\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/91_97/bottom_structure_z_acceleration_FFT.pdf}
\end{tabular}
%\caption{Comparison of FFT of the acceleration of the structure between 
%slipping and no-slipping models for Ricker wave}
\label{fig:3d_ricker_fft_1000}
\end{center}
\end{figure}


\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Gaping Response ($45^\circ$ Ricker Wavelet)}

\vspace*{-0.1cm}
\begin{tiny}
\begin{figure}[H]
\begin{center}
\begin{tabular}{ccc} 
%\hline 
$4.5s$
&
$4.6s$
&
$4.7s$
\\
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/gap450.pdf}
&
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/gap460.pdf}
&
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/gap470.pdf}
\\
$4.8s$
&
$4.9s$
&
$5.0s$
\\
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/gap480.pdf}
&
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/gap490.pdf}
&
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/gap500.pdf}
\\
$5.1s$
&
$5.2s$
&
$5.3s$
\\
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/gap510.pdf}
&
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/gap520.pdf}
&
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/gap530.pdf}
%\\
%
%\hline
\end{tabular}
%\caption{Distribution of gap openings along the contact interface for Ricker wave
%(gray scale given in meters)}
\label{fig:3d_ricker1000_gap_9}
\end{center}
\end{figure}
\end{tiny}



\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Slipping Response and Energy Dissipated ($45^\circ$ Ricker)}





\vspace*{-0.1cm}
\begin{tiny}
\begin{figure}[H]
\begin{flushleft}
\hspace*{-1cm}
\begin{tabular}{ccc} 
%\hline 
$4.5s$
&
$4.6s$
&
$4.7s$
\\
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/slide450.pdf}
&
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/slide460.pdf}
&
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/slide470.pdf}
\\
$4.8s$
&
$4.9s$
&
$5.0s$
\\
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/slide480.pdf}
&
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/slide490.pdf}
&
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/slide500.pdf}
\\
$5.1s$
&
$5.2s$
&
$5.3s$
\\
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/slide510.pdf}
&
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/slide520.pdf}
&
\includegraphics[width=2.3truecm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/Gap_Slide_Magnitude_91_9pieces/slide530.pdf}
%\\
%
%\hline
\end{tabular}
%\caption{Distribution of sliding along the contact interface for Ricker wave
%(gray scale given in meters)}
\label{fig:3d_ricker1000_slide_9}
\end{flushleft}
\end{figure}
\end{tiny}

\vspace*{-5cm}
\begin{figure}[!H]
\begin{flushright}
\includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/NimaTafazzoli/SSI_Contact_Element_01_13/figs/energy_sliding_92/energy_time.pdf}
\hspace*{-1cm}
\end{flushright}
\end{figure}



\end{frame}












%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Liquefaction}
%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
  \frametitle{Passive Base Isolation in Uniform and Layered Soils}
  



\vspace*{-0.5cm}
\begin{figure}[!htbp] 
\begin{flushleft}
\includegraphics[width=5cm,angle=90]{/home/jeremic/tex/works/Papers/2009/SeismicIsolationLiquefaction/Mesh-Isolation.pdf}
\\
\includegraphics[width=4cm]{/home/jeremic/tex/works/Conferences/2009/CompDyn/Present/StackElements-Compare.pdf} 
\end{flushleft}
\end{figure}
\vspace*{-1cm}


\vspace*{-8cm}
%\hspace*{-0.5cm}
\begin{figure}[!htbp] 
\begin{flushright}
\includegraphics[width=6cm]{/home/jeremic/tex/works/Papers/2009/SeismicIsolationLiquefaction/time-history-acc.jpg} \\
%\\
%\includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/GuanzhouJie/thesis/Verzija_Februar/Images/LongMotion/MomentBent1Pile2.pdf}
%\caption{\label{BridgeSFSI01}  FEM  model  for  seismic response of a three bend
%bridge.}
\end{flushright}
\end{figure}
\vspace*{-1cm}



\end{frame}
%



     
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Pile in Liquefiable Sloping Ground}






 

\vspace*{-0.8cm}
\begin{figure}[!htbp]
\begin{flushright}
%  \includegraphics[width=6cm]{/home/jeremic/tex/works/Conferences/2007/PEERAnnualMeeting/Liquefaction/PileBridgeModel01.jpg} \\
  \includegraphics[width=3.3cm]{/home/jeremic/tex/works/Conferences/2007/PEERAnnualMeeting/Liquefaction/PileBridgeModel02.jpg} 
%  \includegraphics[width=4cm]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/GMklot02.pdf}
\end{flushright}
\end{figure}





%
\vspace*{-0.4cm}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[!htbp] 
\begin{center}
\hspace*{-0.5cm}
\begin{tabular}{lllllll} 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\includegraphics[width=0.03\textwidth,angle=0]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/Model_IV.jpg}
&
\includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_4_T002.jpg}
&
\includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_4_T005.jpg}
&
\includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_4_T010.jpg}
&
\includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_4_T015.jpg}
&
\includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_4_T020.jpg}
&
\includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_4_T080.jpg}
\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\includegraphics[width=0.03\textwidth,angle=0]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/Model_V.jpg}
&
\includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_5_T002.jpg}
&
\includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_5_T005.jpg}
&
\includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_5_T010.jpg}
&
\includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_5_T015.jpg}
&
\includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_5_T020.jpg}
&
\includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_5_T080.jpg}
\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\includegraphics[width=0.035\textwidth,angle=0]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/Model_VI.jpg}
&
\includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_6_T002.jpg}
&
\includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_6_T005.jpg}
&
\includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_6_T010.jpg}
&
\includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_6_T015.jpg}
&
\includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_6_T020.jpg}
&
\includegraphics[height=0.09\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_6_T080.jpg}
\\
t=
&
2~sec
&
5~sec 
&
10~sec
&
15~sec
&
20~sec
&
80~sec
\end{tabular}
\includegraphics[width=7cm,height=0.45cm]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/GMklot02.pdf}\hspace*{1cm}
\\
\vspace*{-0.5cm}
\includegraphics[angle=-90,width=0.4\textwidth]{/home/jeremic/tex/works/Papers/2008/Pile_in_liquefied_soil_upU/NewFiga/Snap_scale.pdf}
\end{center}
\end{figure}
%


\end{frame}

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

% 
% \vspace*{-0.5cm}
% \begin{figure}[!hbpt]
% \begin{center}
% %\hspace*{-0.5cm}
% \includegraphics[width=6cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/03_cropped.jpg}
% %\hspace*{-0.5cm}
% %\vspace*{-0.5cm}
% \includegraphics[width=3cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/02_cropped.jpg}
% %\hspace*{-0.5cm}
% %\vspace*{-1.5cm}
% \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 3D, Inclined, \\ Body and Surface  seismic waves
%\vspace*{-0.1cm}
 \item Uncorrelated (incoherent) motions
%\vspace*{-0.1cm}
 \item Foundation slip -- gap 
%\vspace*{-0.1cm}
 \item Isolators, dissipators
%\vspace*{-0.1cm}
 \item Saturated dense vs loose soil with buoyant forces
%\vspace*{-0.1cm}
 \item Piles and pile groups 

\end{itemize}

\end{frame}



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\section{Summary}


\subsection*{Summary}









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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 infrastructure objects

\vspace*{0.1cm}
  \item           Improve {\bf 
%  risk informed 
%  decision making}
design} ({\bf safety} and {\bf economy}) 
   through  
  {\bf high fidelity}, 
%  {\bf  Deterministic}  and  
%  {\bf  Stochastic Elastic-Plastic  Finite Element} 
  modeling and simulation

\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*{0.1cm}
  \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 IAEA,  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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%  \section{Probabilistic Modeling}
%  %
%  
%  
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%  \subsection{Probabilistic Modeling}
%  
%  
%  
%   
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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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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%  \end{frame}
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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{Types of Uncertainties}
%  
%   
%  
%  \begin{itemize}
%  
%  
%  
%  \item Aleatory uncertainty - inherent variation of physical system 
%  %
%      \begin{itemize}
%  %
%        \item Can not be reduced
%  %
%        \item Has highly developed mathematical tools 
%  %
%      \end{itemize}
%  %
%  \vspace*{0.2cm}
%  \item Epistemic uncertainty - due to lack of knowledge
%  
%     \begin{itemize}
%  
%       \item Can be reduced by \\
%             collecting more data
%  
%       \item Mathematical tools \\
%             are not well developed 
%  
%       \item trade-off with \\
%             aleatory uncertainty
%  
%     \end{itemize}
%  
%  
%  %
%  \vspace*{-3.2cm}
%  \begin{figure}[!hbpt]
%  \begin{flushright}
%  \includegraphics[height=5cm,angle=-90]{/home/jeremic/tex/works/Conferences/2007/USC_seminar/Present/uncertain03.pdf}
%  \end{flushright}
%  \end{figure}
%  
%  %\vspace*{1.0cm}
%  
%  \item  Ergodicity  (exchanging ensemble averages for time average) assumed to be
%  valid
%  
%  
%  \end{itemize}
%  
%   
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%  \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}
%  
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%  % \begin{frame} 
%  % 
%  % \frametitle{Uncertainty Propagation through Constitutive Eq.}
%  % 
%  % % 
%  % 
%  % \begin{itemize}
%  % 
%  %  
%  % 
%  % 
%  % \item Incremental el--pl constitutive equation  
%  %      $\Delta \sigma_{ij} = E_{ijkl} \Delta \epsilon_{kl}$
%  % 
%  %  
%  %   
%  % %\begin{normalsize}
%  % 
%  % %    
%  % %    \begin{equation}
%  % %    \nonumber
%  % %    \frac{d\sigma_{ij}}{dt} = E_{ijkl} \frac{d\epsilon_{kl}}{dt}
%  % %    \end{equation}
%  %     
%  %     
%  %     \begin{eqnarray}
%  %     \nonumber
%  %      E_{ijkl} = \left\{\begin{array}{ll}
%  % %
%  %      E^{el}_{ijkl}
%  % %
%  % %
%  %         \;\;\; & \mbox{\large{~for elastic}} \\
%  % %
%  %            \\
%  % %
%  %            E^{el}_{ijkl}
%  %            -
%  %            \frac{\displaystyle  E^{el}_{ijmn} m_{mn} \; n_{pq} E^{el}_{pqkl}}
%  %            {\displaystyle n_{rs} E^{el}_{rstu} m_{tu} - \xi_* h_*}
%  % 
%  %            \;\;\; & \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 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}
%  % 
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % 
%  % 
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % \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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%  
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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}
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \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}
%  % 
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  % - +
%  % - + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % - + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % - + 
%  % - + \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}
%  % - + 
%  % - + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \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}
%  % \begin{center}
%  % \includegraphics[height=2.0cm]{Chapter9_BaseDisplacement.jpg} 
%  % \end{center}
%  
%  \end{itemize}
%  \end{frame}
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  %-- 
%  %--  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %--  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %--  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %--  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %--  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %--  
%  %--  \begin{frame}
%  %--  
%  %--  
%  %--  \frametitle{Seismic Wave Propagation through Stochastic Soil}
%  %--  
%  %--  
%  %--  
%  %--  \begin{figure}
%  %--  \begin{center}
%  %--  \hspace*{-0.75cm}
%  %--  \includegraphics[width=9.0cm]{/home/jeremic/tex/works/Thesis/KallolSett/Dissertation/figures/Chapter9Plots/Chapter9_ElasticPlasticResponse-New.pdf}
%  %--  %\includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2007/USC_seminar/Application_figs/Mean_and_SDElasticPlastic_ps.pdf}
%  %--  \end{center}
%  %--  \end{figure}
%  %--  
%  %--  Mean$\pm$ Standard Deviation
%  %--  
%  %--  
%  %--  
%  %--  %\begin{flushleft}
%  %--  %\includegraphics[height=5.0cm]{PEER2007_3.jpg}
%  %--  %\end{flushleft}
%  %--  
%  %--  % \hspace*{-1.0cm} \noindent Statistics of Top Node Displacement:
%  %--  % 
%  %--  % \vspace*{-0.5truecm}
%  %--  % 
%  %--  % \begin{figure}
%  %--  % \begin{flushleft}
%  %--  % \hspace*{-1.0cm}
%  %--  % \includegraphics[width=4.0cm]{/home/kallol/publication/2007/Presentation/PhDExitSeminar/Chapter9_ElasticPlasticResponse_Mean-New.jpg}
%  %--  % \hspace*{-0.1cm}
%  %--  % \includegraphics[width=4.0cm]{/home/kallol/publication/2007/Presentation/PhDExitSeminar/Chapter9_ElasticPlasticResponse_SD-New.jpg}
%  %--  % \end{flushleft}
%  %--  % \end{figure}
%  %--  % \vspace*{-0.5truecm}
%  %--  % \hspace*{-1.0cm} \tiny{~~~~~~~~~~~~~~~~~~~~~~~~~~~~Mean~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Standard Deviation}
%  %--  % 
%  %--  % \vspace*{-0.3truecm}
%  %--  % 
%  %--  % \begin{figure}
%  %--  % \begin{flushleft}
%  %--  % \hspace*{-0.75cm}
%  %--  % \includegraphics[width=4.0cm]{/home/kallol/publication/2007/Presentation/PhDExitSeminar/Chapter9_ElasticPlasticResponse-New.jpg}
%  %--  % \hspace*{0.4cm}
%  %--  % \includegraphics[width=4.0cm]{/home/kallol/publication/2007/Presentation/PhDExitSeminar/Chapter9_ElasticPlasticResponse_COV-New.jpg}
%  %--  % \end{flushleft}
%  %--  % \end{figure}
%  %--  % \vspace*{-0.3truecm}
%  %--  % \hspace*{-0.5cm} \tiny{~~~~~~~Mean$\pm$ Standard Deviation~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~COV}
%  %--  % 
%  %--  % 
%  %--  % \vspace*{-6.0cm}
%  %--  % \begin{flushright}
%  %--  % \includegraphics[height=4.5cm]{/home/kallol/publication/2007/Presentation/PhDExitSeminar/Chapter9_ElasticPlasticResponse_PDF-New-Edited.jpg} \hspace*{-1.0cm}
%  %--  % \end{flushright}
%  %--  % 
%  %--  \end{frame}
%  %--  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \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}
%  
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  \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}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  \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}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  \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}
%  
%  % 
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % 
%  % 
%  % \begin{frame}
%  % 
%  % 
%  % \frametitle{Probability of Exceedance of $20$cm}
%  % 
%  % 
%  % 
%  % \begin{figure}
%  % \begin{center}
%  % %\hspace*{-0.75cm}                                                                                               
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%  %\hspace*{-0.75cm}                                                                                               
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