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%Methods, Computation Platform, and Case Studies for 
%Time-Domain Soil-Structures-Interaction Modeling and 
%Simulation Incorporating Complex Seismic Loads



\title[1D, 2D, and 3D, ESSI]
{Amplification of Seismic Input due to \\
 1D, 2D and 3D effects, and their \\
 Importance for NPP Structures}


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

%\author[Author, Another] % (optional, use only with lots of authors)
%{F.~Author\inst{1} \and S.~Another\inst{2}}
% - Give the names in the same order as the appear in the paper.
% - Use the \inst{?} command only if the authors have different
%   affiliation.
\pgfdeclareimage[height=0.25cm]{university-logo}{/home/jeremic/BG/amblemi/ucdavis_logo_blue_sm}
\pgfdeclareimage[height=0.9cm]{lbnl-logo}{/home/jeremic/BG/amblemi/lbnl-logo}
\pgfdeclareimage[height=0.9cm]{USNRC-logo}{/home/jeremic/BG/amblemi/5in-color-bl-nrc-logo}

\author[Jeremi{\'c} et al.] % (optional, use only with lots of authors)
%{Boris~Jeremi{\'c}}
{B. Jeremi{\'c},  
N. Tafazzoli,  
N. Orbovi{\'c},
A. Blahoianu}

  
%\institute[Computational Geomechanics Group \hspace*{0.3truecm}
\institute[\pgfuseimage{university-logo}] % (optional, but mostly needed)
{University of California, Davis, CA, U.S.A.\\
%  and\\ 
Canadian Nuclear Safety Commission, Ottawa, ON, Canada}


\date[] % (optional, should be abbreviation of conference name)
{\small SMiRT 21, New Delhi, India, November 2011}

\subject{}
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  \frametitle{Outline}
  \tableofcontents
  % You might wish to add the option [pausesections]
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% Structuring a talk is a difficult task and the following structure
% may not be suitable. Here are some rules that apply for this
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% - Exactly two or three sections (other than the summary).
% - At *most* three subsections per section.
% - Talk about 30s to 2min per frame. So there should be between about
%   15 and 30 frames, all told.

% - A conference audience is likely to know very little of what you
%   are going to talk about. So *simplify*!
% - In a 20min talk, getting the main ideas across is hard
%   enough. Leave out details, even if it means being less precise than
%   you think necessary.
% - If you omit details that are vital to the proof/implementation,
%   just say so once. Everybody will be happy with that.














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\section{Introduction}
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\begin{frame} 
\frametitle{Introduction}
\begin{itemize}

  
\vspace*{0.3cm}
\item High fidelity numerical simulations of seismic effects on NPPs

  \begin{itemize}
    \item    Realistic   seismic   motions  (3D, inclined motions, surface  and 
    body waves, lack of correlation, etc.)
    \item Realistic material behavior (elastic, elastic-plastic, etc.)
    \item  Realistic  solids  and  structures  modeling  (solids, beams, shells,
    contacts, isolators, etc.)
%    \item Verification and Validation
%    \item Education
     
  \end{itemize}

\vspace*{0.3cm}
\item   Understanding modeling issues
related to 3D, 2D, and 1D (reduced dimension) modeling
  
 
\end{itemize}



\end{frame}
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\section{The Issues and Modelling Approaches}

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\subsection{The Problem}


% \begin{frame} 
% \frametitle{Seismic Motions}
% 
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=6cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Reports/SeismicWavePropagation01.pdf}
% \\
% \vspace*{0.5cm}
% \includegraphics[width=6.2cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Reports/SeismicWavePropagation02.pdf}
% %\caption{\label{SeismicWavePropagation02}    Propagation    of  seismic waves in
% %inclined  (close  to vertical) local geology, with stiffness of soil/rock layers
% %increasing  through  geologic  layers,  and  refraction  of  waves away from the
% %vertical direction.}
% \end{center}
% \end{figure}
% %
% 
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 

\begin{frame} 
\frametitle{Seismic Motions: Body and Surface Waves}

\begin{itemize}

  \item Full 3D (3 translations 
        and 3 rotations) seismic motions

  \item Inclined waves

  \item Lack of correlations (incoherence)

  \item Body and Surface waves

  \item Surface waves carry most of the energy

  \item Modeling: 3D and/or 2D and or 1D?


\end{itemize}



\vspace*{-0.5cm}
\begin{figure}[!hbpt]
\begin{center}
%\vspace*{-0.9cm}
%\hspace*{-1.0cm}
\hspace*{-1.0cm}
\includegraphics[width=2.6cm, angle=75]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Presentation/P_body_wave.jpeg}
\hspace*{-0.5cm}
\includegraphics[width=2.6cm, angle=75]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Presentation/S_body_wave.jpeg}
\includegraphics[width=2.6cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Presentation/Love_surface_wave.jpeg}
\includegraphics[width=2.6cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Presentation/Rayleigh_surface_wave.jpeg}
\hspace*{-0.5cm}
\end{center}
\end{figure}
%



\end{frame}
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% - 
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  \begin{frame} 
% -  \frametitle{Importance of Rayleigh Waves}
% -  
% -  
% -  \begin{itemize}
% -  
% -  %\item Rayleigh waves become significant source of seismic motions at distance 
% -  %$R  =  h  /  (\sqrt{(v_p/v_R)^2 - 1 })$ where h is hypocenter depth (for uniform
% -  %half-space)
% -  %%% Kramer pp161
% -  %
% -  %\item For example for $v_R \approx 0.93 v_S = 0.93 \times 0.6 v_p = 0.56 v_p$ it
% -  %follows  that  $R \approx 1.5 h$ (for layered soil/rock, distance is smaller due
% -  %to geology)
% -  %% Semblat pp 179
% -  
% -  \item  Rayleigh  waves  to  carry majority of seismic energy to distance and are
% -  responsible for peak accelerations at distance
% -  % Kramer, Semblat
% -  
% -  \item  Rayleigh  waves  are  produced by interaction of  of p- and SV-waves with
% -  soil/rock surface
% -  %Kramer
% -  
% -  \item Rayleigh produce translational and rotational seismic motion components
% -  
% -  \item Rotational components are NOT measured
% -  
% -  \item  For  example:  Northridge  EQ,  Pacoima dam, tilt velocities of $15^o$/s,
% -  residual tilt $3.5^o$
% -  
% -  \item Velocity of Rayleigh decreases with increase in frequency
% -  %Kramer
% -  
% -  \end{itemize}
% -  %
% -  \end{frame}
% -  
% -  







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\subsection{The Modelling}




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\begin{frame} 
\frametitle{Seismic Motion Development for 3D, 2D, and 1D}

\vspace*{0.8cm}
\begin{itemize}
\item Green's functions \\
      regional model \\
      up to $15$Hz
\item Prof. Hisada's
      program
\item Seismic waves \\
      propagated to NPP site
\item Motions input using the \\
      Domain Reduction Method
\item Lack of correlation \\
      inherent in regional \\
      ground motion modeling

\end{itemize}


%
\vspace*{-6.0cm}
\begin{figure}[!hbpt]
\begin{flushright}
\includegraphics[width=8cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Reports/Map_of_Points.pdf}
\hspace*{-1cm}
%\caption{\label{Map_of_Points} Analytic model  (Green's functions)   setup, with
%locations of hypocenter, epicenter and the DRM model.}
\end{flushright}
\end{figure}
%

\end{frame}



% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame} 
% \frametitle{Finite Element Models for the NPP}
% 
% \begin{itemize}
% 
% \item Developed input motions used as an input (DRM) to FEM models
% 
% \item   Wave   propagation  with small error for   given   frequencies 
%   \begin{itemize}
%     \item $v_s=2600$m/s,  $h=5$m, $f_{max}=65$Hz; 
%     \item $v_s=1500$m/s,  $h=5$m, $f_{max}=37$Hz; 
%     \item $v_s=1000$m/s,  $h=5$m, $f_{max}=25$Hz; 
%     \item $v_s=300$m/s,  $h=5$m, $f_{max}=7$Hz) 
%   \end{itemize}
% 
% \item Developed 3D, 2D, and 1D models
% 
% \item Free field, surface and embedded foundations
% 
%   
% \end{itemize}
% 
% \end{frame}
% 
% 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} 
\frametitle{3D, 2D and 1D,  Free Field and SSI Models}

%
\begin{figure}[!hbpt]
\begin{center}
\hspace*{-0.5cm}
\includegraphics[width=3.5cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/ModelPlots/FreeFieldModel01.jpeg}
\includegraphics[width=4.2cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/ModelPlots/VisIt_Mesh_Surface/NPP_surface01.jpeg}
\includegraphics[width=4.2cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/ModelPlots/VisIt_Mesh_Excavated/NPP_embedded02.jpeg}
\hspace*{-0.5cm}
\\
\hspace*{-0.5cm}
\vspace*{0.2cm}
\includegraphics[width=4.2cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/ModelPlots/2D_surface.jpg}
\includegraphics[width=4.2cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/ModelPlots/2D_embedded.jpg}
\includegraphics[width=4.2cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/ModelPlots/1D_Model.jpg}
\hspace*{-0.5cm}
\end{center}
\end{figure}
%

\end{frame}



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\begin{frame} 
\frametitle{3D, 2D and 1D, Models on Rock and Soil Sites}

\begin{itemize}

  \item Hard rock profile, case \#1, $V_s = 2600$m/s
\vspace*{0.3cm}
  \item Rock profile, case \#2, $V_s = 1500$m/s
\vspace*{0.3cm}
  \item Soil profile, case \#8, $V_s = 300$m/s

\vspace*{0.3cm}
  \item  Observing  free  field,  and  base  and  top of containment on  surface
  foundations for 3D, 2D, and 1D models

\end{itemize}




\end{frame}


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\section{Simulations Results}
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\subsection{Comparison of Motions 3D, 2D, and 1D}



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\begin{frame} 
\frametitle{3D vs 2D vs 1D Free Field, Hard Rock (Case 1)}


\vspace*{-3.0cm}
\begin{figure}[!hbpt]
\begin{center}
\hspace*{-1.0cm}
\includegraphics[width=12cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Reports/FreeField/Comparison/Soil_Top_Node_Case_1_FFT_Frequency_log_X.pdf}
\end{center}
\end{figure}

\end{frame}

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\begin{frame} 
\frametitle{3D vs 2D vs 1D Free Field, Soil (Case 8)}


\vspace*{-3.0cm}
\begin{figure}[!hbpt]
\begin{center}
\hspace*{-1.0cm}
\includegraphics[width=12cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Reports/FreeField/Comparison/Soil_Top_Node_Case_8_FFT_Frequency_log_X.pdf}
\end{center}
\end{figure}
\end{frame}



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% \frametitle{3D Amplification, Hard Rock (Case 1)}
% \begin{figure}[!hbpt]
% \vspace*{-2.4cm}
% \begin{center}
% \includegraphics[width=10cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Reports/FreeField/1D_2D_3D_Comparison_FreeField_with_Base_Motion/Plots/Comparison_Surface_Base_Case_01_3D_FFT_Frequency_log_X.pdf}
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% \end{figure}
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% \begin{frame} 
% \frametitle{3D Amplification, Hard Rock (Case 1)}
% \begin{figure}[!hbpt]
% \vspace*{-2.4cm}
% \begin{center}
% \includegraphics[width=10cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Reports/FreeField/1D_2D_3D_Comparison_FreeField_with_Base_Motion/Plots/Amplification_Surface_Base_Case_01_3D_FFT_Frequency_log_X.pdf}
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% \end{figure}
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% \begin{frame} 
% \frametitle{2D Amplification, Hard Rock (Case 1)}
% \begin{figure}[!hbpt]
% \vspace*{-2.4cm}
% \begin{center}
% \includegraphics[width=10cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Reports/FreeField/1D_2D_3D_Comparison_FreeField_with_Base_Motion/Plots/Comparison_Surface_Base_Case_01_2D_FFT_Frequency_log_X.pdf}
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% \begin{figure}[!hbpt]
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% \includegraphics[width=10cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Reports/FreeField/1D_2D_3D_Comparison_FreeField_with_Base_Motion/Plots/Amplification_Surface_Base_Case_01_2D_FFT_Frequency_log_X.pdf}
% \end{center}
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% \begin{frame} 
% \frametitle{1D Amplification, Hard Rock (Case 1)}
% \begin{figure}[!hbpt]
% \vspace*{-2.4cm}
% \begin{center}
% \includegraphics[width=10cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Reports/FreeField/1D_2D_3D_Comparison_FreeField_with_Base_Motion/Plots/Comparison_Surface_Base_Case_01_1D_FFT_Frequency_log_X.pdf}
% \end{center}
% \end{figure}
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% \begin{frame} 
% \frametitle{1D Amplification, Hard Rock (Case 1)}
% \begin{figure}[!hbpt]
% \vspace*{-2.4cm}
% \begin{center}
% \includegraphics[width=10cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Reports/FreeField/1D_2D_3D_Comparison_FreeField_with_Base_Motion/Plots/Amplification_Surface_Base_Case_01_1D_FFT_Frequency_log_X.pdf}
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% 
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% 
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% \frametitle{3D Amplification, Soil (Case 8)}
% \begin{figure}[!hbpt]
% \vspace*{-2.4cm}
% \begin{center}
% \includegraphics[width=10cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Reports/FreeField/1D_2D_3D_Comparison_FreeField_with_Base_Motion/Plots/Comparison_Surface_Base_Case_08_3D_FFT_Frequency_log_X.pdf}
% \end{center}
% \end{figure}
% \end{frame}
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% \begin{frame} 
% \frametitle{3D Amplification, Soil (Case 8)}
% \begin{figure}[!hbpt]
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% \begin{center}
% \includegraphics[width=10cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Reports/FreeField/1D_2D_3D_Comparison_FreeField_with_Base_Motion/Plots/Amplification_Surface_Base_Case_08_3D_FFT_Frequency_log_X.pdf}
% \end{center}
% \end{figure}
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% \frametitle{2D Amplification, Soil (Case 8)}
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% \includegraphics[width=10cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Reports/FreeField/1D_2D_3D_Comparison_FreeField_with_Base_Motion/Plots/Comparison_Surface_Base_Case_08_2D_FFT_Frequency_log_X.pdf}
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% \frametitle{1D Amplification, Soil (Case 8)}
% \begin{figure}[!hbpt]
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% \begin{center}
% \includegraphics[width=10cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Reports/FreeField/1D_2D_3D_Comparison_FreeField_with_Base_Motion/Plots/Comparison_Surface_Base_Case_08_1D_FFT_Frequency_log_X.pdf}
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\subsection{Amplifications in 3D vs 2D vs 1D}
%\subsection{3D vs 2D vs 1D, Variable Stiffness Single Layer Base Soil/Rock}

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\begin{frame} 
\frametitle{Base of Containment Structure, Hard Rock (Case 1)}


\vspace*{-3.0cm}
\begin{figure}[!hbpt]
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\begin{center}
\hspace*{-1.0cm}
\includegraphics[width=12cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Reports/1D_2D_3D_Comparison_surface_containment/Comparison/Base_Node_Case_1_FFT_Frequency_log_X.pdf} 
\end{center}                
\end{figure}
\end{frame}
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\begin{frame} 
\frametitle{Top of Containment Structure, Hard Rock (Case 1)}


\vspace*{-3.0cm}
\begin{figure}[!hbpt]
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\begin{center}
\hspace*{-1.0cm}
\includegraphics[width=12cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Reports/1D_2D_3D_Comparison_surface_containment/Comparison/Top_Node_Case_1_FFT_Frequency_log_X.pdf}
\end{center}
\end{figure}
\end{frame}


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\begin{frame} 
\frametitle{Base of Containment Structure, Rock (Case 2)}

\vspace*{-3.0cm}
\begin{figure}[!hbpt]
%
\begin{center}
\hspace*{-1.0cm}
\includegraphics[width=12cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Reports/1D_2D_3D_Comparison_surface_containment/Comparison/Base_Node_Case_2_FFT_Frequency_log_X.pdf}
\end{center}                
\end{figure}
\end{frame}
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\begin{frame} 
\frametitle{Top of Containment Structure, Rock (Case 2)}

\vspace*{-3.0cm}
\begin{figure}[!hbpt]
%
\begin{center}
\hspace*{-1.0cm}
\includegraphics[width=12cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Reports/1D_2D_3D_Comparison_surface_containment/Comparison/Top_Node_Case_2_FFT_Frequency_log_X.pdf}
\end{center}
\end{figure}
\end{frame}


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\begin{frame} 
\frametitle{Base of Containment Structure, Soil (Case 8)}

\vspace*{-3.0cm}
\begin{figure}[!hbpt]
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\begin{center}
\hspace*{-1.0cm}
\includegraphics[width=12cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Reports/1D_2D_3D_Comparison_surface_containment/Comparison/Base_Node_Case_8_FFT_Frequency_log_X.pdf}
\end{center}                
\end{figure}
\end{frame}
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\begin{frame} 
\frametitle{Top of Containment Structure, Soil (Case 8)}

\vspace*{-3.0cm}
\begin{figure}[!hbpt]
%
\begin{center}
\hspace*{-1.0cm}
\includegraphics[width=12cm]{/home/jeremic/tex/works/consulting/2010/CanadianNuclearSafetyComission/Reports/1D_2D_3D_Comparison_surface_containment/Comparison/Top_Node_Case_8_FFT_Frequency_log_X.pdf}
\end{center}
\end{figure}
\end{frame}








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\section{Summary}
%\subsection{Summary}

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\begin{frame} 

\frametitle{Summary}


\begin{itemize}

  
  
\vspace*{0.3cm}
\item Reduce modeling uncertainty

\vspace*{0.3cm}
\item  Incident  seismic  waves  are   3D, inclined, uncorrelated, contain body and
surface waves...


\vspace*{0.3cm}
\item  High  Fidelity  modeling  and  simulations  are important, preferable (low
modeling uncertainty) so do full, realistic 3D



\vspace*{0.3cm}
\item Funding by and Collaboration with the CNSC is gratefully acknowledged


 
\end{itemize}



\end{frame}
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\end{document}


