\documentclass[fleqn]{beamer}
%\documentclass[handout]{beamer}
%\usepackage{pgfpages}
%\pgfpagelayout{2 on 1}[letterpaper, border shrink=5mm]
\mode{\setbeamercolor{background canvas}{bg=black!3}}
\usepackage{epstopdf}
%This is a macro to convert eps to pdf files on the fly.
% make sure figure syntax uses graphicx syntax NOT epsfig syntax
%from http://mailman.mit.edu/pipermail/macpartners/2005-January/000780.html
%
% \ifx\pdfoutput\undefined
% % we are running LaTeX, not pdflatex
% \usepackage{graphicx}
% \else
% % we are running pdflatex, so convert .pdf files to .pdf
% \usepackage[pdftex]{graphicx}
% \usepackage{epstopdf}
% \fi
% %*****************************************
% % for not showing eq numbers unless eq is references
% \usepackage[fleqn,tbtags]{mathtools}
% \mathtoolsset{
% showonlyrefs
% }
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FEI LOGO definition
\newcommand{\FEI}
{{\sf \uppercase{F}\kern-0.20em\uppercase{E}\kern-0.20em\uppercase{I}}}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % ovo je za cirilicu
% \input vuk.def
% %\newfont{\cyr}{wncyr10 scaled 1200}
% %\newfont{\cyrimena}{wncyb10 scaled 1800}
% %\newfont{\cyrnaslov}{wncyb10 scaled 2600}
% %\newfont{\cyrpodnaslov}{wncyr10 scaled 1400}
\newfont{\cyr}{wncyss10 scaled 1200}
\newfont{\cyrimena}{wncyss10 scaled 2000}
\newfont{\cyrnaslov}{wncyss10 scaled 2800}
\newfont{\cyrpodnaslov}{wncyss10 scaled 1400}
\newfont{\cyn}{wncyss10 scaled 2200}
%% JB sig
\newfont{\cyrjb}{wncyr10 scaled 600}
\newcommand{\JB}
{{\cyrjb \lower0.50ex\hbox{\uppercase{J}}\kern-.58em\hbox{\uppercase{B}}}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\setbeamertemplate{navigation symbols}{}
\mode
{
% \usetheme{Marburg} % ima naslov i sadrzaj sa desne strane
% \usetheme{Hannover} % ima naslov i sadrzaj sa leve strane
% \usetheme{Singapore} % ima sadrzaj i tackice gore
% \usetheme{Antibes} % ima sadrzaj gore i kao graf ...
% \usetheme{Berkeley} % ima sadrzaj desno
% \usetheme{Berlin} % ima sadrzaj gore i tackice
% \usetheme{Goettingen} % ima sadrzxaj za desne strane
% \usetheme{Montpellier} % ima graf sadrzaj gore
% \usetheme{Warsaw}
% \usetheme{Warsaw}
\usetheme{Dresden}
\usecolortheme[RGB={20,0,128}]{structure}
% or ...
\setbeamercovered{transparent}
% \setbeamercovered{transparent}
% or whatever (possibly just delete it)
% \usecolortheme{albatross} % teget sa svetlim slovima
% \usecolortheme{beetle} % siva pozadina (vrh plav)
\usecolortheme{seagull} % sivo
%%%%%%%
% \usecolortheme{BorisJeremic}
%%%%%%%
% \usecolortheme{rose}
% \usefonttheme[onlylarge]{structuresmallcapsserif}
% \usefonttheme{structuresmallcapsserif}
}
\definecolor{mycolor}{rgb}{0,0.08,0.45}%
\usepackage[english]{babel}
\usepackage{amsmath}
\usepackage{mathrsfs}
\usepackage{amsfonts}
\newcommand{\ud}{{\rm d}}
\usepackage{array}
%%%% HYPERREF HYPERREF HYPERREF HYPERREF HYPERREF
%%%% HYPERREF HYPERREF HYPERREF HYPERREF HYPERREF
\definecolor{webgreen}{rgb}{0, 0.15, 0} % less intense green
\definecolor{webblue}{rgb}{0, 0, 0.15} % less intense blue
\definecolor{webred}{rgb}{0.15, 0, 0} % less intense red
%\usepackage[colorlinks=true,linkcolor=webblue,citecolor=webred,urlcolor=webgreen]{hyperref}
\usepackage{hyperref}
\hypersetup{
pdfmenubar=true,
pdftoolbar=true,
pdfpagemode={None}
}
\usepackage{pause}
% or whatever
%\usepackage{html}
%\usepackage{url}
\usepackage[latin1]{inputenc}
% or whatever
\usepackage{times}
\usepackage[T1]{fontenc}
% Or whatever. Note that the encoding and the font should match. If T1
% does not look nice, try deleting the line with the fontenc.
\title[ESSI Modeling and Simulation]
{Earthquake Soil Structure Interaction \\
(ESSI) \\
Modeling and Simulation }
%\subtitle
%{Include Only If Paper Has a Subtitle}
%\author[Author, Another] % (optional, use only with lots of authors)
%{F.~Author\inst{1} \and S.~Another\inst{2}}
% - Give the names in the same order as the appear in the paper.
% - Use the \inst{?} command only if the authors have different
% affiliation.
\pgfdeclareimage[height=0.2cm]{university-logo}{/home/jeremic/BG/amblemi/ucdavis_logo_blue_sm}
\pgfdeclareimage[height=0.7cm]{lbnl-logo}{/home/jeremic/BG/amblemi/lbnl-logo}
\author[Jeremi{\'c} et al.] % (optional, use only with lots of authors)
%{Boris~Jeremi{\'c}}
{Boris Jeremi{\'c}}
%\institute[Computational Geomechanics Group \hspace*{0.3truecm}
\institute[\pgfuseimage{university-logo}\hspace*{0.1truecm}\pgfuseimage{lbnl-logo}] % (optional, but mostly needed)
%{ Professor, University of California, Davis\\
{ University of California, Davis\\
% and\\
% Faculty Scientist, Lawrence Berkeley National Laboratory, Berkeley }
Lawrence Berkeley National Laboratory, Berkeley }
% - Use the \inst command only if there are several affiliations.
% - Keep it simple, no one is interested in your street address.
\date[] % (optional, should be abbreviation of conference name)
{\small Caltrans Seminar \\
December 2013}
\subject{}
% This is only inserted into the PDF information catalog. Can be left
% out.
% If you have a file called "university-logo-filename.xxx", where xxx
% is a graphic format that can be processed by latex or pdflatex,
% resp., then you can add a logo as follows:
%\pgfdeclareimage[height=0.2cm]{university-logo}{/home/jeremic/BG/amblemi/ucdavis_logo_gold_lrg}
%\logo{\pgfuseimage{university-logo}}
% \pgfdeclareimage[height=0.5cm]{university-logo}{university-logo-filename}
% \logo{\pgfuseimage{university-logo}}
% Delete this, if you do not want the table of contents to pop up at
% the beginning of each subsection:
% \AtBeginSubsection[]
\setcounter{tocdepth}{2}
\AtBeginSubsection[]
% \AtBeginSection[]
{
\begin{scriptsize}
\begin{frame}
\frametitle{Outline}
\tableofcontents[currentsection,currentsubsection]
% \tableofcontents[currentsection]
\end{frame}
\end{scriptsize}
}
% If you wish to uncover everything in a step-wise fashion, uncomment
% the following command:
\begin{document}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\titlepage
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Outline}
\begin{scriptsize}
\tableofcontents
% You might wish to add the option [pausesections]
\end{scriptsize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Structuring a talk is a difficult task and the following structure
% may not be suitable. Here are some rules that apply for this
% solution:
% - 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.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Introduction}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Motivation}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}
%-
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}
%-
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{SPT Based Determination of Shear Strength}
\begin{figure}[!hbpt]
\begin{center}
%
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_RawData_and_MeanTrend-Mod.pdf}
\hfill
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_Histogram_PearsonIV-FineTuned-Mod.pdf}
%
\end{center}
\end{figure}
\vspace*{-0.3cm}
Transformation of SPT $N$-value $\rightarrow$ un-drained shear
strength, $s_u$ (cf. Phoon and Kulhawy (1999B)
Histogram of the residual
(w.r.t the deterministic transformation
equation) un-drained strength,
along with fitted probability density function
(Pearson IV)
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}
%
%
%
%
% %
%
%
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{ESSI Modeling}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{3D, Inclined, Body and Surface}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Realistic 3D Seismic Motions}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Summary}
\subsection*{Summary}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \section{Probabilistic Modeling}
% %
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Probabilistic Modeling}
%
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % - \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}
% % - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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}
%
%
%
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \end{frame}
%
%
%
%
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
%
% \frametitle{Recent State-of-the-Art}
%
% \begin{itemize}
%
% %\vspace*{-0.5cm}
% \item Governing equation
%
% % \vspace*{-0.5cm}
% \begin{itemize}
%
% \item Dynamic problems $\rightarrow$ $ M \ddot u + C \ddot u + K u = F $
%
% \item Static problems $\rightarrow$ $ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ K u = F $
%
% \end{itemize}
%
% %\vspace{-0.4cm}
% \item Existing solution methods
%
% % \vspace*{-0.5cm}
% \begin{itemize}
%
% \item \textbf{Random r.h.s} (external force random)
%
% \begin{itemize}
%
% \item FPK equation approach
%
% \item Use of fragility curves with deterministic FEM (DFEM)
%
% \end{itemize}
%
% % \vspace*{0.2cm}
% \item \textbf{Random l.h.s} (material properties random)
%
% \begin{itemize}
%
% \item Monte Carlo approach with DFEM $\rightarrow$ CPU expensive
%
% % \item Stochastic finite element method (e.g. Perturbation method
% % $\rightarrow$ a linearized expansion! Error increases as a function
% % of COV; Spectral method
% % $\rightarrow$ developed for elastic materials so far)
%
% \item Perturbation method
% $\rightarrow$ a linearized expansion! Error increases as a function
% of COV
%
% \item Spectral method
% $\rightarrow$ developed for elastic materials so far
%
% % \begin{itemize}
% %
% % \item Perturbation method $\rightarrow$ fails if COVs of soil $>$ 20\%
% %
% % \item Spectral method $\rightarrow$ only for elastic material
% %
% % \end{itemize}
%
% \end{itemize}
%
% \end{itemize}
%
% \item Original development of {\bf Probabilistic Elasto--Plasticity}
%
%
% \end{itemize}
%
% \end{frame}
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% %
% % \frametitle{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}
%
%
%
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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}
%
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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}
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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 = 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\%
% %
% $\left = 11.57MPa; Var[G] = 142.32 MPa^2$ \\
% 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}
% % \includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/Plots_with_Labels/ProbabilityOfExceedance20cm_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 $50$cm}
% %
% %
% %
% % \begin{figure}
% % \begin{center}
% % %\hspace*{-0.75cm}
% % \includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/Plots_with_Labels/ProbabilityOfExceedance50cm_Actual_vs_NoData-Edited.pdf}
% % \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{Probabilities of Exceedance vs. Displacements}
% %
% %
% %
% % \begin{figure}
% % \begin{center}
% % %\hspace*{-0.75cm}
% % \includegraphics[width=9.0cm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/Plots_with_Labels/ProbabilityOfExceedance_vs_Displacement_Actual_vs_NoData-Edited.pdf}
% % \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{Probabilities of Unacceptable Deformation}
% %
% % \begin{figure}
% % \begin{center}
% % \vspace*{-0.3cm}
% % \includegraphics[width=10.5cm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/NewPlots/with_legends_and_labels/Exceedance20cm_LomaPrieta-Edited_ps.pdf}
% % \vspace*{-0.5cm}
% % %\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 Unacceptable Deformation ($50$cm)}
%
% \begin{figure}
% \begin{center}
% \vspace*{-0.3cm}
% %\hspace*{-0.75cm}
% \includegraphics[width=10.50cm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/NewPlots/with_legends_and_labels/Exceedance50cm_LomaPrieta-Edited_ps.pdf}
% \vspace*{-0.5cm}
% %\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{Risk Informed Decision Process}
%
% \begin{figure}
% \begin{center}
% %\hspace*{-0.75cm}
% \includegraphics[width=8.0cm]{/home/jeremic/tex/works/Conferences/2009/UNION-Univ-BGD/Present/NewPlots/with_legends_and_labels/Summary_LomaPrieta-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}
% %--
\end{document}
%
%