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\title{High fidelity  modeling  and simulation of SFS 
interaction: \\
energy dissipation by design}
\author{\large {Boris Jeremi{\'c}}\\
%\author{\large {Boris Jeremi{\'c} and Nima Tafazzoli}\\
{\em University of California, Davis, CA, 95616, U.S.A.}\\
~\\
published in a book: \\
Soil-Foundation-Structure  Interaction,  \\
Edited by R.P.  Orense,  N. Chouw,  and  M. Pender, \\
CRC Press, Taylor \& Francis Group, 2010.
}
%\author{\large Mahdi Taiebat\\
%{\em University of British Columbia, Vancouver, BC, Canada}\\
%}
\date{}% No date.

\abstract{It    is  hypothesized  that  interplay of earthquake, soil, foundation
and  structure  (SFS)  dynamic  characteristic,  and  their  interaction in time
domain,
control  the  behavior  of  SFS system during earthquakes. Moreover, (passive and
active)  control  of spatial and temporal location of seismic energy dissipation
(preferably  in soil) can improve safety and economy of SFS systems. Such energy
dissipation  by  design    requires high fidelity modeling and simulations. This
paper  briefly  describes modeling and simulation aspects of energy flow in SFS
system.    In    addition  to  that, examples of directed energy dissipation are
presented  that  show  how soil can be used for the benefit of overall SFS system
response to seismic excitation.}

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\section{INTRODUCTION}
           
Seismic  behavior  of  soil-foundation-structure  (SFS) systems  has  recently  gained
increased attentions. 
%
Improvements         in  modeling  and  simulation  technology  currently allow 
modeling  and  simulations  of  a  complete SFS interaction with high
fidelity.
%
These  models and simulations allow us, in turn, to gain better understanding of
seismic response of the SFS system.
%
Moreover,  such  high fidelity models and simulations allow us to design the SFS
system(s).
%
Of  particular  interest  is  the  notion  that  a designer can/should be able to
direct/design the location, in time and space, where dissipation of seismic energy
takes place.
%
This  notion  is  based  on  understanding  that  incoming seismic energy 
affects both soils and structures.
%
While focus is usually on structural performance, interaction of soil with
foundation/structure plays a very important (crucial) role in seismic response. 
%
The  idea  is  that  while  energy dissipation in structure (and its components)
leads  to damage, and potentially failure, soil medium offers significant energy
dissipation capacity and benefits.



In  this paper  we   briefly  discuss  seismic  energy  dissipation
mechanisms   in   soils   and   their   potential   use   in  improving  seismic
soil-foundation-structure system performance.



While  SFS  interaction has been modeled and simulated for a number of years.
%
We  mention  a  number  of  references related to SFS interaction importance and
modeling,   starting  with  the very first mention of SFS interaction beneficial
and detrimental effects by Late Prof. Suyehiro \shortcite{Suyehiro1932}.
%
A  number  of  researchers  have  developed  and  analyzed SFS systems in last 3
decades, and we mention some of them:
\shortcite{Chen1977},
%\shortcite{Tyapin2007},
\shortcite{Makris1994},
%\shortcite{Sweet1993},
%\shortcite{Dendrou1985},
\shortcite{McCallen1994},
%\shortcite{Zheng1995},
\shortcite{Gazetas98}, 
%\shortcite{Mylonakis2006},
\shortcite{Mylonakis1997},
%\shortcite{Koo2003}, 
\shortcite{Fenves1998},
%\shortcite{Shirkhande1999},
%\shortcite{Small2001},
%\shortcite{Tongaonkar2003},
%\shortcite{Chouw2005},
%\shortcite{Kotsoglou2007},
%\shortcite{Soneji2008},
%\shortcite{Stehmeyer2008},
%\shortcite{Saadeghvaziri2008},
\shortcite{Elgamal2008},
%\shortcite{Kappos2002},
\shortcite{Jeremic2003a},
\shortcite{Jeremic2007d}, 
\shortcite{Jeremic2008a},
%\shortcite{Spyrakos1992},
%\shortcite{Saadeghvaziri2000},        
%\shortcite{Ellis2001},        
%\shortcite{Mylonakis2006a},
%%\shortcite{Song2006},     
%\shortcite{Xia2006},    
%\shortcite{Liao2006},    
%\shortcite{Sarrazin2005},
%\shortcite{Chai2003},    
%\shortcite{Savin2003},    
%%`\shortcite{Rassem1997},    
%\shortcite{Zhang2002}.

% It  is very important to note that assumed beneficial    role  of not performing
% a full  SFSI analysis has been
% turned into dogma. For example the NEHRP-94 seismic code states that:
% %
% {\it  ''These    [seismic]    forces  therefore  can be evaluated conservatively
% without the adjustments recommended in Sec. 2.5 [i.e. for SSI effects]''}.
% %


In  this  paper  we  briefly  describe energy dissipation mechanisms for SFS
system. 
%
In  addition  to  that, it is claimed that only high fidelity models can be used
for such model based simulation (design) of energy dissipation.

Our  main hypothesis is that the interplay of earthquake (nonlinear seismic wave
propagating  from  source  to  the  structure  of  interest)  with  soil and the
structure  plays  major  role  in potentially catastrophic failures, but also in
success.
%
Timing and spatial location of energy dissipation within the SFS system, determines 
amount  of  damages  and  in  general controls survivability of structure during
earthquake.
%
If  timing  and  spatial  location  of energy dissipation can be controlled, one
could optimize the SFS system for safety and economy.
%
This  is particularly true if energy dissipation can be directed to soil instead
of foundation and structure.


Directing      (by      design)    energy  dissipation for SFS systems requires 
development  and simulations on high fidelity numerical models.
%
There    are  a  number  of  cases where  interaction of SFS and 
dissipation  of  seismic  energy  in soil can be deduced by observing structural
damage.
%
The  very  notion  that  soil  SFS  has  significant role in dynamic response of
structures    comes    from  Professor  Kyoji Suyehiro, (a Naval Engineer turned
Earthquake Engineer, 
following  his  personal  experience  of Great  Kant{\=  o}  earthquake   
(11:58am(7.5),  12:01pm(7.3),  12.03pm(7.2)  (shaking until 12:08pm), 1st. Sept.
1923,  in  Tokyo)  who  reported    $4 \times$ (four) more damage to soft wooden
buildings on soft ground than same building on stiff ground \shortcite{Suyehiro1932}.
%
This  was  probably  due  to  the  close  to  resonance  of building (soft) with
foundation soil (soft) with a long lasting (soft, long period) earthquake.
%
Many years later, \shortcite{Trifunac1998},  show  how  during Northridge earthquake,
areas  with    damage    to   buildings (signifying structural damage) was quite
nicely separated from areas of water pipe breaks (signifying much plasticity and
energy dissipation in soil).
%
In  this  case, much energy is dissipated in the (soft) soil, never making it to
the building, while for stiff soil do not have such energy dissipation capacity,
transmitting such energy to the building for dissipation (damage).

There are many other cases where such phenomena is observed. 
%
Our primary goal here is to emphasize how high fidelity modeling and simulations
of SFS systems can help understand mechanics of such interactions.
%
In    addition  to  that,  we use high fidelity models to present
examples of interplay of earthquake, soil and structure dynamic characteristics, 
together with the location and timing of energy dissipation.



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\section{SEISMIC ENERGY INPUT AND DISSIPATION}

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\subsection{\it Seismic energy input into SFS system}


Earthquakes  release  large  amounts  energy  at  the  source\footnote{
for  example,  some  of  the recent large earthquake energy releases are listed:
Northridge, 1994, $M_{Richter} = 6.7$, $E_r = 6.8 \times 10^{16}J$;
Loma  Prieta,  1989, $M_{Richter}   =  6.9$,  $E_r  =1.1  \times  10^{17}J$;  
Sumatra-Andaman,  2004, $M_{Richter}  =  9.3$,  $E_r  =4.8  \times  10^{20}J$;  
Valdivia,  Chile,  1960, $M_{Richter} = 9.5$, $E_r =7.5 \times 10^{20}J$;}
%
Part  of  released  energy  is radiated as mechanical waves ($\approx 1.6 \times
10^{-5}$)  and  part  of that energy makes it to the surface where SFS system is
located.


Mechanical  seismic  wave  energy enters the SFS system through a closed surface
$\Gamma$ that encompasses (significant) soil volume as well as foundation system
and the structure (Fig.~\ref{DRM}).
%
\begin{figure}[!hbpt]
\vspace*{-7cm}
\begin{center}
\includegraphics[width=9.5cm]{DRMidea03.pdf}
\caption{\label{DRM}\small  Geometry of the SFS system. }
\end{center}
\vspace*{-0.5cm}
\end{figure}
%
Kinetic  energy  flux  through closed surface $\Gamma$ includes both incoming
     and  outgoing  waves  and  can  be calculated using Domain Reduction Method
     \shortcite{Bielak2001} as:
%
\begin{eqnarray*}
& &E_{flux} = 
\nonumber \\
& & \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
\times u_i
\end{eqnarray*}
%
where      $M^{\Omega+}_{be}$,    $M^{\Omega+}_{eb}$,    $K^{\Omega+}_{be}$,     
$K^{\Omega+}_{eb}$  are  mass  and stiffness matrices, respectively for a single
layer  of  elements  just outside of the boundary $\Gamma$, while $\ddot{u}^0_e$
and  $u^0_e$  are  accelerations  and  displacements from a free field model for
nodes belonging to that layer of elements.
Alternatively, energy flux can be calculated using \shortcite{Aki2002}:
%
\begin{eqnarray*}
E_{flux} = \rho A c \int_0^t \dot{u}_i^2 dt
\end{eqnarray*}
%
Outgoing  kinetic energy can be  obtained from outgoing  wave field $w_i$, (from
DRM,  \shortcite{Bielak2001}), while the difference then represents the incoming
kinetic energy that needs to be dissipated with SFS region.





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\subsection{\it Seismic energy dissipation  in SFS system}



Seismic  energy  that  enters  the  SFS system will be dissipated in a number of
ways.
%
part  of  the  energy  that  enters SFS system can be reflected back into domain
outside $\Gamma$ by
%
\begin{itemize}
  \item  wave  reflection  from  impedance  boundaries  (free surface, soil/rock
  layers...).
  \item SFS system oscillation radiation.
       \end{itemize}
%
While  the  rest  of  seismic  energy is dissipated through one of the following
mechanisms within SFS domain:
\begin{itemize}
  \item Elasto-plasticity of soil 
  \item Viscous coupling of porous solid with pore fluid (air, water)
  \item Elasto-plasticity/damage of the foundation system
  \item Elasto-plasticity/damage of the structure
  \item viscous coupling of structure with surrounding fluids (air, water)
%   \item potential and kinetic energy
%  \item potential $\leftarrow \! \! \! \! \! \! \rightarrow$ kinetic energy
\end{itemize}                           

It   is  also important to note that in numerical simulations (advocated and used
in  this  work),  part  of  the energy can be dissipated or produced by purely
numerical  means.  That is, numerical energy dissipation (damping) or production
(negative   damping)   has  to  be  carefully  controlled  \shortcite{local-87},
\shortcite{local-86}.


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\paragraph{Energy Dissipation by Plasticity.}

Elastic-plastic  deformation  of  soil,  foundation  and  structure  is probably
responsible  for  major  part  of  the energy dissipation for large earthquakes.
This,  displacement  proportional  dissipation is a result of dissipation of  
plastic work ($W = \int
\sigma_{ij} d \epsilon_{ij}^{pl}$) and is present in all three components of the
system  (soil,  foundation and the structure). Ideally, majority of the incoming
energy  would  be dissipated in soil, before reaching foundation and structures.
The  possibility  to  direct energy dissipation to soil can be used in design by
recognizing    energy  dissipation  capacity  for  different soils. For example,
simple  elastic-plastic  models    of  stiff and soft clay as well as dense and
loose  send  predict  different  energy  dissipation  capacities,  as  shown  in
Figure~\ref{EnergyDissipationCapacity},  for  single loading-unloading-reloading
cycle.
%
\begin{figure}[!hbpt]
\vspace*{-0.5cm}
\begin{center}
\includegraphics[width=9.5cm]{Energy-Capacity2.pdf}
\vspace*{-0.5cm}
\caption{\label{EnergyDissipationCapacity} \small Energy dissipation capacity
for one cycle at various strains for four generic soils.}
\end{center}
\vspace*{-0.5cm}
\end{figure}
%
While  Figure~\ref{EnergyDissipationCapacity}  shows  that  stiff clay and dense
sand  have  much higher dissipation capacity, it is important to note that soft/loose
soils  can  undergo  much  larger  deformation/strain,  thus  offering increased
energy dissipation capacity through flexibility. 
%



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\paragraph{Energy Dissipation by Viscous Coupling.}

Viscous coupling of pore fluid (air,
water...)   and  soil  particles  and/or  foundation  or  structural  components
is  responsible  for  velocity   proportional energy dissipation. In particular,
viscous   coupling  of  porous  solid  and  fluid results in $E_{vc}= n^2 k^{-1}
(\dot{U}_i - \dot{u}_i)^2$ energy loss per unit volume.
%
It       is    noted    that  this  type of dissipation is realistically modeled
using $u-p-U$ formulation \shortcite{Jeremic2007e}.


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\paragraph{Numerical   Energy  Dissipation  and  Production.}  As  noted  above,
numerical  integration  of  nonlinear  equations  of  motions affects calculated
energy  in  various  ways.  Most  common  effect for nonlinear (elastic-plastic)
systems  is  the positive (energy dissipation) and negative (energy production)
damping.
%
For   example      Newmark (N)  \shortcite{Newmark1959}   and    Hilber--Hughes--Taylor
(HHT) \shortcite{Hilber1977}  are  energy preserving  for linear  elastic system with
proper choice of constants ($\alpha=0.0; \beta = 0.25, \gamma = 0.5$). 
Both  methods  can  also  be  used to dissipate higher frequency modes for
linear elastic models by changing constants so that for N: $\gamma     \ge 
0.5, \;\;\; \beta = 0.25(\gamma+0.5)^2$, while for HHT: $-0.3\dot{3}\le\alpha   
\le0, \;\;\;\gamma = 0.5(1-2\alpha), \;\;\; \beta = 0.25(1-\alpha)^2$.
%
However,  for  nonlinear  problems  it  is  impossible to maintain energy of the
system throughout computations \shortcite{local-87}.



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\subsection{UNCERTAINTY ASPECTS}
\label{UA}


Uncertainty  of  soil  material  parameters and forcing represents a significant
source  of  uncertainty  of  a   final  computed  (simulated)  response  of  SFS
system. Recent development of
Probabilistic  Elasto-Plasticity  (PEP)  and Spectral Stochastic Elastic-Plastic
Finite Element Method (SSEPFEM) 
(\shortcite{Jeremic2005a},      \shortcite{Sett2005a},    \shortcite{Sett2005b},
\shortcite{Jeremic2008c},  \shortcite{Sett2009a}, \shortcite{Sett:2009b}) allows
accurate    analysis  of  influence  of uncertain soil   properties and forcing 
on seismic response. Calculation of seismic energy (propagation and dissipation)
is  affected  by  such, ever present uncertainties and such uncertainties should
be taken into
account as best as possible, Above cite (already) published papers and a number of
near future papers (under review) present development of methodology for forward
and  backward propagation of uncertainties in dynamic (and static) simulation of
elastic-plastic            solids         made  of  (geo-)materials.  Such newly
developed,  highly  accurate,   numerical methdology for treatment  of  material
(left  hand  side)  and  forcing  (right  hand side) uncertainty allows for full
quantification of stochastic (probabilistic) aspects of SFS interaction.






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\section{SELECT EXAMPLES OF ENERGY DISSIPATION}

This  section  briefly describes two examples of SFS system modeling, simulation
and energy dissipation.

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\paragraph{Use of Soft Soil.}

Simulations  on high  fidelity  model  for bridge     
SFS  system  \shortcite{Jeremic2008d}  were  used to investigate energy flow and
dissipation.    Proper    modeling  of nonlinear wave propagation required large
number  of  elements  and DOFs ($1.6 \times 10^6$ for largest model). Such large
models  required  development  of  efficient parallel finite element methodology
(Plastic Domain Decomposition, PDD)
that   could   handle   elastic-plastic   computations  on  multiple  generation
distributed  memory  parallel  computers including DataStar at SDSC, Longhorn at
TACC     and     our    own    GeoWulf    at    UCD    \shortcite{Jeremic2007d},
\shortcite{Jeremic2008a}.
% 
Great  care  was  taken to develop high fidelity model for both soil, foundation
and    the    structure.  Seismic  waves  were  input  into  the model using DRM
\shortcite{Bielak2001},      and   no numerical damping was used, leaving energy
dissipation to elasto-plasticity and radiation damping.
%
Figure~\ref{Mesh} shows a detailed FEM model. 
%
\begin{figure}[!hbpt]
\begin{center}
\includegraphics[width=9.0cm]{PrototypeMesh.jpg}
\caption{\label{Mesh} \small Detailed finite element model of a SFS system.}
\end{center}
\vspace*{-0.5cm}
\end{figure}
%
%

It  is  important  to  note  that  a  full  (numerical) construction process was
performed,  with  soil  self  weight applied first,  followed by  excavation and
pile  installation,  pile  self  weight application, with structure construction
(self wight) application preceding application of seismic input via DRM. 



Figure~\ref{Northridge}  shows  moment response (upper) of the top of bent \#~1,
contrasted  with  relative velocity energy (lower) for the same bent.
%
%
\begin{figure}[!hbpt]
\begin{center}
\includegraphics[width=7.5cm,height=3.8cm]{MomentBent1Pile1_25s_SC.pdf}
\\
\includegraphics[width=9.5cm,height=7.5cm]{Northridge-Diff-Comp.pdf}
\vspace*{-4cm}
\caption{\label{Northridge} \small Bending moment response for bent \#~1 (left column)
(top) and relative velocity energy (lower). }
\end{center}
\vspace*{-0.5cm}
\end{figure}
%
Two cases
are analyzed, CCC is a case with all foundations (piles) in a soft clay (Bay mud)
while  SSS  is  for  all  foundations  (piles) resting in dense send soil. Input
motion  is  from  Northridge  earthquake,  characterized with fairly high energy
input in higher frequencies (stiff earthquake).
%
It  is  obvious  that soft soil dissipates seismic energy by plasticity and that
SFS  system  in  soft  clay  does  not sustain much damage (possibly one case of
plastic  yielding on top of bent, at $t$ between 14 and 15 seconds. On the other
hand,    in  stiff sand, soil does not dissipate much  seismic energy, hence bent
\#~1  suffers  much  plastic  yielding  (plastic hinge development between $t$ 8
until  12  seconds.  It  is noted also that the dynamic characteristics of stiff
earthquake,  with  stiff  soil  and stiff structure contribute to early close to
resonance   response   and   increase  damage.  Relative  velocity  energy  plot
(Fig.~\ref{Northridge},  lower) presents similar information, this time in terms
of kinetic energy, that is dissipated through plastic work. Note early peaks for
SSS  SFS system, that get dissipated by plastic hinging, while sole peak for CCC
SFS system contributes to one sided plastic hinge development at $t\approx14s$.



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\paragraph{Use of Liquefaction.}


Liquefaction  has  been consistently put in negative connotation in geotechnical
earthquake  engineering.  There  are many cases where
liquefaction is to be blamed for unacceptable SFS system performance (
\shortcite{Youd89},
%\shortcite{Hamada92},
\shortcite{Yokoyama97},
\shortcite{Berril97}, 
\shortcite{Kawakami66},
\shortcite{Hamada92a},
\shortcite{Hamada92b},
\shortcite{JSCE66}), 
%
However,  there is not much evidence (it was not searched for) that liquefaction
actually  provided  benefit by decreasing (damping out) ground motions. A simple
example    is   used   to   illustrate   this   idea   \shortcite{Taiebat2008a}.
%\shortcite{Taiebat2009a}.
%
Figure~\ref{two_soil_columns}      presents  two  models  for  1D  seismic  wave
propagation, namely one (left) with all dense
sand,  while  the  other one (right)  is dense sand on top of loose sand layers.
%
%
\begin{figure}[!htbp] 
\begin{center}
\vspace*{-0.5cm}
\includegraphics[width=11cm,angle=90]{Mesh-Isolation.pdf}
%\\
\caption{\label{two_soil_columns}  \small Two  soil  column  models,  left is all dense
sand,  right  is dense sand on top of loose sand layers. Seismic motions applied
to the bottom are also shown.}
\end{center}
\vspace*{-0.5cm}
\end{figure}
%
%



Seismic   wave  is  propagated   through   the   soil   (input  is  also  shown  in
Fig.~\ref{two_soil_columns})  with  resulting  acceleration records at different
soil depths shown in Figure~\ref{two_soil_columns_results}.
%
\begin{figure}[!htb]
%\vspace*{-3cm}
\begin{center}
\includegraphics[width=9.5cm]{time-history-acc.jpg} \\
\caption{\label{two_soil_columns_results} \small Acceleration time history, at
different soil levels.  Left is all dense sand model, right is dense with loose
bottom sand layer.}
\end{center}
\vspace*{-0.5cm}
\end{figure}
%\hspace*{2.3cm} EPPR \hspace{1.5cm}  $\gamma$ \hspace{1.7cm}  $u_{hor}$
Since  bottom  loose  soil  layers  do  liquefy (from effective stress results),
seismic  energy  does  not  propagate much above bottom layers. Main dissipation
mechanisms  are  related  to soil plasticity and coupling of solid skeleton with
pore fluid.
%

Figure~\ref{two_soil_columns_energy}  shows  measured (simulated) kinetic energy
at  the  top of both soil models. Layered model (with loose, liquefiable
layer  at  the  bottom) has reduction of top of model kinetic energy of at least
three  times,  which  might  significantly contribute to damage reduction of any
foundation and structure placed on top of such soil system.
%
\begin{figure}[!htb]
\begin{center}
%\vspace*{-1.3cm}
\includegraphics[width=10cm]{StackElements-Compare.pdf} 
\vspace*{-4.0cm}
\caption{\label{two_soil_columns_energy} \small  Kinetic  energy  at  the  top  of soil
layers.}
\end{center}
\vspace*{-0.5cm}
\end{figure}
%\hspace*{2.3cm} EPP







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% 
%     
%  \section{UNCERTAINTY ASPECTS}
%  \label{UA}
%  
%  
%  Uncertainty of soil parameters represents a significant source of uncertainty of
%  a  final  computed  (simulated)  response  of  SFS system. Recent development of
%  Probabilistic  Elasto-Plasticity  (PEP)  and Spectral Stochastic Elastic-Plastic
%  Finite Element Method (SSEPFEM) 
%  (\shortcite{Jeremic2005a},      \shortcite{Sett2005a},    \shortcite{Sett2005b},
%  \shortcite{Jeremic2008c},  \shortcite{Sett2009a}, \shortcite{Sett:2009b}) allows
%  accurate  analysis  of  influence  of  soil  uncertainty  properties  on seismic
%  response.  Calculation  of  seismic energy (propagation and dissipation) will be
%  affected   by  such, ever present uncertainties as well and should be taken into
%  account as best as possible, Above cite (already) published papers and a number of
%  near future papers (under review) present development of methodology for forward
%  and  backward propagation of uncertainties in dynamic (and static) simulation of
%  elastic-plastic            solids         made  of  (geo-)materials.  Such nwely
%  developed, highly accurate  treatment  of  material (left hand side) and forcing
%  (right  hand  side)  uncertainty  allows  for  full quantification of stochastic
%  (probabilistic) aspects of SFS interaction.
%  







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\section{SIMULATION PLATFORM}
\label{SP}


Numerical  simulations  described  in  this  paper  were  done  using sequential
and    parallel application   programs developed at UCD, with use of a number of
publicly available numerical libraries.
%
Parallel  simulation  were  based  on  recently  developed    Plastic   Domain  
Decomposition   (PDD)   method  \shortcite{Jeremic2007d,Jeremic2008a}. 
%
Graph  partitioning used in PDD is based on ParMETIS libraries \shortcite{Karypis98c}).
%
Small part    of   OpenSees framework \shortcite{McKenna97}  was  used to
connect
the finite  element  domain.  In  particular, Finite Element Model Classes from
OpenSees (namely, class abstractions Node, Element, Constraint, Load, Domain and
set of Analysis classes)
where  used to describe finite element model and to store results of 
analysis
performed           on    a  model.  The domain and analysis classes 
were  significantly  modified    to    improve    parallel  performance and were
organized as
Modified OpenSees Services (MOSS) library.  In  addition to that, build
process  and  organization of libraries was completely redone in order to remove
known limitations of OpenSees program.
%
%  An  excellent adoption  of  Actor  model
%  \citep{Hewitt73,Agha84}    and  addition  of  a  Shadow,  Chanel, MovableObject,
%  ObjectBroker,        MachineBroker        classes  within OpenSees framework
%  \citep{McKenna97} also provided an excellent basis for our development.
%  %
%
On      a   lower   level,   a   set   of   Template3Dep   numerical   libraries
\shortcite{Jeremic2000f}
were
used  for  constitutive  level  integrations, nDarray numerical libraries
\shortcite{Jeremic97d} were used to handle vector, matrix
and  tensor  manipulations, while FEMtools  element  libraries from UCD
CompGeoMech      toolset    \shortcite{Jeremic2004d}      were   used to supply other
necessary libraries and components.
%
%
%
Parallel  solution  of system of equations has been provided by PETSc set of
numerical libraries \shortcite{petsc-web-page,petsc-user-ref,petsc-efficient}).
%


Application        programs  used for simulation were created  by  linking above
mentioned libraries in the Finite Element Interpreter (\FEI{}).
%
Large    part   of  simulation was carried out on our local sequential computers
and and our parallel
computer GeoWulf.
Only the largest models (too big to fit on GeoWulf system) were simulated
on  TeraGrid  machine  at  SDSC and TACC. 
%
%It should be noted that the software
%part  of  the  simulation  platform  (executable  program)  is available through
%Author's web site.







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\section{CONCLUSIONS}



Interplay  of Earthquake, Soil, Foundation and Structure dynamics in time domain
plays a major role in catastrophic failures and great successes.
%
High fidelity modeling and simulation offers an unprecedented opportunity  
to  improve  design.  
%
The  ability  to  model  and  simulate  flow  of  seismic  energy  in  the  SFS 
system  with  high  fidelity,  makes  it  possible  to design energy dissipation
in most economical way, in soil, 
%
Directing,  in  space and time, seismic energy flow in the SFS system will
lead to increase in safety and economy.
%
The  main  purpose  of this brief paper was to overview modeling and simulations
issues and show illustrative examples of directing energy flow for SFS systems.


It  is  hoped  that public  domain  modeling  and  simulations  tools,  such  as
\FEI{}   and  recently  developed \url{www.OpenHazards.com} will be used more in
future to increase
safety and reduce cost of infrastructure objects in earthquake prone areas.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section*{ACKNOWLEDGMENT}
%
I  would like to thank Professors 
Zhaohui Yang (University of Alaska), 
Mahdi Taiebat (University of British Columbia), 
Kallol  Sett  (University  of  Akron) 
and Drs. 
Zhao Cheng (EarthMechanics Inc.),
Guanzhou  Jie  (Wells  Fargo Securities), 
Matthias Preisig (Ecole Polytechnique F{\'e}d{\'e}rale de  Lausanne)  
and  graduate  student  researcher 
Mr. Nima Tafazzoli (UCD)
for their contributions to this paper.


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%\newpage

\renewcommand{\baselinestretch}{0.9}
\small  % trick from Kopka and Daly p47.


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