[Dda-cvs] pub/mohrcoloumb mohrcoulomb_rev.tex,1.3,1.4

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	mohrcoulomb_rev.tex 
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some changes in Abs.,intro. and verification section as well as table

Index: mohrcoulomb_rev.tex
===================================================================
RCS file: /cvsroot/dda/pub/mohrcoloumb/mohrcoulomb_rev.tex,v
retrieving revision 1.3
retrieving revision 1.4
diff -C2 -d -r1.3 -r1.4
*** mohrcoulomb_rev.tex	16 Jan 2007 15:04:14 -0000	1.3
--- mohrcoulomb_rev.tex	9 Feb 2007 08:09:25 -0000	1.4
***************
*** 125,142 ****
  validity of nonlinear discontinuous deformation analysis (DDA) by
  comparing its solution for circular tunnel with analytical solutions
! (Salencon solution).  The absolute error in the DDA computed
  displacements is very small, and the relative error diverges slowly
  with distance from the analytical solution.  Overall, absolute and
  relative errors between the DDA results and the Salencon solution
! indicate that DDA is accurate enough for solving practical engineering
! problems over time steps ranging from 0.1 to 0.001 seconds,
! The proposed model is then used to 
  analyze the excavation problem of the pilot of Lavarak power station 
  cavern located in Iran and the results are compared to data 
  collected from extensometes installed in the Lavarack 
! cavern pilot tunnel.  The relative error between the
! simulation and the collected data ranges from 3\% near the 
! cavern free surface, to 18\% at the end of the 7 meter 
! extensometer. 
  \end{abstract}

--- 125,141 ----
  validity of nonlinear discontinuous deformation analysis (DDA) by
  comparing its solution for circular tunnel with analytical solutions
! (Salencon solution), compare the results with those from referred commercial
! software (FLAC).  The absolute error in the DDA computed
  displacements is very small, and the relative error diverges slowly
  with distance from the analytical solution.  Overall, absolute and
  relative errors between the DDA results and the Salencon solution
! as well as commercial software indicate that DDA is accurate enough for solving practical engineering
! problems, The proposed model is then used to 
  analyze the excavation problem of the pilot of Lavarak power station 
  cavern located in Iran and the results are compared to data 
  collected from extensometes installed in the Lavarack 
! cavern pilot tunnel. Same model has been analyzed using FLAC.
! The relative error between the simulation and the collected data ranges from 3\% near the 
! cavern free surface, to 18\% at the end of the 7 meter extensometer. 
  \end{abstract}

***************
*** 228,235 ****
  tunnel for the Lavarak powerhouse near Tehran, Iran, show that DDA
  predicts displacements within 3\% near the cavity to 18\% at 5 meters
! from the free surface.  The growth of relative error away from the
! free surface is attributed to the effect of the mesh coarsening with
! distance and the effect of boundary condition.
! 

  \section{DISPLACEMENT APPROXIMATIONS}
--- 227,240 ----
  tunnel for the Lavarak powerhouse near Tehran, Iran, show that DDA
  predicts displacements within 3\% near the cavity to 18\% at 5 meters
! from the free surface.  
! The further illustrate, the capabilities of the modified DDA, 
! a commercial FDM (e.g. finite difference method) code, FLAC computer program, 
! which is an explicit two-dimensional stress analysis code program developed by 
! Itasca ~\cite{flac:fm1998} was used for the numerical simulation in both verifications.
! %The growth of relative error away from the free surface is attributed to the effect of the mesh coarsening with
! %distance and the effect of boundary condition.
! Through comparisons of numerical results with analytical solution in two excavation
! examples, it is demonstrated that modified DDA is correct and can produce very good results for elastoplastic
! problems.

  \section{DISPLACEMENT APPROXIMATIONS}
***************
*** 703,728 ****

- %\begin{figure}
- %\begin{center}
- %\subfigure[DDA model of a circular tunnel in an infinite Mohr-Coulomb medium.]
- %{\label{subfig:initial_mesh}
- %\includegraphics[width=2.5in]{figs/mesh.eps}}
- %\subfigure[Shaded region shows plastic zone around circular tunnel.]
- %{\label{subfig:deformed_mesh}
- %\includegraphics[width=2.5in]{figs/plastic_zone_tunnel.eps}}
- %\caption{DDA model of a circular tunnel in an infinite Mohr-Coulomb medium}
- %\label{fig:mesh}
- %\end{center}
- %\end{figure}
- 
  \begin{figure}
  \begin{center}
! \includegraphics[width=3.5in]{figs/plastic_zone_tunnel.eps}
! \caption{DDA model of a circular tunnel in an infinite Mohr-Coulomb medium.
! Shaded region shows plastic zone around circular tunnel.}
! \label{fig:mesh}
  \end{center}
  \end{figure}

--- 708,734 ----

  \begin{figure}
  \begin{center}
! \subfigure[]
! {\label{subfig:flac_mesh}
! \includegraphics[width=3.6in]{figs/flac_circular_tunnel_plastic.eps}}
! \subfigure[]
! {\label{subfig:dda_mesh}
! \includegraphics[width=2.5in]{figs/plastic_zone_tunnel.eps}}
! \caption{FLAC (a) and DDA (b) model of a circular tunnel in an infinite Mohr-Coulomb medium
! (Shaded region shows plastic zone around circular tunnel)}
! \label{fig:dda_mesh}
  \end{center}
  \end{figure}

+ %\begin{figure}
+ %\begin{center}
+ %\includegraphics[width=3.5in]{figs/plastic_zone_tunnel.eps}
+ %\caption{DDA model of a circular tunnel in an infinite Mohr-Coulomb medium.
+ %Shaded region shows plastic zone around circular tunnel.}
+ %\label{fig:dda_mesh}
+ %\end{center}
+ %\end{figure}
+ 

***************
*** 740,746 ****
  5000 MPa, Poison's Ratio= 0.2 and Hole Radius= 1 m,
  Cohesion=0.5 MPa, Friction angle = 30° and Dilation angle = 0° The
! calculated radius of plastic zone by close form solution is 2.2 m
! that radius of plastic zone that obtained by new code of DDA is
! approximately 2 m shown in Figure ~\ref{fig:mesh}.

--- 746,753 ----
  5000 MPa, Poison's Ratio= 0.2 and Hole Radius= 1 m,
  Cohesion=0.5 MPa, Friction angle = 30° and Dilation angle = 0° The
! calculated radius of plastic zone by close form solution is 2.5 m
! that radius of plastic zone that obtained by new code of DDA and FLAC is
! approximately 2.4 and 2.7 m respectively, shown in Figure ~\ref{subfig:flac_mesh} 
! and Figure ~\ref{subfig:dda_mesh} .

***************
*** 762,779 ****
  Figure~\ref{fig:circular_tunnel_results}
  shows a direct comparison between new DDA
! code results and analytical solution along a radial line. 
! To investigate whether the error is affected by different time step, a
! set of experiments was performed with 0.001s, 0.01s, and 0.1s.  With
! regard to the obtained results, the modified DDA results are in good
! agreement with the analytical solution. At a distance of about 5 m
! from the opening wall the DDA solution slightly diverges from the
! analytical solution. This is due to not only for a very coarse mesh
! used in this area but also for effecting of boundary condition. The
! behavior like this has been reported by Grayeli and
! Mortazavi~\cite{grayeli:r2005} in modeling at infinite elastic medium
! with \textit{Phase}$^{2}$ 
  %  We need a reference for Phase 2
  %(the powerful 2D elastoplastic finite element stress analysis 
  %program for underground or surface excavations in rock).  
  The error distribution throughout the entire elements are
  also presented.  Figures~\ref{subfig:displacement} and
--- 769,788 ----
  Figure~\ref{fig:circular_tunnel_results}
  shows a direct comparison between new DDA
! code results and analytical solution as well as FLAC along a radial line. 
! % To investigate whether the error is affected by different time step, a
! % set of experiments was performed with 0.001s, 0.01s, and 0.1s.  
! With regard to the obtained results, the modified DDA results are in good
! agreement with FLAC and analytical solution. 
! %At a distance of about 5 m from the opening wall the DDA solution slightly diverges from the
! %analytical solution. This is due to not only for a very coarse mesh
! %used in this area but also for effecting of boundary condition. The
! %behavior like this has been reported by Grayeli and
! %Mortazavi~\cite{grayeli:r2005} in modeling at infinite elastic medium
! %with \textit{Phase}$^{2}$ 
! 
  %  We need a reference for Phase 2
  %(the powerful 2D elastoplastic finite element stress analysis 
  %program for underground or surface excavations in rock).  
+ 
  The error distribution throughout the entire elements are
  also presented.  Figures~\ref{subfig:displacement} and
***************
*** 843,851 ****
  Figure~\ref{fig:lavarak} shows the plastic zones in the rock mass
  surrounding the Lavarak powerhouse. Plastic zones extend approximately
! 6 m in the wall and roof. The further illustrate the capabilities of the modified DDA, 
! a commercial FDM (e.g. finite difference method) code, FLAC computer program, 
! which is an explicit two-dimensional stress analysis code program developed by 
! Itasca ~\cite{flac:fm1998} was used for the numerical simulation. The model grid and its boundary 
! conditions used in the analysis are shown in Figure~\ref{fig:flac_lavarak_grid}. 
  As can be seen from Figure~\ref{fig:flac-lavarak-plastic-zone} and Table~\ref{tab:results}, plastic zone and 
  displacement by FLAC and modified DDA for the pilot tunnel are in very close 
--- 852,857 ----
  Figure~\ref{fig:lavarak} shows the plastic zones in the rock mass
  surrounding the Lavarak powerhouse. Plastic zones extend approximately
! 6 m in the wall and roof.  The model grid and its boundary 
! conditions used in the analysis by FLAC are shown in Figure~\ref{fig:flac_lavarak_grid}. 
  As can be seen from Figure~\ref{fig:flac-lavarak-plastic-zone} and Table~\ref{tab:results}, plastic zone and 
  displacement by FLAC and modified DDA for the pilot tunnel are in very close 
***************
*** 853,857 ****
  rock movements obtained from the DDA are the same or similar at the
  monitoring points. For example, the maximum error of the tunnel
! obtained from DDA is in the order of 0.2535 m.

--- 859,863 ----
  rock movements obtained from the DDA are the same or similar at the
  monitoring points. For example, the maximum error of the tunnel
! obtained from DDA is in the order of 1.014 mm.

***************
*** 943,951 ****
  \begin{tabular}{|l|p{55pt}|p{55pt}|p{55pt}|p{55pt}|}\hline 
  & \multicolumn{4}{|p{200pt}|}{Distance from tunnel boundary}\\\hline
! Model& 0 m& 1.5 m& 3 m& 5 m \\\hline
! In situ (mm)& 8 & 4& 1.7& 1 \\\hline
! DDA (mm)& 7.724& 2.986& 1.628& 0.823 \\\hline
! FLAC (mm)& 9.77& 4.37& 2.26& 0.9 \\\hline
! Relative error& 0.0345 & 0.2535 & 0.04235 & 0.177 \\\hline
  \end{tabular}
  \caption{Displacements at monitoring points and error analysis}
--- 949,958 ----
  \begin{tabular}{|l|p{55pt}|p{55pt}|p{55pt}|p{55pt}|}\hline 
  & \multicolumn{4}{|p{200pt}|}{Distance from tunnel boundary}\\\hline
! Model (mm)& 0 m& 1.5 m& 3 m& 5 m \\\hline
! In situ & 8 & 4& 1.7& 1 \\\hline
! DDA & 7.724& 2.986& 1.628& 0.823 \\\hline
! FLAC & 9.77& 4.37& 2.26& 0.9 \\\hline
! Absolute error(DDA)& 0.276 & 1.014 & 0.072 & 0.177 \\\hline
! Absolute error(FLAC)& 1.77 & 0.37 & 0.56 & 0.1 \\\hline
  \end{tabular}
  \caption{Displacements at monitoring points and error analysis}