\chapter{Use of the Stability Kernel}
\label{sec:UseStabKernel}

For stabilily calculation the DAM engine uses the kernel used by D-Geo Stability 15.1
This use is restricted to the options described in this chapter.

\section{Model}\label{sec:Model}
The DAM Engine must be able to make calculations with following models:
		\begin{itemize}
		\item Bishop
		\item LiftVan (Uplift Van in D-Geostability)
		\item Horizontal balance
	\end{itemize}
	
All models are available for inwards stability. For outward stability only Bishop is used.
	
The choice of the model is partly user-defined, partly automatic:\\
User can choose Bishop, Uplift Van or combination Bishop/Uplift Van.\\
User can not choose Horizontal balance, this is part of the RRD scenario selection, see \autoref{sec:UpliftCalculation}.
	
\subsection{Combination Bishop/Uplift Van}
\label{sec:CombinationBishopUpliftVan}

The combination Bishop/Uplift Van give three results:
\begin{enumerate}
	\item Bishop
	\item Uplift Van (is made when \textit{\textcolor[rgb]{0.65,0.16,0}{UpliftCriterionStability}}) is higher than the uplift safety (see \autoref {sec:CheckUplift}). 
	\item Normative result (lowest safety factor) of both.
\end{enumerate}

\section{Slip plane definition and calculation area}\label{sec:PlaneDeinitionAndCalculationArea}
		
\subsection{Grid generation}
\label{sec:GridGeneration}
	
For the models Bishop and LiftVan a calculation grid must be generated.
The user defines the dimensions; number of gridpoints and distance between the points. The DAM engine defines the position of the grid depending on the characteristic points:
For Bishop and for the left grid of LiftVan the left bottom corner is situated at the surfaceline in the middle of the crest (distance between outer- and innercrest). The right bottom corner of the right grid of LiftVan is situated above the most right x co-ordinate where uplift occurs. With the restriction that the left bottom corner can not be situated left of the x co-ordinate of the DikeToePolder.	
	
\subsection{Tangent lines generation}
\label{sec:TangentLinesGeneration}
For Bishop calcuations the tangent lines are always situated at the layer boundaries (automatic). For LiftVan the tangent lines can either be situated automatic or specified. This is user-defined.
When specified, the user (client of DAM-Engine) must provide the distance between the tangent lines, \textcolor[rgb]{1,0,0}{\textsl{Distance tangent lines (UV) }}.
The lower tangentline is always situated 5.0 m below the upper geometry point of the lowest aquifer. The tangentlines are drawn with the given distance until the upper tangent line is situated above the Z;DikeToeAtPolder.

\subsection{Calculation area}
\label{sec:CalculationArea}
For the model Horizontal balance a calculation area must be defined:
\begin{table*}[h]
	\centering
		\begin{tabular}{|p{50mm}|p{90mm}|} \hline
			\textbf{Parameter} & \textbf{Default value}\\ \hline
			X co-ordinate left side [m]& x co-ordinate DikeTopAtRiver\\ \hline
			X co-ordinate right side [m]& x co-ordinate DikeToeAtPolder\\ \hline
			Highest slip plane level [m]& Z value PL4 or PL3 (when one aquifer present) at x co-ordinate DikeToeAtRiver \\ \hline
			Lowest slip plane level [m]& Maximum Z value of top aquifer within calculation area\\ \hline
			Number of planes in the slip plane level [-]& 12\\ \hline
		\end{tabular}
	\caption{Calculation area for horizontal balance}
	\label{tab:CalcutlationArea}
\end{table*}


\section{Shear strength model}\label{sec:ShearStrengthModel}
The DAM engine must be able to make stability calculations with following shear strength models:
	\begin{itemize}
		\item C-Phi
		\item Stress tables
		\item	Cu calculated (with default inital surface level of D-Geo Stability; toplayer)
		\item Cu measured
		\item Cu gradient
		\item Pseudo values		
	\end{itemize}	
	This shear strength models are defined in the soil parameters per layer.

\section{Zone Plot}
\label{sec:Zoneplot}
The option of zone plot in D-Geo Stability is defined as the distinction of the slip circles in different zones; 1a, 1b, 2a, 2b, 3a and 3b.\newline
DAM only uses zone 1 and zone 2.
Zone Plot is used when\textsl{\textcolor[rgb]{0.65,0.16,0}{ZoneType}} = ZoneAreas

The following settings for the Zone plot of D-Geo Stability are used by DAM:\newline

\begin{itemize}
	\item Dike table heigth: user defined : \textcolor[rgb]{0.65,0.16,0}{\textsl{DikeTableHeight}} 
	\item Dike table width: 3 m
	\item Start x co-ordinate restprofile: Xlocal;DikeTopAtRiver
	\item Boundary of design level influence at x: Xlocal;DSurfaceLevelInside
	\item Boundary of design level influence at y: maximal Y co-ordinate of surface line
	\item Required safety in zones: \textsl{\textcolor[rgb]{0.65,0.16,0}{RequiredSafetyFactorStabilityInnerSlope}}
\end{itemize}
Calculation with zone areas is only possible for inward stability calculations.

\section{Calculation options}\label{sec:CalculationOptions}
D-Geostability offers different following calculation options. DAM uses the following settings:
		
\begin{itemize}
	\item Requested number of slices: default D-Geo Stability
	\item Minimum circle depth: user defined: \textsl{\textcolor[rgb]{0.65,0.16,0}{MinimalCircleDepth}}
	\item Minimum slip plan length: default D-Geo Stability
	\item Start value safety factor: default D-Geo Stability
  \item Minimum x-entrance used: default D-Geo Stability
  \item Maximum x-entrance used: user defined
\end{itemize}

The maximum x-entrance used is not directly user defined, but via Forbidden zones.

\subsubsection{Forbidden zone }
\label{sec:Forbidden zone}
Forbidden zone is an option to define a forbidden zone for the entrance point of the slip plane.
The forbidden zone is situated to the rigth side of a certain x co-ordinate. This x co-ordinate is defined by the \textsl{ForbiddenZoneFactor}. Xlocal;forbidden zone WF =(Xlocal;DikeTopAtPolder) + ForbiddenZoneFactor*(Xlocal;DikeToeAtPolder - Xlocal;DikeTopAtPolder)
A forbidden zone is used when \textsl{ZoneType} = ForbiddenZone. 

\begin{table*}[h]
	\centering
		\begin{tabular}{|p{35mm}|p{75mm}|} \hline
			ForbiddenZonefactor & maximum x-entrance\\ \hline
			0 & x co-ordinate DikeTopAtPolder\\ \hline
			1 & x co-ordinate DikeToeAtPolder\\ \hline
		\end{tabular}
	\caption{Forbidden zone factor}
	\label{tab:ForbiddenZoneFactor}
\end{table*}

In a picture:

\begin{figure}[H]
	\centering
		\includegraphics[width=0.95\textwidth]{pictures/ForbiddenZoneFactor.png}
	\caption{Forbidden zone factor}
	\label{fig:ForbiddenZoneFactor}
\end{figure}