\chapter{REQDesignGeometry} \label{sec:DesignGeometryAdaption}
For the purposes of policy studies or determining impact scope or emergency measures, it can be useful to generate a profile that corresponds to the stated safety factor. The stated safety factor can be given for stability inward and for piping.\ProgramName can make automatic geometry adaptations for this purpose using a number of basic assumptions.\newline

Automatic profile adaptation in \ProgramName consists of the following steps:
\begin{enumerate}
	\item Raising the crest (see \autoref{sec:RaiseCrest})
	\item Reducing the gradient of the slope (see \autoref{sec:ReduceSlope})
	\item Shoulder adaption (see \autoref{sec:ShoulderAdaption})
\end{enumerate}

The order of the steps 2 and 3 of the adeption method is defined by \textit{\textcolor[rgb]{0.65,0.16,0}{StabilityDesignMethod}. There are two options:

 \begin{itemize}
	 \item Optimized Slope And Shoulder Adaption\newline
	Apply slope adaption when slip circle exits in slope, conform \autoref{sec:ReduceSlope}, apply shoulder adaption when slip circle exits in polder (at right side of Dike toe at polder).
  \item Slope Adaption Before Shoulder Adaption\newline
	First apply slope adaption starting with a given slope (\textit{\textcolor[rgb]{0.65,0.16,0}{SlopeAdaptionStartCotangent}}), stepping with a given adaption (\textit{\textcolor[rgb]{0.65,0.16,0}{SlopeAdaptionStepCotangent}}) until a certain given slope (\textit{\textcolor[rgb]{0.65,0.16,0}{SlopeAdaptionStepCotangent}}); only after that apply shoulder adaption.
\end{itemize}

\section{Raising the crest} \label{sec:RaiseCrest}
During this step, \ProgramName checks whether the crest height complies with the required (in other words the stated) dike table height (DTH, \textcolor[rgb]{0.65,0.16,0}{\textsl{DikeTableHeight}}).\\
If the crest height (the Z value for characteristic point Outer crest) is equal to or higher than the stated DTH, the profile will not be adapted. If the profile is lower than the stated DTH, \ProgramName adjusts the geometry and creates a new surface line based on the original slope gradients ($\alpha$ and $\beta$) and the original crest width (B), see \autoref{fig:DTHAdaptedGeometry}.\\
The slope gradients, and the crest width, are determined on the basis of the following characteristic points: 
\begin{itemize}
	\item The outer slope gradient ($\alpha$) follows from the calculated gradient on the basis of the outer toe and the outer crest line. If there is an outer shoulder, the outer slope gradient is determined on the basis of the top of the outer shoulder and the outer crest line.
	\item The crest width (B) follows from the distance between the characteristic points in the outer crest line and inner crest line.
	\item The outer slope gradient ($\alpha$) follows from the calculated gradient on the basis of the inner toe and the inner crest line. If there is a inner shoulder, the inner slope gradient will be determined on the basis of the top of the inner shoulder and the inner crest line. 
\end{itemize}


\begin{figure}[H]
	\centering
		\includegraphics[width=1\textwidth]{pictures/DTHAdaptedGeometry.png}
	\caption{Adapted geometry for DTH}
	\label{fig:DTHAdaptedGeometry}
\end{figure}

The adapted geometry starts at the toe at riverside (outer toe) in the initial profile, see \autoref{fig:DeletedGeometryPoints}.
If there is no inner shoulder, the toe at polderside (inner toe) of the adapted profile will be further away on the profile than the original inner toe, see \autoref{fig:DTHAdaptedGeometry}. If the adapted geometry intersects with a inner shoulder, the top of the inner shoulder will be moved, see \autoref{fig:DeletedGeometryPoints}. 

In all adapted profiles, the geometry points within the adapted profile will be removed. The characteristic points will move in accordance with the adaptation of the geometry.

\begin{figure}[H]
	\centering
		\includegraphics[width=1\textwidth]{pictures/DeletedGeometryPoints.png}
	\caption{Adapted geometry by deleting geometry points}
	\label{fig:DeletedGeometryPoints}
\end{figure}

If there is an outer shoulder, the adapted geometry will start at the shoulder base outside, see \autoref{fig:OuterShoulderAdeptedGeometry}.

\begin{figure}[H]
	\centering
		\includegraphics[width=1\textwidth]{pictures/OuterShoulderAdeptedGeometry.png}
	\caption{Adapted geometry when outer shoulder is present}
	\label{fig:OuterShoulderAdeptedGeometry}
\end{figure}

If the geometry adaptation results in the new dike base being so wide that the entire initial geometry is contained within the adapted profile, all the intermediate geometry points, including the characteristic points in the inner shoulder, will be removed, see \autoref{fig:LargerDikeBase}. 


\begin{figure}[H]
	\centering
		\includegraphics[width=1\textwidth]{pictures/LargerDikeBase.png}
	\caption{Adapted geometry with starting point for geometry of outer toe and larger dike base}
	\label{fig:LargerDikeBase}
\end{figure}

If there is a ditch in the profile, \ProgramName will move the ditch if the adapted inner toe is further away than the location of the inner toe in the initial profile. The ditch is moved along the unchanged part of the initial profile. If the ditch is moved, \ProgramName will maintain the original distance from the inner toe to the outer edge of the ditch ($\Delta$). The original dimensions of the ditch will be maintained. See \autoref{fig:MoveDitch}.

\begin{figure}[H]
	\centering
		\includegraphics[width=1\textwidth]{pictures/MoveDitch.png}
	\caption{Moving the ditch}
	\label{fig:MoveDitch}
\end{figure}

\section{Reducing the gradient of the slope}\label{sec:ReduceSlope}
After the adaptation of the crest height in accordance with DTH (if necessary), \ProgramName will first carry out a stability calculation. If it should emerge that the exit point of the slip circle is on the inner slope and if the calculated safety factor is less than the stated safety factors, \ProgramName will (on condition that the profile adaptation option is on) reduce the gradient of the slope until the calculated safety factor $\ge$ required safety factor and the exit point of the slip circle is on the inner slope, see \autoref{fig:ReduceSlope}. If the exit point is no longer on the inner slope and the calculated safety factor does not comply with the desired safety factor, \ProgramName will generate a stability shoulder, see \autoref{sec:ShoulderDevelop}.

\begin{figure}[H]
	\centering
		\includegraphics[width=1\textwidth]{pictures/ReduceSlope.png}
	\caption{Iterative reduction of the gradient of the inner slope on the basis of the exit point of the slip circle}
	\label{fig:ReduceSlope}
\end{figure}

\section{Shoulder adaption} \label{sec:ShoulderAdaption}
\ProgramName develops a stability shoulder iteratively as long as the slip circle does not intersect with the landslide slope (see \autoref{sec:ReduceSlope}) and the stated safety level has not yet been achieved. The maximum number of iteration stages is 200. This limit prevents \ProgramName getting stuck in an infinite iteration loop if the stated safety level is not achieved.

The algorithm used is based on moving the crest of the landslide shoulder in a straight line along an incline ($\alpha$), see \autoref{fig:ShoulderDevelop}. The default value is 0.33 (1:3) but it can also be stated by the user (attribute StabilityShoulderGrowSlope).

The adaptation of the shoulder involves moving the inner toe in steps ($\Delta_S$). The steps are in the horizontal direction and the standard steps are 1 metre in length but they can be changed by the user (attribute StabilityShoulderGrowDeltaX). Shoulder development stops when the calculated safety factor in the adapted profile $\ge$ the stated safety factor.

The inner toe is used as the starting point for shoulder development. If there is already a shoulder in the original cross-section, the crest inner shoulder point is used as the starting point. During shoulder development, the crest of the shoulder remains horizontal, as with the raising of the crest, see \autoref{sec:RaiseCrest}.

\begin{figure}[H]
	\centering
		\includegraphics[width=1\textwidth]{pictures/ShoulderDevelop.png}
	\caption{Iterative shoulder development for macrostability}
	\label{fig:ShoulderDevelop}
\end{figure}




\section{Restrictions use of design mode}\label{sec:RestrictionsUseOfDesignMode}

In design mode a single stability model must be chosen; option Bishop/LiftVan is not possible.


