Plaxis manual reference

Edu is a platform for academics to share research papers. The widely- used software for geotechnical engineering, plaxis 2d is a user- friendly, finite- element package that provides you with the ability to model diverse geotechnical problems from a single, plaxis manual integrated application.

Polycurvecreates a polycurve at coordinate 4, 5, 6 with a local first plaxis manual axis in the direction of the global z- axis and a local second axis in. The pm4sand model is defined [. Creates a cylinder. Create a cylinder with a specified radius and a specified height at the origin.

Plaxis 2d and 3d are powerful and user friendly plaxis manual finite element package intended for two- dimensional and three- dimensional analyses of deformation and stability in geotechnical engineering and rock mechanics. Plaxis is used worldwide by top engineering companies and institutions in the civil and geotechnical engineering industry. Plaxis modeto connect edition is the most advanced application for designing monopile foundations.

With plaxis modeto you can significantly optimize the designs for your monopile foundation project and lower steel, fabrication, transportation, and installation costs. According to plaxis reference manual, i made the calculation type for the initial phase calculation type to ' field stress', plaxis manual inputted the plaxis manual negative field stresses in the model explorer, and fully.

The reference manual is intended for users who plaxis manual wish to obtain more detailed information about the program features. The manual plaxis manual covers topics that are not covered exhaustively in the tutorial manual. It also contains practical details on how to use plaxis for a wide variety of problem types. Since plaxis connect edition v20, extensive documentation is available regarding the plaxis manual remote scripting functionality.

Manuals plaxis manual of the full version of plaxis 3d tunnel, and theoretical background is given in the corresponding scientific manual. For detailed information on plaxis manual the available program features, the user is referred to the reference manual. The manuals are included on the introductory cd. It is not necessary to create a new model; you can start from the previous model, modify it and store it under a different name.

Right-click the prescribed displacement. In the right mouse button menu point to the Line displacement option. In the expanded menu click on the Delete option Figure 1. Point on Create and select the Plate option in the appearing menu Figure 1. Point on Create and select the Line load option in the appearing menu Figure 1. The input value will later be changed to the real value when the load is activated. Adding material properties for the footing Click the Materials button in the side toolbar.

A new window appears where the properties of the footing can be entered. The Elastic option is selected by default for the material type. Keep this option for this example. Table 1. Note that the shape of the cursor changes to indicate that it is valid to drop the material set. Hint: If the Material sets window is displayed over the footing and hides it, click on its header and drag it to another position. Create the mesh. Use the default option for the Element distribution parameter Medium.

View the mesh. Hint: Regeneration of the mesh results in a redistribution of nodes and stress points. Keep Plastic as Calculation type and keep Staged construction as loading type. The model is shown in Figure 1. Before starting the calculation it is advisable to select nodes or stress points for a later generation of load-displacement curves or stress and strain diagrams. To do this, follow these steps: Click the Select points for curves button in the side toolbar. As a result, all the nodes and stress points are displayed in the model in the Output program.

The points can be selected either by directly clicking on them or by using the options available in the Select points window. Hint: Instead of selecting nodes or stress points for curves before starting the calculation, points can also be selected after the calculation when viewing the output results. However, the curves will be less accurate since only the results of the saved calculation steps will be considered. To select the desired nodes by clicking on them, it may be convenient to use the Zoom in option on the toolbar to zoom into the area of interest.

If this is not the case click the symbol of the calculation phase or right-click and select Mark for calculation from the pop-up menu. Click the Calculate button to start the calculation. Select the plots that are of interest. Click the Select structures button in the side toolbar and double click the footing. Select the various options from the Forces menu to view the forces in the footing. Hint: Multiple sub- windows may be opened at the same time in the Output program.

All windows appear in the list of the Window menu. In order to generate the load-displacement curve as given in Figure 1. The Curves manager window pops up. Select the u option for the Total displacements option of the Deformations. Alternatively, you may open the Settings window by selecting the corresponding option from the Format menu.

As a result the curve of Figure 1. Most of the program features that were used in Tutorial 1 will be utilised here again. In addition, some new features will be used, such as the use of interfaces and anchor elements, the generation of water pressures and the use of multiple calculation phases.

The new features will be described in full detail, whereas the features that were treated in Tutorial 1 will be described in less detail. Therefore it is suggested that Tutorial 1 should be completed before attempting this exercise.

This tutorial concerns the construction of an excavation close to a river. It extends in longitudinal direction for a large distance, so that a plane strain model is applicable. The sides of the excavation are supported by 30 m long diaphragm walls, which are braced by horizontal struts at an interval of 5 m. Along the excavation a surface load is taken into account.

The upper 20 m of the subsoil consists of soft soil layers, which are modelled as a single homogeneous clay layer. Underneath this clay layer there is a stiffer sand layer, which extends to a large depth. The excavation process is simulated in three separate excavation stages.

The diaphragm wall is modelled by means of a plate, such as used for the footing in the previous tutorial. The interaction between the wall and the soil is modelled at both sides by means of interfaces. The strut is modelled as a spring element for which the normal stiffness is a required input parameter. The Modify soil layers window pops up. Two data sets need to be created; one for the clay layer and one for the sand layer.

To create the material data sets, follow these steps: Click the Materials button in the Modify soil layers window. The Material sets window pops up where the Soil and interfaces option is selected by default as the Set type. Set the Drainage type to Undrained A. Table 2. Rinter 0. Select the Manual option in the Strength drop-down menu.

Enter a value of 0. Set the pre-overburden pressure POP value to 5. The material type should be set to Drained. In the Strength box, select the Manual option.

Close the data set. In the expanded menu select the Create plate option Figure 2. Figure 2. Move 30 m down Click the Show materials button in the side toolbar. Set the Set type parameter in the Material sets window to Plates and click the New button. Coinciding points or lines will automatically be reduced to single points or lines. More information is available in Section 5. Point to Create and click on the Positive interface option in the appearing menu Figure 2.

In the same way assign a negative interface as well. This is a purely numerical value, which can be used to optimise the numerical performance of the interface. Non-experienced users are advised not to change the default value. For more information about interface properties see the Reference Manual. Move the cursor 15 m to the right Move to Set the Set type parameter in the Material sets window to Anchor and click the New button.

Click OK to close the data set. The default orientation is valid in this tutorial. Hint: The Equivalent length is the distance between the connection point and the position in the direction of the anchor rod where the displacement is zero.

Move the cursor 5 m to the right to The resulting mesh is displayed in Figure 2. First, the wall is installed to the desired depth.

Then some excavation is carried out to create space to install an anchor or a strut. Special measures are usually taken to keep the water out of the excavation. Props may also be provided to support the retaining wall. The current tutorial explains the use of this powerful calculation option for the simulation of excavations. Keep its calculation type as K0 procedure. Make sure all the soil volumes are active and all the structural elements and load are inactive.

Phase 1: External load In the Phases explorer click the Add phase button to introduce a new phase. In the model the full geometry is active except for the wall, interfaces, strut and load. Click the Select multiple objects button in the side toolbar.

In the appearing menu point to Select line and click on the Select plates option Figure 2. The value can be checked in the Selection explorer. Phase 2: First excavation stage In the Phases explorer click the Add phase button to introduce a new phase. Hint: To copy the settings of the parent phase, select the phase in the Phases explorer and then click the Add phase button.

The strut should turn black to indicate it is active. This short post will be a summary of that presentation. Hardening Soil model will be called HS from now on was presented in an excellent conference for 10th year of Plaxis in a paper called The hardening soil model: Formulation and Verification by Schanz, Vermeer and Bonnier.

Hardening behaviour of soils is shown on the experiments on Tatsuoka and Ishihara on sand samples. We will see that later on on the preconsolidation pressure concept of HS.

Vermeer defines a hardening parameter to expand the yield surface which is also an integral part of the HS model. The yield surface moves in conjunction with some measure for the plastic strains which is called the hardening parameter. The concept of a yield locus or yield surface is felt to be the most important concept of plasticity theory. It is a surface in stress space a curve in the p, q-plane separating stress states which can be reached elastically the elastic domain from those which can only be obtained after plastic deformation or cannot be achieved at all.

Hardening means that yield surface is not fixed as described in Plaxis Material Manual. There are two types of hardening:. According to Plaxis Material Manual, shear hardening is used to model irreversible strains due to primary deviatoric loading. So, here comes the difference between each stiffness modulus in HS. Also, Eu is used in the formulations. Primary deviatoric loading is used everywhere in HS literature. However, I went over google results 2 years ago and there are only two definition.

This is a concept deriven from Kondner and Duncan and Chang : Hyperbolic relationship between deviatoric stress and stiffness. Primary simply means virgin loading. Deviatoric loading is same as we know from triaxial test. Compression hardening is not something unfamiliar to us. It is around here since Terzaghi. Preconsolidation pressure is used in consolidation calculations to seperate the virgin loading and reloading parts.

We should know that: Plastic yielding depends on the position of yield surface. So, if we exceed the yield surface, plasticity comes into action. Puzrin describes it really well:. After the selection of an existing project, the corresponding geometry is presented in the main window. P2D '. Such les need to include a table with the coordinates of the points preceded by the command Points; each new line starting with a number which serves as the point's ID, followed by the point coordinates and lines preceded by the command Lines; each new line starting with a number , which serves as the line's ID, followed by the starting and ending point ID's.

Examples of such les are given below: Table 3. GEO '. This option can only be used to read geometry data; soil data is not imported. If such a le is selected and the Open button is clicked, the corresponding data is read and the corresponding geometry is presented in the draw area. This geometry is considered to be a new geometry model and not an extension to an existing model. If the number of geometry points is very large, the option may not work properly. DXF le formats.

Lines as part of polylines AcdbPolyLine are not imported. In the cases where the imported geometry contains curved elements as well like arcs , the geometry will be partly imported only points and straight lines.

Scaling of the imported geometry When geometry is imported the Import scale factor Figure 3. The scaled geometry will be displayed when the OK button is clicked.

A shortcut to the application can be created as well. The project to be compressed and the archive can be located using the Browse button. The extension of the project le, indicating in which program it was created, and the archiving date are included in the archive name. Support Selecting this option enables including all the information required to give support for the project at hand. Note that support is only provided to VIP users.

Custom The user can dene the information to be included in the archive. The options for compression and volume size are available in the Archive options window Figure 3.

The options available are: Mesh The information related to geometry is imported when the Mesh option is selected. Phases The options available are: Smart When a phase is selected in the tree, the parent phase is selected automatically in order to provide a consistent chain of phases.

Manual Specic phases can be selected by the user. Results The results to be included in the archive can be selected. The options available are: All steps The results of all the calculation steps are included in the archive.

Last step only The results of only the last calculation step of each phase are included in the archive. Manual The results of specic calculation steps can be selected by the user. Note that when the Backup or the Support option is selected, the Content options are automatically selected by the program. Unsaved modications in the project are indicated by a '' in the project name.

General toolbar The general toolbar contains buttons for general actions such as disk operations, printing, zooming or selecting objects. It also contains buttons to start the other sub-programs Calculations, Output.

Hint: If the mouse is moved over a button in a toolbar, a hint about the function of this button is displayed. Mode tabs The mode tabs are used to separate different modelling modes. The following tabs are available: Geometry The geometry of the model is dened. Calculations The calculation phases and calculation process are dened and the project is calculated.

Model toolbar The model toolbar contains buttons for actions that are related to the creation of a geometry model. The buttons are ordered in such a way that, in general, following the buttons on the tool bar from the left to the right results in a fully dened model.

Draw area The draw area is the drawing sheet on which the geometry model is created and modied. The geometry model can be created by means of the mouse and using the buttons available in the Model toolbar. The physical origin is indicated by the intersection of the x and y axes. Each axis is displayed in a different colour and their positive directions are indicated by arrows.

At both the left and the top of the draw area, rulers indicate the physical x- and y-coordinates of the geometry model.

This enables a direct view of the geometry dimensions. The rulers can be switched off in the View menu. When clicking on the rulers the Project properties window appears in which the geometry dimensions can be changed. Status bar The status bar displays information about the location of the mouse cursor in the draw area. The cursor position is given in both in physical units x, y-coordinates and in screen pixels. Manual input of coordinates can be given for all objects, except for Hinges and Rotation xities.

In addition to the input of coordinates, existing geometry points may be selected by their number. The menus available in the Input program are: 3.

In case of a new project, the Project properties window is automatically displayed to dene its properties. Open To open an existing project. The le requester is displayed. Recent projects To quickly open one of the most recent projects.

Import To import geometry data from other le types Section 3. Save To save the current project under the existing name. If a name has not been given before, the le requester is presented. Save as To save the current project under a new name. Pack project To compress the current project. Project properties To activate the Project properties window Section 3.

Print To print the geometry model on a selected printer. Exit To leave the Input program. Repetitive use of the undo option is limited to the 10 most recent actions. Copy to clipboard To copy the view of the model displayed in the draw area to clipboard.

Alternatively, the mouse wheel may be used for zooming. Zoom out To restore the view to before the most recent zoom action. Reset view To restore the full draw area. Table To view the table with the x- and y-coordinates of all geometry points. The table may be used to adjust existing coordinates. Rulers To show or hide the rulers along the draw area. Cross hair To show or hide the cross hair during the creation of a geometry model.

Grid To show or hide the grid in the draw area. Axes To show or hide the arrows indicating the x- and y-axes. Snap to grid To activate or deactivate the snapping into the regular grid points. Change color scheme To change the intensity of the colours indicating the material data sets assigned to soil layers. Point numbers To show or hide the geometry point numbers. Chain numbers To show or hide the 'chain' numbers of geometry objects. Plate To create structural objects with a signicant exural rigidity or bending stiffness Geogrid To create slender structures with a normal stiffness but with no bending stiffness.

Interface To model the soil-structure interaction. Node-to-node anchor To create springs that are used to model ties between two points. Fixed-end anchor To create springs that are used to model a tying of a single point. Tunnel To create circular and non-circular tunnel cross sections which are to be included in the geometry model. Hinge and rotation spring To create a plate connection that allows for a discontinuous rotation in the point of connection. Drain To prescribe lines inside the geometry model where excess pore pressures are reduced.

Well To prescribe points inside the geometry model where a specic discharge is extracted from or inltrated into the soil. The program gives a message indicating whether consistency issues exist. Possible inconsistencies are overlapping lines or multiple points at the same location. Standard earthquake boundaries To impose standard boundary conditions for earthquake loading. Standard absorbent boundaries dynamics To impose standard absorbent boundaries for single source vibrations.

Set dynamic load system To specify which of the load system s will be used as a dynamic load. Total xities To impose total xities. Vertical xities To impose vertical xities.

Horizontal xities To impose horizontal xities. Rotation xities plates To x the rotational degree of freedom of a plate around the z axis. Absorbent boundaries To dene a boundary that absorbs the increments of stresses caused by dynamic loading.

Prescribed displacements To impose special conditions on the model to control the displacement of certain points. Distributed load - static load system A To dene distributed loads for load system A. Distributed load - static load system B To dene distributed loads for load system B.

Point load - static load system A To dene point loads for load system A. Point load - static load system B To dene point loads for load system B.

Design approaches To dene partial factors according to a design approach and to select the design approaches for the current project. Hint: Note that point loads actually represent line loads in the out-of-plane direction. Plates To activate the data base engine for the creation and modication of material data sets for plates.

Geogrids To activate the data base engine for the creation and modication of material data sets for geogrids. Anchors To activate the data base engine for the creation and modication of material data sets for anchors.

The use of the data base and the parameters contained in the data sets are described in detail in Chapter 4. Global coarseness To select one of the available options for the global mesh coarseness. Rene global To rene the mesh globally. Rene cluster To locally rene the selected clusters. Rene line To locally rene the mesh around selected lines. Rene around point To locally rene the mesh around selected points.

Reset all To reset all the renements. Generate To generate the mesh. The options in this menu are explained in detail in Section 3. Disclaimer The complete disclaimer text is displayed. About Information about the program version and license are displayed. A geometry model consists of points, lines and clusters. In addition to these basic components, structural objects or special conditions can be assigned to the geometry model to simulate tunnel linings, walls, plates, soil-structure interaction or loadings.

It is recommended to start the creation of a geometry model by drawing the full geometry contour. In addition, the user may specify material layers, structural objects, lines used for construction phases, loads and boundary conditions.

The geometry model should not only include the initial situation, but also situations that occur in the various calculation phases. After the geometry components of the geometry model have been created, the user should compose data sets of material parameters and assign the data sets to the corresponding geometry components Section 4. When the full geometry model has been dened and all geometry components have their initial properties, the nite element mesh can be generated Section 3.

Selecting geometry components When the Selection tool is active, a geometry component may be selected by clicking once on that component in the geometry model. Properties of geometry components Most geometry components have certain properties, which can be viewed and altered in property windows.

After double clicking a geometry component the corresponding property window appears. If more than one object is located on the indicated point, a selection dialog box appears from which the desired component can be selected.

This item can be selected from the Geometry menu as well as from the second tool bar. When the Geometry line option is selected, the user may create points and lines in the draw area by clicking with the mouse pointer graphical input or by typing coordinates at the command line keyboard input. As soon as the left hand mouse button is clicked in the draw area a new point is created, provided that there is no existing point close to the pointer position.

If there is an existing point close to the pointer, the pointer snaps into the existing point without generating a new point. After the rst point is created, the user may draw a line by entering another point, etc. If a point is to be created on or close to an existing line, the pointer snaps onto the line and creates a new point exactly on that line. As a result, the line is split into two new lines. If a line crosses an existing line, a new point is created at the crossing of both lines.

As a result, both lines are split into two new lines. If a line is drawn that partly coincides with an existing line, the program makes sure that over the range where the two lines coincide only one line is present.

All these procedures accomplish that a consistent geometry is created without double points or lines. The Check consistency option in the Geometry menu may be used to check the consistency of the geometry model. To move a point or line, select the point or the line in the cross section and drag it to the desired position. If more than one object is present at the selected position, a delete dialog box appears from which the object s to be deleted can be selected.

If a point is deleted where one or more geometry lines come together, then all these connected geometry lines will be deleted as well. After each drawing action the program determines the clusters that can be formed. A cluster is a closed loop of different geometry lines.

In other words, a cluster is an area fully enclosed by geometry lines. The detected clusters are lightly shaded. Each cluster can be given certain material properties to simulate the behaviour of the soil in that part of the geometry Section 4. The clusters are divided into soil elements during mesh generation Section 3. Plates can be used to simulate the inuence of walls, plates, shells or linings extending in z-direction.

In a geometry model, plates without assigned material properties appear as 'light blue lines', whereas plates with assigned material properties appear in their material set colour. Examples of geotechnical structures involving plates are shown in Figure 3. The creation of plates in the geometry model is similar to the creation of geometry lines Section 3.

When creating plates, the corresponding geometry lines are created simultaneously. Hence, it is not necessary to create rst a geometry line at the position of a plate. The material properties of plates are contained in material data sets Section 4. The most important parameters are the exural rigidity bending stiffness EI and the axial stiffness EA.

When 6-node soil elements are employed then each plate element is dened by three nodes whereas 5-node plate elements are used together with the node soil elements Figure 3. The plate elements are based on Mindlin's plate theory Bathe, This theory allows for plate deections due to shearing as well as bending. In addition, the element can change length when an axial force is applied. Plate elements can become plastic if a prescribed maximum bending moment or maximum axial force is reached.

Bending moments and axial forces are evaluated from the stresses at the stress points. A 3-node plate element contains two pairs of Gaussian stress points whereas a 5-node plate element contains four pairs of stress points.

If this is done when existing forces are present in the plate element, it would change the distribution of bending moments, which is unacceptable.

Geogrids can only sustain tensile forces and no compression. These objects are generally used to model soil reinforcements. Examples of geotechnical structures involving geotextiles are presented in Figure 3. The creation of geogrids in the geometry model is similar to the creation of geometry lines Section 3.

In a geometry model geogrids without assigned material properties appear as 'light yellow lines', whereas geogrids with assigned properties appear in their material colour. When creating geogrids, corresponding geometry lines are created simultaneously. The only material property of a geogrid is an elastic normal axial stiffness EA, which can be specied in the material data base Section 4. Geogrids can be activated or de-activated in calculation phases using Staged construction as Loading input.

Geogrid elements Geogrids are composed of geogrid elements line elements with two translational degrees of freedom in each node u x , u y. When node soil elements are employed then each geogrid element is dened by ve nodes whereas 3-node geogrid elements are used in combination with 6-node soil lements.

Axial forces are evaluated at the Newton-Cotes stress points. These stress points coincide with the nodes. The locations of the nodes and stress points in geogrid elements are indicated in Figure 3. In this case the geogrid is used to model the grouted anchor section and the node-to-node anchor is used to model the ungrouted part of the anchor free length Section 3.

The higher the virtual thickness is, the more elastic deformations are generated. In general, interface elements are supposed to generate very little elastic deformations and therefore the virtual thickness should be small. On the other hand, if the virtual thickness is too small, numerical ill-conditioning may occur. The virtual thickness is calculated as the Virtual thickness factor times the average element size. The average element size is determined by the global coarseness setting for the mesh generation Section 3.

This value is also provided in the General information window in the Output program. The default value of the Virtual thickness factor is 0. This value can be changed by double clicking on the geometry line and selecting the interface from the selection dialog box. In general, care should be taken when changing the default factor. Further details of the signicance of the virtual thickness are given in Section 4.

The creation of an interface in the geometry model is similar to the creation of a geometry line. The interface appears as a dashed line at the right hand side of the geometry line considering the direction of drawing to indicate at which side of the geometry line the interaction with the soil takes place. The side at which the interface will appear is also indicated by the arrow on the cursor pointing in the direction of drawing.

To place an interface at the other side, it should be drawn in the opposite direction. Note that interfaces can be placed at both sides of a geometry line. This enables a full interaction between structural objects walls, plates, geogrids, etc.

This sign is just for identication purposes; it does not have a physical meaning and it has no inuence on the results. A typical application of interfaces would be in a region which is intermediate between smooth and fully rough. The roughness of the interaction is modelled by choosing a suitable value for the strength reduction factor in the interface R inter. This factor relates the interface strength wall friction and adhesion to the soil strength friction angle and cohesion.

Instead of entering R inter as a direct interface property, this parameter is specied together with the soil strength parameters in a material data set for soil and interfaces. For detailed information about the interface material properties, see Section 4. Interfaces can be activated or de-activated in calculation phases using Staged construction as Loading input. Interface elements Interfaces are composed of interface elements. When using node soil elements, the corresponding interface elements are dened by ve pairs of nodes, whereas for 6-node soil elements the corresponding interface elements are dened by three pairs of nodes.

In the gure, the interface elements are shown to have a nite thickness, but in the nite element formulation the coordinates of each node pair are identical, which means that the element has a zero thickness. The position of the Newton Cotes stress points coincides with the node pairs. Hence, ve stress points are used for a node interface element whereas three stress points are used for a 6-node interface element. Interface properties The basic property of an interface element is the associated material data set for soil and interfaces.

This property is contained in the interface properties window, which can be entered by double clicking an interface in the geometry model and selecting the positive or negative interface element or interface chain from the selection window.

Alternatively, the right-hand mouse button may be clicked, then the Properties option should be selected and nally the positive or negative interface element or interface chain may be selected from the right-hand mouse button menu. As a result, the Interface window appears showing the associated Material set. However, any other existing material data set for soil and interfaces can be selected in the Material set drop down menu to change the associated material data set.

In addition, the interface properties window shows the Virtual thickness factor. This factor is used to calculate the Virtual thickness of interface elements see Page The standard value of the Virtual thickness factor is 0. Care should be taken when changing the standard value. The standard value can be restored using the Standard button.

In a consolidation analysis or a groundwater ow analysis, interface elements can be used to block the ow perpendicular to the interface, for example to simulate an impermeable screen.

In fact, when interfaces are used in combination with plates, the interface is used to block the ow since plate elements are fully permeable. In situations where interfaces are used in a mesh where they should be fully permeable, it is possible to de-activate the interface see Sections 5. Interfaces around corner points Figure 3. Corners in stiff structures and an abrupt change in boundary condition may lead to high peaks in the stresses and strains.

Volume elements are not capable of reproducing these sharp peaks and will, as a result, produce non-physical stress oscillations. This problem can be solved by making use of interface elements as shown in Figure 3. These elements will enhance the exibility of the nite element mesh and will thus prevent non-physical stress results. However, these elements should not introduce an unrealistic weakness in the soil. Therefore special attention should be made to the properties of these interface elements Section 4.

It is strongly advised to extend the interface beyond the end ends of the plate in the soil. This avoids the end ends of the plate becoming xed to the soil. A possible result of not extending the interface may be an unrealistic end bearing capacity. Not extended interface b. Extended interface Figure 3. This type of anchors can be selected from the Geometry menu or by clicking on the corresponding button in the tool bar. Typical applications include the modelling of a cofferdam as shown in Figure 3.

It is not recommended to draw a geometry line at the position where a node-to-node anchor is to be placed. However, the end points of node-to-node anchors must always be connected to geometry lines, but not necessarily to existing geometry points. In the latter case a new geometry point is automatically introduced.