civilfem_gridgen

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FLAC3D Grid Generation with ANSYS+CivilFEM

Prepared by:

Bharath Mukundakrishnan and Thomas L. Ruen

Itasca Consulting Group, Inc.708 South Third Street, Suite 310

Minneapolis, Minnesota 55415USA

November 1, 2002

Ref: 8506


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1.0 GRID GENERATION ................................................................................................ 2

1.1 G ENERAL COMMENTS ........................................................................................... 21.2 S OLID MODEL GENERATION .................................................................................. 31.3 FLAC3D MESH FROM ANSYS+C IVIL FEM MESH ................................................... 41.4 G EOMETRY TESTS IN FLAC3D .............................................................................. 7

1.4.1 Geometric Parameters: Orthogonality, Aspect Ratio, Face Planarity ....... 7 1.5 G RID GENERATION USING RATIOS ........................................................................ 111.6 E XAMPLE OF A GRADED GRID .............................................................................. 141.7 ANSYS+C IVIL FEM MESH EXPORTED AND ATTACHED IN FLAC3D .....................16

1.7.1 Several sub-grids attached together ........................................................... 16

1.7.2 Circular tunnels embedded in a grid.......................................................... 19 1.8 C REATION AND MESHING OF TUNNEL INTERSECTION GEOMETRIES ....................... 24

1.8.1 Building and meshing an intersection between two perpendicular tunnels24 1.8.2 Building and meshing three tunnels perpendicular to each other .............. 27 1.8.3 Building and meshing tunnel intersection with ratios ................................ 30 1.8.4 Building and meshing multiple, intersecting tunnels and shafts ................ 33 1.8.5 Building and meshing tunnel intersection at 45

angle..............................36 1.8.6 Building and meshing tunnel intersection at 45

with different radii ........ 41 1.9 M ISCELLANEOUS EXAMPLES ................................................................................ 43

1.9.1 Importing and using an IGES surface to extrude and mesh a volume ....... 43 1.9.2 Import of *.SAT format files (ASIC format) from AutoCAD ...................... 46 1.9.3 A quarter ellipse model............................................................................... 48 1.9.4 A cubic volume cut by an arbitrary surface................................................ 51 1.9.5 Building and meshing a tunnel extruded along a given path ..................... 54


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1.0

GRID GENERATION

1.1 General Comments

Grid generation in FLAC3D is accomplished using five basic primitives (brick, wedge, pyramid, cylinder and tetrahedron) that are built in as a part of the software. In addition,special geometries, such as tunnel intersections, are built into the software based on the five

basic primitives. The built-in models, although useful, do not cover the entire spectrum of problems. Sometimes it is easier to create the model geometry defining curves, surfaces andvolumes and then use a meshing process to convert the geometrical entities into discrete

points and elements in space for analysis. A solid modeler can be used to accomplish the

building of geometry, which can then be used as an input for a meshing utility to mesh thegeometry. ANSYS+CivilFEM 1 is one such software program that can help in both buildingand meshing the geometry.

It is relatively easy to create solid models, but meshing the created model is a complex process. Meshing a 3D model depends on the type of element used. It is possible to meshalmost any complicated solid model with a basic three-dimensional element, namelytetrahedron. But if the solution analysis requires the model to be meshed with a certain typeof element, then meshing can become an involved process. FLAC3D requires that all elements be hexahedrons in order to provide accurate solutions for plasticity.

ANSYS+CivilFEM provides capabilities to build solid model geometry using two differentapproaches and also provides tools to mesh these geometries. The user can choose the eightnoded SOLID45 element from the database of built-in elements to mesh the created solidmodel into hexahedral zones. This element can automatically degenerate into a wedge typeelement or a tetrahedron.

The resultant mesh from ANSYS+CivilFEM can be exported into a FLAC3D format data filethat translates the nodal positions into FLAC3D gridpoint positions and ANSYS+CivilFEM

primitives to FLAC3D primitives. ANSYS+CivilFEM detaches the problem of meshingfrom the problem of building the solid model.

With any numerical method, the accuracy of the result depends on the grid used to representthe physical system. In general, finer meshes (more zones per unit volume) lead to moreaccurate results. Furthermore, the aspect ratio (ratio of the smallest length to largest length ina zone) also affects accuracy. When creating model geometry with FLAC3D , it should bekept in mind that the greatest accuracy is obtained for a model with equal, square zones. If

1. ANSYS+CivilFEM is available from Ingeciber, S.A. For purchasing information visit http://www.ingeciber.com/eng/index.htm


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the model must contain different zone sizes, then a gradual variation in size should be used

for maximum accuracy; this factor is important enough that a special option is provided inthe GENERATE command in FLAC3D whereby zone sizes can be arranged to increase or decrease by a constant ratio along any grid line. ANSYS+CivilFEM has the capability tospecify ratios while meshing a solid model and thus control the size of elements generated.As a general rule, the aspect ratio of a zone should be kept as close to unity as possible.Anything above 5:1 is potentially inaccurate.

The purpose of this document is to show the potential application of ANSYS+CivilFEM as agrid generator for FLAC3D . Several example grids are given to illustrate the types of geometries that can be considered for grid generation. All save files (*.db) and several scriptfiles (*.log) from ANSYS+CivilFEM v6.1 are provided for the examples in this document.

Also, FLAC3D data files (*.dat) exported from the ANSYS+CivilFEM models are provided.All files are compressed in the file CIVILFEM_DAT. ZIP.

1.2 Solid Model Generation

There are two approaches available in ANSYS+CivilFEM to model any given geometry.One approach is called the bottom-up approach, and the other is called the top-downapproach (also called the constructive solid-geometry approach). The bottom-up approachcan be used for very complex geometries that cannot be defined using conic sections or bysimple Boolean operations of basic solid primitives. Points, lines, areas and volumes can becreated to describe the model geometry using this approach. The constructive solid-geometryapproach, on the other hand, is used to create models using basic primitives provided by

ANSYS+CivilFEM and applying Boolean operations on these primitives to construct amodel. The approach that should be used is dependent on the complexity of the model and

perhaps the resourcefulness of the user. Users should refer to ANSYS+CivilFEM manuals for guidance on solid modeling.

Once a solid model has been created, it should be meshed to generate nodes and elements tofill in the solid. Hexahedral meshing of the solid geometry may require extra effort with sub-division, addition and subtraction of volumes. It should be noted that ANSYS+CivilFEM cangenerate tetrahedral meshing very easily with the least input from the user.

There are two types of meshing: mapped meshing, and sweep meshing for creating zones in3D volumes. Mapped meshing involves filling a model volume with the chosen element.Any geometry that needs to be map-meshed must be made topologically equivalent to certain

basic shapes, which can be trivially meshed with the chosen element. ANSYS+CivilFEM has tools that allow volumes, areas and lines to be manipulated so that they conform to some

basic topological entity that can then be easily meshed. Mapped meshing guarantees the


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same type of element throughout the solid model. Sweep meshing is a technique in which a

particular area (called a source area, which can be automatically determined or manuallyspecified) of a volume is meshed and the mesh pattern is swept through the whole volume upto a target surface (automatically determined or manually specified) interpolating the patternwithin the volume. Internally the meshing algorithm meshes the source area such that theresulting 3D element formed by sweeping corresponds to the element chosen by the user.(For FLAC3D grid generation, the 3D element chosen can only be a SOLID45 element.)Sweep meshing can be used effectively to mesh complicated geometries. However, in acomplex model, sweep meshing may have to be done one volume at a time, specifying thesource and target areas manually. The user should take care to ensure that resulting elementsat the interface share the same nodes in order that the model properly transfers forces andother quantities across the meshed volume in FLAC3D . Also, see the ATTACH command

in the FLAC3D command reference manual.

1.3 FLAC3D mesh from ANSYS+CivilFEM mesh

Figure 1 shows the ANSYS+CivilFEM v 6.1 screen that has the FLAC3D export option.

Figure 1 ANSYS+CivilFEM to FLAC3D export option. CivilFEM Preprocessor menu has to be invoked, for this option to work in ANSYS+CivilFEM v 6.1

Any model geometry meshed with a SOLID45 element in ANSYS+CivilFEM can be


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imported into FLAC3D . ANSYS+CivilFEM export option does not recognize other types of

elements. SOLID45 can automatically degenerate into a wedge or a tetrahedron.

ANSYS+CivilFEM creates a script file that generates gridpoints from the nodal positions of the meshed geometry. This is done by issuing a number of GENERATE point commands tocreate gridpoints. ANSYS+CivilFEM then generates FLAC3D primitives using these newlycreated gridpoints. This is done by issuing a series of GENERATE zone commands for FLAC3D zone generation. Since a SOLID45 element in ANSYS+CivilFEM has eight nodesand can degenerate into a wedge or a tetrahedron, only the GENERATE zone brick,GENERATE zone wedge or GENERATE zone tet commands are used in the script file.The format of the output data file created by ANSYS+CivilFEM is shown in Figure 2.

Figure 2 Data file generated by ANSYS+CivilFEM to export mesh intoFLAC3D

The last line in Figure 2 is necessary to establish links to the grid when structural elementsare generated. It is possible to create cables, beams and shells in ANSYS+CivilFEM andexport them into FLAC3D . This option has not been tested extensively and has not beenincluded here. Structural elements can be easily created on the faces of the FLAC3D gridafter importing the grid from ANSYS+CivilFEM . The data files provided inCIVILFEM_DAT.ZIP have additional commands for saving and turning off informationalmessages echoed to the screen. These commands have been added externally for convenienceand do not form a part of original FLAC3D script file generated by ANSYS+CivilFEM .CFTOFL3D.DAT is the default name of the data file exported by ANSYS+CivilFEM thatcontains grid generation data. The other data file FL3DRES.DAT created by

ANSYS+CivilFEM is for exporting FLAC3D structural element results into an ASCII formatfile which can be input into ANSYS+CivilFEM for post-processing.

GEN POINT ID id xpos ypos zpos....GEN ZONE (primitive) p0 POINT id p1 POINT id SIZE x y z GROUP materialnumber....SEL NODE INIT XPOS ADD 0.0


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Figure 3 ANSYS+CivilFEM to FLAC3D export dialog window

Figure 3 shows the ANSYS+CivilFEM to FLAC3D export dialog window when ExportModel option in ANSYS+CivilFEM window ( Figure 1) is invoked. The size variable thatdetermines the number of elements generated can be specified at the time of exporting of

ANSYS+CivilFEM mesh into FLAC3D . When the ANSYS+CivilFEM model needs to beexported into FLAC3D , the user is presented with the dialog box shown in F igure 3. The firstthree edit boxes can be used to specify the size of zones along x, y and z directions:

X Number of divisions corresponds to division of y sizeY Number of divisions corresponds to division of z sizeZ Number of divisions corresponds to division of x size

Thus, it is possible to have a coarsely meshed geometry in ANSYS+CivilFEM and finelymeshed geometry in FLAC3D . Volumes that need to be grouped in FLAC3D can be meshedwith different material names in ANSYS+CivilFEM . These different material names assignedto different meshed volumes in ANSYS+CivilFEM translate into different group namesduring the export process.

When an exported mesh is plotted in FLAC3D and compared with the ANSYS+CivilFEM default plot, the plots are rotated because FLAC3D by convention plots the geometry on theX-Z plane while ANSYS+CivilFEM plots the geometry on the X-Y plane, even though bothuse a right-handed coordinate system.

The radio buttons provided in the dialog box can be used to create irregular hexahedral zonesout of tetrahedral elements generated by ANSYS+CivilFEM . The model should be meshedcompletely with tetrahedral elements for this option to work.


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1.4 Geometry tests in FLAC3D

FLAC3D has three basic tests built in to check the integrity of meshed models to make surethat the model is adequate for simulation purposes. For example, these tests can be used tocheck if there is improper mapping of node points during export of the model into FLAC3D ,resulting in some zones being inside out and hence not suitable for simulation. It can also beused to check if a zone is degenerate or not. Degeneracy can occur if a primitive is createdwithout satisfying the requirements of geometry conditions such as the number of vertices,edges and faces for that particular primitive. The geometry tests in FLAC3D are designed for hexahedral elements only.

1.4.1 Geometric Parameters: Orthogonality, Aspect Ratio, Face Planarity

The geometric aspects of a hexahedral element are evaluated using three quantities,orthogonality, and aspect ratio and face planarity. The quantities compare the hexahedronsto a perfect cube, which is the ideal shape for hexahedral meshes. The GEOM_TEST command invokes the test for all three of these geometric quantities.

Orthogonality . For each grid point in each zone, the determinant of the matrix defined bythe three edge vectors is computed and divided by the produce of their lengths. This gives 1.0for a cube, and approaches zero as pairs of edges approach being coplanar or all threeapproach being coplanar. Each zone is measured by the worst orthogonality value of all grid

points.

Figure 4 Orthogonality Test


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Aspect ratio For each grid point, the ratio of the shortest edge length by the longest edge

length is computed. This will be 1.0 for a cube. It will approach zero as the zone becomesstretched or flattened. Each zone is measured by the worst aspect ratio of all grid points.

Figure 5 Aspect ratio test

Face Planarity Hexahedrons are composed of 6 quadrilateral faces, just like a cubessquare faces, however geometrically it is possible that a quadrilateral polygon in 3D may nothave all 4 vertices coplanar. FLAC3D allows faces to be non-planar, but the greater thedeviation, the less accurate the solution process will be. There is no clear singular method of measuring planarity. A method which compares the volume of a tetrahedron filling the 4

vertices, and the area of the quadrilateral face, computing the area by adding a central pointm=(A+B+C+D)/4, and computing the 4 triangle areas ABC, ABD, ACD, BCD is chosen.The ratio of the cube root of the volume to the square root of the area (to get a dimensionlessvalue) is computed. This value is zero if planar, and positive if non-planar. This test can bescaled by a constant since there is no fundamental limit on how non-planar a face can be.(Values should be


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Figure 6 Face planarity test

Reporting average values for these tests are meaningless since some meshes might be 90%good and 10% bad and give the same average as a mesh with all 80% test quality. Insteaddistribution of values for all the three parameters across all zones in the range specified isreported. The distribution ranges from -1.0 to 1.0 with a 0.1 interval. Thus all zones fallwithin these 20 intervals. This distribution will help identify how many bad zones there are,and how bad. Note that these tests are useful for relative comparisons between different gridsfor the same geometry. For a model to perform well with FLAC3D orthogonality and aspectratio zone test values should be near 1.0 and planarity test values near 0.0. FISH functionscan be written to group all zones that failed to meet minimum standards and thus visualizethe bad zones. The following example illustrates how to use and interpret the definedgeometric measures. A simple 3-by-3 FLAC3D grid is created (See F igure 7) , and thegeometric measures are reported.


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FLAC3D 2.10

Itasca Consulting Group, Inc.Minneapolis, MN USA

Settings: Model Perspective10:02:48 Wed Oct 30 2002

Center:X: 1.500e+000Y: 1.500e+000Z: 1.500e+000

Rotation:X: 30.000Y: 0.000Z: 50.000

Dist: 9.795e+000 Mag.: 0.64Ang.: 22.500

SurfaceMagfac = 0.000e+000

AxesLinestyle

XY

Z

Figure 7 A simple 3-by-3 FLAC3D grid to illustrate geometric aspects of zones

The MS Excel histogram chart in Figure 8 shows the distribution of zones for the threegeometry parameters described above. The range of all three parameters falls between 0.0 and1.0 for any properly formed element suitable for simulation purposes. The zones are testedfor each parameter and based on the value obtained for each parameter tested, added to the

corresponding range of values. Geometry testing is done by issuing the GEOM_TEST command. Thus, we get a distribution of elements for each geometry parameter, and thisdistribution of elements is directed to a log file and plotted as a histogram using MS Excelsoftware. (Other such graph plotting software can also be used.) For a simple regular 3-by-3model, we find that the aspect ratio and orthogonality of all zones are equal to 1.0. The face

planarity of all zones is also 0.0, as all faces are planar. (Even though the aspect ratio andorthogonality of all zones are identically equal to 1.0 and face planarity is identically 0.0 for all zones, they all fall within a range in the chart). Elements that are found outside of thisrange are bad elements and can cause errors during analysis.


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0

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Orthogonality Aspect ratio Face planarity

Figure 8 Distribution of zones for all the three geometric parameters

1.5 Grid generation using ratios

A simple 10 by 20 by 30 unit parallelepiped solid model geometry is generated using ANSYS+CivilFEM . It is then meshed with SOLID45 elements and exported into FLAC3D .The default size of each element edge is set to 2 units. A mapped mesh is created because thetopology lends itself easily to this sort of meshing. Ratios can be specified by picking lines inthe ANSYS+CivilFEM graphical user interface. It is also possible to specify ratios at thecommand line using the LESIZE command in ANSYS+CivilFEM The user should refer to

ANSYS+CivilFEM documentation and create small examples like the ones illustrated here tounderstand the various options by which ratios can be specified to a solid model. Theexample shows the results of using ratios to generate grids in ANSYS+CivilFEM andexported into FLAC3D .


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FLAC3D 2.10



Center:X: 5.000e+000Y: 1.000e+001Z: 1.500e+001

Rotation:X: 30.000Y: 0.000Z: 220.000

Dist: 9.295e+001 Mag.: 0.8Ang.: 22.500


AxesLinestyle

X Y

Z

Figure 9 A uniform 10 by 20 by 30 unit grid. (750 zones and 1056 gridpoints)

Figure 9 shows a uniform grid generated without using ratios in ANSYS+CivilFEM andexported into FLAC3D . In ANSYS+CivilFEM the parameters that can be controlled for obtaining a graded grid are SIZE (element edge length), NDIV (number of element divisions,

used only when SIZE is blank or zero), SPACE (spacing ratio) and ANGSIZE (division of arc in degrees, used only if NDIV and SIZE are blank or zero). In Figure 10 a spacing ratio isapplied along both x and y axes, so that the edge length of the last element is 4 times thelength of the first element. Spacing ratio can also be specified between center element andthe edge element by using a negative number for ratio values. Figure 11 shows theapplication of spacing ratio such that the boundary element lengths along x- and y-axes are 4times the length of elements in the center. The user should consult the ANSYS+CivilFEM manual and try simple examples to become familiar with specifying ratios to generate gradedgrids. The user can also work with the ANSYS+CivilFEM save files and script files providedto regenerate these examples.


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FLAC3D 2.10



Center:X: 5.000e+000Y: 1.000e+001Z: 1.500e+001

Rotation:X: 30.000Y: 0.000Z: 210.000

Dist: 9.295e+001 Mag.: 0.8Ang.: 22.500


AxesLinestyle

XY

Z

Figure 10 A 10 by 20 by 30 unit exported grid with a ratio of 4 (240 zonesand 400 gps) ( end zone length is 4 times the start zone length)

FLAC3D 2.10



Center:X: 5.000e+000Y: 1.000e+001Z: 1.500e+001

Rotation:X: 30.000Y: 0.000Z: 220.000

Dist: 9.295e+001 Mag.: 0.8Ang.: 22.500


AxesLinestyle

X Y

Z

Figure 11 A 10 by 20 by 30 exported grid with a ratio of 4 (375 zones and 576 gps) applied from center to end( end zone length is 4 times thecenter zone length)


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1.6 Example of a graded grid

The following example gives an illustration of creating a graded grid in ANSYS+CivilFEM and exporting it into FLAC3D . The solid model is a 30 by 20 by 20 unit parallelepiped with a5 by 20 by 5 unit parallelepiped in the center generated using ANSYS+CivilFEM solidmodeler. The division of the ANSYS+CivilFEM solid model into different volumes to

produce this graded grid is shown. A graded grid is produced when the number of elementdivisions is fixed (Number of element divisions is 4, see Figure 12) along the boundary of thevolume and at its interior.

Figure 12 Division of ANSYS+CivilFEM volume for subsequent meshing.Center volume is given a different material ID to group it differently in FLAC3D


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Figure 13 ANSYS+CivilFEM generated mesh

FLAC3D 2.10



Center:X: 1.500e+001Y: 1.000e+001Z: 1.000e+001

Rotation:X: 20.000Y: 0.000Z: 330.000

Dist: 9.295e+001 Mag.: 0.8Ang.: 22.500

Block GroupMAT00001MAT00002

AxesLinestyle

X

Y

Z

Figure 14 Graded grid exported into FLAC3D (160 zones and 267 gridpoints)


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The geometric aspects of the FLAC3D grid are shown below. It can be seen that the aspect

ratio is affected by the gradation of the grids.

020

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Orthogonality Aspect Ratio Face Planarity

Figure 15 Geometric aspects

1.7 ANSYS+CivilFEM mesh exported and attached in FLAC3D

This series of examples show model geometries whose volumes are independently meshedin ANSYS+CivilFEM and attached using the ATTACH command in FLAC3D .

ANSYS+CivilFEM does not allow the interface area between different volumes to havedifferent meshing densities. FLAC3D allows meshes of different densities (refer toATTACH command in the FLAC3D Command Reference volume for details) to be attachedusing the ATTACH command. The ATTACH command is useful only if the ratio of thenumber of divisions between the sub-grid and the main grid is an integral quantity. For verycomplex geometries, one should be careful in setting up the geometry, element sizes andratios in ANSYS+CivilFEM so that meshes can be attached and satisfactorily used for

simulation purposes.

1.7.1 Several sub-grids attached together

A parallelepiped model of dimensions 20 by 10 by 5 units is created in ANSYS+CivilFEM and divided into five separate volumes to be meshed with different densities. In this case, partof the mesh has a two to one ratio with other meshes and part of the mesh has a three to one


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ratio with other meshes. The ratio is fixed by changing the number of element divisions along

x- and y-directions and also specifying a spacing ratio before each volume is meshed. Userscan regenerate the example by referring to the script files to generate the FLAC3D mesh andthe ANSYS+CivilFEM save file (*.db). Please note that z size is increased by a factor of twowhen exporting from ANSYS+CivilFEM . (See Figure 3)

After attaching the grids in FLAC3D using the ATTACH command, a y-velocity of -1.0e-2is applied on the top of the grid and the resulting displacement contour is shown to beuniformly spread across attach boundaries.

Figure 16 ANSYS+CivilFEM model with different volumes for specifying different mesh densities


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FLAC3D 2.10


Step 3986 Model Perspectiv e10:25:59 Wed Oct 30 2002

Center:X: 1.000e+001Y: 5.000e+000Z: 2.500e+000

Rotation:X: 110.000Y: 320.000Z: 0.000

Dist: 6.030e+001 Mag.: 1Ang.: 22.500


AxesLinestyle

X

Y

Z

Figure 17 FLAC3D Attach grid (1108 zones, 1830 gridpoints)

FLAC3D 2.10



Center:X: 1.000e+001Y: 5.000e+000Z: 2.500e+000

Rotation:X: 110.000Y: 330.000Z: 0.000

Dist: 6.030e+001 Mag.: 1Ang.: 22.500

SketchMagfac = 0.000e+000Linestyle

Attach

Figure 18 View of attached grid points


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FLAC3D 2.10



Center:X: 1.000e+001Y: 5.000e+000Z: 2.500e+000

Rotation:X: 110.000Y: 320.000Z: 0.000

Dist: 6.030e+001 Mag.: 1Ang.: 22.500

Contour of Displacement Mag.Magfac = 0.000e+000

0.0000e+000 to 0.0000e+0002.5000e+004 to 5.0000e+0047.5000e+004 to 1.0000e+0051.2500e+005 to 1.5000e+0051.7500e+005 to 2.0000e+0052.2500e+005 to 2.5000e+0052.7500e+005 to 3.0000e+0053.2500e+005 to 3.5000e+0053.7500e+005 to 3.9860e+005

Interval = 2.5e+004

AxesLinestyle

X

Y

Z

Figure 19 Displacement contour plot

1.7.2 Circular tunnels embedded in a grid

This is another example to show how to create individual meshes with different densities in ANSYS+CivilFEM and use the FLAC3D ATTACH command to connect the meshes. Threetunnels with a radius of 2.5 units are embedded in a grid of dimensions 60 by 60 by 1 unit.Square sections of 10 by 10 units with finer mesh densities are attached to the main grid.The mesh density around the circular tunnel has a 2:1 ratio with the mesh density outside thesquare volumes. This is accomplished by specifying the exact number of element divisionsfor all the inner and outer edges (refer to the ANSYS+CivilFEM manual for specification of ratios). The outer dimensions have 30 element divisions and the inner dimensions have 5element divisions. The three tunnels have 10 element divisions along the outer dimensionsand the circular arc is composed of 20 element divisions (5 elements for each quarter of anarc). See the corresponding data file and ANSYS+CivilFEM save file to recreate the modeland the meshed geometry.

A similar mesh is also created directly in FLAC3D using GENERATE zone radcyl commands for comparison to the ANSYS+CivilFEM generated model.

A stress field is applied to the FLAC3D grid and ANSYS+CivilFEM generated grid (refer tothe data file). Comparisons are made between the resultant displacement contour plots for thetwo grids in Figure 20 and Figure 22 . It can be seen that the displacement contour values are


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similar. The results of geometric tests are also included in Figure 21 and Figure 23 for

comparison purposes.FLAC3D 2.10



Center:X: 3.000e+001Y: 3.000e+001Z: -1.000e+000

Rotation:X: 90.000Y: 0.000Z: 0.000

Dist: 1.959e+002 Mag.: 1Ang.: 22.500


0.0000e+000 to 0.0000e+0000.0000e+000 to 5.0000e-0045.0000e-004 to 1.0000e-0031.0000e-003 to 1.5000e-0031.5000e-003 to 2.0000e-0032.0000e-003 to 2.5000e-0032.5000e-003 to 3.0000e-003

3.0000e-003 to 3.5000e-0033.5000e-003 to 4.0000e-0034.0000e-003 to 4.5000e-0034.5000e-003 to 5.0000e-0035.0000e-003 to 5.5000e-0035.5000e-003 to 6.0000e-0036.0000e-003 to 6.5000e-0036.5000e-003 to 6.7323e-003

Interval = 5.0e-004

AxesLinestyle

X

Y

Z

Figure 20 Displacement contour plot of ANSYS+CivilFEM generated mesh with 2166 zones and 3603 gridpoints

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Figure 21 Geometric parameters of ANSYS+CivilFEM generated grid.


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FLAC3D 2.10



Center:X: 3.000e+001Y: 3.000e+001Z: 5.000e-001

Rotation:X: 90.000Y: 0.000Z: 0.000

Dist: 1.959e+002 Mag.: 1Ang.: 22.500


0.0000e+000 to 0.0000e+0000.0000e+000 to 5.0000e-0045.0000e-004 to 1.0000e-0031.0000e-003 to 1.5000e-0031.5000e-003 to 2.0000e-0032.0000e-003 to 2.5000e-0032.5000e-003 to 3.0000e-0033.0000e-003 to 3.5000e-0033.5000e-003 to 4.0000e-0034.0000e-003 to 4.5000e-0034.5000e-003 to 5.0000e-0035.0000e-003 to 5.5000e-003

5.5000e-003 to 6.0000e-0036.0000e-003 to 6.5000e-0036.5000e-003 to 6.8022e-003

Interval = 5.0e-004

AxesLinestyle

X

Y

Z

Figure 22 FLAC3D generated grid with 1185 zones and 2666 gridpoints

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Figure 23 Geometric parameters of FLAC3D generated grid


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This example is repeated without an attached boundary surrounding the tunnels. The circular

tunnel length is divided into 20 elemental divisions (5 divisions for each quarter of thecircular length) and the outer edges are specified an elemental division of 30. Both an

ANSYS+CivilFEM generated model and a FLAC3D generated model are created as before.Meshing for the ANSYS+CivilFEM generated grid was accomplished by first meshing onesection which was subsequently extruded to create volume elements. Refer to the

ANSYS+CivilFEM documentation for details on meshing techniques. In the FLAC3D generated model, circular tunnels are created from square tunnels by remapping thegridpoints using FISH.

A stress field is applied to the FLAC3D generated grid and the ANSYS+CivilFEM generatedgrid and comparisons are made between the resultant displacement contour plots for the two

grids. Compare Figure 24 and Figure 26. It can be seen that the displacement contour valuesare similar. The results of geometric tests are also included for comparison purposes, inFigure 25 and Figure 27 .

FLAC3D 2.10


Step 1987 Model Perspective10:40:45 Wed Oct 30 2002

Center:X: 3.000e+001Y: 3.000e+001Z: -1.000e+000

Rotation:X: 90.000Y: 0.000Z: 0.000

Dist: 1.959e+002 Mag.: 1Ang.: 22.500


0.0000e+000 to 0.0000e+0000.0000e+000 to 5.0000e-0045.0000e-004 to 1.0000e-0031.0000e-003 to 1.5000e-0031.5000e-003 to 2.0000e-0032.0000e-003 to 2.5000e-0032.5000e-003 to 3.0000e-0033.0000e-003 to 3.5000e-0033.5000e-003 to 4.0000e-0034.0000e-003 to 4.5000e-0034.5000e-003 to 5.0000e-0035.0000e-003 to 5.5000e-0035.5000e-003 to 6.0000e-0036.0000e-003 to 6.5000e-0036.5000e-003 to 6.5183e-003

Interval = 5.0e-004

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Figure 24

Displacement contour of ANSYS+CivilFEM generated mesh(882 zones, 1940 gps)


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Figure 25 Geometric parameters of ANSYS+CivilFEM grid

FLAC3D 2.10



Center:X: 3.000e+001Y: 3.000e+001Z: 5.000e-001

Rotation:X: 90.000Y: 0.000Z: 0.000

Dist: 1.959e+002 Mag.: 1Ang.: 22.500


0.0000e+000 to 0.0000e+0000.0000e+000 to 5.0000e-0045.0000e-004 to 1.0000e-0031.0000e-003 to 1.5000e-0031.5000e-003 to 2.0000e-0032.0000e-003 to 2.5000e-0032.5000e-003 to 3.0000e-0033.0000e-003 to 3.5000e-0033.5000e-003 to 4.0000e-0034.0000e-003 to 4.5000e-0034.5000e-003 to 5.0000e-0035.0000e-003 to 5.3768e-003

Interval = 5.0e-004

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Figure 26 FLAC3D mesh with 873 zones and 1898 gridpoints


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orthogonality Aspect Ratio Face Planarity

Figure 27 Geometric parameters for FLAC3D grid

1.8 Creation and meshing of tunnel intersection geometries

In this section a series of examples are shown that illustrate how to model and mesh tunnelintersections using ANSYS+CivilFEM .

1.8.1 Building and meshing an intersection between two perpendicular tunnels

This model consists of two tunnels: a smaller-diameter service tunnel, and a larger-diameter main tunnel intersecting at right angles to each other. The base of the model extends from -5to 10 units along the x-axis, 0 to 8 units along the y-axis and 0 to 6 units along the z-axis. Theradius of the main tunnel is 3 units and the radius of the service tunnel is 2 units.

The ANSYS+CivilFEM solid model corresponding to the dimensions above is shown in

Figure 28.


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Figure 28 ANSYS+CivilFEM generated model volumes

It can be seen that the tunnel volume and the base volume have been divided into manysmaller volumes. This is done to facilitate the sweep meshing for all volumes. The volumesshould also be grouped and appropriate material names given so that all volumescorresponding to one object, e.g., the main tunnel, have the same material name. The

volumes with different material names will be assigned different group names when they areexported. The resultant ANSYS+CivilFEM mesh shown in Figure 29 and consists of 828hexahedral elements and 1160 nodes.


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Figure 29 ANSYS+CivilFEM generated mesh with 819 elements and 1150 nodes

The exported FLAC3D model (See Figure 30) has 6624 zones, which is 8 times the number of elements generated by ANSYS+CivilFEM (828 elements). This zoning is achieved byspecifying a size factor of two along all three axes when exporting to FLAC3D (See section1.3) .

FLAC3D 2.10



Center:X: 2.500e+000Y: 4.000e+000Z: 3.000e+000

Rotation:X: 210.000Y: 0.000Z: 230.000

Dist: 4.548e+001 Mag.: 0.8Ang.: 22.500

Block GroupMAT00003MAT00001MAT00002

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Figure 30 Exported FLAC3D model with 6624 zones and 7887 gridpoints


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Figure 31 Distribution of zones for geometric parameters.

From Figure 31 , it can be seen that the orthogonality values of many of the zones are close to1.0, which usually will result in a better solution using FLAC3D . The aspect ratios vary withthe specification of zoning ratios. It can also be seen that most of the faces are planar.

1.8.2 Building and meshing three tunnels perpendicular to each other

This model consists of a shaft that opens into a service tunnel, which, in turn, connects to amain tunnel perpendicular to the service tunnel. The base of the model extends from -16 to16 units along the x-direction, 0 to 8 units along the y-direction and 0 to 6 units along the z-direction. The radius of the main tunnel is 4 units, the radius of the shaft is 3 units and theradius of the service tunnel is 2 units. The ANSYS+CivilFEM -generated solid modelcorresponding to these dimensions is shown in Figure 32.


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Figure 32 ANSYS+CivilFEM generated solid model

The solid model has been divided into many volumes to facilitate sweep meshing for all thevolumes. The volumes should also be grouped appropriately so that all volumes that belongto a particular entity, say a tunnel, have the same material. This ensures that all these volumesare grouped together as one entity for FLAC3D during the export process. The

ANSYS+CivilFEM generated mesh is shown in F igure 33. The model consists of 1330elements and 1760 nodes.


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Figure 33 ANSYS+CivilFEM generated mesh

FLAC3D 2.10



Center:X: 1.028e+000

Y: 5.226e+000Z: 3.000e+000

Rotation:X: 30.000

Y: 180.000Z: 310.000Dist: 9.248e+001 Mag.: 1.25

Ang.: 22.500

Block GroupMAT00001MAT00004MAT00003MAT00002

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Figure 34 Exported FLAC3D grid


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Figure 35 Distribution of zones for geometric parameters

The geometric aspects of the resultant FLAC3D grid are shown in F igure 35 f rom which itcan be seen that orthogonality values for most of the zones lie in the range 0.7 to 1.0. Face

planarity values are low.

1.8.3 Building and meshing tunnel intersection with ratios

In many analyses, a fine mesh is desired only at particular areas of interest. In other areas, far removed from the problem domain, it is possible to have larger and, hence, fewer numbers of elements. This helps in reducing the time required to complete an analysis. In FLAC3D , thisis achieved by using ratios. ANSYS+CivilFEM also provides the user with such capability.An example to illustrate the use of ratios for a complicated tunnel intersection model isillustrated below.

This model consists of two tunnels of different radii intersecting at right angles to each other.The model extends from 0 to 20 units along the x-direction, 0 to 32 units along the y-direction and 0 to 20 units along the z-direction. The radius of the main tunnel is 3 units and

the radius of the service tunnel is 2 units. All edges have been divided in such a way that theratio between the last element division and the first division is 5.0. The ANSYS+CivilFEM model corresponding to the dimensions above is shown in F igure 36 and meshed model isshown in Figure 37.


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Figure 36 ANSYS+CivilFEM generated solid model

Figure 37 ANSYS+CivilFEM mesh with all edges having a ratio of 5.0 (last division/first division)

The exported FLAC3D mesh with a total of 1783 elements and 2250 nodes is shown inFigure 38. The geometric aspects of the exported FLAC3D mesh are shown in Figure 39.


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FLAC3D 2.10



Center:X: 1.069e+001Y: 1.440e+001Z: 1.135e+001

Rotation:X: 210.000Y: 0.000Z: 220.000

Dist: 7.130e+001 Mag.: 0.64Ang.: 22.500


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Figure 38 ANSYS+CivilFEM exported FLAC3D mesh

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Figure 39

Distribution of zones for geometric parameters

From Figure 39 , it is no surprise that the aspect ratio follows a distribution because we havespecified ratios for edges while meshing.


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1.8.4 Building and meshing multiple, intersecting tunnels and shafts

This model consists of two horseshoe-shaped tunnels running perpendicular to each other andtwo other cylindrical shafts, as shown in Figure 40 and Figure 41. The important dimensionsof the tunnel are given as follows. The lengths of tunnels are arbitrary.

Main-tunnel diameter 34 units

Rectangular cross-section of connection between main tunneland the smaller tunnels 14 units by 5units

Diameter of all the small tunnels,including the cylindrical portion of thehorseshoe-shaped tunnel 8 units

Figure 40 ANSYS+CivilFEM model geometry showing all the tunnels and shafts


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Figure 41 Tunnels and shafts embedded within the volume shown in detail

Figure 42 ANSYS+CivilFEM grid with 25986 elements and 29046 nodes


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FLAC3D 2.10



Center:X: 2.407e+001Y: -2.462e+000Z: 5.383e+001

Rotation:X: 220.000Y: 0.000Z: 140.000

Dist: 3.818e+002 Mag.: 0.8Ang.: 22.500


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Figure 43 ANSYS+CivilFEM exported FLAC3D grid

FLAC3D 2.10



Center:X: 2.590e+001

Y: 6.248e+000Z: 4.728e+001

Rotation:X: 220.000

Y: 0.000Z: 140.000Dist: 3.818e+002 Mag.: 1

Ang.: 22.500

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Figure 44 Detailed view of tunnels embedded inside the volume


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The resulting meshed model has very good geometric properties, as seen by the values of orthogonality and face planarity. The aspect ratio varies with specification of ratios.

1.8.5 Building and meshing tunnel intersection at 45 angle

This example shows the capability of ANSYS+CivilFEM to create tunnel intersections atarbitrary angles, which can be meshed and used for analysis in FLAC3D . A 45

angle of intersection is chosen for illustration. The tunnels in the resultant exported model areexcavated and the model is brought to equilibrium under gravity. The stress state of theresulting analysis is then shown and compared with an equivalent FLAC3D grid. The modelextends from -15 to 15 units along x direction, 0 to 60 units along the y direction and -10 to 0along the z direction. The radius of the intersecting tunnels is 4 units. F igure 46 s hows thedivision of volumes for sweep meshing the model. The generated mesh in

ANSYS+CivilFEM is shown in F igure 47.


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Figure 46 ANSYS+CivilFEM model for tunnel intersection at 45

Figure 47 ANSYS+CivilFEM generated mesh with 2240 elements and 2636 nodes

A size factor of two (See Section 1.3) is applied along the x-, y- and z-directions beforeexporting to FLAC3D . This further refines the mesh and the resultant FLAC3D mesh isshown below.


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FLAC3D 2.10



Center:X: 3.107e+000Y: 2.759e+001Z: 1.468e+000

Rotation:X: 200.000Y: 0.000Z: 220.000

Dist: 1.130e+002 Mag.: 0.64Ang.: 22.500


AxesLinestyle

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Figure 48 Exported FLAC3D mesh with 17920 zones and 19447 gridpoints as a result of specifying NDIV of 2.0

FLAC3D 2.10



Center:X: 3.107e+000Y: 2.759e+001Z: 1.468e+000

Rotation:X: 200.000Y: 0.000Z: 220.000

Dist: 1.130e+002 Mag.: 0.8Ang.: 22.500


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Figure 49 FLAC3D plot showing tunnels only


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From Figure 50 , it can be seen that the orthogonality values of many of the zones are close to0.7, and there is a distribution of orthogonality values. The aspect ratio can be varied withspecification of ratios. It can also be seen that face planarity values are close to zero. Themodel is brought to equilibrium under gravity loading and the z-stress of the resulting grid isshown in Figure 51.


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FLAC3D 2.10



Center:X: 2.985e+000Y: 2.750e+001Z: 2.374e-008

Rotation:X: 200.000Y: 0.000Z: 220.000

Dist: 1.130e+002 Mag.: 0.64Ang.: 22.500

Contour of SZZMagfac = 0.000e+000Gradient Calculation

-6.3465e+005 to -6.0000e+005-6.0000e+005 to -5.5000e+005-5.5000e+005 to -5.0000e+005-5.0000e+005 to -4.5000e+005-4.5000e+005 to -4.0000e+005-4.0000e+005 to -3.5000e+005-3.5000e+005 to -3.0000e+005-3.0000e+005 to -2.5000e+005-2.5000e+005 to -2.0000e+005-2.0000e+005 to -1.5000e+005-1.5000e+005 to -1.0000e+005

-1.0000e+005 to -5.0000e+004-5.0000e+004 to 0.0000e+0000.0000e+000 to 2.4355e+004

Interval = 5.0e+004

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Figure 51 Contour of z-stress for exported FLAC3D grid

FLAC3D 2.10



Center:X: 0.000e+000Y: 3.000e+000Z: 0.000e+000

Rotation:X: 30.000Y: 0.000Z: 320.000

Dist: 3.465e+001 Mag.: 0.64Ang.: 22.500

Contour of SZZMagfac = 0.000e+000Gradient Calculation

-3.5029e+005 to -3.5000e+005-3.2500e+005 to -3.0000e+005-2.7500e+005 to -2.5000e+005-2.2500e+005 to -2.0000e+005-1.7500e+005 to -1.5000e+005-1.2500e+005 to -1.0000e+005-7.5000e+004 to -5.0000e+004-2.5000e+004 to 0.0000e+0000.0000e+000 to 6.3358e+003

Interval = 2.5e+004

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Figure 52 Contour of z-stress for FLAC3D grid created in Example Application 5 (TUN45.DAT)


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The stress state for an equivalent FLAC3D grid is shown in Figure 52. The model generation

for this example can be found in Example Application 5 in the FLAC3D ExampleApplications volume. Data files are also provided to recreate this example.

It can be seen that the stress profiles for both the grids are similar. The ANSYS+CivilFEM mesh can be further improved by extending the geometry to minimize boundary effects.Ratios can also be specified to speed up the analysis.

1.8.6 Building and meshing tunnel intersection at 45 with different radii

The following example shows the meshing for tunnels intersecting at 45

, but with differentradii. The model extends from -15 to 15 units along the x-direction, 0 to 60 units along the y-

direction and -10 to 0 along the z-direction. The radius of the intersecting tunnels is 4 unitsand 3 units. Figure 53 shows the division of volumes for sweep meshing the model.

Figure 53 Division of volumes for meshing of tunnels intersecting at 45 and with different radii


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Figure 54 ANSYS+CivilFEM mesh generated

FLAC3D 2.10



Center:X: -2.985e+000Y: 3.250e+001Z: 2.495e-008

Rotation:X: 200.000Y: 0.000Z: 40.000

Dist: 1.130e+002 Mag.: 0.64Ang.: 22.500


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Figure 55 Exported FLAC3D grid (6956 zones, 8250 gps)


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FLAC3D 2.10



Center:X: -1.069e+000Y: 3.090e+001Z: 8.942e-009

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Figure 56 FLAC3D grid showing only the tunnels

1.9 Miscellaneous examples

In this section, examples are shown that illustrate additional and useful capabilities of ANSYS+CivilFEM . Solid model data from many of the solid modeling packages thatconform to IGES, CATIA, Pro/E, UniGraphics, SAT (ASIC 7.0 and below), PARASOLID,IDEAS can be directly imported into ANSYS+CivilFEM and meshed using the ANSYS mesher. The meshed model can then be imported into FLAC3D . These formats specify howto store solid model data so that the model can be reconstructed at a later time from the data.IGES stores volumes as a set of faces that need to be reconstructed in ANSYS+CivilFEM .

ANSYS+CivilFEM provides tools to import and cure (create solids from these faces andcorrect tolerance errors) IGES format files. Consult the ANSYS+CivilFEM manual for details. AutoCAD 3D models can be output in ASIC format (with extension *.SAT) that can

be imported into ANSYS+CivilFEM , meshed and exported to FLAC3D . Consult the ANSYS+CivilFEM manual on the type and scope of formats that are supported.

1.9.1 Importing and using an IGES surface to extrude and mesh a volume

The following example shows a surface that is stored as an IGES file and imported into ANSYS+CivilFEM . It is then used to extrude a volume, subsequently meshed and exported


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to FLAC3D . The surface geometry is a simplified topological surface. The surface is not

governed by any equation.

Figure 57 An imported IGES surface displayed in ANSYS+CivilFEM

Figure 58 Surface extruded and meshed in ANSYS+CivilFEM


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FLAC3D 2.10



Center:X: 4.857e+005Y: 4.289e+006Z: -2.342e+003

Rotation:X: 130.000Y: 150.000Z: 50.000

Dist: 6.388e+004 Mag.: 1Ang.: 22.500


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Figure 59 Extruded volume imported into FLAC3D

It can be noted that the surface topography is replicated through the depth of extrusion. Oncea volume is generated, Boolean operations can also be performed to modify the volume tosuit the users needs.

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From Figure 60 , it can be seen that the orthogonality values of many of the zones are close to

1.0. The aspect ratio varies with specification of ratios. It can also be seen that most of thefaces are planar.

1.9.2 Import of *.SAT format files (ASIC format) from AutoCAD

Solid models can be constructed in AutoCAD , and stored as an ASIC format file. ANSYS+CivilFEM can import and interpret this format and recreate the same model in itsown solid modeling environment. This can then be meshed and exported to FLAC3D . Usersshould note that DXF files cannot be imported into ANSYS+CivilFEM . This exampleillustrates building a simple cube with an elliptical tunnel embedded in it. The model iscreated in AutoCAD and imported into ANSYS+CivilFEM , meshed and exported to

FLAC3D . The example shows the capability of ANSYS+CivilFEM to read in a AutoCAD model.

Figure 61 AutoCAD generated solid model


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Figure 62 ANSYS+CivilFEM mesh for the exported solid model

FLAC3D 2.10



Center:X: 1.000e+001Y: 1.000e+001Z: 1.000e+001

Rotation:X: 110.000Y: 330.000Z: 0.000

Dist: 6.530e+001 Mag.: 0.64Ang.: 22.500


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Figure 63 Exported FLAC3D model (690 zones , 954 gridpoints)


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From Figure 64 , it can be seen that the orthogonality values of many of the zones are close to1.0. It can also be seen that most of the faces are planar.

1.9.3 A quarter ellipse model

This example illustrates that the symmetric nature of the model can be used to create asimpler ANSYS+CivilFEM model, which is then meshed and exported to FLAC3D. Themodel can then be further manipulated using FLAC3D mesh generation facilities. Onequarter of an ellipse is embedded in a square block and both the block and ellipse are meshedand grouped separately. The dimensions are chosen arbitrarily.


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Figure 65 ANSYS+CivilFEM model with quarter of an ellipse embedded in a cube.

Figure 66 ANSYS+CivilFEM mesh


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FLAC3D 2.10



Center:X: 2.500e+000Y: -2.500e+000Z: -2.500e+000

Rotation:X: 120.000Y: 40.000Z: 0.000

Dist: 1.633e+001 Mag.: 0.64Ang.: 22.500


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Figure 67 Exported FLAC3D model with 288 zones and 385 gridpoints

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From Figure 68 , it can be seen that the orthogonality values of many of the zones are close to0.8, and there are a few zones that have a value close to 0.0 at the center of the ellipse. It canalso be seen that most of the faces are planar.


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It is now possible to complete the model using FLAC3D mesh generation capabilities to

extend the ANSYS+CivilFEM created mesh. Care should be taken so that the boundary facesof the model generated by ANSYS+CivilFEM and exported to FLAC3D coincide with theFLAC3D generated faces. Figure 69 shows the exported ANSYS+CivilFEM grid reflectedabout the x- and y-axis to generate the full scale model.

FLAC3D 2.10



Center:X: 0.000e+000Y: 0.000e+000Z: -2.500e+000

Rotation:X: 30.000Y: 0.000Z: 50.000

Dist: 3.265e+001 Mag.: 0.8Ang.: 22.500

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Figure 69 Reflected FLAC3D model

1.9.4 A cubic volume cut by an arbitrary surface.

Surfaces can be generated in ANSYS+CivilFEM using some of the tools provided for modeling purposes and used to create topography inside a solid model. This example showsthe creation of a surface and a solid model cut by the surface. The solid model is thengrouped into two different parts with the surface topography forming a boundary between thetwo groups of elements.


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Figure 70 An arbitrary surface modeled in ANSYS+CivilFEM

Figure 71 ANSYS+CivilFEM cube cut by the surface and meshed


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FLAC3D 2.10



Center:X: 3.142e+001Y: 0.000e+000Z: 2.850e+001

Rotation:X: 300.000Y: 130.000Z: 0.000

Dist: 1.937e+002 Mag.: 0.8Ang.: 22.500


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Figure 72 Exported FLAC3D grid ( 2000 zones and 2541 gridpoints)

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From Figure 73 , it can be seen that the orthogonality values of many of the zones are close to1.0. It can also be seen that most of the faces are planar with values close to 0.1.


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1.9.5 Building and meshing a tunnel extruded along a given path

In this example, a cylindrical half area is extruded along a line in the shape of a questionmark. This extrusion of volumes is accomplished by using solid modeling tools provided by

ANSYS+CivilFEM . The base extends from -15 to 15 units in the x-direction, 0 to 7 units inthe y-direction, 0 to 40 units in the z-direction, and the radius of the cylindrical half area is 1unit.

Figure 74 ANSYS+CivilFEM volume that corresponds to tunnel in theshape of question mark


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Figure 75 ANSYS+CivilFEM mesh

FLAC3D 2.10



Center:X: -1.732e+000Y: 3.500e+000Z: 1.900e+001

Rotation:X: 310.000Y: 40.000Z: 0.000

Dist: 1.141e+002 Mag.: 0.8Ang.: 22.500


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Figure 76 Exported FLAC3D grid ( 8059 zones, 9308 gridpoints)


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From Figure 77 , it can be seen that the orthogonality values of many of the zones are close to1.0. It can also be seen that most of the faces are planar.

civilfem_gridgen

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