PROBLEM SOLVING WITH FLAC3D 3-9 To see the effects of using the ratio keyword, type the command 510612 ratio1111.2 Each size entry is controlled by a ratio. In this example, the fourth size entry has a geometric ratio of 1.2-1.e, each successive zone is 1. 2 times larger than the preceding zone, moving from the tunnel periphery to the outer boundary(see Figure 3. 3). A ratio smaller than 1.0 can be given to hange from an increasing to a decreasing geometric ratio FLAC3D3. 10 shown Figure 3.3 Radially graded grid around cylindrical tunnel Sizing the grid for accurate results, but with a reasonable number of zones, can be complicated Three factors should be remembered Finer meshes lead to more accurate results in that they provide a better representation of high-stress gradients 2. Accuracy increases as zone aspect ratios tend to unity 3. If different zone sizes are needed, then the more gradual the change from the smallest to the largest, the better the results The examples in the following sections illustrate some applications of these factors Several GENERATE zone commands can be given to connect two or more primitive shapes together to build a grid. For example, to build a horseshoe-shaped tunnel, the radcy linder and radtunnel shapes can be used as demonstrated in Example 3.1 FLAC3D Version 3.1
PROBLEM SOLVING WITH FLAC3D 3-9 To see the effects of using the ratio keyword, type the command gen zone radcyl size 5 10 6 12 ratio 1 1 1 1.2 Each size entry is controlled by a ratio. In this example, the fourth size entry has a geometric ratio of 1.2 — i.e., each successive zone is 1.2 times larger than the preceding zone, moving from the tunnel periphery to the outer boundary (see Figure 3.3). A ratio smaller than 1.0 can be given to change from an increasing to a decreasing geometric ratio. FLAC3D 3.10 Itasca Consulting Group, Inc. Minneapolis, MN USA Settings: Model Perspective 13:45:16 Mon Nov 06 2006 Center: X: 3.509e+000 Y: 4.633e+000 Z: 3.000e+000 Rotation: X: 355.000 Y: 0.000 Z: 20.000 Dist: 2.159e+001 Mag.: 0.8 Ang.: 22.500 Surface Magfac = 0.000e+000 Live & unassigned mech zones shown Axes Linestyle Y X Z Figure 3.3 Radially graded grid around cylindrical tunnel Sizing the grid for accurate results, but with a reasonable number of zones, can be complicated. Three factors should be remembered: 1. Finer meshes lead to more accurate results in that they provide a better representation of high-stress gradients. 2. Accuracy increases as zone aspect ratios tend to unity. 3. If different zone sizes are needed, then the more gradual the change from the smallest to the largest, the better the results. The examples in the following sections illustrate some applications of these factors. Several GENERATE zone commands can be given to connect two or more primitive shapes together to build a grid. For example, to build a horseshoe-shaped tunnel, the radcylinder and radtunnel shapes can be used as demonstrated in Example 3.1. FLAC3D Version 3.1
3-10 User's guide Example 3. 1 Building a horseshoe-shaped tunnel-half model gen zone radcyl size 5 10 6 12 rat 111 1.2& p00,0,0p1100,0,0p20,200,0p30,0,100 gen zone radtun size 5 10 5 12 rat 111 1.2& 00,0,0p10,0,-100p20,200,0p3100,0,0 Figures 1 12 and 1. 13 in the Command Reference should be consulted when building these shapes The model boundary dimensions are 100 x 200 x 100; the boundary coordinates are defined with the po, p1, p2 and p3 keywords. The grid is shown in Figure 3. 4. Note that the radtunnel shape is turned 90 to fit beneath the radcylinder shape. This is accomplished by specifying different pI-, 2-and p3-coordinate entries for the radtunnel shape FLACD3.10 0.0006+000 Figure 3. 4 Horseshoe-shaped tunnel made from radcylinder and radtunnel primmuinves With GENERATE zone, two additional options are available to assist with the creation of a grid composed of multiple shapes: GENERATE zone copy and GENERATEzone reflect. The copy keyword is used to copy a shape or shapes to a new position by adding an offset vector to all the gridpoints The reflect keyword is used to reflect the shape or shapes across a symmetry plane. Example 3. 2 shows the additional command needed to reflect the geometry created by the earlier commands FLAC3D Version 3.1
3 - 10 User’s Guide Example 3.1 Building a horseshoe-shaped tunnel — half model gen zone radcyl size 5 10 6 12 rat 1 1 1 1.2 & p0 0,0,0 p1 100,0,0 p2 0,200,0 p3 0,0,100 gen zone radtun size 5 10 5 12 rat 1 1 1 1.2 & p0 0,0,0 p1 0,0,-100 p2 0,200,0 p3 100,0,0 Figures 1.12 and 1.13 in the Command Reference should be consulted when building these shapes. The model boundary dimensions are 100 × 200 × 100; the boundary coordinates are defined with the p0, p1, p2 and p3 keywords. The grid is shown in Figure 3.4. Note that the radtunnel shape is turned 90◦ to fit beneath the radcylinder shape. This is accomplished by specifying different p1-, p2- and p3-coordinate entries for the radtunnel shape. FLAC3D 3.10 Itasca Consulting Group, Inc. Minneapolis, MN USA Settings: Model Perspective 13:47:20 Mon Nov 06 2006 Center: X: 5.000e+001 Y: 1.000e+002 Z: 0.000e+000 Rotation: X: 0.000 Y: 0.000 Z: 10.000 Dist: 6.530e+002 Mag.: 1 Ang.: 22.500 Surface Magfac = 0.000e+000 Live & unassigned mech zones shown Axes Linestyle Y X Z Figure 3.4 Horseshoe-shaped tunnel made from radcylinder and radtunnel primitives With GENERATE zone, two additional options are available to assist with the creation of a grid composed of multiple shapes: GENERATE zone copy andGENERATE zone reflect. The copy keyword is used to copy a shape or shapes to a new position by adding an offset vector to all the gridpoints. The reflect keyword is used to reflect the shape or shapes across a symmetry plane. Example 3.2 shows the additional command needed to reflect the geometry created by the earlier commands. FLAC3D Version 3.1
PROBLEM SOLVING WITH FLAC3D Example 3. 2 Building a horseshoe-shaped tunnel-full model gen zone radcyl size 5 10 6 12 rat 111 1.2& p00,0,0p1100,0,0p20,200,0p30,0,100 gen zone radtun size 5 10 5 12 rat 111 1.2& 00,0,0p10,0,-100p20,200,0p3100,0,0 gen zone reflect dip 90 dd 270 origin 0,0,0 The resulting grid is shown in Figure 3.5. The symmetry plane is a vertical plane(located by the dip, dd and origin keywords) coincident with the x =0 plane. Note that dip angle(dip)and dip direction(dd) assume that x corresponds to"East, y to"North and z to "Up A third option, the GENERATE point command, is available to position single points in the model region. This is useful for positioning gridpoints of zones. The point can be assigned directly to a gridpoint, rather than specifying global coordinates. Section 3.2.2 presents an example use of GENErATE point to position the invert of two tunnels of different sizes at the same elevation FLAC3D3.0 0.0006+000 Figure 3.5 Complete horseshoe-shaped tunnel made fromthe reflect keyword FLAC3D Version 3.1
PROBLEM SOLVING WITH FLAC3D 3 - 11 Example 3.2 Building a horseshoe-shaped tunnel — full model gen zone radcyl size 5 10 6 12 rat 1 1 1 1.2 & p0 0,0,0 p1 100,0,0 p2 0,200,0 p3 0,0,100 gen zone radtun size 5 10 5 12 rat 1 1 1 1.2 & p0 0,0,0 p1 0,0,-100 p2 0,200,0 p3 100,0,0 gen zone reflect dip 90 dd 270 origin 0,0,0 The resulting grid is shown in Figure 3.5. The symmetry plane is a vertical plane (located by the dip, dd and origin keywords) coincident with the x = 0 plane. Note that dip angle (dip) and dip direction (dd) assume that x corresponds to “East,” y to “North” and z to “Up.” A third option, the GENERATE point command, is available to position single points in the model region. This is useful for positioning gridpoints of zones. The point can be assigned directly to a gridpoint, rather than specifying global coordinates. Section 3.2.2 presents an example use of GENERATE point to position the invert of two tunnels of different sizes at the same elevation. FLAC3D 3.10 Itasca Consulting Group, Inc. Minneapolis, MN USA Settings: Model Perspective 13:48:43 Mon Nov 06 2006 Center: X: -4.263e-014 Y: 1.000e+002 Z: 7.105e-015 Rotation: X: 0.000 Y: 0.000 Z: 10.000 Dist: 6.530e+002 Mag.: 0.8 Ang.: 22.500 Surface Magfac = 0.000e+000 Live & unassigned mech zones shown Axes Linestyle Y X Z Figure 3.5 Complete horseshoe-shaped tunnel made from the reflect keyword FLAC3D Version 3.1
3-12 User's guide 3.2.1.2 Connecting Adjoining Primitive Shapes When building a geometry out of primitives, the sides of the primitives must connect to form an unbroken continuum. During execution of a gENErAtE zone command a check is made for each oundary gridpoint against the boundary gridpoints of zones that already exist. Internal gridpoints are not checked. If two boundary gridpoints fall within a tolerance of 1 x10-7(relative to the magnitude of the gridpoints position vector )of each other, they are assumed to be the same point, and the first gridpoint is used rather than creating a new one for all subsequent calculations The user is responsible for ensuring that all gridpoints along adjoining primitives correspond to one another. The use of reference points with the command GENErATE point during model creation can be useful to make sure that the bounding brick is specified correctly for both primitives. Make sure that the number of zones is correct and that the ratios used for the zone distribution are consistent should be used for one of the primitives to ensure that boundary gridpoints match he inverse ratio Note that if the ratio for one primitive is going the opposite direction of the other, This version of FLAC3D does not issue a warning message if gridpoints at boundaries do not match It is helpful to use the plot sketch or Plot boundary command to check boundary gridpoints visually. Localized velocity anomalies will be observed at non-matching gridpoints in the model when the calculation is started. If some gridpoints are found not to match, the GENERATE merge command can be used to merge these gridpoints after the GENERATE zone command has been appl The ATTACH command can be used to connect prim be specified with this approach. For the most itives with different zone sizes. There are some restrictions, though, to the range in zone size that ma accurate calculations, the ratio of zone sizes should be a multiple integer ratio(e.g, 2 to 1, 3 to 1, 4 to 1). It is recommended that the ratio be tested first by running the model under elastic conditions If a discontinuity is observed in the displacement, or stress distribution across the attached grids then the ratio of zone sizes may need to be adjusted However, if the discontinuity is small and far from the region of interest, it may not have a significant influence on the calculation Example 3. 3 illustrates the use of the aTtACH command and the effect of different zone sizes. a brick primitive with a zone dimension of 0.5 is connected to a brick primitive with a zone dimension of 1. The resulting z-displacement contours are shown in Figure 3.6 FLAC3D Version 3.1
3 - 12 User’s Guide 3.2.1.2 Connecting Adjoining Primitive Shapes When building a geometry out of primitives, the sides of the primitives must connect to form an unbroken continuum. During execution of a GENERATE zone command, a check is made for each boundary gridpoint against the boundary gridpoints of zones that already exist. Internal gridpoints are not checked. If two boundary gridpoints fall within a tolerance of 1 ×10−7 (relative to the magnitude of the gridpoints position vector) of each other, they are assumed to be the same point, and the first gridpoint is used rather than creating a new one for all subsequent calculations. The user is responsible for ensuring that all gridpoints along adjoining primitives correspond to one another. The use of reference points with the command GENERATE point during model creation can be useful to make sure that the bounding brick is specified correctly for both primitives. Make sure that the number of zones is correct and that the ratios used for the zone distribution are consistent. Note that if the ratio for one primitive is going the opposite direction of the other, the inverse ratio should be used for one of the primitives to ensure that boundary gridpoints match. This version of FLAC3D does not issue a warning message if gridpoints at boundaries do not match. It is helpful to use the PLOT sketch or PLOT boundary command to check boundary gridpoints visually. Localized velocity anomalies will be observed at non-matching gridpoints in the model when the calculation is started. If some gridpoints are found not to match, the GENERATE merge command can be used to merge these gridpoints after the GENERATE zone command has been applied. The ATTACH command can be used to connect primitives with different zone sizes. There are some restrictions, though, to the range in zone size that may be specified with this approach. For the most accurate calculations, the ratio of zone sizes should be a multiple integer ratio (e.g., 2 to 1, 3 to 1, 4 to 1). It is recommended that the ratio be tested first by running the model under elastic conditions. If a discontinuity is observed in the displacement, or stress distribution across the attached grids, then the ratio of zone sizes may need to be adjusted. However, if the discontinuity is small and far from the region of interest, it may not have a significant influence on the calculation. Example 3.3 illustrates the use of the ATTACH command and the effect of different zone sizes. A brick primitive with a zone dimension of 0.5 is connected to a brick primitive with a zone dimension of 1. The resulting z-displacement contours are shown in Figure 3.6. FLAC3D Version 3.1
PROBLEM SOLVING WITH FLAC3D Example 3.3 Two unequal sub-grids gen zone brick size 44 4 p00,0,0 pl 4,0,0 p2 0, 4,0 p3,0, 2 gen zone brick size 88 4 p0,0,2 p1 4,0,2 p2,4,2 p3,0, 4 attach face range z 1.9 2 model elas prop bulk 8e9 shear 5e9 fix z range fix x range x-1 fix x range x 3.9 4.1 fix y range y fix y range y 3.9 4.1 apply szz -le6 range z.9 4.1 x0,2 0, 2 hist una save att. sav To test the accuracy, we do a similar run, but for a single grid with a constant zone dimension of 0.5. The data file is given in Example 3. 4. The results are shown in Figure 3. 7. This plot is almost identical to that in Figure 3.6 Example 3. 4 A single grid for comparison to two sub-grids gen zone brick size 888 p00,0,0 p1 4,0,0 p2, 4,0 p3,0, 4 prop bulk 8e9 shear 5e9 1x x range fix x range x 3.9 4.1 Ⅹ y range fix 94.1 hist unbal natt AC3D Version 3
PROBLEM SOLVING WITH FLAC3D 3 - 13 Example 3.3 Two unequal sub-grids gen zone brick size 4 4 4 p0 0,0,0 p1 4,0,0 p2 0,4,0 p3 0,0,2 gen zone brick size 8 8 4 p0 0,0,2 p1 4,0,2 p2 0,4,2 p3 0,0,4 attach face range z 1.9 2.1 model elas prop bulk 8e9 shear 5e9 fix z range z -.1 .1 fix x range x -.1 .1 fix x range x 3.9 4.1 fix y range y -.1 .1 fix y range y 3.9 4.1 apply szz -1e6 range z 3.9 4.1 x 0,2 y 0,2 hist unbal solve save att.sav To test the accuracy, we do a similar run, but for a single grid with a constant zone dimension of 0.5. The data file is given in Example 3.4. The results are shown in Figure 3.7. This plot is almost identical to that in Figure 3.6. Example 3.4 A single grid for comparison to two sub-grids gen zone brick size 8 8 8 p0 0,0,0 p1 4,0,0 p2 0,4,0 p3 0,0,4 model elas prop bulk 8e9 shear 5e9 fix z range z -.1 .1 fix x range x -.1 .1 fix x range x 3.9 4.1 fix y range y -.1 .1 fix y range y 3.9 4.1 apply szz -1e6 range z 3.9 4.1 x 0,2 y 0,2 hist unbal solve save noatt.sav FLAC3D Version 3.1