3-4 User's guide 3.1.3 Step 3: Construct and Run Simple idealized models When idealizing a physical system for numerical analysis, it is more efficient to construct and run simple test models first, before building the detailed model. Simple models should be created at the earliest possible stage in a project to generate both data and understanding. The results can provide further insight into the conceptual picture of the system; Step 2 may need to be repeated after simple models are run Simple models can reveal shortcomings that can be remedied before any significant effort is invested in the analysis. For example, do the selected material models sufficiently represent the expected behavior? Are the boundary conditions influencing the model response? The results from the simple models can also help guide the plan for data collection by identifying which parameters have the most influence on the analysis 3.1.4 Step 4: Assemble Problem-Specific Data The types of data required for a model analysis include details of the geometry(e. g, profile of underground openings, surface topography, dan profile, rock/soil structure) locations of geologic structure(e.g, faults, bedding planes, joint sets) material behavior(e.g, elastic/plastic properties, post-failure behavior ) initial conditions(e.g, in-situ state of stress, pore pressures, saturation); and external loading(e. g, explosive loading, pressurized cavern) Since typically there are large uncertainties associated with specific conditions (in particular, state of stress, deformability and strength properties ), a reasonable range of parameters must be selected for the investigation. The results from the simple model runs(in Step 3)can often prove helpful in determining this range, and in providing insight for the design of laboratory and field experiments to collect the needed data 3.1.5 Step 5: Prepare a Series of Detailed Model runs Most often, the numerical analysis will involve a series of computer simulations that include the different mechanisms under investigation, and span the range of parameters derived from the as- sembled database. When preparing a set of model runs for calculation, several aspects, such as those listed below should be considered 1. How much time is required to perform each model calculation? It can be dificult to obtain sufficient information to arrive at a useful conclusion if model runtimes are excessive Consideration should be given to performing parameter variations on multiple computer to shorten the total computation time FLAC3D Version 3.1
3-4 User’s Guide 3.1.3 Step 3: Construct and Run Simple Idealized Models When idealizing a physical system for numerical analysis, it is more efficient to construct and run simple test models first, before building the detailed model. Simple models should be created at the earliest possible stage in a project to generate both data and understanding. The results can provide further insight into the conceptual picture of the system; Step 2 may need to be repeated after simple models are run. Simple models can reveal shortcomings that can be remedied before any significant effort is invested in the analysis. For example, do the selected material models sufficiently represent the expected behavior? Are the boundary conditions influencing the model response? The results from the simple models can also help guide the plan for data collection by identifying which parameters have the most influence on the analysis. 3.1.4 Step 4: Assemble Problem-Specific Data The types of data required for a model analysis include: • details of the geometry (e.g., profile of underground openings, surface topography, dam profile, rock/soil structure); • locations of geologic structure (e.g., faults, bedding planes, joint sets); • material behavior (e.g., elastic/plastic properties, post-failure behavior); • initial conditions (e.g., in-situ state of stress, pore pressures, saturation); and • external loading (e.g., explosive loading, pressurized cavern). Since typically there are large uncertainties associated with specific conditions (in particular, state of stress, deformability and strength properties), a reasonable range of parameters must be selected for the investigation. The results from the simple model runs (in Step 3) can often prove helpful in determining this range, and in providing insight for the design of laboratory and field experiments to collect the needed data. 3.1.5 Step 5: Prepare a Series of Detailed Model Runs Most often, the numerical analysis will involve a series of computer simulations that include the different mechanisms under investigation, and span the range of parameters derived from the assembled database. When preparing a set of model runs for calculation, several aspects, such as those listed below, should be considered. 1. How much time is required to perform each model calculation? It can be difficult to obtain sufficient information to arrive at a useful conclusion if model runtimes are excessive. Consideration should be given to performing parameter variations on multiple computers to shorten the total computation time. FLAC3D Version 3.1
PROBLEM SOLVING WITH FLAC3D 3-5 2. The state of the model should be saved at several intermediate stages so that the entire run does not have to be repeated for each parameter variation. For example, if the analysis involves several loading/unloading stages, the user should be able to return to any stage change a parameter and continue the analysis from that stage. The amount of disk spac required for save files should be considered 3. Are there a sufficient number of monitoring locations in the model to provide for a clear interpretation of model results and for comparison with physical data? It is helpful to locate several points in the model at which a record of the change of a parameter (such as displacement, velocity or stress)can be monitored during the calculation. Also the maximum unbalanced force in the model should always be monitored to check the equilibrium or failure state at each stage of an analysis 3.1.6 Step 6: Perform the Model calculations on plete runs. The runs sh, two model runs, split into separate sections, before launching a series of It is best to first make on hould be checked at each stage to ensure that the response is as expected Once there is assurance that the model is performing correctly, several data files can be linked together to run a complete calculation sequence. At any time during a sequence of runs, it should be possible to interrupt the calculation, view the results, and then continue or modify the model as appropriate 3.1.7 Step 7. Present Results for interpretation The final stage of problem solving is the presentation of the results for a clear interpretation of the analysis. This is best accomplished by displaying the results graphically, either directly on the computer screen or as output to a hardcopy plotting device. The graphical output should be resented in a format that can be directly compared to field measurements and observations. Plots should clearly identify regions of interest from the analysis, such as locations of calculated stress concentrations. or areas of stable movement versus unstable movement in the model. The numeric ralues of any variable in the model should also be readily available for more detailed interpretation by the modeler We recommend that these seven steps be followed to solve geo-engineering problems efficiently The following sections describe the application of FLac 3d to meet the specific aspects of each of these steps in this modeling approach FLAC3D Version 3.1
PROBLEM SOLVING WITH FLAC3D 3-5 2. The state of the model should be saved at several intermediate stages so that the entire run does not have to be repeated for each parameter variation. For example, if the analysis involves several loading/unloading stages, the user should be able to return to any stage, change a parameter and continue the analysis from that stage. The amount of disk space required for save files should be considered. 3. Are there a sufficient number of monitoring locations in the model to provide for a clear interpretation of model results and for comparison with physical data? It is helpful to locate several points in the model at which a record of the change of a parameter (such as displacement, velocity or stress) can be monitored during the calculation. Also, the maximum unbalanced force in the model should always be monitored to check the equilibrium or failure state at each stage of an analysis. 3.1.6 Step 6: Perform the Model Calculations It is best to first make one or two model runs, split into separate sections, before launching a series of complete runs. The runs should be checked at each stage to ensure that the response is as expected. Once there is assurance that the model is performing correctly, several data files can be linked together to run a complete calculation sequence. At any time during a sequence of runs, it should be possible to interrupt the calculation, view the results, and then continue or modify the model as appropriate. 3.1.7 Step 7: Present Results for Interpretation The final stage of problem solving is the presentation of the results for a clear interpretation of the analysis. This is best accomplished by displaying the results graphically, either directly on the computer screen or as output to a hardcopy plotting device. The graphical output should be presented in a format that can be directly compared to field measurements and observations. Plots should clearly identify regions of interest from the analysis, such as locations of calculated stress concentrations, or areas of stable movement versus unstable movement in the model. The numeric values of any variable in the model should also be readily available for more detailed interpretation by the modeler. We recommend that these seven steps be followed to solve geo-engineering problems efficiently. The following sections describe the application of FLAC3D to meet the specific aspects of each of these steps in this modeling approach. FLAC3D Version 3.1
User's guide 3.2 Grid Generation At first, it may seem that the grid generation scheme in FLAC3D is limited to rather simple, regular shaped regions; the examples given in Section 2.7 are all uniform, polyhedral grids. The FLAC3D grid, however, can be distorted to fit arbitrary and complicated volumetric regions. A powerful grid generator is built into FLAC3D to manipulate the grid to fit various shapes of three-dimensional problem domains. The procedure for implementing the grid generator is described in this section. An overview of the generator operation is given first, in Section 3.2. 1. This is followed, in Sections 3. 2.2 and 3.2.3, by presentations on various aspects of grid generation, along with guidelines to follow in designing the grid for accurate solutions. Examples are given to illustrate each aspect. A special grid-generatio tool is described in Section 3. 2. 4. This tool permits the generation of three-dimensional grids from two-dimensional(FLac) data files by extruding the mesh in the third dimension One important aspect in grid generation is that all physical boundaries to be represented in the model simulation(including regions that will be added, or excavations created at a later stage in the simulation) must be defined before the solution stepping begins. Shapes of structures that will be added later in a sequential analysis must be defined and then removed (via ModeL nulluntil the appropriate time at which they are to be activated. The purpose of the grid generator is to facilitate the creation of all required physical shapes in the model 3.2.1 Overview of the grid Generator Grid generation in FLAC3D involves patching together grid shapes of specific connectivity(referred to as primitives)to form a complete model with the desired geometry. Several types of primitives are available, and these can be connected and conformed to create complex three-dimensional geometries Grid generation is invoked with the GENERATE command. The generation of zones for each primitive type is performed with the GENErATE zone command. Reference points can be defined with the GENERATE point command to assist with positioning gridpoints in the model region. The GENERATE merge command can be used to ensure that separate primitives are connected properly All gridpoints along matching faces of zone primitives must fall within a specified tolerance, for two primitives to be merged. Alternatively, the ATTACH command is available to connect primitive meshes of different zone sizes. FISH can be used to adjust the final mesh, if necessary to conform to the surfaces of the model region. Separate volume regions within the final mesh can be defined by using the GENERATE surface command. The following sections describe the use of each of these facilities to create a Flac3D mesh. See Section 1.3 in the Command Reference for a detailed description of the gEneratE and ATtACh commands Previous versions of FLAC3D also contained an automatic grid adjustment algorithm that used an iteration process to conform the grid to fit within a specified volume. This approach was found to be less efficient than building the grid using primitive shapes and has been discontinued FLAC3D Version 3.1
3-6 User’s Guide 3.2 Grid Generation At first, it may seem that the grid generation scheme in FLAC3D is limited to rather simple, regularshaped regions; the examples given in Section 2.7 are all uniform, polyhedral grids. The FLAC3D grid, however, can be distorted to fit arbitrary and complicated volumetric regions. A powerful grid generator is built into FLAC3D to manipulate the grid to fit various shapes of three-dimensional problem domains. The procedure for implementing the grid generator is described in this section. An overview of the generator operation is given first, in Section 3.2.1. This is followed, in Sections 3.2.2 and 3.2.3, by presentations on various aspects of grid generation, along with guidelines to follow in designing the grid for accurate solutions. Examples are given to illustrate each aspect. A special grid-generation tool is described in Section 3.2.4. This tool permits the generation of three-dimensional grids from two-dimensional (FLAC) data files by extruding the mesh in the third dimension. One important aspect in grid generation is that all physical boundaries to be represented in the model simulation (including regions that will be added, or excavations created at a later stage in the simulation) must be defined before the solution stepping begins. Shapes of structures that will be added later in a sequential analysis must be defined and then removed (via MODEL null) until the appropriate time at which they are to be activated. The purpose of the grid generator is to facilitate the creation of all required physical shapes in the model. 3.2.1 Overview of the Grid Generator Grid generation in FLAC3D involves patching together grid shapes of specific connectivity (referred to as primitives) to form a complete model with the desired geometry. Several types of primitives are available, and these can be connected and conformed to create complex three-dimensional geometries.* Grid generation is invoked with the GENERATE command. The generation of zones for each primitive type is performed with the GENERATE zone command. Reference points can be defined with the GENERATE point command to assist with positioning gridpoints in the model region. The GENERATE merge command can be used to ensure that separate primitives are connected properly. All gridpoints along matching faces of zone primitives must fall within a specified tolerance, for two primitives to be merged. Alternatively, the ATTACH command is available to connect primitive meshes of different zone sizes. FISH can be used to adjust the final mesh, if necessary, to conform to the surfaces of the model region. Separate volume regions within the final mesh can be defined by using the GENERATE surface command. The following sections describe the use of each of these facilities to create a FLAC3D mesh. See Section 1.3 in the Command Reference for a detailed description of the GENERATE and ATTACH commands. * Previous versions of FLAC3D also contained an automatic grid adjustment algorithm that used an iteration process to conform the grid to fit within a specified volume. This approach was found to be less efficient than building the grid using primitive shapes and has been discontinued. FLAC3D Version 3.1
PROBLEM SOLVING WITH FLAC3D 3-7 3. 2. Zone generation The FLAC3D grid is generated with the GENErATE zone command. This command actually accesses a library of primitive shapes; each shape has a specific type of grid connectivity. The primitive shapes available in FLAC3D, listed in order of increasing complexity, are summarized, with their associated keywords, in Table 3.2 Table 3.2 Primitive mesh shapes available with the GENErATE zone command Definition brick brick-shaped mesh wedge dge-shaped mesh uweaae uniform wedge-shaped mesh tetra tetrahedral-shaped mesh pyramid pyramid-shaped mesh cylindrical-shaped mesh brick degenerate brick-shaped mesh radbrick radially graded mesh around brick radtunnel radially graded mesh around parallelepiped-shaped tunnel radcylinder radially graded mesh around cylindrical-shaped tunnel cshell cylindrical shell mesh clint intersecting cylindrical-shaped tunnels tuning intersecting parallelepiped-shaped tunnels As you have already seen in Section 2.2, GENErATE zone commands can be used alone to create a or connected together to create the FLAC3d grid apes, the primitives can be applied individuall As an example, a quarter-symmetry model can be created for a cylindrical tunnel with the command gen zone radcyl size 5 6 12 fill The size keyword defines the number of zones in the grid. For the cylindrical tunnel, each entry following the size keyword corresponds to the number of zones in a specific direction. In this case, there are five zones along the inner radius of the cylindrical tunnel, ten zones along the axis of the tunnel, six zones along the circumference of the tunnel, and twelve zones between the periphery of the tunnel and the outer boundary of the model. Figure 3. 2 shows the model grid. The fill keyword to fill the tunnel with zones FLAC3D Version 3.1
PROBLEM SOLVING WITH FLAC3D 3-7 3.2.1.1 Zone Generation The FLAC3D grid is generated with the GENERATE zone command. This command actually accesses a library of primitive shapes; each shape has a specific type of grid connectivity. The primitive shapes available in FLAC3D, listed in order of increasing complexity, are summarized, with their associated keywords, in Table 3.2. Table 3.2 Primitive mesh shapes available with the GENERATE zone command Keyword Definition brick brick-shaped mesh wedge wedge-shaped mesh uwedge uniform wedge-shaped mesh tetra tetrahedral-shaped mesh pyramid pyramid-shaped mesh cylinder cylindrical-shaped mesh dbrick degenerate brick-shaped mesh radbrick radially graded mesh around brick radtunnel radially graded mesh around parallelepiped-shaped tunnel radcylinder radially graded mesh around cylindrical-shaped tunnel cshell cylindrical shell mesh cylint intersecting cylindrical-shaped tunnels tunint intersecting parallelepiped-shaped tunnels As you have already seen in Section 2.2, GENERATE zone commands can be used alone to create a zoned model. If the 3D domain consists of simple shapes, the primitives can be applied individually, or connected together to create the FLAC3D grid. As an example, a quarter-symmetry model can be created for a cylindrical tunnel with the command gen zone radcyl size 5 10 6 12 fill The size keyword defines the number of zones in the grid. For the cylindrical tunnel, each entry following the size keyword corresponds to the number of zones in a specific direction. In this case, there are five zones along the inner radius of the cylindrical tunnel, ten zones along the axis of the tunnel, six zones along the circumference of the tunnel, and twelve zones between the periphery of the tunnel and the outer boundary of the model. Figure 3.2 shows the model grid. The fill keyword is given to fill the tunnel with zones. FLAC3D Version 3.1
User's guide FLAC3D3. 0 腿 lifestyle Figure 3.2 Grid for cylindrical tunnel model In addition to size and fill, there are several other key words available to define the characteristics of the primitive shapes. The available characteristic keywords for primitive shapes are summarized in Table 3.3. You should refer to Figures 1. 4 through 1. 16 in the Command Reference to identify which key words and numerical entries are applicable for each primitive shape. For example, refer to Figure 1. 13 in the Command reference to check the order in which the size entries (n/, n2, n3 and n4)should be entered for the cylindrical tunnel Table 3.3 Characteristics keywords for GENERATE zone primitive shapes Keyword Definition dimension dimensions of the interior regions edge length for the sides of the mesh po through p1s fill the interior region with zones geometric ratio used to space zones number of zones for each shape The ratio key word is of particular significance when designing a grid to provide an accurate solution without ssive number of zones. For example, iffir lured immediately around the periphery of the cylindrical tunnel in order to provide a more accurate representation of high-stress gradients, ratio can be used to adjust the Zo to be small close to the tunnel and gradually increase in size away from the tunnel FLAC3D Version 3.1
3-8 User’s Guide FLAC3D 3.10 Itasca Consulting Group, Inc. Minneapolis, MN USA Settings: Model Perspective 13:42:44 Mon Nov 06 2006 Center: X: 3.274e+000 Y: 4.615e+000 Z: 2.637e+000 Rotation: X: 15.000 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 X Y Z Figure 3.2 Grid for cylindrical tunnel model In addition to size and fill, there are several other keywords available to define the characteristics of the primitive shapes. The available characteristic keywords for primitive shapes are summarized in Table 3.3. You should refer to Figures 1.4 through 1.16 in the Command Reference to identify which keywords and numerical entries are applicable for each primitive shape. For example, refer to Figure 1.13 in the Command Reference to check the order in which the size entries (n1, n2, n3 and n4) should be entered for the cylindrical tunnel. Table 3.3 Characteristics keywords for GENERATE zone primitive shapes Keyword Definition dimension dimensions of the interior regions edge edge length for the sides of the mesh fill fill the interior region with zones p0 through p16 reference (corner) points for the shape ratio geometric ratio used to space zones size number of zones for each shape The ratio keyword is of particular significance when designing a grid to provide an accurate solution without requiring an excessive number of zones. For example, if fine zoning is required immediately around the periphery of the cylindrical tunnel in order to provide a more accurate representation of high-stress gradients, ratio can be used to adjust the zone size to be small close to the tunnel, and gradually increase in size away from the tunnel. FLAC3D Version 3.1