Flac 3D 3

PROBLEM SOLVING WITH FLAC 3D

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3 PROBLE PROBLEM M SOLVING SOLVING WITH FLAC 3D This section provides guidance in the use of FLAC 3D in problem solving for static mechanical analysis* analysis* in geotechnical geotechnical engineering engineering.. In Section In Section 3.1, 3.1, an outline of the steps recommended for perform performing ing a geomec geomechan hanics ics analys analysis is is given given,, follo followed wed in Sectio Sections ns 3.2 through 3.9 by an exami examinat nation ion of specific aspects that must be considered in any model creation and solution. These include: (Section 3.2); 3.2); • grid generation (Section conditions (Sections (Sections 3.3 and 3.3 and 3.4 3.4); ); • boundary and initial conditions modeling (Section (Section 3.5); 3.5); • loading and sequential modeling • choice of constitutive model model and material properties (Sections (Sections 3.6 and 3.6 and 3.7 3.7); ); modeling efficiency (Section (Section 3.8); 3.8); and • ways to improve modeling (Section 3.9). 3.9). • interpretation of results (Section Each of these modeling modeling aspects is discussed discussed in detail. detail. The user who is familiar familiar with the twodimensional program FLAC will will find that the modeling approach is very similar in FLAC 3D. The major difference is the procedure for grid generation. We recommend that Section that Section 3.2 be 3.2 be studied carefully, and that the example problems in that section be repeated before users create their own model model grids. grids. You will will note that FISH programs programs are used in this section to assist with model generation and problem solving. If you have not used the FISH language language before, we recommend that you first read the FISH tutorial tutorial in Section in Section 4.2. 4.2. Finally, the philosophy of modeling in the field of geomechanics is examined in Section 3.10; 3.10; the novice modeler in this field may wish to consult this section first. The methodology of modeling in geomechanics can be significantly different from that in other engineering fields, such as structural engineering. It is important to keep this in mind when performing any any geomechanics analysis.

* Problem solving for coupled mechanical-groundwater analysis is discussed in Section in Section 1 in 1 in Fluid Fluidin Section 1 in 1 in Optional Mechanical Interaction, Interaction, and for coupled mechanical-thermal analysis in Section Optional in Section 3 in 3 in Optional Features. Features. Problem solving for dynamic analysis is discussed in Section Optional Features. Features.

FLAC 3D Version 3.0

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3.1

User’s Guide

Genera Generall Appr Approac oach h

The modeli modeling ng of geo-en geo-engin gineer eering ing process processes es invo involve lvess specia speciall consid considerat eration ionss and a design design philos philosoph ophy y differe different nt from that that follo followed wed for design design with with fabric fabricate ated d materi materials als.. Analys Analyses es and design designss for structu structures res and excavations in or on rocks and soils must be achieved with relatively little site-specific data and an awareness that deformability and strength properties may vary considerably. It is impossible to obtain complete field data at a rock or soil site. site. For example, information on stresses, properties and discontinuities can only be partially known, at best. Since Since the input input data data necessa necessary ry for design design predic predictio tions ns are limite limited, d, a numeri numerical cal model model in geomec geomechan hanics ics should be used primarily to understand the dominant mechanisms affecting the behavior of the system. system. Once the behavior behavior of the system is understood, understood, it is then appropriate appropriate to develop develop simple calculations for a design process. This approach is oriented toward geotechnical engineering, in which there is invariably a lack of good data. But, in other applicati applications, ons, it may be possible possible to use FLAC 3D directly directly in design if suffici sufficient ent data, data, as well well as an underst understandi anding ng of materi material al behavi behavior or,, are are avail availabl able. e. The results results produce produced d 3D in a FLAC analys analysis is will will be accurat accuratee when when the program program is supplie supplied d with with approp appropria riate te data. data. Modeler Modelerss shoul should d reco recogn gniz izee that that ther theree is a cont contin inuou uouss spect spectru rum m of situ situat atio ions, ns, as illu illust stra rate ted d in Fig Figure ure 3.1 3.1,, below below.

Typical situation Data

Approach

Figure 3.1

Simple geology; $$$ spent on site investigation

Complicated geology; inaccessible; no testing budget

COMPLETE

NONE

Investigation of mechanisms

Bracket field behavior by parameter studies

Predictive (direct use in design)

Spectrum of modeling situations situations

of Figure 3.1) 3.1) or as a FLAC 3D may be used either in a fully predictive mode (right-hand side of Figure “numerical “numerical laboratory” laboratory” to test ideas (left-hand (left-hand side). It is the field situation situation (and budget), budget), rather than the program, program, that determine the types of use. If enough data of a high quality quality is available, available, 3D FLAC can give good predictions. Since most FLAC 3D applications will be for situations in which little data is available, this section discusses the recommended approach for treating a numerical model as if it were a laboratory test. The model should never be considered as a “black box” that accepts data input at one end and




























Table 3.1

3.1.1

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Recommended steps for numerical analysis in geomechanics

Step 1

Define the objectiv objectives es for the model analysis analysis

Step 2

Create a conceptual conceptual picture picture of the physical physical system

Step 3

Construct Construct and run simple simple idealized idealized models

Step Step 4

Assemb Assemble le proble problem-s m-spec pecific ific data data

Step Step 5

Prepare Prepare a series series of detail detailed ed model model runs runs

Step Step 6

Perform Perform the model model calcul calculati ations ons

Step Step 7

Present Present results results for interpr interpreta etatio tion n

Step 1: Define the Objectives for for the Model Analysis

The level level of detail to be included in a model often depends depends on the purpose of the analysis. For example, example, if the objective objective is to decide between between two conflicting conflicting mechanisms mechanisms that are proposed proposed to explain the behavior of a system, then a crude model may be constructed, provided that it allows the mechanisms to occur. It is tempting to include complexity in a model just because it exists in reality. reality. However, However, complicating features should be omitted if they are likely to have little influence on the response of the model, or if they are irrelevant to the model’s purpose. Start with a global view and add refinement as (and if) necessary.

3.1.2

Step 2: Create a Conceptual Picture of the Physical Physical System

It is important to have a conceptual picture of the problem to provide an initial estimate of the expected behavior under the imposed conditions. Several questions should be asked when preparing this picture. picture. For example, example, is it anticipated anticipated that that the system could could become become unstable? unstable? Is the predominant predominant mechanical mechanical response response linear or nonlinear? nonlinear? Are movements movements expected expected to be large or small in comparison with the sizes of objects within the problem region? Are there well-defined discon discontin tinuit uities ies that that may affec affectt the behavi behavior or,, or does does the materi material al behav behavee essent essential ially ly as a contin continuum uum?? Is there an influence from groundwater interaction? Is the system bounded by physical structures, or do its boundaries extend to infinity? Is there any geometric symmetry in the physical structure of the system? These considerations will dictate the gross characteristics of the numerical model, such as the design of the model geometry, the types of material models, the boundar y conditions and the initial equilibrium equilibrium state state for the analysis. analysis. They will determine determine whether whether a three-dimens three-dimensional ional model is required, or a two-dimensional model can be used to take advantage of geometric conditions in the physical system.



























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3.1.3

User’s Guide

Step 3: Construct and Run Simple Idealized 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 the detailed model. Simple models should be created at the earliest possible possible stage in a project project to generate generate both data and understanding 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 Simple models models can revea reveall shortc shortcomi omings ngs that that can be remedi remedied ed before before any any signifi significan cantt effort effort is inves invested ted in the analysis. For example, do the selected material models models sufficiently represent the expected behavior? behavior? Are the boundary boundary conditions conditions influenci influencing ng the model response? response? The results 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 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 post-failure behavior); initial conditions (e.g., in-situ state of stress, pore pressures, saturation); and external loading (e.g., explosive explosive loading, pressurized cavern).

Since, typically, there are large uncertainties associated with s pecific conditions (in particular, state of stress, deformability and strength properties), a reas onable 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 Model Runs

Most often, the numerical analysis will involve a series of computer simulations that include the diff differe erent nt mech mechan anis isms ms under under inve invest stig igat atio ion n and and span span the the range range of para parame mete ters rs deri derive ved d from from the the assem assem-bled database. When preparing a set of model runs for calculation, several aspects, such as those listed below, below, should be considered. 1. How How much much time time is requi required red to perfo perform rm each each mode modell calcu calcula lati tion on?? It can can be diffi difficu cult lt to obta obtain in




























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2. The The stat statee of the the mode modell shoul should d be save saved d at seve severa rall inte interm rmed edia iate te stag stages es so that that the the enti entire re run run does not have to be repeated for each parameter variation. For example, if the analysis involves 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. Consideration should be given to the amount of disk space required for save files. 3. Are there a sufficient number of monitoring locations locations in the model to provide for a clear interpretat interpretation ion of model results and for comparison comparison with physical 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 Perform the Model Calculations

It is best best to first first make make one one or two two mode modell runs runs,, spli splitt into into sepa separa rate te sect sectio ions ns,, befo before re laun launch chin ing g a seri series es 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 for Interpretation

The final stage of problem solving is the presentation of the results for a clear interpretation of the analysis. analysis. This is best accomplished accomplished by displaying displaying the results results graphically graphically, either directly directly on the computer computer screen or as output to a hardcopy plotting plotting device. device. The graphical 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 FLAC 3D to meet the specific aspects of each of these steps in this modeling approach.



























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3.2

User’s Guide

Grid Grid Genera Generatio tion n

At first, it may seem that the grid generation scheme in FLAC 3D is limited to rather simple, regularshaped regions; the examples given in Section in Section 2.7 are 2.7 are all uniform, polyhedral grids. The FLAC 3D grid, however however,, can be distorted distorted to fit arbitrary arbitrary and complicated complicated volumetri volumetricc regions. A powerful 3D grid generator is built into FLAC 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 overview of the generator operation is given first, in Section in Section 3.2.1. 3.2.1. This is followed, in Sections in Sections 3.2.2 and 3.2.2 and 3.2.3 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 illustrate each aspect. 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 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 sha pes in the model.

3.2.1

Overview of the Grid Generator Generator

Grid generation in FLAC 3D involves involves patching together grid shapes shape s 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 comman command. d. The generat generation ion of zones 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 the model region. The ensur e that separate primitives are connected properly. GENERATE merge command can be used to ensure All gridpoints along matching faces of zone primitives must fall within a specified tolerance for two primitives to be merged. Alternatively, Alternatively, the ATTACH command is available to connect primitive meshes of different zone sizes. FISH can 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 usin using g the the GENERATE comman and. d. The foll follow owin ing g sect sectio ions ns desc descri ribe be the the use of each each of these these GENERATE surface comm 3D facilities to create a FLAC mesh. mesh. See Section See Section 1.3 in 1.3 in the Command the Command Reference for Reference for a detailed description of the GENERATE and ATTACH commands.

* Previous Previous versions versions of FLAC FLAC 3D also contained an automatic grid adjustment algorithm that used an






























3.2.1. 3.2.1.1 1

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Zone Zone Genera Generatio tion n

The FLAC 3D grid grid is gene generat rated ed with with the the GENERATE command. This command command actually actually accesses accesses GENERATE zone command. a library of primitive primitive shapes; each shape has a specific specific type of grid connectivi connectivity ty.. The primitive primitive 3D shapes available in FLAC , listed in order of increasing complexity, are summarized, with their associated keywords, in Table in Table 3.2. 3.2.

Table 3.2 Keywor yword d

brick wedge uwedge tetra pyramid cylinder dbrick radbrick radtunnel radcylinder cshell cylint tunint

Primitive mesh shapes available with the GENERATE zone command Defini efiniti tion on brick-shaped mesh wedge-shaped mesh uniform wedge-shaped mesh tetrahedral-shaped mesh pyramid-shaped mesh cylindrical-shaped mesh degenerate brick-shaped mesh radially graded mesh around brick radially graded mesh around parallelepiped-shaped tunnel radially graded mesh around cylindrical-shaped tunnel cylindrical shell mesh intersecting cylindrical-shaped tunnels intersecting parallelepiped-shaped tunnels

As you have already seen in Section in Section 2.2, 2.2, GENERATE zone commands can be used alone to create a zoned zoned model. model. If the 3D domain domain consis consists ts of simple simple shapes, shapes, the primit primitiv ives es can be applie applied d indiv individu iduall ally y, 3D or connected together to create the FLAC grid. As an exam exampl ple, e, a quart quarter er-s -sym ymme metr try y mode modell can can be crea create ted d for for a cyli cylind ndri rica call tunn tunnel el with with the the comma command nd gen gen zone zone radc radcyl yl size size 5 10 6 12 fill fill





























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User’s Guide

FLAC3D 3.00 3.00 Settings: Model Perspective 11:22:01 Fri Feb 04 2005 Center: X: 3.109e+000 Y: 4.581e+000 Z: 2.309e+000 D is t:t: 3 .0 .0 11 11 e+ e+ 00 00 1

Rotation: X: 15.000 Y: 0.000 Z: 20.00 0 M ag ag .:.: 1 .2 .2 Ang.: 22.500

Surface Magfac = 0.000e+000

Axes Linestyle

Z Y X Itasca Consulting Group, Inc. Minneapolis, MN USA

Figure 3.2

Grid for cylindrical 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 primitive shapes are summarized in Table 3.3. 3.3. You should refer to Figures to Figures 1.10 through 1.22 through 1.22 in in the Command the Command Reference to Reference to identify which keywords and numerical entries are applicable for each primitive primitive shape. For example, refer to Figure to Figure 1.19 in 1.19 in the Command the Command Reference to 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 K

d

Characteristics keywords for GENERATE zone primitive shapes D fi ii






























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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 (see Figure 3.3). 3.3). A ratio smaller smaller than 1.0 can be given given to change from an increasing to a decreasing geometric ratio. FLAC3D 3.00 3.00 Settings: Model Perspective 11:25:54 Fri Feb 04 2005 Center: X: 3.234e+000 Y: 4.733e+000 Z: 3.000e+000 D is t:t: 2 .8 .8 24 24 e+ e+ 00 00 1



Axes Linestyle

Z

Y

X

Itasca Consulting Group, Inc. Minneapolis, MN USA

Figure 3.3

Radially graded grid around cylindrical tunnel

Sizing Sizing the grid for accurate accurate results, but with a reasonable reasonable number of zones, can be complicated complicated..





























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 0,0,0 ,0 p1 100, 100,0, 0,0 0 p2 0,2 0,200 00,0 ,0 p3 0,0, 0,0,10 100 0 gen zone radtun size 5 10 5 12 rat 1 1 1 1.2 & p0 0,0 0,0,0 ,0 p1 0,0, 0,0,-1 -100 00 p2 0,20 0,200, 0,0 0 p3 100, 100,0, 0,0 0

Figuress 1.1 Figure 1.18 8 and 1.19 in the the Command should ld be consul consulted ted when when build building ing these these shapes. shapes. Command Reference Referenceshou 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 in Figure 3.4. 3.4. Note that 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.

×

×




Axes Linestyle

Z

Y

X






























Example 3.2

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Building a horseshoe-shaped tunnel — full model

gen zone radcyl size 5 10 6 12 rat 1 1 1 1.2 & p0 0,0 0,0,0 ,0 p1 100, 100,0, 0,0 0 p2 0,2 0,200 00,0 ,0 p3 0,0, 0,0,10 100 0 gen zone radtun size 5 10 5 12 rat 1 1 1 1.2 & p0 0,0 0,0,0 ,0 p1 0,0, 0,0,-1 -100 00 p2 0,20 0,200, 0,0 0 p3 100, 100,0, 0,0 0 gen gen zone zone refl reflec ect t dip dip 90 dd 270 270 orig origin in 0,0, 0,0,0 0

The resulting grid is shown in Figure in Figure 3.5. 3.5. The symmetry plane is a vertical plane (located by the that dip angle angle (dip) and dip dip, dd and origin keywords) coincident with the x = 0 plane. Note that direction (dd) assume that x corresponds to “East,” “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. region. This is useful useful for positioni positioning ng gridpoints gridpoints of zones. zones. The point can be assigned directly 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 3.00 3.00 Settings: Model Perspective 11:30:24 Fri Feb 04 2005 Center: X: -3.908e-014 Y: 1.000e+002 Z: 7.105e-015 D is t:t: 7 .5 .5 65 65 e+ e+ 00 00 2



Axes Linestyle

Z

Y

X































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3.2.1.2 3.2.1.2

User’s Guide

Connecting Connecting Adjoining Adjoining Primitive Primitive Shapes

When building a geometry out of primitives, the sides of the primitives must connect 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 gridpoints fall fall within a tolerance 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 s ubsequent calculations.

×

The user is responsible for ensuring that all gridpoints along adjoining primitives correspond to one anothe anotherr. The use of referen reference ce points points,, with with the comman command d GENERATE during ng mode modell creat creatio ion n can can GENERATE point, duri be useful to make sure that the bounding brick is specified corr ectly 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 FLAC FLAC 3D does not issue a warning message if gridpoints at boundaries do no t 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 with different zone sizes. There are some
































Example 3.3

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Two unequal sub-grids

gen gen zone zone bric brick k size size 4 4 4 p0 0,0, 0,0,0 0 p1 4,0, 4,0,0 0 p2 0,4, 0,4,0 0 p3 0,0, 0,0,2 2 gen gen zone zone bric brick k size size 8 8 4 p0 0,0, 0,0,2 2 p1 4,0, 4,0,2 2 p2 0,4, 0,4,2 2 p3 0,0, 0,0,4 4 atta attach ch face face rang range e z 1.9 1.9 2.1 2.1 model mod el ela elas s prop prop bulk bulk 8e9 8e9 shea shear r 5e9 5e9 fix z range z -.1 .1 fix x range x -.1 .1 fix fix x rang range e x 3.9 3.9 4.1 4.1 fix y range y -.1 .1 fix fix y rang range e y 3.9 3.9 4.1 4.1 appl apply y szz szz -1e6 -1e6 rang range e z 3.9 3.9 4.1 4.1 x 0,2 0,2 y 0,2 0,2 hist his t unb unbal al solve save sav e att att.sa .sav v

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 given in Example in Example 3.4, 3.4, below. below. The results are shown in Figure in Figure 3.7. 3.7. This plot is almost identical to that in Figure in Figure 3.6. 3.6.































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User’s Guide

FLAC3D 3.00 3.00 Step 1220 Model Perspective 11:36:29 Fri Feb 04 2005 Center: X: 2.000e+000 Y: 2.000e+000 Z: 2.000e+000 D is t:t: 1 .9 .9 73 73 e+ e+ 00 00 1


Contour of Z-Displacement Magfac = 0.000e+000 -2.1883e-004 to -2.0000e-004 -2.0000e-004 to -1.7500e-004 -1.7500e-004 to -1.5000e-004 -1.5000e-004 to -1.2500e-004 -1.2500e-004 to -1.0000e-004 -1.0000e-004 to -7.5000e-005 -7.5000e-005 to -5.0000e-005 -5.0000e-005 to -2.5000e-005 -2.5000e-005 to 0.0000e+000 Interval = 2.5e-005

FAP Maximum = 2.500e+005 Linestyle


Figure 3.6

z-displacement contours in two attached attached grids with zone ratio of 2 to 1
































3.2.2

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Fitting Fitting the Grid to Simple Shapes

The intention intention of grid generation generation is to fit the model grid to the physical region region under study. study. For simple geometries, the GENERATE zone command is all that is required to generate a model grid to fit the problem domain. domain. To determine whether whether GENERATE zone is sufficient, sufficient, try defining the problem problem domain by one or more of the primitive primitive shapes listed in Table in Table 3.2 (see 3.2 (see Table Table 1.3 in 1.3 in the Command Reference for Reference for sketches of these shapes). For exampl example, e, consid consider er a proble problem m geomet geometry ry invo involvi lving ng three three parall parallel el tunnel tunnelss (a service service tunnel tunnel locate located d midway midway between two larger larger main tunnels). The three tunnels are all cylindrical cylindrical in shape, so the primitivee shape is the logical choice to build the tunnel grids. A vertical symmetry symmetry radcylinder primitiv plane may be assumed to exist along the centerline of the service tunnel. Thus, it is only necessary to create a mesh for one main tunnel and half of the service tunnel. We have have two two impo import rtan antt conce concern rnss when when buil buildi ding ng any any mode model: l: (1) the the dens densit ity y of zoni zoning ng requi required red for for an accurate solution in the region of interest; and (2) how the location of the grid boundaries influence model results. It is important to have have a high density of zoning in regions of high stress- or -strain gradients. Often, it is possible to perform two-dimensional analyses to define these regions. For this problem, a 2D calculation can easily be run to determine an acceptable density of zones around the tunnels. FLAC calculation For demonstration purposes, we select a zone size of roughly one-half the ser vice tunnel radius for the zones surrounding the tunnels.































3 - 16

User’s Guide

The main tunnel grid is created first: one-quarter of the grid is generated; then the grid is reflected across horizontal horizontal and vertical vertical planes to create the grid for the entire tunnel. tunnel. The reflect option cannot be used for the service tunnel, because the invert of the service tunnel is required to be at the same elevation as that for the main tunnel. tunnel. The vertices locating the service tunnel radius must be adjusted in the radcylinder primitiv primitive. e. This is done by first defining defining these locations locations using the GENERATE point command. The corner points p8 and p10 in one radcylinder primitive, and p9 and p11 p11 in the other primitive, are located at the reference points. This ensures that the two primitives will match at boundary gridpoints when the grid is generated. Figure 3.8 shows the grid for the tunnels. The vertical plane at x = 0 is a symmetry plane. FLAC3D 3.00 3.00 Settings: Model Perspective 11:47:05 Fri Feb 04 2005 Center: X: 1.150e+001 Y: 2.500e+001 Z: 0.000e+000 D is t:t: 1 .3 .3 56 56 e+ e+ 00 00 2



Axes Linestyle

Z

Y

X


































Example 3.6

3 - 17

Creating a liner in the service service tunnel

; line liner r sel shell range cyl end1 0 0 -1

end2 0 50 -1

rad 3

The liner liner contai contains ns 240 struct structuralshell uralshell elemen elements ts and is connec connected ted to the FLAC 3D grid grid at 143 struct structura urallnode links. The grid with the liner is shown in Figure in Figure 3.9. 3.9. FLAC3D 3.00 3.00 Settings: Model Perspective 11:46:39 Fri Feb 04 2005 Center: X: 1.150e+001 Y: 2.500e+001

Rotation: X: 10.000 Y: 0.000

































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User’s Guide

We create the boundary grid with the radtunnel and brick primiti primitives ves for this model. model. The reflect option is used to reflect the grid across the plane at z = 0. We use the range keyword to restrict the action of reflect See Example 3.7, 3.7, below be low.. reflect. See Example The final grid for this problem is shown in Figure in Figure 3.10. 3.10. The GROUP command is used to identify the main tunnel in the figure.

Example 3.7

Creating the boundary grid

; out outer er bou bounda ndary ry gen zone radtun p0 7 0 0 p1 50 0 0 p2 7 50 0 p3 15 0 50 p4 50 50 0 & p5 15 50 50 p6 50 0 50 p7 50 50 50 & p8 23 0 0 p9 7 0 8 p10 23 50 0 p11 7 50 8 &


































3.2.3

3 - 19

Grid Generation with FISH FISH

can be used to specify a geometric shape that is not readily available by using the built-in FISH can primitives in FLAC 3D. For example, an irregular surface on a model can be made by using FISH to to adjust gridpoints via a user-specified topology function (see Example (see Example 3.24). 3.24). It is also possible to create your own primitive shapes using FISH . In the example below, below, we create a radially radially graded mesh around a spherical spherical cavity cavity.. Only one-eighth one-eighth of the grid is generated. generated. The grid can be reflected to create the complete spherical cavity. A radbrick primitiv primitivee is the basis for creating our “radsphere” “radsphere” shape. We first define parameters that describe describe the sphere within a cube: the radius of the spherical cavity; cavity; the length of the outer cube edge; the number of zones along the outer cube edge; and the number of zones in the radial direction from the inner cube to the outer cube. Then we define a radbrick such such that the spherical

































3 - 20

User’s Guide

pz=gp_zpos(p_gp) ; Com Comput pute e A=( A=(ax, ax,ay, ay,az)= az)=poi point nt on sph sphere ere radiall radially y "be "below low" " P. dist=sqrt(px*px+py*py+pz*pz) if dist dist>0 >0 then then k=rad/dist ax=px*k ay=py*k az=pz*k ; Com Comput pute e B=( B=(bx, bx,by, by,bz)= bz)=poi point nt on out outer er box bou bounda ndary ry rad radial ially ly "ab "above ove" " P. maxp=max(px,max(py,pz)) k=len/maxp bx=px*k by=py*k





































3 - 21



































3 - 22

3.3

User’s Guide

Bounda Boundary ry Condit Condition ionss

The boundary conditions in a numerical model consist of the values of field variables (e.g., stress


































z

d-s-n loca lo call fac face e

3 - 23

The d-s-n axes form a right-handed coordinate system in which:

































3 - 24

User’s Guide

The plot in Figure in Figure 3.14 shows 3.14 shows the forces applied to the grid as calculated from the normal stress and the boundary face areas. Note that the size of the force vectors is a function of the face areas over which the stress is applied.


































σ xx xx

= −10 × 106 + (105)z

3 - 25

































3 - 26

plot plot add add hist hist 1 plot plo t sho show w superstep

User’s Guide



































































































































































































































































































































































































































































































































































































































































































































































































































































































3 - 62

User’s Guide

The tensile failure criterion is identical in the Drucker-Prager, Mohr-Coulomb, ubiquitous-joint, strain-softening, bilinear strain-softening/ubiquitous-joint and double-yield models. This criterion defin defines es a tensi tensile le stren strengt gth h sepa separat ratel ely y from from the the shear shear stren strengt gth h and and an assoc associa iate ted d flow flow rule rule for for the the onse onsett of tensile failure. For the Drucker-Prager, Mohr-Coulomb and ubiquitous-joint models, the value assigned to the tensile strength remains constant when tensile failure occurs. Tensile softening can be modeled with the strain-softening, bilinear strain-softening ubiquitous-joint and double-yield models. models. (See Section (See Section 3.7.4.) 3.7.4.) Note that no record record is made of notional notional voids that that may open after tensile tensile failure failure and tensile tensile strain; if the strain rate becomes compressive, compressive, all models models start to take compressive load immediately. immediately. The double-yield and modified Cam-clay models both take into account the influence of volumetric change on material deformability and failure characteristics. In both models, tangential bulk and shear moduli are functions of plastic volumetric deformation. The differences between the two models are summarized as follows. In the Cam-clay model: 1. The elastic deformation is nonlinear, with with the elastic moduli depending on mean stress. 2. Shear failur failuree is affect affected ed by the occurre occurrence nce of plasti plasticc volume volumetri tricc deforma deformatio tion: n: the materi material al can harden or soften depending on the degree of preconsolidation. 3. As shea shearr loadi loading ng incr increas eases es,, the the mate materi rial al evol evolve vess towa toward rd a crit critic ical al stat statee at whic which h unli unlimi mite ted d shear strain occurs with no accompanying change in specific volume or stress. 4. There is no resistance to tensile mean stress. In the double-yield model: 1. Elastic moduli remain constant during elastic loading and unloading. 2. Shear and tensile failure are not coupled to plastic volumetric volumetric change, due to volumetric yielding. The shear yield function corresponds to the Mohr-Coulomb criterion, and the tensile yield is evaluated based on a tensile strength. 3. Mate Materi rial al harde hardeni ning ng or soft soften enin ing, g, upon upon shear shear or tens tensil ilee fail failur ure, e, is defin defined ed by tabl tables es relat relatin ing g friction angle and cohesion to plastic shear strain, and tensile strength to plastic tensile strain. 4. Volumetric yielding occurs; the isotropic stress at which yield yield occurs (the cap pressure) is not influenced by the amount of shear or tensile plastic deformation, but it increases (or hardens) with volumetric plastic strain. 5. A tensile strength limit limit and tensile softening can be defined. The double-yield model was initially developed to represent the behavior of mine backfill material,




























3 - 63

The Hoek-Brown model combines the generalized Hoek-Brown criterion with a plasticity flow rule that varies as a function of the confining stress level. At low confining stress, the volumetric expansion at yield is high, associated with axial splitting and wedging effects. At high confining stress, the material approaches a non-dilatant condition.

3.6.2

Selection of an Appropriate Model

A problem analysis should always start with the simplest material model; in most cases, an elastic model should be used first. This model runs the fastest and only requires two material parameters: bulk modulus and shear modulus (see Section (see Section 3.7). 3.7). The model provides provides a simple simple perspective perspective of stress-deformation behavior in the FLAC 3D grid, and can define locations where stress concentrations may develop. This may assist the definition of zoning density for the grid. It is often helpful to run a simple test of the selected material model before using it to solve the full-scale, full-scale, boundary-valu boundary-valuee problem. This can provide insight insight into the expected response response of the model compared to the known response of the physical material. The following example example illustrates the use of a simple test model. The problem application is the analysis of yielding mine pillars. A simple model is created to evaluate the implementation of the Mohr-Coulomb model versus the strain-softening model. This test also illustrates the effect of the selected measurement location on the reported results. The model is a compression test performed on a cylindrical grid composed of Mohr-Coulomb material.

Example 3.34 Compression test on Mohr-Coulomb Mohr-Coulomb material gen zo zone cy cyl p0 p0 0 0 0 p1 p1 1 0 0

p2 0 2 0

p3 0 0 1

size 4 5 4

gen gen zone zone refl reflec ect t norm norm 1,0, 1,0,0 0 gen gen zone zone refl reflec ect t norm norm 0,0, 0,0,1 1 model mod el moh mohr r prop prop bulk bulk 1.19 1.19e1 e10 0 she shear ar 1.1e 1.1e10 10 prop prop coh coh 2.72 2.72e5 e5 fric fric 44 ten ten 2e5 2e5 fix x y z range y -.1 .1 fix x y z range y 1.9 2.1 ini yvel

1e-7 range y -.1 .1

ini ini yvel yvel -1e-1e-7 7 rang range e y 1.9 1.9 2.1 2.1 ini ini pp 1e5 1e5 hist hist gp ydis ydisp p 0,0, 0,0,0 0 hist hist zone zone syy syy 0,1, 0,1,0 0 hist hist zone zone syy syy 1,1, 1,1,0 0 step ste p 300 3000 0

The axial (y -direction) stress-displacement response is monitored at the center and outer boundary



























3 - 64

User’s Guide

FLAC3D 3.00 3.00

x10^6

Step 3000 16:13:21 Fri Feb 04 2005

History

5.0

Rev 2 SYY Stress Zone 29 Linestyle 4.916e+001 <-> 5.226e+006 Rev 3 SYY Stress Zone 172 Linestyle 4.046e+002 <-> 1.375e+006

4.5

Vs.

4.0

1 Y-Displacement Gp 1 1.000e-006 <-> 3.000e-004

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0 1. 1.0


2 .0

3.0

x10^-4

Figure 3.30 Stress-displacement plots for compression of Mohr-Coulomb ma terial. Response is shown for an interior location (upper curve) and a boundary location (lower (lower curve). The test is now repeated with the strain-softening model:

Example 3.35 Compression test on strain-softening strain-softening material material gen zo zone cy cyl p0 p0 0 0 0 p1 p1 1 0 0

p2 0 2 0

p3 0 0 1

size 4 5 4

gen gen zone zone refl reflec ect t norm norm 1,0, 1,0,0 0 gen gen zone zone refl reflec ect t norm norm 0,0, 0,0,1 1 mode model l ss prop prop bulk bulk 1.19 1.19e1 e10 0 she shear ar 1.1e 1.1e10 10 prop prop coh coh 2.72 2.72e5 e5 fric fric 44 ten ten 2e5 2e5 prop prop ctab ctab 1 ftab ftab 2 table tab le 1 0,2 0,2.72 .72e5 e5 1e-4,2e 1e-4,2e5 5 2e2e-4,1 4,1.5e .5e5 5 3e-4,1. 3e-4,1.03e 03e5 5 1,1 1,1.03 .03e5 e5 tabl table e 2 0,44 0,44 1e-4 1e-4,4 ,42 2 2e-4 2e-4,4 ,40 0 3e-4 3e-4,3 ,38 8 1,38 1,38 fix x y z range y -.1 .1 fix x y z range y 1.9 2.1 ini yvel

1e 7 range y

1

1




























3 - 65

hist hist zone zone syy syy 1,1, 1,1,0 0 step ste p 300 3000 0

The horizontal stress-displacement response is monitored again, as s hown in Figure in Figure 3.31. 3.31. This test produces distinct peak and residual failure stress levels. FLAC3D 3.00 3.00

x10^6

Step 3000 16:10:35 Fri Feb 04 2005

History

5.0


4.5

Vs.

4.0


3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0


1. 1.0

2 .0

3.0

x10^-4

Figure 3.31 Stress-displacement for compression compression test of strain-softening strain-softening ma terial (similar monitoring points to Figure to Figure 3.30 ) The strain-softening model assumes both a brittle softening (due to reduction in cohesion) and a gradual softening (due to a reduction in friction angle). The selection of the properties is discussed further in Section in Section 3.7. 3.7. Comparison of Figures Figures 3.30 and 3.30 and 3.31 3.31 illus illustrates trates the different different responses responses of the two models. The initial response up to the onset of failure is identical, but post-failure behavior is quite different. Clearly, Clearly, more data is required to use the strain-softening model and, typically, typically, the softening model must be calibrated for each specific problem. The effect of confinement on the “measured” response is also demonstrated from these plots. The history recorded in the middle of the grid shows that a higher stress level develops develops in the center of the model than at the free side. The location of monitoring points should correspond as closely as possible to the location of measurements in the physical problem.



























3 - 66

3.6.3

User’s Guide

The Effect of Water Water

Geologic materials generally appear weaker when the pore spaces contain a pore fluid under pressure. This is represented represented in FLAC 3D by the incorporation of an effective stress that accounts for the presence of pore pressure in a zone. The pore pressures in FLAC 3D are taken to be positive in compression. Thus, the effective stress σ  is related to the total stress σ and pore pressure p by σ 

(3.3)

= σ + + p

Effective stresses are used in all of the plasticity models. The effect of water can be seen by b y repeating Example repeating Example 3.34 with 3.34 with constant pore pressure in the zones (i.e., an undrained compression test). Add the command ini ini pp 1e5 1e5

to Example to Example 3.34 before 3.34 before stepping. stepping. The lower lower strength is seen by comparing comparing Figure Figure 3.32 to 3.32 to Fig Figure 3.30 ure 3.30.. FLAC3D 3.00 3.00

x10^6

Step 3000 16:15:37 Fri Feb 04 2005

History

5.0


4.5

Vs.

4.0


3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0


1. 1.0

2 .0

3.0

x10^-4

Figure 3.32 Stress-displacement plots for compression test of Mohr-Coulomb material at constant pore pressure pressure






























3.6.4

3 - 67

Ways to Implement Constitutive Constitutive Models

Ther Theree are are seve severa rall diff differ eren entt ways ways in whic which h a const constit itut utiive mode modell can be impl implem emen ente ted d in FLAC 3D. The standard way is to invoke invoke one of the built-in models with the MODEL command. The user-defined models described in Section in Section 4 in 4 in Optional invoked with the MODEL command. Optional Features are Features are also invoked As discussed in Section in Section 3.6.1, 3.6.1, the built-in models are provided as DLLs that are loaded when 3D executed. ed. The individ individual ual DLL files are containe contained d in the “ FLAC3D300” diFLAC is first execut rectory with with the executable executable code. The source codes for the built-in built-in models are included included in the “ Shared Models Source” sub-directo sub-directory ry.. These files should be reviewed reviewed as examples for users who wish to write and implement their own models. User-defined models are written in C++ and are implemented as DLLs that are loaded with the FLAC 3D executable file in the same manner as the built-in models.* (See Section (See Section 4 in 4 in Optional Optional Features.) Features.)

\

\

\

\

Often, it is desirable to modify an existing constitutive model (either a built-in model or a userdefined model) to make material properties dependent on other model parameters. There are three ways this can be done. 1. change properties of the built-in model via a FISH function function that scans all the zones and is called at a specified step increment (say, every ten steps); 2. chan change ge prope propert rtie iess in a user user-d -defi efined ned cons consti titu tuti tive ve mode modell funct functio ion n at every every step step by refer referen ence ce to a formula; and 3. change properties properties via look-up look-up tables (with (with the TABLE command) that modify strength properties as a function of plastic strain for the built-in strain-softening and double-yield models. The third approach is the most efficient way to change properties in a FLAC 3D model. model. The first approach is the least efficient.





























3 - 68

3.7

User’s Guide

Materi Material al Prope Properti rties es

The material properties required in FLAC 3D are generally categorized in one of two groups: elastic deforma deformabil bility ity propert properties ies and streng strength th propert properties ies.. This This section section provid provides es an overvi overview ew of the deform deformaability and strength properties, and presents guidelines for selecting the appropriate properties for a given model. Additionally, there are special considerations such as the definition of post-failure properties, the extrapolation of laboratory-measured properties to the field scale, the spatial variation of properties and randomness of the property distribution, and the dependence of properties on confinement and strain. These topics are also discussed. The selection of properties is often the most difficult element in the generation of a model because of the high uncertainty uncertainty in the property property database. database. When performing performing an analysis, analysis, especially especially in geomechanics, keep in mind that the problem will always involve a data-limited system; the field data will never be known completely. completely. However, However, with the appropriate selection of properties based upon the available available database, database, important important insight to the physical problem can still be gained. This approach to modeling is discussed further in Section in Section 3.10. 3.10. Material properties are conventionally conventionally derived from laboratory testing testing programs. The following sections describe intrinsic (laboratory-scale) properties and list common values for various rocks and soils.

3.7.1

Mass Density

The mass density is only required in a FLAC 3D model if loading loading due to gravity gravity is specified. specified. The mass density is used to calculate the gravitational stresses within the model. Mass density has the units of mass divided by volume and does not include include the gravitational acceleration. Often in the literature, the unit weight of of a material is given. given. If the unit weight is defined defined with units units of force divided by volume, then this value must be divided by the gravitational acceleration before entering the value as FLAC 3D input for density. density. If a fluid fluid-fl -flow ow calc calcul ulat atio ion n is perfo perform rmed ed and FLAC 3D is confi configu gure red d for for fluid fluid flow flow (CONFIG CONFIG fluid), then 3D the dry density of the solid material must be used. FLAC will compute the saturated density of each element using the known density of water and the po rosity. rosity.






























3.7.2

3 - 69

Intrinsic Deformability Deformability Properties

All mate materi rial al mode models ls in FLAC 3D, exce except pt for the the tran transv sver ersel sely y isot isotro ropi picc Isotropic Elastic Properties — All elastic and orthotropic elastic models, assume an isotropic material behavior in the elastic range describ described ed by two two elasti elasticc consta constants nts:: bulk bulk modulu moduluss (K ) and and shea shearr modu modulu luss (G). The elasti elasticc consta constants nts,, 3D K and G, rather than Young’s modulus, E , and Poisson’s ratio, ν , are used in FLAC because it is believed that bulk and shear moduli correspond to more fundamental aspects of material behavior than do Young’s Young’s modulus and Poisson’s ratio. (See note 13 in Section in Section 3.8 for 3.8 for justification of using (K, G) rather than (E, ν ).) The equations to convert from (E, ν ) to (K, G) are

K

= 3(1 −E 2ν)

G

(3.5)

= 2(1E+ ν)

Eq. (3.5) should (3.5) should not be used blindly when ν is near 0.5, because the computed value of K K will be unrealistically high and convergence to the solution will be very slow. It is better to fix the value of K K at its known physical value (estimated from an isotropic compaction test or fr om the p -wave speed), and then compute G from K and ν . Some Some typica typicall value valuess for elasti elasticc consta constants nts are summar summarize ized d in Table 3.5 for select selected ed rocks rocks andT and Table 3.6 for selected soils.

Table 3.5

Selected elastic constants (laboratory-scale) for rocks (adapted from Goodman 1980)





























3 - 70

User’s Guide

Table 3.6

Selected elastic constants (laboratory-scale) for soils (adapted from Das 1994) Dry Density

Elastic

Poisson’s

Modulus

ratio

(kg/m3 )

E (MPa)

loose uniform sand

1470

10 - 26

0.2 - 0.4

dense uniform sand

1840

34 - 69

0.3 - 0.45

loos loose, e, angu angula larr-gra -grain ined ed,, silt silty y sand sand

1630 1630

dense, angular-grained, silty sand

1940

stiff clay

1730

6 - 14

0.2 - 0.5

soft clay

1170 - 1490

2-3

0.15 - 0.25

loess

1380

soft organic clay

610 - 820

glacial till

2150

0.2 - 0.4

special case case of elasti elasticc anisot anisotrop ropy y, the transv transverse ersely ly isotro isotropic pic,, Anisotropic Elastic Properties — For the special elastic model requires five elastic constants: E1 , E 3 , ν 12 , ν 13 and G 13 ; and the orthotropic elastic model requires nine elastic constants: E1 , E2 , E3 , ν12 , ν13 ν 23 , G12 , G13 and G23 . These constants are defined in Section in Section 2.4.2 in 2.4.2 in Theory Theory and Background. Background. Transversely isotropic elastic behavior is commonly associated with uniformly jointed or bedded rock. Several investigators investigators have developed developed expressions for the elastic constants in terms of intrinsic isotropic elastic properties and joint stiffness and spacing parameters. A short summary of typical values for anisotropic rocks is given in Table in Table 3.7. 3.7.

Table 3.7

Selected elastic constants (laboratory-scale)






























3 - 71

Fluid Elastic Properties — Models created for groundwater analysis also require the bulk modulus of the water, Kf , if the calculation involves incompressible grains, or the Biot modulus, M , if the grains are compressible compressible.. The physical physical value of K Kf is 2 GPa for pure water at room temperature. The value selected selected should depend on the purpose of the analysis. analysis. If only steady-state steady-state flow or an initial pore pressure distribution is required (see Section (see Section 1.7 in 1.7 in Fluid-Mechanical Interaction), Interaction), then as low a value of K Kf as possible should be used, without compromising the physics. This is because the fluid timestep will be small for high Kf ; also, the mechanical convergence will be very 3D slow for high Kf . The fluid timestep, t f f , used by FLAC is related to porosity, n , permeability,  k and Kf :

∝ Knk

t f f

(3.6)

f

We can determine the effect of changing Kf by deriving the coefficient of consolidation, Cv , for the case of a deformable fluid. (The fluid is assumed incompressible in most textbook solutions.)

Cv

=

k mv

+ Kn

f

where

mv

=

1 K

+ 4G/3

and k

=

k  γ f f

(3.7)































3 - 72

User’s Guide

example, pore water will contain some dissolved air, which substantially reduces its apparent bulk modulus. In the case of no flow, flow, the undrained saturated bulk modulus is

Ku

=

K

+

Kf n

(3.8)

and the undrained Poisson’s ratio is

νu

=

3Ku

− 2G 2(3Ku + G)

(3.9)

These values should be compared to the drained constants K and ν to evaluate the effect on the rate of convergen convergence. ce. It is important important to remember that drained properties properties are used for coupled, 3D mechanical fluid-flow calculations in FLAC . For the case of compressible grains, the influence of Biot modulus, M , on the rate of convergence for a model is similar to that of fluid bulk modulus.

3.7.3

Intrinsic Strength Properties Properties
































3 - 73

Tensile yield is detected if f f t t > 0. Tensile strengths from rock and concrete are usually derived for a Brazilian test. Note that the tensile strength cannot exceed the value of σ 3 , corresponding to the apex limit for the Mohr-Coulomb relation. This maximum value is given by t σ max

= tanc φ

(3.12)

Typical values of cohesion, friction angle and tensile strength for a representative set of rock specimens are listed in Table in Table 3.8. 3.8. Cohesion and friction angle values for soil specimens are given in Table in Table 3.9. 3.9. Strength is often described in terms of the unconfined compressive strength, q u . The relation between q u and cohesion, c , and friction angle, φ , is given by qu

Table 3.8

= 2 c tan(45 + φ /2)

(3.13)

Selected strength properties (laboratory-scale) for rocks (adapted from Goodman 1980) Friction

Cohesion

Tensile

Angle

(MPa)

Strength































3 - 74

User’s Guide

Table 3.9

Selected strength properties (drained, laboratory-scale) for soils (Ortiz et al., 1986) Cohesion

Friction Angle Peak

Residual

(kPa)

(degrees)

(degrees)

gravel

—

34

32

sandy gravel with few fines

—

35

32

sandy gravel with silty or clayey fines

1.0

35

32

mixture of gravel and sand with fines

3.0

28

22

uniform sand — fine

—

32

30

uniform sand — coarse

—

34

30

well-graded sand

—

33

32

low-plasticity silt

2.0

28

25

medium- to high-plasticity silt

3.0

25

22

low-plasticity clay

6.0

24

20
































3 - 75

These tests can produce physical properties for joint friction angle, cohesion, dilation angle and tensile strength. Published strength properties for joints can be found, for example, in Jaeger and Cook (1969), Kulhawy (1975) and Barton (1976). Friction angles can vary from less than 10◦ for smooth joints in weak rock, such as tuff, to over 50◦ for rough joints in hard rock, such as granite. J oint cohesion can range from zero cohesion to values approaching the compressive strength of the surrounding rock. It is important to recognize that joint properties measured in the laboratory typically are not represent sentat atiive of those those for real real join joints ts in the the field field.. Scal Scalee depen depende denc ncee of join jointt prop proper erti ties es is a majo majorr quest questio ion n in rock mechanics. Often, comparison to similar joint properties derived from field tests is the only way to guide the choice of appropriate parameters. However, However, field test observations observations are extremely limited. Some results are reported by Kulhawy (1975).

3.7.4

Post-F Post-Failure ailure Properties

In many instances, particularly in mining engineering, the response of a material after failure has initiated is an important factor in the engineering design. Consequently, the post-failure behavior must be simulated simulated in in the material material model. model. In FLAC 3D, this is accomplished with properties that define four types of post failure response: (1) shear dilatancy; dilatancy;































3 - 76

User’s Guide

corresponds to the elastic regime, while the slope used to measure the dilation angle corresponds to the plastic regime.

e c n e r e f f i D s s e r t S

elastic

n i a r t S c i r t e m u l o V

plastic


































3 - 77

Dilation Dilation angle can also be prescribed prescribed for the joints joints in the ubiquitous-jo ubiquitous-joint int model. This property property is typically determined from direct shear tests, and common values can be found in the references discussed in Section in Section 3.7.3. 3.7.3. 3.7.4.2 3.7.4.2

Shear Hardening Hardening/Soft /Softening ening

The initiation of material hardening or softening is a gradual process once plastic yield begins. At failure, deformation becomes more and more inelastic as a re sult of micro-cracking in concrete and rock, and particle sliding in soil. This also leads to degradation of strength in these materials and the initiation initiation of shear bands. These phenomena, phenomena, related to localization, localization, are discussed further further in Section 3.10. 3.10. In FLAC 3D, shear hardening and softening are simulated by making Mohr-Coulomb properties (cohesion and friction, along with dilation) functions of plastic strain (see Section (see Section 2.5.4 in 2.5.4 in Theory Theory

































3 - 78

User’s Guide

Figure 3.34. 3.34. The development of localization localization and shear bands can be observed in Figures in Figures 3.35 and 3.35 and 3.36.. The plastic region is identified as hourglass-shaped with spiral structures radiating from the 3.36 hourglass cones.

Example 3.36 Uniaxial test of a shear-softening shear-softening material ; Uni Uniaxi axial al tes test t of strainstrain-sof soften tening ing mat materia erial l title Uniaxi Uni axial al tes test t of strainstrain-sof soften tening ing mat materia erial l gen z zo one c cy yl p p0 0 0 0 0 p1 p1 1 0 0 gen gen zone zone refl reflec ect t norm norm 1,0, 1,0,0 0 gen gen zone zone refl reflec ect t norm norm 0,0, 0,0,1 1 mode model l ss

p2 0 4 0

p3 0 0 1

size 1 12 2 3 30 0 1 12 2


































else z_grou z_g roup(z p(zp) p) = ’ot ’other her’ ’ endif zp = z_ne z_next xt(z (zp) p) endLoop end ShowPlasticZones plo plo crea crea qqq qqq plo plo add add surf surf red red rang range e grou group p yiel yield d plo plo add add axes axes gree green n plo plo set set rot rot 123 123 313 313 3 plo plo set set mag mag 1.5 1.5 ret

3 - 79

































3 - 80

User’s Guide

FLAC3D 3.00 Step 5000 Model Perspective 13:10:51 Tue Feb 08 2005 Center: X: 0.000e+000 Y: 2.000e+000 Z: 0.000e+000 D is t:t: 1 .4 .4 51 51 e+ e+ 00 00 1

Rotation: X: 120.000 Y: 275.000 Z: 180.000 Ma g. g. : 1 .2 .2 Ang.: 22.500

Contour of Shear Strain Rate Magfac = 0.000e+000 Gradient Calculation Calculation 8.2037e-007 to to 1.0000e-005 1.0000e-005 to to 2.0000e-005 2.0000e-005 to to 3.0000e-005 3.0000e-005 to to 4.0000e-005 4.0000e-005 to to 5.0000e-005 5.0000e-005 to to 6.0000e-005 6.0000e-005 to to 7.0000e-005 7.0000e-005 to to 7.8627e-005 Interval = 1.0e-005

Job Title: Uniaxial test test of strain-softening strain-softening material


































3.7.4.3 3.7.4.3

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Volumetric olumetric Hardenin Hardening/Sof g/Softening tening

Volumetric hardening corresponds to irreversible compaction; increasing the isotropic pressure can cause permanent volume decrease. This behavior is common in materials such as lightly lightly cemented sands and gravels and over-consolidated clays. Volumetric hardening/softening may be simulated in the double-yield model and the Cam-clay model. model. The double-yield double-yield model model assumes that the hardening hardening depends on plastic volume volume strain, while the Cam-clay model treats volumetric hardening as a function of both shear and volume strain. The double-yield model takes its hardening rule from either a TABLE command or a FISH function. function. Section 2.3 in 2.3 in Theory p rocedure to develop these Theory and Background describes Background describes a recommended test procedure parameters parameters from triaxial triaxial tests performed performed at constant constant mean stress, and for loading in which axial



































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User’s Guide

Example 3.37 Tension test on tensile-softening tensile-softening material gen zo zone cy cyl p0 p0 0 0 0 p1 p1 1 0 0

p2 0 2 0

p3 0 0 1

size 4 5 4


































FLAC3D 3.00 3.00 Step 1500 15:15:16 Mon Feb 07 2005

x10^5 1.8

History 2 ax_str (FISH function) Linestyle

1.6

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3.7.4.5 3.7.4.5

User’s Guide

Volume-Pre olume-Pressur ssuree Properti Properties es

The double-yield and modified Cam-clay models require material properties that relate pressur e to volumetric change. For both models, the preconsolidation pressure is the maximum past consoli-


































Gr = intact rock shear modulus; and

stiffness. ks = joint shear stiffness.

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User’s Guide

σ 

1

=

σ 

3

+ σ cici



mb

σ 3 σ ci ci

+s



a

(3.23)



























































































































































































































































































































































































































































































































































Flac 3D 3

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