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Associate Professor Nagaratnam Sivakugan School of Engineering James Cook University Townsville, Qld 4811 Australia Tel.: 61 7 47814431 Email: [email protected] 1 A FLAC Primer A FLAC Primer Table of Content Page 2 2 3 4 5 9 9 10 13 15 15 15 16 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. FLAC versus Others Purchasing FLAC Units and Notations Running FLAC Mesh Generation Boundary Conditions Solving the Problem Outputs to Screen, Printer and Documents Some Constitutive Models Calculation Modes Large/Small Strain Modes FISH Seepage Consolidation Appendices: A – A Note on Permeability B - Geotechnical Applications 19 Dr. Nagaratnam Sivakugan (2006) 2 Sultan Qaboos University (Oman) and State University of Rio de Janeiro (Brazil). it is a horrendous effort to master this wonderful software. reviewing sections of this manual and visit to JCU. However. Briony Rankine. With my limited knowledge of FLAC. Consolidation. There are several programs covering a wide range of applications in these manuals and they are certainly worth trying. Dr. involving mechanical deformation and fluid flow. And… they have become ardent fans of FLAC. the modeling strategies given in Itasca’s FLAC manual (available on-line too) are far superior. FLAC comes with a 10-volume user manual which is not that friendly for a beginner. Since then I had been helping the several postgraduates and honours students (or they help me in fine tuning my understanding) who had been applying FLAC and FLAC3D to geotechnical and mining problems. using FLAC and FLAC3D. It took me three full weeks (and a ruined holiday) to understand the little I know of FLAC. being a coupled problem. a postgraduate who has worked on consolidation extensively.A FLAC Primer Preface I confess I only know about 10% of FLAC. one can understand the key features of FLAC to get started. Michael Coulthard has contributed significantly to our FLAC modeling through his prompt and precise answers to all our queries. requires a bit more had work to master. Kanpur (India). Using this document. Nagaratnam Sivakugan (2006) 3 . The purpose of this manual is to explain the concepts and commands in the simplest possible way for the beginners. The section on consolidation is written by Ms. Siva June 2006 Dr. I was able to teach FLAC to academics and postgraduates at Indian Institute of Technology. For those who try to learn FLAC from scratch. Her contribution is gratefully acknowledged. but I know that 10% quite well. I could teach a 4th year honours student or a postgraduate and get him or her started within an hour. with very little jargon. the 2nd. It is used in civil and mechanical engineering applications.g. ANSYS. FLAC is developed specifically for geotechnical and mining applications and includes most constitutive models that we can think of. CRISP is a critical state soil mechanics program. It operates on portable computers and is widely used in design offices. developed in UK. Many of our honours students and postgraduates use FLAC and FLAC3D comfortably in their research projects. These adjustments take place on the basis of the selected constitutive model and equation of motion (similar to equilibrium equations). The adjustment continues until the error (e. ABAQUS. FLAC is a very useful research tool. 2. The other softwares distributed by ITASCA are in Table 1. Table 1. PLAXIS is a geotechnical software that is popular among geotechnical engineering practitioners. unbalanced force in the system) becomes very small.com) through its agents located in many countries. CRISP etc. USA (http://www. but not specifically developed with geotechnical engineering in mind. Most of the time. and the solution scheme is explicit. in helping the beginners. Nagaratnam Sivakugan (2006) 4 . 33% and 25% of the price of Dr. Purchasing FLAC FLAC is marketed and distributed worldwide by Itasca Consulting Group of Minneapolis. FLAC versus Others FLAC (Fast Lagrangian Analysis of Continua) is one of the most popular general purpose geotechnical modeling softwares used worldwide. in spite of some difficulty in getting started. The purpose of this document is to provide a plain English guide. It is a finite difference software.itascacg. 3rd and 4th keys of the same software can be bought at 50%. The solutions are reached through a process known as time-marching or timestepping. mainly due to its user friendliness. It runs on portable computers.. When you need more than one key. The other numerical modeling software that are used widely are PLAXIS. ABAQUS is quite powerful and operates from mainframe computers. which is simply adjusting the values of each node in the mesh through a series of cycles or steps. Recent addition of CIVIL FEM module makes ANSYS attractive for geotechnical modeling.A FLAC Primer A FLAC Primer 1. Like ABAQUS. The 2-dimensional versions were the ones developed first and were later extended to 3-d. and is quite versatile in features. Itasca Software 2-D 3-D Description FLAC FLAC3D Fast Lagrangian Analysis of Continua – tor treating soil as a continuum UDEC 3DEC Universal Distinct Element Code – for discrete blocks such as jointed rocks 2D 3D PFC PFC Particle Flow Code – for assemblage of circular or spherical particles Universities and educational institutions can purchase Itasca products at discounted prices. ANSYS can be used for geotechnical and structural modeling. It also requires some good learning for one to master the features and use them comfortably. They come with hardware locks (dongles – Itasca calls them keys). strip footings. we have 3 FLAC 5.sav files saved using “save” command. etc). and that is adequate for learning. 3.15 MB.g. Itasca distributor will not entertain queries from more than one person per site license. Density in kg/m3. The student version can solve a mesh of up to about 600 elements.0 keys. but under the same site license with one contact person. A FLAC program will consist of a series of instructions. circular footing. triaxial test.. These are written in FLAC as sxx. The normal stress in z direction is szz. retaining walls. Hardcopies are available in the form of 10 separate volumes. deformations in meters. and PLOT are three of the 50 or so commands available in FLAC. Each line starts with a command. Nagaratnam Sivakugan (2006) 5 . At JCU. Stick to consistent sets of units to avoid any confusion. Time in s.The displacements of a node in x and y directions are denoted by xdisp and ydisp respectively. Compressive stresses are negative in FLAC. Some examples are: MODEL PROPERTY PLOT elastic den = 1600 bulk = 1e8 hold grid bou Here. The shear stress is σxy (often denoted by τ). Obviously. Xvel and yvel are the velocity Dr. When you purchase FLAC. embankments.g. you will get the student version free (only for universities). Pore water pressures at an element or node are denoted by pp and gpp respectively. 6. all FLAC outputs will be in matching units (e. which is followed by appropriate key words and necessary values.) problems. Therefore. That makes it suitable for teaching in classrooms. 1). syy. In the x-y Cartesian coordinate system. the normal stresses in x and y direction are σx and σy respectively (Fig..A FLAC Primer the first one. FLAC is adequate for one to get started.23e5. PROPERTY. and it is much cheaper than FLAC3D which is required for analyzing truly 3-d problems. The student version has default RAM of 0. and negative when it is directed away from the surface. Mass in kg. Whatever that cannot be done using FLAC commands can be done using FISH (for FLACish) language compiler built into FLAC. pore water pressures in Pascals.23 x 105 is written as 6. The main advantage of student version is that it does not require a dongle and can be installed in any personal computer.0 keys and 2 FLAC3D 3. At IIT Kanpur I had postgraduates doing term papers on FLAC applications just using this student version. Gravity in m/s2. Pressure is positive when applied towards a surface. The dongle is only required to run (using step or solve commands) FLAC. FLAC comes with a very comprehensive on-line manual. MODEL. etc.) or axisymmetric (pile foundation. Units and Notations SI or imperial units can be used in FLAC. Most geotechnical problems can be modeled as plane strain (e. Stress or Pressure in Pa. All the examples provided in the extensive FLAC manuals can run on this student version. and sxy respectively. My suggestion is to use the following: Length in m. In FLAC. Force in N. which can be bought at nominal price. These are two different parameters stress and pressure in FLAC. braced cuts. which can solve up to about 500 elements. The student version is adequate for viewing any large mesh and also to manipulate any *.. Some FLAC runs can take several hours to solve. This can be done by adding the required number of RAM (say 16 for 16 MB) at the end of the target string.A FLAC Primer components in x and y directions. Notation for Stresses 4. Right-click the mouse on the FLAC short-cut icon. Itasca suggests command-driven FLAC for the beginners. you may want to save the solved state so that it can be recalled without re-solving.2. select properties and add 16 at the end of the target string. it is always suggested to write the instructions in a batch-file in Notepad. If your mesh is larger. The rest of this document will be based on command-driven FLAC. Now.dat. σyy σxy σxx y x Figure 1. the new RAM allocated will appear on the screen.INI file. which is sufficient for up to 30. and this can be turned off permanently by modifying or deleting the FLAC. These can be then called from FLAC by flac: CALL my_file.. The die-hards of FLAC who had been using command-driven mode still prefer using it instead of the menu-driven. it can be used commanddriven or menu-driven. and FLAC is not case sensitive. Any later modifications require retyping the entire sequence of instructions. Until Version 4.e. you will use both ways – direct and indirect modes. and then use a couple of commands on the flac: prompt (direct mode). The problem here is that none of the lines typed are saved. Nagaratnam Sivakugan (2006) 6 . which are simply the displacements per time step. as an unformatted ASCII file with possible extensions of *. Here. flac: SAVE my_file. In the command-driven mode. “flac:” prompt is where you enter the commands. Therefore.2) covers running FLAC in menu-driven mode.txt or *. write most of the instructions in a batch file and run (indirect mode). FLAC manual Getting Started (Getting Started 2. Although the menu-driven FLAC appears to be easier and friendlier to use thanks to the windows and tool bars available. i. Next time you start FLAC. The menu driven mode (known as GIIC for Graphical Interface for Itasca Codes) is the default setting. Running FLAC By default FLAC allocates 8 MB RAM for FLAC.txt Very often. For example. Commands can be entered one line at a time.sav” extension. Large velocity vectors indicate instability in a geotechnical system. flac: GRID 10.sav Dr.12 flac: MODEL elastic defines a grid of 10x12 and specifies an elastic model. Use “SAVE” command to save the solved sate with “*. FLAC was available only as command-driven.000 elements.0. you need to allocate more memory. For most of our work. A neater way is to have a separate folder (e. All files need to be present in the “exe” directory that is located in c:\\program files\Itasca\flac\exe. flac: SET cd name c:\flacruns FLAC can operate on single or double precision mode. and the node (or grid point) E by i = 3 & j = 2. The boundaries must be selected far enough.53) D(364..g. HELP command will list all possible commands in FLAC. each element and node can be defined by a pair of i and j values. The dark line is defined by i = 3.140) 100 200 300 400 x Figure 2.251) i=1 100 j=1 A(87. A finite difference mesh in FLAC The first step in solving a problem is to divide the problem zone into a suitable grid (or mesh). 5. c:\\flacruns) for these program files through the following command. the hatched element by i=3 & j=2. Nagaratnam Sivakugan (2006) 7 . QUIT command will close the FLAC window. Single precision is twice faster and requires 1/3 of the RAM compared to the double precision mode. Integers i and j (starting with 1 – not zero) are used to denote the grid lines (and elements) in two directions that are not necessarily orthogonal. You will have to type this line every time you start FLAC.sav Remember that the saved or restored files are in binary form unlike your original text files. single precision is adequate. Dr. The following program Example 1 can create this simple grid. Therefore.209) 200 E i=5 C(253.A FLAC Primer and “RESTORE” command to restore it for further manipulation. Figure 2 shows a simple 4x3 grid. such that the entire region influenced by the problem are included in the study. Mesh Generation y j=4 B(116. The x-y Cartesian coordinate system is used to reflect the coordinates of every point within the boundaries ABCD. flac: RESTORE my_file. g. Including “ratio” keyword in the GENERATE command helps in grading the mesh from being coarse at far ends and finer near the regions of interest. The following two commands will show the grid numbers and the element numbers on separate screens. FLAC mesh consists of constant stress elements (or zones). This can be used to create quite complex meshes by attaching several subgrids together. 3). For example “rat = 0.25 5.0 i=1.8 j=1. The following program (Example 3) does just that.3 MODEL elastic PROP den = 1600 bulk = 1e7 shear = 0. Therefore some model (elastic in Ex. which is difficult when using the ratio keyword. Example 2 below shows a simple mesh for the soil beneath a strip footing (see Fig.95 GEN 5. Example 2: GRID 15.25 13.0. GENERATE command is used to create the mesh.53 116. The default model is null.5 j=1.05” will see that the grid spacing decreases from left to right.25 13. Nagaratnam Sivakugan (2006) 8 . 1) has to be specified for the material. PROPERTY command specifies the values of the properties appropriate to the model selected.0 PLOT hold grid GRID command defines the number of elements in the two directions. This can lead to numerical problems and can affect the quality of the output. aspect ratio being too large. the “hold” key word ensures that the screen is paused until the return key is pressed. ATTACH command is particularly useful in making regions of different mesh density and joining them. Remember.95. At least try to see that this does not occur in the regions that are of interest to us.0.0.0 5.251 364. they need to be smaller when there is rapid stress change (e. and MODEL command does just that.3e7 GEN 87.0. around a corner of a footing). Therefore.. In PLOT command.0 0.1. Dr. You just don’t go for the square mesh with the same intensity everywhere for all the problems.95 When generating meshes try to ensure that the elements are not too elongated (i. The key word “ratio” can be used to vary the spacing of the grid lines gradually.140 i=1. and increases upwards.16 j=1.A FLAC Primer Example 1: GRID 4. and can be larger in the farfield. The four plot commands are mainly to see the effect of each line in creating the mesh.25 MODEL elastic PROP den=1600 bulk=13..25 5.1. 1.26 rat=1. Let’s make a 10 m x 10 m mesh and divide into left and right halves with different mesh densities. say larger than 5). and therefore we should optimize the way we generate the mesh for a given number of elements. right half being three times higher in mesh density.26 rat=1.0 i=8.4 rat=1. It may be necessary to use more than one GENERATE line to create the mesh. Only the right half in considered here. every extra element means additional computational time.209 253. PLOT hold grid gnumber PLOT hold grid number Mesh generation is an art.e.33e6 shear=8e6 GEN 0. 0 rat = 1.1 to 5.0 rat = 1.10 11.A FLAC Primer Figure 3.0 0.0 0.10 11.13 PLOT hold grid bou iw attach lm The resulting mesh is shown in Figure 4a.0 i=5. Soil beneath a strip footing (only the left half shown here) Example 3a: GRID 13. Example 3b: GRID 13.1.13 PLOT hold grid Dr.1 for the right side and 1.12 MODEL elastic MODEL null i=4 MODEL null i=1. 1.1 to 4.0 6.0 6. we have used ratio = 1.5 GENERATE 6.331 i=1.14 j=1.14 j=1.14 PLOT hold grid ATTACH aside from 4.3 j=5.12 PLOT hold grid GENERATE 0.4 j=1.1 i=5.0. let’s see what happens if we also want to make the mesh coarser upwards.5 GENERATE 6.4 j=1.13 for the left side to make the grid points match properly.10 5.12 PLOT hold grid GENERATE 0.10 11.5 bside from 5.0 i=1.12 MODEL elastic MODEL null i=4 MODEL null i=1. Nagaratnam Sivakugan (2006) 9 . Now.10 11. Here.3 j=5.10 5.10 5.0.13 PLOT hold grid INITIAL x add -1 i=5.10 5. 14 PLOT hold grid ATTACH aside from 4.167E+01 Grid plot 0 2E 0 1.600 0.667E+00 <x< 1.000 0.200 0.400 (*10^1) 0.800 Boundary plot 0 2E 0 Attached grid points 0.000 0.200 0.1 to 4. Australia 0.13 PLOT hold grid bou iw attach red JOB TITLE : (*10^1) FLAC (Version 5.167E+01 Grid plot 0 2E 0 0.000 Sivakugan .167E+01 -1.800 1.667E+00 <y< 1.School of Engineering James Cook University.600 0.00) LEGEND 26-Jun-06 11:57 step 0 -1.200 0.600 1.School of Engineering James Cook University.A FLAC Primer INITIAL x add -1 i=5.667E+00 <y< 1.000 (b) Ratio ≠ 1 Figure 4.000 (a) RATIO = 1 for both halves JOB TITLE : (*10^1) FLAC (Version 5. Use of ATTACH command (a) Ratio = 1 (b) Ratio ≠ 1 Dr.00) LEGEND 26-Jun-06 11:33 step 0 -1.000 0.800 1. Nagaratnam Sivakugan (2006) 10 .167E+01 -1.000 0.600 0.200 0.400 Attached Gridpoints 0.667E+00 <x< 1. Australia 0.1 to 5.000 Sivakugan .400 (*10^1) 0.400 Attached Gridpoints 0.5 bside from 5.800 Boundary plot 0 2E 0 0. The rest of the nodes will be simply “slaved” to the nearest perfectly attached node in deriving the values linearly The following command will list all perfectly attached and slaved grid points. circle. Gravitational stresses can be included by assigning a value for gravity.A FLAC Primer Along the vertical boundary line between the two halves in Fig. FIX x i=1 FIX x i=16 FIX y j=1 Here.001 for equilbrium ratio. pressures or pore water pressures through APPLY command. arc and table can be used on GENERATE command. Such boundary conditions can also include application of external loads. the stepping goes on until the error (unbalanced force or equilibrium ratio) is within a prescribed value (defaults are 100 N for unbalanced force. Dr. We can simply say STEP 30000 if we know that the system will reach equilibrium in 30000 steps. it is implied that there are no horizontal deformations along the vertical boundaries on the left and right.81 m/s2 Any comments can be added after a semicolon (. The best way to go about is to use SOLVE command. 10th. where half the problem is analysed due to symmetry. and there is no vertical deformation at the bottom horizontal boundary. These default values can be changed by the following lines. the next step is to solve the problem. When you apply loads. It is a good practice to add comments throughout the program so that one can follow the program easily later. where the values are adjusted at every node. It is necessary to select these boundaries quite far from the problem zone. during each cycle.81 . Here. Boundary Conditions Once the mesh is generated. 0.). 100. and 13th nodes on the right half attach perfectly to the nodes on the left half. and this can be done through trial and error. g=9. This is an iterative process. through a series of steps (or cycles). 6. known as time marching or time stepping. it is necessary to assign boundary conditions. pressures or pore pressures within the boundary use INTERIOR command instead of APPLY command which works only on external boundaries. PRINT attach In making a more sophisticated mesh. we will have the following boundary conditions. 4b. keywords such as line. 4th.000 steps for timesteps and 24 hours for runtime). SET gravity = 9. the 1st. Solving the Problem After generating the mesh and assigning the boundary conditions. In Example 2. Nagaratnam Sivakugan (2006) 11 . 7. 7th. flac: STEP continue The best way to detect whether the equilibrium has been reached is to look at the histories of unbalanced force. SOLVE PLOT hold his 1 PLOT hold his 2 PLOT hold his 3 Here.000 steps by the following lines.A FLAC Primer SET force = 50 SET sratio = 0. INI xdisp=0 ydisp=0 Dr. FLAC. use the <Esc> key to interrupt stepping. displacements or pore pressures at a point.e. we can initialize the current stress to zero through the following lines. . . his 1 refers to the first defined history (i.. . considering all nodes. one can also initialize displacements through the following command. stresses. stops when 100. you can change the default setting of 100. For example. maximum unbalanced force). Alternatively. you may need to step this further even after the SOLVE command. unbalanced force . Nagaratnam Sivakugan (2006) 12 . In Mohr-Coulomb. It is a good practice to include a few HISTORY commands in the program. zeroing all stresses can distort the picture. It should be noted that initializing stresses as above will work if the model is elastic.. . SET step 5000000 SOLVE It is a good practice to use a large step number as above.01 . equilibrium ratio Equilibrium ratio is the largest ratio of maximum unbalanced force to average applied force. INI sxx=0 syy=0 sxy=0 szz=0 SOLVE Similarly. to have some assurance that the system has reached equilibrium. Initialising the grid or element values to specific values can be achieved through INITIALIZE command. check histories and then continue till equilibrium is reached. This does not always mean that the equilibrium is reached. Inclusion of the following lines will monitor few histories and plot them..000 steps are reached. . . where one can see whether equilibrium has been reached. by default. HIS unbal HIS syy i=4 j=15 HIS ydis i=1 j=26 . if we are interested in the stress changes from the current state. Therefore. and so on. Stepping can be resumed by the following command on flac: prompt. This is a common practice. The first command below plots the grid in green and boundary in intense white. Alternatively. 8. James Cook University. Try the following two key commands.A FLAC Primer When establishing the initial stresses due to gravity. A better way of preparing figures for embedding in documents is as follows. Dr. The third one plots the y-displacement contours filled. and shows the grid as well. The second one plots the grid in black. flac: PLOT hold grid syy fill flac: PLOT hold syy fill grid To get a printout of last-viewed plot try the following: flac: COPY When cutting and pasting the FLAC image in a document. Once the initial stresses are established. the model can be reset to Mohr-Coulomb with the right value for cohesion and tensile strength. Mohr-Coulomb model can be used with very high cohesion and tensile strength to avoid such yielding. Outputs to Screen. it is a good practice to use elastic model to avoid yielding of any element. flac: plot hold grid green bou iw flac: plot hold syy fill bou flac: plot hold ydisp fill grid Note that the order of key words has an effect in FLAC. Nagaratnam Sivakugan (2006) 13 . and you will see this in many FLAC examples in the manual.. TITLE Embankment Analysis for Company ABCD In addition. the 2-line customer details (e. which are essentially the same but the key words are in different order. The second one plots the σyy (vertical) stress contours and fills the intervals. Printer and Documents Inclusion of the following two lines in the program will ensure that the second line appears in all plots at the top left. flac: set back iw flac: plot grid black The first command above sets the background to intense white.g. it is better to have a white background as opposed to the default black background. School of Engineering) can be changed by the following two lines: SET cust1 ABCD Consultants SET cust2 Geotech Division In FLAC we get to see several plots on the screen. 750 2. and can be used at a later time.917E+01 Grid plot 0 1E 1 1.000 0. One can also create jpg or bmp versions of the plots. Nagaratnam Sivakugan (2006) 14 .emf. lcyan. For example. Dr.A FLAC Primer SET plot emf COPY figure5. 5).000 1. and lmagenta. Minneapolis.750 (*10^1) 1.250 1.emf JOB TITLE : (*10^1) FLAC (Version 4. the command PLOT hold syy yellow grid green bou white will plot the σyy contours in yellow. and we don’t have to worry about changing the background or the plot colours for the hardcopy (see Fig. gray. brown. Inc. The possible colours you can use in FLAC are black.250 Figure 5. grid in green and the boundary in white. The strip footing mesh as a Window-enhanced metafile Here figure5.250 0.500 2. blue.017E+01 <x< 2. lred. Here. white. lgreen.00) LEGEND 22-Nov-05 11:05 step 0 -1.500 2.emf is a Window-enhanced metafile plot of the last-viewed plot.250 0. you can define a new colour for each of them.167E+00 <y< 2. which can be imported directly into a word processing program such as Microsoft Word. You can also have some lighter shades of the above colours with lblue.750 -0. cyan. FLAC looks after the colours nicely. magenta. When you plot few variables on a screen.317E+01 -4. The file is stored along with your flac programs in the default directory as figure5. Use “CTRL + Z” to zoom into any part of the mesh. yellow and iwhite (intense white). green. red. Type WINDOW on flac: prompt to get back to the default screen. Minnesota USA -0.500 0.000 Itasca Consulting Group. and proceed with formatting the data. 1 and 2. Darcy’s law is a constitutive model that governs fluid flow in a porous media often. we want to tabulate all data in a spreadsheet such as Microsoft Excel for further manipulation including generating plots. obtained through PRINT commands. SET log on PRINT syy i=1 SET log off All text that appears on the screen. The material properties are defined by two constants.log. it is necessary to define how the material behaves when subjected to loading. Some Constitutive Models In finite element or finite difference modeling. Section 13. Strain Hardening. Srain Softening. Nagaratnam Sivakugan (2006) 15 . locate it in the folder. and right click the mouse and select “open with Microsoft Excel for Windows”. include the following commands after SOLVE command. Dr. Constitutive model does not have to be always for defining loaddeformation behaviour. and PRINT ydisp i=1 j=26 to get the settlement of the footing at the center in Example 2. Once the file is opened with Excel. FLAC requires bulk modulus (K) and shear modulus (G) instead of the above two for good reasons given in the FLAC manual (Getting Started. which is stored in the default directory. 9. To do this. FLAC has other models such as Mohr-Coulomb. which are commonly the Young’s modulus (E) and Poisson’s ratio (ν). Generally. following Hooke’s law. after the SET log on command.log. To open the file flac. The simplest constitutive model we all are familiar with is the infinitely elastic model that works on the basis of Hooke’s law. page 3-139). Transversely Anisotropic etc. Drucker-Prager. the material is assumed to be isotropic and linear elastic. and give commands such as: PRINT syy i=1 to get the vertical stress distribution along the vertical center line. select “text to columns”. PRINT syy command will simply list the σyy values in all elements. You may rather be selective and want these values only for certain elements or nodes. G and K can be derived from E and ν from Eqns.1 Elastic Model Here.A FLAC Primer PRINT command can be used to print the grid or element variables. Modified Cam-Clay. 9. can be saved in a file flac. Let’s just look at three simple models we will use for now. FLAC outputs. For example. These can be defined through constitutive models. will be copied to this file. 30 18. and that should be the dry density of the material in the case of grids configured for fluid flow (with CONFIG gw command).0. with no yielding ever.0 0. with pore water pressure values specified for the grids).30 3.1. friction angle.23 j=1.only analysis. the elements are voids. and the default is zero.95 GEN 0. mechanical.23 j=21.00e6 9. The input parameters are: density.0 i=13.05. As the name implies. It is also necessary to input a density value here.25 MODEL mohr GEN 0.13 j=1.95 GEN 8.25 PLOT hold grid MODEL elastic i=1.0.0 PLOT hold grid MODEL null i=13.30 i=13.. υ= MODEL elastic PROPERTY den=1600 bulk = 13. trenches etc.3 Null Model This is the default model in FLAC.30 8.25 Dr. we should specify dry density above the water table and saturated density below the water table.0 GEN 8. No properties are required.35 8.27 rat=1.0.0 8.35 18. cohesion and tensile strength.21 rat=1.0. tunnels. When the grid is not configured for fluid flow (i. E= 9 KG 3K + G (3) 3K − 2G (4) 3(3K + G ) It is assumed that the model is infinitely elastic.30 0.2 Mohr-Coulomb Model Mohr-Coulomb is a plastic model.21 rat=1. The maximum possible value for the tensile strength is “c cot φ”.27 rat=1. 3 and 4.13 j=21.30 18. The use of null model in mesh generation is illustrated in the following example. shear modulus.e.A FLAC Primer G= E 2(1 + υ ) E 3(1 − 2υ ) (1) K= (2) E and ν can be derived from G and K using Eqns. Nagaratnam Sivakugan (2006) 16 . 9. Such assumptions are used in most classical elastic models discussed in textbooks. bulk modulus. where the material is assumed to behave elastically until yielding.33e6 shear = 8. These are used in defining excavations.12 j=21.1.0 i=1.35 18.05.30 8.22 j=21. Example 4: GRID 22.35 3.30 i=1. 30 MODEL elastic PROP bulk=2.0.16 j=1. which are modeled as elastic and Mohr-Coulomb materials respectively. Calculation Modes Default mode for computations in FLAC is plane strain. CONFIG axi CONFIG p_stress CONFIG gwflow 10.31 to 6. They are mainly for plane strain and plane stress problems.98 FIX x i=16 FIX y j=1 APPLY pressure=100e3 from 1.6 j=1. Nagaratnam Sivakugan (2006) 17 .0 i=6.5e-3 fill grid PLOT hold syy int=1e4 fill grid Dr. It can also solve axisymmetric.3 SET large GEN 0. In such circumstances.6 1.0. The FLAC program is given below as Example 5.154e7 den=2300 .0 i=1.1 Axisymmetric Problem We deal with several axisymmetric loading situations (circular footing.6 3.0 1. include one of the following lines at the top of the program. Here.31 rat=1.05. triaxial test) in geotechnical engineering and FLAC can model these nicely.6 1.31 rat=1.6 3.31 PLOT hold grid fix bou yel apply lm HIS unbal SOLVE PLOT hold ydisp int=0. plane stress and ground water flow problems including consolidation. 0. Example 5: CONFIG axisymmetry GRID 15. Let’s look at a simple problem where a 2 m diameter horizontal circular area is subjected to 100 kPa pressure.E=30 MPa & nu=0. and hence treat it as a 2-dimensional problem.A FLAC Primer PLOT hold model grid The above example is to create a mesh for an embankment and the underlying soil. we study only a radial plane. and we want to find the vertical stresses and displacements in the underlying soil.5e7 shear=1. All the grid points along the centre line (i=1) are automatically fixed in the x-direction.0 0. It is worth noting that Structural Elements cannot be used on axisymmetric grids. which we will assume is elastic. 10.98 GEN 1. FISH Fish is one of the nicest features in FLAC. In large strain problems.000E+00 Y-displacement contours -5.500E+00 -1.50E-03 -3. Large/Small Strain Modes By default FLAC operates in small strain mode. even if the displacements are large compared to the element size. Whatever we write in FISH is a subroutine with a specific name that can be called from FLAC at any time.00E+04 -2.00E+05 -8.500E+00 <x< 5. Here. FISH is there to help us when FLAC lets us down.50E-03 -2.00E-04 Contour interval= 5. FISH is useful in carrying out mathematical operations.50E-03 -1.50E-03 -5. Very often.00E+00 Contour interval= 1.00E+04 0. using Eq.500E+00 -1.000E+00 YY-stress contours -1. Nagaratnam Sivakugan (2006) 18 . 1 and 2 respectively. with the rest of the instructions sandwiched between these two lines. and enables us to include conditional if statements and loops for repetitive tasks within a program.50E-03 -4. a substantial portion of a program is in FISH. SET large This enables the coordinates of the grid points to be continuously updated at every calculation step. The subroutine starts with DEFINE line and ends with END line. using the 50 or so commands.00E-04 Grid plot 0 2E 0 (a) Vertical normal stresses (b) Vertical displacements Figure 6. it maintains the same coordinates for the grid points. and defining new variables or new functions that are required within a FLAC program. Beneath a uniformly loaded circular area 11. you may include the following line at the beginning of the program.000E+00 <y< 7. We cannot accomplish everything we want in the programming arena.A FLAC Primer LEGEND 10-Jul-06 12:26 step 2557 -2. Dr.00E+04 -6.000E+00 <y< 7. This can also lead to geometric non-linearity with error message from FLAC. 12.00E+04 -4.500E+00 <x< 5. FISH is like any other programming language such as BASIC or FORTRAN. Following (Example 6) is a simple sub-routine in FISH that calculates shear (G) and bulk (K) moduli from E and υ.00E+04 Grid plot 0 2E 0 LEGEND 10-Jul-06 12:31 step 2557 -2. A FLAC Primer Example 6: DEF derive_moduli derive_moduli shear = young/(2*(1+nu)) bulk = young/(3*(1-2*nu)) END SET young = 30e6 nu=0. Example 6: CONFIG gw SET flow=on mech=off GRID 18. . It can be used to draw flow nets. The FLAC code is given below. Here. .6x10-4 cm/s. Nagaratnam Sivakugan (2006) 19 . . Permeability of the soil is 8. . and carry out all the instructions within it. . Always include the following lines at the top of the program. Seepage FLAC can be used to solve most seepage problems. and compute discharge. 1 to find G Eq. pore water pressures and hydraulic gradients. . Due to symmetry. In FLAC mode. . . . we will model only half of the flow domain. and can be considered as an incompressible porous skeleton through which the flow takes place.18 Dr. . in FISH. Flow takes place beneath the sheetpile shown in Figure 7. 2 to find K End of the sub-routine to assign values to E and υ Just type the name of the subroutine to run it. which is quite useful in debugging. and permeability of the porous medium (i. . The first line is to configure FLAC for groundwater flow.25 . it is implied that the soil has consolidated. . . CONFIG gwflow SET flow=on mech=off In addition. PRINT etc. PRINT FISH 13. the following command will print the current values of all FISH variables. . flac: derive_moduli To include any FLAC commands such as PLOT. when dealing with seepage. Determine the flow rate and the pore water pressure distribution. . heads. it is required to specify the bulk modulus and density of the water. just sandwich them between COMMAND and END_COMMAND lines as follows. COMMAND Any FLAC commands END_COMMAND .. soil). The second line is to say that the flow takes place without any mechanical deformation in the soil skeleton.e. Most traditional seepage problems are flow-only problems. name of the routine is Eq. 3e7 GEN 0.s WATER den=1000 bulk=2e9 SET gravity=9. as you would see in many examples in FLAC manual. See Appendix A for further discussion on permeability.7 SOLVE sheetpile 5m 1m 9m 9m 6m soil Impervious material Figure 7.43e3 i=19 j=1.9 9. reducing the bulk modulus of water substantially (to say 105 Pa) can solve the problem quicker.A FLAC Primer MODEL elastic PROP den=1600 bulk=1e7 shear=0. and remain saturated.08 iw sline yel bou green Dr. The variable “perm” in flow problems is the mobility coefficient κ (m2/Pa. Example problem on Seepage Bulk modulus of water is 2x109 Pa.7 FIX sat i=19 j=1.81 APPLY pp=49. in m2/Pa. PLOT hold head int=0. which is simply obtained by dividing the permeability (m/s) by the unit weight of water (9810 N/m3). To see the flow net and pore water pressure distribution.0 i=1.19 j=1.0 0. try the following commands.19 PROP perm = 8.77e-8 .9 9.05e3 j=19 FIX sat j=19 APPLY pp=117. FIX sat command ensures that these boundaries act as a source or sink.s). In some problems.72e3 var 0 -29. Nagaratnam Sivakugan (2006) 20 . and this has no adverse effect on the quality of the solution. through a FISH subroutine flowcalc. The following commands can be used to print them. DEF flowcalc cumflow_exit=0 loop j(1. Nagaratnam Sivakugan (2006) 21 . The flow rate can be computed by summing all the nodal flows at the exit or entry. Let’s do it for both (they should be the same).A FLAC Primer PLOT hold pp int=0.19) end_loop END Flowcalc .j) end_loop cumflow_entry=0 loop i(1. PRINT gpp i=4 j=2 PRINT pp i=7 Dr.28x10-3 m2/s. to run the FISH subroutine PRINT cumflow_entry.19) cumflow_entry=cumflow_entry + gflow(i. This FISH subroutine also demonstrates the use of loops to carry out some repetitive tasks.7) cumflow_exit = cumflow_exit + gflow(19. The key words “gpp” and “pp” are the pore water pressures at the grid point and element respectively.5e4 fill grid The keyword “int” is for interval and the right value can be selected by trial and error. cumflow_exit The PRINT command prints out the flow rate values at the entry and exit as 1. In impermeable rocks such as siltstones. a unit of Darcy is often used for intrinsic permeability.s) = 0.s. and κ (m2/Pa. using appropriate values for ρw and γw (Reddi 2003). which can be modeled by using a reduced apparent permeability value given by (Itasca 2001): kunsaturated = ksaturated S2(3-2S) where S is the degree of saturation. although the latter is more common in geotechnical engineering. For flow of water through soils. FLAC uses quite a different “permeability” throughout. In these partially saturated zones. which makes sense intuitively too. and has units of area (e. Permeability depends on the viscosity and density of the fluid. FLAC calls it the mobility coefficient (coefficient of the pore pressure term in Darcy’s law).02 x 10-5 K (Darcys) = k (cm/s) x 1. As a result. v =κ ∂p K ∂p = ∂x µ w ∂x It can be easily shown that the geotechnical permeability k and FLAC permeability κ are related by: k (m / s ) = κ (m 2 / Pa. where the pores are well connected the intrinsic permeability is large and can be in the order of 1 Darcy.s )γ w ( N / m3 ) Intrinsic permeability and FLAC permeability are related by: K ( m 2 ) = κ (m 2 / Pa. which is not influenced by the fluid properties such as density or viscosity. When Darcy’s law is expressed in terms of a pressure gradient (with dimension of Pa/m) instead of the dimensionless hydraulic gradient it can be seen from the following equation that the FLAC permeability κ has the unit of m2/Pa. and the saturation values are updated to preserve the mass balance.g. water moves under gravity. K (cm2) = k (cm/s) x 1. m2. which has units of m2/Pa. It is specifically for flow of water through soils. which is water in the case of permeability.s/m2) and unit weight (N/m3) of the fluid.01×10-3 kg/m.035 x 103 The fluid equations and boundary conditions in FLAC are expressed in terms of pressure rather than head. κ (m2/Pa.978 µm2.0194 × 10-6 k (cm/s).099 K (cm2).s ) µ w ( Ns / m 2 ) With values of γw = 9810 N/m3 µw = 1.s (or Ns/m2). K and k are related by (Itasca 2002): γ k= K µ Here. Darcy). FLAC sets pore pressure as zero when the saturation is less than 100%. the there is still water in the partially saturated zones. Let’s denote this by κ (“kappa”). It can be deduced from the above equation that heavier the fluid larger the permeability and higher the viscosity lower the permeability. Nagaratnam Sivakugan (2006) 22 . Dr. In rocks and in oil industry.A FLAC Primer Appendix A – A Note on Permeability Physicists define a more general form of permeability known as intrinsic permeability (K). What geotechnical engineers refer to as permeability or hydraulic conductivity (k) is dimensionless. In sandstones.s (Whitaker 1986). µ and γ are the dynamic viscosity (N.s) = 1. However. Intrinsic permeability depends only on the porosity of the soil.. Darcy = 0. the intrinsic permeability can be in the order of 1 milli Darcy.
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