1-DEM_UDEC_Course-Theory

1-DEM_UDEC_Course-Theory - Short Course on DEM-UDEC...

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Unformatted text preview: Short Course on DEM-UDEC Modelling Singapore, 30 Aug - 1 Sep 2010 THEORY - 1 Day 2 (August 31): -Programming in UDEC. -Modelling structural elements in UDEC UDEC. -Examples of modelling supported and unsupported caverns and tunnels in jointed media with UDEC. Day 3 (September 1): -Model groundwater flow in UDEC, with examples. -Examples of modelling groundwater flow around caverns and tunnels in jointed media with UDEC. -Case histories of application of UDEC to design of caverns and tunnels in jointed media. Structure of the course 3 Structure of the course (continued) 1 Objectives of the course 4 2 T teach the discrete element method (DEM) for modelling discontinuum media, o using the commercial code UDEC (Universal Distinct Element Code). T teach the o use of UDEC in the analysis of underground excavations in fractured rock masses. T discuss case histories of application of UDEC to the design of caverns and tunnels o in jointed rock, in reference to cavern support and reinforcement, and groundwater flow. Day 1 (August 30): -Introduction to Distinct Element Method. -General features of UDEC. -Input of model parameters in UDEC. -Basic examples of modelling discontinuum systems in UDEC. Course organized by the Society for Rock Mechanics & Engineering Geology of Singapore and supported by the Protective T echnology Research Centre, NTU. Singapore 30 August – 1 September 2010 Carlos Carranza-T orres Associate Professor of Geotechnical Engineering, Department of Civil Engineering, Engineering University of Minnesota, Duluth Campus, Minnesota, USA Short course on Discontinuum Modelling in Rock Mechanics with UDEC Applications – THEORY Short Course on DEM-UDEC Modelling Singapore, 30 Aug - 1 Sep 2010 THEORY - 2 Schedule of the course Finite Element Method (FEM) Finite Difference Method (FDM) Boundary Element Method (BEM) Discrete Element Method (DEM) See, for example, Brady B.H.G. and E.T Brown, 2004, ‘Rock Mechanics for . Mining Underground Mining’, 3rd Edition Kluwer Academic Publishers. Edition, Publishers 1. 2. 3. 4. Classification of Numerical Methods used in the practice of Geomechanics Afternoon sessions: 13:30-15:00 (1.5 hrs) (1 5 15:15-17:00 (1.75 hrs) Lunch break: 12:30-13:30 Morning sessions: 9:00-10:30 (1.5 hrs) 10:45-12:30 (1.75 hrs) 7 5 From Zienkiewicz O.C. and R.L. Taylor, 2000, ‘The Finite Element Method’, V olume I: The Basis. 5th Edition. Butterworth-Heinemann Example of Finite Element Method Analysis The Discrete Element Method 8 6 Short Course on DEM-UDEC Modelling Singapore, 30 Aug - 1 Sep 2010 THEORY - 3 6m 6m 6m [2] [1] 10 m -4.65 Tension -6.55 -9.15 0 Distribution of tangential stress (MPa) 10 MPa 9 -6.35 CICE-Plotting Time (secs) 0.00 9.79 10 8 velocity (m/sec) CICE-Plotting Tunnel stability gravity loading to failure From Pande G.N., Beer G. and J.R. Williams, 1990, ‘Numerical Methods in Rock Mechanics’. JohnWiley & Sons Ltd. 9.79 10 8 velocity (m/sec) Tunnel stability gravity loading to failure Example of Discrete Element Analysis 11 (∗∗) Crouch S. L. and A. M. Starfield. ‘ Boundary Element Methods in Solid Mechanics: With Application in Rock Mechanics and Geological Engineering’ . George Allen & Unwin, London, 1983 (∗) Beer G. and J. O. ‘ Watson, Introduction to Finite and Boundary Element Methods for Engineers’ . JohnWiley & Sons, 1992 4. Discrete Element Method (DEM) →UDEC/3DEC/PFC/PFC3D (www.itascacg.com) →DDA available at www.ce.berkeley.edu/geo/research/DDA 3. Finite Difference Method (FDM) / →FLAC/FLAC3D ( (www.itascacg.com) g ) 2. Boundary Element Method (BEM) →Examine2D/3D (www.rocscience.com); MAP3D (www.map3d.com) →TWOFS/TWODD/TWOBI available in reference ( ∗∗) 12 -Allows detection of newly created contacts between bodies as motion of the bodies takes place. -Allows simulation of translational and rotational motion of discrete bodies, including detachment or separation of initially bonded bodies. Particularities of the methodology: Family of numerical (computer) implementations that allows the motion of a large number of particles (or blocks) to be computed, with particular reference to mechanical interaction of these particles (or blocks) through contacts. Commercial and freeware software used in rock mechanics problems 1. Finite Element Method (FEM) →Phase2 (www.rocscience.com); PLAXIS (www.plaxis.com) →DEMON available in reference ( ∗) 10 Time (secs) 2.00 Discrete Element Method (DEM) From Crouch S. L. and A. M. Star.eld. ‘Boundary Element Methods in Solid Mechanics: With Application in Rock Mechanics and Geological Engineering’. George Allen & Unwin, London, 1983 18 m 8m 45 o 26 m Example of Boundary Element Analysis Short Course on DEM-UDEC Modelling Singapore, 30 Aug - 1 Sep 2010 THEORY - 4 Classification of the Discrete Element Method - continuation UDEC - Universal Distinct Element Code -3DEC is the 3D version of UDEC. -Current version is UDEC version 4.0 (released in 2004). 15 -Code originally written by P Cundall and maintained and commercialized by Itasca, . Minneapolis (www.itasca.com). 13 -Modal Analysis Programs: Similar to the Distinct Element formulation for the case of rigid blocks. For the case of deformable blocks, modal superposition is used (William and Mustoe, 1987); see also book ‘Numerical Methods in Rock Mechanics’ (1992) by Pande, Beer and Williams. -Distinct Element Programs: Use an explicit time-marching algorithm to solve the equations of motion directly. Bodies can be rigid or deformable. Contacts are deformable. Representative codes are UDEC, 3DEC, PFC and PFC3D (Itasca, Minnesota). -Blocks can be assumed to be rigid or deformable. -Tunnel generator and statistically-based joint-set generator . 16 -Relative motion along the discontinuities i governed by li R l ti li ti l forceth di ti iti is d b linear and non-linear f d displacement laws for the normal and shear directions. -The discontinuous medium (e.g., representative of a rock mass) is treated as an assembly of discrete polygonal blocks with rounded corners. Motion and interaction of blocks are computed based on an explicit solution scheme (that allow tracing of the mechanical evolution of the system, even as the process becomes mechanically unstable). -Allows simulation of motion of blocks (including slip and opening) in a discontinuous medium. Main features of UDEC (and 3DEC) 14 -Programs based on Momentum Exchange Methods: Assume both the contacts and bodies to be rigid. Momentum is exchanged between two contacting bodies during an instantaneous collision (Hahn 1988) (Hahn, 1988). -Discontinuous Deformation Analysis Programs: Assume the contacts are rigid bodies, and bodies can be treated as rigid or deformable. The condition of no-penetration of contacts is achieved by an iterative scheme, while the deformability of blocks comes from superposition of strain modes (Gen-Hua Shi 1989); see also the book ‘Block System Modeling by Discontinuous Deformation Analysis’ (1992) by Gen-Hua Shi. Classification of the Discrete Element Method The computer implementation of the methods can be classified as follows (from Cundall, P A., and R. D. Hart. ‘Numerical Modeling of Discontinua’ Engr Comp., 9(2), . , . 101-113, 1992): Short Course on DEM-UDEC Modelling Singapore, 30 Aug - 1 Sep 2010 THEORY - 5 Examples of application of UDEC modelling ● Dynamic analysis of dam foundation 18 ● Block caving (mining application) ● Failure of jointed column ● Rock wedge failure in tunnel ● Wedge rock failure in slope 19 20 ● Failure of masonry arch bridge ● Failure of system of rock blocks They use the same logic as the codes UDEC and 3DEC but allows simulation of circular particles only (disks in 2D and spheres in 3D). Since the implementation of a contact-treatment logic for circular particles (as in PFC/PFC3D) is simpler than for particles of arbitrary shape (as in UDEC/3DEC), PFC and PFC3D are significantly faster in terms of computation time than UDEC and 3DEC under equivalent conditions (of simulating circular particles) allowing efficient simulation of mechanical interaction of thousand of particles. 17 The codes PFC (Particle Flow Code) and PFC3D ● Water flow into a tunnel Examples of application of 3DEC modelling -Coupled fluid flow in joints and pressure in cavities. -Thermal and thermal-mechanical calculation. -Full dynamic capability, with absorbing boundaries and wave input. -Structural elements (including non-linear cables), with general coupling to continuum blocks (spatially-extensive) or discontinuities (local reinforcement). -Library of material models for discontinuities (e.g., Coulomb slip, continuouslyyielding, and Barton-Bandis). ● Dynamic analysis of tunnel in jointed rock ● Dynamic analysis of slope in jointed rock Main features of UDEC (and 3DEC) - continuation -Library of material models for deformable blocks (e.g., elastic, Mohr-Coulomb plasticity, ubiquitous joint, double-yield, and strain-softening). Short Course on DEM-UDEC Modelling Singapore, 30 Aug - 1 Sep 2010 THEORY - 6 Short Course on DEM-UDEC Modelling Singapore, 30 Aug - 1 Sep 2010 THEORY - 7 Short Course on DEM-UDEC Modelling Singapore, 30 Aug - 1 Sep 2010 THEORY - 8 29 Program installation folders 31 UDEC can also be started from the traditional ‘START’ panel of windows (if this procedure is used, the working directory needs to be specified with a command SYS CD -path of working directory-). From the console window of UDEC the graphical user interface can also be activated by typing the command GIIC. Commands can be entered at the prompt in the UDEC console. Alternatively, a script located in the working directory can be processed by typing the command CALL -name of the script-. The problem involves simulation of the mechanism of failure of blocks of an existing slope. Running UDEC A shortcut to the executable file ‘udec.exe’ (or ‘udec_dp.exe’) is created in an arbitrary working directory. The input box ‘Start In’ should be left blank in the panel ‘Properties’ of the shortcut (accessed from the floating menu that shows up when the shortcut is right-clicked). This ensures that the working directory is the very same directory where the shortcut is installed, once the shortcut is called. 32 30 -Documentation manuals are provided in Acrobat Reader PDF format and are located in a directory called ‘Itasca\Manuals\UDEC400’ . -The UDEC code can be started by executing either of the two files ‘udec.exe’ and ‘udec_dp.exe’ corresponding to single and double precision versions of the code, , respectively. -By default UDEC is installed in a directory called ‘Itasca\UDEC400\’ . An example problem Graphical User Interface (or GIIC) for UDEC Short Course on DEM-UDEC Modelling Singapore, 30 Aug - 1 Sep 2010 THEORY - 9 Execution of the example problem ... pro mat=1 dens 2000 prop mat=1 jkn 1e8 jks 1e8 jfric 5.7 jreg id=1 (30,10) (39.1,50) (61,50) (52,10) jset (76,0) (100,0) (0,0) (4,0) (30,10) range jreg 1 crack 0,10 32,10 crack 30,12.5 65,14 crack 35,30 70,31.5 delete 0,30 10,50 fix 0,80 10,20 block (0,0) (0,50) (80,50) (80,0) new ; File: Model_B_a1.dat UDEC script for the example problem 35 33 The ‘movie’ player for UDEC return plot block hold step 2000 plot block hold step 2000 plot block hold step 2000 plot block hold step 0 ... UDEC script for the example problem - continuation 36 34 Short Course on DEM-UDEC Modelling Singapore, 30 Aug - 1 Sep 2010 THEORY - 10 The UDEC computation 6 VERIFICA TION PROBLEMS (a) AND EXAMPLE APPLICA TIONS (b) 6a.1 6a 1 Cyclic Loading of a Specimen with a Slipping Crack 6a.2 Sliding Block between Two Slightly Skewed Rigid Walls 6a.3 Thick-Walled Cylinder Subject to Internal Pressure 6a.4 Response of an Unlined Circular Tunnel in a Biaxial Stress Field 6a.5 Circular Tunnel Problems 6a.6 Elastic Behavior of a Jointed Medium 6a.7 Crack Shear by Reduced Friction 6a.8 Rough Footing on a Mohr-Coulomb Material 4 THEORYAND BACKGROUND 4.1 4 1 Background - The 2D Distinct Element Method 4.2 Block Constitutive Models 4.3 Continuously Yielding Joint Model 4.4 Dynamic Analysis 4.5 Fluid Flow in Joints 4.6 Energy Calculation UDEC Documentation - continuation 2 COMMAND REFERENCE 2.1 Command Reference 2.2 Error Messages 1 USER'S GUIDE 1.1 Introduction 1.2 Getting Started 1.3 Problem Solving with UDEC g 1.4 FISH Beginner's Guide 1.5 Miscellaneous 1.6 Bibliography The UDEC documentation is structured in the following seven Volumes: 5 SPECIAL FEA TURES 5.1 Structural Elements 5.2 Thermal Analysis 5.4 Barton-Bandis Joint Model 5.5 User-Defined and Extended Constitutive Models 5.6 User-Defined Joint Constitutive Models 39 37 UDEC Documentation The electronic version of the UDEC manuals are accessed through the (hyperlinked) file ‘Contents.pdf’ (located in ‘Itasca\Manuals\UDEC400’). 3 FISH IN UDEC 3.1 FISH Beginner's Guide 3.2 FISH Reference 3.3 Library of FISH Functions 3.4 Program Guide 3.5 FISH Error Messages UDEC Documentation - continuation 4- Starting the cycle from step 1 above. 3- Application of Material Constitutive Laws (for contacts and zones in deformable blocks) based on updated positions of blocks, leading to new forces acting on blocks. 2- Updating block positions, including detection of new contacts, deletion of old contacts, etc. 1- Integration of the Equations of Motion, using an explicit finite difference approach, leading to new velocities and displacements for blocks. In each cycle the following processes take place in: Each computation cycle is associated with a physical time step. Momentum and material constitutive equations are integrated in time, in a successive series of cycles or steps. 40 38 Short Course on DEM-UDEC Modelling Singapore, 30 Aug - 1 Sep 2010 THEORY - 11 (From Section 1.2.6.7, ‘Getting Started’, of the volume USER'S GUIDE). UDEC Commands - continuation 7 COMMAND AND FISH REFERENCE SUMMARY 7.1 Command Summary 7.2 FISH Statement Summary 6b.1 Seismic-Induced Groundfall 6b.2 Open Stoping Using V ertical Retreat 6b.3 Tunnel Support Loading 6b.4 Gravity Dam: Fluid Flow and Dynamic Loading 6b.5 Cement Grouting Simulation 6b.6 Thermomechanical Analysis of a Waste Emplacement Drift 6b.7 Inflow into a Tunnel 6b.8 Flow through a Jointed Rock Slope 6b 9 Flow from a Borehole in a Biaxial Stress Field 6b.9 6b.10 Influence of the Placement of Backfill in a Deep Long-Wall Excavation 6b.11 Shotcrete and Cable Support 6b.12 Blocks Bouncing down Slope UDEC Documentation - continuation 43 41 UDEC Commands UDEC command syntax The Th part of commands and k tf d highlighted ith ‘bold’ t d keywords th t are hi hli ht d with ‘b ld’ type in the d that i th manual are abbreviations of commands and keywords (UDEC will recognize the commands and keywords if the user types the ‘bolded’ part of the command). <> denotes optional parameter(s); the brackets are not to be typed. ... indicates that an arbitrary number of such parameters may be given. COMMAND key word value ... <key word value... > The typical syntax is as follows: 44 All UDEC commands are described in alphabetical order in the COMMAND REFERENCE volume. 42 The following is a list of basic commands used to analyze simple problems in UDEC Short Course on DEM-UDEC Modelling Singapore, 30 Aug - 1 Sep 2010 THEORY - 12 Example of UDEC command BLOCK (0,0) (0,10) (25,10) (25,0) MATERIAL=10 46 Example of command with ‘range’ option B 0 0 0 10 25 10 25 0 MA 10 or in abbreviated form, , 47 BO ST 0 0 -1e6 RA YR 0.99,1.01 or in abbreviated form, , BOUND STRESS 0,0,-1e6 RANGE YRANGE 0.99,1.01 48 Many commands accept a ‘range’ option, by means of which the command will apply to certain parts of the model only (e.g., particular blocks, particular contacts, etc.). The syntax of range definition is explained in Section 1.1.3 (‘Commands Accepting the range Phrase’) of the COMMAND REFERENCE volume. The command below applies a stress boundary condition in the vertical direction to grid points of blocks which y-coordinates lie between the values 0.99 and 1.01 (e.g., the case in which all desired gridpoints have y-coordinates equal to 1.0). Specification of Ranges in UDEC commands 45 g The sign ‘&’ is used to break a line of commands ( (the sign ‘&’ indicates to UDEC that g the command continues in the following line). Comments can be added to the right of a command by using a ‘;’ delimiter (in a script file, comments can span an entire line by starting the line with the ‘;’ delimiter). Commands, keywords and numeric values may be separated by any number of spaces or by any of the following delimiters: ‘()’ , ‘=’ . The command below creates a block which four corners have the specified x-y coordinates and which material number is 10. UDEC command syntax - continuation Commands can be typed in upper or lower cases. Short Course on DEM-UDEC Modelling Singapore, 30 Aug - 1 Sep 2010 THEORY - 13 Sign convention used in UDEC File extensions 49 ' LOG' file: -'.LOG' fil ASCII fil containing th t t th t UDEC prints on th monitor screen. file the text that tii the it it (see S i 1 2 'Si C ( Section 1.2.7, 'Sign Conventions', of the volume USER'S GUIDE). i ' fh l S 'S G ) 51 -'.HIS' file: ASCII file containing a ‘history’ information (e.g., evolution of particular variables during stepping/computation). Pore pressure in joints and blocks means that the liquid is in compression (the liquid will try to expand the domain which fills). (see Section 1.2.7, ‘Files’, of the volume USER'S GUIDE). 52 -'.DCX' files: Binary file containing a 'movie' or animated sequence of 'plots' generated in UDEC. -'.BMP', '.PCX', '.EPS' files: Binary files containing graphics in different formats, created in UDEC. -'.SAV' file: Binary file containing the state of a model for all commands processed before creating the file. Consider two blocks separated by a horizontal contact: positive shear stress means that the upper block acts with a tangential force on the lower block that points to the left. Positive shear displacement means that the upper block moves to the right. -'.DAT' file: ASCII (script) files containing a sequence of UDEC commands. Typical file extensions are: Sign convention used in UDEC - continuation 50 For stresses and strains, UDEC follows the classical notation from mechanics, where tensile stresses (and corresponding material elongations) are positive and compressive stresses (and corresponding material contraction) are negative. Joint normal stress is positive in compression while joint normal displacement is positive in opening. (From Section 1.2.8, ‘System of Units’, of the volume USER'S GUIDE). Displacement and force sign convention refers to the fixed x-y system. Example of consistent system of units. Counterclockwise moments and rotations are positive. Geometry of the model is defined in terms of a fixed orthogonal horizontal-vertical (xy) system where x-positive points rightwards and y-positive points upwards. System of units used in UDEC UDEC does not require a particular system of units to be used. The user should choose a consistent system of units and perform the necessary conversions. Short Course on DEM-UDEC Modelling Singapore, 30 Aug - 1 Sep 2010 THEORY - 14 The integration cycle in UDEC. Case of rigid blocks Theoretical background of UDEC 55 53 The UDEC computation Governing equations solved by UDEC. Case of rigid blocks 56 54 The solution algorithm varies whether the blocks are considered rigidor deformable. A central finite difference scheme is used to integrate equations of motion. UDEC computation is based on a ‘time-marching’ algorithm in which governing equations (equations of motion and material constitutive equations) are integrated explicitly in time, in a series of successive cycles or steps. Short Course on DEM-UDEC Modelling Singapore, 30 Aug - 1 Sep 2010 THEORY - 15 The integration cycle in UDEC. Case of deformable blocks Governing equations solved by UDEC. Case of rigid blocks - continuation 59 57 Governing equations solved by UDEC. Case of deformable blocks Governing equations solved by UDEC. Case of rigid blocks - continuation 60 58 Short Course on DEM-UDEC Modelling Singapore, 30 Aug - 1 Sep 2010 THEORY - 16 61 Governing equations solved by UDEC. Case of deformable blocks - continuation 62 Block-contact implementation in UDEC - continuation Governing equations solved by UDEC. Case of deformable blocks - continuation 64 Corners of blocks are rounded in UDEC to prevent blocks ‘locking’ The user specifies . the rounding length ‘d’ for the corner (using the command ROUND value). 63 A contact surface in UDEC is conformed by 1) two block edges, 2) one block edge and one block corner or 3) two block corners. Block-contact implementation in UDEC - continuation Short Course on DEM-UDEC Modelling Singapore, 30 Aug - 1 Sep 2010 THEORY - 17 Block-contact implementation in UDEC - continuation 66 See Section ‘ 1.2.6. Mechanical Damping’ 67 THEORYAND BACKGROUND volume. in the ● ‘ Rayleigh damping’ for dynamic problems: designed to reproduce the dynamic response of geo-materials, characterized by displaying hysteretic deformation and particle motions that are frequency independent. ● ‘ Local damping’ for quasi-static problems: damping forces (at nodes) are proportional to the unbalanced force and opposes the direction of motion. The damping scheme is designed to converge to the static solution (if it exists) as fast as possible. Damping is used in equations of motion to simulate dissipation of energy in geomaterials as deformation takes place. Two forms of damping are used mainly, depending on whether the model simulates a quasi-static problem (e.g., when loading or unloading rates are low enough that inertia effects can be disregarded) or fully dynamic problem (e.g., when loading rates are high, as it would be the case of loading produced by an earthquake). See Section ‘1 2 7 Mechanical Timestep Determination: Solution Stability in the 1.2.7 Stability’ THEORYAND BACKGROUND volume. 68 This limiting time step is computed by analogy to a one degree-of-freedom oscillator -e.g., tcr ~ [M/K]0.5, where M represents a nodal mass (or block mass) and K the stiffness of zones connected to the node (or the stiffness of contacts for a block). A limiting time step for integration of the dynamic equations of motion is chosen to lead to a stable computation of internal block deformation (for deformable blocks) and stable computation of inter-block relative displacements. Damping schemes 65 ● ‘ Cell Mapping’ Detection: well suited for cases of loose bodies that undergo large relative displacements (e.g., rock fall problems, collapse of openings in granular materials, etc.). This contact detection algorithm is activated with the command CONFIG CELL. ● ‘ Domain Contact’ Detection: well suited for block assemblies in which no large displacements between blocks are expected. This is the default contact detection algorithm. Stable time step Block-contact implementation in UDEC - continuation Two contact detection algorithms are available in UDEC: Short Course on DEM-UDEC Modelling Singapore, 30 Aug - 1 Sep 2010 THEORY - 18 Mass scaling One degree freedom oscillator with no damping 71 69 See Section ‘1.2.8 Mass (Density) Scaling’ in the THEORYAND BACKGROUND volume. Mass scaling should be used to solve quasi-static problems only. The procedure involves correcting the masses of blocks in the assembly to be able to use a larger value of limiting time step, that yields to a more efficient solution. One degree freedom oscillator with velocity damping Illustration of `time marching’ computation procedure in UDEC. The One degree freedom oscillator analogy 72 70 Short Course on DEM-UDEC Modelling Singapore, 30 Aug - 1 Sep 2010 THEORY - 19 Finite difference solution of the one-degree of freedom oscillator - continuation One degree freedom oscillator with acceleration damping - as in UDEC 75 73 Finite difference solution of the one-degree of freedom oscillator 74 ...
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