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UDEC/3DEC Basic Training Course Day 1

UDEC/3DEC Basic Training Course Day 1. Itasca Consulting China Ltd. Wuhan, Hubei Province June 21 – 23, 2007. Instructors: Roger Hart Yanhui Han. Training Schedule June 21, 2007 (morning). 09:00-10:15 Introduction to Itasca Codes and UDEC

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UDEC/3DEC Basic Training Course Day 1

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  1. UDEC/3DECBasic Training CourseDay 1 Itasca Consulting China Ltd. Wuhan, Hubei Province June 21 – 23, 2007

  2. Instructors: Roger Hart Yanhui Han

  3. Training ScheduleJune 21, 2007 (morning) 09:00-10:15 Introduction to Itasca Codes and UDEC - Overview of capabilities in geo-engineering - New features in UDEC Introduction to the UDEC Graphical Interface - Menu-driven versus command-driven operation - Simple tutorial 10:15-10:30 Break 10:30-12:00 DEM Theoretical Background - Discontinuum analysis - Distinct element method - Explicit finite-difference solution scheme Practical Exercise - Failure of a jointed rock slope

  4. Overview of Itasca Consulting Services and Software for theMining, Civil, Petroleum, and Waste Isolation Industries

  5. History Itasca was established in 1981 as a geotechnical engineering consulting firm. Since that time, it has grown to include 13 international offices. Itasca specializes in the development and application of geotechnical, numerical software for analysis and design in mining, civil, petroleum and waste isolation engineering.

  6. ITASCA SOFTWARE Itasca develops and sells the world’s most widely-used set of numerical modeling codes for geotechnical analysis. two dimensional continuum, with joints three dimensional continuum, with joints two dimensional DEM* polygonal bodies three dimensional DEM* polyhedral bodies two dimensional DEM* disks & clumps three dimensional DEM* spheres & clumps * DEM (distinct/discrete element method)

  7. All of Itasca’s codes were originally developed for application to geotechnical problems. General (Common) Features for Geotechnical Analysis • Large deformation • Track sequential rock failure • Library of soil and rock behavior models • Incorporate realistic geological features • Dynamic capability • Groundwater modeling All Itasca codes use an explicit, dynamic solution scheme, even to simulate quasi-static problems. All include coupled fluid and thermal modes, and include many nonlinear constitutive models. All codes treat interactions between separate objects as boundary conditions; there is no concept of a “joint element”. Thus, even for the continuum codes, the “DEM scheme” is used for interactions.

  8. All Itasca codes … … contain a built-in programming language, called FISH, that allows users to: • add new plots or printout options • control a simulation (and the conditions) automatically • access and modify most of the internal variables & properties • set up special in situ conditions & boundary conditions • add coupling between codes, or between physical entities. Also, all codes can accept user-written constitutive (stress/strain) models, written in C++ or FISH (FLAC only). Many users have written their own models. Several models are available that have been written by others.

  9. User support • Extensive manuals, with many examples and useful FISH functions, are provided, both on CD and in hard-copy. • Hundreds of references to papers describing applications of all codes are available on the Itasca web site (www.itascacg.com). • Worked examples are provided and updated regularly on the web site; a new section will provide a repository for new constitutive models. • Latest code updates may be downloaded from the web. • International code-user symposia are held regularly. • Rapid answers to users’ queries are provided, both by telephone and email (many hundreds of such questions are handled every year). • Consulting agreements may be set up for more extensive help with setting up models and interpreting the results.

  10. What is UDEC? UDEC is a DEM code that allows the simulation of the interaction of blocks. This may be a jointed rock mass, a masonry wall, or any material where the mode of displacement may occur along pre-existing planes of weakness or discontinuity. Any geometry can be represented, and the boundary conditions are quite general. UDEC also simulates the behavior of the intact material between the planes of weakness as a nonlinear continuum, using the generalized finite-difference method (arbitrary element shapes), known as the finite volume method. UDEC solves the full dynamic equations of motion even for quasi-static problems. This has advantages for problems that involve physical instability, such as collapse, as will be explained later. To model the “static” response of a system, damping is used to absorb kinetic energy.

  11. … is best suited to modeling discontinuous materials (containing many intersecting discontinuities) that exhibit nonlinear behavior. In particular, it features: UDEC • Discontinuous medium modeled as an assemblage of convex or concave blocks; blocks may be rigid or deformable. • Discontinuities treated as boundary conditions between blocks. • Motion along discontinuities governed by linear and non-linear force-displacement relations for movements in both the normal and shear direction. • Many built-in block and joint constitutive models that are representative of geologic, or similar, materials; optional user-written models. • Plane-strain, plane-stress and axisymmetric geometry modes. • Structural element models for rock-structure interaction – cables, piles, beams, liners, shotcrete, soil reinforcement, etc. • Static and dynamic analysis capabilities. • Transient and steady state fluid flow in joints. • Viscoelastic and viscoplastic (creep) models. • Thermal analysis capability, with coupling to solid and fluid

  12. UDEC Version 4 - Major New Features Graphical user interface Factor-of-safety calculation based on the shear strength reduction method User-defined zone and joint constitutive models Mixed discretization to provide more accuracy for plasticity analysis Two-phase flow in joints Network key license version

  13. Overview of UDEC operation (1) UDEC is a command-driven program - Engineering simulations usually consist of a lengthy sequence of operations. - A UDEC data file can be easily modified with a text editor. Several files can be linked together. - The word oriented input files provide an excellent means for keeping a documented record of analyses. - The command driven structure allows the development of pre- and post-processing programs to manipulate UDEC input or output as desired.

  14. Overview of UDEC operation (2) Command Syntax COMMANDkeywordvalue … < keywordvalue > Example, new (clears the memory) block 0,0 0,10 10,10 10,0 (creates a block) crack 0,2 8,10 (creates a single fracture in block) plot block (draws the block on the screen) There are over 50 commands and 400 keywords in UDEC !!!

  15. Overview of UDEC operation (3) UDEC is a menu-driven program - Point-and-click operation accesses all commands and facilities in UDEC. - Designed to emulate expected Windows features. - Digitized plots or graphics files can be imported to guide model generation. - Provides access to a database of material properties.

  16. Graphical Interface for Itasca Codes • The GIIC is a JAVA-based application that runs independently of UDEC; data are exchanged directly between UDEC and the GIIC so that you may manipulate model results without interfering with the solution process. • UDEC 4.0 with the GIIC runs as a Windows application. • The GIIC requires approximately 40 MB (including the Java Runtime Environment). • UDEC 4.0 can still be run without the GIIC (for die-hard users).

  17. Modeling Stage Tabs Title bar Main Menu Model View Pane Resource Panes The GIIC main window

  18. Model Options Dialog

  19. MODELING-STAGE TABS • [Build] creates the main model block and splits the block to create discontinuities. • [Blocks] controls the creation of zones and assignment of constitutive models and properties within blocks • Boundary and initial conditions are applied via the [In Situ] tool. • [Settings] allows global conditions to be set or changed during the analysis. • If you select structural elements in the [Model Options] dialog, a [Structure] tab will be included in the modeling-stage tab bar to access structural support for this model. • The [Utility] tab provides tools to monitor model variables. • All plotting facilities in UDEC are accessible via the [Plot] tab. • Calculations are performed using tools in the [Run] tab.

  20. Tutorial Sliding Blocks rigid blocks mass density 2000 kg/m3 normal & shear joint stiffness 13.3 MPa/m Case 1: friction angle 20o Case 2: friction angle 11o 22o 17o run UDEC

  21. The Explicit Dynamic Solution Scheme and the Distinct Element Methodin UDEC & 3DEC

  22. DEM Definitions The name “Discrete Element Method” (DEM) should be applied to a method only if it*: • allows finite displacements and rotations of discrete bodies; including complete detachment • recognizes new interactions (contact) automatically as the calculation progresses A discrete element code will embody an efficient algorithm for detecting and classifying contacts. It will maintain a data structure and memory allocation scheme that can handle many hundreds or thousands of discontinuities or contacts. The name “Distinct Element Method” is used for a DEM that uses an explicit dynamic solution to Newton’s laws of motion. *Cundall,P.A., and R.D. Hart.”Numerical Modeling of Discontinua,” Engineering Computations, 9(2), 101-113 (1992)

  23. Finite element codes for modeling “discontinua” are often modified continuum programs, which cannot handle general interaction geometry (e.g. many intersecting joints). Their efficiency may degenerate drastically when connections are broken repeatedly.

  24. Types of Discrete Element Methods for Discontinuum Analysis • Distinct Element Use explicit time-marching scheme to solve equations of motion directly. Bodies may be rigid or deformable, contacts are deformable • Modal Methods Similar to distinct element method in the case of rigid blocks. For deformable bodies, modal superposition is used so non-linearity is difficult to implement • Discontinuous Deformation Analysis Assumes contacts are rigid bodies and bodies may be rigid or deformable. No-penetration is achieved by iteration • Momentum Exchange Methods Assume both the contacts and bodies to be rigid. Momentum is exchanged between two contacting bodies during collision. Can represent friction sliding.

  25. Distinct Element Method Three aspects ... • Geometry • Contact mechanics • Solid body mechanics

  26. Distinct Element Method Geometry • Specification of shapes in 2 and 3 dimensions • Interaction of pairs of contacting blocks or particles • Identification of contact character between 2 blocks

  27. Distinct Element Method Specification of shapes in 2 and 3 dimensions • 2 & 3 dimensions – PFC disks & spheres • 2 dimensions – UDEC arbitrary polygons – convex and concave – with rounded corners • 3 dimensions – 3DEC arbitrary polyhedra – concave bodies are constructed of several convex bodies attached together

  28. Distinct Element Method Interaction of pairs of contacting blocks or particles If we attempt to identify neighboring blocks by an exhaustive scan (i.e. each block tested against each other), then the search-time is proportional to N2 where N is the number of blocks. Two methods to reduce search time: • Cell-mapping, used in UDEC & 3DEC • Circulating data structure, that mimics the topology of the system as used in UDEC

  29. Cell-mapping The solution-space is covered by rectangular cells. Each block deposits a marker in all the cells that it overlaps – this process takes N proportional time. Each block can find all of its neighbors by looking in just those cells that it overlaps - this process is also N proportional, if the cell size is of a similar order to the block size

  30. Circulating data structure Linked lists that describe block boundaries also trace out the void spaces automatically. A block needs only to search its local void spaces to find its neighbors. This scheme breaks down if many blocks become disconnected, but it is well suited to model fluid flow in joints

  31. closed domain can restrict search to the closed domain – any new contacts must be there

  32. Distinct Element Method Identification of contact character between 2 blocks We need to know: • type of contact (e.g. corner-to-corner, corner-to-edge, etc.) • direction of normal to sliding direction • gap between blocks, or contact overlap

  33. Contact Between two Rigid Blocks Initial Position of block 2 un1 Block 2 us1 Joint Block 1 un2 x us2 y block centroid A contact is created at each corner interacting with a corner or edge of an opposing block.

  34. Rounded Corners in UDEC d=r d >> r r r d d d =distance to the corner r=radius of the rounded corner Corner rounding scheme with constant length d d=r d >> r r r d d Corner rounding scheme with constant radius r, showing that small angles in the corner leads to large distances d

  35. Rounded corner-to-edge contact Rounded corner-to-corner contact Definition of contact normal

  36. Contacts and Domains between Two Deformable Blocks Element BLOCK 1 D1 D2 1 2 3 Nodes L2 L3 L1 Corner-Edge contacts 2 1 3 BLOCK 2 L1, L2, L3 Lengths associated to the contacts Domains D2 D1

  37. Distinct Element Method Contact mechanics All contacts are assumed to be “soft”- i.e. contact forces are directly related to the deformations or “overlaps” at contacts. For point-contact, Hertz/Mindlin contact laws can be used. For edge-to-edge contact, such as rock joints, various constitutive laws can be used – e.g., elastic/Coulomb slip. UDEC & 3DEC also have the ”continuously yielding” model, which employs continuous functions for the force displacement relations. There is also internal damage accumulation.

  38. Distinct Element Method Solid body mechanics There are two formulations Rigid body translation and rotation Deformable body mechanics

  39. Distinct Element Method Rigid body translation and rotation If most of the movement in a system takes place in a discontinuous way (e.g. sliding, opening, relative rotation, interlocking), then the bodies may be assumed to be rigid.

  40. Distinct Element Method Deformable body mechanics If there is appreciable deformation of the intact material, compared to discontinuous motion, then the bodies must be taken as deformable.

  41. Deformable body mechanics Distinct Element Method In order to model deformable blocks, there are automatic generators – in UDEC to divide a body into triangles, and in 3DEC to divide bodies into tetrahedra. The finite-difference formulation for these internal elements is identical to that for FLAC. Several linear and non-linear constitutive models can be used in the internal elements.

  42. The Explicit Dynamic Solution Schemeapplied with the Distinct Element Method

  43. Basis of the Solution Scheme UDEC solves the full dynamic equations of motion even for quasi-static problems. This has advantages for problems that involve physical instability, such as collapse. To model the “static” response of a system, a relaxation scheme is used in which damping absorbs kinetic energy. This approach can model collapse problems in a more realistic and efficient manner than other schemes, e.g., matrix-solution methods.

  44. Overview of DEM & explicit, dynamic solution scheme The formulation is very simple. For example, for a ball impacting a wall, (all contacts, in general) One time step, mass (all particles, in general) Full dynamic equations(integration of Newton’s 2nd law) unknowns knowns Explicitsolution scheme (central difference – 2nd order accurate) Three consequences of this formulation are as follows …

  45. force displacement 1. Treating each body as discrete(DEM)allows discontinuous material (such as a rock mass) to be modeled easily. 2.Full dynamic equations of motion allow the evolution of unstable systems to be simulated realistically. 3.Explicit solution scheme makes the task of handling nonlinearity trivial. Examples of nonlinearities are: (a) contact making & breaking; (b) softening material behavior (rock-like); e.g., The explicit scheme uses a time step so small thatinformation cannot propagate between neighbors in one step. m t D < S k OUTPUT Thus, each element is isolated during one step, enabling INPUT

  46. kn Dus ks Dun  Fs Fn xi + M Computation Cycle in UDEC All the contacts CONSTITUTIVE ALL THE BLOCKS zone ALL THE BLOCKS node At the element DEFORMABLE BLOCKS RIGID BLOCKS MOVEMENT At the centroid MOVEMENT At the node Go to

  47. A simple example: Failure of a Jointed Rock Slope jointed rock unit weight 20,000 N/m3 dip angle 76o spacing 3 m joint normal & shear stiffness 100 Mpa/m cohesion 0 friction angle 5.7o 76o 60m 10m 70m 10m run UDEC

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