1、UDEC/3DEC Short CourseItasca Software Training CourseTongji UniversityShanghai,ChinaOctober 27-31,2008Peter Cundall,Yanhui Han&Roger Hart Itasca Consulting Group,Inc.Training ScheduleOctober 28,2008(afternoon)02:00-03:15Overview of UDEC/3DEC Features and Capabilities -Overview of capabilities in geo
2、-engineering -New features in UDEC and 3DEC -Theoretical basis03:15-03:30 Break03:30-05:00 Running Models in UDEC -Menu-driven versus command-driven operation -Simple tutorial.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
3、 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,
4、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
5、 model the“static”response of a system,damping is used to absorb kinetic energy.What is UDEC?.UDECDiscontinuous 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 gov
6、erned 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
7、 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
8、solid and fluid is best suited to modeling discontinuous materials(containing many intersecting discontinuities)that exhibit nonlinear behavior.In particular,it features:.3DEC-similar to UDEC,but in three dimensions-contains the same features as listed for UDEC col lapse of a m asonry arch bri dgefu
9、ll and secti oned vi ew s ofa tow er m odel ed forstabi l ity usi ng thedynam ic opti onModel of arch dam using finite-element blocks.New Features in UDEC 4.0 Graphical user interfaceFactor-of-safety calculation based on the shear strength reduction methodUser-defined zone and joint constitutive mod
10、elsMixed discretization to provide more accuracy for plasticity analysisTwo-phase flow in jointsNetwork key license versionNew Feature in UDEC 4.01Released in October 2008Improved and re-structured graphical user interface(available at no additional charge to current Version 4.0 owners).Planned New
11、Features in UDEC 5.0Generic“virtual-model”generation tool to facilitate model creationSpeedup of double-precision version by converting to Intel Fortran compilerMixed Discretization scheme for triangular elements“Nodal Mixed Discretization”to provide more accurate solution of plasticity problems usi
12、ng triangular gridsRockbolt elements to simulate rock reinforcement including tensile rupture,strain-softening behavior of grout and effect of changing confining stressHelp File containing Command Reference,FISH Reference and Example ApplicationsEstimated release:mid 2009.New Features in 3DEC 4.1Acc
13、elerated interactive graphics(OpenGL based plotting)with new graphical structureNew Mixed Discretization scheme for tetrahedral elements“Nodal Mixed Discretization”provides more accurate solution of plasticity problems using tetrahedral grids64-bit versionFactor of Safety calculation modeImprovement
14、s to user-defined constitutive models and addition of user-defined joint constitutive modelsImprovements to structural element logic including installation at tunnel intersectionsHelp File containing Command Reference,FISH Reference and Example ApplicationsNew PGEN interfaceImproved FISH languageRel
15、eased in January 2008.The Explicit Dynamic Solution Scheme and the Distinct Element Methodin UDEC&3DEC.DEM DefinitionsThe name“Discrete Element Method”(DEM)should be applied to a method only if it*:allows finite displacements and rotations of discrete bodies;including complete detachmentrecognizes n
16、ew interactions(contact)automatically as the calculation progressesA 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 contact
17、s.The name“Distinct Element Method”is used for a DEM that uses an explicit dynamic solution to Newtons laws of motion.*Cundall,P.A.,and R.D.Hart.”Numerical Modeling of Discontinua,”Engineering Computations,9(2),101-113(1992).Finite element codes for modeling“discontinua”are often modified continuum
18、programs,which cannot handle general interaction geometry(e.g.many intersecting joints).Their efficiency may degenerate drastically when connections are broken repeatedly.Types of Discrete Element Methods for Discontinuum AnalysisDistinct ElementUse explicit time-marching scheme to solve equations o
19、f motion directly.Bodies may be rigid or deformable,contacts are deformableModal MethodsSimilar to distinct element method in the case of rigid blocks.For deformable bodies,modal superposition is used so non-linearity is difficult to implementDiscontinuous Deformation AnalysisAssumes contacts are ri
20、gid bodies and bodies may be rigid or deformable.No-penetration is achieved by iterationMomentum Exchange MethodsAssume both the contacts and bodies to be rigid.Momentum is exchanged between two contacting bodies during collision.Can represent friction sliding.Distinct Element MethodThree aspects.Ge
21、ometry Contact mechanics1.Solid body mechanics.Distinct Element MethodGeometrySpecification of shapes in 2 and 3 dimensionsInteraction of pairs of contacting blocks or particlesIdentification of contact character between 2 blocks.Distinct Element MethodSpecification of shapes in 2 and 3 dimensions2&
22、3 dimensions PFC disks&spheres2 dimensions UDECarbitrary polygons convex and concave with rounded corners3 dimensions 3DECarbitrary polyhedra concave bodies are constructed of several convex bodies attached together.Distinct Element MethodInteraction of pairs of contacting blocks or particlesIf we a
23、ttempt 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&3DEC1)Circulating data structure,that mimics the topology of th
24、e system as used in UDEC.Cell-mappingThe 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
25、 N proportional,if the cell size is of a similar order to the block size.1 2 3 4 56 7 8 9 1011 12 13 14 1516 17 18 19 2021 22 23 24 25ACBBlockenvelopeA,B,C=blocks0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 A AB0 C0 C0 B0 AA0 C0 C0 C0 CCell entries in main array.Circulating data structureLinked lists that descr
26、ibe 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.closed domaincan restrict search to the closed dom
27、ain any new contacts must be there.Distinct Element MethodIdentification of contact character between 2 blocksWe need to know:type of contact(e.g.corner-to-corner,corner-to-edge,etc.)direction of normal to sliding directiongap between blocks,or contact overlap.Block 2Jointun2us2Block 1us1un1Initial
28、Positionof block 2xyblock centroidA contact is created at each corner interacting with a corner or edge of an opposing block.Corner rounding scheme with constant length drdd=rd rrdd=distance to the cornerr=radius of the rounded cornerrdd=rdrd rCorner rounding scheme with constant radius r,showingtha
29、t small angles in the corner leads to large distances d.Definition of contact normalRounded corner-to-edge contactRounded corner-to-corner contact.L1L2L3123ElementNodes123Corner-Edge contactsL1,L2,L3Lengths associatedto the contactsD1D2D1D2DomainsBLOCK1BLOCK2.Interaction of two squaresMaximum number
30、 of tests124 corners4 edgescorneredgecorner 16edge 16corner 16edge 16.Interaction of two cubes126 faces12 edges8 cornersface 36edge 72corner 48face 48edge 96corner 64face 72edge 144corner 96Total 676facecorneredge.Modes of contactscorner-corneredge-edgecorner-facecorner-edge.Modes of contactsface-fa
31、ceedge-face.“Common plane”logicAlgorithm executed in parallel with mechanical calculation:“maximize the gap between the common plane(c-p)and the closest vertex”c-p12.“Common plane”logicIf we assume a c-p can be found,blocks are convexthen.test for contacts is easytest corners of both blocks for cont
32、act with c-p(16 dot products)if test for both blocks are positive then blocks are touchingdetermining gap is easysum of min.distances from each blocks corner to c-pcontact normal is.1.the normal of the c-p is always defined.Common plane logicWhat about assumptions?Use the algorithm“maximize the smal
33、lest gap between each block(of a contact-pair)and the plane”1.Construct concave blocks from several convex blocks(the“join”does not exist,as far as physics is concerned)shift,then.rotation.Common plane logicModes of contact can be found easily with contact-plane logic“count the number of corners tha
34、t touch the common plane”mode of contact is determined by counts:e.g.1-4=“corner-face”note:”touch”implies gap 0Block A1 corner2 edge 3 faceBlock B1 corner2 edge 3 face.Distinct Element MethodContact mechanicsAll contacts are assumed to be“soft”-i.e.contact forces are directly related to the deformat
35、ions 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 disp
36、lacement relations.There is also internal damage accumulation.Distinct Element MethodSolid body mechanicsThere are two formulationsRigid body translation and rotationDeformable body mechanics.Rigid body translation and rotationIf most of the movement in a system takes place in a discontinuous way(e.
37、g.sliding,opening,relative rotation,interlocking),then the bodies may be assumed to be rigid.Distinct Element Method.Deformable body mechanicsIf there is appreciable deformation of the intact material,compared to discontinuous motion,then the bodies must be taken as deformable.Distinct Element Metho
38、d.Deformable body mechanicsIn 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
39、 constitutive models can be used in the internal elements.Distinct Element Method.The Explicit Dynamic Solution Schemeapplied with the Distinct Element Method.UDEC and 3DEC solve the full dynamic equations of motion even for quasi-static problems.This has advantages for problems that involve physica
40、l 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.Basis of the Solution Schemem
41、ovie.Overview of DEM&explicit,dynamic solution scheme(/2)(/2)()()()(/2)/ttttttttttuuFt mxxut()()()If ,0If ,()tttnxR FxR FRxkThe formulation is very simple.For example,for a ball impacting a wall,RxFmmassOne time step,tunknownsknowns(all contacts,in general)(all particles,in general)Full dynamic equa
42、tions(integration of Newtons 2nd law)Explicit solution schemeu Three consequences of this formulation are as follows(central difference 2nd order accurate).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 a
43、llow 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.,forcedisplacementINPUTOUTPUTThe explicit scheme use
44、s a time step so small that information cannot propagate between neighbors in one step.Thus,each element is isolated during one step,enablingmtk S.ksknFnFsDunDus ssnsssssnnnnFsgnF,FminFukFFukFF All the contactsCONSTITUTIVEciF+MxiI/Mm/FuFxeMFFiijiijici S S S S At the centroidALL THE BLOCKSMOVEMENTzon
45、eciFnodeAt the element ,.,Ctdxuddxud21ijijijijjiij At the nodem/FuFFFdsnFiicieiizjijei MOVEMENTALL THE BLOCKSRIGIDBLOCKSDEFORMABLEBLOCKSttt Go to.TIMESTEPThe solution scheme used in DEM is conditionally stable.A limiting timestep must satisfy both the calculation for internal block deformation and i
46、nter-block relative displacement.For stability of the block deformation computation:where mi is the mass associated with block node i;and ki is the measure of stiffness of the elements surrounding the node.For calculations of the inter-block relative displacement,the limiting timestep iswhere Mmin i
47、s the mass of the smallest block in the system;and Kmin is the maximum contact stiffness.The controlling timestep is iinkmt2minmin)(2KMfractb),min(bnttt.MECHANICAL DAMPINGMechanical damping is used in UDEC and 3DEC for static(non-inertial)solutions and for dynamic solutions.For static analysis,the a
48、pproach is similar to“dynamic relaxation.”The equations of motion are damped to reach a static state as quickly as possible under the applied initial and boundary conditions.DYNAMIC RELAXATIONIn dynamic relaxation blocks(and gridpoints)are moved according to Newtons law of motion.The equations of mo
49、tion are damped to reach a force equilibrium state as quickly as possible Damping is velocity-proportional i.e.,the magnitude of the damping force is proportional to the velocity of the blocks.Velocity-proportional damping introduces body forces that can affect the solution.UDEC and 3DEC provide two
50、 different types of damping to minimize this problem for static analysis:adaptive global damping(DAMP auto)local damping(DAMP local).ADAPTIVE GLOBAL DAMPINGAdaptive global damping is a servo-mechanism used to adjust the damping constant automatically such that the power absorbed by damping is propor
