Modelling Discontinuous Rock With FLAC and UDEC
-
Upload
abhishek-p-sai -
Category
Documents
-
view
67 -
download
3
description
Transcript of Modelling Discontinuous Rock With FLAC and UDEC
Modeling Discontinuous Rock with FLAC and UDEC
FLAC
• Theory– Explicit Finite Difference Method– Constitutive Models
• Steps needed
• How to run program
• Example problems
FLAC Theory-Explicit Finite Difference Method
• The finite difference method is perhaps the oldest numerical technique used for the solution of sets of differential equations, given initial values and/or boundary values. In the finite difference method, every derivative in the set of governing equations is replaced directly by an algebraic expression written in terms of the field variables (e.g., stress or displacement) at discrete points in space; these variables are undefined anywhere else.
Explicit-time marching scheme
Lagrangian Analysis
– Since we do not need to form a global stiffess matrix, it is a trivial matter to update coordinates at each timestep in large strain mode. The incremental displacements are added to the coordinates so that the grid moves and deforms with the material it represents. This is termed a "Lagrangian" formulation, in contrast to an "Eulerian" formulation, in which the material moves and deforms relative to a fixed grid.
Equations
• Motion and equilibrium
• Constitutive relations
• Darcy’s law for fluid flow
• Fourier’s law for heat flow
Equations of motion
Equations of motion
Constitutive relationships
Constitutive Models
• Null
• Elastic, isotropic
• Transverse , tranverse isotropic
• Mohr-Coulomb plastic
• Ubiquitous joint
• Strain hardening/softening
• Double yield
Elastic, Isotropic
Elastic, Transversely
Isotropic
Mohr-Coulomb
Ubiquitous Joint Model
Ubiquitous Joint Model
FLAC - Steps
• 1) Develop a specific objective for using FLAC
• 2) Create a conceptual model (expected behavior under imposed conditions)
• 3) Assemble data
FLAC steps
• 4) Make a simple model first
• 5) Define monitoring locations
• 6) Run the FLAC model
• 7) Present results for a clear interpretation
FLAC - How to run program
• 1) Generate grid
• 2) Deform grid
• grid icol irow
• gen 0,5 0,20 20,20 5,5 i=1,11
• initial x 1.234 i=5 j=4
FLAC - How to run program
• 3) Boundary and initial conditions
• fix x j=1,11• free y j=2• apply pressure=10 j=5• initial sxx=-10 syy=5
Notes: Initial and boundary conditions
• Apply– pressure– sxx– sxy– syy– xforce– yforce– xvel – yvel
• Fix– x– y– pp
• Initial– pp– sat– pressure– sxx– sxy– syy– xforce– yforce– xvel – yvel– xdis– ydis
FLAC - How to run program
• 5) Assign constitutive behavior and material properties
• model elastic• model mohr• prop dens=2000 • prop bulk=1e8 j=6.10
FLAC - How to run program
• 6) Step to initial equilibrium state
• 7) Examine model response
• set grave=9.81• step 200 .. step 200• solve
• plot grid• print grid • plot hist• (hist ydisp i=5 j=5)
Notes: tracking model
• Plot– grid– sxx, sxy, syy, stress– xforce, yforce– xvel, yvel, velocity– displacement– fail, plastic, state– hist 1 (histogram)
• Hist– pp– sxx, sxy, syy, sig1, sig2– unbalanced
• Print– pp
– state
– pressure
– sxx, sxy, syy
– x, y,
– xdis, ydis
– xvel ,yvel
– hist
FLAC - How to run program
• 8) Alterations – excavate material
– change boundary conditions
– add support
• 9) Repeat steps 5-8
• model null• apply xforce j=1
• structure beam ….• structure cable ….• structure support ….
Notes: Program control
• call
• return• new• save• restore
• stop/quit
• reads in a text file with FLAC commands
• return control from a call• start new problem, lose everything• save the state of an analysis to disk• restore the state of an analysis from
disk• exit program
Simulating Discontinuities:Interfaces
• Joint, fault, bedding plane
• Interface, e.g. soil/foundation
• Contact between materials
• Contact between colliding objects
Simulating Discontinuities:Interfaces
• Glued interfaces• Coulomb shear
strength• Tension bond
Simulating Discontinuities:Interfaces
• Conceptual Model
• Generate – grid 50 30
– model elas
– model null j=14 i=1,28
– model null j=29
– model null j=20 i=30,50
Simulating Discontinuities:Interfaces
• Distort grid
• gen 0,-45 0,0 70,0 65.926,-28.519 i=1,29 j=15-31
• gen ….
Simulating Discontinuities:Interfaces
• Add excavation– model null ….
• Add interface properties– interface 1 coh= ...
UDEC
• Theory
• Constitutive models
• Steps needed
• How to run program
• Example problem
Discrete Models
– A discontinuous medium is distinguished from a continuous one by the existence of contacts or interfaces between the discrete bodies that comprise the system. Discontinuum methods can be categorized both by the way they represent contacts and by the way they represent the discrete bodies in the numerical formulation.
Modeling discontinuous systems
• Behavior of the discontinuities
• Behavior of the solid material
• Calculation cycle
nnn uk
Constitutive equations, contacts
• relationship between force, joint stiffness and displacement
sss uk
Contacts (rounded corners)
• Equations of motion
– velocity, time, force, mass
m
F
dt
ud
.
• Deformable blocks
– Finite difference triangular elements
Blocks constitutive Models
• Null
• Elastic, isotropic
• Drucker-Prager
• Mohr-Coulomb plastic
• Ubiquitous joint
• Strain hardening/softening
• Double yield
Joint constitutive model:Continuously yielding model
rF m
1
1
ss uFk
Simple UDEC model
Conceptual model
UDEC - Steps
• 1) Develop a specific objective for using UDEC
• 2) Create a conceptual model (expected behavior under imposed conditions)
• 3) Construct and run simple idealized models
UDEC - Steps
• 4) Assemble data
• 5) Detailed model runs
• 6) Presentation of data
UDEC - How to run program
• 1) Generate a block
• 2) Round corners
• 3) Generate discontinuities
• block 0,0 0,5 5,5 5,0
• round 0.5
• crack 0,0 5,5• jset 20,0 0.5,0 0,0 5,0• jregion 0,0 0,5 5,5 5,0
UDEC - How to run program
• 4) Set boundary and initial conditions
• 5) generate structures
• fix range 0,20 0,5
• free range 0,20 0,5
• boundary stress a,b,c range 0,0 5,5
• crack … delete …• tunnel …• arc ...
UDEC - How to run program
• 6) Make blocks deformable
• 7) Assign model to blocks
• 8) Assign rock material properties
• gen edge v
• change cons=1 elastic model
• prop mat 1 dens=2000
UDEC - How to run program
• 9) Assign joint material properties
• prop jmat 1 jfric=20.0