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