Transcript Slide 1

Numerical modeling of rock
deformation:
13 FEM 2D Viscous flow
Stefan Schmalholz
[email protected]
NO E 61
AS 2008, Thursday 10-12, NO D 11
Numerical modeling of rock deformation: FEM 2D Elasticity. Stefan Schmalholz, ETH Zurich
Closed sys. of eqns: incompressible fluid
Seven
unknowns
 xx ,
 yy ,
 yx ,
 xy ,
p,
Conservation of
linear momentum,
Force balance,
Two equations
 xx  yx

0
x
y
 xy  yy

0
x
y
Conservation of
angular momentum,
One equation
 yx   xy
Conservation of mass,
One equation
vx v y
1 p


, for K  
x y
K t
 vx
ux ,
1  v v y  
  x

 x 3  x y  
 v y 1  vx v y  
  p  2 
 


 y 3  x y  
1  v v y 
 2  x 

2  y x 
 xx   p  2 
uy
Rheology,
Three equations
 yy
 yx
Numerical modeling of rock deformation: FEM 2D Elasticity. Stefan Schmalholz, ETH Zurich
Tasks
The Matlab script “FEMS_2D_VISCOUS” includes a finite element algorithm that
solves the equations of the previous page describing slow viscous flow. The model
setup generates single-layer folding under pure shear shortening. After running the
finite element code you can visualize the results using the script
“Fems_visualization”. The finite element algorithm is described in detail in the
PDF-file “FEM_Frehner.pdf”.
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Document the Matlab scripts for you.
Describe the model setup, i.e. boundary conditions, initial geometry, material
properties etc.
Describe how the deformation of the mesh is done and programmed in the
algorithm.
Where are the shear stresses “SXZ” highest during folding?
Where are the shear strain rates “SRXZ” highest during folding?
Where are the horizontal stresses “SXX” highest during folding?
Make the model width a factor 3 smaller and a factor 5 larger. What do you
observe concerning the fold amplification and the final fold amplitude? Can you
explain the result?
Numerical modeling of rock deformation: FEM 2D Elasticity. Stefan Schmalholz, ETH Zurich