example2

Example #2: En-echelon strike-slip faults

We extend example #1 (below) by rotating the earlier deformation field and placing another fault en echelon to the first, giving a left-step in a right-lateral strike-slip system, which should yield a region of uplift in the step (think New Madrid).

Example 1 (above), which can be viewed in more detail here.

Example 2 (above) which has both the deformation field and the faults striking at 45-degrees.

To rotate the deformation field counter-clockwise, as shown above, we rotate the coordinate axes clockwise, which is a negative rotation (using the convention described here).

Thus: Dn = R.D.R'

where D is the previous displacement gradient tensor (dgt), Dn the new, rotated dgt, and R is the rotation matrix (R' is its transpose).

Example #2

The input file

* POISSONS RATIO    YOUNGS MOD   #PLANES     COEFF INTERNAL FRICTION    BACKGROUND DEFORMATION (See manual)
 .25                   7.E10      2                            0.6                           displacement gradient
* Background (blank; Exx,Exy,Exz,Eyy,Eyz,Ezz; Sxx,Sxy,Sxz,Syy,Syz,Szz; dUx/dx /dy /dz,dUy/dx /dy /dz,dUz/dx /dy /dz)
-.5e-4 .5e-4 0     -.5e-4  .5e-4 0    0 0 0

* for each plane:
* ORG:XO   YO   ZO                WDTH:STK  DIP  #SUB-ELEM:STK  DIP  STK    DIP
     10.0  10. 0.0                 50.   20.            3    2   45.   90
    38.2843 52.4264  0.0            50.   20.            3   2   45.   90

* for each plane (at each fixed distance along strike, going up-dip):
* PLN,SUB-ELEM           code    BC-shear(STK)   BC2-shear(DIP)  BC3-normal                         
1
     1   1       12         0.         0.0             0.0
     1   2       12         0.         0.0             0.0
     2   1       12         0.         0.0             0.0
     2   2       12         0.         0.0             0.0
     3   1       12         0.         0.0             0.0
     3   2       12         0.         0.0             0.0
2
     1   1       12         0.         0.0             0.0
     1   2       12         0.         0.0             0.0
     2   1       12         0.         0.0             0.0
     2   2       12         0.         0.0             0.0
     3   1       12         0.         0.0             0.0
     3   2       12         0.         0.0             0.0

* Run everything else interactively
Non-interactive grid specification
plane
vector
* Coordinate system of output
in-plane
* Output files to create
stress
elements
* Output file suffix
pln
* Xo, Yo, Zo (Ref.corner), strike,dip,length,width:
10.1 10.1 0.  45. 90.  50. 20.
* number of grid points in the strike and dip directions
50 20.

Highlights of this input file are:

each fault is discretized into 6 subelements
fault (elements) are free to slip
results are calculated in the in-plane coordinate system
results are output in both xyz and vector (matrix) format
stresses are to be calculated at grid points on the inspection plane that is essentially coincident with the SW fault plane
the inspection plane is slightly offset from the SW fault-element to avoid singularities.

Look at the traction in the strike direction (ts).
Remember that the boundary conditions set this to zero - but only at the center point!


Green corresponds to zero shear stress; ts=0 is only satisfied in the centers!


If we discretize more finely

The input file: (same as above except that the faults are now discretized into 50 subelements)

* POISSONS RATIO    YOUNGS MOD   #PLANES     COEFF INTERNAL FRICTION    BACKGROUND DEFORMATION (See manual)
 .25                   7.E10      2                            0.6                           displacement gradient
* Background (blank; Exx,Exy,Exz,Eyy,Eyz,Ezz; Sxx,Sxy,Sxz,Syy,Syz,Szz; dUx/dx /dy /dz,dUy/dx /dy /dz,dUz/dx /dy /dz)
-.5e-4 .5e-4 0     -.5e-4  .5e-4 0    0 0 0

* for each plane:
* ORG:XO   YO   ZO                WDTH:STK  DIP  #SUB-ELEM:STK  DIP  STK    DIP
     10.0  10. 0.0                 50.   20.            10    5   45.   90
    38.2843 52.4264  0.0            50.   20.            10   5   45.   90

* for each plane (at each fixed distance along strike, going up-dip):
* PLN,SUB-ELEM           code    BC-shear(STK)   BC2-shear(DIP)  BC3-normal                         
1
     1   1       12         0.         0.0             0.0
     1   2       12         0.         0.0             0.0
     1   3       12         0.         0.0             0.0
     1   4       12         0.         0.0             0.0
     1   5       12         0.         0.0             0.0
     2   1       12         0.         0.0             0.0
     2   2       12         0.         0.0             0.0
     2   3       12         0.         0.0             0.0
     2   4       12         0.         0.0             0.0
     2   5       12         0.         0.0             0.0
     3   1       12         0.         0.0             0.0
     3   2       12         0.         0.0             0.0
     3   3       12         0.         0.0             0.0
     3   4       12         0.         0.0             0.0
     3   5       12         0.         0.0             0.0
     4   1       12         0.         0.0             0.0
     4   2       12         0.         0.0             0.0
     4   3       12         0.         0.0             0.0
     4   4       12         0.         0.0             0.0
     4   5       12         0.         0.0             0.0
     5   1       12         0.         0.0             0.0
     5   2       12         0.         0.0             0.0
     5   3       12         0.         0.0             0.0
     5   4       12         0.         0.0             0.0
     5   5       12         0.         0.0             0.0
     6   1       12         0.         0.0             0.0
     6   2       12         0.         0.0             0.0
     6   3       12         0.         0.0             0.0
     6   4       12         0.         0.0             0.0
     6   5       12         0.         0.0             0.0
     7   1       12         0.         0.0             0.0
     7   2       12         0.         0.0             0.0
     7   3       12         0.         0.0             0.0
     7   4       12         0.         0.0             0.0
     7   5       12         0.         0.0             0.0
     8   1       12         0.         0.0             0.0
     8   2       12         0.         0.0             0.0
     8   3       12         0.         0.0             0.0
     8   4       12         0.         0.0             0.0
     8   5       12         0.         0.0             0.0
     9   1       12         0.         0.0             0.0
     9   2       12         0.         0.0             0.0
     9   3       12         0.         0.0             0.0
     9   4       12         0.         0.0             0.0
     9   5       12         0.         0.0             0.0
     10  1       12         0.         0.0             0.0
     10  2       12         0.         0.0             0.0
     10  3       12         0.         0.0             0.0
     10  4       12         0.         0.0             0.0
     10  5       12         0.         0.0             0.0
2
     1   1       12         0.         0.0             0.0
     1   2       12         0.         0.0             0.0
     1   3       12         0.         0.0             0.0
     1   4       12         0.         0.0             0.0
     1   5       12         0.         0.0             0.0
     2   1       12         0.         0.0             0.0
     2   2       12         0.         0.0             0.0
     2   3       12         0.         0.0             0.0
     2   4       12         0.         0.0             0.0
     2   5       12         0.         0.0             0.0
     3   1       12         0.         0.0             0.0
     3   2       12         0.         0.0             0.0
     3   3       12         0.         0.0             0.0
     3   4       12         0.         0.0             0.0
     3   5       12         0.         0.0             0.0
     4   1       12         0.         0.0             0.0
     4   2       12         0.         0.0             0.0
     4   3       12         0.         0.0             0.0
     4   4       12         0.         0.0             0.0
     4   5       12         0.         0.0             0.0
     5   1       12         0.         0.0             0.0
     5   2       12         0.         0.0             0.0
     5   3       12         0.         0.0             0.0
     5   4       12         0.         0.0             0.0
     5   5       12         0.         0.0             0.0
     6   1       12         0.         0.0             0.0
     6   2       12         0.         0.0             0.0
     6   3       12         0.         0.0             0.0
     6   4       12         0.         0.0             0.0
     6   5       12         0.         0.0             0.0
     7   1       12         0.         0.0             0.0
     7   2       12         0.         0.0             0.0
     7   3       12         0.         0.0             0.0
     7   4       12         0.         0.0             0.0
     7   5       12         0.         0.0             0.0
     8   1       12         0.         0.0             0.0
     8   2       12         0.         0.0             0.0
     8   3       12         0.         0.0             0.0
     8   4       12         0.         0.0             0.0
     8   5       12         0.         0.0             0.0
     9   1       12         0.         0.0             0.0
     9   2       12         0.         0.0             0.0
     9   3       12         0.         0.0             0.0
     9   4       12         0.         0.0             0.0
     9   5       12         0.         0.0             0.0
     10  1       12         0.         0.0             0.0
     10  2       12         0.         0.0             0.0
     10  3       12         0.         0.0             0.0
     10  4       12         0.         0.0             0.0
     10  5       12         0.         0.0             0.0

* Run everything else interactively
Non-interactive grid specification
plane
vector
* Coordinate system of output
in-plane
* Output files to create
stress
* Output file suffix
out
* Xo, Yo, Zo (Ref.corner), strike,dip,length,width:
10.1 10.1 0.  45. 90.  50. 20.
* number of grid points in the strike and dip directions
50 20.

Now the tractions in the strike direction (ts) are zero over more of the plane - but not all!




Next look at the surface displacement field.

Change only the output portion (2nd half) of the input file:

* Run everything else interactively
Non-interactive grid specification
plane
xyz
* Coordinate system of output
global
* Output files to create
displacements
* Output file suffix
out
* Xo, Yo, Zo (Ref.corner), strike,dip,length,width:
-50 -50 0 0 0 200 200
* number of grid points in the strike and dip directions
50 50

Highlights of this input file:

the inspection plane is now a horizontal surface at ground level
results are output in the global coordinate system

Here are the surface displacements: