[CIG-SHORT] Kinematic faults vs dynamic faults and fault opening

[Brad Aagaard]

Brad,

A more complete explanation of the fault opening condition and zero 
tractions is summarized mathematically by:

   T_n * u_n = 0

T_n = normal traction
u_n = normal displacement

If T_n <= 0, then u_n = 0 and if u_n > 0, then T_n = 0. Also note that 
if u_n = 0, we set T_f = 0 even if the cohesion is nonzero because 
contact is lost.

Brad



Brad Hager pointed out that we also impose the condition

On 04/23/2012 01:44 PM, Brad Aagaard wrote:
> On 04/23/2012 11:34 AM, bhhager wrote:
>> I am confused by your description.  I think that dike intrusion
>> should result when the magma pressure is large relative to the
>> background (compressive) stress, thereby forcing the dike to open by
>> exerting a large compressive normal traction on the medium bounding
>> the dike.  (Imagine a flat jack wedging the medium apart.)
>>
>> In other words, crack opening is aided by high fluid pressures (that
>> is, highly-compressive) that push the fault open.  (Ahead of the
>> fault, the medium might go into tension, but that's another story.)
>>
>> Following this "logic,"  I don't see why putting the compressive
>> tractions on a fault that are needed to push the adjacent planes
>> apart should be inconsistent with the frictional sliding case
>> requiring either compressive or zero normal tractions.
>>
>> If this is correct, you can shorten your TODO list.
>>
>> What am I missing?
>
> In the current version of PyLith, the FaultCohesiveDyn object implements
> what I would describe as a frictional contact:
>
>     T_f = C - mu_f*Tn if Tn<= 0
>
>     T_f = 0 if Tn>  0
>
> T_f = shear traction (friction) on fault
> C = Cohesion
> mu_f = coefficient of friction
> T_n = normal fault traction
>
> In implementing this contact condition, if the fault opens then we
> enforce zero tractions (shear and normal) on the fault surface so that
> it is a free surface. This corresponds to frictional contact behavior.
>
> If the deformation causing the fault opening is part of the elasticity
> solution, then the frictional contact implementation allows the fault to
> open (with the fault surface becoming traction free). On the other hand,
> if one wants to simulate a dike intrusion via imposed tractions on an
> interior surface (a flat jack wedging the medium apart) to approximate
> intrusion of a fluid, this is incompatible with enforcing a free surface
> when fault opening occurs. One can simulate dike intrusion via
> prescribed slip, but it is more naturally done via tractions.
>
> In the past we have discussed modeling dike intrusions by adding a
> FaultCohesiveTract object. I think we can add in the functionality that
> most people would want for dike intrusions by simply adding a switch
> that allows initial tractions to be imposed even when the fault is open.
> This alone would not allow for transient intrusions but when combined
> with the planned spatial and temporal perturbations in fault tractions
> (intended for earthquake rupture nucleation), it could extend the
> behavior to cover some simple transient intrusions as well.
>
> Brad
> _______________________________________________
> CIG-SHORT mailing list
> CIG-SHORT at geodynamics.org
> http://geodynamics.org/cgi-bin/mailman/listinfo/cig-short
>