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

[Hongfeng Yang]

Brad,

Do you mean

if u_n>  0, we set T_f = 0 even if the cohesion is nonzero?

In my rupture simulations, I run into the fault opening case on a curved fault surface. The error is the following

WARNING! Fault opening with nonzero traction., v_fault: 7063, opening: 10.7885, normal traction: -4870.89
mpinemesis: faults/FaultCohesiveDyn.cc:348: virtual void pylith::faults::FaultCohesiveDyn::integrateResidual(const pylith::topology::Field<pylith::topology::Mesh>&, double, pylith::topology::SolutionFields*): Assertion `fabs(tractionNormal)<  _zeroTolerance' failed.
[0]0:Return code = 0, signaled with Aborted

What may be the reason to cause the large u_n in the above case?  Ill shape element? And how can I fix it in addition to increase the value of zero_Tolerance?

Another question is whether there is an option toenforce u_n to be a small value if u_n>  zero_Tolerance,  in order to avoid fault opening during dynamic rupture simulation?I looked into thefaults/FaultCohesiveDyn.ccand did not find  such thing.

Thanks,

Hongfeng

On 04/23/2012 05:02 PM, Brad Aagaard wrote:
> 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
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-- 
Postdoc Investigator
Woods Hole Oceanographic Institution
Dept. Geology and Geophysics
360 Woods Hole Rd, MS 24
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