[CIG-SHORT] problem getting fault rupture (slip weakening)

Thu Apr 25 11:26:39 PDT 2013

Lucas,

When you are run quasi-static problems I recommend using the 
quasi-static nondimensionalization parameters, and when you run dynamic 
problems I recommend using the dynamic nondimensionalization parameters. 
In these cases, the appropriate values will seem more natural. For 
example, in a quasi-static problem the relaxation time is on the order 
of the time step, whereas the minimum period would be orders of 
magnitude smaller than the time step. As you have noted before, you can 
get the same nondimensionalization scales using either, but the values 
are more natural when the nondimensionalizer corresponds to the type of 
problem.

In numerical models the slip-weakening parameters in slip-weakening 
friction and critical slip distance in rate-state friction often must be 
order of magnitudes larger than laboratory values in order to regularize 
the problem. It is not clear to me if this is your problem or whether 
you have other scaling or setup issues.You might want to try a much 
larger slip-weakening parameter to see if this fixes the issue.

Also be sure to note the healing parameter in the slip-weakening model 
that is used in quasi-static simulations when you want the slip confined 
to a single time step. This isn't the cause of your very small slip 
values but it would cause slip to extend over multiple time steps and 
not give stick-slip behavior in a quasi-static simulation.

Regards,
Brad

On 04/25/2013 11:08 AM, Lucas Abraham Willemsen wrote:
> Hello Brad,
>
> Thanks for your detailed answer. By reducing the length scale it is possible to get some slip on the fault. But I need to reduce the length scale to very small values: Some slip (see figure, displays slip history on middle fault node) starts to occur with the following settings:
>
> normalizer.length_scale = 1.0*m
> normalizer.shear_modulus = 1.0e+10*Pa
> normalizer.relaxation_time = 1.0*day
>
> As a reminder, the length scale of my elements is 10 meters and the P and S-wave velocities are chosen such that the elastic moduli are in the range of 10GPa, just like the shear modulus normalizer.
> If I further decrease the length scale, all the way down to 0.1 millimeter, the increase in fault slip is negligible, and still has a maximum around 1e-9 meter. This is not caused by a geometry that relaxes stress very easily, since the ratio of shear traction to normal traction is not reduced to the friction coefficient (strength) when this slip takes place. This can be seen in the figures I attached.
>
> The problem seems to be related to the slip weakening distance of 5.0mm, which is really not unreasonably small when you look at laboratory results. There are researchers who argue that the value should be larger on real faults and they may be right, but I'm trying to model the results of the 2011 Cappa and Rutqvist paper. They model a faulted reservoir in a carbon sequestration setting. The fault is represented by a thin plastic shear zone with slip-weakening distance replaced by critical plastic shear strain. The critical plastic shear strain value they use in combination with the thickness of the fault zone corresponds to a slip-weakening distance of exactly 5 millimeters.
>
> But even when I use normalizer.length_scale of 0.1mm (which is less than the critical fault slip) the final slip on the fault is only in the order of 1e-9m and the stress ratio is way above the the friction coefficient. Any smaller length scale and the solver does not converge anymore. Do you know if it is always going to cause a problem if the slip-weakening distance (5mm) and the element dimensions (10m) mismatch several orders of magnitude? The geological setting I described doesn't use unreasonable values from a geophysical perspective and is actually quite reasonable I think.
>
> If I increase the slip-weakening distance to 1.0m there will be slip, even though this is not really the scenario I want to model. I decrease time timestep to 1 day. The linear solves are very quick, ~150 linear iterations for each linear solve. At t = 23 days the first minor slip event takes place at a shear to normal traction ratio of 0.6 as expected. Displacements are in the order of millimeters. But going from t = 22 to t = 23 required a lot of nonlinear iterations even though convergence to a norm of 1e-10 is eventually achieved. The next step, going from t = 23 days to t = 24 days has the nonlinear solver divergence.
>
> So as a summary, it seems like:
> -If I use slip-weakening distance of 5mm in combination with 10m elements, I am unable to normalize things appropriately so that slip takes place when it should (compare shear stress / normall stress ratio with friction coefficient)
> -If I use a larger slip weakening distance of 1.0 meter (which changes the problem and is something I do not prefer) and a timestep of 1 day, slip will start at the right moment, but the nonlinear solver diverges very early on. The simplified problem I sent to the mailing list has gravity disabled and uses a different stress situation than I'll use when I try to model the situation of Cappa and Rutqvist. It may be that I have less nonlinear solver convergence problems there, but I'm somewhat doubtful. It took many nonlinear iterations to go from t = 22days to t = 23days even though the final slip was only in the order of a few millimeters. I wouldn't be surprised if similar convergence problems will occur when I try to model Cappa and Rutqvist.
>
> Do you perhaps have a suggestion on how to work around these problems?
> with kind regards,
> Lucas
>
>
> ________________________________________
> From: cig-short-bounces at geodynamics.org [cig-short-bounces at geodynamics.org] on behalf of Brad Aagaard [baagaard at usgs.gov]
> Sent: Wednesday, April 24, 2013 19:56
> To: cig-short at geodynamics.org
> Subject: Re: [CIG-SHORT] problem getting fault rupture (slip weakening)
>
> Lucas,
>
> If the nondimensional slip is less than the zero tolerance, then it will
> be set to zero after a nonzero slip value is computed. This insures that
> roundoff errors don't prevent the fault from being locked when it should.
>
> I went into the fault implementation and dumped some values out to a log
> file and it looks like this is what is happening for your problem. The
> nondimensionalized slip values are on the order of 1.0e-12 to 1.0e-13.
> Because these are less than the zero tolerance they are set to zero. So
> the code is computing slip, it is just so small that it set it back to
> zero, because it is treating it like roundoff error.
>
> You may have other dimensionalization issues or your problem is setup in
> such a way that it doesn't take much slip at all to relieve the stress
> and satisfy the friction criterion.
>
> The solver looks like it is behaving properly. The KSP and SNES
> residuals get small and the solves converge.
>
> Regards,
> Brad
>
>
> On 04/24/2013 02:43 PM, Lucas Abraham Willemsen wrote:
>> Hello Brad,
>>
>> Thanks for the suggestion. I tried reducing the period to get a smaller length scale. I also tried reducing the shear wave speed to get a smaller length scale. At the end there is a minimal slip, ~O(1e-10). The shear traction to normal traction ratio still exceeds 1.0 even though the static coefficient is 0.6.
>>
>> I also tried the quasi-static nondimensionalizer with values:
>>
>> normalizer = spatialdata.units.NondimElasticQuasistatic
>> normalizer.length_scale = 10.0*m
>> normalizer.shear_modulus = 1.0e+10*Pa
>> normalizer.relaxation_time = 1.0*day
>>
>> But this did not help either. The slip at step 20 is 0.0 again.
>>
>> with kind regards,
>> Lucas
>> ________________________________________
>> From: cig-short-bounces at geodynamics.org [cig-short-bounces at geodynamics.org] on behalf of Brad Aagaard [baagaard at usgs.gov]
>> Sent: Wednesday, April 24, 2013 16:57
>> To: cig-short at geodynamics.org
>> Subject: Re: [CIG-SHORT] problem getting fault rupture (slip weakening)
>>
>> Lucas,
>>
>> I finally found some time to start looking at this. The first thing I
>> have noticed is that your length scale for nondimensionalizing is too
>> big. It looks like your discretization size is 10 m but your length
>> scale for nondimensionalization is 1 km. You chose to use the dynamic
>> nondimensionzalizer so you provided a shear wave speed and a period. It
>> looks like your shear wave speed for nondimensionalizing is close to
>> your physical properties, so decreasing your period should give you an
>> appropriate length scale.
>>
>> I am not sure if this fixes everything, but it is a place to start. I
>> may have some additional minutes later this afternoon to dig deeper.
>>
>> Brad
>>
>>
>> On 04/24/2013 01:44 PM, Lucas Abraham Willemsen wrote:
>>> Hello CIG,
>>> I still haven't quite figured out what is causing this strange behavior. Could someone please shed some light on what I am doing wrong?
>>>
>>> with kind regards,
>>> Lucas
>>> ________________________________
>>> From: Lucas Abraham Willemsen
>>> Sent: Monday, April 22, 2013 11:28
>>> To: cig-short at geodynamics.org
>>> Subject: problem getting fault rupture (slip weakening)
>>>
>>> Hello,
>>>
>>> I'm sometimes encountering issues where the shear stress on the fault is larger than the shear strength, yet no slip occurs. I know several of the SCEC benchmarks have successfully been implemented for slip-weakening, so my problems are probably caused by misconfiguration. I've tried changing several settings, but have so far not found the one that is the cause of my problems.
>>>
>>> Therefore I created a minimal working example illustrating the difficulties I'm having. This example does the following:
>>>
>>> -Block of material: roller BC on left and bottom.
>>> -Initial normal stress on the top boundary is -10 MPa.
>>> -Initial normal stress on the right boundary is -25 MPa.
>>> -Gravity is turned off. This way the initial stress field is uniform.
>>> -Normal traction rate of -1MPa per day is applied on a part of the right boundary. The reason for applying the traction rate to only a section of the right boundary is that this way the entire fault will probably not rupture simultaneously.
>>> -Static friction coefficient is 0.6, dynamic is 0.2 and slip weakening distance is 5mm. 0 Cohesion
>>> -Fault has a dip of 50 degrees.
>>> -Implicit simulation
>>>
>>> With these settings, the initial normal traction on the fault should be -18.8 MPa and the shear traction should be -7.4 MPa. This is correctly calculated by Pylith.
>>>
>>> -The initial ratio of shear traction to normal traction is 0.39, which is below the static friction coefficient of 0.6. No rupture should occur, and it doesn't. So far so good..
>>> -The figure attached to this email shows evolution of the shear traction [traction (0)] and evolution of normal traction [traction (1)] as function of each of the 20 10-year timesteps for the fault node displayed as a purple dot. (total simulation time 200 years). The figure shows that the ratio of shear traction / normal traction quickly exceeds the static friction coefficient of 0.6. After 200 years the shear traction is even larger than the normal traction. Yet there is 0 slip.
>>>
>>> As I mentioned before, this phenomenon probably indicates that I have incorrectly implemented a certain setting. I'd be grateful if someone could point me in the right direction. I have attached the code in the zip file. Running it should take a couple of minutes at most.
>>>
>>> cheers,
>>> Lucas
>>>
>>>
>>>
>>>
>>>
>>>
>>> _______________________________________________
>>> CIG-SHORT mailing list
>>> CIG-SHORT at geodynamics.org
>>> http://geodynamics.org/cgi-bin/mailman/listinfo/cig-short
>>>
>>
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