[CIG-SHORT] Mesh interpenetration

[Brad Aagaard]

Teng,

The first thing to do is to make sure your problem is being 
nondimensionalized with the appropriate scales.

In a dynamic problem the length scale we use for nondimensionalizing the 
parameters is the minimum wavelength of a shear wave, which we compute 
from the NondimElasticDynamic shear_wave_speed and wave_period properties.

The minimum period is a function of the resolution of your mesh. In 
generally, for a P1 (linear) discretization most people use 10-12 cells 
per wavelength. For spontaneous rupture problems, the breakdown zone 
should be at least 3-5 times the cell size. If this isn't familiar, 
there are a number of journal papers on these issues.

Also, first try running the problem with the single, main planar fault. 
Make sure the solution is well resolved by testing a couple different 
resolutions. Do you get almost identical results with a cell size that 
is 8m? 25m?

Once the single fault is working, then add the other faults, BUT use 
prescribed slip with a slip of zero. Look at the traction changes on 
those faults? Make sure they are well resolved. Do the results depend on 
the discretization size? cell type (tri vs quad)? In a 2-D domain with 
complex geometry, you can almost always get a higher quality mesh with 
triangular cells.

Regards,
Brad



On 11/07/2017 06:10 PM, Li, Teng wrote:
> Hi Brad,
> 
> Right now, I only apply initial traction perturbation. The normal compression is 50Mpa along the main fault. As for the shear stress, the overstress is 31Mpa, and in other regions shear stress is 20Mpa. The static strength is 30Mpa, while the dynamic shear strength is 15Mpa. In the secondary faults, the normal stress and shear stress are decomposed according to the angle, which is 60 degrees to the horizantal in this case.
> 
> The density of the material is 2670, Vs = 3464m/s and Vp = 6000m/s.
> 
> Best,
> Teng
> 
> Teng Li
> 
> Master Candidate in Structures
> 
> Department of Civil and Environmental Engineering
> 
> University of Illinois at Urbana-Champaign
> 
> 205 North Mathews Ave, Urbana, IL. 61801
> 
> Phone:(217)8196210, Email: tengli2 at illinois.edu
> 
> 
> 
> ________________________________________
> From: Brad Aagaard [baagaard at usgs.gov]
> Sent: Tuesday, November 07, 2017 1:21 PM
> To: Li, Teng
> Subject: Re: [CIG-SHORT] Mesh interpenetration
> 
> Li,
> 
> What are the fault traction values (constant background values and the
> perturbation) on each fault? What are your material properties?
> 
> Brad
> 
> 
> On 11/05/2017 08:49 PM, Li, Teng wrote:
>> Hi Brad,
>>
>> I am sorry for the late reply.
>>
>> Please see the pictures for model setup and slip values in the HDF5 files.  (The red lines means the positions of the secondary faults).
>>
>> Here I will give a description of my problem. The model is an 18000*25130 rectangular domain. In the model, there are a main fault and secondary faults. The main fault in the middle split the whole body into two equal rectangular. While in some places, there are 60-degree secondary faults link directly to the main fault. The friction model for all the faults is slip-weakening friction. And this is a dynamic problem. For the initial shear stress on the main fault, I apply overstress in a certain length in the bottom of the main fault and apply smaller stress in later part of the main fault. And I apply a certain compressive normal stress along the main fault. For the secondary fault, I apply same normal stress and smaller shear stress (same as the stress on the main fault where no overstress applied). The stresses in the secondary faults are decomposed according to their angles. The total time is 9.5s to make sure the rupture will go to the other end of the main fault, and dt is 0.0004s. The output is 200, which means 0.08s a step.
>>
>> The mesh size is 12.5m. All the elements are quad elements. In the junction area where the main fault and lowest secondary fault link together, the mesh shapes are irregular.  And I also find the main fault open in this part. Now the only thing I am not sure is the negative normal slip in this region.
>>
>>
>> Best,
>> Teng
>>
>>
>> Teng Li
>>
>> Master Candidate in Structures
>>
>> Department of Civil and Environmental Engineering
>>
>> University of Illinois at Urbana-Champaign
>>
>> 205 North Mathews Ave, Urbana, IL. 61801
>>
>> Phone:(217)8196210, Email: tengli2 at illinois.edu
>>
>>
>>
>> ________________________________________
>> From: CIG-SHORT [cig-short-bounces at geodynamics.org] on behalf of Brad Aagaard [baagaard at usgs.gov]
>> Sent: Wednesday, November 01, 2017 3:39 PM
>> To: cig-short at geodynamics.org
>> Subject: Re: [CIG-SHORT] Mesh interpenetration
>>
>> On 11/01/2017 12:59 PM, Li, Teng wrote:
>>> Hi Brad,
>>>
>>> Thank you. Actually, I asked the similar questions in the last month. I find normal traction become zero in the junction area. And also shear traction become zero in this area. After analyzing HDF5 file, I find there are both positive and negative normal slip occur in different time steps. Last time, we thought it was because the inappropriate parameters chosen for my problem. For my problem, the mesh size is 12.5m. And I first choose nordimensinalizer: normalizer.shear_wave_speed = 1*km/s,  normalizer.wave_period = 1*s. Now I change them to 0.1*km/s and 0.1s. Furthermore, I add formulation.norm_viscosity = 0.4. And I still see the both positive and negative normal slips. The magnitudes for both are about 0.005m.
>>>
>>> Is it because the rounding error brought by Matlab? Or is it because the mesh? I use Trellis to mesh all the domain.
>>
>> Teng,
>>
>> I went back to our email exchange in Aug and looked at your JSON
>> parameter file that you provided then. It looks like you are running a
>> dynamic simulation with multiple intersecting faults with a friction
>> interface.
>>
>> The JSON parameter file doesn't contain your spatial databases so I
>> don't know what sort of tractions you have on the fault or what your
>> material properties are. What information are you using to select your
>> new nondimensionalization scales? The shear wave speed should be close
>> to your minimum shear wave speed and the wave period should be close to
>> the minimum wave period you can resolve with your discretization (a
>> wavelength of usually 10-12 times your cell size). You updated
>> nondimensionalization scales correspond to a wavelength (length scale)
>> of 0.01 km or 10m. I suspect that the wavespeed you use for
>> nondimensionalization should be on the order of 1 km/s not 0.1 km/s.
>>
>> With a geometric incompatibility, usually you can keep the fault closed
>> with an appropriate normal traction. That is, if you have a small amount
>> of slip relative to your cell size, then the local transient normal
>> tractions are usually much smaller than the compressive normal tractions
>> arising from the overburden pressure.
>>
>> If you need further help, I suggest sending a diagram of what you are
>> trying to do along with a description (include approximate values for
>> your materials and BC) and the JSON parameter file.
>>
>> Regards,
>> Brad
>> _______________________________________________
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>>
> 
>