[CIG-SHORT] Bizarre tractions on dynamic fault with gravity

Thu Nov 13 14:18:37 PST 2014

Romain,

If you are using a purely elastic model, then you can go straight to 
applying initial fault tractions and bypass this issue. Otherwise, I 
don't think the fault edge feature will help because it will pin the 
edges of the fault. The most robust way to resolve the issue is to use a 
finer mesh to reduce the discretization error.

Brad

On 11/13/14, 1:39 PM, Romain Jolivet wrote:
> Dear Brad,
>
> Thank you for the clarification. I understand the issue now.
> Would it be possible to use the fault edge implementation to prescribe the traction on the edges?
> Or does it require some coding (I could give it a try, but that would be quite experimental)?
>
> Cheers,
> R
>
> Romain Jolivet
> California Institute of Technology
> Pasadena, CA, USA
> Tel: +1 626 560 6356
>
>> On Nov 13, 2014, at 20:00, cig-short-request at geodynamics.org wrote:
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>> Today's Topics:
>>
>>    1. Re: Bizarre tractions on dynamic fault with gravity (Brad Aagaard)
>>    2. Re: Bizarre tractions on dynamic fault with gravity (Brad Aagaard)
>>
>>
>> ----------------------------------------------------------------------
>>
>> Message: 1
>> Date: Wed, 12 Nov 2014 12:01:22 -0800
>> From: Brad Aagaard <baagaard at usgs.gov>
>> To: <cig-short at geodynamics.org>
>> Subject: Re: [CIG-SHORT] Bizarre tractions on dynamic fault with
>>     gravity
>> Message-ID: <5463BC92.9040502 at usgs.gov>
>> Content-Type: text/plain; charset="windows-1252"; format=flowed
>>
>> Romain,
>>
>> I can reproduce the apparently incorrect fault normal tractions at the
>> ends of the fault. This is puzzling.
>>
>> Please send me the journal files you used to create the mesh.
>>
>> Thanks,
>> Brad
>>
>>
>>> On 11/11/2014 10:26 AM, Romain Jolivet wrote:
>>> Dear Brad et al.,
>>>
>>> I am running a 2-D problem with an elastic rectangle (200km*50km) cut by a fault to simulate a thrust fault.
>>> Gravity is on in this problem. For a picture, please look at the file geometry.png.
>>>
>>> Because gravity is on, I have to prescribe initial stress conditions (isotropic stress tensor everywhere = rho*g*depth).
>>> For the same reason, I prescribe a Neumann condition on the bottom boundary with sigma_n = rho*g*depth and tau = 0 Pa
>>>
>>> The fault is a RateStateAgeing with slip strengthening properties. I push on the right side (dirichlet condition, 1 cm/year) and I want to see it sliding all the way, steady. The other side is fixed.
>>> Because I do not want to wait for too many time steps, I prescribe an initial shear stress along the fault equal to the normal stress multiplied by the standard friction coefficient (normal stress which should be equal to rho*g*depth).
>>> Figure initialTraction.png shows the prescribed traction on the fault (x-axis is depth in m, 0 m is the surface).
>>>
>>> Still, when I run the problem, it turns out that the pre-step computes a normal traction on the fault that is not equal to rho*g*depth, at least not everywhere. It seems fine for all the nodes inside the material, but the two nodes on the edges are off the linear trend where they should be (see afterElasticPrestep.png). I might be doing something wrong, but I wonder how tractions are estimated on the edges of the fault?
>>> This case leads to non-constant slip along the fault, especially for the first time step.
>>>
>>> I could compute the pre-step and then feed the tractions as a spatialdb, but I feel this problem is too simple to require that and there should be a solution.
>>>
>>> I joined a tar ball with the problem configure files, spatialdb, etc, if you want to try it (If you feel like numbers for stress are a bit awkward, it is because I want to do as if the whole thing was buried under 500 m of material. Removing that 500m of excess does not change anything in my case.).
>>> Let me know what you think,
>>> Romain
>>>
>>> ?????????????????????????????????????
>>> ?????????????????????????????????????
>>> !!!!!! ADDRESS CHANGED !!!!!
>>>
>>> Romain Jolivet
>>> Postdoctoral Fellow
>>>
>>> University of Cambridge
>>> Department of Earth Sciences
>>> Bullard Labs
>>> Madingley Rise
>>> Madingley Road
>>> Cambridge CB3 0EZ
>>> United Kingdom
>>>
>>> email: rpj29 at cam.ac.uk
>>> Phone: +44 1223 748 938
>>> Mobile: +44 7596 703 148
>>>
>>> France: +33 6 52 91 76 39
>>> US: +1 (626) 560 6356
>>> ?????????????????????????????????????
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>>>
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>>
>>
>> ------------------------------
>>
>> Message: 2
>> Date: Wed, 12 Nov 2014 15:16:38 -0800
>> From: Brad Aagaard <baagaard at usgs.gov>
>> To: <cig-short at geodynamics.org>
>> Subject: Re: [CIG-SHORT] Bizarre tractions on dynamic fault with
>>     gravity
>> Message-ID: <5463EA56.2020208 at usgs.gov>
>> Content-Type: text/plain; charset="windows-1252"; format=flowed
>>
>> Romain,
>>
>> I believe I understand the source of the problem you are getting with
>> gravity, initial stresses, and a fault with friction.
>>
>> I plotted the fault normal traction at time step 0 and compared it
>> against rho*g*(y-500); the 500 comes from your additional overburden
>> imposed at the top of the domain. I see a residual that has a depth
>> dependence with outliers at the top and bottom. A similar plot for the
>> stress in the cells shows a match to rho*g*(y-500).
>>
>> The stress field within the material has a linear variation with depth.
>> The stresses get projected onto the fault via the finite-element
>> formulation. The fault vertices in the middle of the domain have cells
>> above and below, so they get some average of the stress in the cells
>> that are above and below the fault vertices. As a result, they end up
>> quite close to -rho*g*(y-500), where y is the coordinate of the fault
>> vertex. The vertices at the top and bottom boundary have cells only
>> below or above them, so the projection from the finite-element
>> formulation comes from only below or above the vertex, so it has a
>> greater residual. Decreasing the size of the cells will reduce the residual.
>>
>> An additional note is that linear triangular cells are constant
>> strain/stress cells, so the stresses/strains within a cell are uniform.
>> As a result, they cannot represent a linearly varying stress field as
>> well as quadrilateral cells or higher order triangular cells. Thus, for
>> a similar resolution mesh, quad cells may reduce the residuals with
>> respect to rho*g*y. We don't yet have higher order basis functions
>> implemented in PyLith (this is high on our TODO list).
>>
>> Brad
>>
>>
>>> On 11/11/2014 10:26 AM, Romain Jolivet wrote:
>>> Dear Brad et al.,
>>>
>>> I am running a 2-D problem with an elastic rectangle (200km*50km) cut by a fault to simulate a thrust fault.
>>> Gravity is on in this problem. For a picture, please look at the file geometry.png.
>>>
>>> Because gravity is on, I have to prescribe initial stress conditions (isotropic stress tensor everywhere = rho*g*depth).
>>> For the same reason, I prescribe a Neumann condition on the bottom boundary with sigma_n = rho*g*depth and tau = 0 Pa
>>>
>>> The fault is a RateStateAgeing with slip strengthening properties. I push on the right side (dirichlet condition, 1 cm/year) and I want to see it sliding all the way, steady. The other side is fixed.
>>> Because I do not want to wait for too many time steps, I prescribe an initial shear stress along the fault equal to the normal stress multiplied by the standard friction coefficient (normal stress which should be equal to rho*g*depth).
>>> Figure initialTraction.png shows the prescribed traction on the fault (x-axis is depth in m, 0 m is the surface).
>>>
>>> Still, when I run the problem, it turns out that the pre-step computes a normal traction on the fault that is not equal to rho*g*depth, at least not everywhere. It seems fine for all the nodes inside the material, but the two nodes on the edges are off the linear trend where they should be (see afterElasticPrestep.png). I might be doing something wrong, but I wonder how tractions are estimated on the edges of the fault?
>>> This case leads to non-constant slip along the fault, especially for the first time step.
>>>
>>> I could compute the pre-step and then feed the tractions as a spatialdb, but I feel this problem is too simple to require that and there should be a solution.
>>>
>>> I joined a tar ball with the problem configure files, spatialdb, etc, if you want to try it (If you feel like numbers for stress are a bit awkward, it is because I want to do as if the whole thing was buried under 500 m of material. Removing that 500m of excess does not change anything in my case.).
>>> Let me know what you think,
>>> Romain
>>>
>>> ?????????????????????????????????????
>>> ?????????????????????????????????????
>>> !!!!!! ADDRESS CHANGED !!!!!
>>>
>>> Romain Jolivet
>>> Postdoctoral Fellow
>>>
>>> University of Cambridge
>>> Department of Earth Sciences
>>> Bullard Labs
>>> Madingley Rise
>>> Madingley Road
>>> Cambridge CB3 0EZ
>>> United Kingdom
>>>
>>> email: rpj29 at cam.ac.uk
>>> Phone: +44 1223 748 938
>>> Mobile: +44 7596 703 148
>>>
>>> France: +33 6 52 91 76 39
>>> US: +1 (626) 560 6356
>>> ?????????????????????????????????????
>>> ?????????????????????????????????????
>>>
>>>
>>>
>>> _______________________________________________
>>> CIG-SHORT mailing list
>>> CIG-SHORT at geodynamics.org
>>> http://lists.geodynamics.org/cgi-bin/mailman/listinfo/cig-short
>>
>>
>>
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