[CIG-SHORT] problem with rate-and-state friction model

[Brad Aagaard]

Lucas,

Sorry the delay. I am out of the office. If you are still stuck on this 
issue, please supply a small example (something that runs in a few 
seconds) that displays this behavior. You may want to try starting from 
the bar_shearwave rate-state friction example in 
examples/bar_shearwave/quad4.

You may also want to examine the SCEC dynamic rupture benchmarks that 
use rate-state friction (TPV1XX). Eric Dunham set those up with a 
different nucleation technique. Rate and state friction behaves quite 
different from slip-weakening due to the direct effect associated with 
coefficient 'a'.

Regards,
Brad


On 7/3/12 1:18 PM, Lucas Abraham Willemsen wrote:
> Hi,
>
> Currently I have adapted the TPV205 example (from the workshop) to model
> a fault patch with rate-and-state friction. Just as in the example I
> apply initial tractions to the fault by using a spatialdb.
>
> The problem is that with the values I use for the parameters, rupture
> should take place on a specific fault patch. According to the source
> code, the rate-and-state friction model is implemented as follows when
> the 'slip rate' is less than the 'minimum slip rate' (linearization):
>
>        mu_f = f0 + a*log(slipRateLinear / slipRate0) + b*log(slipRate0*theta/L) -
> 	a*(1.0 - slipRate/slipRateLinear);
>
> (This is different from what is currently written in the manual, eqn
> 6.66.) Since the fault starts with zero slip rate, verified by paraview,
> (v = 0), the line of code above should calculate the friction
> coefficient. Below I list the meaning of the symbols, and the values I used.
>
> ------------------------------------------------------------------------------------------------
> mu_f:                    friction coefficient:                     will
> be calculated by pylith
> f0:                         reference friction coefficient:    0.4
> a:                          rate-state parameter a:              0.02
> b:                          rate-state parameter b:              0.05
> L:                          characteristic slip distance:       0.005m
> slipRateLinear:   Also known as Vmin:                  1.0e-12m/s
> slipRate0:            Reference slip rate:
> 0.367879e-12m/s         (1/e)*10^(-12)
> theta:                   State variable (at t=0)               1.359e10*s
> ------------------------------------------------------------------------------------------------
>
> With these values, mu_f should reduce to f0 (=0.4) at t = 0.
>
> I apply a uniform normal stress of 190 MPa on the fault. With mu_f = 0.4
> everywhere on the fault, the strength of any fault patch should be 0.4 *
> 190 = 76 MPa (0 cohesion). The initial tractions are defined in the file
> 'tractions.spatialdb'. This file creates three initial shear stress
> perturbations around the uniform shear stress of 70 MPa. The middle
> perturbation has a shear stress of 82 MPa. Since this is larger than the
> shear strength of 76 MPa I would expect a rupture to initiate at the
> middle stress perturbation. But nothing happens.
>
> Could someone please tell me what I am doing wrong? The strength is less
> than the shear stress on the middle stress perturbation. I'd therefore
> expect it should rupture.
>
> I uploaded the source code at the following location:
> http://web.mit.edu/lawillem/www/ratestate.zip
> The model can be run with the following command:
>
> pylith tet4_200m.cfg tet4.cfg       (I suggest you add --nodes=4 or
> something like that, because it may run for half an hour otherwise)
>
> Cheers,
> Lucas
>
> (P.S. When I reduce the parameter 'a' to 0.002 the middle patch does
> rupture. But I do not see why the parameter a has any influence. I have
> chosen my parameters in such a way that 'log(slipRateLinear /
> slipRate0)' goes to 1, cancelling the  '(1.0 - slipRate/slipRateLinear)
> ' term since the slipRate is initially zero. Changing the b parameter
> does not seem to have an effect. This suggests that the parameter 'a'
> does not cancel, but I fail to see why.)
>
>
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