# Terzaghi's principle (pore fluid pressure ratio and effecttive stress) in viscoelastic yielding?

Hi all,

I was recently testing and running the benchmark of the thrust-belt wedge taper (Coulomb wedge, eg. Dahlen 1984) following the tutorial video on Youtube of Dr. Anne Glerum. Thanks for your detailed introduction, I could reproduce the benchmark by charm.

However, I was wondering whether the pore fluid pressure ratio stuff (e.g., Hubbert & Ruby 1959, Terzaghi’s principle) was included in our Drucker Prager plastic deformation criteria in ASPECT? I did not see that in the paper of Glerum et al., (2018) in SOLID EARTH.

I think this might be important because the geophysical community observed and assumed a high fluid pressure from both the plate interface (almost lithostatic) and the upper plate (between lithostatic and hydrostatic). This will significantly affect the evolution of the stress and our anticipation of the deformation pattern (fore-thrust and back-thrust) in a fold-and-thrust belt and the modeled taper angle of the subduction zone.

May I kindly ask, am I neglecting this stuff from the manual, or this is still under development?

Cheers,
Yueyang

Hi Yueyang,

Thank you for posting this question to the forum!

Short answer, this is not implemented in ASPECT. To speed up discussion, can you post the equations for how you think the yield criterion should be modified?

If this essentially requires the approach of Keller et al. (2013) for hydrofracturing, it is slowly being worked on, but will not be available for some time.

Cheers,
John

Hi John,

The physical meaning of the pore fluid pressure, fluid pressure ratio, and the effective yield stress are the ones described in Keller et al., 2013. But I should admit this paper is a difficult one for me to understand. The equations in their paper to define the effective stress considers the melt fraction \phi, and I guess they are calculating the exact fluid pressure from Darcy law rather than simply pre-defining the pore fluid pressure ratio \lambda as a physical attribute for the compositional field, as we define the rock’s density and internal friction angle in the ASPECT input file.

But anyway, the fluid pressure influences the effective yield stress of the rock and thus affects both the Mohr-Coulomb type (or Drucker-Prager) shear and the Griffith type tensile (eq37 in Keller et al., 2013).

I was thinking about a pretty simple approach to incorporate the effective yield stress and pore fluid pressure thing into the Drucker-Prager yield equation in the way of Ruh et al., (2016 in JGR). Jonas defined a constant pore fluid pressure ratio \lambda and the dynamic pressure P(1-\lambda), in eq 1 in his paper. (But, I am confused about his eq 4 and 5…)

Then, if I look at the equations in Glerum et al., (2018), I guess what we need to modify are equations 8 and 9. I guess we may substitute the P as P(1-\lambda), in which the \lambda is a constant fluid pressure ratio, which we could define as an attribute in the input prm file for each compositional field. Like, \sigma_y =Ccos(\phi) + sin(\phi)P(1-\lambda) in 2-D.

Treating \lambda as a constant attribute in time domain may not be so realistic, since the fluid will drain and migrate. But I guess it would be helpful to use this simple mean value to simulate and model the subduction structural evolution as Jonas did in several of his publications (e.g. Ruh et al., 2016 in JGR, and Ruh, 2016 in Terra Nova ).

Please forgive me if I said something very amateur.

Do you think this will work out?

Many thanks, and please have a nice day!

Regards,
Yueyang

Hi Yueyang,

Sure thing and thank you for writing out the detailed description!

We can certainly modify the Drucker Prager yield criterion as shown above, but I think it would be good to discuss the physics and more detailed equations with the broader ASPECT group first.

Can you attend one of the bi-weekly ASPECT user meetings, which are held every other Tuesday from 8-9 am Pacific?

Thanks!
John

Hi John,

yes, I agree. The ASPECT community should definitely discuss physics before incorporating the new physical attribute into the yield equations.

Thanks for inviting me, and I would like to join the ASPECT user meeting to discuss that. May I ask, when will the next meeting take place, and how can I join that?

All the best,
Yueyang

Hi Yueyang,

The next bi-weekly ASPECT community meeting will be on February 14th from 8-9 am Pacific.