Baotang Shen, the developer of FRACOD, using classic theory linking stress anisotropy and Poisson's ratio to explain exceedence of critical extension strain in a fully 3D compressive stress field, but close to an opening (hence the anisotropy), has recently discovered the reason for the approx. principal stress = 0.4 x UCS onset of AE in lab tests and the onset of fracturing in tension (i.e. extension strain limit exceeded) around tunnels at the same ratio of max. tangential stress and UCS. It depends on typical ratios of UCS/sigma t (often about 10) and Poisson's ratio (often about 0.25). The '0.4' is the result of simple arithmetic, not scale effects, nor rough boundaries. We have subsequently used this in a simple equation to suggest cliff and mountain wall height limits in a wide variety of rocks. SRF is 'accelerated' beyond the same stress/strength ratio in the Q-system to increase support. At significantly higher ratios of stress/strength it is unstable shear failure one is trying to guard against, while it is even deeper 'break-out' in the later Martin et al. model.
Dear Dr. Barton,
Interesting discussion point. As you know, I also provided a 3D spalling criterion explaining the role of the 3D directionality of extensional fracturing on strength of brittle rocks under polyaxial stress states:
https://www.onepetro.org/conference-paper/ARMA-2016-763
In my ARMA 2016 paper, I briefly explained why the 1D extensional strain criterion fails to capture the dependency of strength on the intermediate principal stress. I will soon submit a Journal paper in which I present an extended version of my criterion.
Kind Regards,
Masoud Rahjoo
Dear Masoud,
Nice to hear from you! Sorry - no ARMA this year. Please send me the ARMA paper you refer to - and I will forward to Baotang Shen for his assessment - he is the fracture mechanics expert. Only the abstract
and dollar bill in the link. Sounds interesting. Nick
Dear Nick,
I uploaded the full text on my researchgate account. Here is the link:
https://www.researchgate.net/publication/304938544_Stress-induced_Spalling_Analysis_of_Extraction_Level_Pillars_using_a_3D_Extensional_Strain_Failure_Criterion
I am looking forward to receiving your and Dr. Sheng's opinion on the proposed 3d extensional strain-based criterion.
Kind Regards,
Masoud
Thank you Masoud / Rahjoo....am unsure of which name to use! I have now sent - very belatedly - to Baotang Shen. Best regards, Nick
Dear Nick,
Masoud is my first name, but my last name, Rahjoo, means pathfinder (in Persian) and helps my friends to remember me.
I am looking forward to hearing from you and Dr. Shen.
Best Regards, Masoud
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