User talk:Ungtss/Rapid bending granite

In the report by Hidebumi Itō and Naoiti Kumagai, "On a New Creep Experiment of Large Granite Beam Started in 1980" and Kumagai’s “Two Findings in Long-Term On-Going Laboratory Experiments on Creep of Granite Beams by Bending”¹ the creep of a granite bar 2150 mm long under small (2 MPa maximum pressure) loads show a deflection rate of 0.005 mm/year for 30 years and an associated viscosity (μ) of 5.3X10¹⁹ Pa-s for a sample kept near 23.9C . At that rate, it would take ~100000 years to deform to a 1m radius. If we take granite viscosity at higher temperature² we get μ =10¹² at 1075.7 – 1124.8 K. Using the earth conditions at ~1.7km depth ³ we have a differential stress of 40 MPa and an ambient temperature of 40C (317.05 K). Assuming an Arrhenius equation for the thermal dependency of granite viscosity these values and temperatures give μ = 9.2X10¹⁸-1.4X10¹⁹ at 317.05K. Since viscosity is defined as stress/(strain rate), the viscous deflection rate is linear in both stress and viscosity, giving us a time of ~1000-1500 years to get the same 1m radius. This amount of time appears to be short enough to fit into anybody’s geological time frame.

Notes

^Note 1: Khan, Akhtar, and Tokuda, Masataka (eds.) (1989). 1989 Advances in Plasticity. Pergamon Press: Printing Press. ISBN 0080401821. {{cite book}}: |author= has generic name (help)CS1 maint: multiple names: authors list (link)

^Note 2: "Viscosities of granitic (sensu lato) melts: Influence of the anorthite component" (PDF). Retrieved February 2, 2005.

^Note 3: "Rheology". Retrieved February 2, 2005.