Gouge from a fault beneath a planned geothermal field is tested in a stiff laboratory…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Earth, Climate & Energy Physics · Seismology, tectonics and geodynamics

The Solid Earth, Ch Faults, the earthquake cycle and seismic hazard

Problem

Gouge from a fault beneath a planned geothermal field is tested in a stiff laboratory friction press at the fault's temperature. Sliding steadily at

1\,\mathrm{\mu m\,s^{-1}}

with friction coefficient

0.6000

, the load point's speed is stepped up tenfold. The friction coefficient jumps at once to

0.6184

and then, over a few tens of micrometres of slip, settles to a new steady value of

0.5931

. ((a)) Using the rate-and-state friction law, find

a

b

and

a-b

for this gouge. ((b)) Is the gouge velocity-weakening? Say what the sign of

a-b

does, and does not, tell you about whether a patch of this fault can nucleate an earthquake. ((c)) At the depth of injection the fault carries normal stress

\sigma_n=100\,\mathrm{MPa}

, pore pressure

p_f=40\,\mathrm{MPa}

and shear stress

|\tau|=33\,\mathrm{MPa}

, with

\mu_f=0.6

. Find the pore-pressure rise

\Delta p_f

from injection that brings it to Coulomb failure.

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