Creep, compaction and the weak rheology of major faults
Norman H. Sleep & Michael L. Blanpied
Ge 277 – February 19, 2010
The problem
• San Andreas Fault: low heat flow=> Sliding causes little frictional heating=> < 20 Mpa
• Across the fault, = 200 – 570 MPa- pf
pf=hydrostatic
=> = 90 – 260 MPa
The suggestion
• Low (0.2) ? No material would account for it…
• - pf
if we have pf then can be low.
Need a mechanism to have high fluid pressure:permanently ?transiently ?
Role of fluid pressure in Rock mechanics
Permanently high fluid pressure
• Dehydration of minerals ? Subduction zone only.
• Regional high fluid pressure ? No, more favorably orientated planes in the country rock would also be weakened.
• Where would the water come from ? No big reservoir available.
Transiently high fluid pressure
Pore pressure cycle: Water trapped around the fault by seals.
Interseismic compaction of fault zone by ductile creep
=> porosity decreases=> fluid pressure (pf) increases
Coseismic restoration of porosity (dilatancy)=> fluid pressure (pf) back to initial
Role of frictional heating
• Increases pore pressure during earthquake once the slip has started (>1mm/s)
[Segall & Rice, 2006]
Constant pore volume => scale length of slip to increase Pf to lithostatic pressure = 0.24m. (low)
• Increase porosityConstant pore pressure => variation of porosity =
0.04/m.
Blanpied, Lockner & Byerlee, Nature (1992)
= 100 MPa
Confining pressure = 400 MpaTemperature = 600oCV = 8.66 x 10-5 mm/s
Axial displacement (mm)
app
-
p p
undrainedFault with gouge
Blanpied, Lockner & Byerlee, Nature (1992)
Confining pressure = 400 MpaTemperature = 600oC
Axial displacement (mm)
app
-
p p
Pp = 100 MPa
drained
dry granite = 0.7
Results from the experiment:
– Water at high temperature:lowers rock’s strength at low strain rates
– Pore fluid in fault may be isolated from surrounding rock by seals
– Shear + compaction in the fault zone=> increase in pore pressure=> sliding at low effective stress
Field evidences
• Low permeability seals exhumed from 2 to 5 km.• Arrays of subsidiary faults in surrounding rocks
=> near-fault-normal compression=> low sliding resistance
• Episodes of formation and healing of fractures=> fluid pressure reached lithostatic level
(hydrofracturation)
Deformation: linear viscous
€
=η∂V2y
∂x
x
y
€
Pf − Ps =K∂Φ
∂t
€
Pf
€
Ps
Velocity of the rock
Shear viscosity
Bulk viscosity
Porosity
€
∂Pf∂t
=Pf − Psth
MODEL
Seals:
Variable parameters
Models
Parameters studied:
W, fault widthi, intrinsic viscosity (i.e. shear and bulk
viscosity)
Seal :
€
∂Pf∂t
=Pf − Phydro
th
c, fraction of the faulting energy that goes into creating cracks
Earthquake cycle < th < time fault active
Time for pores to compact a significant amount of their volume:
€
tp =η i
Tn − Phydro≈ 3,850years
Analogous time for cracks
€
tc =η i fc
Tn − Phydro≈ 80years
MODEL 1THIN FAULT WITH HIGH VISCOSITY
least compressive stress
MODEL 3BROAD FAULT WITH LOW VISCOSITY:
CREEPING FAULT
Cracks close too rapidly to havean effect on the earthquake cycle.
Viscosity low => Pf increases to nearlithostatic before much shear tractionbuilds up.
Porosity as a state variable
• Rate and state friction law:
Aging evolution of the state variable
€
=0 + a lnV
V0
⎛
⎝ ⎜
⎞
⎠ ⎟+ b ln
ψ
ψ 0
⎛
⎝ ⎜
⎞
⎠ ⎟
€
∂ψ∂t
=1
t0−Vψ
Dc
INTERSEIMIC REGIMEDuctile compaction of cracks:
where is the crack porosityP = - pf
ηm is the bulk viscosity
V is the sliding velocity€
∂∂t
= −ΔP
η m= divV
[Mc Kenzie, 1984]
• Crack production rate:
where V is the sliding velocitym fraction of the energy that goes into
crack productionc critical porosity
€
∂∂t
=Vβm (Φc − Φ)τ
ΔPWΦc
€
∂(Φc − Φ)
∂t=
ΔP n
η m−Vβm (Φc − Φ)τ
ΔPWΦc
€
ψ =c − Φ
€
∂ψ∂t
=1
t0−Vψ
Dc
Accounts for the friction change in experiencesfrom Linker and Dieterich (1992).
P not constant…
Doesn’t considerthe thermal effecton porosity…
Conclusions
• Small amount of ductile creep allows porous fault zone to compact
=> In partially sealed fault zone, increases fluid pressure
=> earthquake failure at low shear traction.• Porosity restored during earthquake.• Nucleation size: Rubin & Ampuero [2005]:
would be too large…
€
L∝1/σ