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