materials physics of faults in rapid shear and...

Symposium in honor of Rodney J. CliftonSymi, Greece, 24-29 June 2012

Materials Physics of Faults in Rapid Shearand Consequences for Earthquake Dynamics

James R. Rice (Harvard)

Underlying studies done collaboratively with some of:

Nicolas Brantut (Univ Col Lond) Massimo Cocco (INGV Rome) Eric Dunham (Stanford) Nadia Lapusta (Caltech) Hiroyuki Noda (JAMSTEC) John Platt (Harvard) Alan Rempel (Oregon) John Rudnicki (Northwestern) Victor C. Tsai (Caltech)

Rod Clifton's influence on, and direct contributions to, mechanics in earth science and engineering:

Pioneer of the mechanics of hydraulic fracture • Fracture mechanics of crack development from pressurizedboreholes. • Hydrofracture measurements to infer in-situ principal stresses. • Vertical containment of fractures. • Efficient numerical procedures to address the coupled fluid-solidmechanics in 3D.

Dynamics of shear localization in thermally-softening ductile solids

Frictional sliding at high rates - oblique plate impact • Friction is low at high rates. • Abrupt change in normal stress σ does not cause abrupt change inshear stress τ -- critical to well-posed bimaterial fault sliding models!

[Rice, JGR 2006]

Punchbowl PSS, composite based on Chester & Chester [Tectonophys ‘98] & Chester & Goldsby [SCEC ‘03]

5 mm

Earthquake shear is highly localized!

[Heermance, Shipton & Evans, BSSA, 2003]Core retrieved across the Chelungpu fault, which hosted the 1999 Mw 7.6 Chi-Chi,Taiwan, earthquake: Suggests slip at 328 m depth traversewas accommodated within a zone ~ 50–300 μm thick.

• Hole B, fault at 1136 m depth: PSZ is ~3 mm thickPSZ layering defined by variations in concentrations of clay minerals and clasts,comparable to structures produced in high-rate rotary shear experiments.

Two other Chelungpu Fault,Taiwan boreholes[Boullier et al., GGG 2009, GSL 2011]:Principal Slip Zone (PSZ) localized within black gouges

• Hole A, fault at 1111 m depth: PSZ is ~2 cm thick

A

B

h ≈ 3 mmWibberley (2003)

Median TectonicLine Fault, Japan

k,

q = −k

η f(∇p − ρ f g)

= fluid flux relative to solid host

Quandary in seismology:

• Lab estimates of friction coefficient are usually high, f ~ 0.6-0.8.

Shear strength τ = f x (σn – p), where:

σn = normal stress clamping the fault shut p = pore pressure in infiltrating fluid phase

• Fault slip zones are thin (despite wide damage zones, 1-103 m).

==> If those f prevail during seismic slip, we should find

• measurable heat outflow near major faults, and/or

• extensive melting along exhumed faults.

Neither effect is generally found.

One line of explanation: Weak faults: τ = f x (σn – p)

• Fault core materials are different, have very low f (e.g., like some clays).

• f isn’t low, but pore pressure p is high over much of the fault.

Another line: Statically strong but dynamically weak faults, e.g., due to thermalweakening in rapid, large slip:

• Processes expected to be important from start of seismic slip:

- Flash heating of asperity contacts, reduces f in rapid slip.

- Thermal pressurization of in-situ pore fluid, reduces effective stress.

• Other processes that may set in at large enough slip or rise in T: - Thermal decomposition, fluid product phase at high pressure

(e.g., CO2 from carbonates; H2O from clays or serpentines).

- Gel formation at large slip in wet silica-rich faults.

- Nanoparticle weakening, physics still unclear.

• Ultimately:

- Melting at large slip, if above set has not limited increase of T.

One line of explanation: Weak faults: τ = f x (σn – p)

• Fault core materials are different, have very low f.

• f isn’t low, but pore pressure p is high over much of the fault.

Another line: Statically strong but dynamically weak faults, e.g., due to thermalweakening in rapid, large slip:

• Processes expected to be important from start of seismic slip:

- Flash heating of asperity contacts, reduces f in rapid slip.

- Thermal pressurization of in-situ pore fluid, reduces effective stress.

• Other processes that may set in at large enough slip or rise in T: - Thermal decomposition, fluid product phase at high pressure

(e.g., CO2 from carbonates; H2O from clays or serpentines).

- Gel formation at large slip in wet silica-rich faults.

- Nanoparticle weakening, physics still unclear.

• Ultimately:

- Melting at large slip, if above set has not limited increase of T.

V = slip rate

asperity diameter

T = asperity temperature

Tf = average temperature of fault surfaces

Flash heating of microscopic frictional asperity contacts[Rice, EOS 1999; JGR 2006; Beeler and Tullis, EOS 2003, Beeler et al. JGR 2008,

building on Bowden and Thomas, 1954; Archard, 1958/59; Ettles,1986; Lim and Ashby, 1987.]

contact shear stress

T, asperity temperature

Tf Tw , weakening temperature

τc

"Weakening" slip rate:

Vw = π αthD

Tw − Tfτc ρc

⎛⎝⎜

⎞⎠⎟

2

When V > Vw , asperity

is weak for some of its

life; suggests friction coef

f ≈ fslowVwV

+ fweak 1−VwV

⎛⎝⎜

⎞⎠⎟

= fweak + ( fslow − fweak )VwV

when V > Vw .

~ 0.1 μ

Arkansas novaculite (~100% quartzite)

0.36 m/s

Vw ≈ 0.14 m/s

[Tullis & Goldsby, SCEC, 2003; EOS, 2003]

Rotary shear, 1.2 mm pre-slip at ~10 μm/s, followed by rapid

slip for remaining 43 mm.

At low V, f ≈ 0.65

At V > 0.3 m/s, f ≈ 0.30

Torsional Kolskybar apparatus

[Yuan & Prakash, Int. J.Solids & Structures, 2008]

Slip at V ≈ 2-4 m/s, resulting in f ≈ 0.20.

Arkansas novaculite (quartzite)

(Experiment becomesuninterpretable after smallslip, marked, due to crackingin wall of specimen.)

One line of explanation: Weak faults: τ = f x (σn – p)

• Fault core materials are different, have very low f.

• f isn’t low, but pore pressure p is high over much of the fault.

Another line: Statically strong but dynamically weak faults, e.g., due to thermalweakening in rapid, large slip:

• Processes expected to be important from start of seismic slip:

- Flash heating of asperity contacts, reduces f in rapid slip.

- Thermal pressurization of in-situ pore fluid, reduces effective stress.

• Other processes that may set in at large enough slip or rise in T: - Thermal decomposition, fluid product phase at high pressure

(e.g., CO2 from carbonates; H2O from clays or serpentines).

- Gel formation at large slip in wet silica-rich faults.

- Nanoparticle weakening, physics still unclear.

• Ultimately:

- Melting at large slip, if above set has not limited increase of T.

Shear of a fluid-saturated gouge layer

• Two undeforming half-spaces are moved relative toeach other at a speed V.

• All deformation accommodated in gouge layer, leadinga to a nominal strain rate,

γ 0 =

V

h .

Thermo-mechanical model in gouge layer

∂p∂t

−αhy

∂2 p∂y2

= Λ ∂T∂t

τ = f (γ )(σ n − p)

∂T∂t

−α th

∂2T∂y2

= τγρc

Mechanical equilibrium

• Shear stress modeled using the effective stress andrate-strengthening friction,

Conservation of fluid mass

Conservation of energy

• To model the deforming gouge layer we use,

f (γ ) = f0 + (a − b)logγγ 0

⎛⎝⎜

⎞⎠⎟

(we assume a − b ≡ γ df (γ ) / dγ( )γ =γ 0> 0)

∂τ∂y

= 0, ∂σn∂y

= 0

Rice, Rudnicki & Platt (in prep for JGR 2012)

V / 2

V / 2

h

Shear between moving rigid blocks of perfectly insulating, impermeable material :

Exact homogeneous shear solution (Lachenbruch,

JGR, 1980,version ignoring dilatancy) :

τ (t) = f σn − p(t)( ) = f σn − p(0)( )exp −foΛρc

γ ot⎛⎝⎜

⎞⎠⎟

, γ o =V

h

[characteristic weakening strain =ρcfoΛ

≈ 10-20, for fo ≈ 0.4]

But is that solution stable?

Not unless h is very small ! (Rice & Rudnicki, AGU, 2005) :

Thickest possible h (call it Wcrit ) for stable

homogeneous shear is Wcrit = λshr / 2,

[λshr = longest wavelenth λ for stable linearized response

to infinitesimal exp(2πiy / λ) perturbation], implying

Wcrit =π 2

2 + foa − b

⎛⎝⎜

⎞⎠⎟

ρcfoΛ

αth +αhy( )V

.

u(y,t) = γ oy =

V

hy

σnτ (t)

Stable only if h ≤Wcrit .

Rice, Rudnicki & Platt (in prep for JGR 2012)

Estimates of maximum stable shear layer thickness Wcrit :

Wcrit =π 2

2 + foa − b

⎛⎝⎜

⎞⎠⎟

ρcfoΛ

αth +αhy( )V

(indep. of σn )

Results, using fo = 0.4, fo

a − b= 20, V = 1

m

s, αth = 0.7

mm2

s, ρc = 2.7

MPa

ºC :

Low estimate (Based on lab properties of intact Median Tectonic Line gouge [Wibberley and Shimamoto,

2003] at effective confining stress = 125 MPa and T = 200ºC -- corresponding to ~ 7 km depth):

Λ = 0.70 MPa

ºC , and αhy = 1.5

mm2

s ⇒ Wcrit = 10 μm

High estimate (Accounts very roughly for fresh damage of the initially intact fault gouge, introduced at the

rupture front just before and during shear, by increasing permeability k to kdmg = 5-10 k, and increasing

drained compressibility βd to βddmg = 1.5-2 βd ):

Λ ≈ 0.34 MPa

ºC , and αhy ≈ 3.5

mm2

s ⇒ Wcrit ≈ 40 μm

Rice, Rudnicki & Platt (in prep for JGR 2012)

(Kitajima, Chester, Chester & Shimamoto, JGR 2010): Rapid rotary shear of thePunchbowl fault gouge: Disaggregated to form Unit 1. Early shear forms Unit 2.Unit 3 (fluffier) formed by T-induced fluid phase change (thermal pressurization). Unit 4 is a localized shear structure.

0.1

ms

0.7

ms

1.3

ms

Veq

For all:σn = 0.6 MPa

δeq = 24-29 m

(Kitajima, Chester, Chester & Shimamoto, JGR 2010)

Blue arrows ( ) below: f vs. slip when σn = 0.6 MPa compared for V = 0.1 & 1.3 m/s.

V = 0.1 m/s

V = 1.3 m/s

Shear of a fluid-saturated gouge layer:Full nonlinear numerical solutions

(vs. linearized perturbations)

• Two undeforming half-spaces are moved relative toeach other at a speed V.

• All deformation accommodated in gouge layer leadinga to a nominal strain rate, γ 0 =

V

h

Platt, Rice & Rudnicki (AGU, Fall 2010, in prep for JGR 2012)

Strain localization• Simulations using representative physical valuesshow that strain localization does occur.

h = 5mm

• Deformation has localized to a zone orders ofmagnitude thinner than the layer, W << h.

Platt, Rice & Rudnicki (AGU, Fall 2010, in prep for JGR 2012)

Independence of h

• We want to understand if the localization width W isbeing influenced by the initial choice of h.

• W is almost independent of h for large enough value of h.

Platt, Rice & Rudnicki (AGU, Fall 2010, in prep for JGR 2012)

Formula for localized zone width• Numerical simulations show how W depends on thephysical properties of the gouge layer.

W ≈ 9.4 a − bf0

ρcΛf0

αhy +1.9α th

V• We infer the formula,

Λρc

(similar to R&R linear stability result)

Platt, Rice & Rudnicki (AGU, Fall 2010, in prep for JGR 2012)

Implications for dynamic weakening• Now we investigate the weakening behavior of thegouge layers during localization,

h = 0.5 mm h = 5 mm

• Localization leads to additional weakening.

Platt, Rice & Rudnicki (AGU, Fall 2010, in prep for JGR 2012)

One line of explanation: Weak faults: τ = f x (σn – p)

• Fault core materials are different, have very low f.

• f isn’t low, but pore pressure p is high over much of the fault.

Another line: Statically strong but dynamically weak faults, e.g., due to thermalweakening in rapid, large slip:

• Processes expected to be important from start of seismic slip:

- Flash heating of asperity contacts, reduces f in rapid slip.

- Thermal pressurization of in-situ pore fluid, reduces effective stress.

• Other processes that may set in at large enough slip or rise in T: - Thermal decomposition, fluid product phase at high pressure

(e.g., CO2 from carbonates; H2O from clays or serpentines).

- Gel formation at large slip in wet silica-rich faults.

- Nanoparticle weakening, physics still unclear.

• Ultimately:

- Melting at large slip, if above set has not limited increase of T.

Examples, thermal decomposition:

Dolomite, CaMg(CO3)2 (De Paola et al., Tectonics, 2008, Geology, 2011; Goren et al., J. Geophys. Res., 2010):

• At T ~ 550ºC, dolomite decomposes to calcite, periclase, and carbon dioxide:CaMg(CO3)2 CaCO3 + MgO + CO2

• At T ~ 700-900ºC, the calcite further decomposes to lime and carbon dioxide:CaCO3 CaO + CO2

Many clays and hydrous silicates (Brantut et al., J. Geophys. Res., 2010):

• At T ~ 500ºC (~300ºC for smectite, ~ 800ºC for chlorite), decompositionreleasing H2O starts.

Gypsum, CaSO4(H2O)2) (Brantut et al., Geology, 2010):

• At T ~ 100ºC, gypsum dehydrates to form bassanite:CaSO4(H2O)2 CaSO4(H2O)0.5 + 1.5 H2O

• At T ~ 140ºC, bassanite turns into anhydriteCaS4(H2O)0.5 CaSO4 + 0.5 H2O

[From N. Brantut (2011)]

Han, Shimamoto, Hirose, Ree & Ando [Sci., 2007]: Carbonate faults

One line of explanation: Weak faults: τ = f x (σn – p)

• Fault core materials are different, have very low f.

• f isn’t low, but pore pressure p is high over much of the fault.

Another line: Statically strong but dynamically weak faults, e.g., due to thermalweakening in rapid, large slip:

• Processes expected to be important from start of seismic slip:

- Flash heating of asperity contacts, reduces f in rapid slip.

- Thermal pressurization of in-situ pore fluid, reduces effective stress.

• Other processes that may set in at large enough slip or rise in T: - Thermal decomposition, fluid product phase at high pressure

(e.g., CO2 from carbonates; H2O from clays or serpentines).

- Gel formation at large slip in wet silica-rich faults.

- Nanoparticle weakening, physics still unclear.

• Ultimately:

- Melting at large slip, if above set has not limited increase of T.

Model for decomposing gouge material

∂p∂t

= Λ ∂T∂t

+αhy

∂2 p∂y2

+ Pr∂ξ∂t

∂T∂t

= τγρc

+α th

∂2T∂y2

− Er

∂ξ∂t

• We assume that the reaction follows an Arrheniuskinetic law,

• To model the deforming gouge layer we use,

∂ξ∂t

= A 1− ξ( )exp − Q

RT⎛⎝⎜

⎞⎠⎟

Platt, Brantut & Rice (AGU, Fall 2011)

Linear stability analysis(linear perturbation from homogenously sheared state)• We track the critical half-wavelength as a function ofthe ambient fault temperature,

λc = 2π αth +αhy( ) (a − b)ρc

f02Λγ 0

λc = 2π αhyErPr

(a − b)ρcf02γ 0

ºCPlatt, Brantut & Rice (AGU, Fall 2011)

Like R&Rthermal press.result.

Different materials• Using the linear stability analysis, we now try to finda prediction for localized zone width by setting,

100

800

500

550

900

Tc (°C)

2163589Gypsum

32586496Talc

8615993627Kaolinite

61252228Lizardite

1864213093Calcite

W (μm)Pr (MPa)Er (K)Mineral

Table from N. Brantut (Platt, Brantut & Rice, AGU, Fall 2011)

Some Consequences for Earthquake Dynamics

Possibly resolving a quandary in seismology:

Major faults operate under low overall drivingstress, in a manner that generates negligibleheat outflow and involves slip on extremelythin zones.

What thermo-hydro-mechanical processesmight cause that?

coworkers:Eric M. Dunham (Stanford Univ.)

Nadia Lapusta (Caltech)Hiroyuki Noda (Caltech)

Alan W. Rempel (Univ. Oregon)

Dynamic rupture simulations, incorporatingflash heating of asperity contacts and thermalpressurization of pore fluid, with parametersconstrained (to the extent possible) bylaboratory observations

[Noda, Dunham & Rice, JGR 2009]

τ bRupture nucleated (bylocal overstressing) onfault under uniformbackground shear stress

τ bτ = σe f = (σn − p z=0 ) f

x

z

Flash heating (in dynamic rupture simulations, Noda, Dunham & Rice, JGR 09)

Rate and state friction concepts, together with flash heating atmicroscopic contacts during rapid slip:

Effective stress law:

τ = σe f = (σn − p z=0 ) fpore pressure on slip surface

given, fixed compressive normal stress

friction coefficient

df

dt=a

V

dV

dt−V

Lf − fss (V )[ ]

• fLV (V ) = fo + (a − b)lnV

Vo

⎛⎝⎜

⎞⎠⎟

• fss (V ) =fLV (V ) , V ≤ Vw ,

fw + fLV (V ) − fw( )VwV

, V ≥ Vw ,

⎧⎨⎪

⎩⎪

with Vw = π αthD

Tw − Tτc ρc

⎛⎝⎜

⎞⎠⎟

2

;

[Noda, Dunham & Rice, JGR `09]

Based on Tullisand Goldsby [SCEC, `03] parameters

fo, fw and Vw for granite.

Based on Zheng & Rice (BSSA,1999), sustained rupture propagation expected to be possible, once nucleated, for background stress

τ b > τ pulse ≈ 0.25σ0

Thermal pressurization (in dynamic rupture simulations, Noda, Dunham & Rice, JGR 09)

Effective stress law:

τ = σe f = (σn − p z=0 ) f

∂T∂t

= αth∂2T

∂z2+

τρc

V

2π wexp −

z2

2w2

⎛

⎝⎜

⎞

⎠⎟

∂p∂t

= αhy∂2p∂z2

+ Λ∂T∂t

Thermal pressurization, finite thickness of slipping zone, with Gaussian shear distribution having r.m.s. width w:

pore pressure on slip surface

Conservation of energy (first law of thermodynamics):

Conservation of fluid mass(neglecting dilatancy):

given, fixed compressive normal stress

friction coefficient

αth ~ 0.7 mm2/s; αhy ~ 0.9 - 6 mm2/s at mid-seismogenic depths; ρc ~ 2.7 MJ/m3K;Λ ~ 0.3 - 1.0 MJ/m3K (Rice [JGR 2006] & Rempel & Rice [ibid], based on Wibberley [EPS

2002, priv comm 2003] & Wibberley & Shimamoto [JSG 2003], and estimates of damage)

τ

τper = 30MPaDper = 5cm

τpulse

[Noda, Dunham & Rice, 2008; work preliminary to JGR 2009]

Shown:The case

w = 0,slip on a

plane.

τ

τper = 30MPaDper = 5cm

τpulse

[Noda, Dunham & Rice, 2008; work preliminary to JGR 2009]

Shown:The case

w = 0,slip on a

plane.

Noda, Dunham & Rice [JGR, 2009] longest simulation to date: ~30 m rupture length

left: Distribution of slip δ showing a ~linear increase with x by 0.14 mm/m.right: History of slip rate V and shear stress τ at x = 8 m:

• Peak V is extremely high (> 100 m/s). • τ b (= initial shear stress) ~ 29 MPa = 0.23 (σ – po) [σ – po = 126 MPa]. • τ peak (= peak stress at rupture front) ~ 107 MPa = 0.85 (σ – po) • τ b – τ final (= seismic stress drop Δσ) ~ 3 MPa

V (

m/s

)

τ (M

Pa)

Comparing a growing slip pulse at τb = 0.230 (σ0 – p0)to an enlarging shear crack at τb = 0.238 (σ0 – p0)

Noda, Dunham & Rice [JGR, 2009]

For self-healing slip pulse simulation,seismic stress drop τ b – τ final ~ 3 MPa.

For crack-like simulation,seismic stress drop τ b – τ final ~ 19 MPa.

approximate region slippingat a particular moment in time

Heaton [PEPI, 1990]

… and Seismic Slip Inversions forNatural Events Suggest Self-Healing!

For self-healing pulsesimulation shown,seismic stress dropτ b – τ final ~ 3 MPa.

For crack-likesimulation shown,seismic stress dropτ b – τ final ~ 19 MPa.

[Allmann & Shearer,“Global variations of

stress drop for moderateto large earthquakes”,

JGR, 2009]

Noda, Dunham & Rice [JGR, 2009]

Both predict (if projected to circular fault) Seismic Moment Mo [Nm] ≈ λ ×1017 t [s]( )3;

λ ≈ 1.7 for slip pulse, λ 10.5 for crack; compare, λ ≈ 2 for Parkfield 2004 [Uchide]

[Using δ 3D /δ 2D= 0.73, μ=35 GPa, ρ=2800 kg/m3 ( cs = 3.5 km/s ), and vr = 0.8cs ]

Comparing a growing slip pulse at τb = 0.230 (σ0 – p0)to an enlarging shear crack at τb = 0.238 (σ0 – p0)

[Hickman & Zoback, GRL 2004]

Simulations show growing pulse for ~ 0.22-0.24

Partial Summary:

The simulations are based on laboratory friction andporomechanical studies, on geological characterizations of faultzones, and on mathematical modeling of heating andweakening and of elastodynamics.

They have no input from seismology, heat flow, or regionalstress magnitude/direction studies!

Yet they predict results, in particular: • fault operation at low overall shear stress, • self-healing rupture mode, • plausible magnitude range of static stress drop, • scaling of slip with rupture extent, and • scaling of slipping pulse length with rupture extent*,which look somewhat like earthquakes on major faults asconstrained by seismology, heat flow and stress studies.

* May be too small? And what sets scale (nucleation?) not yet clear.

Implications for seismic hazardThe fact that a segment is creeping does notpreclude it from having large coseismic slip.

Page adapted from H. Noda and N. Lapusta (2012)

[Tanikawa and Shimamoto, 2009]

Summary of lab-measured physical propertiesfor the fault that hosted Chi-Chi earthquake

using core-samples (from 200 - 300 m depth)

page from H. Noda and N. Lapusta

page from H. Noda and N. Lapusta

Earthquake sequence simulationwith lab-measured physical properties

60

page from H. Noda and N. Lapusta

Long-term fault behavior page from H. Noda and N. Lapusta

•

•

•

•

Important consequence of high-velocity frictional weakening

(studies by Hiroyuki Noda and Nadia Lapusta, 2009-2011)

page from H. Noda and N. Lapusta

Conclusions:

• τstatic much larger than τseismic.

• Documented weakening (and localization) processes:- flash heating;- thermal pressurization, in-situ & decomp product;- nanoparticle-related (physics remains unclear);- melting.

• Static strength τstatic = fsσn is unreliable predictor of pre- earthquake stress on major, well-slipped , smooth faults.

• Such faults may operate near or slightly above τpulse (a τ at which a small event, once nucleated, propagates indefinitely).

• Roughness may keep less mature faults from full benefit of dynamic weakening; to slip, side-walls must be deformed

• The fact that a segment is creeping does not preclude it from having large coseismic slip (Chi-Chi, 1999, Tohoku-Oki, 2011).