Adv Advanced anced Worksho shop p on n Ea Earthquake Fa Fault Mechanics: The Theory, , Simulation on and Observation ons ICTP, Trieste, Sept 2-14 2019 Lecture 3: fault friction Jean Paul Ampuero (IRD/UCA Geoazur)
Lecture 3: earthquake dynamics from the standpoint of fault friction • Zoom on the process zone • Laboratory-based friction laws • Rupture pulses • Stress drop scaling J. P. Ampuero - Earthquake dynamics 2
Rock strength is finite Byerlee’s law ! ∼ 0.6& J. P. Ampuero - Earthquake dynamics 3
The process zone Secondary micro-cracks generated by a dynamic rupture Process zone imaged by acoustic emissions in (mode II, numerical simulation by laboratory fracture of intact rock Yamashita 2000 ) Orientation Density Stress singularities are unphysical: inelastic processes occur at the small scale (damage, weakening) J. P. Ampuero - Earthquake dynamics 4
Fault zone thickness Fault zone thickness and maturity (Savage and Brodsky, 2011) [Chester and Chester, 1998] J. P. Ampuero - Earthquake dynamics 5
Cohesive zone models Slip and stress along a shear crack Assumption: dissipative processes (only half crack shown, Andrews 1976) are mapped onto the fault plane, represented by a distribution of Slip Stress cohesive stresses near the crack tip Usual cohesive models: • constant (Dugdale, Barenblatt) Singular crack • linearly dependent on distance to Process crack tip (Palmer and Rice, Ida) zone t s • linearly dependent on slip (Ida, Andrews) t d Slip weakening crack J. P. Ampuero - Earthquake dynamics 6
Cohesive zone size Cohesive stresses t (x) generate a negative stress intensity factor • K c = - Slip Stress t s that cancels the singularity : K + K c = 0 That condition determines the size of the cohesive zone • t d with C 1 ≈1 (for a linear distribution: C 1 =9 p /32) From last lecture (mode III): Cohesive zone size 1 − % & /( & Λ ) & Λ = where Λ ) = * + 2-. / / 0 1 − 0 2 J. P. Ampuero - Earthquake dynamics 7
Cohesive zone size 1 − % & /( & Λ ) Λ = where Λ ) = * + 2-. / / 0 1 − 0 2 & t 45 = Λ/% Increasing rupture velocity à contraction of the process zone à higher frequency radiation à larger ground acceleration ∼ 1/ 7 J. P. Ampuero - Earthquake dynamics 8
Tohoku: high-frequency radiation deeper than low-freq slip Brownish symbols: 1Hz radiators extracted from back- projection movies Colored contours: static slip from GPS & tsunami data Spatial complementarity of high- and low-frequency slip: HF radiation is deeper than static slip HF radiation occurs even where the rupture is slow Ito et al (2007)
Tohoku: high-frequency radiation deeper than low-freq slip |<- Bottom Trench ->| |<- Bottom Trench ->| Ito et al (2007) Huang, Ampuero, Kanamori (2013)
Friction ! Fault resistance is classically described by friction Byerlee’s law ! ~ 0.6& More lateral force is needed to slide a taller, heavier object The resisting force is friction at the base of the object Friction force is proportional to the compressive force J. P. Ampuero - Earthquake dynamics 11
A brief history of fault friction • Coulomb friction: strength S STRENGTH T R E S S SLIP
A brief history of fault friction • Coulomb friction: strength • Static/dynamic friction: stress drop S Static Stress T drop R E Dynamic S S SLIP
A brief history of fault friction • Coulomb friction: strength • Static/dynamic friction: stress drop • Cohesion models: fracture S Fracture T energy G c energy R G c E S S Nucleation size SLIP L c ~ µ G c / Dt 2
A brief history of fault friction • Coulomb friction: strength • Static/dynamic friction: stress drop • Cohesion models: fracture S T energy Gc W = weakening R rate • Slip weakening friction: critical E slip Dc, weakening rate W S S SLIP Lc ~ µ / W D c
A brief history of fault friction • Coulomb friction: strength • Static/dynamic friction: stress drop • Cohesion models: fracture S energy Gc T STATE • Slip weakening friction: R E critical slip Dc, weakening S rate W S • Rate-and-state friction: SLIP RATE healing, velocity weakening (a,b)
Laboratory-derived friction laws Sandwich configuration (Ohnaka and Shen 1999) Requirements : High normal stress (100 MPa) • High slip rate (1 m/s) • Large displacements (>1 m) • Large sample (>L c ) and high resolution • Gouge + fluids • Only partially met by current experiments Rotary configuration (Chambon et al 2002) J. P. Ampuero - Earthquake dynamics 17
Laboratory-derived friction laws Low resolution experiments (≈ spring+block ) record the average stress and slip à macroscopic friction High resolution experiments are densely instrumented à local friction + rupture nucleation and propagation S = stress D = slip Large scale experiment Dieterich (1980) J. P. Ampuero - Earthquake dynamics 18
Slip weakening friction Slip weakening occurs during fast dynamic rupture. Linear slip weakening is a usual simplified model. Chambon et al (2000) Important parameters: • D c = characteristic slip, associated to micro-contact evolution or grain rearrangement. Without gouge D c ≈ 0.1 mm. With gouge D c >10 cm Slip (cm) Strength drop: t s – t d • Usually a small fraction of normal stress ≈ 0.1 s • Fracture energy of a linear slip weakening model : G c = ½ ( t s - t d ) D c J. P. Ampuero - Earthquake dynamics 19
Slip-weakening friction model Primary parameters: dynamic friction coefficient ! " and fracture energy Gc They control stress drop, rupture speed and rupture arrest Secondary parameters: critical slip distance Dc and strength drop ! # − ! " They control nucleation, supershear transition and peak slip velocity
Dynamic Rupture Simulation J. P. Ampuero - Earthquake dynamics 21
Nucleation size $% & Nucleation size: ! " = ' ( )' * Uenishi and Rice (2003)
̇ Exponential initiation Kobe earthquake M7.2 Linear slip-weakening: Δ" = " $ − " & '/' ) If there is some viscosity in the fault behavior: Δ" = * ̇ ' Equating both: ' = ,' Hence ' - ∼ exp ,- where , = " $ − " & /*' ) One form of viscosity is radiation damping, * = 2/24 $
Seismological observations A Mw3.9 earthquake in Alaska triggered by Love waves from the April 11, 2012 Mw 8.6 Sumatra earthquake Tape et al (2013)
Seismological observations Nucleation phase of the Mw3.9 Alaska triggered earthquake Tape et al (2013)
Exponential initiation ! = ' & − ' ) /., - ! " = 2% & ' & − ' ) /+, - Simulations Ripperger et al (2007) Observations Tape et al (2013)
Seismological constraints Finite source Guatteri and Spudich (2000) + FDM inversion à slip à stress Dynamic friction parameters suffer from strong trade-off A B Same G c à same strong motion <1Hz Ide and Takeo (1997)
Faults operating at low stress How large is stre ss drop Δ" compared to stren gth drop " # − " % ? From seismological observations: Δ" = 1 − 10 Mpa From friction and lithostatic overburden: " # − " % = ) * # − * % ~100 ,-. à Δ" ≪ " # − " % Why so small?
Faults operating at low stress Fault loaded by deep creep à stress concentration at the base of the seismogenic zone Interseismic slip Interseismic stress Seismogenic zone Creeping zone z z
Faults operating at low stress Static strength ! " Interseismic stress Strength Stress drop drop $ % − $ ' Dynamic strength ! # z Seismogenic depth W
Faults operating at low stress Static strength ! " Interseismic stress Average Strength stress ≪ drop drop % & − % ( $% Dynamic strength ! # z Seismogenic depth W
Faults operating at low stress Fracture energy balance: ! " = $ % &' ∼ )* % + &' à Δ- ∼ 2/! " /1 '3 4 Uenishi and Rice’s nucleation size: 2 " = * 5 6* 7 )* 8 4 * 5 6* 7 ∼ + ≪ 1 à
̇ Rate-and-state friction Second order effects: logarithmic healing (micro-contact creep) and velocity- weakening à Phenomenological rate-and-state friction law introduced by Dieterich and Ruina in the early 1980s Essential ingredients: • non-linear viscosity • evolution effect Most important during slow slip ( ∗ + ) ln ( ∗ * ( ! = ! ∗ + % ln (nucleation and post-seismic) + During fast dynamic rupture, an equivalent D c can be estimated: * = 1 − (* D c ≈ 20 L + ( = slip velocity, * = state variable J. P. Ampuero - Earthquake dynamics 33
Rate-and-state friction at high speed? Most important during slow slip (nucleation and post- seismic) Rate-and-state behaves as slip-weakening during fast dynamic rupture Equivalent : ' ! " = $ ln ≈ 20 $ ' ∗ 0 , " ≈ 1 ' 2 ./$ ln Kaneko et al (2008) ' ∗ J. P. Ampuero - Earthquake dynamics 34
Dramatic velocity-weakening at high speed Goldsby and Tullis (2011) v c Di Toro et al When sliding at high velocity: ! ∼ 1/% J. P. Ampuero - Earthquake dynamics 35
Dramatic velocity-weakening at high speed At high velocity: ! ∼ 1/% Thermal weakening effects Predicted by flash heating (Rice, 2005) Sutter and Ranc (2010) J. P. Ampuero - Earthquake dynamics 36
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