Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary Physics Scripps Institution of Oceanography University of California San Diego, USA Batsheva Seminar, Jan 26, 2009

NN F friction

Rate and state dependent friction Rate effect State effect Total   - coef. of friction at reference velocity V 0 V - slip rate a, b - empirical constants O( )  - state variable L - critical slip distance Dieterich, 1979; Ruina, 1983 … established for slip rates of O( m/s). Extrapolation to seismic slip rates O(1 m/s) predicts reductions in  of order of 10%.

Is physics different for high- speed sliding? High-speed rotary shear experiments: complex evolution of shear stress on the slip interface (Tutsumi and Shimamoto, 1997; Hirose and Shimamoto, 2003; Brown and Fialko, 2008) What are the mechanisms of frictional sliding at seismic slip rates? How efficient is melt lubrication? Is “viscous braking” (Fialko, 1999; 2004; Koizumi et al., 2005) relevant to seismic faulting? Hirose and Shimamoto, 2003

Is physics different for high- speed sliding? High-speed rotary shear experiments: complex evolution of shear stress on the slip interface (Tutsumi and Shimamoto, 1997; Hirose and Shimamoto, 2003; Brown and Fialko, 2008) What are the mechanisms of frictional sliding at seismic slip rates? How efficient is melt lubrication? Is “viscous braking” (Fialko, 1999; 2004; Koizumi et al., 2005) relevant to seismic faulting?

Pseudotachylites: Field evidence for frictional melting on a fault plane

viscous stress singularity at w=0 Stefan problem: start with some finite w, and solve for w(t) (Fialko, 1999; Sirono et al., 2006)

critical melt fraction (Kitano et al., 1981) - thermal conductivity L – latent heat of melting/crystallization  – melt fraction Rheology of melt-solid suspension: (Fialko and Khazan, 2005)

High-speed friction experiments on argillite: Both shear stress and melt thickness increase with slip Increases in melt viscosity, likely due to dehydration  :  Shear stress  : Viscosity of melt layer d  /dt : Shear strain rate V : Slip rate w : Thickness of melt layer Shear stress,  1.25 Shear strain rate, v/w Fraction of solid grain2119 Ujie et al., JGR (in press)

? Flash melting (Rice, 1999; 2006) Silica gel formation (DiToro et al., 2004)

High-speed experimental apparatus - A horizontal rotary lathe with controlled normal load, torque, and velocity -Temperature sensors within 1-2mm from the shear zone and the back of the sample to monitor frictional heating - Real-time data acquisition and display for interactive control We use ring-shaped samples with internal diameter of 5.8 cm and external diameter of 8.1 cm to minimize variations in slip rate across the sample. An example (top): a sample of granite after a high-speed run. Note the uniform loss of gouge across the surface. (Left): Experim ental apparatu s.

residual friction  r

Evolution of residual friction  r with velocity diabase

Possible mechanisms Flash melting (Rice 1999, 2006) Thermally activated plasticity Flash melting: - extreme localization - asperities have to be sufficiently large - difficulty explaining observed strengthening Other mechanisms: - silica gels - nanopowders - ablation (for C-rich rocks) … Temperature-dependent rheology with heating/yielding distributed through asperity; peak temperature is lower

Theoretical yield strength: Elastic moduli are temperature-dependent: Wachtman-Anderson relation for temperature dependence of elastic modulus G(T)~ (1-  T) G 0

(olivine!)

Mathematical model Assumptions: The average strength of individual asperities is a direct proxy for the coefficient of friction (area of true contact is independent of V); Heat transfer is dominated by conduction The asperity strength depends on two components: 1) Temperature of the shear zone (calculated based on the measured evolution of shear stress) 2) Flash heating (calculated using the temperature dependence of theoretical strength) asperity size slip velocity “flash” heating background temperature

Monitoring shear zone temperature

Thermal evolution of the shear zone: measurements vs. predictions based on 1-D unsteady conduction model in the shear zone elsewhere mm

Initial surface textureMelt initiation Melting and aggregation of small grains Striations on melt surface SEM images of the wear products (gouge): effective asperity size O(  m) Gouge

Example of simulated flash heating of an individual asperity a=5  m, T b =200 o C, V=0.1 m/s

… non-adiabatic heating … strain localization

“Best-fitting” models ( x 5)

Conclusions Coefficient of friction shows a systematic and significant decrease at slip velocities greater than 0.1 m/s, with an approximate scaling  ~V -D (D depends on normal stress) We propose that this decrease results from temperature dependence of intrinsic strength of transient contacts Melting is not required to explain the observed weakening … nor is the assumption of adiabatic heating (i.e., asperities don’t need to be >>  m) As the local asperity temperature approaches solidus, flattening and collapse of asperities result in increases in the nominal contact area (and possibly in increases in the effective friction, depending on the normal stress) In the post-melting regime, the dynamic shear stress is nearly independent of normal stress and is O(MPa) -> stress drops due to pseudotachylite-generating events are nearly complete

Summary of theoretical modeling of macroscopic melting: Melt zone localization and significant weakening occurs once the melt fraction exceeds a critical value (~50%) After the onset of weakening, melting of the wallrock is slow and inefficient -> PT layers likely formed instantaneously by bulk melting of a slip zone, rather than by progressive thermal erosion of the fault walls

DiToro et al., Science 2006

Evolution of friction with slip distance

Incipient Melting

F – axial force M – torque if normal stress

Direct shear experiments slip rates – m/s ambient temperatures – o C normal stress – 1-20 MPa

critical weakening rate for flash melting (Rice, 2006)