Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and...
-
Upload
lindsey-bailey -
Category
Documents
-
view
217 -
download
5
Transcript of Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and...
![Page 1: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/1.jpg)
Theoretical and Theoretical and experimental investigation experimental investigation
of dynamic friction at of dynamic friction at seismic slip ratesseismic 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
![Page 2: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/2.jpg)
€
F friction = μ ⋅N
€
F friction = τ cAcontact
€
μ =F friction
N=τ cσ n
AcontactAtotal
N N Ffriction
![Page 3: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/3.jpg)
Rate and state dependent friction
Rate effect
State effect
Total
€
τσn
= μ0 + a lnV
V0
⎛
⎝ ⎜
⎞
⎠ ⎟+ b ln
V0θ
L
⎛
⎝ ⎜
⎞
⎠ ⎟
μ - coef. of friction at reference velocity V0
V - slip ratea, b - empirical constants O(10-3-10-2) - state variableL - critical slip distance
Dieterich, 1979; Ruina, 1983
… established for slip rates of O(10-
6-10-3 m/s). Extrapolation to seismic slip rates O(1 m/s) predicts reductions in μ of order of 10%.
![Page 4: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/4.jpg)
Is physics different for high-Is physics different for high-speed sliding? 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
![Page 5: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/5.jpg)
Is physics different for high-Is physics different for high-speed sliding? 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?
![Page 6: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/6.jpg)
Pseudotachylites: Field evidence for frictional melting on a fault plane
![Page 7: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/7.jpg)
![Page 8: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/8.jpg)
w
Vητ ∝ viscous stress
singularity at w=0
Stefan problem: start with some finite w, and solve for w(t) (Fialko, 1999; Sirono et al., 2006)
![Page 9: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/9.jpg)
2
01
11exp),(
−
⎟⎟⎠
⎞⎜⎜⎝
⎛
−−
−⎟⎠
⎞⎜⎝
⎛=φφφη
TB
AT
46.00 =φ 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)
![Page 10: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/10.jpg)
![Page 11: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/11.jpg)
High-speed friction experiments on argillite: Both shear stress and melt thickness increase with slip
Increases in melt viscosity, likely due to dehydration
€
τ =η⋅ dε
dt
⎛
⎝ ⎜
⎞
⎠ ⎟=η ⋅
V
w
⎛
⎝ ⎜
⎞
⎠ ⎟
τ : Shear stress
η : Viscosity of melt layer
d/dt : Shear strain rate
V : Slip rate
w : Thickness of melt layer
Shear stress, τ 1.25Shear strain rate, v/w 0.661
1Fraction of solid grain 21 19
Ujie et al., JGR (in press)
![Page 12: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/12.jpg)
?
Flash melting (Rice, 1999; 2006)Silica gel formation (DiToro et al., 2004)
![Page 13: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/13.jpg)
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): Experimental apparatus.
![Page 14: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/14.jpg)
![Page 15: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/15.jpg)
residual friction μr
![Page 16: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/16.jpg)
Evolution of residual friction μr with velocity
diabase
![Page 17: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/17.jpg)
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 rheologywith heating/yielding distributed through asperity; peak temperatureis lower
![Page 18: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/18.jpg)
€
μ∝1
V1/3
€
μ∝1
V
![Page 19: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/19.jpg)
![Page 20: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/20.jpg)
€
τ c = τ c0 −
1
10
∂G
∂TT
€
τc =G
10
Theoretical yield strength:
Elastic moduli are temperature-dependent:
Wachtman-Anderson relation for temperature dependence of elastic modulus G(T)~ (1-T) G0
![Page 21: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/21.jpg)
€
.
= A sinh ατ c( )[ ]n
exp −B
T
⎛
⎝ ⎜
⎞
⎠ ⎟
![Page 22: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/22.jpg)
€
.=V
a
0.1 m/s
5 μm
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟
τ c =1
αsinh−1 ε
.
Aexp
B
T
⎛
⎝ ⎜
⎞
⎠ ⎟
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥
1
n
€
τ c = τ c0 −
1
10
∂G
∂TT
(olivine!)
![Page 23: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/23.jpg)
Mathematical modelAssumptions: 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)
€
τ c =1
tcτ c T, t( )dt
0
tc
∫
T = Ta (t) + Tb
Ta
Tb
tc =a
V
τ c T( ) =
0.1G T( )
1
αsinh−1 ε
.
Aexp
B
T
⎛
⎝ ⎜
⎞
⎠ ⎟
⎡
⎣
⎢ ⎢
⎤
⎦
⎥ ⎥
1
n
⎧
⎨
⎪ ⎪
⎩
⎪ ⎪
asperity size
slip velocity
“flash” heatingbackground temperature
![Page 24: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/24.jpg)
Monitoring shear zone temperature
![Page 25: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/25.jpg)
Thermal evolution of the shear zone: measurements vs. predictions based on 1-D unsteady conduction model
€
∂T∂t
=∂
∂xκ (x)
∂T
∂x+
μ(t)σ nV
ρcw
€
∂T∂t
=∂
∂xκ (x)
∂T
∂x
in the shear zone
elsewhere
€
w = 0.2 mm
![Page 26: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/26.jpg)
Initial surface texture Melt initiation
Melting and aggregation of small grains Striations on melt surface
SEM images of the wear products (gouge): effective asperity size O(μm)
Gouge
![Page 27: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/27.jpg)
Example of simulated flash heating of an individual asperity
a=5 μm, Tb=200 oC, V=0.1 m/s
![Page 28: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/28.jpg)
… non-adiabatic heating
… strain localization
![Page 29: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/29.jpg)
![Page 30: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/30.jpg)
![Page 31: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/31.jpg)
“Best-fitting” models
( x 5)
![Page 32: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/32.jpg)
ConclusionsConclusions Coefficient of friction shows a systematic and significant
decrease at slip velocities greater than 0.1 m/s, with an approximate scaling μ~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 >> μm) 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
![Page 33: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/33.jpg)
Summary of theoretical modeling Summary of theoretical modeling of macroscopic melting: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
![Page 34: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/34.jpg)
DiToro et al., Science 2006
![Page 35: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/35.jpg)
Evolution of friction with slip distance
![Page 36: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/36.jpg)
Incipient Melting
![Page 37: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/37.jpg)
∫ σμπ=2
1
)()(2 2R
Rn drrrrM
€
σn =F
π (R22 − R1
2)F – axial force
M – torque
21
22
31
32
3
2
RR
RRFM
−−
= μ
22 1
1
2
3
αααμ++
+=
FRM
appif constrr n =)(),( σμ
21 / RR=α
normal stress
![Page 38: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/38.jpg)
Direct shear experiments
slip rates – 10-6-10-3 m/sambient temperatures – 20-500 oCnormal stress – 1-20 MPa
![Page 39: Theoretical and experimental investigation of dynamic friction at seismic slip rates Yuri Fialko and Kevin Brown Institute of Geophysics and Planetary.](https://reader038.fdocuments.us/reader038/viewer/2022110405/56649efc5503460f94c10288/html5/thumbnails/39.jpg)
Vw= ( cth/D)[pc(Tw-Tf)/2, critical weakening rate for
flash melting (Rice, 2006)