Shear Localization in FluidSaturated Fault Gouge

1
Shear Localization in Fluid-Saturated Fault Gouge

• James R. Rice1,2, John W. Rudnicki3, Victor C.
  Tsai1
• 1. Department of Earth and Planetary Sciences,
  Harvard University
• 2. Division of Engineering and Applied Sciences,
  Harvard University
• 3. Dept. of Mechanical Engineering and Dept. of
  Civil Environmental Engineering, Northwestern
  University

2
Motivation/Observations

• Heat flow at major faults Smaller than predicted
• Extreme localization Prominent slip surfaces
  observed
• e.g. Chester, Evans Biegel 1993, Chester
  Chester 1998, Chester Goldsby 2003, Wibberley
  Shimamoto 2003
• Permeability measured in fault core very small
• e.g. Wibberley Shimamoto 2003, Lockner et al
  2000
• ? Thermal pressurization of fluids may be
  important

3
1-D Model for Shear in a Fluid-Saturated Layer
h
Building on Sibson 1973, Lachenbruch 1980, Mase
Smith 1987, Segall Rice 1995, Sleep 1995,
Andrews 2002, Garagash Rudnicki 2003
4
1-D Model for Shear in a Fluid-Saturated Layer
Building on Sibson 1973, Lachenbruch 1980, Mase
Smith 1987, Segall Rice 1995, Sleep 1995,
Andrews 2002, Garagash Rudnicki 2003
5

• Governing equations
• Energy Equation Fluid Mass Conservation
• Equations of Motion Friction Law
• p/T dependence of rf nel

6
Stability Analysis

• Assume qh, qf 0 at edge, const. material
  parameters
• Spatially uniform case (Lachenbruch 1980)

• Is this solution stable?
• No Localizes to plane since f const and
  dnpl/dt 0
• We add two stabilizing features (separately) and
  ask whether shear then localizes and, if so, what
  thickness is predicted
• 1. Rate strengthening friction
• 2. Dilatancy increasing with shear rate

7
Linear Stability Analysis

• Rate strengthening , assuming
  dnpl/dt 0
• Add exp(2piy/l) perturbations and linearize (RR,
  in prep.)
• Obtain ODE for ?
• Which solutions are stable?
• V 1 m/s, H 0.04 0.12
• ath 0.7 mm2/s, ahy 1.5 3.5 mm2/s
• lcr h ? h 10 80 mm

8
Linear Stability Analysis
Segall Rice 1995

• , no rate dependence
  of f
• Proceed as before
• Growth of all perturbations are finite
• When is growth significant?
• Cumulative perturbation strain gt 105
  characteristic strain
• lcr h ? h 7 11 mm

9
Nonlinear Calculations

• Examine dependencies on
• nonlinear terms
• material property (f, k, bf, lf, hf ) changes
  with p, T
• Use values from Blanpied et al 1998, Keenan et
  al 1978, and Wibberley Shimamoto 2003
• Most terms give rise to small effects

10
Typical Dynamics
y (mm)

• Initially consistent with Linear Stability
  Analysis

11
Conclusions Future Work

• Shear localizes, even w/ stabilizing mechanisms
• however
• Parameters for the Earth are not well known
• Permeability, friction law,
• To do
• Perform systematic analysis of parameter space
• Include full rate-state dependence of friction
• May be difficult without better experimental data

12
Linear Stability Analysis
Rice Rudnicki, in prep.
drawn for z 40 V 1 m/s cth 1 mm2/s
Homogeneous shear possible
High end parameters
Homogeneous shear not possible
Low end parameters