GEOL599 Strain localizationIntroduction

Localization mechanisms

● Rarefied zones in granular media facilitate dilatation

● Brittle material hosts cracks and voids which lead to stress concentrations

● Stress dependent grain size and grain size dependent viscosity

● Viscous heating and temperature dependent viscosity

How do these processes interact in the brittle-ductile transition to form

plate boundaries?

Minor questions...

● What is the constitutive law for faults? ● How do fault systems (and seismic hazard

evolve)? ● How are plate boundaries formed and

maintained?● What is the role of transform faults for plate

tectonics? ● What controls the efficiency of mantle

convection?● What makes Earth have plate tectonics, while

other planets ended up empty handed?

Ramsay (1970)

Brittle shear zone

Byerlee (1978)

Resistance to sliding on existing planes

Rutter et al. (2001)

Comparison of Byerlee with in situ stress

Aydin (1978)

Deformation bands in sand stone

2 mm

Aydin and Johnson (1978)

Deformation zones Slip surfaces

Brittle fault system evolution

Aydin and Johnson (1978)

Brittle fault system evolution

Ben-Zion and Sammis (2003)

Ben-Zion and Sammis (2003)

A fault constitutive law that captures all spatio-temporal scales of strain

release does not exist

● But there are heuristic frictional descriptions● And there are damage theories

Marone (1998)

Rate and state friction

One state variable limit cycle

Becker (1999)

Two state variables period doubling

Becker (1999)

Becker (1999)

Scholz (2003)

Stability

Scholz (2003)

Ramsay (1970)

Ramsay (1970)

Ramsay (1970)

Rutter et al. (2001)

~ 50 kmRutter et al. (2001)

Kohlstedt et al. (1995)

Goetze/Peierls creep

Dislocation creep Diffusion creep

Byerlee's law

Brittle - plastic

Ductile

Kohlstedt et al. (1995)

Kohlstedt et al. (1995)

Kohlstedt et al. (1995)

Most of the strength in oceanic lithosphere resides in the poorly

understood transition region between brittle and ductile domain

First principles damage theories

● Elastic● Viscous

Ashby and Sammis (1990)

Ashby and Sammis (1990)

Lyachovsky et al. (1997)

or

Lyachovsky et al. (2001)

Bercovici et al. (2001); Landuyt et al. (2008)

Void-volatile, surface energy theory in the porosity(void)-fineness limit

Bercovici et al. (2001)

Landuyt et al. (2008)

So how does plate tectonics work?

And can we use large scale dynamics as a constraint for

rheology?

Kreemer et al. (2001)

HS3

poloidal

toroidal

RVV flow model

Becker (2006)

new hotspotref. frame

(HS3)

geodesymodel

(GSRM)

viscosity depth 

dependent

viscositytemp.

dependent

dry olivine

creep law

tectonicmodels

geodynamicmodels

Becker (2006)

Bercovici (1995)

Which rheology creates the weak zones?

Bercovici (1995)

Bercovici (1995)

Richards et al. (2002)

Convection models

Tackley (2000)

Increase

in yield

stress

Foley & Becker (2009)

Tackley (2000)

ar = f(d

ss)= f(B -p)

The role of memory

Additional stuff

Constant strain Constant force Constant effectiveforce

Porth (2002)