GEOL599: Strain localization

Fall 2009

Times: Mon 9 – 10am; Wed, 8 – 10am, Location: ZHS200

Instructor: Profs. Thorsten Becker and Yehuda Ben-Zion

Becker contact: ZHS269; (213)740-8365; twb -at- usc.edu

Ben-Zion contact: ZSH109; (213)740-06734; benzion -at- usc.edu

Summary

When materials deform to large strain, they typically enter a non-linear regime where deformation becomes progressively concentrated in narrow zones of shear that can lead to catastrophic failure or ductile deformation. Such behavior is observed at micro-scales during laboratory deformation experiments of metals or rocks, in natural samples such as rock thin sections, at meso-scales of exposed geological fault and fold structures, and at the macro-scale at the boundaries between lithospheric plates. It is clear that complex thermo-mechanical interactions of heterogeneous media govern this process, yet many aspects of the expression of strain localization are poorly understood.

Important issues related to strain localization include structural design in engineering, the mechanics of earthquakes and fault systems, and the operation of plate tectonics on Earth and other planets. The complex nature of this subject matter is reflected in the study of phenomena such as damage across several natural science disciplines, and we intend to make new connections between fields and also try to connect localization and damage processes at the short, elastic (e.g. earthquake) and long, viscous (e.g. plate boundary formation and maintenance) timescales.

The class targets graduate students from all Earth science fields, applied math, and engineering and will include reading and in-class discussion of the recent literature and classic papers. We will have lectures from members of the faculty and outside speakers, student presentations, and students are expected to work on a term paper. The latter can be a research project (preferred), or an in depth review of a subject area. The grade will be based 50% on the final project, 40% on student presentations and homework projects, and 10% on student participation.



Link to PDF files for selected reading

Link to lecture material including slides




Monday 9 – 10am

Wednesday 8-10am

Week 1: 08/24

Organizational meeting

Introduction (TWB)

Aydin and Johnson (1978); Ramsay (1980); Rutter et al. (2001), Bercovici (2003)

Week 2: 08/31

Basic concepts I (YBZ)


Basic concepts II (YBZ)


Week 3: 09/07

Labor day

Observations: brittle crust I (YBZ)

Ben-Zion and Sammis (2003), Chester et al., 2005; Rockwell and Ben-Zion (2007)


Week 4: 09/14

SCEC

SCEC

Week 5: 09/21

Observations: brittle crust II (YBZ)

Rheology I: viscous macro (TWB)

Reading:

Tackley (2000a)

Week 6: 09/28

Rheology II viscous micro (Platt)

Reading:

Kohlstedt et al. (1995), Hirth and Kohlstedt (2003), Warren and Hirth (2006)

Rheology III: friction and fracture (YBZ)

Reading:

Ben-Zion (2003, sections 4 and 5)

Week 7: 10/05

Viscous flow models (TWB)

Student presentations

Braun et al. (1999), Hobbs et al. (1990)

Week 8: 10/12

Student presentations

Precigout and Gueydan (2009)

Student presentations

Montesi and Zuber (2002)

Montesi & Hirth (2003), Burlini & Bruhn (2005)

Reading:

Regenauer-Lieb and Yuen (2003), Vissers et al. (1995), Regenauer-Lieb et al. (2006)

Week 9: 10/19

Elastic Damage I (Sammis)

Ashby and Sammis (1990)


Elastic Damage II (YBZ)

Ben-Zion (2008, sections 6)

Lyakhovsky et al. (1997), Sammis and Ben-Zion (2008)

Week 10: 10/26

Elastic damage III

Student presentations

Lyakhovsky & Ben-Zion (2009); Finzi et al. (2009); Hamiel et al., (2009); Lyakhovsky et al. (2009).

Viscous Damage I (TWB) Introduction

Bercovici et al. (2001), Bercovici and Ricard (2003, 2005), Ricard and Bercovici (2009)

Week 11: 11/02

Discussion session

Viscous damage II – Shear zones

Student presentation

Landuyt & Bercovici (2009)

Week 12: 11/09

Implementation of strain localization in mantle convection models

Student presentations

Bercovici & Karato (2003), Tackley (2000a), Gurnis et al. (2000)

Convection

Student presentations

Moresi & Solomatov (1998), Tackley (2000b, 2000c), Auth et al. (2002), Landuyt & Bercovici (2008)

Week 13: 11/16

Viscous shear zones in nature and lab (Davis)

Work on term paper

Week 14: 11/23

Work on term paper

Thanksgiving

Week 15: 11/30:

Work on term paper

Work on term paper

Week 16: 12/07:

Presentations of term papers

Presentations of term paper





References

Ashby, M. F. and Sammis, C. G.: The damage mechanics of brittle solids in compression. Pure App. Geophys., 133, 490, 1990.

Auth, C., Bercovici, D., and Christensen, U. R.: Two-dimensional convection with a self-lubricating, simple-damage rheology. Geophys. J. Int., 154, 783-800, 2003.

Aydin, A. and Johnson, A. M.: The development of faults as zones of deformation bands and as slip surfaces in sandstone. PAGEOPH, 116, 913-930, 1978.

Bazant, Z.P. and L. Cedolin: Stability of structures. Elastic, Inelastic, fracture and damage theories, pp. 984, Oxford University Press, 1991.


Ben-Zion, Y., Appendix 2, Key Formulas in Earthquake Seismology, in International Handbook of Earthquake and Engineering Seismology, eds. W. HK Lee, H. Kanamori, P. C. Jennings, and C. Kisslinger, Part B, 1857-1875, Academic Press, 2003.


Ben-Zion, Y., Collective Behavior of Earthquakes and Faults: Continuum-Discrete Transitions, Evolutionary Changes and Corresponding Dynamic Regimes, Rev. Geophysics, 46, doi:10.1029/2008rg000260, 2008.

Ben-Zion, Y. and C. G. Sammis, Characterization of Fault Zones, Pure Appl. Geophys., 160, 677-715, 2003.

Bercovici, D.: A source-sink model of the generation of plate-tectonics from non-Newtonian mantle flow. J. Geophys. Res., 100, 2013, 1995a.

Bercovici, D.: On the purpose of toroidal motion in a convecting mantle, Geophys. Res. Lett., 22, 3107, 1995b.

Bercovici, D. and Ricard, Y. and Schubert, G.: A two-phase model for compaction and damage. 3. Applications to shear localization and plate boundary formation, J. Geophys. Res., 106, 8925, 2001.

Bercovici, D.: Mantle dynamics, Past, Present and Future: An Overview, in Treatise on Geophyiscs, vol. 7, Mantle Dynamics, D. Bercovici editor; G. Schubert, editor in chief, Elsevier, New York; Ch. 1, p. 1-30, 2007.

Bercovici, D., The generation of plate tectonics from mantle convection, Earth Planet. Sci. Lett., 205, 107, 2003.

Braun, J., Chery, J., Poliakov, A., Mainprice, D., Vauchez, A., Tomassi, A., and Daignieres, M.: Parameterization of strain localization in the ductile regime due to grain size reduction: A case study for olivine, J. Geophys. Res., 104, 25167, 1999.

Budiansky, B., & O'Connell, R.J.: Elastic moduli of a cracked solid. Int. J. Solids Struct., 12, 81, 1976.

Burlini, L. and Bruhn, D.: High-strain zones: laboratory perspectives on strain softening during ductile deformation. High-strain Zones: Structure and Physical Properties, Geol. Soc. Lond. Spec. Pub., 245, p. 1-24, 2005.

Chester, J. S., F. M. Chester, and A. K. Kronenberg (2005), Fracture surface energy of the Punchbowl fault, San Andreas system, Nature, 437, 133-136.

Davies, G. F. and Richards, M. A., Mantle convection, J. Geology, 100, 151, 1992.

Ekland, I., and Temam, R.: Convex analysis and variational problems. Elsevier, 1976.


Gurnis, M., Zhong, S., and Toth, J.: On the competing roles of fault reactivation and brittle failure in generating plate tectonics from mantle convection. In: The history and dynamics of global plate motions. Richards, M. A., Gordon, R. G. and van der Hilst, R. D., eds., Geophys. Mono., 121, p. 73-94, AGU, Washington DC, 2000.

Hirth, G. and Kohlstedt, D. L., Rheology of the Upper Mantle and the Mantle Wedge: A View From the Experimentalists, In: Inside the Subduction Factory, Eiler, J. (ed), Geophys. Monograph, 138, p. 83-105, 2004.

Hobbs, B. E., Ord, A., and Teyssier, C.: Earthquakes in the ductile regime? Pure App. Geophys., 124, 309, 1986.

Hobbs, B. E., Muhlhaus, H.-B., and Ord, A.: Instability, softening and localization of deformation. Geol. Soc. London Spec. Pub., 54, p. 143-165, 1990.

Hudson, J. A. (1980), Overall properties of a cracked solid. Cambridge Phil. Soc., Math. Proc. 88, 371, 1980.

Jin, D., Karato, S.-i., and Obata, M.: Mechanisms of shear localization in the continental lithosphere: inference from the deformation microstructure of peridotites from the Ivrea zone, northwestern Italy. J. Struct. Geol., 20, 195, 1998.


Kachanov, M.: Effective elastic properties of cracked solids: Critical review of some basic concepts, Appl. Mech. Rev. 45, 304, 1992.


Kameyama, M., Yuen, D. A., Fujimoto, H.: The interaction of viscous heating with grain-size dependent rheology in the formation of localized slip zones. Geophys. Res. Lett., 24, 2523, 1997.

Kohlstedt, D. L., Evans, B. and Mackwell, S. J.: Strength of the lithosphere: constraints imposed by laboratory experiments. J. Geophys. Res., 100, 17587, 1995.

Kaus B.J.P., Podladchikov Y.Y. (2006) Initiation of localized shear zones in viscoelastoplastic rocks. Journal of Geophysical Research. Vol 111, B04412, doi: 10.1029/2005JB003652.

Lawn, B., Fracture of brittle solids (2nd edition), Cambridge Press, 1993.

Landuyt, W. and D. Bercovici, Formation and structure of lithospheric shear zones with two-phase damage, Phys. Earth Planet. Int., 175, 115, 2009.

Landuyt, W., D. Bercovici and Y. Ricard, Plate generation and two-phase damage theory in a model of mantle convection, Geophys. J. Int. 174, 1065, 2008.

Lyakhovsky, V., Ben-Zion, Y. & Agnon, A.: Distributed damage, faulting, and friction, J. Geophys. Res., 102, 27635-27649, 1997.



Lyakhovsky, V., Ben-Zion, Y., and Agnon, A.: Earthquake cycle, fault zones and seismicity patterns in a rheologically layered lithosphere. J. Geophys. Res., 106, 4103-4120, 2001.



Malvern, L. E., Introduction to the mechanics of a continuous medium, Prentice Hall, Inc., 1969.



Mavko, G., Mukerji, T., and Dvorkin, J. The Rock Physics Handbook; Tools for Seismic Analysis in Porous Media (CambridgeUniversity Press 1998).

Montési, L. and Hirth, G.. Grain size evolution and the rheology of ductile shear zones: from laboratory experiments to postseismic creep. Earth. Planet. Sci. Lett., 211, 197, 2003.

Montési, L. and Zuber, M.: A unified description of localization for application to large-scale tectonics, J. Geophys. Res., 107, 2045, doi:10.1029/2001JB000465, 2002.

Montési, L.: A constitutive model for layer development in shear zones near the brittle-ductile transition. Geophys. Res. Lett., 34, L08307, doi:10.1029/2007GL029250, 2007.

Needleman A., and J. R. Rice, "Limits to Ductility Set by Plastic Flow Localization", in Mechanics of Sheet Metal Forming (Proceedings of General Motors Research Laboratories Symposium, October 1977, ed. D.P. Koistinen and N.-M. Wang), Plenum Press, pp. 237-267, 1978.

Poirier, J. P.: Shear localization and shear instability in materials in the ductile field. J. Struct. Geol., 2, 135, 1980.

Precigout et al. Strain localisation in the subcontinental mantle — a ductile alternative to the brittle mantle. Tectonophysics, 445, 318-336, 2007.

Raimbourg, H., Toyoshima, T., Harima, Y. and Kimura, G.: Grain-size reduction mechanisms and rheological consequences in high-temperature gabbro mylonites of Hidaka, Japan. Earth Planet. Sci. Lett., 267, 637, 2008.

Ramsay, J. G.: Shear zone geometry, a review. J. Struct. Geol., 2, 83, 1980.


Regenauer-Lieb, K., Yuen, D. A., and Branlund, J.: The initiation of subduction; criticality by addition of water? Science, 294, 578, 2001.


Regenauer-Lieb, K., and D. A. Yuen: Modeling shear zones in geological and planetary sciences: solid-and fluid-thermal–mechanical approaches, Earth-Sci. Rev., 63, 295, 2003.


Regenauer-Lieb, K., Weinberg, R. F., and Rosenbaum, G.: The effect of energy feedbacks on continental strength. Nature, 442, 67, 2006.


Ricard, Y. and Bercovici, D.: A continuum theory of grain size evolution and damage, J. Geophys. Res., 114, B01204, 10.1029/2007JB005491, 2009.


Rice J. R., The Localization of Plastic Deformation, in Theoretical and Applied Mechanics (Proceedings of the 14th International Congress on Theoretical and Applied Mechanics, Delft, 1976, ed. W.T. Koiter), Vol. 1, North-Holland Publishing Co., 1976, 207-220.

Rockwell, T. K., and Y. Ben-Zion: High localization of primary slip zones in large earthquakes from paleoseismic trenches: Observations and implications for earthquake physics, J. Geophys. Res., 112, B10304, doi:10.1029/2006JB004764, 2007.


Rudnicki, J. W. and J. R. Rice: Conditions for the localization of deformation in pressure-sensitive, dilatant materials, J. Mech. Phys. Solids, 23, 371, 1975.

Rutter, E. H., Holdsworth, R. E., and Knipe, R. J.: The nature and tectonic significance of fault-zone weakening: an introduction. Geol. Soc. London Spec. Pub., 186, pp. 1-11, 2001.

Sammis, C. G., and Y. Ben-Zion, Mechanics of grain-size reduction in fault zones, J. Geophys. Res., 113, B02306, doi:10.1029/2006JB004892, 2008.

Scholz, C. H., The mechanics of earthquakes and faulting, Cambridge, 2002.

Schreyer, H.L. and M.K. Neilsen, Analytical and numerical tests for loss of material stability, Int. J. Numerical Methods in Engineering, 39, 1721, 1996a.


Schreyer, H.L. and M.K. Neilsen, Discontinuous bifurcation states for associated smooth plasticity and damage with isotropic elasticity, Int. J. Solids Structures, 33, 3239, 1996b.

Tackley, P.J.: The quest for self-consistent incorporation of plate tectonics in mantle convection, in History and Dynamics of Global Plate Motions, edited by M.A. Richards, R. Gordon, R. van der Hilst, AGU Geophysical Monograph Series, 121, 2000a.

Tackley, P.J., Self-consistent generation of tectonic plates in time-dependent, three-dimensional mantle convection simulations, part 1: Pseudoplastic yielding, Geochemistry, Geophysics, Geosystems, 1, 2000GC000036, 2000b.

Tackley, P.J., Self-consistent generation of tectonic plates in time-dependent, three-dimensional mantle convection simulations, part 2: Strain weakening and asthenosphere, Geochemistry, Geophysics, Geosystems, 1, 2000GC000043, 2000c.


Ueda, T., Obata, M., Di Toro, G., Kanagawa, K., and Ozawa, K.: Mantle earthquakes frozen in mylonitized ultramafic pseudotachylytes of spinel-lherzolite facies: Geology, 36, 607–610, 2008.

Vissers, R. L. M., Drury, M. R., Hoogerduijn Strating, E. H., Spiers, C. J., and van der Wal, D.: Mantle shear zones and their effect on lithosphere strength during continental breakup. Tectonophysics, 249, 155, 1995.

Walsh, J. B.: The effect of cracks on the uniaxial elastic compression of rocks, J. Geophys. Res. 70, 399, 1965.

Warren, J. M., and Hirth, G., 2006, Grain size sensitive deformation mechanisms in naturally deformed peridotites: Earth and Planetary Science Letters, v. 248, p. 438–450.

White, S., Burrows, S., Carreras, J., Shaw, N., Humphreys, F.: On mylonites in ductile shear zhones, J. Struct. Geol., 2, 175, 1980.

Yuen, D. and Schubert, G.: Shear heating instabilities in the Earth's upper mantle, Tectonophysics, 50, 197, 1978.



Other references

Brodie and Rutter: Deformation mechanisms and rheology: why marble is weaker than quartzite. J. Geo. Soc., 157, 1093-1096, 2000.
Drury et al. Shear localisation in upper mantle peridotites. Pure and Applied Geophysics (1991)

Vitale and Mazzoli. Heterogeneous shear zone evolution: The role of shear strain hardening/softening. Journal of Structural Geology (2008) pp. 13

Brodie, K. H., and Rutter, E. H., 1987, The role of transiently fine-grained reaction products in syntectonic metamorphism: natural and experimental examples.: Canadian Journal of Earth Sciences, v. 24, p. 556-564.

Dijkstra, A. H., Drury, M. R., Vissers, R. L. M., Newman, J., and Van Roermund, H. L. M., 2004, Shear zones in the upper mantle: evidence from alpine- and ophiolite-type peridotite massifs: Geological Society of London Special Publication, v. 224, p. 11-24.

Gessner, K., Wijns, C., and Moresi, L., 2007, Significance of strain localization in the lower crust for structural evolution and thermal history of metamorphic core complexes.: Tectonics, v. 26, p. TC20012.

Jefferies, S. P., Holdsworth, R. E., Wibberley, C. A. J., Shimamoto, T., Spiers, C. J., Niemeijer, A. R., and Lloyd, G. E., 2006, The nature and importance of phyllonite development in crustal scale fault cores: an example from the Median Tectonic Line, Japan.: Journal of Structural Geology, v. 28, p. 220-235.

Rutter, E. H., Faulkner, D. R., Brodie, K. H., Phillips, R. J., and Searle, M. P., 2007, Rock deformation processes in the Karakoram fault zone, Eastern Karakoram, Ladakh, NW India: Journal of Structural Geology, v. 29, p. 1315-1326.





Disability notice

Students requesting academic accommodations based on a disability are required to register with Disability Services and Programs (DSP) each semester. A letter of verification for approved accommodations can be obtained from DSP when adequate documentation is filed. Please be sure the letter is delivered to us (or to your TA) as early in the semester as possible. DSP is open Monday Friday, 8:30 5:00. The office is in Student Union 301 and the phone number is (213) 740 0776.