A model of damage mechanics for the deformation of the continental crust

[1] We derive a continuum rheology for the deformation of the continental crust using continuum damage mechanics. It is hypothesized that when a constant strain rate is applied to a solid material, the stress σ and damage increase until failure occurs, which is analogous to an earthquake. We further assume that this process is repeated, in analogy to the reoccurrence of earthquakes on a fault. Our model assumes that the continental crust behaves elastically below a yield stress σy. Above this stress the continuum deformations can be modeled as a non-Newtonian viscous flow with ∝ (σ − σy)n, where n is constant. We derive the modified Omori's law for aftershock decay using a viscoelastic version of our model and get good agreement with observations taking n = 6. Using parameter values appropriate for aftershocks, we obtain a continuum crustal rheology that can explain major orogenies such as the Indian-Asian collision.

[1]  Kazuyoshi Z. Nanjo,et al.  Damage and rheology in a fibre‐bundle model , 2005 .

[2]  D. Turcotte,et al.  A Damage Mechanics Model for Aftershocks , 2004 .

[3]  D. Sornette,et al.  Multifractal scaling of thermally activated rupture processes. , 2004, Physical review letters.

[4]  D. Turcotte,et al.  A damage model for the continuum rheology of the upper continental crust , 2004 .

[5]  Donald L. Turcotte,et al.  Damage and self-similarity in fracture , 2003 .

[6]  D. Turcotte,et al.  Micro and macroscopic models of rock fracture , 2003 .

[7]  J. Jackson.  Faulting, Flow, and the Strength of the Continental Lithosphere , 2002 .

[8]  S. Ciliberto,et al.  Disorder enhances the effects of thermal noise in the fiber bundle model , 2001 .

[9]  S. Ciliberto,et al.  The effect of disorder on the fracture nucleation process , 2001, cond-mat/0108514.

[10]  M. Nakatani.  Conceptual and physical clarification of rate and state friction: Frictional sliding as a thermally activated rheology , 2001 .

[11]  Yehuda Ben-Zion,et al.  Accelerated Seismic Release and Related Aspects of Seismicity Patterns on Earthquake Faults , 2001 .

[12]  A. F. Pacheco,et al.  A model for complex aftershock sequences , 2000, cond-mat/0012058.

[13]  D. Turcotte,et al.  Precursory Seismic Activation and Critical-point Phenomena , 2000 .

[14]  D. Sornette,et al.  Self-consistent theory of rupture by progressive diffuse damage. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  George Z. Voyiadjis,et al.  Advances in Damage Mechanics: Metals and Metal Matrix Composites With an Introduction to Fabric Tensors , 1999 .

[16]  John B. Rundle,et al.  Physical Basis for Statistical Patterns in Complex Earthquake Populations: Models, Predictions and Tests , 1999 .

[17]  A Vespignani,et al.  Avalanches in breakdown and fracture processes. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[18]  Jacek Skrzypek,et al.  Modeling of Material Damage and Failure of Structures: Theory And Applications , 1998 .

[19]  S. Ciliberto,et al.  An experimental test of the critical behaviour of fracture precursors , 1998 .

[20]  Hans Jürgen Herrmann,et al.  Transition from damage to fragmentation in collision of solids , 1998, cond-mat/9810315.

[21]  Y. Ben‐Zion,et al.  Distributed damage, faulting, and friction , 1997 .

[22]  D. Sornette,et al.  Scaling with respect to disorder in time-to-failure , 1997, cond-mat/9707114.

[23]  H. Stanley,et al.  FIRST-ORDER TRANSITION IN THE BREAKDOWN OF DISORDERED MEDIA , 1996, cond-mat/9612095.

[24]  J. Sethna,et al.  Statistical mechanics of cracks: Fluctuations, breakdown, and asymptotics of elastic theory , 1996, cond-mat/9610008.

[25]  Wayne Thatcher,et al.  Microplate versus continuum descriptions of active tectonic deformation , 1995 .

[26]  F. Amelung,et al.  Block versus continuum deformation in the Western United States , 1994 .

[27]  G. King,et al.  STATIC STRESS CHANGES AND THE TRIGGERING OF EARTHQUAKES , 1994 .

[28]  J. Dieterich.  A constitutive law for rate of earthquake production and its application to earthquake clustering , 1994 .

[29]  Philip England,et al.  Crustal thickening versus lateral expulsion in the Indian‐Asian continental collision , 1993 .

[30]  Patrick Wu,et al.  Rheology of the Upper Mantle: A Synthesis , 1993, Science.

[31]  A. Hansen,et al.  The Distribution of Simultaneous Fiber Failures in Fiber Bundles , 1992 .

[32]  Wang,et al.  Statistical-thermodynamic approach to fracture. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[33]  T. Hirata.  Fractal dimension of fault systems in Japan: Fractal structure in rock fracture geometry at various scales , 1989 .

[34]  J. Rundle,et al.  The growth of geological structures by repeated earthquakes, 1, conceptual framework , 1988 .

[35]  Peter Schwartz,et al.  Temperature dependence of lifetime statistics for single Kevlar 49 filaments in creep-rupture , 1988 .

[36]  S. Kirby,et al.  Rheology of the lithosphere: Selected topics , 1987 .

[37]  D. L. Turcotte,et al.  A fractal model for crustal deformation , 1986 .

[38]  Geoffrey C. P. King,et al.  Speculations on the geometry of the initiation and termination processes of earthquake rupture and its relation to morphology and geological structure , 1986 .

[39]  Philip England,et al.  FINITE STRAIN CALCULATIONS OF CONTINENTAL DEFORMATION .2. COMPARISON WITH THE INDIA-ASIA COLLISION ZONE , 1986 .

[40]  P. England,et al.  Finite strain calculations of continental deformation: 1. Method and general results for convergent zones , 1986 .

[41]  A. Ruina.  Slip instability and state variable friction laws , 1983 .

[42]  Geoffrey C. P. King,et al.  The accommodation of large strains in the upper lithosphere of the earth and other solids by self-similar fault systems: the geometrical origin of b-Value , 1983 .

[43]  S. Kirby.  Rheology of the lithosphere , 1983 .

[44]  P. England,et al.  A thin viscous sheet model for continental deformation , 1982 .

[45]  Christopher H. Scholz,et al.  Theory of time-dependent rupture in the Earth , 1981 .

[46]  Peter Bird,et al.  Plane-stress finite-element models of tectonic flow in southern California , 1980 .

[47]  J. Dieterich.  Time-dependent friction and the mechanics of stick-slip , 1978 .

[48]  M. Ashby,et al.  Micromechanisms of flow and fracture, and their relevance to the rheology of the upper mantle , 1978, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[49]  M. F. Ashby,et al.  On the rheology of the upper mantle , 1973 .

[50]  Markus Båth,et al.  Lateral inhomogeneities of the upper mantle , 1965 .

[51]  T. Utsu.  A statistical study on the occurrence of aftershocks. , 1961 .

[52]  B. Gutenberg,et al.  Seismicity of the Earth and associated phenomena , 1950, MAUSAM.

[53]  M. Polanyi,et al.  Über eine Art Gitterstörung, die einen Kristall plastisch machen könnte , 1934 .

[54]  E. Orowan.  Zur Kristallplastizität. I , 1934 .

[55]  G. Taylor.  The Mechanism of Plastic Deformation of Crystals. Part I. Theoretical , 1934 .

[56]  Geoffrey Ingram Taylor,et al.  The Mechanism of Plastic Deformation of Crystals. Part II. Comparison with Observations , 1934 .

[57]  D. Turcotte,et al.  Aftershock Statistics , 2005 .

[58]  A. Nicolas,et al.  Crystalline plasticity and solid state flow in metamorphic rocks , 1976 .

[59]  J. E. Dorn.  Some fundamental experiments on high temperature creep , 1955 .

[60]  F. Omori,et al.  On the after-shocks of earthquakes , 1894 .