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Ge277-2010 Stress in the crust Implications for fault mechanics and earthquake physics

Ge277-2010 Stress in the crust Implications for fault mechanics and earthquake physics. Motivation Basics of Rock Mechanics Observational constraints on the state of stress in the crust. Landers (1992, Mw=7,3). Hernandez et al., J. Geophys. Res., 1999. Nord. Sud. Nord. Sud. Nord. Sud.

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Ge277-2010 Stress in the crust Implications for fault mechanics and earthquake physics

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  1. Ge277-2010Stress in the crust Implications for fault mechanics and earthquake physics • Motivation • Basics of Rock Mechanics • Observational constraints on the state of stress in the crust

  2. Landers (1992, Mw=7,3) Hernandez et al., J. Geophys. Res., 1999

  3. Nord Sud

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  27. Nord Sud Hernandez et al., J. Geophys. Res., 1999

  28. Observed and predicted waveforms Strong motion data Hernandez et al., J. Geophys. Res., 1999

  29. (Bouchon et al., 1997)

  30. (Bouchon et al., 1997)

  31. (Bouchon et al., 1997)

  32. Heterogeneity on fault Initial stress in simulation by Peyrat et al. (2000) • For dynamic models of the rupture to match observation we need: • - heterogeneous prestress distribution • or heterogeneities of fault-constitutive parameters (Aochi et al, 2003; Peyrat et al, 2000, 2004, Aagard and Heaton, 2008)

  33. Dynamic models of the seismic cycle on faults must account for the complexity of seismic ruptures which requires some mechanism to maintain stress heterogeneities.

  34. Dynamic modeling (Kaneko et et al, in press)

  35. (Kaneko et et al, in press)

  36. The complexity (sustained heterogeneities of stress distribution) could be all due to the earthquake process itself, or to inerseismic processes.

  37. Basics of Rock Mechanics

  38. The stress (red vector) acting on a plane at M is the force exterted by one side over the other side divided by plane area…

  39. The stress tensor The state of stress at a point can be characterizes from the stress tensor defined as …

  40. Stress acting on a plane at point M… Let n be the unit vector defining an oriented surface with elementary area da at point M. (n points from side A to side B) Let dT be the force exerted on the plane by the medium on side B. It can be decomposed into a normal and shear component parallel to the surface. The stress vector is: n Side B Side A Normal stress Shear stress

  41. Principal stresses Because the matrix is symmetric, there is coordinate frame such that…. Engineering sign convention tension is positive,Geology sign convention compression is positive… Plane perpendicular toprincipal direction has no shear stress…

  42. The deviatoric stress tensor… Stress tensor = mean stress + deviatoric stress tensor

  43. The Mohr diagram 2-D stress on all possible internal planes… Sum of forces in 1- and 2-directions…

  44. 2-D stress on all possible internal planes… Sum of forces in 1- and 2-directions…

  45. Rearrange equations… Rearrange equations yet again… Get more useful relationship betweenprincipal stresses andstress on any plane….

  46. The Mohr diagram

  47. Representation of the stress state in 3-D using the Mohr cirles. This circle represent the state of stress on planes parallel to 2 The state of stress of a plane with any orientation plots in this domain t n 3 2 1 This circle represent the state of stress on planes parallel to 3 This circle represent the state of stress on planes parallel to 1

  48. Fracture strength of rocks The proportionality constant is the modulus of elasticity(in units if stress) Failure: Bonds are broken Deformation is permanent Cataclastic flow Elastic deformation Bonds are elastically deforming Deformation is recoverable Bonds are reorganizing Deformation is permanent Brittle regime (‘low’ temperature and pressure)

  49. Fracture strength of rocks The Mohr-Coulomb envelope Failure of rocks does not depend on the intermediate principal stress.

  50. Fracture strengths of dry sedimentary rocks…

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