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Stress and Deformation: Part II (D&R, ; ) 1. Anderson's Theory of Faulting 2. Rheology (mechanical behavior of rocks) - Elastic: Hooke's Law - Plastic - Viscous 3. Brittle-Ductile transition

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Rocks in the crust are generally in a state of compressive stress Based on Coulomb's Law of Failure, at what angle would you expect faults to form with respect to 1?

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c = critical shear stress required for failure 0 = cohesive strength tan = coefficient of internal friction N = normal stress Recall Coulomb's Law of Failure In compression, what is the observed angle between the fracture surface and 1 ( )? ~30 degrees!

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Anderson's Theory of Faulting The Earth's surface is a free surface (contact between rock and atmosphere), and cannot be subject to shear stress. As the principal stress directions are directions of zero shear stress, they must be parallel (2 of them) and perpendicular (1 of them) to the Earth's surface. Combined with an angle of failure of 30 degrees from 1, this gives:

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conjugate normal faults

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conjugate thrust faults

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A closer look at rock rheology (mechanical behavior of rocks) Elastic strain: deformation is recoverable instantaneously on removal of stress – like a spring

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An isotropic, homogeneous elastic material follows Hooke's Law Hooke's Law: = Ee E (Young's Modulus): measure of material "stiffness"; determined by experiment

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Elastic limit: no longer a linear relationship between stress and strain- rock behaves in a different manner Yield strength: The differential stress at which the rock is no longer behaving in an elastic fashion

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Mechanics of faulting

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What happens at higher confining pressure and higher differential stress? Plastic behavior produces an irreversible change in shape as a result of rearranging chemical bonds in the crystal lattice- without failure! Ductile rocks are rocks that undergo a lot of plastic deformation E.g., Soda can rings!

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Ideal plastic behavior

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Strength increases with confining pressure

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Strength decreases with increasing fluid pressure

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Strength increases with increasing strain rate

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Role of lithology ( rock type) in strength and ductility (in brittle regime; upper crust)

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Role of lithology in strength and ductility (in ductile regime; deeper crust) STRONG ultramafic and mafic rocks granites schist dolomite limestone quartzite WEAK

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Temperature decreases strength

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Viscous (fluid) behavior Rocks can flow like fluids!

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For an ideal Newtonian fluid: differential stress = viscosity X strain rate viscosity: measure of resistance to flow

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The brittle-ductile transition

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The implications Earthquakes no deeper than transition Lower crust can flow!!! Lower crust decoupled from upper crust

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Important terminology/concepts Anderson's theory of faulting significance of conjugate faults rheology elastic behavior Hooke's Law Young's modulus Poisson's ratio brittle behavior elastic limit yield strength plastic behavior (ideal) power law creep strain hardening and softening factors controlling strength of rocks brittle-ductile transition viscous behavior ideal Newtonian fluid

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