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Elastic Behavior = E Strain, is linearly proportional to stress E = elasticity or Young’s modulus Rock values of E are generally in GPa

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Rock TypeModulus of Elasticity -(MPa x 1000) Limestone3-27 Dolomite7-15 Limestone (very hard)70 Sandstone10-20 Quartz-sandstone60-120 Greywacke10-14 Siltstone3-14 Gneiss - fine9-13 Gneiss - coarse13-23 Schist - Micaceous21 Schist - Biotite40 Schist - Granitic10 Schist - Quartz14 Granite - very altered2 Granite - slightly altered10-20 Granite - good20-50 Quartzite - Micaceous28 Quartzite - sound50-80 Dolerite70-100 Basalt50 Andesite20-50 Amphibolite90

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Rock Type Modulus of Elasticity -(MPa x 1000) Limestone3-27 Dolomite7-15 Limestone (very hard) 70 Sandstone10-20 Quartz- sandstone 60-120 Greywacke10-14 Siltstone3-14 Gneiss - fine9-13 Gneiss - coarse13-23 Schist - Micaceous 21 Schist - Biotite40 Schist - Granitic 10 Schist - Quartz14 Granite - very altered 2 Granite - slightly altered 10-20 Granite - good20-50 Quartzite - Micaceous 28 Quartzite - sound 50-80 Dolerite70-100 Basalt50 Andesite20-50 Amphibolite90

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Rock nameSchmidt Hammer data (this work)Young’s modulus-E (GPa) Density-D (kg m -3 ) Uniaxial strength-C 0 (MPa)Source of E Mean reboundStandard deviation Maresha chalk23.91.4 2.4 ± 1.1 1,22011[13] Cordoba-C limestone41.52.2 12.5 ± 0.96 2,07032[14] Berea sandstone50.81.919.32,10074[12] Indiana limestone50.61.2 25.3 ± 1.2 2,36062[18] Carrara marble58.60.8 39.2 ± 5.6 2,71095[16] Gevanim syenite65.01.9 53.4 ± 2.4 2,468259This work Mt. Scott granite73.42.775.62,650243This work

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VISCOUS BEHAVIOR Continuous flow at constant stress Linear, or Newtonian, viscous behavior is expressed as: – = ( *t)/visc, where visc = viscosity Typical viscosities for rocks are between 10 20 to 10 28 Poise. 1 Poise = 1 Pa*sec Viscous flow occurs in the solid earth below melting temperatures Rate is extremely slow and requires 10 6 yrs or more Typical strain rates, /t = 10 -7 /sec to 10 -14 /sec

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SubstanceViscosity (Pa s) Air (at 18 oC)1.9 x 10 -5 (0.000019) Water (at 20 oC)1 x 10 -3 (0.001) Canola Oil at room temp.0.1 Motor Oil at room temp.1 Corn syrup at room temp.8 Pahoehoe lava100 to 1,000 A'a lava1000 to 10,000 Andesite lava10 6 to 10 7 Rhyolite lava10 11 to 10 12

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Table 1: Viscosity of Selected Fluids and Materials Fluid/MaterialTemperature ( C) Viscosity (Pa-s; Pascal-seconds = Newton-seconds/m 2 )* Air20 1.8 10 -5 Water20 1.0 10 -3 Honey201.6 Flowing hot lava (Hawaiian volcano) ~ 1150~ 80 Glass~ 20~ 10 12 Ice0~ 10 12 Rock Salt20~ 10 14 Shallow mantle~ 1000~ 10 23 -10 24 Asthenosphere~ 1300~ 10 19 -10 20 Deep mantle> 1500~ 10 21 -10 22 *Viscosity is often given in units of Poise; 10 Poise = 1 Pa-s.

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Poisson’s Ratio Poisson’s Ratio, = transverse / longitudinal In uniaxial tension, an incompressible material should have a = 0.5 Most rocks have values of 0.25 – 0.35

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FRACTURES AND FAULTS

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STRENGTH and DUCTILITY Strength= max stress before failure Ductility = max strain before failure

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FRACTURES IN ROCKS In uniaxial compression only extension fractures form. They always form parallel to the maximum compressive stress (mcs) and perpendicular to the least compressive stress ( which may also be a tensile stress)

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Shear fractures form in biaxial and triaxial cases Shear fractures form at acute angles to the mcs The extension fractures form the acute bisector Shear fractures dominate over extension fractures in terms of frequency Faults are big shear fractures (slip amounts > 1 m)

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BRITTLE BEHAVIOR Notice how tiny cracks form early on before the visible crack occurs

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When there is only one stress direction, only extension fractures form In biaxial and triaxial cases, shear fractures dominate

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FAULTS (LARGE-SCALE SHEAR FRACTURES) FORM MAINLY AT PLATE BOUNDARIES

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DIVERGENT PLATE BOUNDARY RED SEA AND SINAI PENINSULA

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TRANSFORM PLATE BOUNDARY, CALIFORNIA

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CONVERGENT PLATE BOUNDARY: Andean Type

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CONVERGENT PLATE BOUNDARY: ALASKA Seismicity and Wadati-Benioff Zone

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