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Elastic Behavior

Elastic Behavior. s = E e Strain, e, is linearly proportional to stress E = elasticity or Young’s modulus Rock values of E are generally in GPa. Retrn to text. Rock Type . Modulus of Elasticity. - . (MPa x 1000). Limestone . 3-27. Dolomite . 7-15. Limestone (very hard) . 70.

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Elastic Behavior

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

  2. Retrn to text

  3. Rock Type Modulus of Elasticity - (MPa x 1000) Limestone 3-27 Dolomite 7-15 Limestone (very hard) 70 Sandstone 10-20 Quartz-sandstone 60-120 Greywacke 10-14 Siltstone 3-14 Gneiss - fine 9-13 Gneiss - coarse 13-23 Schist - Micaceous 21 Schist - Biotite 40 Schist - Granitic 10 Schist - Quartz 14 Granite - very altered 2 Granite - slightly altered 10-20 Granite - good 20-50 Quartzite - Micaceous 28 Quartzite - sound 50-80 Dolerite 70-100 Basalt 50 Andesite 20-50 Amphibolite 90

  4. Rock Type Modulus of Elasticity - (MPa x 1000) Limestone 3-27 Dolomite 7-15 Limestone (very hard) 70 Sandstone 10-20 Quartz-sandstone 60-120 Greywacke 10-14 Siltstone 3-14 Gneiss - fine 9-13 Gneiss - coarse 13-23 Schist - Micaceous 21 Schist - Biotite 40 Schist - Granitic 10 Schist - Quartz 14 Granite - very altered 2 Granite - slightly altered 10-20 Granite - good 20-50 Quartzite - Micaceous 28 Quartzite - sound 50-80 Dolerite 70-100 Basalt 50 Andesite 20-50 Amphibolite 90

  5. Rock name Schmidt Hammer data (this work) Young’s modulus-E (GPa) Density-D (kg m-3) Uniaxial strength-C0 (MPa) Source of E Mean rebound Standard deviation Maresha chalk 23.9 1.4 2.4 ± 1.1 1,220 11 [13] Cordoba-C limestone 41.5 2.2 12.5 ± 0.96 2,070 32 [14] Berea sandstone 50.8 1.9 19.3 2,100 74 [12] Indiana limestone 50.6 1.2 25.3 ± 1.2 2,360 62 [18] Carrara marble 58.6 0.8 39.2 ± 5.6 2,710 95 [16] Gevanim syenite 65.0 1.9 53.4 ± 2.4 2,468 259 This work Mt. Scott granite 73.4 2.7 75.6 2,650 243 This work

  6. VISCOUS BEHAVIOR • Continuous flow at constant stress • Linear, or Newtonian, viscous behavior is expressed as: • e = (s*t)/visc, where visc = viscosity • Typical viscosities for rocks are between 1020 to 1028 Poise. 1 Poise = 1 Pa*sec • Viscous flow occurs in the solid earth below melting temperatures • Rate is extremely slow and requires 106 yrs or more • Typical strain rates, e/t = 10-7/sec to 10-14/sec

  7. 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 lava 100 to 1,000 • A'a lava 1000 to 10,000 • Andesite lava 106 to 107 • Rhyolite lava 1011 to 1012

  8. Table 1: Viscosity of Selected Fluids and Materials Fluid/Material Temperature (C) Viscosity (Pa-s;Pascal-seconds =Newton-seconds/m2)* Air 20 1.8  10-5 Water 20 1.0  10-3 Honey 20 1.6 Flowing hot lava(Hawaiian volcano) ~ 1150 ~ 80 Glass ~ 20 ~ 1012 Ice 0 ~ 1012 Rock Salt 20 ~ 1014 Shallow mantle ~ 1000 ~ 1023-1024 Asthenosphere ~ 1300 ~ 1019-1020 Deep mantle > 1500 ~ 1021-1022 *Viscosity is often given in units of Poise; 10 Poise = 1 Pa-s.

  9. Poisson’s Ratio • Poisson’s Ratio, n = etransverse/elongitudinal • In uniaxial tension, an incompressible material should have a n = 0.5 • Most rocks have n values of 0.25 – 0.35

  10. FRACTURES AND FAULTS

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

  12. 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)

  13. 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)

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

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

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

  17. RED SEA AND SINAI PENINSULA DIVERGENT PLATE BOUNDARY

  18. TRANSFORM PLATE BOUNDARY, CALIFORNIA

  19. CONVERGENT PLATE BOUNDARY: Andean Type

  20. CONVERGENT PLATE BOUNDARY: ALASKA Seismicity and Wadati-Benioff Zone

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