Elastic Behavior

= E • Strain, is linearly proportional to stress

• E = elasticity or Young’s modulus

• Rock values of E are generally in GPa

•

Retrn to text

Elastic Behavior

y = 2x

y = x

y = 0.5x

05

1015202530354045

0 5 10 15 20 25

Strain

Stre

ss

Case1

Case2

Case3

Series4

Series5

Linear (Case3)

Linear (Case1)

Linear (Case2)

Rock Type Modulus of Elasticity

- (MPa x 1000)Limestone 3-27Dolomite 7-15

Limestone (very hard) 70

Sandstone 10-20Quartz-sandstone 60-120Greywacke 10-14Siltstone 3-14Gneiss - fine 9-13Gneiss - coarse 13-23Schist - Micaceous 21Schist - Biotite 40Schist - Granitic 10Schist - Quartz 14

Granite - very altered 2

Schist - Biotite 40Schist - 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

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 1.42.4 ± 1.1

1,220 11 [13]

Cordoba-C limestone 41.5 2.212.5 ± 0.96

2,070 32 [14]

Berea sandstone 50.8 1.9 19.3 2,100 74 [12]

Indiana limestone 50.6 1.225.3 ± 1.2

2,360 62 [18]

Carrara marble 58.6 0.839.2 ± 5.6

2,710 95 [16]

Gevanim syenite 65.0 1.953.4 ± 2.4

2,468 259 This work

Mt. Scott granite 73.4 2.7 75.6 2,650 243 This work

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 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, /t = 10-7/sec to 10-14/sec

Viscous

y = 2x

y = x

y = 0.5x

0

10

20

30

40

50

0 10 20 30

Strain Rate, %/sec

Str

ess

Case1

Case2

Case3

Series4

Series5

Linear (Case3)

Linear (Case1)

Linear (Case2)

• 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

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. 

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

FRACTURES AND FAULTS

STRENGTH and DUCTILITY

Strength= max stress before failure

Ductility = max strain before failure

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)

• 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)

BRITTLE BEHAVIOR

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

When there isonly one stressdirection, onlyextension fracturesform

In biaxial and triaxialcases, shear fracturesdominate

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

DIVERGENT PLATE BOUNDARY

RED SEA AND SINAI PENINSULA

TRANSFORM PLATE BOUNDARY, CALIFORNIA

CONVERGENT PLATE BOUNDARY:Andean Type

CONVERGENT PLATE BOUNDARY: ALASKASeismicity and Wadati-Benioff Zone