fff

Stress Analysis & Mohr circle : 

Stress Analysis & Mohr circle Some additional aspects of Mohr diagram for stress that we will talk about: Coulomb failure – for real rocks…that have cohesion Mohr-Coulomb failure -empirical modification at low confining pressures Von Mises failure – Incorporates increased ductility with increasing depth Byerlee’s Law of rock friction – What happens when rocks have pre-existing weaknesses? The effect of pore fluid pressure on faulting – principal of “effective stress”

Slide 2: 

Coulomb failure envelope

Slide 3: 

One commonly becomes dominant s1 s1 s3 Conjugate Shear fractures/faults

Slide 4: 

Conjugate Shear fractures/faults s1 s3 A conjugate pair of shear fractures in a 10-cm diameter core of a porous aeolian (Locharbriggs) sandstone

Slide 5: 

Normal faulting Find the conjugate faults and determine the orientations of principal stresses. South North

Slide 6: 

Normal faulting South North

Slide 7: 

s1 s1 s3 s2 Normal faulting South North

Slide 8: 

Anderson’s Theory of Faulting Shallow faults are basically Coulomb fractures. linear failure envelope ---> And recall Hartman’s rule: s1 bisects the acute angle s2 is parallel to the intersection s3 bisects the obtuse angle 2. Earth’s surface is a plane of no shear stress. Because it is a fluid-solid contact and fluids cannot support shear stresses. This means that one of the principal stress axes will always be perpendicular to the Earth’s surface. Two main assumptons:

Slide 9: 

Normal Fault

Slide 10: 

s1 s1 s3 s2 Normal faulting South North

Slide 11: 

Thrust Fault

Slide 12: 

Strike-slip Fault

Slide 13: 

Anderson’s Theory of Faulting Three possible scenarios arise: Normal faults Reverse faults Strike-slip faults

Slide 14: 

Some exceptions to Anderson’s theory 1. Some thrust faults are shallower than 30° with respect to the Earth’s surface. 2. Some reverse faults have dips as high as 60°, even 70°. 3. Some normal faults seem to have been active at very shallow dips (Low-angle normal faults).

Slide 15: 

Mohr failure envelope Whereas Coulomb failure envelope is a straight line, the slope for “Mohr” failure envelope steepens towards the ss axis. The shear fracture orientations change.

Slide 16: 

Von Mises failure envelope At high confining pressures (increasing P & T), rocks begin to behave plastically. This can be “approximated” on Mohr diagram with failure envelope parallel to sn axis. Plastic yielding become essentially independent of differential stress. Shear planes will develop at ~45° to s1.

Slide 17: 

Failure Models

Slide 18: 

Byerlee’s Law of Rock Friction mf = ss sn mf = coefficient of sliding friction

Stress Analysis & Mohr circle : 

Stress Analysis & Mohr circle Some additional aspects of Mohr diagram for stress that we will talk about: Coulomb failure – for real rocks…that have cohesion Mohr-Coulomb failure -empirical modification at low confining pressures Von Mises failure – Incorporates increased ductility with increasing depth Byerlee’s Law of rock friction – What happens when rocks have pre-existing weaknesses? The effect of pore fluid pressure on faulting – principal of “effective stress”

Slide 20: 

Influence of Pore Fluid Pressure Applied Stress Effective Stress pf Pore fluid pressure decreases normal stresses by the fluid pressure amount. Rock can then fail under the Mohr-Coulomb Law. Hubbert, M.K. and Rubey, W.W., 1959. Role of fluid pressure in mechanics of overthrust faulting. Part 1. GSA Bulletin, v. 70, p. 115-166.

Slide 21: 

klippe “allochthonous” “autochthonous” Chief Mountain, Glacier Nat. Park

Hubbert & Rubey beer can experiment : 

Hubbert & Rubey beer can experiment Drink two room-temperature beers and put 1 empty can in freezer. Turn warm beer can upside down on a wet glass plate (coffee table?) and tilt the plate. Typical angles for the can to move are ~17° (coefficient of sliding friction [mf] is ~0.3). Turn frozen can upside down on same wet glass plate and tilt the plate. This time the can will move down the plate at angles as low as 1°. The reason is that as air warms inside the can, it expands and causes pressure to increases, which offsets the normal stress exerted by the can on the glass. ~17° <5° Air-temp. can Frozen can

Slide 23: 

Large thrust sheet paradox Pfluid = 0; no pore fluid pressure Pfluid≈Plith ; high pore fluid pressure