Geology 3120 - Failure ModelsGeology 3120 - Failure Models

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OutlineOutline

• Virtual rock deformation experiment

• Influence of pore fluid pressure

• Andersonian faulting

• Byerlee’s law

• Other failure models

Virtual Rock Deformation ExperimentVirtual Rock Deformation Experiment

Run 1 (MPa) 3 (Mpa) Failure ()

1 250 150 none

2 250 50 +37°

3 490 190 +37°

4 690 310 +37°

11

11

33

Run 1: Run 1: 11= 250 MPa; = 250 MPa; 33=150 MPa; no =150 MPa; no

fracturefracture

Run 1: Run 1: 11= 250 MPa; = 250 MPa; 33=150 MPa; no =150 MPa; no

fracturefracture

Run 2: Run 2: 11= 250 MPa; = 250 MPa; 33= 50 MPa; 37° = 50 MPa; 37°

fracturefracture

Run 2: Run 2: 11= 250 MPa; = 250 MPa; 33=150 MPa; no =150 MPa; no

fracturefracture

74°

Run 3: Run 3: 11= 490 MPa; = 490 MPa; 33=190 MPa; 37° =190 MPa; 37°

fracturefracture

Run 3: Run 3: 11= 490 MPa; = 490 MPa; 33=190 MPa; 37° =190 MPa; 37°

fracturefracture

74°

Run 4: Run 4: 11= 690 MPa; = 690 MPa; 33=310 MPa; 37° =310 MPa; 37°

fracturefracture

Run 4: Run 4: 11= 690 MPa; = 690 MPa; 33=310 MPa; 37° =310 MPa; 37°

fracturefracture

74°

Determining the Failure EnvelopeDetermining the Failure Envelope

= 16tan = 0.290 = 60 MPac = 0.29n + 60 MPa

c = 0.29n + 60 MPa

Predicting FailurePredicting Failure

Run 5: Run 5: 33= 250 MPa; at what = 250 MPa; at what 1 1 fracture occur?fracture occur?

Predicting FailurePredicting Failure

Run 5: Run 5: 33= 200 MPa; at what = 200 MPa; at what 1 1 fracture occur?fracture occur?

74°

Influence of Pore Fluid PressureInfluence of Pore Fluid Pressure

Applied Stress

Effective Stress

pf

Pore fluid pressure decreases normal stresses by the fluid pressure Pore fluid pressure decreases normal stresses by the fluid pressure

amount.amount.

Rock can then fail under the Mohr-Coulomb Law.Rock can then fail under the Mohr-Coulomb Law.

Principal StressesPrincipal Stresses

• 1 - greatest principal stress

• 2 - intermediate principal stress

• 3 - minimum principal stress

• Principal stress directions are mutually perpendicular to each other

Conjugate FaultsConjugate Faults

Most simply - two fault planes that intersect to form a straight line

Perhaps more typical - two fault surfaces that intersect to form a line

Acute angle - < 90° angle

Obtuse angle - > 90° angle

Acute

Obtuse

Assumptions for Andersonian Assumptions for Andersonian

FaultingFaulting

• Coulomb brittle failure - no pre-existing faults

• = 90 - 2

• Most rocks have = 30° so = ±30°

n

c

n

Y = mX + b

Y = mX + b

(

(

Assumptions for Andersonian Assumptions for Andersonian

FaultingFaulting Normal stress (1 , 2, 3)

Zero shear stress

• No shear stress exists at the Earth’s surface

• One principal stress must act normal to the surface

• 1 , 2, or 3 must be perpendicular to the surface

Rules of Thumb for Rules of Thumb for

StressesStresses• 1 bisects the acute angle

• 2 is parallel to the intersection of conjugate faults

• 3 bisects the obtuse angle

Normal FaultNormal Fault

Strike-slip FaultStrike-slip Fault

Thrust FaultThrust Fault

Normal faultingNormal faulting

Find the conjugate faults and

determine the orientations of

principal stresses.

SouthSouth NorthNorth

Normal faultingNormal faulting SouthSouth NorthNorth

Normal faultingNormal faulting SouthSouth NorthNorth

11

11

33 22

Determining Sense of SlipDetermining Sense of Slip

11

33

22

Determining Sense of SlipDetermining Sense of Slip

11

Determining Sense of SlipDetermining Sense of Slip

11

Determining Sense of SlipDetermining Sense of Slip

11

Determining Sense of SlipDetermining Sense of Slip

11

Determining Sense of SlipDetermining Sense of Slip

11

22

33

Byerlee’s Law of Rock FrictionByerlee’s Law of Rock Friction

f f = = ss

nn

f f = coefficient of = coefficient of

sliding friction sliding friction

Byerlee verses Mohr-Coulomb Byerlee verses Mohr-Coulomb

FailureFailure

For a given differential

stress, brittle failure

will occur by frictional

sliding on pre-existing

fractures (if they exist)

prior to Coulomb

failure

Failure ModelsFailure Models

ReferencesReferences

Slides 21, 22, 24, 39, 40Davis. G. H. and S. J. Reynolds, Structural Geology of Rocks and Regions, 2nd ed., John Wiley & Sons, New York, 776 p., 1996.

Slide 41

Twiss, R. J. and E. M. Moores, Structural Geology, W. H. Freeman & Co., New York, 532 p., 1992.