Post on 27-Mar-2022
Geology 3120 Geology 3120 -- Failure ModelsFailure Models
PowerpointPowerpoint notes are available online at:notes are available online at:http://www.colorado.edu/geolsci/courses/GEOL3120http://www.colorado.edu/geolsci/courses/GEOL3120
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 σ1 (MPa) σ3 (Mpa) Failure (Θ)1 250 150 none2 250 50 +37°3 490 190 +37°4 690 310 +37°
σσ11
σσ11
σσ33
+Θ+Θ
Run 1: Run 1: σσ11= 250 = 250 MPaMPa; ; σσ33=150 =150 MPaMPa; no fracture; no fracture
Run 1: Run 1: σσ11= 250 = 250 MPaMPa; ; σσ33=150 =150 MPaMPa; no fracture; no fracture
Run 2: Run 2: σσ11= 250 = 250 MPaMPa; ; σσ33= 50 = 50 MPaMPa; 37° fracture; 37° fracture
Run 2: Run 2: σσ11= 250 = 250 MPaMPa; ; σσ33=150 =150 MPaMPa; no fracture; no fracture
74°
Run 3: Run 3: σσ11= 490 = 490 MPaMPa; ; σσ33=190 =190 MPaMPa; 37° fracture; 37° fracture
Run 3: Run 3: σσ11= 490 = 490 MPaMPa; ; σσ33=190 =190 MPaMPa; 37° fracture; 37° fracture
74°
Run 4: Run 4: σσ11= 690 = 690 MPaMPa; ; σσ33=310 =310 MPaMPa; 37° fracture; 37° fracture
Run 4: Run 4: σσ11= 690 = 690 MPaMPa; ; σσ33=310 =310 MPaMPa; 37° fracture; 37° fracture
74°
Determining the Failure EnvelopeDetermining the Failure Envelope
φ = 16tan φ = 0.29σ0 = 60 MPaσc = 0.29σn + 60 MPa
φσc = 0.29σn + 60 MPa
Predicting FailurePredicting Failure
Run 5: Run 5: σσ33= 250 = 250 MPaMPa; at what ; at what σσ1 1 fracture occur?fracture occur?
Predicting FailurePredicting Failure
Run 5: Run 5: σσ33= 200 = 200 MPaMPa; at what ; at what σσ1 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 pressPore fluid pressure decreases normal stresses by the fluid pressure amount.ure amount.
Rock can then fail under the MohrRock can then fail under the Mohr--Coulomb Law.Coulomb Law.
Principal StressesPrincipal Stresses
• σ1 - greatest principal stress
• σ2 - intermediate principal stress
• σ3 - 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 Assumptions for AndersonianAndersonian FaultingFaulting
σn
σc
σn
Y = Y = mXmX + b+ b
(
(
• Coulomb brittle failure - no pre-existing faults
• φ = 90 - 2Θ
• Most rocks have φ = 30° so Θ = ±30°
Assumptions for Assumptions for AndersonianAndersonian FaultingFaulting
Normal stress (σ1 , σ2, σ3)
Zero shear stress
• No shear stress exists at the Earth’s surface
• One principal stress must act normal to the surface
• σ1 , σ2, or σ3 must be perpendicular to the surface
Rules of Thumb for StressesRules of Thumb for Stresses
• σ1 bisects the acute angle
• σ2 is parallel to the intersection of conjugate faults
• σ3 bisects the obtuse angle
Normal FaultNormal Fault
StrikeStrike--slip Faultslip Fault
Thrust FaultThrust Fault
SouthSouth NorthNorthNormal faultingNormal faulting
Find the conjugate faults and
determine the orientations of
principal stresses.
Normal faultingNormal faulting SouthSouth NorthNorth
Normal faultingNormal faulting SouthSouth NorthNorth
σσ11
σσ11
σσ33 σσ22
Determining Sense of SlipDetermining Sense of Slip
σσ11
σσ22
σσ33
Determining Sense of SlipDetermining Sense of Slip
σσ11
Determining Sense of SlipDetermining Sense of Slip
σσ11
Determining Sense of SlipDetermining Sense of Slip
σσ11
Determining Sense of SlipDetermining Sense of Slip
σσ11
Determining Sense of SlipDetermining Sense of Slip
σσ11
σσ22
σσ33
Byerlee’sByerlee’s Law of Rock FrictionLaw of Rock Friction
µµf f = = σσss
σσnn
µµf f = coefficient of = coefficient of
sliding friction sliding friction
ByerleeByerlee verses Mohrverses Mohr--Coulomb FailureCoulomb Failure
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 41Twiss, R. J. and E. M. Moores, Structural Geology, W. H. Freeman & Co., New York, 532 p., 1992.