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Geology 3120 - Failure Models
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Outline Virtual rock deformation experiment
Influence of pore fluid pressure Andersonian faulting Byerlee’s law Other failure models
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Virtual Rock Deformation Experiment
Run s1 (MPa) s3 (Mpa) Failure (Q) 1 250 150 none 2 50 +37° 3 490 190 4 690 310 s1 s3 +Q
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Run 1: s1= 250 MPa; s3=150 MPa; no fracture
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Run 1: s1= 250 MPa; s3=150 MPa; no fracture
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Run 2: s1= 250 MPa; s3= 50 MPa; 37° fracture
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Run 2: s1= 250 MPa; s3=150 MPa; no fracture
74°
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Run 3: s1= 490 MPa; s3=190 MPa; 37° fracture
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Run 3: s1= 490 MPa; s3=190 MPa; 37° fracture
74°
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Run 4: s1= 690 MPa; s3=310 MPa; 37° fracture
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Run 4: s1= 690 MPa; s3=310 MPa; 37° fracture
74°
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Determining the Failure Envelope
sc = 0.29sn + 60 MPa f f = 16 tan f = 0.29 s0 = 60 MPa sc = 0.29sn + 60 MPa
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Predicting Failure Run 5: s3= 250 MPa; at what s1 fracture occur?
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Run 5: s3= 200 MPa; at what s1 fracture occur?
Predicting Failure 74° Run 5: s3= 200 MPa; at what s1 fracture occur?
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Influence of Pore Fluid Pressure
Effective Stress Applied Stress pf Pore fluid pressure decreases normal stresses by the fluid pressure amount. Rock can then fail under the Mohr-Coulomb Law.
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Principal Stresses s2 - intermediate principal stress
s1 - greatest principal stress s2 - intermediate principal stress s3 - minimum principal stress Principal stress directions are mutually perpendicular to each other
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Conjugate 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
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Assumptions for Andersonian Faulting
sn sc Y = mX + b ( Coulomb brittle failure - no pre-existing faults f = Q Most rocks have f = 30° so Q = ±30°
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Assumptions for Andersonian Faulting
Normal stress (s1 , s2, s3) Zero shear stress No shear stress exists at the Earth’s surface One principal stress must act normal to the surface s1 , s2, or s3 must be perpendicular to the surface
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Rules of Thumb for Stresses
s1 bisects the acute angle s2 is parallel to the intersection of conjugate faults s3 bisects the obtuse angle
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Normal Fault
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Strike-slip Fault
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Thrust Fault
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Normal faulting South North
Find the conjugate faults and determine the orientations of principal stresses.
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Normal faulting South North
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Normal faulting South North s1 s3 s2 s1
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Determining Sense of Slip
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Determining Sense of Slip
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Determining Sense of Slip
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Determining Sense of Slip
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Determining Sense of Slip
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Determining Sense of Slip
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Byerlee’s Law of Rock Friction
ss mf = sn mf = coefficient of sliding friction
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Byerlee verses Mohr-Coulomb Failure
For a given differential stress, brittle failure will occur by frictional sliding on pre-existing fractures (if they exist) prior to Coulomb failure
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Failure Models
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References Slides 21, 22, 24, 39, 40 Davis. 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.
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