Transcript Perspectives of Japan

Geology 3120 - Failure Models
Powerpoint notes are available online at:
http://www.colorado.edu/geolsci/courses/GEOL3120
Outline
•
Virtual rock deformation experiment
•
Influence of pore fluid pressure
• Andersonian
faulting
•
Byerlee’s law
•
Other failure models
Virtual Rock Deformation Experiment
Run
s1
s3
+Q
s1
1
2
3
4
s1 (MPa)
250
250
490
690
s3 (Mpa)
150
50
190
310
Failure (Q)
none
+37°
+37°
+37°
Run 1: s1= 250 MPa; s3=150 MPa; no fracture
Run 1: s1= 250 MPa; s3=150 MPa; no fracture
Run 2: s1= 250 MPa; s3= 50 MPa; 37° fracture
Run 2: s1= 250 MPa; s3=150 MPa; no fracture
74°
Run 3: s1= 490 MPa; s3=190 MPa; 37° fracture
Run 3: s1= 490 MPa; s3=190 MPa; 37° fracture
74°
Run 4: s1= 690 MPa; s3=310 MPa; 37° fracture
Run 4: s1= 690 MPa; s3=310 MPa; 37° fracture
74°
Determining the Failure Envelope
sc = 0.29sn + 60 MPa
f
f = 16
tan f = 0.29
s0 = 60 MPa
sc = 0.29sn + 60 MPa
Predicting Failure
Run 5: s3= 250 MPa; at what s1 fracture occur?
Predicting Failure
74°
Run 5: s3= 200 MPa; at what s1 fracture occur?
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.
Principal Stresses
•
s1 - greatest principal stress
•
s2 - intermediate principal stress
•
s3 - minimum principal stress
Principal stress directions are
mutually perpendicular to each other
•
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
Obtuse
Acute angle - < 90° angle
Obtuse angle - > 90° angle
Assumptions for Andersonian Faulting
sc
sn
sn
•
Coulomb brittle failure - no pre-existing faults
•
f = 90 - 2Q
•
Most rocks have f = 30° so Q = ±30°
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
Rules of Thumb for Stresses
•
s1 bisects the acute angle
•
s2 is parallel to the intersection of conjugate faults
•
s3 bisects the obtuse angle
Normal Fault
Strike-slip Fault
Thrust Fault
Normal faulting
Find the conjugate faults and
determine the orientations of
principal stresses.
South
North
Normal faulting
South
North
Normal faulting
s1
s3
s2
s1
South
North
Determining Sense of Slip
s2
s3
s1
Determining Sense of Slip
s1
Determining Sense of Slip
s1
Determining Sense of Slip
s1
Determining Sense of Slip
s1
Determining Sense of Slip
s2
s3
s1
Byerlee’s Law of Rock Friction
mf =
ss
sn
mf = coefficient of
sliding friction
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
Failure Models
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.