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 (MPa) s3 (Mpa) Failure (Q) 1 250 150 none 2 50 +37° 3 490 190 4 690 310 s1 s3 +Q

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?

Run 5: s3= 200 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 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

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

Assumptions for Andersonian Faulting sn sc Y = mX + b ( 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 South North Find the conjugate faults and determine the orientations of principal stresses.

Normal faulting South North

Normal faulting South North s1 s3 s2 s1

Determining Sense of Slip

Determining Sense of Slip

Determining Sense of Slip

Determining Sense of Slip

Determining Sense of Slip

Determining Sense of Slip

Byerlee’s Law of Rock Friction ss mf = 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.