mohr's circles - john t. fosterjohnfoster.pge.utexas.edu/pge334-resgeomechanics/slides/...yield...
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Mohr's circles
Mohr Envelope
© Cambridge University Press (Fig. 4.2b, pp. 88)Zoback, Reservoir Geomechanics
Linearized Mohr Envelope
© Cambridge University Press (Fig. 4.2a,c pp. 88)Zoback, Reservoir Geomechanics
Mohr-Coulomb failure
Triaxial tests on sandstone
© Cambridge University Press (Fig. 4.3a pp. 90)Zoback, Reservoir Geomechanics
Mohr Envelope for Sandstone
© Cambridge University Press (Fig. 4.3a, pp. 88)Zoback, Reservoir Geomechanics
Cohesion and internal friction data
© Cambridge University Press (Fig. 4.4, pp. 91)Zoback, Reservoir Geomechanics
Cohesion and internal friction data
© Cambridge University Press (Fig. 4.5, pp. 92)Zoback, Reservoir Geomechanics
Yield surface
. Licensed under CC BY-SA 3.0 via WikipediaMohr Coulomb Yield Surface 3Da
-plane
. Licensed under CC BY-SA 3.0 via WikipediaMohr Coulomb Yield Surface 3Db
Pressure dependence
© Blackwell Publishing (Fig. 4.5, pp. 86)Jaeger, et al., Fundamentals of Rock Mechanics
Other failure criteria
© Cambridge University Press (Fig. 4.6, pp. 94)Zoback, Reservoir Geomechanics
Recall: Mohr Envelope for Sandstone
© Cambridge University Press (Fig. 4.3a, pp. 88)Zoback, Reservoir Geomechanics
Hoek-Brown criterion (parabolic �tting)
and are �tting parameters that depend on rock properties and the degress of fracturing.Typical values
TypicalRange of Types of rocks
carbonate rocks (dolomite, limestone, marble)lithi�ed argillaceous rocks (sandstones, quartizite)arenaceous rocks (andesite, dolerite, diabase, rhyolite)course-grained polyminerallic gineous and metamorphic (amphibolite,gabbro, gneiss, norite, quartz-diorite)
Intact Rocks --
Completely Granualated --
Lade Criterion
with
(�rst invariant of )
(third invariant of )
is atmospheric pressure, and are material constants
Modi�ed Lade Criterion (dependece on )
with
and from Mohr-Coulomb criterion
Comparison
Mohr-Coulomb modi�ed Lade
© Cambridge University Press (Fig. 4.8b and 4.9b, pp. 96-97)Zoback, Reservoir Geomechanics
Others
modi�ed Wiebols-CookDruker-Pragermany more!