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Mohr's circles
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Mohr Envelope
© Cambridge University Press (Fig. 4.2b, pp. 88)Zoback, Reservoir Geomechanics
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Linearized Mohr Envelope
© Cambridge University Press (Fig. 4.2a,c pp. 88)Zoback, Reservoir Geomechanics
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Mohr-Coulomb failure
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Triaxial tests on sandstone
© Cambridge University Press (Fig. 4.3a pp. 90)Zoback, Reservoir Geomechanics
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Mohr Envelope for Sandstone
© Cambridge University Press (Fig. 4.3a, pp. 88)Zoback, Reservoir Geomechanics
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Cohesion and internal friction data
© Cambridge University Press (Fig. 4.4, pp. 91)Zoback, Reservoir Geomechanics
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Cohesion and internal friction data
© Cambridge University Press (Fig. 4.5, pp. 92)Zoback, Reservoir Geomechanics
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Yield surface
. Licensed under CC BY-SA 3.0 via WikipediaMohr Coulomb Yield Surface 3Da
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-plane
. Licensed under CC BY-SA 3.0 via WikipediaMohr Coulomb Yield Surface 3Db
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Pressure dependence
© Blackwell Publishing (Fig. 4.5, pp. 86)Jaeger, et al., Fundamentals of Rock Mechanics
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Other failure criteria
© Cambridge University Press (Fig. 4.6, pp. 94)Zoback, Reservoir Geomechanics
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Recall: Mohr Envelope for Sandstone
© Cambridge University Press (Fig. 4.3a, pp. 88)Zoback, Reservoir Geomechanics
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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 --
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Lade Criterion
with
(�rst invariant of )
(third invariant of )
is atmospheric pressure, and are material constants
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Modi�ed Lade Criterion (dependece on )
with
and from Mohr-Coulomb criterion
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Comparison
Mohr-Coulomb modi�ed Lade
© Cambridge University Press (Fig. 4.8b and 4.9b, pp. 96-97)Zoback, Reservoir Geomechanics
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Others
modi�ed Wiebols-CookDruker-Pragermany more!