mohr's circles - john t. fosterjohnfoster.pge.utexas.edu/pge334-resgeomechanics/slides/...yield...

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!