compressive strength of rocks - john t. foster | john t...
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Compressive strength of rocks
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
Recall: Yield surface
. Licensed under CC BY-SA 3.0 via WikipediaMohr Coulomb Yield Surface 3Da
Shear enhanced compaction
Porosity loss in sandstone
© Cambridge University Press (Fig. 4.20, pp. 120)Zoback, Reservoir Geomechanics
Cam-Clay model
with
Cam-Clay model
Sandia geomodel (Kayenta)
R.M. Brannon, A.F. Fossum, and O.E. Strack: Tech. rep.
Sandia National Laboratories, 2009.
Kayenta: Theory and User’s Guide.
Tensile strength of rocks
Relatively unimportant!
Reasons:Tensile strength is low compared to compressive strength.When a large enough volume of rock is considered, �aws are bound to existmaking the tensile strength near zero.In situ stress at depth is never tensile.
Opening mode fracture (Mode I)
© Cambridge University Press (Fig. 4.21, pp. 122)Zoback, Reservoir Geomechanics
Recall: Slip on faults
Coulomb failure function
Critically stressed crust
© Cambridge University Press (Fig. 4.25, pp. 129)Zoback, Reservoir Geomechanics
Stress magnitudes controlled by frictionalstrength
© Cambridge University Press (Fig. 4.26, pp. 129)Zoback, Reservoir Geomechanics
Limits on in situ stress
Optimal angle for frictional sliding:
© Cambridge University Press (Fig. 4.27b,c, pp. 131)Zoback, Reservoir Geomechanics
Principle stress ratio
Asuming
Stress bounds
Pore pressure, stress di�erence, and faultslip
© Cambridge University Press (Fig. 4.30, pp. 136)Zoback, Reservoir Geomechanics