Compressive strength of rocks

Recall: Mohr Envelope for Sandstone

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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 --

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