Page 103 - Reservoir Geomechanics

87 Rock failure in compression, tension and shear

of triaxial compression and triaxial extension tests can be used to determine the
importance of the intermediate principal stress, S 2 ,onfailure. As discussed below,
the importance of S 2 is often ignored.
Polyaxial, or true triaxial, tests (S 1 > S 2 > S 3 ) are the only tests in which the three

principal stresses are different. While these tests can most accurately replicate in
situ conditions, such tests are extremely hard to conduct for several reasons: the test
apparatus is somewhat complicated and difficult to use, it is nearly impossible to
include the effects of pore pressure, and sample preparation is quite difficult.
Not shown in Figure 4.1 are thick-walled cylinder tests. In these tests a small axial
hole is drilled along the axis of a cylindrical sample. These tests are done to determine
the approximate strain around the axial hole at which failure is first noted. Such tests
are done to support sand production studies such as those briefly discussed at the end
of Chapter 10.

Rock strength in compression

The failure of rock in compression is a complex process that involves microscopic
failures manifest as the creation of small tensile cracks and frictional sliding on grain
boundaries (Brace, Paulding et al. 1966). Eventually, as illustrated in Figure 4.2a,
there is a coalescence of these microscopic failures into a through-going shear plane
(Lockner, Byerlee et al. 1991). In a brittle rock (with stress–strain curves like that shown
in Figure 3.2) this loss occurs catastrophically, with the material essentially losing all of
its strength when a through-going shear fault forms. In more ductile materials (such as
poorly cemented sands) failure is more gradual. The strength is defined as the peak stress
level reached during a deformation test after which the sample is said to strain soften,
which simply means that it weakens (i.e. deforms at lower stresses) as it continues to
deform. Simply put, rock failure in compression occurs when the stresses acting on a
rock mass exceed its compressive strength. Compressive rock failure involves all of
the stresses acting on the rock (including, as discussed below, the pore pressure). By
rock strength we typically mean the value of the maximum principal stress at which a
sample loses its ability to support applied stress.
The strength of rock depends on how it is confined. For the time being we will
restrict discussion of rock strength to triaxial compression tests with non-zero pore
pressure (with effective stresses σ 1 >σ 2 = σ 3 ). It is universally observed in such tests
that sample strength is seen to increase monotonically with effective confining pressure
(e.g. Jaeger and Cook 1979). Because of this, it is common to present strength test results
using Mohr circles and Mohr failure envelopes (Figure 4.2b,c).
The basis for the Mohr circle construction is that it is possible to evaluate graphically
the shear stress, τ f , and effective normal stress (σ n = S n − P p )on the fault that forms