Page 123 - Reservoir Geomechanics

107 Rock failure in compression, tension and shear

bedding planes did not occur and a lower strength, defined by the cohesion, S w , and
internal friction, µ w ,of the weak bedding planes which would apply. These parameters
are only relevant, of course, when slip occurs along the pre-existing planes of weakness
and affects rock strength.
Mathematically, it is possible to estimate the degree to which bedding planes lower
rock strength using a theory developed by Donath (1966) and Jaeger and Cook (1979).
The maximum stress at which failure will occur, σ 1 , will depend on σ 3 , S w , and σ w by
2(S w + µ w σ 3 )
σ 1 = σ 3 (4.33)
(1 − µ w cot β w ) sin 2β
This is shown in Figure 4.12c. At high and low β, the intact rock strength (shown
◦
normalized by S w )is unaffected by the presence of the bedding planes. At β ∼ 60 , the
strength is markedly lower. Using
1
tan 2β w =
µ w
it can be shown that the minimum strength is given by
1
σ min = σ 3 + 2(S w + µ w σ 3 ) µ 2 2 (4.34)
1 w + µ w
As shown in the schematic example in Figure 4.12c, the rock strength is reduced
markedly. Strength tests performed on a granitic muscovite gneiss (a metamorphic
rock) from the KTB scientific research borehole in Germany with pronounced foliation
planes (Vernik, Lockner et al. 1992) are fitted by this theory extremely well (Figure
4.13). Note that when the foliation planes have their maximum effect on rock strength
(at β = 60 ), strength is reduced approximately by half and the dependence of strength
◦
on β w is well described by equation (4.33).
The importance of weak bedding planes in shale is quite important in two case
studies presented in Chapter 10.In northern South America, shales which have a
UCS of about 10,000 psi (when measured normal to bedding) have very weak bed-
ding planes with S w = 300 psi and µ w = 0.5 which greatly affects wellbore stability
for wells at some trajectories to the steeply dipping bedding planes. Off the eastern
coast of Canada, a formation with a UCS of about 8000 psi (when measured normal
to bedding) has weak bedding planes with S w = 700 psi and µ w = 0.2. In this case,
bedding is nearly horizontal and horizontal stress magnitudes are relatively low, but
long reach-deviated wells are severely affected by the formation’s low bedding-plane
strength.

Estimating rock strength from geophysical log data

As alluded to above, many geomechanical problems associated with drilling must be
addressedwhencoresamplesareunavailableforlaboratorytesting.Infact,coresamples