Page 118 - Applied Petroleum Geomechanics

110 Applied Petroleum Geomechanics

Figure 3.19 Shear stresses developed in an inclined plane in the rock under far-field
compressive stresses.

rocks, the MohreCoulomb failure criterion says that when the shear stress,
s, is greater than c þ s n tan4, the shear failure occurs. The MohreCoulomb
failure criterion can be written as the following linear form between shear
and normal stresses (originally proposed by Coulomb in 1785):
s ¼ c þ s n tan 4 (3.37)

where s n is the normal stress; s is the shear stress; c is the cohesion (also
called the inherent shear strength); 4 is the angle of internal friction,
m ¼ tan4; m is the coefficient of friction. For a fractured rock, it can be
assumed c ¼ 0.
In the principal stress space, (s 1 , s 2 , s 3 ), the MohreCoulomb failure
criterion can be expressed as follows:

(3.38)
s 1 ¼ UCS þ qs 3
where s 1 and s 3 are the maximum and minimum principal stresses, respec-
tively; and
1 þ sin 4
q ¼ (3.39)
1 sin 4

Based on the MohreCoulomb failure criterion, the UCS, angle of
internal friction and cohesion have the following relation:

2c cos 4
UCS ¼ (3.40)
1 sin 4