Page 119 - Applied Petroleum Geomechanics

Rock strengths and rock failure criteria 111

Figure 3.20 Effective stresses at failure in a Darley Dale sandstone. (Based on the data
of Murrell, S.A.F., 1965.)

When the experimental results of the maximum and minimum effective
stresses (difference of total stress and pore pressure) are plotted at failure in a
Darley Dale sandstone (Murrell, 1965), the failure data nearly form a single
failure curve, which in this particular case is nearly a straight line, but
slightly concave downward (Fig. 3.20). Therefore, for the porous rock in
the principal effective stress space, the MohreCoulomb failure criterion can
be expressed as the following:
0
s ¼ UCS þ qs 0 (3.41)
1 3
0
where s 1 and s 3 are the maximum and minimum effective principal
0
stresses, respectively.
Therefore, the MohreCoulomb failure envelope of Eq. (3.37) can be
expressed in the effective stress forms as follows:
s ¼ c þðs n p p Þtan 4 (3.42)

s ¼ c þ s tan 4 (3.43)
0
n
It can be observed from Eq. (3.42) that pore pressure reduces rock shear
strength. A simple physical interpretation of this condition is that, while the
normal stress tends to strengthen a fracture inside the rock, by pushing the
two opposing rock faces together, the pore pressure acts to weaken it, by
pushing the two opposing rock faces apart.