Page 117 - Applied Petroleum Geomechanics

Rock strengths and rock failure criteria 109

excavation because of the far-field stresses and pore pressure need to be
considered for failure initiation. It is commonly accepted that rock failure is
controlled by Terzaghi’s effective stress because Biot’s effective stress co-
efficient approaches 1.0 when rock failure is approached (e.g., Zhang, 2002;
Zhang et al., 2003). Terzaghi’s effective stress can be expressed as follows:
0
s ¼ s ij d ij p p (3.36)
ij
0
where s ij is the effective stress tensor, p p is the pore pressure and d is the
Kronecker delta, and d ¼ 1 when i ¼ j; d ¼ 0 when i s j.
3.4.2 MohreCoulomb failure criterion
3.4.2.1 Linear MohreCoulomb failure criterion
Shear failure occurs when the shear strength of a formation is exceeded.
Even for compressive loading, shear failure can also happen in the rock as
shown in Fig. 3.17B and C. Fig. 3.18 is field-observed Z-shape sigmoidal
veins (shear fractures) developed by the shear stresses.
When a rock is loaded by the far-field principal stresses, shear stresses can
be generated on an inclined plane where shear and normal stresses can be
obtained from Eq. (1.12), as shown in Fig. 3.19. Shear failures will occur in
the rock when shear stress overcomes the friction stress (ms n or s n tan4) plus
rock inherent shear strength or cohesion (c). The MohreCoulomb failure
criterion uses this principle to describe shear failure mechanism. For dry

Figure 3.18 Field example of shear failures in sigmoidal veins (Bons et al., 2012).