Table 1.

Modes of brittle/frictional failure and associated failure criteria

Failure mode (field of application)τ/σ′n space (Mohr diagram) (σ1–σ3)/Pf space (BFM plot)Attitude with respect to stress axes
Extensional
1–σ3)<4To
τ2=4TonPf)+4To2
Pf3+To when (σ1–σ3)<4To
Extension fractures forming perpendicular to σ3
Extensional shear
4To<(σ1–σ3)<5.66To
(Griffith criterion)
τ2=4TonPf)+4To2
Pf3+[8To1–σ3)]/3
Extensional shear fractures along planes containing σ2, lying at ±θ <θi to σ1
Compressional shear
1–σ3)>5.66To
(Coulomb criterion)
τ=C+μinPf)
Pf3+[8To1–σ3)–(σ1–σ3)2]/16To
for μi=0.75
Shear fractures developing on planes containing σ2, lying at ±θi=0.5tan−1(1/μi) to σ1
Cohesionless fault re-shear
(Amontons law)
τ=μsnPf)
Pf3+[(σ1–σ3)(1–0.6tanθr)]/ [0.6(cotθr+tanθr)]
for μs=0.6
Re-shear along fractures containing σ2, lying at ±θr to σ1