Page 306 - Mechanical Behavior of Materials
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Section 7.7 Coulomb–Mohr Fracture Criterion 307
τ , MPa
fitted line (a)
Siliceous sandstone τ + μσ = τ i 600
400
test result
200
σ, MPa
−1200 −800 −400 0 200
τ , MPa
Siliceous sandstone
fit (b)
60
30
σ, MPa
−120 −90 −60 −30 0 30
σ' uc σ uc σ ut σ' ut
Figure E7.7
7.7.2 Graphical Representation of the Coulomb–Mohr Criterion
If the assumption σ 1 ≥ σ 2 ≥ σ 3 is dropped, so that there are no restrictions on the relative
magnitudes of the principal normal stresses, Eq. 7.46 needs to be expanded into three relationships.
For the form of Eq. 7.46(c), these are
|σ 1 − σ 2 | + m(σ 1 + σ 2 ) = σ (1 − m) (a)
uc
|σ 2 − σ 3 | + m(σ 2 + σ 3 ) = σ (1 − m) (b) (7.54)
uc
|σ 3 − σ 1 | + m(σ 3 + σ 1 ) = σ (1 − m) (c)
uc
