Failure occurs to any solid material when:
Sufficiently large stress is applied.
The material does not return to its original state after
Mode of failure depends on:
Type and geometry of material
Fatigue makes failure to occur below the stress
Stress is applied to the end
faces of the specimen.
No radial (confining stress)
Also called Unconfined
returns to its
not return to its
after removal of
deformation, but can
still support load.
Ability to withstand
rapidly as deformation
In addition to axial stress,
confining pressure of
different magnitude is
applied to the
circumference of the
cylinder (by a confining oil
Two of the principal stresses are equal.
Axial & confining loads are increased simultaneously
until a prescribed hydrostatic stress level is reached.
Confining pressure is kept constant while axial load
increases until failure occurs.
Difference in principal stresses is plotted against axial deformation.
Specimen can still support load after failure due to high confining
pressure. It is called Work Hardening or Strain Hardening.
Tensile failure occurs when the
effective tensile stress across
some plane is the sample
exceeds a critical limit called
Tensile failure is caused by the stress concentrations
at the edges of thin cracks oriented normal to the
direction of the least compressive principal stress.
For isotropic rocks, conditions for failure will always
be fulfilled first for the lowest principal stress.
3 3 P To
To = tensile strength (in Pa, atm, psi or bar).
Most sedimentary rocks have a rather low tensile
strength, typically only a few MPa or less.
Standard approximation for several applications is
that the tensile strength is zero
It occurs when the shear stress
along some plane in the sample is
So = cohesion or inherent shear strength of material (in
Pa, atm, psi or bar).
µ = coefficient of internal friction.
Shear stress must overcome the cohesion plus the
internal friction in order to produce a macroscopic
If the Mohr’s circle lies below the failure line, the rock does not
fail and remains intact.
φ = angle of internal friction. It varies from 0 to 90o
A = attraction (in Pa, atm, psi or bar).
β = angle that fulfils the failure criterion. It gives
orientation of the failure plane. Varies between 45o and
At point P:
Angle 2β gives the position of coincidence of Mohr’s
circle and the failure line.
Coordinates are given as:
1 3 sin 2
1 3 1 3 cos 2
Co = uniaxial compressive strength (in Pa, atm, psi or
2 So cos
Co 2 So tan
1 a b 3
1 Co 3 tan 2
Principle of effective stress is introduced, i.e.
subtract fluid pressure from the total stress.
1 a b 3
1 1 Pf
And 3 3 Pf
1 a b 3
Pore fluid can affect the failure of the rock in 2 ways:
Mechanical effect of pore pressure.
Chemical interactions between the rock and the fluid.
Effect of pore pressure on failure:
Shear stress is unaffected by the pore pressure
Minimum & maximum principal stresses are
decreased by the same amount.
Radius of the Mohr circle in unchanged.
Center of the circle has shifted to the left.
Circle moves towards the failure line when the fluid
pressure is increased for a material obeying the