Mechanics of Fracturing and
Faulting: Experiment and Theory
Investigate the experimental and
theoretical relationships between stress
and the formation of rock fractures.
Formulate fracture criteria, and given a
set of conditions, we can expect a rock
to be stable or to fracture.
8.1 Experimental fracturing of Rocks
Failure: sample is unable to support an
increase in stress without permanent
deformation
Brittle failure: occurs with the formation
of a brittle fracture, surface or zone across
which material loses cohesion
Ductile failure: occurs when material
deforms permanently without losing
cohesion
Pore fluid pressure: confined isostatic
pressure of water in the pore spaces of
rocks causing internal stress on the
material
Extension fractures: the fracture plane is
perpendicular to the minimum principal
stress σ3 and parallel to the maximum
principal stress σ18.2 A Fracture
Criterion for Tension Fractures
Tensile strength (To): the amount of
stress in the extensional direction where
the material fractures
Tension fracture envelope: (σn* = T0) on a
Mohr diagram, the boundary between
stable and unstable states of tensile stress
Fracture plane angle (αf): angle b/n the
max principal stress σ1 and the fracture
Fracture angle (θf): angle b/n the max
principal stress σ1 and the normal to the
fracture plane
8.3 Coulomb Fracture Criterion for
confined compression
Coulomb fracture criterion: the critical
shear stress |σ*s| is equal to a constant c
(cohesion) plus the tangent of the slope
angle  of the line times the normal stress
σn
|σ*s| = c + µσn where µ = tan
Characterized by “stick” intervals of no
motion alternating with “slip” intervals of
sliding
8.5 Effects of pore fluid pressure on
fracturing and frictional sliding
 s*  c   ( n( Eff ) )  c   ( n  p f )
where
Cohesion(c): resistance to shear fracture
on a plane across which the normal stress
is zero
µ: Coefficient of internal friction : angle
of internal friction
Riedel shears: (secondary shears) are
“synthetic”, having the same sense as the
imposed shear and are oriented about 15
degrees from the plane of imposed shear.
The shears are not parallel to the imposed
direction of shearing.
8.4 Effects of confining pressure on
fracturing and frictional sliding
*Coulumb fracture criterion does not
apply in the tensile part of the Mohr
diagram
von Mises criterion: on a Mohr diagram,
it consists of a pair of parallel lines of
constant shear stress symmetric about the
normal stress axis; implies that ductile
deformation begins at a critical shear
stress
Amontons’ second law of friction: the
critical shear stress for frictional sliding is
proportional to the normal stress
Stable sliding: at low confining pressure,
frictional sliding occurs as a smooth,
continuous motion
Stick-slip behavior: compressive stress
across the sliding surface increases with
increasing
confining
pressure.
 n( Eff )   n  p f
Hydrostatic pore fluid pressure (pf) and
vertical lithostatic normal stress (σv) are
found at depth
Pf = ρwgh and σv = ρrgh

pf
v

 w gh
 0.4
 r gh
Where density of water = 10^3 kg/m^3
and that of sediment is 2.3 * 10^3 kg/m^3
8.6 Effects on fracturing of anisotropy,
the intermediate principal stress,
temperature and scale
Mechanically isotropic: rocks have the
same mechanical properties in all
directions
Mechanically anisotropic: strength is
different in different directions
Increased temperature causes increased
ductility of material.
Larger the scale, more heterogeneous
your system. There are flaws such as
joints and faults.
8.7 Limitations of the coulomb fracture
criterion
This is only a two dimensional version of
a more general criterion, it is missing the
third dimension of stress.
8.8 Griffith theory of fracture
EPS116 Chapter Summary 2011
1
Adam Casias and Tyler Seaman
Edited by: James Dabalos 2013
Griffith cracks: All solids contain a
myriad of microscopic to sub-microscopic
randomly oriented cracks
References & Resources
Robert J. Twiss, Eldridge M. Moores,
Structural Geology 2nd edition, (W. H.
Freeman), p. 209-230, 2006
EPS116 Chapter Summary 2011
2
Adam Casias and Tyler Seaman
Edited by: James Dabalos 2013