2. what is joint?
• Joints are defined as fracture surface along or
across which the movement is negligibly small.
• A joint may not show a displacement in the
mesoscopic scale, but may show evidence of
displacement in microscophic scale.
• An array of parallel joints constitutes a joint set.
Planar, parallel joints are also described as
systematic joints.
• Joints may range from the shortest few mm (micro
joints) to many tens of meters (master joints)in
length.
3. Formation of joints
• Joints are brittle fractures which
develop either by tensile failure or by
shear failure.
• When this happens, the rock fractures
in a plane parallel to the maximum
principal stress and perpendicular to
the minimum principal stress (the
direction in which the rock is being
stretched).
• A large number of joints form after the
close of the tectonic cycle and during a
slow uplift of the rocks.
4. Aerial image of ENE-trending joint pattern in granite of Texas Canyon,
east of Benson, Arizona.
5. Types of brittle
deformation.
(a) Orientation of the
remote principal
stress directions
with respect to an
intact rock body.
(b) A tensile crack,
forming parallel to
σ1 and
perpendicular to
σ3 (which may be
tensile).
(c) A shear fracture,
forming at an
angle of about 30°
to the σ1
direction.
7. • Mode I is the opening (extension)
mode where displacement is
perpendicular to the walls of the
crack.
• Mode II (sliding mode) représentas
slip (shear) perpendicular to the
edge.
• Mode III(tearing mode) involves
slip parallel to the edge of crack.
• Modes II and III occur along
different parts of the same shear
fracture and it may therefore be
confusing to talk about Mode II
and Mode III cracks as individual
fractures. Combinations of shear
(Mode II or III) fractures and
tension (Mode I) fractures are
called hybrid fractures.
8. Joints in relation to stresses
• Effective stress: if the rock is porous its behavior
will depend upon both the total stress and pore
pressure. The both total stress and pore pressure
are known as effective stress.
• For isotropic rock the principal effective stresses
are (σ1–αp) (σ2–αp) (σ3–αp).
where p is the pore pressure,
α is a constant which is generally taken as 1.
9. Joints in relation to stresses
• Experiments (see Paterson 1978, Jaeger & cook
1979)on deformation of isotropic rocks shows
that brittle fracture are symmetrically oriented
with respect to the effective principal stresses.
• The fractures are either parallel to the principal
compressive stress(σ3) or occur at an angle of
less than 45˚ with it.
• The angle between brittle o
fracture and principal
stress is dependent on the absolute value of the
stress difference(σ1─σ3) relative to the tensile
strength (T) of the rock.
10. Griffith law of failure
Relation between shear stress and normal stress at the
time of fracture is represented by the following
equation:
11. • Brittle failure develops
when the stress condition is
such that the Mohr circle
touches the Mohr envelop.
• The parabolic Mohr
envelop has following
characters, its axis is
parallel to the σ-axis of the
Mohr diagram. Its vertex is
at a point σ=T , τ=0.
• It intersects the τ-axis at 2
points,τ=±2T.
• The radius of curvature at
the vertex (T,0) as
determined from
(eqn.19.1)is 2T
12. • The radius of curvature of
the Mohr envelop at the
vertex is 2T and diameter
4T with center at (-T,0)
and with σ1=T and σ3=
─3T
• The angle for this Mohr
circle is 2ϴ=0.
13. • This is a case of either
uniaxial or biaxial
compression in the
σ1 σ3- plane. If
σ1=0,we find from
the below eqn σ3=
─8T.
• The Mohr circle (fig)
which touches the
Mohr envelop has
then a diameter 8T.
• which (σ1 ─ σ3)≥8T,
the dihedral angle
between the shear
fracture is 2ϴ=60˚.
14.
15. Among these three main case:
(a) Normal stress on joint σ=0 ,
we find from eqn (19.1) that τ=
2T. The slope of Mohr envelop
at this point (0,2τ) is dτ/dσ=
─1. Thus the normal to the
curve at this point makes
dihedral angle of 2ϴ=45˚ with
the σ1- axis. Diameter of Mohr
circle (σ1-σ3)=5.7T.
(b) If (σ1-σ3) is less than 5.7T but is
greater than 4T, the normal
stress σ on the joints will be
tensile. The dihedral angle 2ϴ <
45˚.
(c) If (σ1-σ3) is more than 5.7T but
is less than 8T, the 2ϴ > 45˚,but
less than 60˚. The normal stress
on them will be compressive.
16.
17. Geometrical relation with fold
• The different geometric
relation some times
expressed in terms of three
mutually perpendicular
tectonic axes a,b and c
(sandar 1930) with the b-axis
parallel to the fold axis
and c-axis normal to the
bedding.
• Orientation of b-axis
remains constant, but the
orientation of c and a-axis
change in different parts of
fold.
18. • Joints develop normal to the fold axis
called ac-joint or cross-joints(fig.a)
• Joints develop parallel to the axial
plane of fold called bc-joints or
longitudinal joints(fig.b).
• h0l- joints are conjugate joints
intersecting along the fold axis(b-axis)
and are symmetrically oriented with
respect to the axial plane. Symbol 0
indicate that these are parallel to the
b-axis at the hinge.(fig.c)
• hk0-joints are conjugate joints
intersecting along a line which is
perpendicular fold axis and lies parallel
to the axial plane (fig.d)
• hk0-joints indicates that these are
parallel to the c-axis at the hinge and
0kl-joints indicates that these are
parallel to the a-axis at the hinge zone.
19.
20. Geometrical relation with fault
• Joints of different types may
develop during faulting
among these the feather or
pinnate joint are important.
• The angle between fault
plane and joint is 45˚ which
is help to sense the
movement of the fault
block.
21. Surface morphology of joints
• Joints surface sometimes characteristic surface
marking. In generally two type; Hackle marks and
rib marks.
• Hackle marks are faint ridge on the joint surface.
Plume structure common type of hackle mark,
feather-like marking on the joint surface with a
central axis from which the rays or barbs branch
out either side.
• Normally found in shear fracture zone rare in
extensional fracture zone.
22. Markings similar to plumose structures are seen on fracture
surfaces in glass and other brittle materials.
27. Relationship between joint spacing and bed
thickness
• Harris et al.(1960) showed that
the spacing between joints
increases with the bed thickness.
• So most author are believe that
the joints spacing is proportional
to the bed thickness.
• According to (Ladeira &Price
1981) however this relationship is
valid for thin competent layer .
• Very thick competent beds may
have closely spaced fractures and
the fracture spacing is than
independent of the bed thickness.
• According to these author, the
spacing between two joints in
competent beds is also related to
the thickness of adjacent
incompetent beds.
28. Cross-sectional sketch illustrating a multilayer that is
composed of rocks with different values of Young’s
modulus. The stiffer layers (dolomite) develop more
closely spaced joints
Young’s modulus, E:
stress related to strain (elasticity): s= E.e
Large E, large s, more fractures
Small E, small s, fewer fractures
29. Rose diagram
• The strike frequency of joints
is sometimes represented by
rose diagram.
• Say ,for example that we have
measured the strike of 225
joints in a sub-area.
• Out of these,20 joints have a
strike range 030-035. The
percentage for 8.9 for joints
within this strike range.
• After calculating the
percentage for each 5˚
interval of the compass
directions.
• A suitable scale is chosen to
represent the percentage
value by the length of radius
of a circle.
30. • Basalt solidifies at about 1,000˚C and during
subsequent cooling it contracts of lave flow.
• The resulting tensional forces act primarily in
the horizontal plane and equal in all direction
within this plane.
• When rupture eventually take place, three
vertical fracture, making angles of 120˚ with
each other, radiate out from numerous centers.
34. Sheeting (Exfoliation)
• Sheeting is a
tensional due to
release of loading
during erosion.
• The release of the
compressional force
on rock that have
been under high
confining pressure
sometimes cause
ruptures
perpendicular to axis
of compression.
37. Importance of joints
• Mineral exploration in mining industries.
• Granite industries for quarrying rock blocks.
• To find the ground water flow in Hydro-geological
aspect.
• Bed rock analysis for Construction of tall
building in hill area.
