Week 7

Joints and Shear Fractures I. Read pages 204-256 in Chapter 5: Joints and Shear Fractures.

You are expected to read all the sections listed below. Information from the sections in italics will be discussed in class. You are expected to read the other sections and you may be called on in class to answer questions based on that material.

Definitions and distinctions p.204-214
General Nature of Joints

General Nature of Shear Fractures

Systems of Joints and Shear Fractures

Other Fractures
A Detailed Look at Individual Joint Surfaces p.214-221
Shapes of Joint Surfaces

Joint-Face Ornamentation

Propagation of Individual Fracture Surfaces
A Close Look at Propagation Relationships Among Joint Surfaces p.221-226
Columnar Joints

Connections Between Joints in a Siltstone Sequence

Patterns of Intersection and Termination of Joints
Creation of Joints and Shear Fractures in the Laboratory p.226-245
Incentives for Experimental Testing

Basic Approach in Experimental Testing

Tensile Strength Tests

Tensile and Compressive Strength Tests

Compressive Strength Tests

The Coulomb Law of Failure

Application of the Coulomb Criterion

Raising Confining Pressurs Even Higher

The Envelopes, All Together

Testing of Prefractured Rocks
The Influence of Pore Fluid Pressure p.245-251
The Classic Paper by Hubbert and Rubey

Fluid Pressures in the Real World

Fluid Pressure and the Development of Joints

Gelatin-Hydrofrac Experiment

Fluid Pressure and the Development of Veins
A Microscopic Look at the Mechanics of Fracturing p.252-256

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You should become familiar with the following terms during this weeks lectures and readings:

abnormal fluid pressure	angle of internal friction	angle of sliding friction	antitaxial veins
asperities	Byerlee's law	cohesive strength	Coulomb envelope
Coulomb law of failure	crack-seal vein	crystal fibers	en echelon joints
effective stress	fluid pressure ratio	Griffith cracks	hackles
hydraulic fracture	hydrostatic pressure	joint	joint bands
joint fringe	joint intersections	joint system	opening (Mode I) fractures
origin	plume axis	plumose structure	process zone
ribs	ridge-in-groove lineations	scissors (Mode III) fractures	shear fractures
slickenlines	sliding (Mode II) fractures	structural domains	syntaxial vein
systematic joint	tensile strength	vein	von Mises criterion

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You should be able to answer the questions below following this week:

Describe the ornamentation associated with a joint surface.
How can joint intersections be used to determine the relative ages of joints?
What is the approximate ratio of critical shear stress to normal stress needed to cause brittle failure?
What is the relative orientation of shear fractures predicted by the Coulomb law of failure?
Use a copy of the Mohr diagram in Figure 5.42 to answer the following question. What is the maximum compressive stress needed to cause failure if the confining pressure is zero. What is the critical shear stress at failure?
Use Figure 5.44 to estimate the angle of shear fractures during failure of: a) Westerly granite; b) Carrera marble; c) Berea sandstone.
What are the differences between syntaxial and antitaxial veins?
How does fluid (pore) pressure influence the stress necessary to cause faulting in both undeformed and previously faulted rocks. Use relevant equations in your answer.
What is the Mohr-Coulomb law of failure and how is it related to the Mohr circle for stress?

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Joints and Shear Fractures

Fracture classification

Mode I (opening) fractures: extension perpendicular to fracture surface (joints)
Mode II (sliding) fractures: shear parallel to the fracture surface and perpendicular to the fracture front (shear fractures)
Mode III (scissors) fractures: shear parallel to the fracture surface and parallel to the fracture front (shear fractures)

Joint surface characteristics

main joint face bordered by fringes (= joint termination)
joint ornamentation
origin - point where joint propagated
hackles - linear or curved markings on joint face (collectively = plumose structure)
ribs - curved steps in joint face, oriented perpendicular to hackles, old joint terminations

Joint intersections and terminations

joint appearance varies with level of exposure
individual en echelon joints at surface
single continuous surface at deeper levels
Y-intersections - contraction joints due to cooling or dessication

X-intersections - typical when systematic joint sets occur

T-intersections - younger joints terminate against older joint surfaces
hook patterns form at joint terminations, common in proximity to other joints (parking lot)

Creation of Joints and Shear Fractures in the Lab

multiple experiments with brittle deformation yield several Mohr circles that can be used to define the envelope of failure. Failure stress can therefore be predicted for a range of conditions.

envelope is parabolic in tensile field of Mohr diagram and linear in compressive field
tensile strength is less than compressive strength (at least 1:2 ratio)
failure envelope (Coulomb envelope) has a slope of f, (the angle of internal friction)

Coulomb law of failure

critical shear stress = cohesive strength + coefficient of internal friction (normal stress)

for unfaulted rocks where:

cohesive strength of rock = point where failure envelope intersects y-axis)
coefficient of internal friction = tangent of slope of failure envelope

We can use the equation to determine the:

approximate ratio of shear stress to normal stress for failure;

angle of failure envelope is typically 25-35, so tangent of slope ~ 0.5-0.7

cohesive strength is typically small so we can ignore it in this approximation

therefore, critical shear stress ~ 0.5 to 0.7 normal stress

approximate orientation of the fault formed by brittle failure

based on the geometry of the Mohr diagram, slope angle (f) = 90 - 2q, where q is the angle between the fault and principal stress direction

q = (90-f)/2 = (90-30)/2 ~ 30 degrees

The Mohr stress diagram with the Coulomb failure envelope can be used to illustrate the relative magnitudes of the principal stresses needed for failure

With additional confining pressure the rock will deform with plastic behavior and the von Mises criterion will govern deformation.

The failure envelope will become concave-downward and may flatten
A Mohr circle constructed for this part of the failure envelope will intesect the envelope with a failure angle (2q) of 90 degrees
indicating a shear zone oriented at 45 degrees to maximum principal stress.

Coulomb failure criterion deals with fracture at a point in a homogeneous isotropic material that is homogeneously stressed.

However, in nature, most faulting occurs on pre-existing faults.

Failure of pre-fractured rocks

Thus we must consider the implications for failure along faults that will not necessarily be oriented at the optimum angle to the maximum principal stress.

for pre-existing faults, cohesive strength no longer applies
the coefficient of internal friction (tanf) is replaced by the coefficient of sliding friction

Frictional resistance to sliding is greater for rough surfaces which contain asperites - irregularities on the sliding surface.

Mohr circle for stress plotted for experiments with pre-fractured rocks shows a linear relationship between shear stress and normal stress.

the angle of the slope is ff

the "new" failure criterion for pre-fractured rocks is critical shear stress = tanff (normal stress), Byerlee's law
where tanff is the coefficient of sliding friction

for low confining pressures, sc = 0.85sn

for moderate to high confining pressure, sc = 0.5sn

Under normal conditions, pre-existing fractures with a range of orientations may fail prior to the formation of a new fracture oriented at 30o to maximum principal stress. (see Fig. 5.48)

Influence of Pore Fluid Pressure

Hubbert & Rubey showed that high pore pressures can decrease the effect of normal stress

effective stress = (normal stress - pore pressure[Pf])
critical shear stress = cohesive strength + tanf (normal stress) becomes
critical shear stress = cohesive strength + tanf (normal stress - Pf) and

critical shear stress = tanff (normal stress) becomes critical shear stress = tanff (normal stress - Pf)

In both cases, critical shear stress, is substantially reduced

fluid pressure ratio = fluid pressure/lithostatic (normal) pressure fpr = Pf/Pl [Pf = fpr(Pl) = fpr (normal stress)]

Pf = fluid density x depth x gravity
Pl (= normal stress) = rock denisty x depth x gravity
fpr = fluid density/rock density ~ 1000/2500 = 0.4

The equation, critical shear stress = tanff (normal stress - Pf) can be rewritten as

critical shear stress = tanff x normal stress(1 - fpr)
under upper crustal conditions, where fluids can not readily escape,

sc = 0.85sn(1 - 0.4) = 0.51sn

at greater depths, where fluids can not readily escape,

sc = 0.5sn(1 - 0.4) = 0.3sn

at greater depths, with elevated pore pressures,

sc ~ 0.5sn(1 - 0.9) ~ 0.05sn
for unfractured rocks, sc = s0 + tanf sn(1 - l) , with elevated fluid pressures
critical shear stress = cohesive strength

Vein Formation

Elevated fluid pressures can explain the formation of joints at substantial depths (Fig. 5.49).

As joints open, they may be filled with vein material to form crystal fiber veins, which may preserve a record of the veins opening.

crystals grow in opening direction (direction of least principal stress)
antitaxial veins - add material along the vein wall

syntaxial veins - add material along the center of the vein

crack-seal veins - preserve inclusions indicating repeated fracturing

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