GLG345 Term Test 2: Text Notes
Chapter 4: Stress
Definitions pressure is limited to media with no or very low shear resistance (fluids), stress
()is for media with min shear resistance, body forces affects the entire volume of rock (e.g.
gravity), surface forces act only on the surface and require a push or pull
Stress on a surface is a vector (1 -order tensor), while state of stress at a point is a 2 -order
tensor, described by the equation: ( ).
Stresses in the lithosphere are almost everywhere compressional, even in rifts and other areas
undergoing extension. Compressive stresses normally considered positive in geology, while
tension is negative.
Normal stress: ,
Shear stress: ,
In general, stress vectors act obliquely on planes and can be resolved into the normal and shear
The stress ellipsoid and its orientation tell us everything about the state of stress at a given point
in a rock, or in a rock volume in which stress is homogeneous. At the principal stress axes, the
shear stress is zero because they are the poles to the principal planes of stress.
Can define a stress tensor or stress matrix where the normal stresses , ,11nd 22occupy 33e
diagonal and the off-diagonal terms represent the shear stresses. [ ]
Stress tensors represent the same state of stress regardless of our choice of coordinate system.
They can be decomposed into the isotropic and anisotropic components with the mean stress,
Hydrostatic stress is isotropic stress where and the stress ellipsoid is a perfect
sphere. Deviatoric stress, , is anisotropic stress and is smaller than the isotropic
mean stress but of higher importance in geologic structure formation (strain).
The Mohr circle describes the normal and shear stress acting on planes of all possible
orientations through a point in the rock. Differential stress is the difference between the max and
min principal stresses and is the diameter of the circle. Great differential stress promotes rock
fracturing. Max shear stress occurs for planes where 2 = 90 , or where the angle to is 45 .
1 Chapter 5: Stress in the lithosphere
Stress measurements are important for many reasons, including in oil fields, underground
construction, tunnelling, etc. This is because at any level in the crust, stresses are related to the
formation and orientation of geologic structures. However, stress cannot be observed directly
only the effects of elastic or permanent strain can be observed.
Borehole breakouts are zones of failure of the wall of a well that give the borehole an irregular
and typically elongated shape. Ejection of fragments occur parallel to the min horizontal stress
h. Ellipticity indicated the local orientation of the horizontal stress axes.
Overcoring is a strain relaxation method where a sample is extracted, measured, and then
released so that it can expand freely. Max expansion occurs in direction of , although the shape
change depends on elasticity and the compressive stresses. Usually done to map state of stress at
or near the surface.
Elasticity is how a rock responds to non-permanent stress and is applied to calculate orientations
and magnitudes of principal stresses. Youngs modulus (E = /e) and Poissons ratio can be
Hydraulic fracturing means increasing the fluid pressure until the rock fractures. Frequently
applied to oil reservoirs to increase near-well permeability.
Our information about the current stress field below a few (4-5) kilometres depth is indirect, in
accurate and incomplete.
Reference states of stress define idealized states of stress in the crust as if the crust were a static
planet with no tectonic processes. The lithostatic reference state is an isotropic state of stress,
where the vertical and horizontal stresses are equal, represented as a point on the MC and
In real rocks, we deal with hydrostatic pressure and effective stress (). But the pore fluid
pressure reduces the effective stress, which is the stress at grain contacts in porous rocks.
Overpressure forms when fm fluid in porous fms is trapped between non-permeable layers. High
overpressure reduces the effective stress, which is particularly important in oil wells. Can cause
cataclasis, grain reorganization, detachment during deformation, etc. Also, can induce artificial
overpressure by increasing mud weight.
Uniaxial-strain reference state: no elongation occurs in the horizontal directions, triaxial stress,
e.g. compaction of sediments where and increases with depth depending on the physical
properties of the rock, given by , predicts that the vertical stress is
considerably larger than the horizontal stress ( ).
Constant-horizontal-stress reference state: avg stress in lithosphere is everywhere the same to
the depth of isostatic compensation under the thickest lithosphere, plane strain model with
vertical and one horizontal strain, most realistic for lithosphere unaffected by tectonics, avg
horizontal stress * + ( )* + where z 1s the thickest lithosphere.
2Effect of temperature changes can be calculated as follows:
Joints are more likely to initiate in sandstones than in shale during uplift of clastic sedimentary
Residual stress is the stress that is locked in and preserved after the external field has been
removed. Usually, it is the elastic strain that remains after the external stress field is removed and
can be caused by overburden, tectonic stress or thermal effects.
Tectonic stress is stress related to plate movements and plate tectonics. They are those parts of
the local stress state that deviate from the reference state of stress as a consequence of tectonic
processes. Current tectonic stress = Total stress (ref state of stress + non-tectonic residual stress
+ thermal stress + terrestrial stress).
Andersons classification has three regimes: normal-fault ( = ), strikv-slip1fault ( = ), v 2
thrust-fault ( =v ). 3hey are only valid in coaxial deformational regimes and the deforming
rock must be isotropic. Making the horizontal tectonic stress, for a lithostatic state of stress
we have . For the uniaxial-strain reference state, we have .
Since , we have that > t. Ttus, the def of tectonic stre