stress (σ 1 ) and a radial stress (σ 3 ) representing the
initial in situ stress condition. The initial pore pressure
in the specimen is also the same as the one in situ and
thus the initial effective stresses. Then the axial stress
is increased while the lateral stress is kept constant.
The loading is performed so slowly that any tendency
to overpressure in the pore fluid is avoided by allowing
the fluid to drain out of the specimen (dissipate), so
that the pore pressure remains at its initial value. In
geomechanics this is called a drained test, as compared
to an undrained test in which the fluid is not allowed to
drain and overpressures (positive or negative) build-up
during the loading.
The recorded stress–strain curve for this axial loading is shown in Fig. 11.5b. Loading occurs from the
initial point I to point A. The initial section of the
curve is fairly straight (linear), but as the axial stress
increases the curve starts to bend. The slope of the
curve at any point is called the tangent Young’s modulus (E t ). The secant from point I to A gives the secant
modulus (E s ) up to that stress level. If the axial stress
at point A is reduced down to the original axial stress
level, the unloading curve goes down to point B and an
irrecoverable strain given by the distance IB has been
accumulated. Upon reloading the curve climbs back
up to point A. The slopes of the unloading-reloading
curves are very similar and close to the initial slope of
the curve I to A. When the axial stress is increased
beyond point A, the curve continues to bend as the
specimen approaches a shear failure condition. Both
the tangent and secant modulus decrease significantly.
As the stress difference (σ 1 À σ 3 ) becomes even
larger, so does the maximum shear stress in the specimen. The stress difference cannot exceed a certain
level (strength), as the specimen is not able to carry
any more load, and large axial strains (and shear
strains) ensue.
If one were to start the test described above with a
higher horizontal effective stress level, the
stress–strain curve would be steeper and climb higher.
For loose sediments the moduli and shear strength are
strong functions of the horizontal effective stress level,
therefore it is so important to be able to estimate the
effective stresses. For sedimentary rocks (shales and
sandstones) with strong cementation caused by chemical processes, the modulus and strength are also
influenced by the horizontal effective stress, though
to a much smaller extent. Note that the triaxial test
shown in Fig. 11.5b may also be run as a uniaxial
strain test. This is done by adjusting the horizontal
stress at all stages of the test such that no horizontal
strain is allowed to occur. This is called a K 0 test.
11.4.4 Brittle Versus Ductile Stress–Strain
Behaviour
For some sedimentary rocks, and depending on the
magnitude of the lateral effective stress, the
stress–strain curve in Fig. 11.5b may drop abruptly
after it has reached a peak at point P (the peak
strength). This is accompanied by a drop in shear
resistance with further strain down to a level R
which is called the residual strength after the failure.
The behaviour from the peak down to residual is
termed strain-softening or strain-weakening.
For other sedimentary rocks there is no strainsoftening, and the stress–strain curve is fairly horizontal or even slightly climbing as the strain increases.
This is called ductile behaviour. A sedimentary rock
found to behave as a brittle material at low horizontal
effective stress, may well behave as a ductile material
when the effective horizontal stress becomes sufficiently high, i.e. the horizontal stress has reached the
brittle-to-ductile transition stress level (e.g. Goodman
1989).
Other factors also affect the degree of brittleness.
The higher the temperature and the lower the stain
rate, the less tendency for brittle behaviour. In this
connection it should be pointed out that the rate of
stress change in and around a reservoir during petroleum production is orders of magnitude higher than the
geological stress changes, except for earthquake
occurrences. Some rocks behave very differently at
low strain rates compared with at high strain rates.
Rock salt is brittle when loaded at a very high strain
rate, but flows like a viscous fluid over geological
time. Also carbonate sandstones and shales yield to
stress in a ductile manner by mechanical as well as
chemical compaction if the strain rate is low enough.
11.5 Compaction in Sedimentary Basins
The deformation characteristics for sedimentary rocks
are complex as shown above. The strain rate in sedimentary rocks is normally rather low except during
11 Introduction to Geomechanics: Stress and Strain in Sedimentary Basins
311
initial in situ stress condition. The initial pore pressure
in the specimen is also the same as the one in situ and
thus the initial effective stresses. Then the axial stress
is increased while the lateral stress is kept constant.
The loading is performed so slowly that any tendency
to overpressure in the pore fluid is avoided by allowing
the fluid to drain out of the specimen (dissipate), so
that the pore pressure remains at its initial value. In
geomechanics this is called a drained test, as compared
to an undrained test in which the fluid is not allowed to
drain and overpressures (positive or negative) build-up
during the loading.
The recorded stress–strain curve for this axial loading is shown in Fig. 11.5b. Loading occurs from the
initial point I to point A. The initial section of the
curve is fairly straight (linear), but as the axial stress
increases the curve starts to bend. The slope of the
curve at any point is called the tangent Young’s modulus (E t ). The secant from point I to A gives the secant
modulus (E s ) up to that stress level. If the axial stress
at point A is reduced down to the original axial stress
level, the unloading curve goes down to point B and an
irrecoverable strain given by the distance IB has been
accumulated. Upon reloading the curve climbs back
up to point A. The slopes of the unloading-reloading
curves are very similar and close to the initial slope of
the curve I to A. When the axial stress is increased
beyond point A, the curve continues to bend as the
specimen approaches a shear failure condition. Both
the tangent and secant modulus decrease significantly.
As the stress difference (σ 1 À σ 3 ) becomes even
larger, so does the maximum shear stress in the specimen. The stress difference cannot exceed a certain
level (strength), as the specimen is not able to carry
any more load, and large axial strains (and shear
strains) ensue.
If one were to start the test described above with a
higher horizontal effective stress level, the
stress–strain curve would be steeper and climb higher.
For loose sediments the moduli and shear strength are
strong functions of the horizontal effective stress level,
therefore it is so important to be able to estimate the
effective stresses. For sedimentary rocks (shales and
sandstones) with strong cementation caused by chemical processes, the modulus and strength are also
influenced by the horizontal effective stress, though
to a much smaller extent. Note that the triaxial test
shown in Fig. 11.5b may also be run as a uniaxial
strain test. This is done by adjusting the horizontal
stress at all stages of the test such that no horizontal
strain is allowed to occur. This is called a K 0 test.
11.4.4 Brittle Versus Ductile Stress–Strain
Behaviour
For some sedimentary rocks, and depending on the
magnitude of the lateral effective stress, the
stress–strain curve in Fig. 11.5b may drop abruptly
after it has reached a peak at point P (the peak
strength). This is accompanied by a drop in shear
resistance with further strain down to a level R
which is called the residual strength after the failure.
The behaviour from the peak down to residual is
termed strain-softening or strain-weakening.
For other sedimentary rocks there is no strainsoftening, and the stress–strain curve is fairly horizontal or even slightly climbing as the strain increases.
This is called ductile behaviour. A sedimentary rock
found to behave as a brittle material at low horizontal
effective stress, may well behave as a ductile material
when the effective horizontal stress becomes sufficiently high, i.e. the horizontal stress has reached the
brittle-to-ductile transition stress level (e.g. Goodman
1989).
Other factors also affect the degree of brittleness.
The higher the temperature and the lower the stain
rate, the less tendency for brittle behaviour. In this
connection it should be pointed out that the rate of
stress change in and around a reservoir during petroleum production is orders of magnitude higher than the
geological stress changes, except for earthquake
occurrences. Some rocks behave very differently at
low strain rates compared with at high strain rates.
Rock salt is brittle when loaded at a very high strain
rate, but flows like a viscous fluid over geological
time. Also carbonate sandstones and shales yield to
stress in a ductile manner by mechanical as well as
chemical compaction if the strain rate is low enough.
11.5 Compaction in Sedimentary Basins
The deformation characteristics for sedimentary rocks
are complex as shown above. The strain rate in sedimentary rocks is normally rather low except during
11 Introduction to Geomechanics: Stress and Strain in Sedimentary Basins
311