compacted sediments have either been subjected to
low effective stress or they have a low compressibility.
The hydro-mechanical properties at shallow depths
may be very different for a normally consolidated
sediment sequence compared with an overconsolidated one, depending on the magnitude of the
OCR. For the overconsolidated sediment, the compressibility and permeability are usually much lower
and the shear strength significantly higher. As
discussed
below,
the
lateral
stresses
in
overconsolidated sediments may be higher than in
normally consolidated sediments.
11.3 Horizontal Stresses in Sedimentary
Basins
Knowledge of the magnitude and distribution of horizontal stresses in sedimentary basins is important in
relation to petroleum exploration, drilling and production. Their magnitude is also important in the interpretation of seismic signals used in field exploration and
in reservoir production management. In a sedimentary
basin the geomechanical properties vary from those of
loose cohesionless sediments at shallow depths to
dense and cemented sedimentary rocks at greater
depth. This affects the horizontal (lateral) stress distribution with depth.
While the vertical stresses are determined by vertical equilibrium (Eq. 11.1), the magnitude of lateral
stresses cannot be determined by equilibrium
equations and is statically indeterminate. Their
magnitudes are governed by a number of factors,
including the overburden/erosion (loading/unloading)
and uplift history of the basin and the deformation
characteristics of the sedimentary rocks. These are a
result of gravitational and tectonic forces, and also of
stress changes caused by chemical compaction and the
accompanying volume change. Their magnitude is
determined based on an understanding of the geological history, theoretical and semi-empirical
relationships, and field measurements. Horizontal
stresses can be measured in wells, and particularly in
area of uplift and erosion they may exceed the vertical
stresses. At high pore pressures this will result in
horizontal fractures rather than vertical which is the
case when the vertical stress is highest.
11.3.1 Theoretical and Semi-empirical
Relationships
In a basin which is wide compared to its thickness, the
compaction process due to added overburden may be
modelled as a one-dimensional deformation situation
(i.e. only strain in the vertical direction, no strain
horizontally). This is often denoted as a uniaxial strain
compaction situation. If the sediment mineral skeleton
(framework) may be assumed to behave in a linearly
elastic and isotropic manner (see Sect. 11.4), the horizontal stress which is built up as the vertical overburden is increased, is defined by:
σ
0
H ¼
ν
1 À ν
σ
0
v
(11.5)
where ν is the Poisson’s ratio for the sediment mineral
skeleton. The same relationship would hold for
unloading if the material really exhibits linearly elastic
behaviour. Furthermore, for isotropic material, the
magnitude of horizontal stress would be the same in
all directions. If one assumes anisotropic behaviour,
the equations corresponding to Eq. (11.5) would be
somewhat more complicated, and the horizontal
stresses would be different in the different directions.
The horizontal stress coefficient for a uniaxial deformation situation is commonly called K 0 in geomechanics.
For an assumed Poisson’s ratio ν ¼ 1/3, K 0 becomes
0.5 from Eq. (11.5).
As discussed in Sect. 11.4, linearly elastic
behaviour may be an acceptable approximation for a
cemented sediment (sedimentary rock) undergoing
minor deformation. However, during the initial gradual build-up of loose sediments in a basin, it is not
realistic to assume linear elastic behaviour of the sediment framework. Its behaviour is very non-linear and
inelastic, undergoing mainly permanent deformation.
In soil mechanics one uses the following semiempirical relationship for normally consolidated
(NC) sediments. It is based on idealised theoretical
considerations and on laboratory and field
measurements:
K 0nc ¼ 1 À sin φ
0
(11.6)
where φ
0 is the angle of shearing resistance (friction
angle) used in the Mohr-Coulomb failure criterion
11 Introduction to Geomechanics: Stress and Strain in Sedimentary Basins
305
low effective stress or they have a low compressibility.
The hydro-mechanical properties at shallow depths
may be very different for a normally consolidated
sediment sequence compared with an overconsolidated one, depending on the magnitude of the
OCR. For the overconsolidated sediment, the compressibility and permeability are usually much lower
and the shear strength significantly higher. As
discussed
below,
the
lateral
stresses
in
overconsolidated sediments may be higher than in
normally consolidated sediments.
11.3 Horizontal Stresses in Sedimentary
Basins
Knowledge of the magnitude and distribution of horizontal stresses in sedimentary basins is important in
relation to petroleum exploration, drilling and production. Their magnitude is also important in the interpretation of seismic signals used in field exploration and
in reservoir production management. In a sedimentary
basin the geomechanical properties vary from those of
loose cohesionless sediments at shallow depths to
dense and cemented sedimentary rocks at greater
depth. This affects the horizontal (lateral) stress distribution with depth.
While the vertical stresses are determined by vertical equilibrium (Eq. 11.1), the magnitude of lateral
stresses cannot be determined by equilibrium
equations and is statically indeterminate. Their
magnitudes are governed by a number of factors,
including the overburden/erosion (loading/unloading)
and uplift history of the basin and the deformation
characteristics of the sedimentary rocks. These are a
result of gravitational and tectonic forces, and also of
stress changes caused by chemical compaction and the
accompanying volume change. Their magnitude is
determined based on an understanding of the geological history, theoretical and semi-empirical
relationships, and field measurements. Horizontal
stresses can be measured in wells, and particularly in
area of uplift and erosion they may exceed the vertical
stresses. At high pore pressures this will result in
horizontal fractures rather than vertical which is the
case when the vertical stress is highest.
11.3.1 Theoretical and Semi-empirical
Relationships
In a basin which is wide compared to its thickness, the
compaction process due to added overburden may be
modelled as a one-dimensional deformation situation
(i.e. only strain in the vertical direction, no strain
horizontally). This is often denoted as a uniaxial strain
compaction situation. If the sediment mineral skeleton
(framework) may be assumed to behave in a linearly
elastic and isotropic manner (see Sect. 11.4), the horizontal stress which is built up as the vertical overburden is increased, is defined by:
σ
0
H ¼
ν
1 À ν
σ
0
v
(11.5)
where ν is the Poisson’s ratio for the sediment mineral
skeleton. The same relationship would hold for
unloading if the material really exhibits linearly elastic
behaviour. Furthermore, for isotropic material, the
magnitude of horizontal stress would be the same in
all directions. If one assumes anisotropic behaviour,
the equations corresponding to Eq. (11.5) would be
somewhat more complicated, and the horizontal
stresses would be different in the different directions.
The horizontal stress coefficient for a uniaxial deformation situation is commonly called K 0 in geomechanics.
For an assumed Poisson’s ratio ν ¼ 1/3, K 0 becomes
0.5 from Eq. (11.5).
As discussed in Sect. 11.4, linearly elastic
behaviour may be an acceptable approximation for a
cemented sediment (sedimentary rock) undergoing
minor deformation. However, during the initial gradual build-up of loose sediments in a basin, it is not
realistic to assume linear elastic behaviour of the sediment framework. Its behaviour is very non-linear and
inelastic, undergoing mainly permanent deformation.
In soil mechanics one uses the following semiempirical relationship for normally consolidated
(NC) sediments. It is based on idealised theoretical
considerations and on laboratory and field
measurements:
K 0nc ¼ 1 À sin φ
0
(11.6)
where φ
0 is the angle of shearing resistance (friction
angle) used in the Mohr-Coulomb failure criterion
11 Introduction to Geomechanics: Stress and Strain in Sedimentary Basins
305