13.2 Compaction, Flow Mechanisms
such as aragonitic bioclasts, high-Mg calcite, and
opaline silica, become cemented and lithified earlier
than their clay-rich interbeds which maintain a rather
high porosity. Instead of continuous hard beds, layers
of isolated carbonate concretions or chert nodules
can be formed. The role of microbial decomposition
of organic matter in the formation of carbonate nodules is briefly described in Sect. l3.3.
There are numerous other factors influencing the porosity
evolution of sediments. Sediments rich in finely dispersed
organic matter (e.g. lake gyttjas and marine sapropels) have
particularly high initial porosities. Clayey sediments deposited in freshwater lakes tend to develop higher initial porosities than marine clays, but they can be surpassed by
marine diatomaceous and radiolarian oozes (see below).
When exposed to freshwater circulation, carbonates especially tend to become rapidly lithified. In slowly reactive
and low permeable sediments, such as shales devoid of
carbonate, age is an important factor in diagenesis, because
the escape ofboth the excess pore water and water released
by dehydration of clay minerals as a result of their transformation into stable phases takes a long time.
In conclusion, the effects of mechanical compaction
are in most cases overprinted by chemie al diagenesis,
particularly in sediments with large proportions of
highly soluble, unstable components. Variations in
temperature gradients and differences in age further
modify the porosity-depth relationship in sediments
of similar composition. For a11 these reasons, the
porosity-depth curves summarized in many articles
and special volumes mentioned above displaya wide
scatter, even within sediments of approximately identical composition. It is therefore frequently not possible to successfu11y describe the porosity-depth relationship and compaction of natural sediments in a
general way by simple rules or equations (see below).
This can be done for compaction or consolidation
experiments in the laboratory, and to some extent for
young, sha11ow-buried sediments below the present
sea or lake floors.
13.2 Compaction, Compaction Flow,
and Other Flow Mechanisms
13.2.1 Analytical Equations to Describe
Compaction
General concepts. In spite of the complexity of sediment compaction and the constraints mentioned
above, several authors have made an attempt to describe the porosity-depth relationship or consolidation of sediments by simple analytical equations.
They were encouraged by the observation that the
reduction of porosity versus depth takes place in a
more or less exponential fashion, i.e., the porosities
of succeeding depth intervals decrease systemati653
ca11y. Figure l3.5 illustrates four different ways to
approach this problem:
(1) Soil engineers (Terzaghi 1925, Fig. l3.5a) have
leamed from laboratory consolidation tests that the
compaction of clayey materials renders straight line
relationships, if the void ratio, e, is plotted versus the
logarithm of the effective overburden pressure, Pe
(see above and Fig. 13.1). The void ratio, e, is the
ratio between the volumes taken by the voids and the
solid material of a sediment sampie (cf. Fig. l3.6a,
Eq.3).
(2) The effective pressure Pe is not a linear function
of depth, z, and therefore not very convenient to use
in the study of sedimentary colurnns with downwardincreasing bulk density. Therefore, Athy (1930) proposed plotting porosity versus log z according to the
equation
(13.1)
where n o = initial porosity
n z = porosity at the depth z .
Athy's exponential equation (Fig. l3.5b) is characterized by the initial porosity, n o , and an exponent, ß,
the value of which depends on the sediment type and
the dimension of z (m or km). Y oung marine sediments frequently have ß values between 5 and 15 x
10-\ if z is measured in meters (Brückmann 1989).
However, while both the Terzaghi and the Athyequations
describe the true situation fairly weil in medium depth
ranges (Fig. 13.5b, Wetze I 1986), they render differing
results for shallow burial depths. Furthermore, the
"Terzaghi curve" cannot be used for deeply buried sediments. The reason for this is that the straight lines approach
zero porosity with depth, which is on the whole unrealistic.
(3) To overcome these difficulties, Beaudoin et a1.
(1985) and Maillart (1989) set certain limits for the
initial porosity, n o , and the residual porosity, n,., at
great depth (several kilometers). Between these two
boundaries, the porosity changes exponentia11y (Fig.
13.5c). The specific parameters, a and ß, are empirical and may include effects of chemical diagenesis.
(4) Instead of using an exponential equation,
Baldwin and Butler (1985) emphasize that a powerlaw equation (Fig. l3.5d) may suit the porosity-depth
relations hip better than an exponential equation.
Their equation is based on the average porosity-depth
relationship of a number of fine-grained sediments.
In this case, however, the sediments start with an
(unrealistic) porosity of 1 (100%) at the sediment
surface. The power-Iaw equation plots as a straight
Ene on log-log paper (Fig. l3.5d). In addition, these
authors replace porosity by "solidity" (S = l-n),
which is '.he complement of porosity.
such as aragonitic bioclasts, high-Mg calcite, and
opaline silica, become cemented and lithified earlier
than their clay-rich interbeds which maintain a rather
high porosity. Instead of continuous hard beds, layers
of isolated carbonate concretions or chert nodules
can be formed. The role of microbial decomposition
of organic matter in the formation of carbonate nodules is briefly described in Sect. l3.3.
There are numerous other factors influencing the porosity
evolution of sediments. Sediments rich in finely dispersed
organic matter (e.g. lake gyttjas and marine sapropels) have
particularly high initial porosities. Clayey sediments deposited in freshwater lakes tend to develop higher initial porosities than marine clays, but they can be surpassed by
marine diatomaceous and radiolarian oozes (see below).
When exposed to freshwater circulation, carbonates especially tend to become rapidly lithified. In slowly reactive
and low permeable sediments, such as shales devoid of
carbonate, age is an important factor in diagenesis, because
the escape ofboth the excess pore water and water released
by dehydration of clay minerals as a result of their transformation into stable phases takes a long time.
In conclusion, the effects of mechanical compaction
are in most cases overprinted by chemie al diagenesis,
particularly in sediments with large proportions of
highly soluble, unstable components. Variations in
temperature gradients and differences in age further
modify the porosity-depth relationship in sediments
of similar composition. For a11 these reasons, the
porosity-depth curves summarized in many articles
and special volumes mentioned above displaya wide
scatter, even within sediments of approximately identical composition. It is therefore frequently not possible to successfu11y describe the porosity-depth relationship and compaction of natural sediments in a
general way by simple rules or equations (see below).
This can be done for compaction or consolidation
experiments in the laboratory, and to some extent for
young, sha11ow-buried sediments below the present
sea or lake floors.
13.2 Compaction, Compaction Flow,
and Other Flow Mechanisms
13.2.1 Analytical Equations to Describe
Compaction
General concepts. In spite of the complexity of sediment compaction and the constraints mentioned
above, several authors have made an attempt to describe the porosity-depth relationship or consolidation of sediments by simple analytical equations.
They were encouraged by the observation that the
reduction of porosity versus depth takes place in a
more or less exponential fashion, i.e., the porosities
of succeeding depth intervals decrease systemati653
ca11y. Figure l3.5 illustrates four different ways to
approach this problem:
(1) Soil engineers (Terzaghi 1925, Fig. l3.5a) have
leamed from laboratory consolidation tests that the
compaction of clayey materials renders straight line
relationships, if the void ratio, e, is plotted versus the
logarithm of the effective overburden pressure, Pe
(see above and Fig. 13.1). The void ratio, e, is the
ratio between the volumes taken by the voids and the
solid material of a sediment sampie (cf. Fig. l3.6a,
Eq.3).
(2) The effective pressure Pe is not a linear function
of depth, z, and therefore not very convenient to use
in the study of sedimentary colurnns with downwardincreasing bulk density. Therefore, Athy (1930) proposed plotting porosity versus log z according to the
equation
(13.1)
where n o = initial porosity
n z = porosity at the depth z .
Athy's exponential equation (Fig. l3.5b) is characterized by the initial porosity, n o , and an exponent, ß,
the value of which depends on the sediment type and
the dimension of z (m or km). Y oung marine sediments frequently have ß values between 5 and 15 x
10-\ if z is measured in meters (Brückmann 1989).
However, while both the Terzaghi and the Athyequations
describe the true situation fairly weil in medium depth
ranges (Fig. 13.5b, Wetze I 1986), they render differing
results for shallow burial depths. Furthermore, the
"Terzaghi curve" cannot be used for deeply buried sediments. The reason for this is that the straight lines approach
zero porosity with depth, which is on the whole unrealistic.
(3) To overcome these difficulties, Beaudoin et a1.
(1985) and Maillart (1989) set certain limits for the
initial porosity, n o , and the residual porosity, n,., at
great depth (several kilometers). Between these two
boundaries, the porosity changes exponentia11y (Fig.
13.5c). The specific parameters, a and ß, are empirical and may include effects of chemical diagenesis.
(4) Instead of using an exponential equation,
Baldwin and Butler (1985) emphasize that a powerlaw equation (Fig. l3.5d) may suit the porosity-depth
relations hip better than an exponential equation.
Their equation is based on the average porosity-depth
relationship of a number of fine-grained sediments.
In this case, however, the sediments start with an
(unrealistic) porosity of 1 (100%) at the sediment
surface. The power-Iaw equation plots as a straight
Ene on log-log paper (Fig. l3.5d). In addition, these
authors replace porosity by "solidity" (S = l-n),
which is '.he complement of porosity.