Page 108 - Physical Principles of Sedimentary Basin Analysis

90 Compressibility of rocks and sediments

the effective stress exceeds the maximum effective stress the soil has been subjected to.
The maximum effective stress the soil has previously experienced is called the preconsol-
idation stress, and the slope of the preconsolidation line is called the swelling index.The

ratio of the preconsolidation stress σ and the current effective stress σ is called the
max

overconsolidation ratio,OCR = σ /σ .
max
We have seen that Young’s modulus for linear elastic materials was defined as stress
over strain, where the strain is the relative elongation. The normal consolidation line can
be used to compute a similar modulus for soils, where the strain is the relative thickness
of a soil sample. The thickness of a sample can be expressed by the porosity (or the void
ratio) using the net (porosity-free) thickness ζ of the sample, which is a constant during
compression:
ζ
h = = (1 + e)ζ. (4.64)
1 − φ
A change e in the void ratio leads to a change h = ζ e in the height of the sample.
The strain then becomes
h e
= . (4.65)
h 1 + e
The stress over strain, where the strain is caused by this change in the effective stress, is
σ 1 + e

E = = σ . (4.66)
h/h C v

The modulus E is not constant since it is proportional to σ and 1 + e. This statement tells

us that the soil gets “stiffer” the more it is compressed.

Exercise 4.3 What is the subsidence caused by a weight σ = 10 kPa placed on top of
a h = 2 m clay layer? The clay layer covers incompressible bedrock and has never been
preconsolidated. The normal consolidation line for the clay is e 0 = 1.5, C v = 0.2 and
σ = 1 kPa. It is assumed that e = e 0 through the entire thickness of the clay layer.

0

Solution: The change in the void ratio caused by the load is e = C v ln( σ /σ ) = 0.46,
0
which leads to the subsidence h = h e/(1 + e 0 ) = 0.37 m.
Exercise 4.4 Show that the void ratio of the normal consolidation line becomes zero for

the effective vertical stress σ = σ exp(e 0 /C v ). What is the stress for e 0 = 1.5, C v = 0.2
0
and σ = 1kPa?

0
Exercise 4.5 Derive equation (4.66).
4.6 Gravitational compaction of a hydrostatic clay layer
The weight of sediments alone will make the sediments compact. How much the porosity
is reduced with depth due to gravitational compaction can be computed using the nor-
mal consolidation line assuming hydrostatic conditions. The void ratio as a function of