Page 107 - Physical Principles of Sedimentary Basin Analysis

4.5 Compaction of sediments 89

1.50
Overconsolidation line
Reloading

1.00 Normal consolidation line
void ratio [−]

0.50 Unloading

Preconsolidation stress
0.00
0.1 1 10 100
effective vertical stress [MPa]
Figure 4.2. The normal consolidation line and the overconsolidation line. (The normal consolidation

line (4.63) has the parameters e 0 = 1, σ = 1 MPa and C c = 0.2.)
0
a confined cylindrical test sample is compressed axially. The oedometer test is close to
the compaction that often takes place in nature because the test sample is not allowed to
expand in the plane normal to the cylinder. The results of a compaction experiment with an
oedometer can be plotted in a semi-logarithmic plot like the one shown in Figure 4.2.The

void ratio can be approximated by a straight line when plotted as a function of ln(σ /σ ),
0

where σ and σ are the effective stress and a reference effective stress, respectively. This
0
straight line is called the normal consolidation line, and it is written
σ

e = e 0 − C c ln (4.63)
σ
0
where the slope of the line C c is called the compression index. The void ratio e 0 is the sur-
face void ratio obtained at the reference effective stress σ . The reference effective stress

0
σ can be set to 1 kPa, which corresponds to the weight of 10 cm of water. A reference

0
effective stress also serves to make the argument to the ln-function dimensionless. The nor-
mal consolidation line is an approximation that applies for effective stresses over a limited
4
range, typically from 10 kPa to 10 kPa. We notice that the void ratio of equation (4.63)
for the normal consolidation line can be made negative for a sufficiently large effective
stress. Such stresses are obviously beyond the interval where the normal consolidation line
applies, because negative void ratios do not make sense.
When a soil sample is unloaded the soil does not decompact and recover its original
void ratio, like an elastic spring that always recovers its length when unloaded. The path
followed during unloading can be approximated by another line called the overconsolida-
tion line. When reloaded (after unloading) the soil follows the overconsolidation line until