Compression and swelling - The Mechanics of Soils and Foundations - page 108

The parameters and N are material parameters and their values depend only on

the nature of the grains. Relationships between these and other material parameters
and soil classifications are discussed in Chapter 18. Soil could be unloaded from any
point on the normal compression line and there are any number of swelling lines. For
each line there is a particular value of v κ and a particular value for the yield stress
p y . Using Eqs. (8.2) and (8.3) it is possible to calculate the current specific volume of
any isotropically compressed sample given the history of loading and unloading and
to calculate the recoverable and irrecoverable volume changes.
From Eq. (8.2), differentiating with respect to p and dividing by v we have

λ , κ

= vp

d v
v

d p =

− d ε (8.4)

v

and, comparing with Eq. (8.1),

vp
λ

K =

(8.5)

which is appropriate for first loading. Similarly, for unloading and reloading, we have
K vp / . Notice that the bulk modulus K

, which are material
parameters and so are constants for a particular soil, and vp which changes during
loading and unloading. As a result K is not a constant and isotropic compression and
swelling lines are non-linear, as shown in Figs. 8.2 and 8.3(a).

= κ contains λ or κ

8.3 Overconsolidation and yield stress ratio
In Fig. 8.4 the state of a soil during first loading, after deposition, travels down the
normal compression line OACD and soil that has been unloaded or reloaded travels
on a swelling and recompression line such as ABC characterized by v κ or p y . The state
of the soil can reach any point below and to the left of the normal compression line
by unloading, but the state cannot reach the region above and to the right. Hence the

Figure 8.4 Overconsolidation.