Geotechnical Engineering

DHARM

220 GEOTECHNICAL ENGINEERING

Substituting for ∆e in terms of the compression index, Cc

from Eq. 7.4, recognising (e – e 0 ) as ∆e, we have:

Sc = ∆H = H 0.

C

e

c

()

.log

1 + 0 10 0

σ

σ ...(Eq. 7.13)

or Sc = H

C

e

0 c

0

10 0

(^10)
()
.log

• F +
  HG
  I
  KJ
  σσ
  σ ...(Eq. 7.14)
  This is the famous equation for computing the ultimate or total settlement of a clay
  layer occurring due to the consolidation process under the influence of a given effective stress
  increment.

7.3 A Mechanistic Model for Consolidation

The process of consolidation, and the Terzaghi theory to be presented in section 7.4, can be

better understood only if an important simplifying assumption is explained and appreciated.

The pressure-void ratio relationship for the increment of pressure under question is

taken to be linear as shown in Fig. 7.18, when both the variables are plotted to the natural or

arithmetic scale. It is further assumed that this linear relationship holds under all conditions,

with no variation because of time effects or any other factor. If there were no plastic lag in clay,

this assumption would have been acceptable; however, clays are highly plastic.

The process of consolidation may be explained on the basis of this simplifying assump-

tion as follows:

Let the soil sample be in equilibrium under the pressure σ 1 throughout its depth, at the

void ratio e 1. Immediately on application of the higher pressure σ 2 , the void ratio is e 1 only.

The pressure σ 2 cannot be effective within the soil until the void ratio becomes e 2 , and the

effective pressure is still σ 1. The increase in pressure, ()σσ 21 − tends to produce a strain (e 1 – e 2 ).

On account of hydrodynamic lag, this cannot take place at once. Thus, there is only one possi-

bility – the increase in pressure is carried by the pore water, with the pressure in the soil

skeleton still being σ 1. This increase in pressure in the pore water produced by transient

conditions as given above, is called ‘hydrostatic excess pressure’, u. The initial value, ui, for

this is ()σσ 21 −.

Ds=–=us 21 s i

u

E P

C BD

s 1 s s 2

Void ratio

e 1 A

e

e 2

Effective stress

Fig. 7.18 Idealised pressure-void ratio relationship