Geotechnical Engineering

DHARM

COMPRESSIBILITY AND CONSOLIDATION OF SOILS 225

7. Certain soil properties such as permeability and modulus of volume change are con-
   stant; these actually vary somewhat with pressure. (k and mv are independent of pres-
   sure).


8. The pressure versus void ratio relationship is taken to be the idealised one, as shown in
   Fig. 7.18 (av is constant).


9. Hydrodynamic lag alone is considered and plastic lag is ignored, although it is known to
   exist. (The effect of k alone is considered on the rate of expulsion of pore water).
   The first three assumptions represent conditions that do not vary significantly from
   actual conditions. The fourth assumption is purely of academic interest and is stated because
   the differential equations used in the derivation treat only infinitesimal distances. It has no
   significance for the laboratory soil sample or for the field soil deposit. The fifth assumption is
   certainly valid for deeper strata in the field owing to lateral confinement and is also reason-
   ably valid for an oedometer sample. The sixth assumption regarding flow of pore water being
   one-dimensional may be taken to be valid for the laboratory sample, while its applicability to
   a field situation should be checked. However, the validity of Darcy’s law for flow of pore water
   is unquestionable.

The seventh assumption may introduce certain errors in view of the fact that certain
soil properties which enter into the theory vary somewhat with pressure but the errors are
considered to be of minor importance.

The eighth and ninth assumptions lead to the limited validity of the theory. The only
justification for the use of the eighth assumption is that, otherwise, the analysis becomes
unduly complex. The ninth assumption is necessitated because it is not possible to take the
plastic lag into account in this theory. These two assumptions also may be considered to intro-
duce some errors.

Now let us see the derivation of Terzaghi’s theory with respect to the laboratory oedometer
sample with double drainage as shown in Fig. 7.21.

2H

Increment of pressureDs

Ds

Clay sample

Porous stone

Porous stone

dz

u=i Ds

t=¥ t=0

(a) Consolidating clay sample

(b) Distribution of hydrostatic

excess pressure with depth

z

Fig. 7.21 Consolidation of a clay sample with double drainage
Let us consider a layer of unit area of cross-section and of elementary thickness dz at
depth z from the pervious boundary. Let the increment of pressure applied be ∆σ. Immediately