Geotechnical Engineering

DHARM

224 GEOTECHNICAL ENGINEERING

Pressure increment

1

2

3

Q Q

t=0

h=Dsg/w

P 123 P

4

DsJ

4

t=t 1

t=t 2

t=t 3

t=¥

Fig. 7.20 Mechanical analogy to consolidation process
Since water is permitted to escape only at one end, it is similar to the case of a single
drainage face for a consolidating clay sample. The distribution of hydrostatic excess pressure
will be symmetrical about mid-depth for the situation of a double drainage face, the maximum
occurring at mid-depth and the minimum or zero values occurring at the drainage faces.

7.4 TERZAGHI’S THEORY OF ONE-DIMENSIONAL CONSOLIDATION

Terzaghi (1925) advanced his theory of one-dimensional consolidation based upon the follow-
ing assumptions, the mathematical implications being given in parentheses:

1. The soil is homogeneous (kz is independent of z).


2. The soil is completely saturated (S = 100%).


3. The soil grains and water are virtually incompressible (γw is constant and volume change
   of soil is only due to change in void ratio).


4. The behaviour of infinitesimal masses in regard to expulsion of pore water and conse-
   quent consolidation is no different from that of larger representative masses (Principles
   of calculus may be applied).


5. The compression is one-dimensional (u varies with z only).


6. The flow of water in the soil voids is one-dimensional, Darcy’s law being valid.

∂

∂

=

∂

∂

==

∂

∂

F

HG

I

KJ

v

x

v

y

vk

h

z

x y 0and zz..

Also, flow occurs on account of hydrostatic excess pressure (h = u/γw).