DHARM

240 GEOTECHNICAL ENGINEERING

Another way of expressing the time–rate of secondary compression is through the ‘coef-
ficient of secondary compression’, Cα, in terms of strain or percentage of settlement as follows:

ε =

∆H

H

C

t

t

=−

F

HG

I

α KJ

log 10 2

1

...(Eq. 7.34)

In other words, Cα may be taken to be the slope of the straight line representing the
secondary compression on a plot of strain versus logarithm of time.
The relation between α and Cα is

Cα =

α

()1+e ...(Eq. 7.35)

Generally α and Cα increase with increasing stress.

Some common values of Cα are given below:

Table 7.1. Values of coefficient of secondary compression (Cernica, 1982)

Sl. No Nature of Soil Cα – Value

1. Over consolidated days 0.0005 to 0.0015


2. Normally consolidated days 0.005 to 0.030


3. Organic soils, peats 0.04 to 0.10

7.9 Illustrative Examples

Example 7.1: In a consolidation test the following results have been obtained. When the load
was changed from 50 kN/m^2 to 100 kN/m^2 , the void ratio changed from 0.70 to 0.65. Determine
the coefficient of volume decrease, mv and the compression index, Cc.

(S.V.U.—B.Tech., (Part-time)—Sep., 1982)

e 0 = 0.70 σ 0 = 50 kN/m^2

e 1 = 0.65 σ = 100 kN/m^2

Coefficient of compressibility, av =

∆

∆

e

σ

, ignoring sign.

=

(.. )

()

070 065

100 50

−

− m

(^2) /kN = 0.05/50 m (^2) /kN = 0.001 m (^2) /kN.
Modulus of volume change, or coefficient of volume decrease,
mv =
a
e
v
()
.
(.)
.

1. 0 001
   1070
   0 001

• 
  

  0 17

  
  


• 
  

  = m^2 /kN.
  = 5.88 × 10–4 m^2 /kN
  Compression index, Cc =
  ∆
  ∆
  e
  (log )
  (.. )
  σ (log log )

  
  

  −
  −
  070 065
  10100 1050

  
  

  005
  100
  50
  005
  2
  0 050
  0 301
  10 10
  .
  log
  .
  log
  .
  .
  == = 0.166.