Foundation Settlement and Soil Compression - Elements of Soil Mechanics - page 345

Fig. 11.13 Typical shape of the isotropic normal consolidation of a saturated cohesive soil.

Fig. 11.14 Idealised form of v-ln p ′ plot.

p m and the pressure at D, a point on the swelling
line, is p ′ then we can say that the degree of overconsolidation represented by point D is R

If the maximum previous pressure on a swelling line is ′

= ′

′ .

p /p p

(Note the use of the subscript 'p' in R p to indicate isotropic consolidation.)
Fig. 11.14 is a close-up of Fig. 11.13c . In the diagram let the slope of AC, the normal isotropic consoli-
dation line, be − λ , and the slope of the swelling line, DB, be − κ . N = the specific volume of a soil normally
consolidated at ln p ′ value of 0.0. This gives ln p ′ = 0. Then the equation of line AC is:

′

v N = − λ ln p

A swelling line, such as BD, can lie anywhere beneath the line AC as its position is dependent upon the
value of the maximum pressure on the line, p m , which determines the position of B.
Let v κ = the specific volume of an overconsolidated soil at p ′ = unity (i.e. 1.0 kPa). Then the equation
of line DB is:

v = − v κ ln p ′

κ

λ , N and κ are measured values and must be found from appropriate tests.

Note: The normal consolidation line, AC, is often referred to as the λ line, i.e. the lambda line, and the
swelling line BD is often called the κ line, i.e. the kappa line.