Consolidation Settlement - Part 02

The coefficient of volume compressibility (mv)

The coefficient of volume compressibility (mv) defined as the volume change per unit volume, per unit increase in effective stress.

The Compression Index (Cc)

The compression index (Cc) is the slope of the linear portion of the e log (sigma') curve. it is dimensionless parameter.

Example :
A 5 m thick clay layer is subjected to a stress increment of 100 K Pa. if the coefficient of volume compressibility of the clay is 1x10^-4 K pa, estimate the total consolidation settlement of the clay layer. (assume the clay layer is saturated)

 



delta H = 1x10^-4 x 5 x 100 = 0.05 m = 5 mm

The British standards recommends the use of  "mv" calculated for a stress increment of 100 K Pa in excess of the effective overburden pressure of the in-situ soil at the depth of interest. ( that means half the thickness of the considered soil length)

Preconsolidation Pressure (sigma c ')

Casagrande proposed an empirical construction to obtain from the e log sigma' curve for over consolidated clay the maximum effective vertical stress that has acted on the clay in the past, referred to as the preconsolidation pressure -  sigma c '


Procedure to find the preconsolidation pressure

1) locate the point D ( maximum curvature on the recompression part AB)
2) draw tangent to the curve at D and draw a horizontal line also
3) divide the angle of FDG using a line (DE)
4) draw the tangent to liner portion of the graph BC
5) the intercept of BC tangent and DE is shows the preconsolidation pressure

Over Consolidation Ratio (OCR) 

If,
OCR = 1 ; the soil is " Normally consolidated "
OCR > 1 ; the soil is " Over consolidated "

Note : A soil can never have an OCR < 1 ( as such a soil is one that has been recently deposited and equilibrium stresses have get to be attained )

 Estimation of final consolidation settlement 

 

where,
H = initial height
e0 = initial void ratio
delta e = change of the void ratio
S = final settlement

For normally consolidated soil

where,
Cc = compression index
sigma v0 ' = initial effective overburden pressure
delta sigma = changing strss

Example :
e0 = 0.6, Cc = 0.11, sigma v0' = 75 K Pa, delta sigma = 25 K Pa, H = 5 m what is the total settlement (OCR = 1)

S = 5 x 0.11 {log (75+25/75) } / ( 1 + 0.6 ) = 0.043 m = 43 mm

For over consolidated soil 

 

Example :
e0 = 0.6, Cc = 0.11, Cr = 0.011 sigma v0' = 75 K Pa, delta sigma = 100 K Pa what is the total settlement (OCR = 1.6, H = 5m)

OCR = 1.6
1.6 = sigma c' / sigma v0'
sigma c' = 1.6 x 75 = 120

S = {5 / (1 + 0.6) } x 0.011 log (120/75) + {5 / (1 + 0.6) } x  0.11 log {(75 + 100 )/ 120} = 63 mm 

from same example for normally consolidated soil OCR = 1

S = 5/(1+0.6) x 0.11 x log {( 75 + 100)/75} = 126 mm 

When soil is over consolidated the settlement is low, therefore we can improve the soil using increasing OCR for that we can use Pre loading method.