DHARMCOMPRESSIBILITY AND CONSOLIDATION OF SOILS 2197.2.10 Modulus of Volume Change and Consolidation Settlement
The ‘modulus of volume change, is defined as the change in volume of a soil per unit initial
volume due to a unit increase in effective stress. It is also called the ‘coefficient of volume
change’ or ‘coefficient of volume compressibility’ and is denoted by the symbol, mv.mv = – ∆
∆e
()e.
11
+σ 0...(Eq. 7.9)∆e represents the change in void ratio and represents the change in volume of the saturated
soil occurring through expulsion of pore water, and (1 + e 0 ) represents initial volume, both for
unit volume of solids.
But we know from Eq. 7.2 that−∆
∆e
σ= av, the coefficient of compressibility.∴ mv =a
ev
()1+ 0...(Eq. 7.10)When the soil is confined laterally, the change in volume is proportional to the change
in height, ∆H of the sample, and the initial volume is proportional to the initial height H 0 of
the sample.
∴ mv = −∆
∆H
H 0.^1
σ
or ∆H = mv.H 0 .∆σ ...(Eq. 7.11)
ignoring the negative sign which merely indicates that the height decreases with increase in
pressure.
Thus, the consolidation settlement, Sc, of a clay for full compression under a pressure
increment ∆σ, is given by Eq. 7.11.
This is under the assumption that ∆σ is transmitted uniformly over the thickness. How-
ever, it is found that ∆σ decreases with depth non-linearly. In such cases, the consolidation
settlement may be obtained as:
Sc = mdzvH
..∆σ
z 0
...(Eq. 7.12)
This integration may be performed numerically by dividing the stratum of height H into
thin layers and considering ∆σ for the mid-height of the layer as being applicable for the thin
layer. The total settlement of the layer of height H will be given by the sum of settlements of
individual layers.
The consolidation settlement Sc, may also be put in a different, but more common form,
as follows:
mv =e
()e.
11
+∆σ 0
, ignoring sign.∆∆H
He
001 e=
()+Sc = ∆H =∆e
eH
().
1 + 0 0