Geotechnical Engineering

DHARM

398 GEOTECHNICAL ENGINEERING

The principle of superposition may be used for determining the settlement underneath

any point of the loaded area by dividing the area into rectangles such that the point forms the

corner of each. The method can be extended to determine the immediate settlement of a clay

layer which is located at some depth below the foundation as in Fig. 11.3(b); the settlement of

a layer extending from below the foundation of thickness H 2 (using Es 2 ), is determined first;

from this value of imaginary settlement of the layer H 1 (again using Es 2 ) is subtracted. Since
this settlement is for a perfectly flexible foundation usually the value at the centre is deter-
mined and is reduced by a rigidity factor (0.8 usually) to obtain a mean value for the settle-
ment.
Effect of depth: According to Fox (1948), the calculated settlements are more than the
actual ones for deep foundations (Df > B), and a reduction factor may be applied. If Df = B, the
reduction factor is about 0.75; it is taken as 0.50 for very deep foundations. However, most
foundations are shallow. Further, in the case of foundations located at large depth, the com-
puted settlements are, in general, small and the reduction factor is customarily not applied.

Determination of Es: Determination of Es, the modulus of elasticity of soil, is not simple
because of the wide variety of factors influencing it. It is usually obtained from a consolidated
undrained triaxial test on a representative soil sample, which is consolidated under a cell
pressure approximating to the effective overburden pressure at the level from which the soil
sample was extracted. The plot of deviator stress wersus axial strain is never a straight line.
Hence, the value must be determined at the expected value of the deviator stress when the
load is applied on the foundation. If the thickness of the layer is large, it may be divided into a
number of thinner layers, and the value of Es determined for each.

11.3.2Consolidation Settlement or Primary Compression

The phenomenon of consolidation occurs in clays (chapter seven) because the initial excess

pore water pressures cannot be dissipated immediately owing to the low permeability. The

theory of one-dimensional consolidation, advanced by Terzaghi, can be applied to determine

the total compression or settlement of a clay layer as well as the time-rate of dissipation of

excess pore pressures and hence the time-rate of settlement. The settlement computed by this

procedure is known as that due to primary compression since the process of consolidation as

being the dissipation of excess pore pressures alone is considered.

Total settlement: The total consolidation settlement, Sc, may be obtained from one of the

following equations:

Sc =

HC

e

. c
()

log

1 0 10

0

+ 0

F +

HG

I

KJ

σσ

σ

∆

...(Eq. 11.7)

Sc = mν. ∆σ.H ...(Eq. 11.8)

Sc =

∆e

e

H

()

.

1 + 0

...(Eq. 11.9)

These equations and the notation have already been dealt with in chapter seven. The
vertical pressure increment ∆σ at the middle of the layer has to be obtained by using the
theory of stress distribution in soil.