Geotechnical Engineering

DHARM

636 GEOTECHNICAL ENGINEERING

15.7.3Bearing Capacity of Rafts on Clays

The net ultimate bearing capacity is divided by the factor of safety to obtain the net allowable

soil pressure for a footing. The same principle is applicable to rafts on clay. Accordingly, the

factor of safety, η, in terms of net soil pressure, is given by

η =

cN

qD

c

()−γf

...(Eq. 15.23)

where, c = unit cohesion,

Nc = bearing capacity factor for cohesion,

q = gross soil pressure or contact pressure,

γ = unit weight of soil,

and Df = depth of raft below ground surface.

It is obvious that the factor of safety is very large for rafts established at such depths

that γDf is nearly equal to q. In fact, the theoretical value of η is infinite, when γDf equals q; in

such a case, the raft is said to be a ‘fully compensated foundation’ (Peck, Hanson and Thornburn,

1974).

15.7.4Coefficient of Subgrade Reaction

The ‘coefficient of subgrade reaction’ or ‘subgrade modulus’ is defined as the ratio between the

pressure and the settlement at a given point:

k =

q

S′

...(Eq. 15.24)
where, k = coefficient of subgrade reaction in N/mm^3 ,
q = pressure against the footing or raft at a given point in N/mm^2 ,
and S′ = settlement at the particular point in mm.
In other words, the coefficient of subgrade reaction is the pressure required to produce
unit settlement. This is difficult to determine for clayey soils in view of the long time required
for the consolidation settlement to occur. Equation 15.24 is based on the following assump-
tions:

(i)k is independent of pressure.

(ii)k is the same at every point of the footing or mat.

Actually, a number of factors affect the value of coefficient of subgrade reaction (Terzaghi,

1955):

Effect of size

The value of k decreases with increaseing width of footing.

k = k 1

b

b

F +

HG

I

KJ

03

2

.^2
... granular soils ... ...(Eq. 15.25)

k =

k

b

(^1) ... cohesive soils ... ...(Eq. 15.26)
where k = coefficeint of subgrade reaction for a very long footing of width b m, and
k 1 = coefficient of subgrade reaction for a very long footing of width 1 m.