Geotechnical Engineering

DHARM

566 GEOTECHNICAL ENGINEERING

In fact, the experimental relationships deduced by Skempton are not exactly linear
with respect to Df /b, but straight lines are fitted for the sake of simplicity.

For a surface footing of square or circular shape on purely cohesive soil

Qnet ult = 6c ...(Eq. 14.93)

as against 7.4c from Terzaghi’s theory.

It must be noted that Terzaghi’s theory is limited to shallow foundations wherein
Df /b ≤ 1, but Skempton’s equations do not suffer from such a limitation.

14.5.8Brinch Hansen’s Method

Brinch Hansen (1961) has proposed the following semi-empirical equation for the bearing ca-
pacity of a footing, as a generalisation of the Terzaghi equation:

qult =

Q

A

ult = cN

cscdcic + qNqsqdqiq +

1

2

γ b Nγsγiγ ...(Eq. 14.94)

where Qult = vertical component of the total load (= V),

A = effective area of the footing (this will arise for inclined and eccentric loads, when
the area A is transformed to an estimated equivalent rectangle with sides b and L, such that
the load is central to the area),

q = overburden pressure at the foundation level (= γ. Df),
Nc, Nq and Nγ = bearing capacity factors of Hansen, given as follows:
Nq = Nφ. eπ tan φ ...(Eq. 14.95)
Nc = (Nq – 1) cot φ ...(Eq. 14.96)
Nγ = 1.8 (Nq – 1) tan φ ...(Eq. 14.97)
(Nφ = tan^2 (45° + φ/2), with the usual notation.)
s′s = shape factors
d′s = depth factors, and
i′s = inclination factors.
The bearing capacity factors of Hansen, shape factors, depth factors, and inclination
factors are given in Table 14.4 to 14.7.

It has been found that Hansen’s theory gives a better correlation for cohesive soils than
the Terzaghi theory, although it may not give good results for cohesionless soils.

Table 14.4 Brinch Hansen’s bearing capacity factors

Hansen’s Bearing Capacity Factors

Angle of shearing Nc Nq Nγ

Resistance φ°

0 5.14 1.00 0

5 6.49 1.57 0.09

10 8.34 2.47 0.47

15 10.98 3.94 1.42

20 14.83 6.40 3.54

(Contd.)...