Geotechnical Engineering

DHARM

BEARING CAPACITY 549

Equation 14.7 is rewritten sometimes, to give Df , which is termed the minimum depth

required for a foundation:

Df =

q

γ

φ

φ

1

1

2

−

+

F

HG

I

KJ

sin

sin

...(Eq. 14.8)

An alternative approach based on Rankine’s earth pressure theory which takes into
account the size b of the footing is as follows (Fig. 14.2).

It is assumed that rupture in the soil takes place along CBD and CFG symmetrically.
The failure zones are made of two wedges as shown. It is sufficient to consider the equilibrium
of one half.

Wedge I is Rankine’s active wedge, pushed downwards by qult on CA; consequently the

vertical face AB will be pushed outward.

Wedge II is Rankine’s passive wedge. The pressure P on face AB of wedge I will be the

same as that which acts on face AB of wedge II; consequently, the soil wedge II is pushed up.

The surcharge, q = γDf, due to the depth of footing resists this.

b/2 b/2

Df

II

AA

BB

P

P

— tan

aa

b 2 aa

ap D

Tp Np

qult q= Dg f

C aa

Ta

Na

C

F

G

q= Dg f qult

E

II I I II

aa

aa A ap D

q= Dg f

B

afa= 45° + /2

afp= 45° – /2

Fig. 14.2 Rankine’s method taking into account the size of the footing

From wedge II,

AB =

b

2

tan αa =

b

2

tan (45° + φ/2) =

b

2

Nφ

P =^1

24 2

(^2232)
..γγb NDφφ+ f.bN / ...(Eq. 14.9)
from Rankine’s theory for the case with surcharge. From Wedge I, similarly,
P =
1
24 2
11
24 2
.. .γγ^22 φ.....^1
φ
φ
φ φ
b N
N
q b N
N
b q b
N
+=+ult ult ...(Eq. 14.10)