Geotechnical Engineering

DHARM

BEARING CAPACITY 557

Thus, the corrected expression for bearing capacity is

qult^ = (c + c′) cot φ (Nφeπ tan φ – 1) ...(Eq. 14.49)

or qult^ = (c cot φ + γH 1 )(Nφeπ tan φ – 1) ...(Eq. 14.50)

Taylor’s Correction

Taylor (1948) suggested a correction factor for c cot φ as follows:

qult = cbNcotφγ+ φ

F

HG

I

KJ

1

2 (Nφe

π tan φ – 1) ...(Eq. 14.51)

Taylor’s correction is simple and easy to apply, while Terzaghi’s correction is more logi-
cal but more difficult to calculate. However, nothing was said as to how Taylor’s correction
factor was derived.
Taylor has also attempted to include the effect of overburden pressure in the case of a
footing founded at a depth Df below the ground surface, proceeding in an exactly similar way
as is done in deriving Prandtl’s equation (Eq. 14.46). The additional value, q′ult, of the bearing
capacity in this case is

q′ult = γDf Nφ. eπ tan φ ...(Eq. 14.52)

The general equation for the bearing capacity of a footing founded at a depth Df below

the ground surface is then given by,

qult = FcbNcotφγ+ φ

HG

I

KJ

1

2

(Nφ. eπ tan φ – 1) + γDf Nφ eπ tan φ ...(Eq. 14.53)

according to Taylor.
However, Jumikis (1962) prefers Terzaghi’s correction in the final expression as fol-
lows:
qult = (c + c′) cot φ (Nφeπ tan φ – 1) + γz Nφ eπ tan φ ...(Eq. 14.54)
where γz is considered to be the surcharge at the base level of the footing, either because of the
depth of the footing below the ground or because of any externally applied surcharge load.

Discussion of Prandtl’s Theory

(i) Prandtl’s theory is based on an assumed compound rupture surface, consisting of an

arc of a logarithmic spiral and tangents to the spiral.

(ii) It is developed for a smooth and long strip footing, resting on the ground surface.

(iii) Prandtl’s compound rupture surface corresponds fairly well with the mode of failure

along curvilinear rupture surfaces observed from experiments.

In fact, for φ = 0°, Prandtl’s rupture surface agrees very closely with Fellenius’

rupture surface (Taylor, 1948).

(iv) Although the theory is developed for a c – φ soil, the original Prandtl expression for

bearing capacity reduces to zero when c = 0, contradicting common observations in

reality. This anomaly arises from the fact that the weight of the soil wedge directly

beneath the base of the footing is ignored in Prandtl’s analysis.

This anomaly is sought to be rectified by the Terzagthi/Taylor correction.

(v) For a purely cohesive soil, φ = 0, and Prandtl’s equation, at first glance, leads to an

indeterminate quantity; however this difficulty is overcome by the mathematical

technique of evaluating a limit under such circumstances.