Geotechnical Engineering

DHARM

570 GEOTECHNICAL ENGINEERING

If the water table is above the base of the footing, the reduction factor for the third term
is obviously limited to the maximum of 0.5. Further, in such a case, reduction will be indicated
for the second term, which indicates the contribution to the bearing capacity of the surcharge
due to the depth of the foundation. Proceeding with a similar logic, one comes to the conclusion
that the maximum reduction of 0.5 is indicated for the second term when the water table is at
the ground level itself (or above it), since γ′ is to be used for γ in the second term. While no
reduction in the second term is required when the water table is at or below the base of the
footing, a proportionate reduction, with a suitable linear interpolation, is indicated when the
water table is at a level intermediate between the ground level and the base of the footing.
Thus, both the second and third terms will be modified in this case.
The first term, cNc, does not get affected significantly by the location of the water table;
except for the slight change due to the small reduction in the value of cohesion in the presence
of water.
In the case of purely cohesive soils, since φ ≈ 0°, Nq = 1 and Nγ = 0, the net ultimate
bearing capacity is given by c. Nc, which is virtually unaffected by the water table, if it is below
the base of the footing. Even if the water table is at the ground level, only the gross bearing
capacity is reduced by 50% of the surcharge term γDf (Nq = 1), while the net value is again only
c. Nc.
In the case of purely cohesionless soils, since c = 0, and φ > 0, and Nq and Nγ are signifi-
cantly high, there is a substantial reduction in both the gross and net values of the bearing
capacity if the water table is at or near the base of the footing and more so if it is at or near the
ground surface.
For locations of ground water table within a depth of the width of the foundation below
the base and the ground level, the equation for the ultimate bearing capacity may be modified
as follows:

qult = *c′Nc + γDf NqRq +

1

2

** γb Nγ. Rγ ...(Eq. 14.101)

where c′ = effective cohesion (may be taken as c itself, in the absence of suffi-

cient data).

Nc, Nq, and Nγ = bearing capacity factors based on the effective value of friction angle

φ′ and,

Rq and Rγ = reduction factors for the terms involving Nq and Nγ owing to the

effect of water table.

Rq and Rγ may be obtained as follows, from Fig. 14.14:

zq = 0...Rq = 0.5 zγ = 0...Rγ = 0.5

zq = Df...Rq = 1.0 zγ = b...Rγ = 1.0

These conditions and the linear relationship of the chart are also expressed by the

following equations:

Rq = 0.5^1 +

F

H

G

I

K

J

z

D

q

f

...(Eq. 14.102)

Rγ = 0.5^1 +

F

HG

I

KJ

z

b

γ

...(Eq. 14.103)

*appropriate multiplying factor should be used for isolated footings.

**Appropriate shape factor.