Page 173 - Civil Engineering Formulas

110 CHAPTER FOUR

The net bearing capacity per unit area, q , of a long footing is convention-
u
ally expressed as
(4.14)
q u f c u N c vo N q f BN
where 1.0 for strip footings and 1.3 for circular and square footings
f
c undrained shear strength of soil
u
effective vertical shear stress in soil at level of bottom of
vo
footing
0.5 for strip footings, 0.4 for square footings, and 0.6 for
f
circular footings
unit weight of soil
B width of footing for square and rectangular footings and
radius of footing for circular footings
N , N , N bearing-capacity factors, functions of angle of internal
c
q

friction
For undrained (rapid) loading of cohesive soils, 0 and Eq. (4.7) reduces to
(4.15)
q u N c c u
where N N . For drained (slow) loading of cohesive soils, and c are
f
c
u
c
defined in terms of effective friction angle and effective stress c u .
Modifications of Eq. (4.7) are also available to predict the bearing capacity of
layered soil and for eccentric loading.
Rarely, however, does q control foundation design when the safety factor is
u
within the range of 2.5 to 3. (Should creep or local yield be induced, excessive
settlements may occur. This consideration is particularly important when select-
ing a safety factor for foundations on soft to firm clays with medium to high
plasticity.)
Equation (4.7) is based on an infinitely long strip footing and should be
corrected for other shapes. Correction factors by which the bearing-capacity
factors should be multiplied are given in Table 4.2, in which L footing
length.
The derivation of Eq. (4.7) presumes the soils to be homogeneous throughout
the stressed zone, which is seldom the case. Consequently, adjustments may be
required for departures from homogeneity. In sands, if there is a moderate varia-
tion in strength, it is safe to use Eq. (4.7), but with bearing-capacity factors repre-
senting a weighted average strength.
Eccentric loading can have a significant impact on selection of the bearing
value for foundation design. The conventional approach is to proportion the
foundation to maintain the resultant force within its middle third. The footing is
assumed to be rigid and the bearing pressure is assumed to vary linearly as
shown by Fig. 4.2(b). If the resultant lies outside the middle third of the foot-
ing, it is assumed that there is bearing over only a portion of the footing, as
shown in Fig. 4.2(d). For the conventional case, the maximum and minimum
bearing pressures are
P 6e
q m 1 (4.16)
BL B