Bearing capacity and settlement of shallow foundations - The Mechanics of Soils and Foundations - page 354

level and if the water table is just below the foundation level you should put γ w = 0in

φ = the term containing N q only. If the soil is water so 0

and Eq. (22.12) states that the weight of the foundation and the applied load is equal
to the weight of water displaced, which is Archimedes' principle.

0 we have N q = 1 and N γ =

22.6 Foundations on sand
Foundations on sand will be drained and the settlements ρ d will occur as the loads are

applied, as shown in Fig. 22.4(b). Figure 18.5 illustrates the different behaviour of a
foundation on a dense sand and a loose sand and shows that for a given allowable
settlement

a the allowable bearing pressure q a depends on the initial state. A simple
and logical design procedure would be to relate the allowable bearing pressure directly
to the distance of the initial state from the critical state line measured in some suitable
in situ test.
The routine test to measure state in the ground is the standard penetration test (SPT)
described in Sec. 16.5. The result is given as a blowcount value N which varies from
small values (1 to 5) when the soil is at its loosest state to large values (over 50) when
the soil is at its most dense state. A simple relationship between the SPT- N value and
the allowable bearing pressure was given by Terzaghi and Peck (1967) and a simple
rule of thumb is

ρ

q a = 10 N kPa (22.13)

This bearing pressure will give settlements of the order of 25 mm (1 inch). Because at
relatively small loads the load settlement curve in Fig. 18.5(b) is approximately linear,
halving the bearing pressure will give about half the settlement and so on.

22.7 Combined vertical and horizontal loading on
shallow foundations
Normally the loading on a foundation is vertical but there are many examples where
a foundation is required to support both vertical and horizontal loads. Horizontal
loads may be due to wind, waves or earthquakes or from the design of the structure.
Figure 22.8 shows a foundationwith a horizontal load H and a vertical load V . We have
already obtained solutions for the bearing capacity for the case where H 0 and the

loading is vertical. If V is small failure will occur when the shear stress on the base of
the foundation exceeds the soil strength and the foundation slides sideways. There are
other combinations of V and H which cause the foundation to fail.
A simple and effective approach is to construct a failure envelope which separates
safe from unsafe states. This can also be considered to be a plastic potential fromwhich
movements as the foundation fails can be found. The principles are similar to those
shown in Figs. 3.14 and 3.15.
Figure 22.8(b) shows a failure envelope for a simple foundation for undrained load-
ing. (The axes have been plotted in the directions of the loads and they have been
normalized by dividing by s u B .) When H

=

= 0 the foundation fails when V is given by

Eq. (22.6) with V / S u B = (2 + π ). When V = 0 the foundation slides sideways when