Civil Engineering Reference
In-Depth Information
δ
q
are given by
δσ
=
δ
qI
σ
(22.16)
z
2
qB
1
−
ν
δρ
=
δ
I
ρ
(22.17)
E
where
I
σ
and
I
ρ
are dimensionless influence factors and
B
is the width or the diameter
of the foundation. The values for the influence factors depend principally on the geom-
etry of the foundation and, to a lesser extent, on the value of Poisson's ratio. Notice
Eqs. (22.16) and (22.17) do not contain either
E
or
and so the vertical stress in elastic
soil depends only on the shape and loading of the foundation. A comprehensive set of
tables and charts for influence factors for a wide variety of loading cases are given by
Poulos and Davis (1974). Values for the most common simple cases for circular and
rectangular loaded areas are shown in Figs. 22.10 and 22.11.
To determine values inside or outside a rectangular or irregularly shaped area you
can simply divide the region into a number of rectangles, determine
ν
at the
corners of the various rectangles and, making use of the principle of superposition, add
or subtract the individual effects. For example, for the L-shaped building in Fig. 22.12
the stresses and settlements at the corner E can be found by adding the effects of
the rectangles DABE, BCFE and HGDE; the stresses and settlements at the external
δσ
z
or
δρ
Figure 22.10
Influence factors for stresses and settlements below the centre of a circular
foundation.
