three times the width of a square footing or the diameter of a circular
footing, the stresses can be approximated by considering the footing to be a
point load. A strip load may also be treated as a line load at depths
greater than three times the width of the strip.
c. Vertical Stresses Beneath Regular Loads. Charts for computations of
vertical stress based on the Boussinesq equations are presented in Figures 3
through 7. Use of the influence charts is explained by examples in Figure
8. Computation procedures for common loading situations are as follows:
(1) Square and Strip Foundations. Quick estimates may be obtained
from the stress contours of Figure 3. For more accurate computations, use
Figure 4 (Reference 1, Stresses and Deflections in Foundations and
Pavements, by the Department of Civil Engineering, University of California,
(2) Rectangular Mat Foundation. For points beneath the mat, divide
the mat into four rectangles with their common corner above the point to be
investigated. Obtain influence values I for the individual rectangles from
Figure 4, and sum the values to obtain the total I. For points outside the
area covered by the mat, use superposition of rectangles and add or subtract
appropriate I values to obtain the resultant I. (See example in Figure 9.)
(3) Uniformly Loaded Circular Area. Use Figure 5 (Reference 2,
Stresses and Deflections Induced by Uniform Circular Load, by Foster and
Ahlvin) to compute stresses under circular footings.
(4) Embankment of Infinite Length. Use Figure 6 (Reference 3,
Influence Values for Vertical Stresses in a Semi-Infinite Mass Due to an
Embankment Loading, by Osterberg) for embankments of simple cross section.
For fills of more complicated cross section, add or subtract portions of
this basic embankment load. For a symmetrical triangular fill, set
dimension b equal to zero and add the influence values for two right
(5) Sloping Fill of Finite Dimension. Use Figure 7 (Reference 1)
for stress beneath the corners of a finite sloping fill load.
d. Vertical Stresses Beneath Irregular Loads. Use Figure 10 (Reference
4, Soil Pressure Computations: A Modification of Newmark's Method, by
Jimenez Salas) for complex loads where other influence diagrams do not
suffice. Proceed as follows:
(1) Draw a circle of convenient scale and the concentric circles
shown within it. The scale for the circle may be selected so that when the
foundation plan is drawn using a standard scale (say 1"=100'), it will lie
within the outer circle.
(2) Plot the loaded area to scale on this target with the point to
be investigated at the center.
(3) Estimate the proportion A of the annular area between adjacent
radii which is covered by the load.