Volume 6 – Geotechnical Manual, Site Investigation and Engineering ...

Chapter 3 FUNDAMENTAL PRINCIPLES
3.3 VERTICAL STRESS DISTRIBUTION
When a very large area is to be loaded, the induced stress in underneath soil would be would be
100% of the applied stress at the contact surface. However, near the edge or end of the loaded
area you might expect a certain amount of attenuation of stress with depth because no stress is
applied beyond the edge. Likewise, with a footing of limited size the applied stress would dissipate
rather rapidly with depth.
Figure 3.4 illustrated a schematic of the vertical stress distribution with depth along the center line
under an embankment of height, h, constructed with a soil having total unit weight, γ t .
Figure 3.4 Schematic of the Vertical Stress Distribution with Depth under an Embankment
generated by FoSSA Program (from Soil and Foundation - FHWA)
One of the simplest methods to compute the distribution of stress with depth for a loaded area is to
use the 2 to 1 (2:1) method. This is an empirical approach based on the assumption that the area
over which the load acts increases in a systematic way with depth. Since the same vertical force is
spread over an increasingly larger area, the unit stress decreases with depth, as shown in Fig. 3.4.
In Fig. 3.5a, a strip or continuous footing is seen in elevation view. At a depth z, the enlarged area
of the footing increases by z/2 on each side. The width at depth z is then B + Z and the stress σ z
at that depth is
σ z =
load
B+z×1 = σ o(B×1)
(B+z)×1
(3.3)
By analogy, the corresponding stress at depth z for a rectangular footing of width B and length L
(as illustrated in Figure 3.5b would be
∆σ z =
load
B+z(L+z) =
σ o BL
B+z(L+z)
(3.4)
3-4 March 2009