Building Design and Construction Handbook - Merritt - Ventech!

SOIL MECHANICS AND FOUNDATIONS 6.45
where � w � unit weight of water
z w � depth below the groundwater table
If the total unit weight of the soil (Eq. 6.11), and the pore water pressure (Eq.
6.12) are known, then the vertical effective stress (� �v ) can be calculated. An alternative
method is to use the buoyant unit weight (�b, see Table 6.6) to calculate the
vertical effective stress. For example, suppose that a groundwater table corresponds
with the ground surface. In this case, the vertical effective stress (� �v ) is simply the
buoyant unit weight (�b) times the depth below the ground surface. More often, the
groundwater table is below the ground surface, in which case the vertical total stress
of the soil layer above the groundwater table must be added to the buoyant unit
weight calculations.
6.4.2 Stress Distribution
The previous section described methods used to determine the existing stresses
within the soil mass. This section describes commonly used methods to determine
the increase in stress in the soil deposit due to applied loads. This is naturally
important in settlement analysis because the settlement of the structure is due directly
to its weight, which causes an increase in stress in the underlying soil. In
most cases, it is the increase in vertical stress that is of most importance in settlement
analyses. The symbol � z is often used to denote an increase in vertical stress
in the soil, although �� v (change in total vertical stress) is also used.
When dealing with stress distribution, a distinction must be made between onedimensional
and two- or three-dimensional loading. A one-dimensional loading
applies a stress increase at depth that is 100% of the applied surface stress. An
example of a one-dimensional loading would be the placement of a fill layer of
uniform thickness and large areal extent at ground surface. Beneath the center of
the uniform fill, the in-situ soil is subjected to an increase in vertical stress that
equals the following:
where h � thickness of the fill layer
� t � total unit weight of the fill
� � �� � h� (6.13)
z v t
In this case of one-dimensional loading, the soil would only be compressed in the
vertical direction (i.e., strain only in the vertical direction).
Another example of one-dimensional loading is the uniform lowering of a
groundwater table. If the total unit weight of the soil does not change as the groundwater
table is lowered, then the one-dimensional increase in vertical stress for the
in-situ soil located below the groundwater table would equal the following:
� � �� � h� (6.14)
z v w
where h � vertical distance that the groundwater table is uniformly lowered
� w � unit weight of water
Surface loadings can cause both vertical and horizontal strains, and this is referred
to as two- or three-dimensional loading. Common examples of twodimensional
loading are from strip footings or long embankments (i.e., plane strain
conditions). Examples of three-dimensional loading would be square and rectan-