Shear Strength Applications in Plastic and Limit Equilibrium - Unsaturated Soil Mechanics in Engineering Practice - page 626

horizontal pressure is even higher than that shown for the
previous case (i.e., C 1 ).
The exact stress path followed by the soil during wet-
ting is dependent upon (1) the initial at-rest pressure state,
(2) the deformation moduli of the soil, and (3) the rigidity
of the retaining structure. In other words, the problem is one
involving soil-structure interaction. It would be necessary to
use a numerical technique such as the finite element method
to more closely model changes in stress state.
There are undoubtedly conditions in practice where back-
fill with a material that has high matric suction is placed
against a rigid wall or where a heavy structural member
is cast against clay with an at-rest coefficient greater than
1.0. The horizontal stresses can become as large as the pas-
sive resistance of the soil in these circumstances. Generally,
this situation would correspond to the passive resistance of
the saturated soil. When this happens, either the structural
member may fail or the soil may fail in shear. A structural
member placed against an expansive soil must be designed
to not move or resist the passive earth pressure.

laboratory specimen to a vertical pressure corresponding to
a particular depth and immerse the specimen in water. It
would then be necessary to measure the lateral swelling
pressure of the soil in order to obtain an indication of the
horizontal pressure against a retaining structure. Clearly, it
is difficult to apply conventional swelling pressure measure-
ments to retaining wall design. Also, several oedometer tests
would need to be run to represent the respective depths.
The stress paths shown in Fig. 12.61 assist in understanding
why walls with cohesive backfills may undergo large move-
ments during the life of the structure. As the soil dries, a crack
may open between the soil and the wall. Dust and debris col-
lect in the opening, partially filling the crack. As the matric
suction decreases during wetter seasons, the soil swells and
pushes the wall until the resistance of the wall is in equilibrium
with the soil mass. This cycle may be repeated many times
over the years, gradually moving the wall.

12.4 BEARING CAPACITY

The bearing capacity of unsaturated soils, like other plastic-
ity problems, can be viewed as an extension of the approach
used in saturated soil mechanics. The unsaturated soil can
be visualized as having a cohesion consisting of two com-
ponents. One component is the effective cohesion, and the
other component is cohesion associated with matric suction.
With this concept in mind, the conventional bearing capacity
theory can be applied to unsaturated soils.
Prandtl (1921) analyzed the case of a strip footing with a
smooth base located at ground surface (Fig. 12.62). The load
Q was increased until the strip footing penetrated the soil.
The unit pressure q f at this point was called the ultimate
bearing capacity. The loading of the strip footing gives rise
to an active pressure zone immediately below the footing and
a passive zone where the soil pushes laterally and upward.
The intermediate portion of the slip surface is defined by a
logarithmic spiral. The soil is assumed to be weightless. The
rigorous and demanding nature of the solution to this idealized
problem has led to the consideration of other approximate
solutions.

12.3.18 Relationship between Swelling Pressures
and Earth Pressures
The question can be asked, “What is the relationship between
the above earth pressures and the swelling pressure of a soil?”
Suppose the swelling pressure of the soil was measured in
an oedometer using the “constant-volume” procedure. The
measured swelling pressure corresponds to conditions of no
volume change (i.e., vertically or horizontally). The swelling
pressure will be a function of the initial stress state and the
change in matric suction. However, it is difficult to relate
the swelling pressure to the active or passive earth pres-
sure states. The stress paths followed in the two situations
are different.
The vertical stress will be the overburden pressure in the
case of an earth-retaining structure. Its magnitude is constant
while both the vertical and horizontal movement is restricted
in the laboratory oedometer test (i.e., using the constant-
volume testing technique). To more closely simulate the in
situ retaining structure, it would be necessary to subject the

B

Q

Figure 12.62 Idealized bearing capacity for failure geometry below footing using Prandtl log
spiral (from Prandtl, 1921).