Solving Stress-Deformation Problems with Unsaturated Soils - Unsaturated Soil Mechanics in Engineering Practice - page 759

and a reduction in evapotranspiration commonly contribute
to an increase in the water content of the soil. A perched
water table may develop which controls final equilibrium
pore-water pressures in the soil if an aquatard is encoun-
tered. The zone of wetting and the final pore-water pressures
will depend upon water balance calculations at ground sur-
face in the case where an expansive soil layer is extensive
and no aquatard exists. A transient seepage analysis can be
used in this case to assess the zone over which wetting is
likely to occur.
There are several terms that have been used to define dif-
ferent types and amount of wetting that might occur in an
expansive soil layer. The general term for the zone of wet-
ting is the “active zone” (Nelson et al., 2001; Overton et al.,
2011). This term has also been used for other applications
(e.g., permafrost) and is too general to clearly define the
degree and type of wetting. Nelson et al., (2001) provided
several definitions that provide a more detailed description
of the zone of wetting in an expansive soil:
(i) “ Active Zone, z a , is that zone of soil that is contribut-
ing to heave due to soil expansion at a particular
point in time. The depth of the active zone will vary
as heave progresses, and therefore, varies with time.”
(ii) “ Zone of Seasonal Moisture Fluctuation, z s , is that
zone of soil in which water contents change season-
ally due to climate changes.”
(iii) “ Zone of Wetting, z w , is the zone in which water
contents have increased over pre-construction equi-
librium conditions. Factors contributing to this could
include capillary rise after the elimination of evapo-
transpiration from the surface, infiltration due to irri-
gation from the surface, or introduction of water from
off-site. Underground sources may include broken
water lines, development of perched water tables, or
flow through permeable strata that are recharged at
distant locations.”
(iv) “ Depth of Potential Heave, z p , is the depth to which
the overburden vertical stress is equal or exceeds the
swelling pressure of the soil. This represents the max-
imum depth of the Active Zone that could occur.”
The above-mentioned definitions infer that there are
numerous factors that affect the depth and amount of
wetting that might occur at a particular site. These factors
form the boundary conditions for a heave analysis and must
be assessed for each expansive soils problem. It is generally
possible to make an appropriate assumption regarding the
final wetting conditions (or pore-water pressure conditions)
that should be analyzed. It is also possible to use weather
conditions and saturated-unsaturated hydraulic properties to
assess realistic boundary conditions.

example considers a 2-m-thick layer of swelling clay
(Fig. 14.38). The initial void ratio of the soil is 1.0, the
total unit weight is 18.0 kN/m 3 , and the swelling index
C s is 0.1. One oedometer test was performed on a sample
taken from a depth of 0.75 m. The test data showed a
corrected swelling pressure of 200 kPa. It is assumed that
the corrected swelling pressure is constant throughout the
2-m layer.
Let us consider the case where the ground surface is
covered with an impermeable layer such as asphalt. The
negative pore-water pressure in the soil below the asphalt
will increase with time as a result of the reduction in evap-
oration and evapotranspiration. Let us assume for analysis
purposes that the final pore-water pressures increase to zero
throughout the entire depth.
The 2-m layer is subdivided into three sublayers. The
amount of heave in each layer is computed by considering
the stress state changes at the middle of the layer. The ini-
tial stress state P 0 is equal to the corrected swelling pressure
at all depths. The final stress state P f will be the overbur-
den pressure. Equation 14.18 is used to calculate the heave
for each sublayer. The calculations in Fig. 14.38 show that
a total heave of 11.4 cm is likely to occur. Approximately
36% of the total heave occurs in the upper quarter of the
clay strata. The calculations also show the amount of heave
that would occur if each layer became wet from the surface
downward.

14.5.6 Second Example of One-Dimensional Heave
Calculations
The second example illustrates a more complex loading
situation and the results are presented in Fig. 14.39. The
expansive clay layer is 2m in thickness. The initial void
ratio is 0.80, the total unit weight is 18.0 kN/m 3 , and the
swelling index C s is 0.21. Three oedometer tests were per-
formed which show a decrease in the corrected swelling
pressure with depth (Fig. 14.39).
Suppose the engineering design suggests the removal of
1 / 3 m of swelling clay from ground surface followed by
the replacement with 2 / 3 m of gravel. The unit weight of
the gravel is assumed to be equal to that of the clay. The
remaining 1 2 / 3 m of swelling clay is subdivided into three
layers for calculation purposes. The thickness of each layer
is shown in Fig. 14.39.
The initial stress state P 0 for the midpoint of each layer
can be obtained by interpolating between the measured
swelling pressures. The final stress state P f must take into
account the final pore-water pressure and changes in the
total stress. The final pore-water pressure is assumed to
be 7.0 kPa. Equation 14.18 can be used to calculate the

change in volume that should occur within each layer. The
total heave for the three layers is computed to be 22.1 cm.
Two assumptions were made during the heave analysis.
First, it was assumed that the independent processes of exca-
vation of the expansive soil and the placement of the gravel

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14.5.5 First Example of One-Dimensional Heave
Calculations
The following example problems are presented to illustrate
the calculations associated with total heave. The first