State Variables for Unsaturated Soils - Unsaturated Soil Mechanics in Engineering Practice - page 95

constant value with depth. The pore-air pressure is generally
assumed to be in equilibrium with atmospheric pressure (i.e.,
zero gauge pressure). Figure 3.12a shows a typical profile
of the vertical net normal stress for geostatic conditions.
Total stresses can be computed by integration of Eq. 3.27
across each layer when there are soil strata with distinctly
different densities. The total vertical stress in a level soil
mass is computed in the same manner for both saturated
and unsaturated soils (Fig. 3.12). The total vertical stress σ v
can be computed as follows if only one soil is involved:

The coefficient of lateral earth pressure K 0 can be defined
as the ratio of horizontal net normal stress to vertical net
normal stress (Fig. 3.12). This is a slight variation from
saturated soil mechanics since the horizontal and vertical
stresses are now referenced to the pore-air pressure (which
is generally at atmospheric pressure):

σ h − u a

K 0 = (3.30)

σ v − u a

where:

H

σ v = ρg dy (3.28)

σ h − u a = horizontal net normal stress.

0

where:

The geostatic stress condition where there is no horizontal
strain is referred to as the coefficient of lateral earth pressure
at rest, K 0 (Terzaghi, 1925). The coefficient of lateral earth
pressure at rest depends on several factors such as the type
of soil, its stress history, and its density. Saturated soils
commonly have K 0 values ranging from as low as 0.4 to
values in excess of 1.0. Unsaturated soils are often over
consolidated and can have coefficients of earth pressure at
rest greater than 1.0 (Brooker and Ireland, 1965). On the
other hand, the coefficients of earth pressure at rest can go
to zero for the case where the soil becomes desiccated and
cracked. A profile of the horizontal net normal stresses under
at-rest conditions is shown in Fig. 3.12b.
The application of the theory of lateral earth pressures to
cracked, unsaturated soils is challenging to understand. The
horizontal total stress in the crack through a soil mass is
zero. However, the soil immediately adjacent to the crack is
being held together by soil suction. Consequently, one hor-
izontal stress condition can be observed in the crack of the
soil mass while another completely different stress condition
is observed in the adjacent intact soil.
The theory of elasticity can be used to compute changes
in total stress states. Elastic theory can be applied in a
similar manner for both saturated and unsaturated soils.
The total stress state within a continuum (i.e., including the
horizontal stress state) can be solved as a “boundary value”
problem when the ground surface is not horizontal and
where several soil types may be present. In this case, the
ground surface geometry and the soil strata can be modeled
using a finite element numerical stress analysis. Elasticity
parameters, including Young's modulus and Poisson's ratio,
need to be input for each soil layer. The computed stress
state is quite insensitive to the input soil parameters and as
a result it is possible to calculate reasonable estimates of
the total stress state. Figure 3.13 shows contours of vertical
stresses and horizontal stresses computed by “switching
on” the gravity forces in a numerical modeling analysis.
The switching-on type of analysis can readily be performed
even for complex geometric and soil conditions. Further
details pertaining to the stress-versus-strain relationship for
an unsaturated soil are presented in Chapter 13.

y = vertical distance from ground surface and

H = depth of soil under consideration.

The total vertical stress at any depth can be written as
follows if the soil mass is homogeneous:

σ v = ρ gH (3.29)

The pore-air pressure is generally at equilibriumwith atmo-
spheric pressure. The pore-water pressure above the ground-
water table can be either estimated or measured. The negative
pore-water pressure profile is largely controlled by the loca-
tion of the water table in the immediate region above the
water table. The negative pore-water pressures are largely
controlled by the net moisture influx at the ground surface in
the region near the ground surface. In other words, the local
climatic conditions significantly influence the near-ground-
surface pore-water pressures. The negative pore-water pres-
sure profile tends toward hydrostatic conditions if the annual
net moisture flux at ground surface approaches zero.
The matric suction profile is closely related to the near-
ground-surface climatic environment. The approximation or
determination of the initial soil suction profile is required
when analyzing a geotechnical engineering problem. The
in situ profile of pore-water pressures (and thus soil suc-
tion) can vary significantly throughout each year. The effect
of climatic conditions in a region should be analyzed by
taking moisture flux boundary conditions into consideration
throughout a year.

3.4.2 Coefficient of Lateral Earth Pressure
It is difficult to theoretically quantify the coefficient of earth
pressure at rest due to complexities arising from the stress
history to which the soil mass has been subjected. Consid-
eration of elastic equilibrium within a soil mass can provide
some insight into the coefficient of earth pressure at rest.
Elastic equilibrium can also provide some indication of the
depth of potential cracking in a soil mass. Further details on
elastic equilibrium can be found in Chapter 13.