Solving Stress-Deformation Problems with Unsaturated Soils - Unsaturated Soil Mechanics in Engineering Practice - page 757

it is possible to perform a one-dimensional solution as a
numerical modeling problem (e.g., a finite element analysis).
Both solutions should give essentially the same answer for
total heave.
Two- and three-dimensional heave simulations that use
independent changes in matric suction and total stresses are
solved later in this chapter. The two- and three-dimensional
heave calculations are performed using a finite element mod-
eling procedure.

14.5.1 Theory of Heave Predictions (One-Dimensional
Heave)
Volume change coefficients or indices and matric suction
changes need to be measured or estimated for the prediction
of one-dimensional heave. The stress state variable changes
can be large, and consequently the soil properties can vary
as the stress levels change. It is necessary to integrate volu-
metric strain between the initial and final stress states. The
constitutive surface takes on a linear form when plotting
the total stress state on a logarithmic scale. It is possible to
transfer matric suction onto the total stress plane, thereby
simplifying the prediction of total heave.
The total heave formulation is first presented with the
initial and final stress states projected onto the total stress
plane. The results from a one-dimensional oedometer test
are plotted on a semilogarithmic scale of total stress state
and the slope of the plot is used in the formulation for
total heave.
The in situ stress state is equal to the vertical swelling
pressure of the soil, which is measured in a one-dimensional
oedometer under K 0 loading conditions. Only vertical or
one-dimensional heave is calculated. The vertical heave pre-
diction is of importance in the design of shallow foundations
for light structures. Two case histories dealing with highly
expansive soils in Saskatchewan, Canada, are later analyzed
and used to illustrate the calculation of total heave.
Volume change can also occur in the lateral directions
for loading configurations other than K 0 conditions. The
swelling pressure in the lateral direction depends on several
variables, such as the initial at-rest earth pressure coeffi-
cient and the horizontal deformation modulus for the soil.
In a soil with wide desiccation cracks, substantial volume
changes may occur in the horizontal direction prior to the
development of the lateral swelling pressure. The ratio of the
lateral to vertical swelling pressures can range from as low
as the at-rest earth pressure coefficient, which may be zero,
to as high as the passive earth pressure coefficient (Pufahl
et al., 1983; Fourie, 1989).

Figure 14.36 One-dimensional oedometer test results showing
effect of sampling disturbance.

the swelling index. The formulation can be visualized on a
plot of void ratio versus the logarithm of the stress state.
The formulation assumes that the stress path followed dur-
ing heave can be projected onto the total stress plane, as
shown in Fig. 14.36. The total heave stress path follows the
rebound curve (i.e., C s ) from the initial stress state to the
final stress state. The equation for the rebound portion of
the oedometer test data can be written as

log P f
P 0

e = C s (14.14)

where:

e = change in void ratio between the initial and final

stress states (i.e., e f − e 0 ),

e 0 = initial void ratio,

e f = final void ratio,

C s = swelling index,

P 0 = initial stress state, assumed to be equal to the cor-

rected swelling pressure (i.e., P 0 = P s ), and

P f = final stress state.

The initial stress state P 0 and the corrected swelling pres-
sure P s consist of the sum of the overburden pressure and
the matric suction equivalent (Fig. 14.10), as follows:

P 0 = (σ v − u a ) + (u a − u w ) e

(14.15)

where:

14.5.2 Total Heave Analysis Using Longhand
Calculations
The longhand calculation procedure for total heave is essen-
tially the reverse of the settlement analysis used for soft
compressible clays. Total heave is computed from changes
in void ratios between the initial and final stress states and

σ v = total overburden pressure,

σ v − u a = net overburden pressure,

u a = pore-air pressure,

u a −

u w e = matric suction equivalent, and

u w = pore-water pressure.