Compressibility and Pore Pressure Parameters - Unsaturated Soil Mechanics in Engineering Practice - page 801

Figure 15.15 Initial and final pressure and volume conditions used in Hilf (1948) analysis.

n = 1 − S 0 n 0

u af , can be written as
the initial absolute pore-air pressure plus the change (i.e.,
increase) in pore-air pressure:

The final absolute air pressure,

(15.60)

Substituting Eq. 15.60 into Eq. 15.59 gives the absolute
pore-air pressure change (i.e., increase) required for saturat-
ing a soil:

u af = u a 0 + u a (15.56)

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where:

− S 0
S 0 h

u as = u a 0 (15.61)

u a = change (i.e., increase) in absolute pore-air pres-

sure.

where:

Boyle's law can be applied to the initial and final condi-
tions of the free and dissolved air:

u as = pore-air pressure change (i.e., increase) required

for saturation.

u a 0 V a 0 = u af V af (15.57)

Equation 15.61 is equivalent to the equation for comput-
ing the saturation pressure from the density of an air-water
mixture. Equation 15.59 can be written in an alternate form
by replacing n with V ν /V 0 :

Substituting the initial conditions and the final conditions
into Eq. 15.57 gives

u a 0 [ ( 1 hS 0 n 0 ] V 0

= u a 0 + u a 1

− S 0 )n 0 +

u a
u a 0 + u a

( 1

− S 0 n 0 + hS 0 n 0 − n V 0

V ν
V 0

(15.58) = − S 0 + hS 0 )n 0 (15.62)

Rearranging Eq. 15.58 yields an expression for the change
in pore-air pressure: u a

where:

:

V ν /V 0 = change in volume of voids referenced to the

initial volume of the soil (i.e., porosity change
n ).

n

u a = u a 0

(15.59)

( 1 − S 0 )n 0 + hS 0 n 0 − n

The above equation is commonly referred to as Hilf's
equation. It provides a relationship between the change in
pore-air pressure and the change in pore-air volume (i.e.,
n ) during K 0 -undrained loading. The change in pore-air
pressure can be computed from Hilf's equation if the change
in porosity is known.
The soil can reach a point of saturation when the soil
volume change, V ν , is equal the volume of free air [i.e.,

The above equation describes the volume change due to
the compression of air. The soil volume change can also
be computed from the constitutive relationship for the soil
structure. Hilf (1948) assumed that the matric suction in the
soil was small and that a change in pore-air pressure was
equal to a change in pore-water pressure (i.e., u a = u w ).
It was also assumed that the constitutive relation for the
soil structure could be measured by saturating the soil in an
oedometer test (i.e., under constant-volume conditions) and

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− S 0 n 0 V 0 ] (see Fig. 15.15). The change in porosity cor-
responding to this condition can be written as