Compressibility and Pore Pressure Parameters - Unsaturated Soil Mechanics in Engineering Practice - page 802

measuring its volume change upon increased loading. The
volume change of the soil structure can be expressed as

value of m v can be used in Eqs. 15.65 and 15.66 when
considering a total stress change σ y . The secant pore-air
pressure parameter B ah is obtained by dividing the pore-
air pressure increase by the total stress increase. The B ah
pore-air pressure parameter is assumed to be equal to the
B wh pore-water pressure parameter in Hilf's analysis. As a
result, the difference between a pore-air pressure change and
a pore-water pressure change cannot be isolated when using
Hilf's analysis. Changes in pore-water pressure are gener-
ally assumed to be equal to the changes in pore-air pressure
when using Hilf's analysis. The initial pore-water pressure in
Hilf's analysis was assumed to be zero. Therefore, the com-
puted pore pressures in a compacted soil may be somewhat
high or conservative for design purposes.

= m v σ y − u a

V v
V 0

(15.63)

where:

m v = coefficient of volume change measured on a satu-

rated soil in a one-dimensional oedometer test.

The soil compressibility m 1 is assumed to be equal to the
coefficient of volume change m v measured under saturated
conditions. The pore-pressure parameter for K 0 -undrained
loading can be derived using Hilf's analysis by equating the
volume change of the soil structure to the volume change
due to the compression of air:

15.6 SOLUTIONS OF PORE PRESSURE
EQUATIONS AND COMPARISONS WITH
EXPERIMENTAL RESULTS
The pore pressure parameter equations can be solved and
compared with typical laboratory-measured results. The
effect of changing one or more of the variables in the pore
pressure equations is illustrated. The theoretical pore pres-
sure parameters can be used to estimate the pore pressures
that are likely to develop during construction.

1

hS 0 n 0
(15.64)

u a
u a 0 + u a

m v σ y − m v u a = − S 0 +

The above equation can be rearranged and solved for the
change in pore-air pressure:

⎛ ⎞

⎝ ⎠

1

u a = σ y (15.65)

( 1 hS 0 )n 0

[ ( u a 0 + u a )m v ]

− S 0 +

B a Derived 15.6.1 Secant Pore Pressure Parameter

1 +

from Hilf's Analysis
Measurements of pore-water pressures within compacted
cores of several earth dams have been conducted by Hilf
(1948). The measurements were made using piezome-
ters with coarse porous tips; consequently, only positive
pressures could be measured. Figure 15.16 presents the pore-
water pressure measurements from two piezometers installed
in the Anderson Ranch dam. The pore-water pressures
increased as the overburden pressure increased (i.e., σ y )
during construction.
The pore-water pressure development during construction
can be simulated using Hilf's analysis. Equation 15.65 is
applicable to both pore-air and pore-water pressures in the
sense that capillary effects are ignored in its derivation.
The soil has an initial degree of saturation S 0 of 87.4%
and an initial porosity n 0 of 28.1%. The volumetric coeffi-
cient of solubility h for air in water is assumed to be 0.02.
The initial absolute pore-air pressure

The secant B ah pore pressure derived from Hilf's analysis
can be written as

1

B ah = (15.66)

( 1 hS 0 )n 0

[ ( u a 0 + u a )m v ]

− S 0 +

1 +

where:

B ah =

secant pore-air pressure parameter (i.e., u a /
σ y ), for K 0 -undrained loading in accordance
with Hilf's analysis. The prime signifies a secant
pore pressure parameter.

An increase in pore-air pressure due to a total stress
increase can be predicted using Eq. 15.65. The final pore-air
pressure can be computed from the initial pore-air pressure
u a 0 and the change in pore-air pressure u a . This procedure
considers only the initial and final stress conditions without
using a marching-forward technique. The total stress
increment does not have to be small, as required when
using the B tangent pore pressure parameters. However,
Eq. 15.65 is nonlinear because the unknown term u a
appears on both sides of the equation. An iterative technique
is required in solving Eq. 15.65.
The coefficient of volume change m v varies depending
upon the magnitude of total stress σ y . Therefore, an average

u a 0 was assumed to
be atmospheric (i.e., 101.3 kPa). The coefficient of vol-
ume change m v was measured in a conventional oedometer.
Substituting the above data into Eq. 15.65 results in a rela-
tionship between u (or u a ) and σ y . The relationship
between u a and σ y is also assumed to be the relationship
between u w and σ y since capillary effects are ignored.
The pore-water pressure u w can then be plotted against the
major principal stress σ y using the u w and σ y relation-
ship as shown in Fig. 15.16. The initial pore-water pres-
sure was also assumed to be atmospheric (i.e., zero gauge