Nature and Phase Properties of Unsaturated Soil - Unsaturated Soil Mechanics in Engineering Practice - page 71

2.4.6.5 Changes in Volume-Mass Properties
The basic volume-mass relationship (Eq. 2.81) provides a
relationship among commonly used variables in geotechni-
cal engineering (e.g., S , e , and w ). A change in any one
of the three volume-mass properties may produce changes
in the other two properties. Changes in two of the volume-
mass quantities must be determined through an independent
analysis or independent measurements in order to compute
the change in the third variable. If changes in the void ratio
e and the water content w are known, the change in degree
of saturation S can be computed. Similarly, if changes in S
and e or S and w are known, then the change in w or e ,
respectively, can be computed.
The relationship between changes in the volume-mass
properties can be derived from the basic volume-mass
relationship expressed in Eq. 2.81. Consider a soil that
undergoes a process such that changes occur in the volume-
mass properties of the soil. The volume-mass properties of
the soil have the following relationship prior to the initiation
of a process:

Equation 2.87 can be rearranged such that the degree of
saturation S can be written in terms of change in void ratio,
e , and the change in gravimetric water content, w :

w G s − S i e

S = (2.88)

e f

Similarly, the change in the void ratio, e , is obtained by
substituting Eq. 2.85 into Eq. 2.87 and solving for e :

w G s − S e i

e = (2.89)

S f

The change in water content, w , can similarly be writ-
ten as

S f e − S e i

w = (2.90)

G s

Each of the above three equations reveals that if changes
in any two volume-mass properties are known as a result of
a process that has occurred, then it is possible to compute all
other volume-mass properties. These equations also reveal
that it is necessary to have two independent volume-mass
constitutive relationships when solving problems involving
unsaturated soils.

S i e i = w i G s (2.82)

where:

S i = initial degree of saturation,

e i = initial void ratio, and

w i = initial water content.

2.4.7 Volume-Mass Relations When Pore Fluid
Is Not Water
There are situations where the pore fluid may be heavier or
lighter than “pure” water. Let us consider the situation where
the pore fluid is miscible with water. A couple of examples
where the pore fluid might differ in density from that of pure
water are (i) the application of liquors to heap leach and (ii)
brine solutions seeping into a freshwater aquifer. The heap
leach process commonly involves the application of fluids
referred to as liquor that is added to tailings. The application
of the liquor produces a reaction which releases minerals
from the tailings that can subsequently be recovered in the
leachate. The specific gravity (and density) of the pore fluid
is different than that of pure water and also changes with
time as a result of minerals released from the solid phase
that go into solution.
Another example involves the refining of potash which
results in the accumulation of piles of salt tailings as well
as brine ponds where the concentration of salts may be con-
siderably higher than that of seawater. Laboratory testing of
these materials or analyses on field situations often requires
the calculation of volume-mass properties corresponding to
various times in the life of the facility.
Calculations used in conjunction with a heap leach sim-
ulation are used as an example to illustrate changes in the
volume-mass equations when the pore fluid has a density
other than that of pure water.

The final volume-mass properties at the end of a process
are also related by the basic volume-mass relationship:

S f e f = w f G s (2.83)

where:

S f = final degree of saturation,

e f = final void ratio, and

w f = final water content.

The relationships between initial and final conditions for
each variable can be written as follows:

S f = S i + S (2.84)

e f = e i + e

(2.85)

w f = w i + w (2.86)

where:

S = change in the degree of saturation,

e = change in the void ratio, and

w = change in the water content.

The final properties can be written as follows using the
initial properties and changes in each property:

S i e = Se i + S e = w G s (2.87)