State Variables for Unsaturated Soils - Unsaturated Soil Mechanics in Engineering Practice - page 107

3.6.2 Description of Osmosis
Osmosis is the term used to describe the phenomenon by
which a solvent passes from a solution of lower solute con-
centration through a semipermeable membrane into a solu-
tion of higher solute concentration. A membrane is described
as semipermeable if it allows the passage of solvent but not
solute. If the flow of water is restricted, a pressure imbal-
ance equal to the osmotic pressure difference between the
two solutions needs to be present. Osmotic pressure can be
calculated from thermodynamic principles (Robinson and
Stokes, 1968). Osmotic pressure can also be approximated
by the van't Hoff equation (Metten, 1966):

pore-water pressure are the result of osmotic pressures and
are called osmotically induced consolidation.
The osmotic flow of water through a soil can be described
using a flow law:

π
x =

π
x

q π = k π o e k h (3.66)

where:

q π = water flux, m/s,

k π = coefficient of osmotic permeability, m/s,

k h = coefficient of (hydraulic) permeability, m/s,

π = osmotic pressure head ( π o / ρ f g ), m,

π = R T K C (3.65)

π o = osmotic pressure, kPa,

pore fluid density, kg/m 3 ,

ρ f =

where:

gravitational acceleration, m/s 2 ,

g =

o e = osmotic efficiency, and

π = osmotic pressure, kPa,

x = distance, m.

C = sum of the molar concentrations in solution, mol/L,

R = universal gas constant = 8.314 J/(mol · K), and

The coefficient of osmotic permeability, k π , is similar to
the coefficient of hydraulic permeability if the soil behaves
as a perfect semipermeable membrane. In this case, pure
water will flow in response to osmotic gradients. However,
if the membrane is “leaky,” the osmotic permeability k π will
be the hydraulic permeability multiplied by an osmotic effi-
ciency. The moving water will carry some dissolved salts
in this situation. Osmotic efficiency is a measure of the
degree to which the clay behaves as a perfect semipermeable
membrane. The above description clearly defines the state
variables associated with flow even though the efficiency of
the water flow system is not perfect.
Force equilibrium considerations can be applied to a sat-
urated clay-water system within the context of multiphase
continuum mechanics. The procedure is similar to that used
for determining the state variables associated with a sat-
urated or unsaturated soil. Barbour and Fredlund (1989b)
analyzed a clay-water system from a continuum mechanics
equilibrium standpoint. The soil was considered as a three-
phase system consisting of soil particles, pore fluid, and
the diffuse double hull surrounding each clay particle. The
resulting stress state tensor was as follows:
⎡

T K = absolute temperature, K.

3.6.3 Mechanisms Associated with Osmotic Suction
Conceptual models have been used to explain the influence
of pore fluid chemistry on the mechanical behavior of clays
in a quantitative way (Barbour, 1987). Macroscopic descrip-
tions of physical processes such as the flow of the pore
fluid, volume change, and change in shear strength must
all commence with the selection of suitable state variables.
Studies on two particular processes related to the physico-
chemical processes in clay soils have assisted in under-
standing the state variables that should be used to describe
mechanical processes. The processes can be referred to as
(i) osmotic consolidation and (ii) osmotically induced con-
solidation (Barbour and Fredlund, 1989a).
Osmotic consolidation occurs as a result of a change in
the electrostatic repulsive stress minus the attractive stress
( R

A ) between clay particles. Osmotically induced con-
solidation occurs as a result of fluid flow from the clay in
response to osmotic gradients. The volume of a clay spec-
imen will change as a result of the combined processes
of osmotic flow and osmotic compressibility when clay is
exposed to a concentrated salt solution. Changes occur in the
interparticle repulsive stresses as salt moves into the clay.
These changes lead to the suppression of the double layer
and changes in void ratio. Changes in the osmotic suction
π in the pore fluid are referred to as osmotic consolidation.
There is another volume change process that occurs as
a result of fluid flow responding to osmotic gradients. An
osmotic gradient between the electrolyte concentration inside
the clay and the external electrolyte solution results in water
flow in or out of the clay soil. An outward flow causes negative
pore fluid pressures to develop within the specimen, which
then leads to increases in the intergranular stresses between
particles and possible volume changes in the soil. Changes in

−

⎤
⎦

(σ x − u f ) − (R − A) τ yx τ zx

⎣

τ xy (σ y − u f ) − (R − A) τ zy

τ xz τ yz (σ z − u f ) − (R − A)

(3.67)

where:

σ x ,σ y ,σ x = total normal stresses,

τ xy ,τ yx ,τ yz ,τ zy ,τ zx ,τ xz = shearing stresses,

u f = pore fluid pressure, and

R − A = net interparticle repulsive

stress minus attractive stress.