Volume Change Testing
Volume Change Coefficients or Indices
The parameters required for constitutive equations relating
deformation state variables and stress state variables.
Table 1 - Volume Change Coefficients or Indices
Derivation of Relationships for Volume Change
Requirements for Volume Change Theory
Representation of deformation behavior requires constitutive
equations relating a deformation state variable related to
two independent stress state variables.
Unsaturated Soil Shear Strength Parameters Measurements
Control of Stress States
The stresses , ua and uw can be measured or controlled so
that the stress state variables ( - ua), (1 - 3) and
(ua - uw) will be known.
The axis translation method is used t
Shear Strength of Unsaturated Soil
Shear Strength Characterization
Requirements for Shear Strength
Cannot use saturated soil parameters c' and ' and
effective stresses because effective stresses are
To characterize the shear strength of unsatura
Derivation of Governing Equations
Description of Mass Balance Consideration
Derivation of governing differential equation is obtained
by considering a volumetric element.
The statement of mass balance is:
The difference between the total
Measurement of Unsaturated Permeability
Water Coefficient of Permeability
Direct Permeability Methods
1) Steady State Methods
Under steady state conditions, i.e., (ua - uw) = constant,
the flow rate is independent of time.
Flow in Unsaturated Soil
Requirements for Flow Laws
Requires a law relating the diffusion or flow rate with the
For diffusion, the driving potential is either due to a
chemical, thermal or electrical gradient.
For flow, it is necessary
Total soil suction is defined in terms of the free energy or the
relative vapor pressure (relative humidity) of the soil
u v = partial vapor pressure of pore water vapor
u vo = saturation
Stress State Variables
Stress variables are used to determine the state of stress in a
soil that is then used to model mechanical behavior.
These stress state variables cannot be dependent on the
properties of the soil.
= M / V = mass per unit volume
= s(soil), w(water) or a(air)
v0 = V / M
Ideal gas law (for moist and dry air)
u V = (M / ) R T
u = absolute press. = gage press. + atmos. press.
Mechanics of Unsaturated Soils
Soil Mechanics for Unsaturated Soils by D. G. Fredlund
and H. Rahardjo
Course emphasizes topics related to the mechanics of
unsaturated soils with some applications to the soi