Hydro-Mechanical Properties of an Unsaturated Frictional Material

2.7. VOLUMETRIC BEHAVIOR OF PARTIALLY SATURATED SOILS 61
Void ratio (-)
0.73
0.70
0.71
0.72
Δlog σ
Δe Cc
Vertical stress (kPa)
Cs Loading path Hostun sand
Unloading path Reloading path 1000 100 10 1
Vertical strain (-)
0.00
0.01
0.01
Vertical stress (kPa) 200 250 150 100 50 0.020
Figure 2.28: Vertical stress versus void ratio (left) as well as vertical stress versus vertical
strain curves (right) including loading, unloading and reloading path for Hostun sand
ratio between thickness and diameter is kept as small as possible (e.g. 1:3 or 1:4) (Lambe &
Whitman 1969).
Important parameters derived from one-dimensional compression tests are the stiffness
modulus Eoed,ur, the compression index Cc as well as swelling index Cs. Following equations
are used to calculate these parameters (DIN 18135):
Cc = − ∆e
∆ log σ
Cs = − ∆e
∆ log σ
(2.23)
where: e is the void ratio and σ is the vertical net stress. According to Eqs. 2.24 the stress
dependent stiffness moduli Eoed and Eur can be calculated, where E ref
oed is the reference stiffness
modulus for initial loading and E ref
ur is the reference stiffness modulus for un-/reloading path
determined for a reference stress σref and ˆm is a parameter (Ohde 1939, Schanz 1998):
Eoed = E ref
oed ·
� � ˆm
σ
σref
Eur = E ref
� � ˆm
σ
ur ·
σref
(2.24)
The parameter ˆm and the normalized stiffness modulus E ref
oed and Eref ur respectively are derived
by regression process, that is presented in the diagrams in Fig 2.29. To linearize the function
between vertical net stress and strain ε(σ) the logarithm of the strain ln(ε) and the logarithm
of the normalized stiffness modulus ln(σ/σref ) is used:
� �
σ
ln(ε) = α · ln + β E
σref
ref 1 σref
oed,ur = ·
α expβ ˆm = 1 − α (2.25)
where: α and β are parameters.
The influence of suction on the stress-strain behavior of unsaturated soils has been exam-
ined experimentally based on the independent stress state variables, namely the net stress as