Deformation behaviour of railway embankment ... - Liikennevirasto

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Figure 5.2.5:2 Vertical resilient strain versus confining pressure at different moisture
contents (σ 1max / σ 3 = 2) (Numrich 2003).
Lade and Nelson (1987) derived a relationship between Poisson's ratio and the
resilient modulus based on a thermodynamic constraint. The derivation of the
equation is based on the principle of the conservation of energy and the path
independence of the energy density function. After the study by Lytton et al. (1993)
and Liu (1993), an expression that relates the stress state and the rate of change of
Poisson's ratio with a changing stress state was derived taking into account the
resilient modulus and the thermodynamic constraints. This relationship between
Poisson's ratio and the stress state is as follows:
2
3
∂v
∂J
where
1
+
I
∂v
∂I
⎡1
k
= v⎢
⎣3
J
k
+
I
⎤ ⎡ 1
⎥ + ⎢−
⎦ ⎣
'
3 2
2
2 1 1
2 1
6
k
J
'
3
2
k
+
I
2
2
1
⎤
⎥ , (Eq. 5.2.5:5)
⎦
ν = Poisson's ratio,
k 1 ,k 2 ,k 3 = material parameters,
I l = normalized first stress invariant,
J 2 = normalized second invariant of the deviatoric stress.
5.3 Resilient modulus using shear-volumetric approach
In order to characterize the stress-strain relationship in unbound granular materials, a
different approach can be used. The approach consists of decomposing both stresses
and strains into volumetric and shears components. In this case, resilient modulus and