Deformation behaviour of railway embankment ... - Liikennevirasto

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ε 1,p = accumulated permanent strain after N load cycles,
ε N = permanent strain for load cycle N,
ε i = permanent strain for first load cycle ,
N = number of load cycles,
h = repeated load hardening parameter, a function of stress to
strength ratio.
The basic hierarchical model defines the magnitude of the permanent strain occurring
during the first cycle of loading. Under repeated loading, the cyclic hardening behaviour
of the material is modeled by expressing the permanent strain for any load cycle as a
power function of the permanent strain during the first load cycle. The accumulated
permanent strain is then calculated as the sum of the permanent strain in each cycle.
Other researchers tried to relate the cyclic permanent deformations to both the applied
stresses and the number of load cycles. Gidel et al. (2001) proposed a comprehensive
relationship, taking into account the number of load cycles and the maximum applied
cyclic stresses p max , q max :
−B
n
⎡ ⎤
p
p
⎛ N ⎞ ⎡ L
max
⎤ 1
ε ⎢
⎜
⎟
1
( N)
= ε10
⋅ 1−
⎥ ⋅ ⎢ ⎥
, (Eq. 7.5:9)
⎢ ⎥ ⎣ ⎦ ⎛
⎞
⎣ ⎝ N
0 ⎠ pa
⎦
s qmax
⎜m
+ −
⎟
⎝ pmax
pmax
⎠
where
L max =
2 2
p
max
+ qmax
,
p a = 100 kPa,
ε p 10, B, n = model parameters,
m,s = parameters of the failure line of the material of equation
q = m*p + s.
The empirical model of Gidel, which is written as the product of a function of the
number of load cycles by a function of the maximum stresses, of the form ε p j(N) =
f(N) * g(p max , q max ) was studied by El abd et al. (2004). Comparisons with their
experimental results indicated that the function g proposed by Gidel gave satisfactory
predictions, but that the function f(N) could not be used, because the tests performed
in their study did not show a complete stabilization of permanent strains. It was
therefore replaced by the function proposed by Sweere (1990), f(N) = AN B which gave
better results.
This empirical model has been implemented in the program first because of its
simplicity. One of its drawbacks is that it describes only the variation of permanent
axial strains. Work is also under way to implement in the programme a more accurate,
incremental, elasto-plastic model, also used at LCPC for unbound granular materials,
the model of Chazallon (2000).