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Constitutive model and simulation of non-segregation freezing and thawing in soils
Modèle de comportement et simulation du gel et le dégel des sols sans ségrégation
Zhang Y., Michalowski R.L.
Department of Civil and Environmental Engineering, University of Michigan, Ann Arbor, USA
ABSTRACT: An elasto-plastic constitutive model for non-segregation freezing and thawing soils is developed to capture the
deformation behavior and strength evolution of the soil subjected to arbitrary loading as well as temperature changes. The model is
based on the critical state framework, with the yield condition as in the modified Cam clay model. It uses the pore ice ratio as a scalar
parameter to describe the evolution of the yield condition due to freezing and thawing. The model has been implemented in the finite
element system ABAQUS. A thermal and mechanical process in a soil column was simulated to illustrate the response of the model.
RÉSUMÉ : On présente un modèle élasto-plastique de comportement pour les sols soumis à des cycles de gel-dégel, ségrégation
exclue. Ce modèle représente la réponse en déformation et l’évolution de la résistance du sol sous n’importe quel chargement
mécanique, avec variations de température. Il s’inscrit dans le cadre de la théorie de l’état critique, avec une fonction de charge du
type Cam Clay modifié. Un paramètre scalaire appelé pore ice ratio est défini, qui régit l’évolution de la fonction de charge sous
l’effet du gel et du dégel. Le modèle a été implémenté dans le code de calcul aux Eléments Finis ABAQUS. La réponse du modèle est
illustrée par la simulation d’une colonne de sol soumise à un chargement thermique et mécanique.
KEYWORDS: non-segregation soil freezing, pore ice, soil thawing, constitutive model
1 INTRODUCTION
Various soils experiencing freezing and thawing may exhibit
dramatically different behaviors. For a non-frost-susceptible
soil, such as medium sand, no ice segregation will take place
during freezing. The pore water and pore ice will co-exist while
the temperature drops below freezing point. An increase in
strength occurs as the soil freezes; weakening is expected
during the melting process. The bulk volume of the soil expands
and contracts little due to the phase change. The same may
occur in frost susceptible soils subjected to quick freezing. In
this paper, both of these conditions will be considered as non-
segregation cases in which no ice lenses are generated during
freezing.
Elasto-plastic models and models accounting for viscous
properties of ice (creep), as well as ice melting, have been
developed (Lai
et al.
, 2009, Wei
et al.
, 2011). Most of these
models are based on continuum approach, and are suited for one
type of the frozen soil. Changes of the soil components upon
freezing and thawing, and the corresponding changes in
strength, are not addressed by these models. Some effort was
made to include the governing parameters of soil freezing into
the constitutive model (Shastri and Sanchez, 2012), but its
applicability is yet to be assessed.
This paper focuses on developing an elasto-plastic
constitutive model including freezing and thawing, to capture
the deformation behavior and strength evolution of the soil
subjected to loading and temperature changes. The model is
based on the critical state framework and it is formulated by
introducing the influence of ice ratio into the modified Cam clay
model. The model developed is suited for non-segregation
freezing and thawing soils (no ice lens formation). In non-
segregation soils, the strength of the soil upon thawing will
return to the strength prior to freezing, i.e, if the soil only
experiences freeze-thaw cycle, but no change in loading, no
thaw-settlement will take place. This is because the soil volume
variations during freezing/thawing are only due to the phase
change of pore water. Creep effect of frozen soil is not
considered in this paper.
2 THE MODEL
The model developed is temperature-dependent, with the
ice
ratio
being the key parameter that describes the influence of
the ice content. The ice ratio is defined as
i
e
i
i
s
V e
V
(
1
)
where
V
i
is the volume of ice and
V
s
is the volume of the solid
constituent (skeleton).
is related to the unfrozen water
content in the frozen soil.
i
e
2.1
Constitutive model
Compression tests on frozen soils indicate that the behavior of
frozen soil in the
v
,
p
-plane (specific volume, isotropic stress)
can be represented by normal compression line (NCL) and
unloading-reloading line (URL) (Qi
et al.
, 2010, Lee
et al.
,
2002). The slopes of these lines vary, however, depending on
the extent of freezing. The slopes for the two lines are defined
by
and
for unfrozen soil, and
f
and
f
for frozen soil,
respectively. The specific volume upon isotropic compression
of frozen soil is given by
ln
f
f
p
(
2
)
and elastic behavior in unloading-reloading regime is given by
