255
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
1
Rational expression of time-dependent behavior from normally consolidated soil to
naturally deposited soil
Expression rationnelle du comportement dépendant du temps des sols normalement consolidés et
déposés naturellement
Nakai T., Shahin H.M.
Department of Civil Engineering, Nagoya Institute of Technology, JAPAN
Kyokawa H.
Institute of Industrial Science, University of Tokyo, JAPAN
ABSTRACT: Fundamental concepts of the ordinary elasto-viscoplastic modelings, which are the non-statonary flow surface model
and the over-stress type model, are explained in one-dimensional (1D) compression of normally consolidated soil for easy
understading. Then, a new approach to describe various time-dependent behaviors of soils is presented extending the advanced
elastoplasitic theory based on the subloading surface concept without employing usual elasto-viscoplastic theories. Throughout the
simulations of various time-dependent behaviors of normally consolidated clay, the features of these three types of time-denpendent
models are clarified. In addtoin, 1D anlyses using the proposed model are carried out not only for normally consolidated clay but also
for over-consolidated clay and strauctured clay such as nuturally deposited clay. The analytical results simulate well the features of
time-dependent behavior of various clays including the delayed settlement of sturctured clay.
RÉSUMÉ: Les concepts fondamentaux de la théorie classique de l’élasto
-viscoplasticité que sont la surface potentiel et la notion de
surcontrainte s
ont expliqués pour une meilleure compréhension à partir d’une compression 1D sur un sol normalement consolidé.
Ensuite, une nouvelle approche permettant de décrire différents comportements fonction du temps des sols est présentée, étendant la
théorie de l’
élasto-
plasticité basée le concept de la subsurface de charge sans s’appuyer sur les concepts usuels de l’élasto
-
viscoplasticité. A partir de simulations de différents comportements dépendant du temps d’argiles normalement consolidées, les
éléments propres à ces trois types de modèles sont clarifiés. De plus, des analyses 1D à partir du nouveau modèle sont menées non
seulement sur des argiles normalement consolidées mais aussi surconsolidées et sur des argiles structurées, telles que des argiles
naturelles. Les résultats analytiques démontrent que les principales caractéristiques du comportement dépendant du temps de ces sols
sont bien reproduites, y compris le tassement différé des argiles structurées.
KEYWORDS: constitutive modeling, time-dependent behavior, nornally consolidated clay, over consolidated clay, structured clay
1 INTRODUCTION
Previous time-dependent models for soils are mostly formulated
based on one of the following two viscoplastic concepts: the
non-stationary flow surface type and the over-stress type. In the
non-stationary flow surface models (e.g., Sekiguchi 1977), the
flow surface is function of time in addition to stress and plastic
strain, and flow rule is assumed on this flow surface, in the
same way as elastoplastic models. Another type of model is
based on the over-stress viscoplastic theory by Perzna (1963)
(e.g., Adachi and Oka 1982), in which the strain rate effects are
described by assuming a Bingham like body and utilizing the
difference of sizes of the static yield surface related to the
current plastic strains and the dynamic yield surface related to
the current real stresses.
In the present paper, for understanding the features of the
above models, one-dimensional (1D) formulation of these
models are firstly described for the case of a normally
consolidated clay. A simple model to describe time-dependent
behavior of normally consolidated soils, over consolidated soils
and structured soils such as naturally deposited clays is
presented, not using the usual viscoplastic theories but focusing
on the experimental results that normally consolidation line
(NCL) on
e
–
ln
plane shift depending on the strain rate and
using the subloading surface concept by Hashiguchi (1980).
2 EXPLANATION OF ORDINARY VISCOPLASTIC
MODELS IN ONE-DIMENSIONAL CONDITION
Formulation of 1D time-dependent models for normally
consolidated soil based on the ordinary viscoplastic theories is
shown here. Figure 1 show the normal consolidation line (NCL)
on
e
-ln
plane at reference state in which the rate of void ratio
change (or strain rate) is sufficiently small (
( ) ( )
p
p
ref
e
e
).
Here, the clay at point A has a finite strain rate, and its creep
behavior (
e
-ln
t
relation) is illustrated in the interpolated diagram,
where
is the coefficient of secondary compression. The stress,
void ratio, time and rate of plastic void ratio change at initial,
current and reference states are denoted by (
0
,
e
0
,
t
0
,
0
( )
p
e
),
(
,
e
,
t
,
( )
p
e
) and (
ref
,
e
ref
,
t
ref
,
( )
p
ref
e
), respectively. Now,
let us formulate time-dependent models of normally
consolidated soil based on the ordinary viscoplasticities under
the condition of Figure 1.
2.1
Non-stationary flow surface model (1D Sekiguchi
model)
It is experimentally known that for normaly consolidated clays
there is a unique relation between stress, void ratio (or strain)
and strain rate in one-dimensional compresson (e.g., Bjerrum
1967), and the well-known linear relation in
e
-ln
plane (NCL)
shift due to the stain rate. Now, points I and P in Figure 2
NCL ; (
)
(
)
p
p
ref
e
e
Figure 1.
e
-ln
relation and creep behavior of normally consolidated
clay
