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Numerical analysis on prediction for residual deformation of earth structure using
rigid plastic dynamic deformation analysis
Étude numérique pour prévoir la déformation résiduelle dun ouvrage en terre
à l'aide de l’analyse de la déformation dynamique rigide plastique
Hoshina T., Isobe K.
Nagaoka University of Technology
ABSTRACT: Recently, some deformation for against earth structure has been allowed in the current design code. Elastic plastic
deformation analysis can evaluate properly of behavior of the ground. But may not be able to evaluate appropriate the amount of
residual displacement from problems of initial stress and stress history. From such problem, we propose dynamic deformation
analysis based on the rigid plastic constitutive model like limit equilibrium method.
RÉSUMÉ: Récemment, une certaine déformation des ouvrages en terre a été autorisée dans les codes de dimensionnement actuels.
L’analyse de la déformation plastique-élastique permet d'évaluer exactement le comportement du sol. Pourtant, elle n’est appropriée
pour la mesure de la déformation résiduelle des problèmes de contrainte initiale et d’histoire de contrainte. Face aux problèmes ci-
dessus, nous proposons une analyse de la déformation dynamique basée sur un modèle constitutif rigide-plastique comme la méthode
d'équilibre limite.
KEYWORDS:
rigid plastic constitutive equation
，
dynamic deformation analysis
，
residual deformation
1 INTRODUCTION
Recently, the stability evaluation is done by a residual
deformation from viewpoint of rationalization in the designing
earth structure. Example, it has been proposed the elasto plastic
deformation analysis method using the elasto plastic
constitutive equation as a method to predict the residual
deformation. The analysis method can properly evaluate
behavior of the ground. But there are some problems as such
effect by stress history and initial stress, and setting of analysis
parameters. Therefore, may not be able to evaluate properly a
residual displacement against conditions of target problem. In
addition, it feels limitation of applicability against complex
problems of the slope because the governing equation is
expressed by incremental equation.
In this study, we developed a rigid plastic dynamic finite
deformation analysis based on the rigid plastic finite element
method (RPFEM) assuming the rigid plastic theory to the soil
material. The RPFEM has been applied to the stability
evaluation as such the bearing capacity problems of the earth
structure in the geotechnical engineering field. It has advantage
that it isn't necessary assuming slip surface, and considering a
geometric nonlinearity is easy, and applicability to express the
ground characteristic is good. Therefore, it can reasonably
express behavior of the earth structure.
In this paper, we will explain about formulation of the proposed
method used a rigid plastic constitutive equation. In addition,
we will do simulations of the bearing capacity problem in the
horizontal ground and the slope. And, we will show
applicability to deformation problems by the proposed method
from simulation's results.
2 ANALYSIS METHOD
2.1
The rigid plastic constitutive equation
We formulated the rigid plastic constitutive equation using the
Drucker-Prager yield function from the upper bound theorem of
the limit theorems. Here,
I
1
is first invariable value of stress
tensor.
J
2
is second invariable value of deviatoric stress tensor.
And,
and
relate to a cohesion and an angle of shear
resistance based on the mohr coulomb's failure criterion is
coefficients. The tensile stress has been defined positive.
( )
1
2
0
f
I
J
σ
= + - =
(1)
A stress
decompose to a stress
and a stress
. Here, the
stress
can define by a strain velocity, the stress
can not
define by the strain velocity. The stress
is expressed from
the associated flow rule. The stress
is expressed using a
condition equation (volume change characteristic) on the strain
velocity and the indefinite constant. Here,
ε
is the strain
velocity. is a equivalence strain velocity.
v
e
is a volume
strain velocity.
I
is a unit tensor.
( )
1
2
3 +1 2
e
ε
σ
=
，
:
e
ε ε
=
(2)
( )
2
3
0
3 1 2
v
v
h
e
e
ε
= -
= -
=
+
(3)
( )
2
2
3
3 1 2
h
e
ε
σ
I
ε
ì
ü
ï
ï
¶
ïï
= = - í ï
ï
¶
+
ï
ï
ï
ï
î
ïïý
þ
(4)
Finally, it is obtained the equation (5) as the rigid plastic
constitutive equation from the equation (2) and the equation (4).
In addition, the condition equation (3) has been incorporated to
the constitutive equation (5) by applying the penalty method (
is the penalty constant) because speed up of calculation.
(
)
2
2
3
3 +1 2
3 +1 2
v
e
e
e
ε
ε
σ
I
ì
ü
ï
ï
ï
ï
ï
ï
=
+ -
- í
ý
ï
ï
ï
ï
ï
ï
î
þ
(5)
2.2
Formulation of the governing equation
A magnitude of strain velocity in the rigid plastic constitutive
equation (a relationship of the stress and the strain velocity) is
