730
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
similar result against the collapse mode obtained by the limit
bearing capacity analysis showing at the Figure 6.
Next, we show a relationship of the loading and the
displacement based on both theories to the Figure 8 and the
Figure 9. Firstly, we explain result based on the infinitesimal
deformation theory at the Figure 8. If the case [1], it indicated
the rapid increase inclination of the displacement by occurrence
of the acceleration (displacement acceleration) with the loading
speed by continuing the loading after it exceeds the limit
bearing capacity. If the case [2], it indicated similar increase
inclination against the case [1]. But it indicated the increase
inclination smaller than the case [1]. If the case [3], it indicated
the inclination which keep the constant displacement (the
residual displacement) with the unloading after the
displacement increased. This behavior shows to occur the strain
velocity in the ground by to receive effect of previous motion
after the unloading. So, it is conceivable that the displacement is
kept by to occur the acceleration of opposite direction to
converge by a gap of the loading as the dynamical reason.
Figure 6. The collapse mode and the equivalence strain velocity
distribution by the limit bearing capacity analysis (the limit bearing
capacity is 195.94 kPa)
Secondly, we explain result based on the finite deformation
theory at the Figure 9. If the case [1], it indicated the increase
inclination of the displacement after it exceeds the limit bearing
capacity like result of the infinitesimal deformation theory.
However it indicated the gentle increase inclination against the
infinitesimal deformation theory. If the case [2], it indicated the
inclination which keep the constant displacement after increased
the displacement by to keep the constant loading like the case
[3] of the infinitesimal deformation theory. This inclination is
different inclination against the case [2] of the infinitesimal
deformation theory. It is conceivable that deformation decreased
because increased the limit bearing capacity of the ground by to
occur effect of embedment with deformation of the ground by
the loading as this reason. If the case [3], it indicated the
inclination which keep the constant displacement like the case
[3] of the infinitesimal deformation theory. However it
indicated the inclination the residual displacement is smaller
than the infinitesimal deformation theory from effect of
embedment. It is proved that it can evaluate effect of the
geometry form by based on the finite deformation theory from
all analysis cases.
Figure 7. The collapse mode and the equivalence strain velocity
distribution by the dynamic deformation analysis (the limit bearing
capacity is 196.0 kPa)
20.0
60.0
100.0
140.0
180.0
220.0
260.0
300.0
340.0
-12.0
-8.0
-4.0
0.0
4.0
8.0
12.0
0 2 4 6 8 10 12 14 16 18 20
[1]
[2]
[3]
[1]
[2]
[3]
Loading
[
kPa
]
Time
[
sec
]
Displacement
[
m
]
Figure 8. Difference of the residual displacement by the loading history
in the infinitesimal deformation theory
It has been shown applicability of the finite deformation
analysis by the proposed method from this chapter's result. But
the proposed method has the problem that it can't calculate by to
occur distortion of the finite element by shear deformation with
deformation of the ground. Example, such as the case [1] of the
finite deformation theory. Therefore it need to improve so that
can be applied to large deformation calculation of the ground.
Example, such as the remesh techniques. We are going to
improve this problem in the future.
60.0
100.0
140.0
180.0
220.0
260.0
300.0
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
0 2 4 6 8 10 12 14
[1]
[2]
[3]
[1]
[2]
[3]
Time
[
sec
]
Displacement
[
m
]
Loading
[
kPa
]
5 CONCLUSIONS
We developed the rigid plastic dynamic deformation analysis
using the rigid plastic constitutive equation to predict the
residual deformation of the earth structure. The proposed
method has characteristic that it can be done deformation
analysis in the stress boundary problems which to apply in the
rigid plastic constitutive equation is difficulty. Therefore the
proposed method can do the residual deformation analysis by
collapse of the earth structure. We compared the Prandtl’s
theoretical solution and the limit bearing capacity analysis in the
horizontal ground to verify applicability of the proposed method.
And we were carried out simulation in the slope to show that it
can evaluate properly deformation behavior of the ground
against the loading history. We showed that it can evaluate
properly problems such as effect of the geometry form by using
the proposed method from these result.
Figure 9. Difference of the residual displacement by the loading history
in the finite deformation theory
6 REFERENCES
Hoshina, T. Ohtsuka, S. and Isobe, K. 2011. Discussion on
applicability of rigid plastic dynamic deformation analysis to soil
structures, Journal of applied Mechanics JSCE. Vol.14, 251-259. (in
Japanese)
JSTP. 1994. Non-linear Finite Element Method, CORONA Publisher.
(in Japanese)
max
e
min
e
horizontal ground to verify applicability of the proposed method.
And we were carried out simulation in the slope to show that it
can evaluate properly deformation behavior of the ground
agai st the loading history. We showed that it can evaluate
properly problems such as effect of the geometry form by using
the proposed method from these result.
Hoshina, T. Ohtsuk
applicability of rigid p
structures, Journal of a
Japanese)
JSTP. 1994. Non-line
(in Japanese)
max
e
min
e
similar result ag inst the collaps mode obtained by the limit
bearing capacity analysis showing at he Figure 6.
N xt, we show a relationship of t loading a th
displaceme t b d on both theori s to th Figure 8 and the
Figure 9. Firstly, we ex in r sult bas d on the infinitesimal
deformation theory at the Figure 8. If he cas [1], it indicated
th rapid increase inclination of the displacement by occurrence
of the cceleration (displacement acceleration) with
loading
speed by continuing the loading after it exceeds he limit
bearing capacity. If the cas [2], it i dica ed imilar increase
incl nation against th case [1]. But it indic ted the increase
inclin tion smalle than the case [1]. If t e case [3], it indicated
th inclination which keep the constant dis lacement ( he
residual displacement) with the unloading after the
dis lacement in reased. This b h vior shows t occur the strain
velocity in the ground by to receive effect of previous motion
aft r the unloading. So, it i conceivable that the displacemen is
kept by to occur the acceleration of opposite direction to
co verge by a gap of the loadi g s the dynamical reason.
Figure 6. The collapse mode and the equivalence strain velocity
distribution by the limit bearing capacity analysis (the limit bearing
capacity is 195.94 kPa)
Secondl , w explain result based on the finite deformati n
the ry at the Figure 9. If th case [1], it indicated the increase
incl a ion of th displacement after it x eeds the l mit bearing
capacity like result of the i finitesimal deform tion theory.
However it indicated the g ntle in rea e inclination against the
infinitesimal deformation the ry. If the case [2], t indicated the
inclination wh ch keep the constant di placemen after incr ased
th displ cement b to keep the cons an loading l ke the c
[3] of the infinit simal deform t on theory. This inclination is
different in lination agains the case [2] f the infinitesimal
deform tio theory. It is conceivabl th t deforma io decr ased
because ncreased th limit bearing capacity of the ground by to
occur e fect of embedment with deformation f the ground by
the lo ding as this reason. If the case [3], it i dicated th
incli ation which keep the const nt displacement like the ase
[3] of the infinitesimal deformatio theory. However it
indicat d the inclination the residual isplaceme t is smaller
than the infinitesimal deformation theory from effect of
embedment. It is proved th t can evaluate ffect of he
geometry form by based on the finite deformation theory from
all analysi cases.
Figure 7. The collapse mode and the equivalence strain velocity
distribution by the dynamic deformation analysis (the limit bearing
capacity is 196.0 kPa)
20.0
60.0
100.
140.
18 .
220.
260.
300.
340.
-12.0
-8.0
-4.0
0.0
4.0
8.0
12.0
0 2 4 6 8 10 12 14 16 18 20
[1]
[2]
[3]
[1]
[2]
[3]
Loading
[
kPa
]
Time
[
sec
]
Displacement
[
m
]
Figure 8. Difference of the residual displacement by the loading history
in the infinitesimal deformation theory
It has been shown appl cability of the finit deformation
analysis by the proposed method from this chapt r's r sult. But
the proposed method as the problem that it can't calculate by to
o cur distortion of the finit element by she r def rmation with
defor ation of the ground. Exampl , such a the case [1] of the
f nite deformati n theory. Therefore it need to improve so that
can be applied to large deformation calculation of the ground.
Example, such as the remesh techniques. We are going to
improve this problem in the future.
60.0
100.0
140.0
180.0
220.0
260.0
300.0
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
0 2 4 6 8 10 12 14
[1]
[2]
[3]
[1]
[2]
[3]
Time
[
sec
]
Displacement
[
m
]
Loading
[
kPa
]
5 CONCLUSIONS
We developed t e rigid plas ic dynamic d formation analysis
using the rigid pla tic constitutive equation to predict the
residual deformation of the earth structure. The pr posed
method has c ara teristic that it c n be done deformation
ana ysi in the stress boundary problems which to apply i the
rigid plastic constitutive equat on is difficulty. Therefore the
pr posed method can do the residua deformation analysis by
collapse of the earth structure. We compared he Prandtl’s
theoretic solution and the limit bearing capacity analysis in the
horizon al groun to verify applicability of the proposed method.
And we we e carried out simulation in the slope to show that it
can evaluate properly deformation behavior of the ground
against the loading history. We showed that it can evaluate
properly problems such as effect of the geometry form by using
the proposed method from these result.
Figure 9. Difference of the residual displacement by the loading history
in the fin te deformation theory
6 REFERENCES
Hoshina, T. Ohtsuka, S. and Isobe, K. 2011. Discussion on
applicability of rigid plastic dynamic deformation analysis to soil
structures, Journal of applied Mechanics JSCE. Vol.14, 251-259. (in
Japanese)
JSTP. 1994. Non-linear Finite Element Method, CORONA Publisher.
(in Japanese)
max
e
min
e
