© 2002 WIT Press, Ashurst Lodge, Southampton, SO40 7AA, UK. All rights reserved.
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Paper from: Structures Under Shock and Impact VII, N Jones, CA Brebbia and AM Rajendran (Editors).
ISBN 1-85312-911-9
Shaking table test and numerical
simulation of seismic response of subway
structures
A. Che and T. Iwatate
Department of Civil Engineering, Tokyo Metropolitan Universi@,
Tokyo, Japan.
Abstract
In order to clarify the dynamic behaviors and damage mechanism of subway
structures due to the 1995 Hyogoken-nanbu earthquake, scaled model shaking
tests and its simulation analyses were performed. The dynamic responses,
dynamic forces (shear earth pressures, lateral earth pressures) acting on the
structure and bending strains induced in the center columns were verified due to
horizontal and vertical input motions, individually and simultaneously. In case of
horizontal input motions, dynamic horizontal forces acting on the structure, and
bending strains induced in the center columns were very larger than those in case
of vertical input motions. The dynamic responses of the structure and dynamic
earth pressures due to simultaneous horizontal and vertical input motions were
approximately equal to those by horizontal input motions. The experimental
results were verified by simulation analyses using SHAKE (one- dimensional
analysis) and TDAP (two-dirnensioml analysis) programs. From these results, the
subway structure collapsed due to strong dynamic horizontal forces mainly acting
on the structure.
1 Introduction
On January 17, 1995, the Hyogoken-nanbu earthquake in Kobe, Japan, caused
serious damage to underground structures that had previously been considered to
be strong to earthquake effects, The most si~ficant damage was caused to
subway structures, most of which had been constructed using the cut-and-cover
technique, More than half of the center columns at the Daikai station completely
collapsed and ceiling slabs failed. Shaking table tests were performed on a
l/30-scaled model of Daikai Station (Photo 2) in Tokyo Metropolitan University
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Paper from: Structures Under Shock and Impact VII, N Jones, CA Brebbia and AM Rajendran (Editors).
ISBN 1-85312-911-9
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strmwws [ >zk+rSIlocka,zd impact 171
in August 1995 and verified the dynamic behaviors of subway structure due to
horizontal motions between 1995 and 1999 [1,2].
Generally, the vertical seismic forces are considered as smaller than horizontal
ones, usually as half of horizontal forces in the existing seismic design standard
in Japan [4]. In addition, few studies on vertical earthquake motions have been
presented, so after Hyogoken-nanbu earthquake it is important to clari@ the
dynamic behaviors of the underground structures and the earth pressures acting
on structures due to vertical motions. In this paper. in order to determine why the
subways in Kobe collapse~ horizontal, vertical, simultaneous horizontal and
vertical movements with sinusoidal and random input motions are investigated,
by both scaled model shaking table tests and its simulation analyses.
2 Scaled model shaking table tests of the subway structure
2.1
Ground and subway models
A new soil container has developed to reproduce ideal horizontal shear motions in
the ground. as shown in Photo 1[3]. The model ground was constructed from fine
Q sand (Gifu-Sand) in two layers, a 0.4 m thick subsurface layer and a 0.6 m
thick bearing stratum. A l/30-scaled model of the subway structure was placed on
the bearing stratum. The subway model was a box type frame structure with
seven center columns (three columns were fitted with a flexible joint, and the
remainder with rigid joints) of dimensions 60 mm x 60 mm x 240 mm
constructed from polyvinyl chloride resin. The thickness of the overburden soil
was 16 cm (Photo 2). A 5 mm thick rubber board was placed between the column
and slab to represent the flexible joint [2].
.
.
“ ‘$%
Photo 1 Soil container of shaking table
tests
Photo 2 Subway structore model of
Daikai
station
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Paper from: Structures Under Shock and Impact VII, N Jones, CA Brebbia and AM Rajendran (Editors).
ISBN 1-85312-911-9
2.2 Experimental items
The shaking table tests were performed as follows.
(1) Seismic Exploration Tests and Free Vibration Tests
The dynamic material properties of the model ground were estimated.
(2) White-noise Tests
Seven different accelerations ranging from 10gal. 20gal, 50gal, lo~g~$ 2@g~,
400gal,and 800gal were selected as the horizontal input motions. From these tests,
the shear wave velocity (Vs m/s) and the strain-dependency of the soil properties
of the ground were evaluated (Figure 4).
(3) Sine Sweep Tests
In case of horizontal input motions, the sinusoidal \tibrations \vith a constant base
acceleration and alternating frequency were from 5 Hz to 30 Hz. Five ditTerent
accelerations of 20gal, 50gal, 100gal, 200gal and 400gal were selected.
In case of vertical input motions. the sinusoidal vibrations with a constant base
acceleration and alternating frequency were from 20 Hz to 50 Hz. Also, five
different accelerations of 10gal, 25gal, 50gal, 100gal and 200gal were selected,
which are a half of the horizontal accelerations [4].
In case of simultaneous horizontal and vertical input motions, the alternating
frequency was from 3Hz to 50Hz.The amplitude of input motions were selected 5
sets (20gal, 50gal. lOOgal, 200gal and 400gal for horizontal components. 10gal,
25gal, 50gal, 100gal and 200gal for vertical ones). In addition the phase
difference between horizontal motions and vertical ones was varied 00 and900.
(4) Random Vibration Tests
Random vibration tests were conducted, wherein the recorded accelerations at
Kobe meteorological agency station, during Hyogoken-nanbu earthquake were
used as the input motion (Figure 1). In case of horizontal input motions, duration
time ranged between five shorting processes (1/1, 1/5,1/10. 1/20, 1/30) considering
the scaling law and maximum acceleration was changed in two cases of 1/2(50%),
and l/l(100Y0). In case of vertical input motions, duration time ranged 1/1 and
maximum acceleration was changed in two cases of l/2(50Yo), and 1/1(IOO”A).In
case of simultaneous horizontal and vertical input motions, duration time ranged
1/1 and maximum acceleration was changed in two cases of 1/2(50%), and
1/1(10070).
-d
“
I
051015
zlz53
35
t(sec)
NS (Timeaxis 1/1,amplitude10OYO)
Figure 1 Kobe marine meteorological obsematory record of F@ogoken-nanbu
earthquake
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Paper from: Structures Under Shock and Impact VII, N Jones, CA Brebbia and AM Rajendran (Editors).
ISBN 1-85312-911-9
370
.Ttrl[crzirps
( ‘tldershock atld [mpact [‘[l
From tests (3) and (4), the acceleration responses of the s~cture model and the
ground- the dynamic earth pressures acting on the structure (ceiling slab and
sidewalls), and the bending s@ains Mduced on the center ~oIumns and tie
side-walls were also evaluated From sine sweep tests. the resonant curves were
evaluated.
Numerical simulations
3
3.1 Numerical Method
A schematic of the numerical simulation is shown in Figure 2. The first step is the
analysis of the gxound’s response OIW, and the second ~ep is fie a@’sis Of the
combined response of the subway structure and ground.
9rnMicrlA14Y?is
%uim”
‘r=
.%1Qadin
~w
I
W.&e* 11i&4CnCRi
%e”wit=ni=
Teas
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“ql‘“
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E===l
Figure 2 Analysis Flow
3.2
Numerical procedure
(1) Earthquake gound response analysis (Step one)
The dynamic responses of the model ground during an earthquake was estimated
using the SHAKE program (one-dimensional seismic response analysis using
with multiple-reflection theory) (Figure 3). considering the non-linearity of soil
properties as equivalent linear properties from G-Y. h-y cuwes generated from
experimental results (Figure 4) [2.5]. The converged values (shear modulus and
damping constants) of the ground were calculated.
© 2002 WIT Press, Ashurst Lodge, Southampton, SO40 7AA, UK. All rights reserved.
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Paper from: Structures Under Shock and Impact VII, N Jones, CA Brebbia and AM Rajendran (Editors).
ISBN 1-85312-911-9
Sttwctwes
[ under Shock and Itnpact 1‘[l
371
(2) Simulation analysis (Step two)
The two-dimensional dynamic response of the subway structure was analyzed
using TDAPIII (time domain dynamic analysis programIII ). The ground was
modeled using two-dimensional finite elements and the converged values of the
soil properties using the results of step one. The structure was modeled as a set of
elastic beam elements (Figure 5). The dynamic behaviors of the structure,
dynamic forces (shear earth and lateral earth pressures) acting on the structure
and bending strains induced in the side-walls and center columns were evaluated,
and the results compared with experimental values.
6x20=120
Lkit:an
1
2
T
!
1
30
30 ;
60
1
I_
I
—-
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.
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+PFigure 3 One-dimensional analysis
model of the ground
u“
‘-,
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‘(-n
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13errert)
Figure 5 Two-dimensional analysis
model of the subway structure
1.LKI
0.80
.-0
2
0.00
:
~
043
0
:
0.20
m
4)
:
0,00
1.COE-06
SW*
1COE-04
Shear Strain
1.00E-02
T
Figure 4 Strain-dependency curves
1.00E+CQ
© 2002 WIT Press, Ashurst Lodge, Southampton, SO40 7AA, UK. All rights reserved.
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Paper from: Structures Under Shock and Impact VII, N Jones, CA Brebbia and AM Rajendran (Editors).
ISBN 1-85312-911-9
372
4
.Ytru.mws( “mler.T170ck
and ln7pact1_ll
Results
4.1 Dynamic Behaviors of the Ground Model
The simulated resonance eumes of the model ground were agreed well with
experimental ones. So, the dynamic properties of aualytieal model (initial shear
modulus and damping constants, and G-y ,h- Yrelations) were reasonable. The
response characteristics of the ground model were determined from the resonant
curves (Figures 6.7). The main results are as follows.
(1) In case of horizontal motions. the resonant fiequeney of the model ground was
20 Hz for weak motion (20 gal) and 8 Hz for large motions (400 gal). The model
ground exhibited strong nordinear properties from low levels of strain.
(2) In case of vertical motions, the resonant frequeney of the model ground was
47 Hz for weak motion (10 gaI) and 41 Hz for large motion (200 gal). The
amplification and resonant frequency did not decrease notably with increasing
has; acceleration. The model ground did not exhibit strong nonlinear properties.
!m.s”e.
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1!
I
o
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“.
Expenmenb.al Results
sweep
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Analysis
Ratio
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Results
Resonant
450 500
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mant
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250
300
35,0
f(Hz)
400
450
500
200
(b) In case of vertical motions
250
300
350
f(Hz)
400
45o
500
© 2002 WIT Press, Ashurst Lodge, Southampton, SO40 7AA, UK. All rights reserved.
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Paper from: Structures Under Shock and Impact VII, N Jones, CA Brebbia and AM Rajendran (Editors).
ISBN 1-85312-911-9
Sttvictwes
s
,“.
.’,,
Horizontal
{
esonent Fr.
22.OHZ
Element
?espons.e
Vertical
Ratlc
10.29
373
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es.nmt
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47.OHZ
Element
?.sponse
Ratic
15,89
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2ogal
v
1;:’=
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051015202530354045
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051015202530354045
f(Hz)
esonmt
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—
50
f(Hz)
?esponse
Ratic
—
es. ”ant
F,.,
—
?esponse
Ratic
—
H
400gal
:
v
+ 00
200gal
e-
—
...........
4
0510152025303540
i;!=
4550
051015202530354045
50
f(Hz)
f: Hz)
(c) In case of simultaneous horizontal and vertical motions
Figure 6 Resonant curves of the model ground
(3) In case of simultaneous horizontal and vertical input motions, two resonance
points were observed in both cases of phase lag ( a =0°&900). The low resonant
point corresponds to the predominant frequency of horizontal motions and the
high resonant point corresponds to the predominant frequency of vertical motions.
There were no significant differences about dynamic responses between
simultaneous and individual input motions. No clear interaction behaviors were
identified.
.
0.0
I
?j
8.0
,:
;
=
6.0
j
2.0
4.0
00
I
o
I
2C0
lco
kwt
3C0
4C0
5fM
Acceedicm (WI)
(a) Horizontal motion
Figure 7 Relationship between acceleration and the maximum amplitude of the
input motions
4.2 Dynamic Behaviors of the Subway structure
(1) Behaviors of the subway structure
The subway structure was deformed si@lcantly in shear and rocking modes and
large strains induced in the center columns at the resonant frequency due to
horizontal input motions. These vibration modes can also observed at the same
resonant frequencies due to simultaneous horizontal and vertical motions. But,
shear and rocking modes did not occurred, and no shear deformation of structure
induced at the resonant frequency due to vertical input motions (Figure 8).
© 2002 WIT Press, Ashurst Lodge, Southampton, SO40 7AA, UK. All rights reserved.
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Paper from: Structures Under Shock and Impact VII, N Jones, CA Brebbia and AM Rajendran (Editors).
ISBN 1-85312-911-9
374
(
.Strt{ciz(res 1 under Shock atzd [nlpuct I‘[1
I
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I
I
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~“”
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:.._.___j
. . . . . . . . . ...’ . .. . .. . . . ..J
b) Verticalinput motion
a) Horizontal input motion
Figure 8 Vibration modes of the subway structure
(2) Dynamic earth pressures acting on the structure (Figure 9)
a) Dynamic shear earth pressures acting on the ceiling slab
In case of horizontal motions, the dynamic shear earth pressures increased with
input level. The distribution of shear earth pressures varied with the input motions.
In case of a weak input motion (20 gal& 100 gal). the distribution shape was
approximately uniform, but in case of a strong motion (400gal &Ko-motion). the
distribution was not uniform. From test data. a slide and e.tioliation phenomena
occurred at center of slab when the input motion was greater than 100g,al [5]. But
in case of vertical input motions, the dynamic shear was negligible. In case of
simultaneous horizontal and vertical motions, the dynamic shear earth pressures
tended to increase with input level at the horizontal resonant frequency for both
phase lags. The distribution shape showed maximum values at the edges.
Comparing the results of the two cases. the phase lag did not influence.
b) Lateral dynamic earth pressure acting on sidewalls
The lateral earth pressure increased with input leveL and the distributions shape
were out of phase because of rocking vibration of the structure were occurred in
case of horizontal input motions. In case of vertical motions. the lateral earth
pressure was negligible. In case of simultaneous horizontal and vertical input
motions, the lateral earth pressures were ahnost the same as those in case of
horizontal input motions at the horizontal resonant frequency.
(3) Bending strain induced in center columns and sidewalls
In case of horizontal input motions, bending strain in the center column was
approximately five times larger than that in the sidewalls when a rigid connection
was used. However, when a flexible joint was used the strain was 1/(5- 1/1O of
that for the rigid connection, In case of vertical input motions. the bending strains
induced in the center column and sidewalls were negligible. The axial strains
induced in the center columns were 1/5 of the bending strains by horizontal input
motions. In case of simultaneous horizontal and vertical input motions. the results
were as for the horizontal input motions (Figure 10).
S Conclusions
From the scaled model shaking tests and simulation analyses. the dynamic
behaviors of the subway structure and the dynamic earth pressures acted on the
structure were clarified as follows.
(1) The results of the numerical simulations agree well ~vithexperimental ones.
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Paper from: Structures Under Shock and Impact VII, N Jones, CA Brebbia and AM Rajendran (Editors).
ISBN 1-85312-911-9
<Ce, d,ng
slab>
Shear
Earthpress.
re(kg/&j
,,
1>
<Ceiling
Shea r
slab>
Lateral
--.!,,.
Earth
Earthpressure (kg/&i
She 2CQg7d
Ko-motionl
I=,,,
!.
~’
,,
b
9
■
H
H
-005
(b) k case of VeItlCalInOtlOnS<Ri ght
,,, ~
s ide-wal
I>
Latera I Earthpressure
,,, ~
(Ceiling
,,,
slab>
~:~~alv,s,al
Shear
-0.05
00s
0
EarthPressure
005
D
(kg/&
1“-- =“’
“=-”1
(kg/d
1,, –m,,,,.
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.
~j
j!
‘~,
II
:7’
!~
~~
T
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,
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~~””.,~
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I
(c) In case
of
horizontal
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simultaneous“”’
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i ‘,.
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;315
si ‘e-w’11 >
;
k
,; . ,
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.’ !
:
Earthpressure
Figure 9 Dynamic earth pressures on the structure
.-
(kg/&i
2 :8
© 2002 WIT Press, Ashurst Lodge, Southampton, SO40 7AA, UK. All rights reserved.
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Paper from: Structures Under Shock and Impact VII, N Jones, CA Brebbia and AM Rajendran (Editors).
ISBN 1-85312-911-9
376
.$trl{rrl,r~~,s
( tlcier shock atd [mpuct 1‘[I
‘ %-w
...
fi-,
k-———l——l ,“:.,
H
,,h,
g?t
$.r.
ct
C.r
~-,
.,t,
,n
1
—1
,,1-,
r,
1% IWI
r,-
Figure 10 Bending strains of the sidevvall and ~;enter column by Ko-motion
(2) The earth pressures acting on the structure and the bending strain induced in
the center columns by vertical input motions. were negligible in comparison with
those induced by the horizontal input motions.
(3) The bending strain in the center column due to horizontal input motions was
five times larger than which at the sidewalls, and the bending strain of center
column with flexible-type joint, was about 1/5 smaller than that with fixed-type
joints. The flexible-type joint between center column and ceiling slave would
have reduced the level of damage to the center column.
(4) In case of simultaneous horizontal and vertical input motions, dynamic
responses and dynamic earth pressures (shear forces, lateral forces) at resonant
frequency approximate those of the horizontal motions. Therefore, it is concluded
that vertical earthquake motion did not have a significant effect on the structure
and the subway structure collapsed due to strong dynamic horizontal forces and
instilcient shear capacity of the center columns.
References
[1] T,Iwatate, The Hyogoken-nanbu earthquake of 1995 investigation into
damage to civil engineering structure, Committee of earthquake engineering
JSCE. pp256-295. 1996.
[2] T.Iwatate. H,Kusu. K.Rin, & T.Tanaka. Scaled model vibration tests and
simulation analyses on nonlinear response of subway structure. Proceedings
of the 25* JSCE earthquake engineering q-mposium, pp481 -484, 1999.
[3] T.Kokusyo. T.Iwatate. Scaled model vibration tests and numerical analysis on
nonlinear dynamic response of subway structure. Proceedings of the 24*
JSCE earthquake engineering symposium. pp233-236. 1979.
[4] Earthquake resistant design codes in Japan (Chapter 6). Japan society of civil
engineering, January 2000.
[5] T,Iw’state. YKobayashi, H,Kusu. &K.Lin. Investigation and shaking table
tests of subway structures of the Hyogoken-nabu earthquake. 12& ~vorld
conference on earthquake engineering, (1043). 2000,