Influence of Soil

Pile

Structure Interaction
on Seismic Response of Long Span Suspension Bridge
Xun XU
1
and
Shi

zhong QIANG
2
1
School of Civil Engineering, Southwest Jiaotong University, P.O.BOX 559, Chendu
610031, P. R. China
2
School of Civil Engineeri
ng, Southwest Jiaotong University, P.O.BOX 559, Chendu
610031, P. R. China
A
BSTRACT
For obtaining the accurate dynamics behavior of suspension bridge,
t
he
L
ancangjiang River Bridge is taken as an example, which is a suspension bridge
with steel concrete
composite stiffening girder.
The spatial dynamic FE model is
established and soil

pile

structure interaction is
simulated using the lumped

mass
model of single

pile by modifying Penzien J model.
Then a 3

dimensional nonlinear
time history analysis for the
bridge is investigated
by
the nonlinear dynamic analysis
method
of inconsistent excitations
established based on Large Mass Method and
Pseudo

Static Displacement
C
onception.
Analytical results show that the effects of
soil

pile

structure
interaction on dyn
amic characteristic of long

span suspension
bridge mainly embody in
the decrease of structure stiffness and the change of mode
order, and
that the effects of soil

pile

structure interaction on seismic response of
long

span suspension bridge are closely
rel
ated to the simulation way of seismic
ground motion and traveling wave effect. It’s greatly necessary to utilize soil

pile

structure interaction model to seismic analysis and design even if the stiffness of the
pile foundation is ensured.
I
NTRODUCTION
Chin
a is one of many earthquakes
.
I
n the disaster prevention and reduction
studies, an important part is the disaster prevention and reduction studies of the
lifeline engineering,
and among them, the
seismic resistance
of t
raffic
h
ub
p
roject

bridge
are
particu
larly important.
Data from a large number of
s
eismic
d
amage
of
bridges
indicate that
soil

pile

structure interaction
is one of the factors leading to
th
at
damage
(
Fan
, 2001)
.
F
ewer among
t
he current research of suspension bridge’s
seismic response
have con
sidered the soil

pile

structure interaction effects
(
V
iola
et
al
,
2005
,
Shuo
, 2005
and Cai
et al
,
2000)
, and the mechanics influencing factors
considered in their dynamic models is not comprehensive enough. In this paper, a
380m

span
suspension bridges
wit
h steel concrete composite stiffening girder
is
taken as an example,
the spatial dynamic finite element model for the bridge was
established by the software ANSYS and soil

pile

structure interaction is simulated
using the lumped

mass model of single

pile b
y modifying Penzien’s
model. Based
on the Large Mass Method of Leger and Pseudo

Static Displacement Conception,
the nonlinear dynamic analysis method of inconsistent excitations for long

span
suspension bridge w
as
established
.
Based on these,
a 3

dimension
al nonlinear time
history analysis for the bridge is investigated
.
Th
is
research can provides some
experience and reference for dynamic behavior and seismic
design
of long

span
suspension bridge.
M
ODEL
OF
SOIL

PILE

STRUCTURE INTERACTION
The nonlinear char
acteristics of soil is the most important factor controlling
soil dynamic action. Firstly, under the action of earthquake load, seismic waves
inputting the structure will greatly change comparing with that in bedrock because
the seismic wave filtering and
amplification of site soil. Secondly, under the
inputting of earthquake ground motion, pile foundation can not freely deform
because the restraining effect of soil around the foundation, while the existence of
free

field ground soil make the mass effect of
the structure system increase, thus the
damping effect of soil around the pile will become more prominent. Penzien J model
(
Penzien et al
,
19
64)
is
shown in Figure 1. In this model, a certain range of soil
around the pile is considered to the commonly mov
ement attaching to the pile, and
that is named soil mass around the pile. Soil of 200 times the area of pile cap as a
free

field ground soil is taken as mass effects of soil acting the pile foundation. Soil
among the piles is simulated equivalent stiffness
longitudinal bar. Soil around the
pile is simulated linear spring

damper, and one end of spring links to the pile and the
other end links to a mass element which is simulated mass effects of soil acting the
pile foundation.
Pile Cap
Pile
Freefield ground soil
Springdamper
Ground soil around the pile
Superstructure
Mass
V
Figure
1
. Lumped

mass
s
pring

d
amper
m
odel of
soil

pile

structure
s
ystem
The stiffness
s
K
of equivalent soil spring is determined by the “m” method
(
Zhang
et al.
2002)
.
s
K
can be written as
Zx Z
p Z
s Zx
s p
s s Z
mZx
ab mZx
P A
K ab mZ
x x x
(1)
Where:
Zx
the
transverse
resistance of the soil to the pile
,
Z
is the
depth
of soil,
Z
x
is the
tran
sverse
d
isplacement
of soil,
a
is the thickness of soil,
p
b
is
the calculation
width of pile
,
m
is
the proportion coefficient of foundation soil.
NONLINEAR DYNAMIC EQUATIONS OF INCO
NSISTENT EXCITATION
Seismic load is external excitation acting on the support point of bridge
structure. When establishing the
dynamic
model of bridge structure under seismic
excitation, the equations of the whole bridge system are blocked according to non

support nodes and support nodes
(
Clough
et al
,
1993)
. Because of the geometrical
nonlinearity of suspension bridge and the time

dependent characteristics of
nonlinear structure, its motion equations
are
suit
able
to be solved by increment
method. Dividing
the duration of ground motion into a number of time

steps, and
the stiffness and damping of structure almost
do
not change in each time

step, while
the stiffness and damping of structure of each time

step change with the structural
configuration. Thus the
motion equations can be written as:
g
g
s
gg
gs
sg
ss
g
s
gg
gs
sg
ss
g
s
gg
gs
sg
ss
F
Δ
U
Δ
U
Δ
K
K
K
K
U
Δ
U
Δ
C
C
C
C
U
Δ
U
Δ
M
M
M
M
t
t
t
t
t
t
t
t
t
t
t
t
t
t
t
0
(
2
)
Where: left upper subscript
t
represents time moment; lower subscript
s
and
g
separa
tely represents non

support node and support node of the structure; Δ
t
U
is
the increment of
t

t
+Δ
t
;
M
,
C
and
K
separately represents mass matrix, damping
matrix and stiffness matrix;
F
g
the reaction vector on support node.
Based on Large Mass Method
(
Leger
et al.
19
90)
, attaching Large Mass
M
0
to structural support point, and taking
M
0
as 10
6
times of the total mass
M
ss
of the
structure, thus
M
ss
can be neglected in comparison with
M
0
.Releasing the restraint
degree of freedom of the excitation direction of
the support point, then utilizing
inertia force
M
0
Δ
t
a
0
of Large Mass
M
0
to realize the excitation of seismic load Δ
t
F
g
on the structure.
Based on Pseudo

Static Displacement Conception of Clough
(
Clough
et
al.
1993)
, structural total displacement Δ
t
U
s
can be resolved into pseudo

static
displacement Δ
t
U
ps
an
d dynamic response displacement Δ
t
U
ds
. Thus through Eq.
2
we
can derive to obtain Δ
t
U
ps=
t
K

1
ss2
t
K
sg
Δ
t
U
pg
=
R
sg
Δ
t
U
pg
,
R
sg
is Influence Matrix and its
mechanics meaning is the unit pseudo

static displacement of no support point of the
bridge structure caused
by unit static displacement of no support point of the bridge
structure. Neglecting the time

dependent property of
R
sg
, namely that
R
sg
can be
solved on the tangent stiffness matrix of the dead

load configuration. Adopting
lumped mass matrix, the different
ial equation of Δ
t
U
ds
can be written as:
g
1
0
sg
ss
ds
ss
ds
ss
ds
ss
F
Δ
M
R
M
U
Δ
K
U
Δ
C
U
Δ
M
t
t
t
t
t
t
(
3
)
E
quation
3
is the nonlinear dynamic equilibrium equation of multi

support
excitations for suspension bridge structure based on Large Mass Method and
Pseudo

Static Di
splacement Conception.
I
f the traveling wave effect is considered,
g
t
F
Δ
can be obtained according to the same acceleration of seismic wave with
certain phase difference.
SPATIAL FINITE ELEMENT MODEL OF SUSPENSION BRIDGE
Yunnan Lancangji
ang River Bridge is taken as a example, which is a long
span suspension bridge with a main span of 380m. Based on the software ANSYS,
the spatial finite element model is established, as shown in Fig.3. Modeling features
are : (1) Longitudinal beams, transv
erse beams, bridge towers and pile foundation
are simulated as spatial beam element BEAM44, suspenders and main cables are
simulated as the space bar element of only tension LINK10. (2) Pile caps are
simplified to the space beam grillage system according t
o the principle with
equivalent stiffness and mass. The stiffness effects and damping effects of soil
around the pile on the pile foundation are simulated as spring

damper COMBINE14.
(3) The secondary dead load of bridge deck is simulated as mass element M
ASS21
acting on bridge deck. (4) The nonlinear effect of main cable sag is considered by
the method of using Ernst formula to correct the elastic modulus of main cable.
Stress stiffness matrix is used to consider stress stiffening effect of main cable and
suspender. (5) Main cable is erected on the top of main tower through the saddle,
and displacement relation of principal and subordinate is established to consider
displacement relation between main cable and the top of main tower.
Fig.
2
Spatial FEM of
l
ancangjiang suspension bridge
ANALYSIS OF
SELF

VIBRATION CHARATERISTICS
Based on the above tow dynamic models(Model A: fixed the tower bottom;
Model B: considering
soil

pile

structure
Interaction), Subspace Method is adopted
to calculate out the first 20
0 orders natural vibration frequency and characteristics,
and Table 1 has listed the first
1
0 orders. Figure
3
gives the comparison of the first 4
orders mode shape. In the following Tables and Figures,
M
A and
M
B represent the
above Model A and Model B res
pectively.
Table 1.
Comparison of
Self

Vibration Behavior
Mode
n
umber
M
A
M
B
Natural
f
requency (Hz)
Mode
s
hape
Natural
f
requency (Hz)
Mode
s
hape
1
0.1464
S

L

F
0.1445
S

L

F
2
0.1499
A

V

F
L
G

D
0.1499
A

V

F
L
G

D
3
0.2154
A

V

F
0.2154
A

V

F
4
0.2373
A

T
0.2373
A

T
5
0.2652
S

V

F
0.2648
S

V

F
6
0.3429
A

L

F
0.2970
A

L

F
FT
7
0.3437
S

T
0.3430
S

T
8
0.3511
S

V

F
0.3505
S

V

F
9
0.3784
VC
0.3561
A

L

F
10
0.4123
VC
A

L

F
0.3783
VC
Note: L is lateral;
LG is longitudinal
;
V is the vertical; T is the tor
sion; S is
symmetrical; A is the antisymmetrical
; D is the drift
;
VC
represent the vibration of
main cable
;
FT
represent the lateral flexure of main tower
.
The
f
irst
o
rder
m
ode
The
s
econd
o
rder
m
ode
The
t
hird
o
rder
m
ode
The
f
ourth
o
rder
m
ode
Figure
3
.
Comparison of t
he
f
irst 4 orders
m
ode
s
hape
By comparing and analysis of the natural frequency and modes of Model A
and Model B, the following conclusions c
an be obtained:
(1)
The basic period of the bridge is 6.83s (Model A) and 6.92s (Model B),
and the first 4 periods are greater than 5s, so the bridge belong to the long period
structure; For its width

span ratio is only 1/30.69 , the first order mode is
s
ymmetrical lateral flexure. These consist with the characteristics of long

span
suspension (Xu et al
,
1997).
(2)
The modes appear very obvious grouping phenomenon, the mode with
the vibration of stiffening girder as the main role appears at first, then do
es the mode
with the vibration of stiffening girder and cables as the main role, the mode with the
vibration of towers as the main role appears at last.
(3)
T
he appearing sequence
of
mode change to some extent
w
hen
considering
soil

pile

structure
interacti
on.
(4)
Because
long

span
suspension bridge is a flexible suspension structure
,
the stiffness difference
of main tower and main span structure is great. It lead
s
to
that soil

pile

structure interaction mainly affects the mode with the vibration of
towers
as the main role
. These above characteristic of long

span suspension bridge
make that if comprehensively researching the contribution of towers and the
influence of soil

pile

structure interaction, adequate orders must be considered in
the calculation of
seismic response.
(5)
The first order mode is symmetrical lateral bending, so this mode
contributes to dynamic response of this bridge most greatly. This consists with the
following calculation result of seismic response.
ANALYSIS OF SEISMIC RESPONSE
Accor
ding to the field ground soil at the location of this bridge, natural
seismic waves are adopted as the inputting earthquake ground motion. And we
choose the south

north wave of Elcentro waves of American in 1940, which have
representative meaning in the st
ructural seismic design, as shown in Fig
ure
4.
0
5
10
15
20
0.15
0.10
0.05
0.00
0.05
0.10
0.15
Acceleration/g
Time/s
Fig
ure
4
.
Acceleration time history of earthquake
Newmark algorithm of unconditional steady implicit integral is adopted, but
also fetching δ =0.5 and α =0.25 can not cause amplitude decay to ensure the
contribution of high

order modal to seismic response. In the analysis process,
geometric nonlinearity,
sag effects and stress stiffening of main cable are considered.
Damping ratio of the structure
ξ
=0.02
.
The time

step is fetched for 0.02s, the total
calculating time

steps are 1000 steps, and the total calculating time is 20s.
The inputting combination way
s of earthquake ground motion are four.
C
MB
1: longitudinal + vertical;
C
MB
2: longitudinal + transverse, C
MB
3: transverse
+ vertical, C
MB
4: longitudinal + transverse + vertical
,
CM
B
5: longitudinal +
transverse + vertical, and considering the traveling wave
effect of 0.
4
s phase
difference between the two towers.
Table
2
and Table
3
separately provides the
maximum stress and the maximum displacement of the key sections of the
suspension bridge under four kinds of inputting ways; Fig
ure
5 and Fig
ure
6
separatel
y provides the maximum stress time

history and the maximum stress
displacement time

history of the key sections of the suspension bridge under four
kinds of inputting ways.
Table
2
.
Maximum
s
tress of
s
tructural
k
ey
s
ections of
s
eismic
r
esponse (unit: MPa)
Inputting Way
CMB1
CMB2
CMB3
CMB4
CMB5
MA
MB
MA
MB
MA
MB
MA
MB
MA
MB
Midspan
of Main Beam
28.78
15.59
31.58
30.58
26.61
29.12
33.31
29.08
78.76
68.11
L/4
of Main Span
20.61
10.42
34.48
31.69
36.02
30.79
36.45
30.51
61.26
50.58
Midspan
of Main Cable
9
.66
5.46
10.23
6.5
8.93
8.57
11.69
9.25
34.70
45.63
Bottom
of Main Tower
14.89
10.59
15.22
11.73
7.9
7.62
15.09
10.88
10.90
10.71
Trans

beam
of Main Tower
0.12
0.16
7.02
7.52
7.16
7.11
7.02
7.18
7.18
7.08
Table
3
.
Maximum
d
isplacement of
s
tructural
k
ey
s
ections of
s
eismic
r
esponse (unit: cm)
Inputting Way
CMB1
CMB2
CMB3
CMB4
CMB5
MA
MB
MA
MB
MA
MB
MA
MB
MA
MB
Transverse of
Midspan of
Main Beam
0.00
0.00
18.17
21.45
17.98
21.16
18.10
21.03
18.69
21.93
Longitudinal of
Midspan of
Main Beam
11.76
11.77
11.81
11.82
0.04
0.04
11.77
11.76
11.08
11.06
Transverse of
The Top of
Main Tower
0.00
0.00
7.81
9.11
8.02
8.61
7.83
8.73
7.89
8.25
Longitudinal of
The Top of
Main Tower
1.88
1.68
1.93
2.16
0.71
0.33
1.81
1.71
4.51
4.28
Longitudinal
Relative of
Inter
section
16.06
19.58
16.07
20.01
0.73
0.67
15.70
19.06
11.77
18.40
0
5
10
15
20
16
12
8
4
0
4
8
12
16
Stress/MPa
Time/s
0
5
10
15
20
16
12
8
4
0
4
8
12
16
Stress/MPa
Time/s
MA
MB
Stress of the
b
ottom of
m
ain
t
ower
0
5
10
15
20
80
60
40
20
0
20
40
60
80
Stress/MPa
Time/s
0
5
10
15
20
80
60
40
20
0
20
40
60
80
Stress/MPa
Time/s
MA
MB
Stress of
m
idspan of
m
ain
b
eam
Fig
ure
5
.
Stress time history curve of structural seismic response
0
5
10
15
20
10
5
0
5
10
Displacement/cm
Time/s
0
5
10
15
20
10
5
0
5
10
Displacement/cm
Time/s
MA
MB
Displacement of the top of
m
ain
t
ower
0
5
10
15
20
25
20
15
10
5
0
5
10
15
20
Displacement/cm
Time/s
0
5
10
15
20
25
20
15
10
5
0
5
10
15
20
Displacement/cm
Time/s
MA
MB
Displacement of
m
idspan
of m
ain
b
eam
Fig
ure
6
.
Transversal displacement time history curve of structural seismic response
C
ONCLUSION
(1)
From Fig.5~6 and Table
2
~
3
, we can conclude that the seismic response
stress values of
MA
are greater than those of
MB
on the whole, while the seismic
response displacement values are less. This is mainly because the structure becomes
flexible and its integral stiffness decreases considering soil

pile

structure interaction.
(2) While considering soil

pile

structure intera
ction, the stress of each key
section of the suspension bridge decreases obviously, this decrease can be up to
49.44% (at the L/4 location of main span under the combination way of
longitudinal+vertical). This has reflected that soil

pile

structure interac
tion have
great influence on seismic response of suspension bridge structure.
(3) While considering soil

pile

structure interaction, the maximum decrease
of the key section stress is 49.44% at the L/4 location of main span under the
combination way of long
itudinal+vertical, but this decrease is 36.50% under the
combination way of longitudinal+transverse, and that is 14.50% under the
combination way of transverse+vertical, and that is 20.87% under the combination
way of longitudinal+ transverse+vertical. The
se indicate the influence of soil

pile

structure interaction on seismic response of the suspension bridge is related to the
inputting combination ways of earthquake ground motion, but also this influence is
relatively great.
(
4
)
U
nder the combination way o
f longitudinal+vertical
,
soil

pile

structure
interaction
make
the stress of each key section
change
great
ly
, while make
the
displacement
of each key section
change
little
.
These indicate
when
the structure
stress response
is
i
nfluenced
greatly
by
soil

pile

structure interaction
,
the structure
displacement
response
may not also be
i
nfluenced
greatly u
nder the
same
combination way
(
5
)
From the calculation results under
the combination way
of CM
B
5, the
influence of soil

pile

structure
on seismic response of suspension bridge is related to
the traveling effect of seismic waves.
(
6
)
The analysis of self

vibration characteristics indicates that the pile

foundation stiffness o
f the bridge is adequate large.
However, the seismic response
a
nalysis indicates that the influence of soil

pile

bridge interaction is great. So for the
special
flexible suspension c
ombination
structure of suspension bridge, soil

pile

structure
interaction should be considered for seismic design.
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