Influence of Soil-Pile-Structure Interaction on Seismic Response of Long Span Suspension Bridge

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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
Free-field ground soil
Spring-damper
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

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.

REFERENCES

Cai, Y.

X.

, Gould, P.

L. and Desai, C.

S. (2000).

Nonlinear analysis of 3D seismic
interaction of soil
-
pile
-
bridge systems and application.

Engineering
Structure,

22(2):191
-
199.

Clough, R.

W.

and

Penzien J. (1993).
Dynamics of structures
.
McGraw Hill, New
York.

F
an, L. C. (2001).
Earthquake resistance of bridge
, Tongji University Press, Shanghai.

Leger, P.,

MIde, I.

and Paultre, P. (1990).

Multiple
-
support seismic analysis of large
structures.”
Computers & Structures,

36: 1153
-
1158.

Penzien, J.

, Scbeffey, C. F.

and Parmelee, R. A.. (1964).

Seismic analysis of brides on
long piles.

American Society of Civil Engineering
,

90(3),
223
-

254.

Shuo,F. Y.

, Xiang, Q.

and Xie, X. (2005). “Dynamic characteristics and multi
-
support
seismic response analysis of a super
-
lar
ge
-
span suspension bridge”,
Journal of
Highway and Transportation Research and Development
,
22(8),
31
-
35
.

Viola, J. M., Syed, S. , and Clenance, J. (2005). “The new tacoma narrows suspension
bridge: construction support and engineering.”
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2005
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