Analysis of the Displacement of Buried Pipelines Caused by Adjacent Surcharge Loads

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15 Νοε 2013 (πριν από 3 χρόνια και 11 μήνες)

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Analysis of the

Displacement of Buried

P
ipeline
s Caused by


A
djacent
S
urcharge
L
oads


Zhongju Sun
1
,

Xiaonan

Gong
2
,

Jianlin Yu
3

and Jialin Zhang
4


1

Master
, Research Center of Coastal and Urban Geotechnical Engineering
,

Zhejiang
University
,

Room B4
03
,

Anzho
ng Building
;
Zhejiang University,

Yuhangtang Road
No.866.Xihu District
; Tel:

1
8267169263; Email:

juhua199088
@16
3
.com

2 Professor,

Research Center of Coastal and Urban Geotechnical Engineering
,

Zhejiang University
,

R
oom 1
-
1602,

Jinghuyuan,

Tiyuchang Road No.415
;Tel:

13906508026
;Email:

xngong@hzcnc.com


3
Professor,

Research Center of Coastal and Urban Geotechnical Engineering
,

Zhejiang University
,

Room B420,

Anzhong Building
;

Zhej
iang University,

Yuhangtang Road No.866.Xihu District
; Tel:

13906525721
;

Email:

yujianlin72@126.com

4 Master,

Research Center of Coastal and Urban Geotechnical Engineering
,

Zhejiang
University
,

Room B4
07
,

Anzhong
Building
;
Zhejiang University,

Yuhangtang Road
No.866.Xihu District
; Tel:

18868817011
; Email:

zhjldz076@163.com


A
BSTRACT


T
his re
search focuses on the effects of

the adjacent surcharge loads on pipelines
buried nearb
y.
A

calculation model is established
b
ased on the theory of Winkler
elastic foundation short beam
, taking into account

the impact of soil deformation
which is leaded by adjacent surcharge loads
.

T
he
Boussinesq basic formulas and the

finite difference meth
od
are

also
applied in this
model. Consequently
, analyses are
performed for
pipelines

varying the
load

location,

geologic condition
,
pipeline

depth
,

diameter and
stiffness

through a
n

example.

After i
ncreas
ing

to a certain value
, the
pipeline diameter

and t
he
coefficients of foundation bed

would

have little impact on
the pipeline maximum displacement. However
,

the buried
pipeline

deform
s

significantly as the burial depth soars.
As expected
, the maximum displacement of
pipeline decreases
while the

pipe stiffn
ess increases and the location of adjacent
surcharge loads
pose

large

effect on buried pipe
line
s.


K
EYWORDS


Adjacent

S
urcharge
L
oad
s;
A
dditional

S
tress
;

D
isplacements of
B
uried

P
ipeline
s
;
Winkler

E
lastic
F
oundation

S
hort
B
eam;

F
inite

D
ifference
M
ethod


IN
TRODUCTION



W
ith

the rapid
construction

of

l
arge
-
scale building

and

national highway

i
n recent
years
,

the problem of
ove
rcharg
e
on ground

in city
construction

received increasing
attention from environmentalists and geotechnical engineer
s
.
S
urcharge load
s

transferred to the
buried pipeline

by
subsoil
,

and
sometimes
accidents of pressure
pipes

such as
cracks
,
joint
dislocation
,

water penetration and leaks
may occur
when
pipelines subjected to additional pressure and horizontal thrusts
under

overloading
.
T
his

may
adversely affects

public facilities

especially water supply and drainage
.

In
more serious cases
,
a
lso affect the ground traffic
,
adjacent
buildings

and other
pipelines
.

What

s more,
to

repair

the damage
is n
ot easy.
Consequently
, it is
necessary
to
an
aly
ze

the displa
cement of buried pipelines

resulting from the
adjacent
surcharge loads.

By far, a
ssociated with the field
effects and

displacement of buried pipelines under
adjacent surcharge loads,

substantial studie
s

have been
done on the meshing of the
architectural free
-
form surface on this topic.

Li

et al
. (
1999)

founded

that

the
equations of vertical and horizontal displacements of underground pipeline
are
affected by deep excavation

with

the

elastic
theory of Winkler
; Li

et al
.

(
2004) used
the
curve
-
fitting method to infer the deformation
,
shear force and moment o
f buried
pipelines
; Dai
et
al
.

(
2006) establis
hed a numerical model
to

analy
ze

the effect
s

of
new
construction

loads
to

buried pipelines
,

us
ing the

finite difference

method

which

simplify the

complexity of the problem
.
The

mechanical characteristics
of buried
pipelines

under vertical
static
load

w
ere

simulated by three
-
dimension finite element
analysis software Abaqus
(
Yang
,
2006).
To be noticed
, t
he

previous

work
s

are

all

base
d on the
theory

of

Winkler
elastic
foundation

short beam
.

Although some
progress has been made in this area

during
these years
,

a more
convenien
t

approach

is needed to
calculate the deformation
caused by adjacent loads
of buried pipelines
.

The

present

paper

proposed

a rel
atively

accurate
approach

to
analyze

the effect of
buried pipeline
under

adjacent
surcharge loads
. A

mode
l

was us
ed

to integrate the
influence of the
non
-
uniformly distributed pressure on the settlement, which

contain
s

t
he deformation

and
lateral displacem
ent

of soil
.
A
fter a statement of
Winkler elastic
foundation

short beam

theory
,
a

calculation m
odel
to

analyz
e

the

adjacent surcharge
load
s

effects o
n the buried pipelines
had been carried out
.

Then, t
heoretical stress
calculations
were

performed
by
us
e of

Boussinesq
solution
.
Finally
,

f
inite difference
method

wa
s
used to calculate

the settlement of buried pipe
line
.

Furthermore,

the
effect of a number of factors
,

including the

load location

S
,
surcharge load
P
,
embedded depth

of pipeline

H
, pipeline

stiffne
ss

E
p
I
, diameter
D

and geologic
condition

k

were

discussed
.
It

s hoped that the work
in this paper

can supply
technical support and guidance to the design and

protection

of
buried
pipeline
s
.


ASSUMPTIONS



The key assumptions of the computing model are:
(1
)

T
he

soil

is
s
upposed to be

iso
tropic

continuum

linear elastic
material
, without
any regard to the concepts of
layering
; In addition, the effect of deformation and stress
under the action of
deadweight

on
the
pipeline
i
s stabled after

a
long

time
,
therefo
re
,
no account is made
about

the
soil consolidation

and load
change

over time, only consider
ing

the addition
stress
caused

by adjacent
surcharge

loads.

(2)
It is assumed
in this analysis
that the pipe may be represented adequately as a
n

isotropic

continuum

linear

tube of constant
diameter

and

thickness
, no account
i
s
made
about
pipeline joint
.
During the analysis,

the
calculation system

i
s assumed
to
be
accord
ing

with
Winkler
elastic foundation
-
beam hypothesis
.
Another assump
tion
is that

the pipeline
i
s tre
ated as short
beam
. W
hat’s

more,

t
he

l
ongitudinal
bend

in the
pipeline

conform
s

to the assumption of
Bernoulli

beam.

(3)
T
he affected length

of surcharge load to the adjacent pipe
i
s
assumed

to be 3 times
of the length of surcharge load.
G
eneral
ly
, when con
sidering the

coactions

between
the

overburden

depth
and
construction technological process
,

the

fixed support

would
rotate

if

the
overburden

depth is too thin. On the other side, the rotated support
might be fixed and could bear a certain moment wh
en the
o
verburden

depth
i
s thick
enough. The pipe is assumed to be pinned at both ends with moment zero and full
restraint against movement
,

namely the

boundary
suppo
rt
conditions

are

fixed in this
view.


NUMERICAL MODEL

OF
BURIED
PIPLEINE


Fundamental solution fo
r the overloading model
.
T
he
c
ase

being analyzed is
illustrated in Fig
.
1
, the

pipe

is modeled as a horizontal strip of
external diameter
D
,
having a constant flexibility

E
p
I
along its length
,

and the depth of
pipe

crown
is

H
.
A
uniform

r
ectangular

surcharg
e

loading
P

of
length 2
a
and width 2
b

is located
vertically
about
S
distance from the pipe axis
.

For
convenien
ce
,
the origin
is set at the
left of pipe,
and
x

axis
being along the pipeline length
.

So

t
he center coordinates of

the
surcharge load
i
s
(
x
p

y
p

z
p
)
, and

the
coordinate

of a

random

point on

the
pipeline

i
s
(
x
0

0

0
)
.

Even though the
soil around
the
pipeline is not an elastic material, the
elasticity solution originally developed by Boussinesq (1876) has been commonly
adopted to estimate the earth pre
ssure due to surface loads.

T
he surface of the
Boussinesq solution is infinitely deep and infinitely wide in all directions, which is
called a semi
-
infinite solid or elastic half
-
space.
Hence, t
he
formula
s

for calculating

horizontal and vertical
addi
tional

stress
can be

acquired
by

integra
tion method
.










a
x
a
x
b
y
b
y
v
p
p
p
p
dxdy
R
Pz
q
5
3
1
2
3






(1a)











































a
x
a
x
b
y
b
y
u
p
p
p
p
dxdy
z
R
R
z
R
y
z
R
R
z
R
z
R
R
z
y
P
q
2
3
2
3
2
5
2
2
3
2
1
2
3






(1b)




2
2
2
0
2
z
y
x
x
R





(1c)

w
here

P

is the surcharge load,
x

and
y

are pla
n dimensions from the left of pipeline

to
element in soil,
z

is the depth from

the

axis

of

pipeline
to element in soil, and
μ
is
the
Poisson ratio of soil mass
.



F
igu
re.1 Numerical
calculation
model

of buried pipeline


Under the effect of
adjacent

surcharge

load
s
, the
foundation
soil
has

lateral distortion
.

The amount of compression
i
s calculated with

layer
-
wise summation method

according to t
he

Code for Design of Building Foundation

(GB50007
-
2002
,

2002
)
.







dz
z
x
E
z
x
q
x
z
z
s
v


2
1
,
,
1







(
2
)

w
here
E
s
(
x ,z
)

is
the foundation

compressive modulus

at the depth of
z
;

z
1

is
the depth
of buried pipeline
;

z
2

is
the thickness of compressed layer
.

T
he

lateral
displacements
of foundation
can be
estimat
ed

as follows

(Zeng
, 196
2
)
.




















a
x
a
x
b
y
b
y
s
p
p
p
p
dxdy
z
R
R
x
R
xz
z
x
E
P
x
)
(
)
2
1
(
)
,
(
2
)
1
(
5
2








(
3
)


DISPLACEMENT

OF BURIED PIPELINE


The

pipeline displacement
can

be classified in
horizontal and vertical

to
calculate

on
two sides
.

V
ertical

displacement

F
oundation model
.
Based
on the theory of Winkler
,
there
is
not
only
addition

stress
from the

surface surcharge
load
s
,
but also
a
ground reacting force

on
the pipeline
.



kv
p

1




(
4
)

w
here

v

is

the
vertical

displacement of buried pipeline;
k

is
the

coefficient of
f
oundation soil
.


D
ifferential equations of elastic foundation
-
beam
.
Thus the
space curve differential
equation of elastic foundation
-
beam (displacement equation) is

shown as follows.

)
(
1
4
4
x
k
q
Dkv
dx
v
d
I
E
v
p








(
5a
)

So then we
let
)
(
)
(
1
1
x
k
q
x
q
kD
K
v





,

there is

)
(
1
4
4
x
q
Kv
dx
v
d
I
E
p




(
5b
)

w
here
E
p
I

is
the

bending stiffness

of buried pipeline;

D

is
the width of buried pipe

s
cross section
, and
D

is diameter
of
c
ircular tubes
.

F
inite

difference method
.
D
erivation
operation

is

take
n

on the

i

point

for

v
=
f
(
x
)
,
which can
put

forward
in a
method of fourth
-
order central difference

schemes
.

4
2
1
1
2
4
4
4
6
4
x
v
v
v
v
v
dx
v
d
i
i
i
i
i
i




















(
6
)

With this formula
, we
can

transform
the

o
rdinary
d
ifferential
e
quation into differen
ce

equation
s
.

Differen
ce

equations

building and solving
.
Obviously
,
the stress on the pipe is
non
-
uniform
. T
he
addition

stress

i
s
decompose
d

into a few
focus
q
i

and

calculate
d

separately

during

the

analysis.

Then

we
set up the
total pipe

into

n

components
. T
he
length of each part is
c
, here the middle displacement of each part is
expressed in

v
i
,

the
foundation counterforce

is
p
i
;
As shown in
Fig.
2.

The model
consider
s

not only

the interaction be
tween the
pipe
lines

and soil around, but
also

the load
transmitted

by
the soil around

actually
.

Consequently,

the relationship among load, soil and pipe is
analyzed. For the
i

part
, there
i
s
an

equation according to
equation
(5a) as follows:

i
i
i
i
i
i
i
p
q
Kv
c
v
v
v
v
v
I
E










4
2
1
1
2
4
6
4





(
7a
)



F
igure.
2

F
D
M meshes

of pipeline





i
i
i
i
i
i
i
q
Kv
v
v
v
v
v
C










2
1
1
2
4
6
4



(
7b
)



Namely

i
i
i
i
i
i
q
v
v
v
C
K
v
v
C










]
4
)
6
(
4
[
2
1
1
2




(
7c
)

w
here
C
c
EI

4
/


i
=2,3
,……,(
n
-
2
)。

B
oth ends

of the pipel
ine

are

fixed.



0
=
dy/dx

0
=
θ
0
0
0
0
0
1
1
10
10
equal
L
x
x
L
L




















w
here
θ

is
the rotation of pipe.

After adding
the lack

equation from the boundary conditions, the
linear algebraic
equations

group
ed
with unknowns of each segment
midpoint

s
deflectio
n

parameter
are

formed
.
The
procedu
re

c
an

be shown
as
matrice
s form
.







P
v
A



(
8
)

w
here [
A
] is the stiffness matrix of the pipe composed of standard beam elements,



v
is
the
vertical
displacement
vector,


P

is the force ve
c
tor representing

surcharge
loads acting on the beam elements.

Throu
gh the numerical solution of

equation

(8)
, the

pipeline
displacement
at the
random

point can be

obtained
.

Horizontal

displacement

F
oundation model
.
Adopt
the Winkler

F
oundation model
.

ku
p

2


(
9
)

w
here

u

is
the horizont
al

displacement of buried pipeline.

D
ifferential equations of elastic foundation
-
beam
.



x
K
q
Ku
dx
u
d
I
E
u
p
2
4
4











(
10
)

Differen
ce

equations

building and
solution.
Applying
the pipe
to segment,

th
e
linear algebraic equations

group
ed

with unknowns

of each segment
midpoint

s
deflectio
n

parameter
are

formed
.
The
procedure

could be shown in the for
m of
matrices
.







P
u
A



(
11
)

w
here


u
is the
horizont
al

displacement vector
.

Then the
boundary condition
i
s unified

to solve the diffusion equation.

Thereby the
horizont
al

di
splacement of buried pipeline
i
s acquired.

Total

displacement


According to the principle of vector addition
, the total displacement of buried
pipeline on the effect of adjacent surcharge load
d

i
s obtained.


2
2
u
v
d







(12)

w
here
d
is the total displacement of buried pipeline.


N
UMERICAL EXAMPLE


The pipe, foundation, adjacent
surcharge
load
s

are depicted schematically in Fig.3. A
pipe of diameter 4 meters and
E
p
I

1.0
×
10
7
kN
·
m
2

is embedded at a dep
th 5 meters
below the surface of ground. A 0.1MPa uniform
rectangular load
ing of
length

20
meters and width 8 meters is located 3 meters above from the axis of buried pipe.
The soil has a
compressive modulus

E
s

of
3MPa,

P
oisson’s ratio
μ
of 0.5.

Foundation
soil coefficient
k

is

1.0
×
10
4
kN
/m
3
.

A
nd the affected length of the

ground adjacent
load to the buried pipe is 3 times of the

ground surcharge

load,
which

is 60 meters.
Here, the pipe is

divided

into 30 segments and 2
meters

each.



Fig
ure
.3
O
verview

of th
e pipe, foundation

and
adjacent loads


P
ARAMETERS ANALYSIS





Figure.
4
Addition stress of subsoil

Figure.
5 Deformation

of subsoi
l


Subsurface soil s
ettlement curve at the pipeline

depth
.
Fig.4 and
Fig.
5 show the
vertical
,
horizontal

addition stress and each direction deformation at different

locations of foundation soil using equations

(
1
)
,
(
2
)
,

(
3
)
, which

expressed in
c
omputer programs

with software MATLAB.

From the above
-
mentioned analysis
, different

parameters that influ
ence pipe
deformation are discussed as follows.


Location

of adjacent surcharge
load
.

The

analyses

indicate
that

changing
the
location

between

buried pipe

and surcharge load

S

has
unignorable

effect

on
calculated pipe response, since the
surcharge load

and

pipeline remain

unchanged
.

As
is
shown in
Fig.6 (
a), the max
imum

displacement
d

values
increasing

with
S

heighten
, and it

i
s almost 0
when

S

bigger

than a certain number
, which i
s

about 10
meters in this paper. So in

the actual projects
, pipelines should

be buried far away
from surcharge loads.


P
ropert
y

of the subsoil
.
The

type of subsoil
also

has effect on buried pi
pelines,
generally

represented by

f
oundation soi
l
coefficient
k
. A series of different
f
oundation soil coefficient
k

are

developed for same

burial depths ranging from 1.0
×







( a )

L o c a t i o n o f a d j a c e n t s u r c h a r g e l o a d
S


(
b
)
Foundation soil c
oefficient
k




( c )
P
i p e s t u f f i n e s s

E
p
I



(
d
)

P
i pe di a me t e r




(
e
)
Embedment depth of pipeline

H




(
f
)

L o a d ma g n i t u d e

P

F
i g u r e
.
6

P a r a me t e r s a n a l y s i s



10
4
kN
/m
3

to 20
×
10
4
kN
/m
3
.

For the maximum displacement
Max d
i
s not change

dramatically

w
hen
k

comes to a certain
number. From

Fig.6(b) it

i
s easy to know the
k

value is 1.0
×
10
5
kNm
-
3
.


Pipe

stuffiness
.

As
i
s shown in Fig.6(c
), with the pipe
stuffiness

E
p
I

increasing, the
maximum displacement
Max
d
i
s decreasing.
It

s mainly because

the compatible
deformation
capability of
pipe

weakens

as the rigidity
of pipe
E
p
I

incre
ases.
This is
why

flexible pipeline

can work

well while rig
id pipeline break
s

down in
the same
circumstances
. Consequently,

practical engineer
ing should choose

lower stiffness

pipe

if
other
condition permi
t
t
ed, so that it can

be in

coordination with

the soil

around
.


Pipe diameter.
E
ffects
of
pipe diameters
are

in
vestigated
in

the analysis
and we
confirm
ed

that the actual dimension of pipe
i
s significant to
its
displacement. Results

present

in Fig. 6(d)

indicate that as the pipe diameter
D

increases the maximum
displacement
Max d
decreases. This
indicates

the

large
r

of the
pipe diameter the
easier to
coordination with

the soil

around (
Jin

et al.
, 2009
)
.


Embe
dment

depth of pipeline.

C
hanging the depth of buried pipeline

H
,
but
the
modulus of the pipe

remains
const
ant.
Not
surprisingly, the

analyses indicate

that
cha
nging
H

ha
s

a negligible effect on calculated pipe response, since the max
imum

displacement
d

value
de
creases

with the

grow
th of

embedded

depth.
As shown in
Fig.
6(
e
)
, e
mbedment depth has little effect on the maximum displacement
when

H

is
9.5m
.
The
reason

is that the
interaction between soil and pipe
enhances with
the
embedment depth

increase
.
In this way, the movement of buried pipe is
limited (
Jin
,
2009
).

Conversely
,

it is
benefit

for pipe t
o
resist

distort
ion
.
T
he
analysis

in this paper

ignore

the probl
em
s

of
soil

consolidation

and
the time effect of
load which
overlying
pressure
and
pore water pressure

brings, and
only considering

the addition stress
caused

by adjacent
surcharge

loads. Pore

water pressure
,
internal

pressure of pipe
and soil characters w
ould
have negative effect
s

on

pipe. So it
is not

the deeper the
safer for buried pipe.


Surcharge l
oad
.
Max
imum

d
isplacement for the pipe
i
s shown in
Fig.
6

(
f
) for
various

P

value. It is
evident

that maximum displacement increases with the
growth
of

P

valu
e.

Furthermore
, the
displacement of pipe

gr
o
ws

linearly as the workload
increase
s
.

Thus the load magnitude
P

ha
s
a significant impact on

pipe displacement.


C
ONCLUSION

AND
DISCUSSION


Influence on adjacent buried pipeline

of surcharge

is an urgent problem
to be solved.
In this research,
finite

difference
numerical analysis ha
s

been carried out. The

d
ifferential equations
b
ased on the theory of Winkler elastic beam
a
re

established

first. A simplified method to calculate pipeline maximum displacement
i
s propo
sed
for pipel
ine. Then the effect of a numerous

factors
including the e
ffect of

surcharge
load
P
,

load location

S
, embedded depth

of pipeline

H
, pipeline

diameter
D
,
pipeline

stiffness

E
p
I
and geologic condition
k

are
analy
zed
.

Based on the results,
a
qual
itative
analysis

to protect
buried
pipe
line

i
s given.

The r
esearch shows that the pipeline
maximum
displacement

will change when
these
parameters

change
d
. However, for
general engineering situations, the normalized maximum displ
acement changes little
when
diameter of pipeline and
foundation
coefficient
k

reaches

a certain number.

In
actual
city pipeline engineering
, it is important to consider the adjacent load when set
buried pipelines.

Based on the actual situation

and us
ing

the
finite

difference
numerica
l method,

proper depth, diameter
, stiffness

of pipeline and suitable location
to adjacent surcharge load

can be chosen

in this paper
.

T
he
analysis of the problem has been perform
ed using Winkler spring models
and
the weakness of the Winkler model is its ch
aracterization of soil pressure in terms of

the absolute pipe displacement.
Furth
er
more

it neglects interaction through the soil
from location to locatio
n. So

the paper
doesn’t

have

considered the nonlinearity of
soil, which would be further researched in
the future.


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