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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