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Applied Ocean Research 35 (2012) 105– 114

Contents lists available at SciVerse ScienceDirect

Applied Ocean Research

journal homepage: www.elsevier.com/locate/apor

refined analytical model for landslide or debris flow impact on pipelines – PartI: Embedded pipelines

eng Yuan, Lizhong Wang ∗, Zhen Guo, Yonggui Xieollege of Civil Engineering and Architecture, Zhejiang University, Hangzhou, China

r t i c l e i n f o

rticle history:eceived 14 April 2011eceived in revised form 7 December 2011ccepted 7 December 2011vailable online 2 January 2012

eywords:

a b s t r a c t

In deepwater, the pipeline is directly laid on the seabed without any protection, but the heavy pipelineswill embed into the seabed during installation. The behavior of heavy pipeline under the impact of land-slide is different from that of light pipeline because the heavy pipeline will move downwards whenmoving laterally under the impact of landslide. This work divides the pipeline into four segments: thefirst segment in the landslide zone, which is exposed to landslide drag force and nonlinear lateral soilresistance; the second one adjacent to the landslide zone, which is only externally loaded by lateral soil

eavy pipelinenalytical modelubmarine landslideipe–soil interaction

resistance; the third one is further away from the landslide, which is loaded by linearly increasing lateralsoil resistance; the last segment is uniquely loaded by axial resistance. The governing equations of thefour segments are expressed according to their different loading conditions, and an equation system isestablished on the basis of boundary conditions and continuity conditions. The final solution is obtainedthrough a numerical method. The model proves to be simple and reliable. The parametric study revealsthat the behaviors of heavy pipelines are different from those of the surface light ones.

. Introduction

Submarine landslide and debris flow are frequently triggered byurricanes and earthquakes, which are great risks to offshore struc-ures, especially to pipelines laid on the seabed surface. Muldernd Alexander [1] investigated the physical characters of landslide,ebris flow and other density flows, and provide a clear classifica-ion of subaqueous density flows and their deposits. Canals et al.2] revealed the submarine landslide dynamics and the impactshrough a case study. Deepwater pipelines are at greater risk fromandslide and debris flow impact than other subsea structures, for

ainly two reasons: their length which increases exposure to land-lide hazard, and their low structural resistance [3].

Zakeri [4] provided a review of the state-of-the-art on the dragorces on submarine pipeline by landslide or debris flow, whichiscussed both the available geotechnique and fluid dynamicsethods. As the pipeline is pushed laterally by the drag force of

he landslide or debris flow, the large-amplitude lateral responseepends on the ratio of pipeline weight to the seabed strength. For/suD < 1.5, where w is the pipeline submerged self-weight, su is

he undrained shear strength of the sliding soil mass, D is the outeriameter of the pipeline, the pipeline is defined as light pipe which

∗ Corresponding author. Tel.: +86 571 88208678; fax: +86 571 88206240.E-mail address: wlzzju@163.com (L. Wang).

141-1187/$ – see front matter © 2011 Elsevier Ltd. All rights reserved.oi:10.1016/j.apor.2011.12.002

© 2011 Elsevier Ltd. All rights reserved.

is investigated in a separate paper [5]; for w/suD > 2.5, the pipelineis defined as heavy pipe.

There have been few previous studies on pipe–soil interaction ofheavy pipelines exposed to large-amplitude lateral movement. Themajor difference between the light pipe and heavy pipe is that thelight pipe has a relatively smaller initial penetration depth thanthe heavy pipe, and the light pipe will rise to the seabed surfacewhen exposed to large-amplitude lateral movement which makesthe residual soil resistance remains almost constant [6,7]. In starkcontrast, the heavy pipe will move downwards when moving lat-erally, thus the downward movement, coupled with the growthof the soil berm ahead of the pipe makes the residual resistancerises steadily. The influence of different moving path of light andheavy pipes has been studied by Hodder and Cassidy [8] throughdisplacement-controlled tests and theoretical analysis. They havealso found the steady increase of soil resistance for a pipeline mov-ing laterally with an angle 22.5◦ to the horizontal, and the residualresistance to a pipe moving horizontally is a constant. This workaims to investigate the influence of landslide to heavy pipeline andreveal the difference between light and heavy pipelines.

2. Loading conditions

The movement of the landslide or debris flow is accompaniedwith scour, which makes the embedded pipelines exposed to land-slides [9]. The loading condition of the embedded heavy pipeline isshown in Fig. 1, where q is the landslide drag force which is assumed

106 F. Yuan et al. / Applied Ocean Research 35 (2012) 105– 114

p

wt

slope

wt

w

pipe

wn

scour landsli de

φ

Y

XO

P1

P2

x1 x2

P0

P3

ffq

Fig. 1. Sketch of

p

yO

p=k1y

p=0. 1Dk1+k2(y-0.1D)p0.1

psoiprs

tafta

tltsmiisdsotfsmw

cde

3

ti

2

+ e−˛x[c3 cos(ˇx) + c4 sin(ˇx)]

(2)

OX

P3 fP2

P0 P1

x3x1 x2

Y

x4

P4

0.1D

Fig. 2. Load–displacement relationship.

erpendicular to the pipeline, p is the passive soil resistance, ϕ is thelop angle, wt and wn are the tangential and normal componentsf the pipeline submerged self-weight w to the slope direction, fs the axial soil resistance to the pipeline. As shown in Fig. 1, theipeline is assumed to be geometrically symmetrical and symmet-ically loaded with Y-axis as the symmetry axis in the coordinateystem XOY.

The embedment depth of the heavy pipelines is typically oneo two diameters, which makes the pipelines exposed to landslidefter scour occurs at the back of the pipeline. Therefore, the dragorce of the landslide to embedded heavy pipelines is the same ashat to surface light pipelines. This work simplifies the drag forces a uniformly distributed force q in the landslide zone.

The passive soil resistance is one of the distinguishing charac-eristics to the embedded pipelines. When the pipeline is movingaterally, the pipeline generally moves downwards after the ini-ial break-out resistance is mobilized which leads to larger passiveoil resistance. A typical bilinear relationship between the displace-ent y and the passive resistance p to a heavy pipeline is shown

n Fig. 2 [8]. For small displacement, the passive soil resistancencreases with the displacement with the rate of k1; and for largeroil displacement, the increasing rate largely decreases to k2. Theemarcation point between small and large displacement is casepecific and y = 0.1D is adopted in this work [10,11], where D is theuter diameter of the pipeline. The corresponding lateral soil resis-ance for y = 0.1D is donated as p0.1 which is the transition resistanceor the case of heavy pipeline. Therefore, the passive resistance formall pipeline displacement is p = k1y, for large pipeline displace-ent is p = 0.1k1D + k2(y − 0.1D), where k1 and k2 are closely relatedith the soil and pipeline properties.

In the axial direction, the resistance depends on the boundaryondition. This work simplifies the axial resistance as a uniformlyistributed constant force f. The different boundary conditions arexpressed through different axial resistances f.

. Governing equations

As both the pipeline and the loads are symmetrical, one half ofhe pipeline is considered in this work. Similar to the light pipelinen a separate work [5], the heavy pipeline in this work is divided

the model.

into four segments according to their different loading conditionsas shown in Fig. 3,

(1) Segment One locates at the extent from P0 to P1 which is thelandslide zone. The landslide drags the pipeline laterally, andmeanwhile the pipeline will move downwards, which is themajor difference between heavy and light pipelines in landslide.The axial tension at this segment is very large, so the axial soilfriction is ignored for simplicity.

(2) Segment Two lies between P1 and P2, which is uniquely loadedby lateral soil resistance. The displacement of the segment isgreater than 0.1D, so the lateral soil resistance increases linearlywith the transverse displacement. The axial soil resistance isalso ignored at this segment.

(3) Segment Three is also loaded by lateral soil resistance, but thetransverse displacement of the pipeline is smaller than thatof Segment Two. The displacement in the Y-axis direction isbetween 0.1D and �1 which is a small quantity, starting fromP2 and ends at P3.

(4) Segment Four locates at the right of P3, where the lateraldisplacement of the pipeline is smaller than the adopted �1.Therefore, the lateral resistance to the pipeline is very small,and the pipeline is assumed to be uniquely loaded by axial soilresistance.

3.1. Segment One

By taking the force equilibrium in the Y-axis direction, the gov-erning equation of the pipeline from P0 to P1 can be obtained:

EIy′′ ′′

1(x) − Ty′′1(x) + k2y1 = wt + q + 0.1Dk2 − 0.1Dk1 (0 ≤ x ≤ x1)

(1)

where y1(x) is the pipeline configuration, x1 is the x-coordinate ofP1, E is the elastic modulus, I is the inertia moment, T is the unknownconstant axial tension. The solution can be obtained:

y1(x) = q + wt + 0.1Dk2 − 0.1Dk1

k+ e˛x[c1 cos(ˇx) + c2 sin(ˇx)]

Segmen t One

Segment Two

Segmen t Three

Segmen t Four

Fig. 3. Scheme of the pipeline.

an Res

wb

˛

ˇ

s

2

T

w

M

ε

3

rb

E

wP

y

w

3

tdT

E

y

w

�

ı

l

EA 2fEA

F. Yuan et al. / Applied Oce

here 0 ≤ x ≤ x1, c1, c2, c3 and c4 are the unknown coefficients toe determined later, and

= 12

√2

√k2

EI+ T

EI(3.1)

= 12

√2

√k2

EI− T

EI(3.2)

As can be seen in Eq. (3.2), the following inequality should beatisfied:√

k2

EI− T

EI≥ 0 (4)

Therefore, the upper bound of the tension T can be obtained:

≤ 2√

k2EI (5)

hich should be checked at the end of calculationThe bending moment can be written as:

= −EIy′ ′1(x) (6)

Then, the strain of pipeline can be obtained:

= T

EA+

D∣∣M∣∣

2EI(7)

.2. Segment Two

This segment is externally loaded by the constant lateral soilesistance p, extending from P1 to P2, The governing equation cane written as:

Iy′′ ′′2(x) − Ty′ ′

2(x) + k2y2 = wt + 0.1Dk2 − 0.1Dk1 (x1 ≤ x ≤ x2)

(8)

here y2(x) is the pipeline configuration, x2 is the x-coordinate of2. Then, the solution can be obtained:

2(x) = wt + 0.1Dk2 − 0.1Dk1

k2+ e˛x[c5 cos(ˇx) + c6 sin(ˇx)]

+ e−˛x[c7 cos(ˇx) + c8 sin(ˇx)] (9)

here x1 ≤ x ≤ x2, c5, c6, c7 and c8 are the unknown coefficients.

.3. Segment Three

The pipeline displacement at this segment is less than 0.1D, sohe soil resistance at this segment is proportional to the pipelineisplacement, which is different from Segment One and Segmentwo. Thus, we have a different governing equation:

Iy′′ ′′3(x) − Ty′ ′

3(x) + k1y3(x) = wt (x2 ≤ x) (10)

The solution of Eq. (10) can be obtained:

3(x) = wt

k1+ e�x[c9 cos(ıx) + c10 sin(ıx)] + e−�x[c11 cos(ıx)

+ c12 sin(ıx)](x2 ≤ x) (11)

here c9, c10, c11 and c12 are unknown coefficients and

= 12

√2

√k1

EI+ T

EI(12.1)

1

√ √k T

=2

2 1

EI−

EI(12.2)

Considering that x3 is large at the location of P3, e�x is veryarge in the following calculation, therefore, the two coefficients

earch 35 (2012) 105– 114 107

c9 and c10 should be very small. To ensure high accuracy, a small �1should be chosen to make x3 large. In this work, c9 and c10 are setequal to zero. This permits remarkable simplification in mathemat-ical formulation, still providing reliable results, and the accuracy isdemonstrated through comparison with a finite element code inSection 5 of this paper.

By virtue of Eq. (12.2), the equation must satisfy:

T ≤ 2√

k1EI (13)

In comparison with Eq. (5), the upper bound of the axial tensionT should be 2

√k2EI as k2 is generally smaller than k1.

3.4. Segment Four

As the lateral displacement of the pipeline is very small over thissegment, the lateral soil resistance is very small too. The pipeline istherefore assumed to be only loaded externally by axial soil resis-tance.

4. Solution procedure

An set of 11 nonlinear equations and 12 unknowns c1, c2, c3,c4, c5, c6, c7, c8, c11, c12, x2 and T is established by considering thecontinuity of displacement, inclination slope, bending moment andshear at P0, P1 and P2:

P0 :

{y′

1(0) = 0

y′ ′ ′1(0) = 0

(14.1-2)

P1 :

⎧⎪⎪⎨⎪⎪⎩

y1(x1) = y2(x1)

y′1(x1) = y′

2(x1)

y′′1(x1) = y′′

2(x1)

y′′′1 (x1) = y′′′

2 (x1)

(15.1-4)

P2 :

⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩

y2(x2) = 0.1D

y3(x2) = 0.1Dy′

2(x2) = y′3(x2)

y′′2(x2) = y′′

3(x2)

y′′′2 (x2) = y′′′

3 (x2)

(16.1-5)

An extra equation is obtained by equating the increase ofpipeline length of the deformed shape �l1 with the pipeline exten-sion due to tension �l2. The extension of the pipeline �l1 can beobtained by integrating along the pipeline:

�l1 =∫ x1

0

√1 + y

′21 (x)dx +

∫ x2

x1

√1 + y

′22 (x)dx

+∫ x3

x2

√1 + y

′23 (x)dx − x3 (17)

The pipeline �l2 under the axial tension can be obtained:

�l2 = T

EAx3 + T2

2fEA(18)

where x3 is the location where the pipeline displacement is verysmall shown in Fig. 3, and �1 = 1 × 10−5 m is adopted in this workto guarantee high accuracy.

The extra equation is obtained by equating �l1 with �l2:

Tx3 + T2

=∫ x1 √

1 + y′21(x)dx +

∫ x2 √1 + y′2

2(x)dx

0 x1

+∫ x3

x2

√1 + y′2

3(x)dx − x3 (19)

108 F. Yuan et al. / Applied Ocean Research 35 (2012) 105– 114

Knowns: p, q, EI, wt and T

Eq. (14 .1- 2) Eq. (15 .1- 4) Eq. (16 .1- 4)

Eq. (19)

|f − f0|<η3

T, x , yσ, ε, l2

Inpu t

Outpu t

Eq. (16.5)

Solutio n

c1, c2, c3, c4, c5, c6, c7, c8, c11, c12

Inpu t

''' '''2 2 3 2( ) ( )y x y x− <η1

NY

x2=x2+dx2

N Y

T =T+dT

Inpu t

(sTT

5

tFwpollcu

0 50 10 0 15 0 20 0 25 0 300-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

P1P3

P2

P3

P2

P1

M (M

Nm

)

ligh t pipeline hea vy pipel ine ABAQ US

li ght pipeline heavy pipeli ne ABAQ US

Fig. 4. Calculation scheme.

The complete equation system constituted by Eqs. (14.1-2),15.1-4), (16.1-5) and (19) is too complicated to obtain an explicitolution, so a numerical method is adopted to find the solution.he method is similar to that used in the work of Yuan et al. [5].he detailed information of this method is illustrated in Fig. 4.

. Example and comparison

A comparison is made to investigate the difference betweenhe landslide influence on light and heavy pipelines, as shown inigs. 5 and 6. For heavy pipeline, the solution is presented in thisork, and for light pipeline, we refer to a separate work [5]. Thearameters are listed in Table 1, where d is the inner diameterf the pipeline, ϕ is assumed to be zero for simplicity, and the

ateral soil resistance to heavy pipelines is different from that toight pipelines. The soil resistance to a light pipeline remains aonstant after it reaches p0.1, while, to heavy pipeline, it contin-ously increases after reaching p0.1. The increasing rate k2 is listed

0 50 10 0 150 20 0 250 30 03.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0

-0.5

y (m

)

x (m)

P1 P3P2

P3P2

P1

li ght pipeli ne he avy pipe line ABAQU S

light pipeline hea vy pipeline ABAQU S

Fig. 5. Comparison of pipeline configurations.

x (m)

Fig. 6. Comparison of bending moment distributions.

in Table 1 and k1 can be easily obtained by dividing the p0.1 by0.1D. The finite element code ABAQUS, Ver. 6.7-1, is used to provethe accuracy of the present model. And the finite element modelis established by referring to the work of Randolph et al. [12] andYuan et al. [5]. The pipeline configurations and bending momentdistributions obtained by ABAQUS and the present model coin-cides well, as shown in Figs. 5 and 6. Fig. 5 shows that the peakdisplacement and length of the light pipeline moving laterally arefar larger than that of the heavy pipeline, which proves that theheavy pipeline has a better stability in landslide. In Fig. 6, boththe peak positive and negative bending moments of the heavypipeline are smaller than those of the light pipeline. Besides, theaxial tension for light pipeline 5.303 MN, which is far larger thanthat for heavy pipeline 1.837 MN. Therefore, the combined effect ofaxial tension of bending moment results in different peak pipelinestrain εp, with εp = 0.079 (%) for light pipelines and εp = 0.034(%) for heavy pipelines. Though greater pipeline weight is notbeneficial for pipeline safety during installation process in deep-water, the heavy pipelines are much safer than light pipelines inlandslides.

6. Parametric study

The length scale shown in the parametric study is the same asthat in another paper [5], which is 5 times of the landslide width,to enable direct comparison of the two papers.

6.1. Effect of the landslide drag force

The drag force of the landslide is case specific, and thiswork adopts five different drag forces to investigate its effect onpipelines: q = 5.0 kN/m, 6.0 kN/m, 7.0 kN/m, 8.0 kN/m, and 9.0 kN/m.The pipeline displacement increases with the increase of the land-slide drag force, especially at the landslide zone, as shown in Fig. 7.The pipeline within the landslide zone is greatly influenced bythe landslide. Table 2 shows that the peak displacement growsfrom approximately 0.27 m to about 0.65 m with the drag forceincreasing from 5.0 kN/m to 9.0 kN/m, and the position of the peakdisplacement remains at the left of Segment One as Fig. 7 shows.Beyond the landslide zone, the increase of pipeline displacement isvery small.

Fig. 8 shows that the bending strain is very small at P0, whichis followed by an increase at Segment One. After reaching the peakat Segment One, the bending strain sharply drops and then climbsto the peak at Segment Two before gradually increasing back to

F. Yuan et al. / Applied Ocean Research 35 (2012) 105– 114 109

Table 1Summary of parameters.

q (kN/m) p0.1 (kN/m) D (m) d (m) x1 (m) k2 (kN/m2) f0 (kN/m) ϕ (◦) E (GPa)

7.0 3.0 0.6 0.55 60 1.0 0.5 0 210

Table 2Results summary for different drag forces.

q (kN/m) Mp (MNm) T (MN) yp (m) �p (MPa) εp (%) xε (m) x2 (m) x3 (m)

5.0 −0.123 1.279 0.27 41.05 0.023 68.2 62.5 82.66.0 −0.162 1.581 0.36 61.07 0.029 69.3 67.5 84.77.0 −0.194 1.837 0.46 71.92 0.034 70.5 70.7 86.98.0 −0.221 2.062 0.56 81.25 0.039 71.6 73.4 89.19.0 −0.244 2.266 0.65 89.46 0.043 72.4 75.8 91.2

0 1 2 3 4 5

1.0

0.8

0.6

0.4

0.2

0.0q=9 .0kN/mq=8 .0kN/mq=7 .0kN/mq=6 .0kN/mq=5 .0kN/m

Nor

mal

ized

late

ral d

efle

ctio

n y/

D

Normalized ho rizontal distance x/x1

zdcadiso

0 1 2 3 4 50.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

Nor malized hor izontal dis tance x/x1

q=9 .0kN/m q=8.0kN/mq=7 .0kN/m

q=6.0kN/mq=5 .0kN/m

com

bine

d pi

pelin

e st

rain

(

%)

ε

Fig. 7. Pipeline configurations for different drag forces.

ero. The magnitudes of peak bending strain increases with therag force. Considering that the axial tension from P0 to P3 keepsonstant, the location of the peak strain xε is therefore the sames the peak bending strain, as shown in Figs. 8 and 9. The strainistribution under the combined effect of axial tension and bend-

ng moment is illustrated in Fig. 9. There are two apexes of thetrain curve: the smaller one belongs to Segment One and the largerne locates at the neighborhood of Segment Two. The peak strain

0 1 2 3 4 5

0.00 0

0.00 5

0.01 0

0.01 5

0.02 0

Nor malized hor izonta l dist ance x/x1

q=9.0kN/mq=8.0kN/mq=7.0kN/mq=6.0kN/mq=5.0kN/m

ben

ding

stra

in

(%

)ε b

Fig. 8. Bending strain distributions for different landslide drag forces.

Fig. 9. Strain distributions for different landslide drag forces.

increases quickly with the drag force. Meanwhile, the location ofthe peak strain slightly moves further away from P0.

As the drag force increases, both the contributions from the axialtension and bending to the peak strain exhibit an increasing trend,with the contribution from the axial tension larger. As shown in

Fig. 10, the combined effect of the axial tension and bending leadsto a quick increase of the combined strain.

1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

0.01 0

0.01 5

0.02 0

0.02 5

0.03 0

0.03 5

0.04 0

0.04 5 strain by M strain by T co mbined st rain

peak

pip

elin

e st

rain

(%)

Nor malized dra g forc e q/ p0.1

ε p

Fig. 10. Variation of peak strain for different landslide drag forces.

110 F. Yuan et al. / Applied Ocean Research 35 (2012) 105– 114

Table 3Results summary for different slide widths.

x1 (m) Mp (MNm) T (MN) yp (m) �p (MPa) εp (%) xε (m) x2 (m) x3 (m)

10 0.241 0.681 0.11 53.73 0.026 0.0 15.2 36.020 0.273 1.309 0.27 72.89 0.035 0.0 30.2 46.130 0.200 1.610 0.37 67.83 0.032 0.0 40.8 56.440 −0.197 1.753 0.42 70.46 0.034 50.6 50.8 66.760 −0.194 1.837 0.46 71.92 0.034 69.3 70.7 86.9

71.871.571.2

6

e4si6wwlkl

i3itdnc

2aabaiaagwwa

0 10 0 20 0 30 0 40 0 500

0.00 0

0.00 5

0.01 0

0.01 5

0.02 0

0.02 5

Nor maliz ed hori zontal distanc e x/D

x1=40mx1=30mx1=20mx1=10m

x1=120mx1=100mx1=80mx1=60m

Ben

ding

stra

in

(%

)ε b

80 −0.194 1.833 0.46

100 −0.194 1.818 0.46

120 −0.194 1.806 0.46

.2. Effect of the slide width

In order to investigate the influence of the heavy pipelines,ight slide widths are selected in this work: x1 = 10 m, 20 m, 30 m,0 m, 60 m, 80 m, 100 m, 120 m. It is obvious in Fig. 11 that largerlide width makes longer pipeline move laterally. The slide widthncreases the peak displacement with x1 increasing from 10 m to0 m, but it has very little influence on the peak displacementhen x1 exceeds 60 m. In contrast, Yuan et al. [5] pointed out thatider landslide results in greater pipeline peak displacement for

ight pipelines. Therefore, the heavy pipelines have better station-eeping ability than the light pipelines when exposed to widerandslide.

Fig. 12 shows that, for x1 = 10 m, 20 m and 30 m, the peak bend-ng strain appears at P0 of Segment One. However, when x1 exceeds0 m, the bending strain increases from a low at P0 before reach-

ng a peak at Segment One. Then it drops sharply before reachinghe peak at the neighborhood of P2, which is followed by a steadyecrease. The location of the peak bending strain locates at theeighborhood P2 for x1 > 30 m, which is also the location of the peakombined strain, as shown in Fig. 12 and Table 3.

Special attention should be paid to situations when x1 = 10 m and0 m. The peak bending strains are obviously larger for x1 = 10 mnd 20 m, as shown in Fig. 12. However, Fig. 13 shows that thexial tension due to landslide is so small for x1 = 10 m that the com-ined strain is the smallest. In contrast, when x1 = 20 m, which isbout 33D, although the tension is also small, the combined strains the largest. For greater slide widths, the peak combined strainsre smaller than that for x1 = 20 m, and they do not change much,s Figs. 13 and 14 show. Therefore, greater landslide width is not a

reater risk to heavy pipeline, and it only shifts the position of theeakest point further away from P0. In contrast, for smaller slideidth of x1 = 20 m, the peak strain, which is slightly higher, locates

t P0.

0 10 0 200 300 40 0 50 0

0.8

0.6

0.4

0.2

0.0

x1=120mx1=100mx1=80mx1=60mx1=40mx1=30mx1=20mx1=10m

Nor

mal

ized

late

ral d

efle

ctio

n y/

D

Normalized hor izontal dis tance x /D

Fig. 11. Pipeline configurations for different slide widths.

1 0.034 90.5 90.7 106.92 0.034 110.5 110.7 126.98 0.034 130.5 130.7 146.8

As shown in Fig. 14, the peak bending strain is obviously largerthan strain due to axial tension for very small slide widths. Thecontribution of bending strain reaches its peak for x1 = 20 m, whichresults in the peak combined strain. With the increase of the slidewidth, the peak strain caused by tension gradually increases and itsurpasses that resulted from bending at about x1/D = 43. For widerlandslide with x1 larger than 40 m, which is approximately 67D,the strains causes by tension and bending, as well as the combinedstrain become stable, keeping almost constant.

Fig. 12. Bending strain distributions for different slide widths.

0 100 20 0 300 400 5000.00 5

0.01 0

0.01 5

0.02 0

0.02 5

0.03 0

0.03 5

Normalized horizont al dist ance x/D

x1=120 mx1=100 mx1=80 mx1=60 mx1=40 mx1=30 mx1=20 mx1=10 m

Com

bine

d pi

pelin

e st

rain

(

%)

ε

Fig. 13. Strain distributions for different slide widths.

F. Yuan et al. / Applied Ocean Research 35 (2012) 105– 114 111

20 40 60 80 100 12 0 14 0 160 18 0 20 00.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

Nor malized horizon tal distance x1/D

strain by M strain by T co mbined stra in

Peak

pip

elin

e st

rain

(%)

ε p

6

fatwrerkva

adwlfivTb

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

y/D=0.1 (y=0 .06 m)

Nomalized latera l deflection y/D

Nor

mal

ized

pas

sive

resi

stan

ce p

/q

k2=2.5 kN/mk2=2.0 kN/mk2=1.5 kN/mk2=1.0 kN/mk2=0.5 kN/m

Fig. 16. Passive soil resistance for different k2.

0 50 100 150 200 25 0 3000.6

0.5

0.4

0.3

0.2

0.1

0.0p0.1=6.0kN/mp0.1=5.0kN/mp0.1=4.0kN/mp0.1=3.0kN/mp0.1=2.0kN/m

Nor

mal

ized

late

ral d

efle

ctio

n y/

D

Normalized ho rizontal distance x/x

Fig. 14. Variation of peak strain for different slide widths.

.3. Effect of the lateral soil resistance

The lateral soil resistance for heavy pipelines is differentrom that for light pipelines, as discussed in Section 2. Therere two key factors that determine the lateral soil resistance:he soil resistance p0.1 at y = 0.1D and the increasing rate k2hen y > 0.1D. In order to investigate the influence of lateral soil

esistance, this work adopts five different p0.1 and five differ-nt increasing rate k2 to investigate the effect of the passive soilesistance: p0.1 = 2 kN/m, 3 kN/m, 4 kN/m, 5 kN/m and 6 kN/m; and2 = 0.5 kN/m2, 1.0 kN/m2, 1.5 kN/m2, 2.0 kN/m2 and 2.5 kN/m2. Theariations of soil resistance with the lateral pipeline displacementre shown in Figs. 15 and 16.

As can be seen from Figs. 17 and 18, the impacts of p0.1nd k2 on the pipeline configuration are similar. The pipelineisplacement becomes smaller with p0.1 and k2 getting larger,ith the smallest displacement occurs for p0.1 = 2 kN/m and the

argest for p0.1 = 6 kN/m with the increasing p0.1, and the largestor k2 = 0.5 kN/m2 and the smallest for k2 = 3.0 kN/m2 with k2 ris-ng. The location of the peak displacement remains at P0 with theariation of the lateral soil resistance. In addition, as indicated by

able 4, both the increases of p0.1 and k2 shorten the zone exertedy passive soil resistance.

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.0

0.4

0.8

1.2

1.6

2.0

y/D=0 .1 ( y=0.06 m)

Nor

mal

ized

pas

sive

resi

stan

ce p

/q

Nomalized latera l de flec tio n y/D

p0.1=6.0 kNp0.1=5.0 kNp0.1=4.0 kNp0.1=3.0 kN p0.1=2.0 kN

Fig. 15. Passive soil resistance for different p0.1.

1

Fig. 17. Pipeline configurations for different p0.1.

As shown in Figs. 19 and 20, the influences of p0.1 and k2 on

bending strain distributions are slightly different, especially at theneighborhood of P0. For greater p0.1, the increase of bending strainis very small at P0, while, for greater k2, large bending strain appears

0 1 2 3 4 5

1.2

1.0

0.8

0.6

0.4

0.2

0.0

Nor

mal

ized

late

ral d

efle

ctio

n y/

D

Normalized horizon tal dis tanc e x /x1

k2=3.0kN /m2

k2=2.0kN /m2

k2=1.5kN /m2

k2=1.0kN /m2

k2=0.5kN /m2

Fig. 18. Pipeline configurations for different k2.

112 F. Yuan et al. / Applied Ocean Research 35 (2012) 105– 114

Table 4Results summary for different passive soil resistances.

p0.1 (kN/m) k2 (kN/m2) Mp (MNm) T (MN) yp (m) �p (MPa) εp (%) xε (m) x2 (m) x3 (m)

2.0 1.0 −0.187 2.06 0.56 75.83 0.036 73.3 76.7 95.03.0 1.0 −0.194 1.84 0.46 71.92 0.034 69.3 70.7 86.94.0 1.0 −0.179 1.58 0.36 63.91 0.030 67.9 65.8 81.75.0 1.0 −0.145 1.28 0.27 51.73 0.025 66.4 61.1 78.36.0 1.0 −0.099 0.90 0.17 35.94 0.017 66.4 55.8 76.83.0 0.5 −0.245 2.51 0.78 94.94 0.045 73.1 77.3 93.33.0 1.5 −0.162 1.49 0.34 59.20 0.028 69.6 67.9 84.93.0 2.0 −0.142 1.28 0.27 51.15 0.024 69.4 66.2 84.03.0 3.0 −0.127 1.13 0.23 45.621 0.022 69.5 65.0 83.5

0 1 2 3 4 5

0.00 0

0.00 2

0.00 4

0.00 6

0.00 8

0.01 0

0.01 2

0.01 4

0.01 6p0.1=6.0kN/mp0.1=5.0kN/mp0.1=4.0kN/mp0.1=3.0kN/mp0.1=2.0kN/m

Nor

mal

ized

ben

ding

stra

in

(%

)ε b

atpatf

ttpft

0 1 2 3 4 50.00 5

0.01 0

0.01 5

0.02 0

0.02 5

0.03 0

0.03 5

Normalized horizonta l dist ance x/x

p0.1=6.0k N/mp0.1=5.0k N/mp0.1=4.0k N/mp0.1=3.0k N/mp0.1=2.0k N/m

Com

bine

d pi

pelin

e st

rain

(%)

ε

Nor maliz ed hori zontal distanc e x/x1

Fig. 19. Bending strain distributions for different p0.1.

t P0. The peak bending strain always appears at Segment Two withhe variation of lateral soil resistance. As listed in Table 4, larger0.1 and k2 decrease the magnitude of the peak bending moment,s well as the axial tension. Therefore, the combined effect of axialension and bending moment results in smaller peak pipeline strainor greater lateral soil resistance, as shown in Figs. 21 and 22.

The distributions of the pipeline strain for different soil resis-ances are overall similar, as shown in Figs. 21 and 22. However,

he variations of p0.1 and k2 have slightly different influence on theipeline strain distribution. Two apexes appear on the strain curveor all soil resistances, with the value of the first apex lower andhe second one higher. The difference between the values of the

0 1 2 3 4 5

0.00 0

0.00 5

0.01 0

0.01 5

0.02 0

Nor

mal

ized

ben

ding

stra

in

(%

)

Nor malized hori zontal dis tanc e x /x1

k2=3.0kN/m2

k2=2.0kN/m2

k2=1.5kN/m2

k2=1.0kN/m2

k2=0.5kN/m2

ε b

Fig. 20. Pipeline configurations for different k2.

1

Fig. 21. Pipeline strain distributions for different p0.1.

two apexes drops quickly with the increase of k2. However, withthe variation of p0.1, the variation of the difference is not obvious.Therefore, there would be two weak points that should be paidmuch attention for heavy pipelines laid on soil with large k2.

Although both the increases of p0.1 and k2 decrease thepeak bending strain, but obvious difference can be seen fromFigs. 23 and 24 for both tension and the combined peak strain. Whenp0.1 is relatively small, the combined peak strain drops slowly. Asp0.1 increases, the decreasing rate of εp gradually rises, reaching the

peak at p0.1/q = 2. In contrast, with the growth of k2, the decreasingrate of εp is larger for smaller k2, and it decreases to the minimumat k2/k1 = 0.05.

0 1 2 3 4 50.01 0

0.01 5

0.02 0

0.02 5

0.03 0

0.03 5

0.04 0

0.04 5

0.05 0

Normalized hori zontal dis tanc e x /x1

k2=3.0kN/m2

k2=2.0kN/m2

k2=1.5kN/m2

k2=1.0kN/m2

k2=0.5kN/m2

Com

bine

d pi

pelin

e st

rain

(%)

ε

Fig. 22. Strain distributions for different k2.

F. Yuan et al. / Applied Ocean Research 35 (2012) 105– 114 113

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040 strain by M strain by T co mbined st rain

Peak

pip

elin

e st

rain

(%)

Normalized soi l resi stance p0.1/q

ε p

Fig. 23. Variation of peak strain for different p0.1.

0.01 0.02 0.03 0.04 0.050.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045 strain by M strain by T combined strain

Peak

pip

elin

e st

rain

(%)

Nor malized inc reas ing rate k2/k1

ε p

6

tfi1tmswlaaoof

asstasd

0 1 2 3 4 5

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

Nor

mal

ized

late

ral d

efle

ctio

n y/

D

Nor malized hor izon tal dis tanc e x/x1

f=2.5kN /mf=1.5kN /mf=1.0kN /mf=0.5kN /mf=0.1kN /m

Fig. 25. Pipeline configurations for different axial resistances.

0 1 2 3 4 5

0.00 0

0.00 2

0.00 4

0.00 6

0.00 8

0.01 0

0.01 2

0.01 4

0.01 6

0.01 8

Normaliz ed hor izontal distanc e x/x1

f=2.5k N/mf=1.5k N/mf=1.0k N/mf=0.5k N/mf=0.1k N/m

Nor

mal

ized

ben

ding

stra

in

(

%)

ε b

Fig. 26. Bending strain distributions for different axial resistances.

0 1 2 3 4 5

0.01

0.02

0.03

0.04

0.05

Normalized hor izont al dis tanc e x/x1

Com

bine

d pi

pelin

e st

rain

(%)

f=2.5kN/mf=1.5kN/mf=1.0kN/mf=0.5kN/mf=0.1kN/mε

Fig. 24. Variation of peak strain for different k2.

.4. Effect of axial resistance

The axial resistance to a pipeline is different in different situa-ions. In order to investigate the influence of boundary condition,ve different axial resistances are selected: f = 0.1 kN/m, 0.5 kN/m,.0 kN/m, 1.5 kN/m and 2.5 kN/m. As shown in Fig. 25, it is obvioushat the influence of the axial tension on pipeline displacement

ainly lies in the localized zone near P0. The peak displacementlightly decreases with the increase of the axial resistance. Mean-hile, the impact of the axial resistance on the bending strain is

ocalized at two neighborhoods of the two apexes at Segment Onend Segment Two, as shown in Fig. 26. The peak bending strainlways appears at Segment Two, and it deceases with the increasef axial resistance. In stark contrast, the influence of axial resistancen the axial tension is opposite, the axial tension increases quicklyrom 1.75 MN for f = 0.1 kN/m to 3.82 MN for f = 2.5 kN/m.

The variations trend of the bending strain and the axial tensionre opposite, so their combined effect should be investigated. Ashown in Fig. 27, the variation trend of combined strain is oppo-ite to that of the bending strain. As shown in Fig. 28 and Table 5,he axial tension is the dominating factor, and the increase of the

xial tension contributes to the growth of the pipeline stress andtrain. For f = 0.1 kN/m, the pipeline strain is merely 0.026 (%), and itoubled for f = 2.5 kN/m. The position of the peak stress and strain

Fig. 27. Strain distributions for different axial resistances.

114 F. Yuan et al. / Applied Ocean Research 35 (2012) 105– 114

Table 5Results summary for different axial resistances.

f (kN/m) Mp (MNm) T (MN) yp (m) �p (MPa) εp (%) xε (m) x2 (m) x3 (m)

0.1 −0.217 1.75 0.48 53.57 0.026 70.2 69.9 83.20.5 −0.194 1.84 0.46 71.92 0.034 69.3 70.7 86.91 −0.181 2.53 0.45 81.5 −0.172 3.05 0.44 92.5 −0.160 3.82 0.43 11

0.0 0.2 0.4 0.6 0.80.00 5

0.01 0

0.01 5

0.02 0

0.02 5

0.03 0

0.03 5

0.04 0

0.04 5

0.05 0

0.05 5 strain by M strain by T co mbined stra in

Peak

pip

elin

e st

rain

(%)

ε p

rr

7

gwtp

(

(

[

f /p0.1(kN/m)

Fig. 28. Variation of peak strain for different axial resistances.

emain at the neighborhood of P2 with the variation of the axial soilesistance, as Table 5 shows.

. Conclusions

The analytical model presented in this work is capable of investi-ating the behavior of heavy pipelines in landslide. The comparisonith the finite element code ABAQUS has proved the accuracy of

he model, and some important conclusions are obtained througharametric study.

1) The heavy pipeline has better stability and safety than the lightpipeline in landslide. The pipeline displacement and the peakpipeline strain of the heavy pipeline are smaller than those ofthe light pipeline in the same landslide. We suggest that theself-weight of pipelines should be increased to reduce dam-age in landslides. Concrete coating is an economical way ofincreasing the pipeline self-weight. And increasing the pipelinethickness is an alternative when concrete coating is not feasible.

2) Larger landslide width does not mean a greater risk to pipelinesafety for heavy pipelines. The peak strain appears for a nar-row slide width, which is approximately 33D for the pipelinediscussed in this work. For slide width greater than about 67D,the pipeline peak displacement and peak strain become stable,

and greater slide width just makes longer pipeline deviate fromits original routine and make the location of the weakest pointfurther away from P0 for a heavy pipeline. Therefore, in orderto avoid the encounter of the most unfavorable condition, the

[

[

5.27 0.041 70.7 71.3 90.05.22 0.045 70.8 71.7 92.40.39 0.053 71.0 72.2 96.8

scale of the pipeline should be designed based on geotechnicalsite investigation.

(3) The increase in axial soil resistance induces larger peak pipelinestrain, which is a risk to pipeline safety, especially when land-slide occurs near a fixed pipeline end. It is suggested that fixedmanifolds or wellheads should be located further away fromregions where landslides are likely to occur. If it is necessaryto fix the pipeline end near a landside zone, the axial directionof the pipeline should at least be adjusted to reduce the dragforce.

(4) The bending strain is an important component of the com-bined strain for different drag forces, slide widths and lateralsoil resistances, except for large axial resistances. This is differ-ent from traditional assumptions that the bending resistance isvery small or even can be ignored.

Acknowledgments

The authors would like to acknowledge the support of the GrantNo. 51079128 from the National Natural Science Foundation ofChina, the Grant No. R1100093 from the Excellent Youth Foun-dation of Zhejiang Scientific Committee and Zhejiang InnovationProgram for Graduates.

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