Research Article Uplifting Behavior of Shallow Buried Pipe ...downloads.hindawi.com/journals/tswj/2014/838546.pdf · Model Pipe. e model pipes are made of aluminum tube, with a density

Research ArticleUplifting Behavior of Shallow Buried Pipe in Liquefiable Soil byDynamic Centrifuge Test

Bo Huang1 Jingwen Liu1 Peng Lin2 and Daosheng Ling1

1 MOE Key Laboratory of Soft Soils and Geoenvironmental Engineering Department of Civil EngineeringZhejiang University Hangzhou 310058 China

2 State Key Laboratory of Hydroscience and Engineering Tsinghua University Beijing 100084 China

Correspondence should be addressed to Daosheng Ling dslingzjueducn

Received 28 March 2014 Accepted 11 June 2014 Published 10 July 2014

Academic Editor Xiao-Wei Ye

Copyright copy 2014 Bo Huang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Underground pipelines are widely applied in the so-called lifeline engineerings It shows according to seismic surveys that thedamage from soil liquefaction to underground pipelines was the most serious whose failures were mainly in the form of pipelineuplifting In the present study dynamic centrifuge model tests were conducted to study the uplifting behaviors of shallow-buriedpipeline subjected to seismic vibration in liquefied sites The uplifting mechanism was discussed through the responses of the porewater pressure and earth pressure around the pipeline Additionally the analysis of force which the pipeline was subjected to beforeand during vibration was introduced and proved to be reasonable by the comparison of the measured and the calculated resultsThe uplifting behavior of pipe is the combination effects of multiple forces and is highly dependent on the excess pore pressure

1 Introduction

Pipelines are the artery of modern industries and urbanlife widely used in lifeline engineerings such as watersupply electricity supply natural gas transportation lineand communication cables According to a large numberof seismic disaster surveys [1 2] the damage probabilityof the underground pipelines in liquefied soil is far greaterthan that in the nonliquefied soil Shallow buried pipelinesin liquefied sands might float upward displaying deflectiondeformation and sometimes they even go above the groundwhich often aggravates the damage degree In the 1964rsquosNiigata earthquake among a total pipeline length of 470kilometers 68 of pipelines were destroyed The pipelineslocated under water were damaged particularly seriouslywhose failures were mainly due to uplifting deformationHereafter ldquoupliftingrdquo phenomena of underground pipelinesand other underground structures were more and morefrequently observed in seismic incidents such as the LomaPrieta earthquake and the Nansei-Oki earthquake [3ndash6]

There have been quite a lot of studies concentrating on theldquoupliftingrdquo phenomenon of pipelines during soil liquefactionprocesses The factors that affect the stress and deformationof pipelines during floating for example the buried depthdiameter thickness stiffness of the pipelines the type liq-uefied area stiffness and strength of soil have been studied[7 8] It is generally considered that the diameter of pipelineliquefied depth stiffness of soil are critical parameters whichhave great effects on the structure deformation of buriedpipeline the largest floating displacement occurs in thecentral of the pipe Some expertsmade a number of numericaland experimental researches on the response differencesbetween the free field and field with pipelines during seismicvibration Kitaura et al [9] developed a hybrid procedureto study the pipeline response in the liquefied field Thenumerical model shows that the pipeline response to seismicvibration is more significant when the excess pore pressure islow and the buoyancy force increases with increasing excesspore pressure Ling et al [10] conducted centrifuge tests toinvestigate the seismic response differences of free field and

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 838546 15 pageshttpdxdoiorg1011552014838546

2 The Scientific World Journal

field with pipelines with respect to the acceleration excesspore pressure and settlement of ground surface and so forthOther experts [11 12] investigated the effects of dilatancyangle and relative density of soil diameter and buried depthof pipeline underground water table level and thickness ofthe saturated soil layer and so forth on the uplifting behaviorof pipeline which indicated that the buried depth of pipe hadthe most significant impact

Despite that the above mentioned studies have inves-tigated the pipeline uplifting behaviors in liquefied fieldswith respect to influencing factors involving the pipe itselfand the soil properties through a comprehensive meansof field investigations numerical simulations and modeltests there still exists disagreement on the understanding ofthe mechanism of pipeline uplifting Some [13 14] believethat the uplifting of pipelines is associated with the lossof soil shear strength due to soil liquefaction Others [15]come to a conclusion that uplifting is simply related to thevibration rather than soil liquefaction based on the observedphenomenon that uplifting starts when the soil is not fullyliquefied and ceases when the shaking is finished even whenthe excess pore pressure is still very high Due to lack ofunderstanding of the pipeline uplifting mechanism differentapproaches are adopted to calculate the buoyancy force thatpipelines are subjected to during soil liquefaction In generalit is calculated using the formula 119865Buoyancy = 120588sat119892119881 wherethe saturated soil is considered as fluidized material having aunit weight equivalent to its saturated unit weight [16ndash18] Itis worth mentioning that the buoyancy force is estimated interms of excess pore pressure as well [19]

It is significantly favorable that researches are made onthe stress conditions of the pipelines during uplifting for anin-depth understanding of the mechanism of pipe upliftingbehaviors In the present study dynamic centrifuge modeltests were conducted to investigate themechanismof pipelineuplifting phenomenon during soil liquefaction Based on themeasurements of acceleration excess pore pressure and earthpressure around the pipelines the forces on the pipelinesbefore and during soil liquefaction were estimated and themechanism and the main influencing factors of pipelineuplifting were analyzed

2 Test Equipment and Programs

21 Centrifuge Shaking Table and Rigid Container The testsare conducted on the ZJU400 centrifuge with a shaking tableshown in Figure 1 The beam type centrifuge with a payloadcapacity of 400 gt has double platforms and an effective armradius of 45m The maximum centrifugal acceleration is100 g for dynamic tests The centrifuge platforms have anoverall dimension of 15m times 12m times 15m Meanwhile an in-flight uniaxial electrohydraulic shaking table has been madeto simulate seismic excitationThe shaking table has vibrationfrequencies ranging from 10Hzsim200Hz Its payload capacityis 500 kg and its maximum lateral displacement and acceler-ation are 06 cm and 40 g respectively More details about thedevice can be found in [20]

A Rigid container was used to prepare the model whoseinner dimension is 06m (length) times 04m (width) times 05m(height) and its front perspexmadewindow is convenient fordirect observation of the experimental phenomena A 25mmthick piece of mouldable Duxseal was placed on each side ofthe container to reduce reflecting incident stress waves by atleast 65 [21]

22 Model Pipe The model pipes are made of aluminumtube with a density of 27 gcm3 a length of 390mm and aninner and outer diameter of 36mm and 40mm respectivelyAnd they are used to simulate large diameter pipes like oil orgas pipelines Each end of the pipes was sealed by a perspexdisc with PTFE and petroleum jelly was also used to reduceend friction Microearth pressure transducers were installedon the bottom side and crown of pipes to measure earthpressures (the normal stress)

Two model pipes were buried in the ground One wasused for measuring the uplift displacement named pipe1 the other was used for measuring the stabilizing forceduring soil liquefaction named pipe 2 Pipe 1 couldmove freely during tests Pipe 2 was installed to the rigidcontainer through a connecting rod The force provided bythe connecting rod to keep pipe 2 stable in the verticaldirection was defined as stabilizing force In order to acquirethe stabilizing force of pipe in the centrifuge a load cell wasinstalled on the connecting rod

In order to measure vertical displacements of under-ground structures in the centrifuge draw-wire displace-ment potentiometers are commonly used [22] Howeverthe potentiometer cable has tension force which will reducethe structurersquos self-weight to some extent Moreover thetension force varies with the centrifugal acceleration which ishard to be calibrated Therefore two aluminum alloy spokeswith discs on the end were installed on pipe 1 as shownin Figure 2 The vertical displacements of the discs couldbe measured by potentiometers which guaranteed a moreprecise and reliable measurement while pipe 1 moved freely

A simple device of a connecting rod with ball joint wasdeveloped as shown in Figure 2 This device kept pipe 2stable in the vertical direction and meanwhile moved freelyin the horizontal direction As pipe 2 was stable in thevertical direction the shear strength of the overlaying soilwould not take a part in the measured data of the force thatpipe 2 is subjected to during vibration

23 Sand and Viscous Fluid Fujian standard sand which iswidely used in China for geotechnical physicalmodeling tests[23 24] was adopted in the present study It has a meandiameter (119863

50) 016mm the uneven coefficient (119862

119906) and

the curvature coefficient (119862119888) are 16 and 095 respectively

The maximum and the minimum void ratios are 096 and061 respectively The model foundation was prepared bypluviation method The sand was rained from a sieve in ahopper into the container where the falling height of thehopper and the shape of the sieve were kept unchangedbased on the precalibrated results to obtain a constant relative

The Scientific World Journal 3

(a) Centrifuge (b) Shaking table

Figure 1 Centrifuge and shaking table

1cm

Rigid container

DuxsealSpoke

PotentiometerBall joint

Load cell

AccelerometerEarth pressure transPore pressure trans

Connecting rod

25 cm 175 cm 20 cm

29 cm

A0

P3

P1

P2

E4

A4A3

A6

A2

A7 E6P5

A5

A1

P4 E2E1

E3 E6

P58 cm

4 cm

2 cm

8 cm

7 cm

1 2

Shaking direction

(a) Test 1

1cm

Rigid containerDuxseal Spoke

Potentiometer Ball jointLoad cell

Shaking direction

Connecting rod

A0

A5

8 cm

4 cm

4 cm

25 cm 175 cm

32 cm

20 cm

8 cm

8 cm

1 2


P3

P1

P2

A4A3

A6

A2

A1

A7P4E2E1

E3 E6P6

E5E4P5

(b) Test 2

Figure 2 The layout of pipes and sensors

density The designed relative density of the two tests was60 The heights of the model foundation were 29 cm and32 cm in test 1 and test 2 respectively

There is a conflict between dynamic and permeabilitytime scale for the former is 1119899 and the latter is 1119899

2 Tosolve the problem viscous fluid was introduced to reducethe permeability of soil Methyl cellulose fluid which iscommonly used in geotechnical centrifuge modeling testshas similar compressibility and density towater [25] Further-more it is also capable of sustaining high pore pressure forliquefaction studies and can have any viscosity by changingthe mixture ratio of hydroxypropyl methylcellulose (HPMC)powder to water Based on the precalibrated relationship ofmixture ratio permeability and temperature the mixtureratio was determined to be 30 at a centrifugal acceleration30 g Methyl cellulose fluid was prepared in water with atemperature of 70∘C and introduced at a rate of 01 Lh into

the model foundation when cooling down which was slowenough to avoid sand boil phenomenonThe vacuummethodis chosen to saturate the soil the whole process of saturationtook over 200 h and the water level was kept 1 cm above theground when the saturation is completed

24 Seismic Excitations Three types of excitation waves wereadopted that is EL-Centro wave Taft wave and Zhejiangseism wave El-Centro wave was recorded in the ImperialValley earthquake of California in 1940 with a primaryperiod of 05 s belonging to near earthquake Taft wave wasrecorded in the earthquake happened in Kern of Californiain 1952 with a primary period of 05 s belonging to distantearthquake These two waves are commonly used Zhejiangseism wave is an artificial seismic wave suited the seismiczoning type of Zhejiang Province in China with a 10 sduration Assuming the exceeding probability of Zhejiang


Table 1 Centrifuge testing program and uplifting status of pipe 1 during tests

Test number Seismic excitationSeismic wave Duration (s) Amplitude (g) Uplifting status

Test 1

Noise

30

002Zhejiang seism wave 01 Remain still

EL-Centro 01 Remain stillNoise 002

Zhejiang seism wave 015 Sink slightlyEL-Centro 015 Rise slightlyNoise 002

EL-Centro 05 RiseTaft 04 RiseNoise 002

Test 2

Noise

30

002EL-Centro 01 Remain still

Zhejiang seism wave 01 Remain stillNoise 002


seism wave to be 10 and 2 the maximum acceleration is631 cms2 and 153 cms2 respectively

25 Testing Procedures In the present study two centrifugetests were conducted on pipes of different buried depthsunder the same ground conditions The centrifuge acceler-ations were both 30 g The buried depths measured fromthe top of pipes to the ground surface were 20mm (equalto 05119863) for test 1 and 80mm (equal to 2119863) for test 2Accelerometers pore pressure transducers earth pressuretransducers potentiometers and load cell were used in thetests [26] The layout of the sensors and pipes for each test isshown in Figure 2

When started the centrifuge was accelerated to 30 ggradually The relative densities of the ground before shakingwere 652 for test 1 and 619 for test 2 The excitationprogress was divided into 3 stages based on the accelerationamplitudes from weak to strong White noise excitationswere applied before and after each stage to test the dynamiccharacteristics of the model The schedule of excitations aswell as the uplifting status of the pipe 1 at each shakingstage is shown in Table 1 There was at least a 30min intervalbetween two shaking stages so that the excess pore pressurecan dissipate entirely After all the excitations were appliedthe test data as will be mentioned in the following sectionsare converted to the prototype scale

3 Results of Tests

31 The Degrees of Soil Liquefaction and the Pore PressureResponse around the Pipe

311 The Degrees of Soil Liquefaction The excess pore pres-sure ratio Δ119906120590

1015840 defined as the value of the excess pore

pressure normalized by the initial vertical effective stressrepresents the degree of soil liquefaction If the value ofΔ119906120590

1015840

reaches one it means the soil is fully liquefied As the build-up of excess pore pressure in the two tests was similar onlypart of the results is given that is the variations of Δ119906120590

1015840

in test 2 under 01 g and 04 g excited by El-Centro wave asshown in Figure 3The buried depths of P1 and P5 were 84mand 36m respectively It shows that the excess pore pressuregenerated from the start of the earthquake vibration As soonas the vibration stopped the excess pore pressure ratio beganto dissipate In the two tests although no excitations led thesoil to fully liquefied state the ldquoupliftingrdquo phenomenon stillexisted which suggests that there is a high potential for theoccurrence of pipe uplifting in incompletely liquefied soil

312 The Pore Pressure Response around the Pipe The vari-ations of Δ119906120590

1015840 around the pipe in test 1 under 015 g and05 g excited by El-Centro wave are shown in Figure 4 P3 andP4 were fixed at the bottom and side of pipe 1 18m and12m below the surface respectively As the buried depth ofpipes in test 1 was so shallow that the pore pressure couldnot be measured well at the crown of pipe therefore notransducer was installed there In test 2 transducers P2 P3and P4 were installed at the bottom side and crown of pipe1 respectively P6 was embedded in the soil layer overlyingpipe 1The variations ofΔ119906120590

1015840 for P3 P4 and P6 under 01 gand 04 g excited by El-Centrowave are given in Figure 5 Dueto the damage of P2 there is no measured data from P2

It can be figured out from Figures 4 and 5 that excesspore pressures around the pipes respond rapidly once theearthquake load is applied For a small amplitude excitationthe excess pore pressure dissipates gradually when the excita-tion ends Considering that the amplitude of real earthquakewave decreases obviously at the late stages the excess pore


00

03

00

03

0 200 400

00

01

P1

P5

Acc (

g)

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

minus01

Δ120590

998400u

Δ 120590

998400u

El-Centro wave 01 g

(a) 119886max = 01 g

00

05

10

00

05

10

0 200 400

00

04

P1

P5

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

minus04

El-Centro wave 04 g

Acc (

g)Δ

120590998400

uΔ

120590998400

u

(b) 119886max = 04 g

Figure 3 Ground response of Δ1199061205901015840 in test 2 under El-Centro wave

pressures might even dissipate before the end of vibrationas is shown in Figure 5(a) For stronger seismic excitationsthe excess pore pressures of soil below the pipe dissipatewhen the vibration is ceased but the dissipation rate slowsdown obviously as shown in Figure 4(b) Meanwhile at theside and crown of pipe the excess pore pressures retainsfor a while after the vibration is ceased This phenomenonis attributable to the supply of the pore fluid draining fromthe base of the rigid container which was more sufficientthan the dissipation of the excess pore pressures at shallowlocation so that the excess pore pressures at shallow placeskeep generating as shown in Figure 4(b) (location P4) andFigure 5(b) (location P6)

It can be seen that the stronger the excitation is the largerthe excess pore pressures ratio will be The dissipation rateof the excess pore pressure decreases with the decreasingburied depth of the pipe And in some cases the excesspore pressures even keep generatingThe frictional resistancebetween soil grains was largely reduced by the increase inpore pressure Therefore pipe floats upward more easilythrough the soil on the condition of stronger excitations orlower buried depths of pipe

32 Earth Pressure Response The layout of the earth pressuretransducers is shown in Figure 2 And the earth pressure (thetotal stress which contains both effective stress and pore


0 400 800

000

015

Acc (

g)

Time (s)

minus015

00

03

P3

0 400 800

Time (s)

Δ 120590

998400u

00

03

P4

0 400 800

Time (s)

Δ 120590

998400u

El-Centro wave 015 g

(a) 119886max = 015 g

00

05

10

00

05

10

0 400 800

00

05

P3

P4

Time (s)

0 400 800

Time (s)

0 400 800

Time (s)

minus05

El-Centro wave 05 g

Acc (

g)Δ

120590998400

uΔ

120590998400

u

(b) 119886max = 05 g

Figure 4 Pipe response of Δ1199061205901015840 in test 1 under El-Centro wave

pressure) around the circumference of pipe under 015 g and05 g excited by EI-Centro wave in test1 is shown in Figure 6The value of earth pressure changed while the vibration wasactivated and recovered gradually to 0 after the vibrationended The responses of the earth pressure were differentbetween pipe 1 and pipe 2 due to the different constraintconditions Responses of pipe 1 which could move freelywere larger than that of pipe 2 which was fixed in the verticaldirection It can be seen in Figure 6 that the increments of theearth pressure at the bottom and side of pipe are proportionalto the amplitude of the excitations However response of theearth pressure at the crown was weak or even showed a slightdecrease which might indicate the weight reduction of theoverlay soil

33 Pipe Uplifting It is found that pipeline uplifting takesplace once the vibration starts and ceases when the vibrationstops despite the presence of high excess pore pressuresSome researchers hold the view that the uplifting of the pipeis highly dependent on the input earthquake motion andweakly related to the increase of excess pore water pressure[15 19] Figure 7 shows uplifting responses of pipe 1 underTaft wave in test 1 and test 2 And uplifting responses of pipe1 under different amplitudes of EL-Centro wave are shownin Figure 8

It is seemingly that the uplifting phenomenon of pipeoccurred after shaking and ceased when the shaking ceasesNevertheless the uplifting movement is not directly deter-mined by the shaking itself but the response of the pore


00

05

10

00

05

10

00

05

10

0 200 400

00

01

P3

P4

P6

Acc (

g)

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

minus01

Δ

El-Centro wave 01 g

120590998400

uΔ

120590998400

uΔ

120590998400

u

(a) 119886max = 01 g

00

05

10

00

05

10

00

05

10

0 200 400

00

04

P3

P4

P6

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

minus04

El-Centro wave 04 g

Acc (

g)Δ

120590998400

uΔ

120590998400

uΔ

120590998400

u

(b) 119886max = 04 g


pressure and the soil pressure It can be seen that the upliftingof the pipe takes place only after considerable excess porepressure is generated rather than immediately after thevibration startedThe excess pore pressure ratios of P5 (which

were at the same depth of the bottom of pipe 1) when pipe1 began to move up were shown in Figure 9 The excesspore pressure ratios distributed between 01 and 02Howeverit does not mean that the pipe will float upward once the


0

3

6

0

0

3

6

3

0 50 100 150 200

0 50 100 150 200

000

E1 E4

E2 E5

Incr

emen

t of e

arth

pre

ssur

e (kN

)In

crem

ent o

f ear

th p

ress

ure (

kN)

Incr

emen

t of e

arth

pre

ssur

e (kN

)

E3 E6

Acc (

g)

Time (s)

Time (s)

0 50 100 150 200

Time (s)

0 50 100 150 200

Time (s)

minus3

minus3

minus6

minus015

015


(a) 119886max = 015 g

0

11

0

11

0

6

12

0 200 400 600 800

0 200 400 600 800

00

04

Time (s)

Time (s)

0 200 400 600 800

Time (s)

0 200 400 600 800

Time (s)

minus6

minus12

minus04

minus11

minus11

El-Centro wave 05g

E1 E4

E2 E5

E3 E6

Incr

emen

t of e

arth

pre

ssur

e (kN

)In

crem

ent o

f ear

th p

ress

ure (

kN)

Incr

emen

t of e

arth

pre

ssur

e (kN

)Ac

c (g)

(b) 119886max = 05 g

Figure 6 Increment of earth pressure in test 1 under El-Centro wave


0

30

60

90

00

04

08

12

0 10 20 30 40 50 60 70 80 90 100

00

04

Disp

lace

men

t (m

m)

Displacement

P5

Acc (

g)

Time (s)

0 10 20 30 40 50 60 70 80 90 100

Time (s)

0 10 20 30 40 50 60 70 80 90 100

Time (s)

Start rising

Still rising

minus30

minus04

Δ

Taft wave 04 g

120590998400

u

(a) 119867119863 = 05

0

30

60

90

00

04

08

0 20 40 60 80 100

00

04

Stop rising

Disp

lace

men

t (m

m)

Displacement

Start rising

P5

Acc (

g)

Time (s)

0 20 40 60 80 100

Time (s)

0 20 40 60 80 100

Time (s)

minus30

minus04

Taft wave 04 g

Δ 120590

998400u

(b) 119867119863 = 2

Figure 7 Uplift displacement of pipe 1 at different depth under Taft wave

excess pore pressure ratio has reached 02 As can be seen inFigure 8(a) the pipe settled alongwith the soil particles under01 g excited by EL-Centro wave although the maximumexcess pore pressure ratio was above 02

Actually the maximum uplift displacement was notpresent right after the vibration stopped each time It canbe seen in Figure 7(a) the tendency of uplifting still existedwhen the earthquake ceased The uplifting behavior of pipein liquefied soil is a multiforce coupled behavior which isnot only dependent on the build-up of excess pore pressurebut also determined by the shear strength of the soil relativedisplacement of pipe and soil the amplitude of the inputseismic wave and so forth

34 The Response of Stabilizing Force The stabilizing forcewhich kept the pipe 2 stable in the vertical direction wasmeasured by a load cell fixed on the device The variation ofstabilizing force in test 1 under El-Centro wave with differentamplitudes is shown in Figure 10 Herein negative values ofthe stabilizing force mean that the pipe is prone to settledown as seen in Figure 10(a) and positive values represents

that the pipe has the tendency to uplift as shown in Figures10(b) and 10(c)

Figure 11 gives the relationship between the stabilizingforce and the excess pore pressure The abscissa is thestabilizing force at the end of shaking for all tests andthe ordinate is the maximum value of P5 The stabilizingforce shows a power function relationship with excess porepressure It can be seen that the stabilizing force is larger whilethe buried depth of the pipe is shallower at the same excesspore pressure ratio It is probably because that the lateralconstraint pressure of soil at shallowdepth is smaller than thatin deep place so that the deflection deformation of shallowersoil layer can be more intense which makes the pipe upliftmore easily

4 Analysis of the Force of Pipe

The force components acting on pipes were investigated withthe results obtained from centrifuge tests in this sectionThese components were adapted from static analysis to adynamic condition where soil liquefaction occurs Further-more the force analysis was validated by the comparisonbetween the measured and calculated data


0

5

4

8

00

02

04

06

10 20 30 40 50 60

00

01

Disp

lace

men

t (m

m)

Displacement

P

Acc (

g)

Time (s)

10 20 30 40 50 60

Time (s)

10 20 30 40 50 60

Time (s)

minus4

minus01

Δ

El-Centro wave 01 g

120590998400

u

(a) 119886max = 01 g

0

30

60

00

04

08

0 20 40 60 80 100

0 20 40 60 80 100

0

5

20 40 60 80 100

00

04

Disp

lace

men

t (m

m)

Displacement

P

Acc (

g)

Time (s)

Time (s)

Time (s)

Start rising

El-Centro wave 04 g

minus04

Δ 120590

998400u

(b) 119886max = 04 g

Figure 8 Uplift displacement of pipe 1 in test 2 under El-Centro wave

41 Force Analysis before Shaking The force state before shak-ing is shown in Figure 12 And force equilibrium equation isexpressed as follows

119879 + 119882119904+ int

1198632

minus1198632

(1199061) 119889119863 sdot 119871 + 119882

119901= int

1198632

minus1198632

(1199062) 119889119863 sdot 119871 + 119873

(1)

where 119871 and 119882119901are the length and weight of the pipe

respectively which can be obtained according to scalingprinciple from the length and density of pipe in 1 g conditionT is the stabilizing force of pipe 2 which can be measuredby load cells (T of pipe 1 is 0) 119882

119904is the effective weight of

overlying soilN is the support force from the soil underlyingthe pipe 119906

1and 119906

2are pore pressures around the pipe The

total force of these three parts can be calculated by the integralof the earth pressure difference between the upper and thebottom of pipe It can be written as

119875 = int

1198632

minus1198632

(1199062minus 1199061) 119889119863 sdot 119871 + 119873 minus 119882

119904 (2)

where 119875 denoted the integral of earth pressure differencewhich can be obtained by the interpolation according to the

earth pressure transducers distributed on the pipes definedas (3) Consider

119875 = int

1198632

minus1198632

(1198902minus 1198901) 119889119863 sdot 119871 (3)

where 1198901and 1198902denote the vertical component of linearized

earth pressure distributed on the upper half and on the inverthalf of the pipe respectively The earth pressure is the totalstress which contains both effective stress and pore waterpressure The earth pressure mentioned below has the samemeaning

Equation (2) is checked based on the data measuredbefore shaking which proved to be reasonable with only alittle bit difference as stresses around the pipe are estimatedbased on the interpolating method

It should be noted that the integral of the pore pressurearound the pipe under static state is buoyancy force whichis the static buoyancy force in the present study and can becalculated based on Archimedes principle as follows

int

1198632

minus1198632

(1199062minus 1199061) 119889119863 sdot 119871 = 120588

119908119892119881pipe (4)


00

01

02

03

04

05

Different shaking

Δu

(P8

and P5

)

Test 1-EL 015 g

Test 1-EL 05 g

Test 2-EL 04 g

02minus

01minus

minus03

120590998400

Test 1-Taft 04 g

Test 2-Taft 04 g

Figure 9 Excess pore pressure of P5 when pipe 1 starts to float

42 Force Analysis during Shaking for Pipe 2 As pipe 2 wasfixed to the rigid container no displacement in the verticaldirection occurred during vibration And consequently theshear strength of soil could not excite The force state ofpipe 2 during vibration is shown in Figure 13 And forceequilibrium equation is expressed in as follows

1198791015840+ 1198821015840

119904+ int

1198632

minus1198632

(1199061015840

1) 119889119863 sdot 119871 + 119882

119901

= int

1198632

minus1198632

(1199061015840

2) 119889119863 sdot 119871 + 119873

1015840

(5)

where the superscript sign ( 1015840) represents the correspondingforces or stresses during shaking of pipe 1 Subtracting (1)from (5) gives

Δ119879 = int

1198632

minus1198632

(Δ1199062minus Δ1199061) 119889119863 sdot 119871 + Δ119873 minus Δ119882

119904 (6)

where Δ119879 is the increment of the stabilizing force whichcan be measured by the load cell Δ119906

1and Δ119906

2are excess

pore pressures around the pipe int1198632minus1198632

(Δ1199062minus Δ1199061)119889119863 sdot 119871 is

the integral of excess pore pressure during soil liquefactionlabelled as Δ119880 Δ119882

119904and Δ119873 are the increments of support

force of soil underlying the pipe and the effective weightof soil overlying the pipe respectively due to the flowingdeformation of soil around the pipe during vibration [22]Thethree parts on the right-hand side of (6) can also be calculatedby the integral of earth pressure differences around the pipemarked as Δ119875

Δ119879 Δ119875 and Δ119880 of pipe 2 under 05 g excited by El-Centro wave are given in Figure 14 It is clear that thegrowth patterns of Δ119879 and Δ119875 are almost the same As thenumber of earth pressure transducers installed around the

pipe is limited the slight difference between Δ119875 and Δ119879

is reasonable The integral of the excess pore pressure Δ119880which is defined as the dynamic buoyancy force in this paperis smaller than both Δ119875 and Δ119879 Obviously the upliftingbehavior of pipe is not only affected by the build-up of theexcess pore pressure but also by the variations of the effectiveweight of the overlying soil and the support force of theunderlying soil

The value of (120574satminus120574119908) sdot119881pipe which is commonly adopted

by other researchers to calculate the buoyancy force is givenin Figure 14 When the soil is fully liquefied the excess porepressure then reaches the value of the initial effective verticalearth pressure (the pore pressure at the crown surface of thepipe is 1199061015840

1= 120574sat119891(ℎ

1) and the value on the bottom of the pipe

is 1199061015840

2= 120574sat119891(ℎ

2)) Integrating the difference between 119906

1015840

1and

1199061015840

2gives

int

1198632

minus1198632

(1199061015840

2minus 1199061015840

1) 119889119863 sdot 119871

= 120574sat sdot int1198632

minus1198632

[119891 (ℎ2) minus 119891 (ℎ

1)] 119889119863 sdot 119871 = 120574sat119881pipe

(7)

It indicates that the dynamic buoyancy force Δ119880 isequal to (120574sat minus 120574

119908) sdot 119881pipe for fully liquefied ground The

value of dynamic buoyancy force will be overestimated forincompletely liquefied soil by (7)

43 Force Analysis during Shaking for Pipe 1 The force stateof pipe 1 during uplifting is shown in Figure 15 And forceequilibrium equation is expressed as follows

119865119904+ 11988210158401015840

119904+ int

1198632

minus1198632

11990610158401015840

1119889119863 sdot 119871 + 119882

119901

= int

1198632

minus1198632

11990610158401015840

2119889119863 sdot 119871 + 119873

10158401015840+ 119898119901119886

(8)

where 119886 represents the uplift acceleration of pipe 119865119904repre-

sents the frictional resistance from the overlying soil whichvaries with the degree of soil liquefaction and reduces to0 if the soil is fully liquefied The physical meanings of11990610158401015840

1 11990610158401015840

211988210158401015840

119904 and119873

10158401015840 are the same as 11990610158401 1199061015840

21198821015840

119904 and119873

1015840 exceptthe superscript sign ( 10158401015840 ) represents the corresponding forcesor stresses during vibration of pipe 1 Subtracting (1) from(8) gives

119898119901119886 = 119865119904+ Δlowast119882119904minus int

1198632

minus1198632

(Δlowast1199062minus Δlowast1199061) 119889119863 minus Δ

lowast119873 (9)

where Δlowast1199061and Δ

lowast1199062are excess pore pressures around the

pipe int1198632minus1198632

(Δlowast1199062minus Δlowast1199061)119889119863 sdot 119871 is dynamic buoyancy force

during soil liquefaction labelled as Δlowast119880 Δlowast119882

119904and Δ

lowast119873 are

the increments of support force of soil underlying pipe 1and the effective weight of soil overlying pipe 1 respectivelydue to the excess pore pressure variation induced flowingdeformation of soil around the pipe during vibration As thedifferent motion patterns of pipe 1 and pipe 2 the stresses


Time (s)

00

25

50Fo

rce (

kN) Shaking

EL 01g

minus25

0 10 20 30 40 50

(a)

0

Forc

e (kN

)

Shaking

EL 015 g

minus15

minus 45

minus30

0 10 20 30 40 50Time (s)

(b)

0 10 20 30 40 50

0

160

Shaking

Forc

e (kN

)

EL 05 g

minus 160

minus 320

Time (s)

(c)

Figure 10 Increment of stabilizing force of pipe 2 under El-Centro wave in test 1

0 20 40 60 80 100 120 140 160

02

06

05

09

08

00

01

03

04

07

10

HD = 05 HD = 2

EL-01 gZ-015 g

Z-01 g

EL-015 gEL-05 gTaft-04 g

EL-01 gZ-01 gEL-04 gTaft-04 g

Δ

ΔT

120590998400 (P5)

u

Figure 11 Relationship among increment of stabilizing forceΔ1199061205901015840

and excitation

measured by the transducers around them are different Thetotal force of the three parts can also be calculated by theintegral of earth pressure around pipe 1 All the forces in (9)can be calculated by the measured data except 119865

119904

H

T + WS

u1

u2

2 Wp

N

Figure 12 Schematic diagram of force of pipe 2 before shaking

The frictional force 119865119904from the shear plane is estimated

using the equation introduced byDNV (2007) [27] as follows

119865119904= 119891119901[119863

119867times (

119867

119863+ 05)

2

] 1205901015840

119867119863119871 (10)

where 1205901015840

119867refers to the effective vertical stress of the overlying

soil Before vibration 12059010158401198670

= 1205741015840119867 119891119901is a parameter related to


H

+

2 WP

f1(h

f2(h)

)

W998400s

u9984001

u9984002

f(h) is the

the burialdepth of

pipe surface

function of

T998400

N998400

Figure 13 Schematic diagram of force of pipe 2 during shaking

0 20 40 60 80 100 120 140 160 180 200

0

100

200

300

Time (s)

Forc

e (kN

)

ΔTΔU

ΔP

sat minus w)Vpipe

minus100

minus200

minus300

(120574 120574

Figure 14 Relationship among Δ119879 Δ119875 and Δ119880 under 05 g El-Centro wave in test 1

the soil property ranging from 04 to 06 for medium densesand

Given the relationship between the degree of liquefactionand the frictional contact between the soil grains verticaleffective stress declines linearly with the increase of excesspore pressure Consider

1205901015840

119867= 1205901015840

1198670minus Δ119906 (11)

Substituting (10) and (11) into (9) the uplift acceleration (a)can be obtained And acceleration time-history is shown inFigure 16(a) The concept of the Newmarkrsquos method which is

H

Wpmpa

Fs

(decreased during

shaking)u9984009984001

u9984009984002N998400998400

W998400998400s


used to predict earthquake-induced permanent deformationis adopted in the case of a floating pipe [28] The angle ofthe sliding surface is considered to be vertical rather thaninclined And the rigid pipe can be treated as sliding blockof the Newmarkrsquos model with vertical movement

As the behavior of pipe in liquefied soil is extremelycomplicated a few assumptions are made in the following tocalculate the displacement of pipeThe uplifting of the pipe 1occurs as soon as the value of the uplift acceleration is greaterthan zero Zero is deemed as the yield accelerationThemove-ment of pipe occurs when its acceleration exceeds the yieldacceleration which is in accordancewithNewmarkrsquos analysisThe excess in acceleration above yield acceleration is termedas effective vertical acceleration (119886eff) And effective verticalacceleration time-history is illustrated in Figure 16(b) Inaddition pipe is incapable of sinking considering the bearingcapacity of the underlying soil and the flowing of soil fromthe top or side to the bottom of the pipe As pipe 1 is in thestatic status before shaking the initial value of accelerationvelocity and displacement should be zero

Based on the assumptions above the accumulated uplift-ing displacement can be obtained by integrating the effectivevertical acceleration 119886eff twice The uplifting displacementtime history of the pipe 1 calculated under 04 g Taft wave intest 1 is shown in Figure 16(d) The predicted displacementsare slightly larger than the experimental ones observed inFigure 16 and fluctuate around the experimental ones in othercasesThe difference between themeasured and the predicteddisplacements is lower than 20mm which is deemed to beacceptable as the number of transducers installed around thepipe is limited And the motion patterns of them are almostthe sameTherefore the proposed approach to estimating thestabilizing force around pipe is reasonable


0

6

0 10 20 30 40 50

a(m

s)

a

minus6

minus12

Time (s)

(a)

0

2

4

6

0 10 20 30 40 50

aeff

aef

f(m

s2)

Time (s)

(b)

00

01

02

03

0 10 20 30 40 50

V

V

(ms

)

minus01

Time (s)

(c)

0 10 20 30 40 50

0

45

90

Disp

lace

men

t (m

m)

Calculated resultsTest results

minus45

Time (s)

(d)

Figure 16 Acceleration velocity and displacement of pipe 1 under 04 g Taft wave in test 1

5 Conclusions

Theuplifting behavior of shallow buried pipe in liquefied fieldwas investigated through dynamic centrifuge model tests inthe present study and the main conclusions of the researchare summarized as follows

(1) Although the uplifting phenomenon of pipelines inthe liquefied soils always happens during the seismicvibration the observation in our tests shows thebegin and end time point of uplifting is not directlyrelated to the seismic motion The uplifting is highlydependent on the buildup of the excess pore pressureMoreover the quantitative relationship between theuplifting behavior and the generation of the excesspore pressure needs further studies

(2) The uplifting movement of pipe is the combinationeffects of multiple forces During seismic vibrationexcess pore pressure generates and soil around thepipeline gradually flow in an oval-like trace whichcauses both the variation of effective weight of over-lying soil and supporting force of soil underlying thepipeline as well as the shear resistance from shearplanes that varies with the degree of liquefaction Asa result the equilibrium of pipeline during shaking isbroken and the pipe consequently uplifts However inmost existing research the variations of the overlyingsoil weight and the supporting force of the underlyingsoil are ignored

(3) For incompletely liquefied field the buoyancy forceis overestimated by multiplying the saturated unitweight of soil and pipeline volume

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research work was supported by National Natural Sci-ence Foundation of China (nos 51178427 and 51278451) andKey Innovation team support project of Zhejiang Province(2009R50050)

References

[1] M Kitaura and M Miyajima ldquoQuantitative evaluation ofdamage to buried pipelines induced by soil liquefactionrdquo inPro-ceedings of the 9thWorld Conference on Earthquake Engineeringpp 11ndash16 Tokyo Japan August 1988

[2] S Yasuda and H Kiku ldquoUplift of sewage manholes and pipesduring the 2004 Niigataken-Chuetsu Earthquakerdquo Soils andFoundations vol 46 no 6 pp 885ndash894 2006

[3] W J Hall and T D OrsquoRourke ldquoSeismic behavior and vulnera-bility of pipelinesrdquo Lifeline Earthquake Engineering ASCE pp761ndash773 1991

[4] T D ORourke and P A Lane Liquefaction Hazards and TheirEffects on Buried Pipelines National Center for EarthquakeEngineering Research 1989

[5] T D OrsquoRourke T E Gowdy H E Strwart and J W PeaseldquoLifeline and geotechnical aspects of the 1898 Loma PrietaEarthquakerdquo in Proceedings of the 2nd International Conferenceon Recent Advances in Geotechnical Earthquake Engineeringand Soil Dynamics pp 1601ndash1612 University of Missouri-RollaRolla Mo USA 1991


[6] YMohri M Yasunaka and S Tani ldquoDamage to buried pipelinedue to liquefaction induced performance at the ground bythe Hokkaido-Nansei-Oki Earthquake in 1993rdquo in Proceedingsof the 1st International Conference on Earthquake GeotechnicalEngineering pp 31ndash36 Tokyo Japan 1995

[7] O Kiyomiya and K Minami ldquoEvaluation of stresses on sub-marine pipelines in liquefied seabedrdquo in Proceedings of the 9thWorld Conference on Earthquake Engineering pp 91ndash96 Tokyo-Kyoto Japan August 1988

[8] X Zhu S Xue X Tong and X Sun ldquoUplift response oflarge-diameter buried pipeline in liquefiable soil using pipe-soil coupling modelrdquo in Proceedings of the ASCE-InternationalConference on Pipelines and Trenchless Technology (ICPTT rsquo11)pp 1790ndash1801 Beijing China October 2011

[9] M Kitaura M Miyajima and H Suzuki ldquoResponse analysisof buried pipelines considering rise of ground water table inliquefaction processesrdquo Japan Society of Civil Engineers vol 4no 1 pp 147ndash154 1987

[10] H I Ling Y Mohri T Kawabata H Liu C Burke andL Sun ldquoCentrifugal modeling of seismic behavior of large-diameter pipe in liquefiable soilrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 129 no 12 pp 1092ndash11012003

[11] Z Xia G Ye J Wang B Ye and F Zhang ldquoNumerical analysison the influence of thickness of liquefiable soil on seismicresponse of underground structurerdquo Journal of Shanghai Jiao-tong University vol 15 no 3 pp 279ndash284 2010 (Chinese)

[12] R Saeedzadeh andNHataf ldquoUplift response of buried pipelinesin saturated sand deposit under earthquake loadingrdquo SoilDynamics and Earthquake Engineering vol 31 no 10 pp 1378ndash1384 2011

[13] D G Zou X J Kong H I Ling and T Zhu ldquoExperimentalstudy on the uplift behavior of pipeline in saturated sandfoundation and earthquake resistant measures during an earth-quakerdquo Chinese Journal of Geotechnical Engineering vol 24 no3 pp 323ndash326 2002 (Chinese)

[14] S C Chian and S P G Madabhushi ldquoDisplacement of tunnelsin lquefied sand depositsrdquo in Proceedings of the 8th InternationalConference on Urban Earthquake Engineering pp 517ndash522Tokyo Japan 2011

[15] L Sun Centrifuge Modeling and Finite Element Analysis ofPipeline Buried in Liquefiable Soil Columbia University 2001

[16] N Nishio ldquoMechanism of projection of sewerage manholesabove ground due to soil liquefactionrdquo Japan Society of CivilEngineers vol 11 no 3 pp 145ndash148 1994

[17] K Sekiguchi S Matsuda and H Adachi ldquoNumerical study onthe effectiveness of stabilizing techniques of offshore pipelinesagainst liquefactionrdquo in Proceedings of the 11thWorld Conferenceon Earthquake Engineering 1996

[18] J Q Lin Z H Li and M Y Hu ldquoStudy on the floatationresponse of buried pipelines due to soil liquefactionrdquo Journal ofEarthquake Engineering and Engineering Vibration vol 24 no3 pp 120ndash123 2004 (Chinese)

[19] S C Chian and K Tokimatsu ldquoFloatation of undergroundstructures during the Mw90 Tohoku earthquake of 11th March2011rdquo in Proceedings of the 15thWorld Conference on EarthquakeEngineering Lisboa Portugal 2012

[20] M Y Chen C Han D S Ling L G Kong and Y GZhou ldquoDevelopment of geotechnical centrifuge ZJU400 andperformance assessment of its shaking table systemrdquo ChineseJournal of Geotechnical Engineering vol 33 no 12 pp 1887ndash1894 2011 (Chinese)

[21] R S Steedman and S P G Madabhushi ldquoWave propagation insandmediumrdquo in Proceedings of the International Conference onSeismic Zonation Stanford California 1991

[22] S C Chian Floatation of Underground Structures in LiquefiableSoil University of Cambridge 2012

[23] L G Kong J Y Fan R P Chen and Y M Chen ldquoPile-soil-pile interaction between two piles moving along differentdirectionsrdquo Chinese Journal of Geotechnical Engineering vol 33no 12 pp 1887ndash1894 2011 (Chinese)

[24] Y Guo M T Luan C S Xu and Y He ldquoEffect of variationof principal stress orientation on undrained dynamic strengthbehavior of loose sandrdquo Chinese Journal of Geotechnical Engi-neering vol 25 no 6 pp 666ndash670 2003 (Chinese)

[25] D Yang E Naesgaard P M Byrne K Adalier and TAbdoun ldquoNumerical model verification and calibration ofGeorge Massey Tunnel using centrifuge modelsrdquo CanadianGeotechnical Journal vol 41 no 5 pp 921ndash942 2004

[26] T Yi H Li and M Gu ldquoOptimal sensor placement forstructural health monitoring based on multiple optimizationstrategiesrdquo The Structural Design of Tall and Special Buildingsvol 20 no 7 pp 881ndash900 2011

[27] J Wang S K Haigh G Forrest and N I Thusyanthan ldquoMobi-lization distance for upheaval buckling of shallowly buriedpipelinesrdquo Journal of Pipeline Systems Engineering and Practicevol 3 no 4 pp 106ndash114 2012

[28] N M Newmark ldquoEffect of earthquakes on dams and embank-mentsrdquoMilestones in Soil Mechanics pp 109ndash129 1965

International Journal of

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Control Scienceand Engineering

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Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



field with pipelines with respect to the acceleration excesspore pressure and settlement of ground surface and so forthOther experts [11 12] investigated the effects of dilatancyangle and relative density of soil diameter and buried depthof pipeline underground water table level and thickness ofthe saturated soil layer and so forth on the uplifting behaviorof pipeline which indicated that the buried depth of pipe hadthe most significant impact

Despite that the above mentioned studies have inves-tigated the pipeline uplifting behaviors in liquefied fieldswith respect to influencing factors involving the pipe itselfand the soil properties through a comprehensive meansof field investigations numerical simulations and modeltests there still exists disagreement on the understanding ofthe mechanism of pipeline uplifting Some [13 14] believethat the uplifting of pipelines is associated with the lossof soil shear strength due to soil liquefaction Others [15]come to a conclusion that uplifting is simply related to thevibration rather than soil liquefaction based on the observedphenomenon that uplifting starts when the soil is not fullyliquefied and ceases when the shaking is finished even whenthe excess pore pressure is still very high Due to lack ofunderstanding of the pipeline uplifting mechanism differentapproaches are adopted to calculate the buoyancy force thatpipelines are subjected to during soil liquefaction In generalit is calculated using the formula 119865Buoyancy = 120588sat119892119881 wherethe saturated soil is considered as fluidized material having aunit weight equivalent to its saturated unit weight [16ndash18] Itis worth mentioning that the buoyancy force is estimated interms of excess pore pressure as well [19]

It is significantly favorable that researches are made onthe stress conditions of the pipelines during uplifting for anin-depth understanding of the mechanism of pipe upliftingbehaviors In the present study dynamic centrifuge modeltests were conducted to investigate themechanismof pipelineuplifting phenomenon during soil liquefaction Based on themeasurements of acceleration excess pore pressure and earthpressure around the pipelines the forces on the pipelinesbefore and during soil liquefaction were estimated and themechanism and the main influencing factors of pipelineuplifting were analyzed

2 Test Equipment and Programs

21 Centrifuge Shaking Table and Rigid Container The testsare conducted on the ZJU400 centrifuge with a shaking tableshown in Figure 1 The beam type centrifuge with a payloadcapacity of 400 gt has double platforms and an effective armradius of 45m The maximum centrifugal acceleration is100 g for dynamic tests The centrifuge platforms have anoverall dimension of 15m times 12m times 15m Meanwhile an in-flight uniaxial electrohydraulic shaking table has been madeto simulate seismic excitationThe shaking table has vibrationfrequencies ranging from 10Hzsim200Hz Its payload capacityis 500 kg and its maximum lateral displacement and acceler-ation are 06 cm and 40 g respectively More details about thedevice can be found in [20]

A Rigid container was used to prepare the model whoseinner dimension is 06m (length) times 04m (width) times 05m(height) and its front perspexmadewindow is convenient fordirect observation of the experimental phenomena A 25mmthick piece of mouldable Duxseal was placed on each side ofthe container to reduce reflecting incident stress waves by atleast 65 [21]

22 Model Pipe The model pipes are made of aluminumtube with a density of 27 gcm3 a length of 390mm and aninner and outer diameter of 36mm and 40mm respectivelyAnd they are used to simulate large diameter pipes like oil orgas pipelines Each end of the pipes was sealed by a perspexdisc with PTFE and petroleum jelly was also used to reduceend friction Microearth pressure transducers were installedon the bottom side and crown of pipes to measure earthpressures (the normal stress)

Two model pipes were buried in the ground One wasused for measuring the uplift displacement named pipe1 the other was used for measuring the stabilizing forceduring soil liquefaction named pipe 2 Pipe 1 couldmove freely during tests Pipe 2 was installed to the rigidcontainer through a connecting rod The force provided bythe connecting rod to keep pipe 2 stable in the verticaldirection was defined as stabilizing force In order to acquirethe stabilizing force of pipe in the centrifuge a load cell wasinstalled on the connecting rod

In order to measure vertical displacements of under-ground structures in the centrifuge draw-wire displace-ment potentiometers are commonly used [22] Howeverthe potentiometer cable has tension force which will reducethe structurersquos self-weight to some extent Moreover thetension force varies with the centrifugal acceleration which ishard to be calibrated Therefore two aluminum alloy spokeswith discs on the end were installed on pipe 1 as shownin Figure 2 The vertical displacements of the discs couldbe measured by potentiometers which guaranteed a moreprecise and reliable measurement while pipe 1 moved freely

A simple device of a connecting rod with ball joint wasdeveloped as shown in Figure 2 This device kept pipe 2stable in the vertical direction and meanwhile moved freelyin the horizontal direction As pipe 2 was stable in thevertical direction the shear strength of the overlaying soilwould not take a part in the measured data of the force thatpipe 2 is subjected to during vibration

23 Sand and Viscous Fluid Fujian standard sand which iswidely used in China for geotechnical physicalmodeling tests[23 24] was adopted in the present study It has a meandiameter (119863

50) 016mm the uneven coefficient (119862

119906) and

the curvature coefficient (119862119888) are 16 and 095 respectively

The maximum and the minimum void ratios are 096 and061 respectively The model foundation was prepared bypluviation method The sand was rained from a sieve in ahopper into the container where the falling height of thehopper and the shape of the sieve were kept unchangedbased on the precalibrated results to obtain a constant relative




1cm

Rigid container

DuxsealSpoke


Load cell


Connecting rod

25 cm 175 cm 20 cm

29 cm

A0

P3

P1

P2

E4

A4A3

A6

A2

A7 E6P5

A5

A1

P4 E2E1

E3 E6

P58 cm

4 cm

2 cm

8 cm

7 cm

1 2

Shaking direction

(a) Test 1

1cm



Shaking direction

Connecting rod

A0

A5

8 cm

4 cm

4 cm

25 cm 175 cm

32 cm

20 cm

8 cm

8 cm

1 2


P3

P1

P2

A4A3

A6

A2

A1

A7P4E2E1

E3 E6P6

E5E4P5

(b) Test 2










Test 1

Noise

30





Test 2

Noise

30







3 Results of Tests





1015840


1015840







00

03

00

03

0 200 400

00

01

P1

P5

Acc (

g)

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

minus01

Δ120590

998400u

Δ 120590

998400u

El-Centro wave 01 g

(a) 119886max = 01 g

00

05

10

00

05

10

0 200 400

00

04

P1

P5

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

minus04

El-Centro wave 04 g

Acc (

g)Δ

120590998400

uΔ

120590998400

u

(b) 119886max = 04 g






0 400 800

000

015

Acc (

g)

Time (s)

minus015

00

03

P3

0 400 800

Time (s)

Δ 120590

998400u

00

03

P4

0 400 800

Time (s)

Δ 120590

998400u


(a) 119886max = 015 g

00

05

10

00

05

10

0 400 800

00

05

P3

P4

Time (s)

0 400 800

Time (s)

0 400 800

Time (s)

minus05

El-Centro wave 05 g

Acc (

g)Δ

120590998400

uΔ

120590998400

u

(b) 119886max = 05 g






00

05

10

00

05

10

00

05

10

0 200 400

00

01

P3

P4

P6

Acc (

g)

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

minus01

Δ

El-Centro wave 01 g

120590998400

uΔ

120590998400

uΔ

120590998400

u

(a) 119886max = 01 g

00

05

10

00

05

10

00

05

10

0 200 400

00

04

P3

P4

P6

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

minus04

El-Centro wave 04 g

Acc (

g)Δ

120590998400

uΔ

120590998400

uΔ

120590998400

u

(b) 119886max = 04 g





0

3

6

0

0

3

6

3

0 50 100 150 200

0 50 100 150 200

000

E1 E4

E2 E5

Incr

emen

t of e

arth

pre

ssur

e (kN

)In

crem

ent o

f ear

th p

ress

ure (

kN)

Incr

emen

t of e

arth

pre

ssur

e (kN

)

E3 E6

Acc (

g)

Time (s)

Time (s)

0 50 100 150 200

Time (s)

0 50 100 150 200

Time (s)

minus3

minus3

minus6

minus015

015


(a) 119886max = 015 g

0

11

0

11

0

6

12

0 200 400 600 800

0 200 400 600 800

00

04

Time (s)

Time (s)

0 200 400 600 800

Time (s)

0 200 400 600 800

Time (s)

minus6

minus12

minus04

minus11

minus11

El-Centro wave 05g

E1 E4

E2 E5

E3 E6

Incr

emen

t of e

arth

pre

ssur

e (kN

)In

crem

ent o

f ear

th p

ress

ure (

kN)

Incr

emen

t of e

arth

pre

ssur

e (kN

)Ac

c (g)

(b) 119886max = 05 g



0

30

60

90

00

04

08

12

0 10 20 30 40 50 60 70 80 90 100

00

04

Disp

lace

men

t (m

m)

Displacement

P5

Acc (

g)

Time (s)

0 10 20 30 40 50 60 70 80 90 100

Time (s)

0 10 20 30 40 50 60 70 80 90 100

Time (s)

Start rising

Still rising

minus30

minus04

Δ

Taft wave 04 g

120590998400

u

(a) 119867119863 = 05

0

30

60

90

00

04

08

0 20 40 60 80 100

00

04

Stop rising

Disp

lace

men

t (m

m)

Displacement

Start rising

P5

Acc (

g)

Time (s)

0 20 40 60 80 100

Time (s)

0 20 40 60 80 100

Time (s)

minus30

minus04

Taft wave 04 g

Δ 120590

998400u

(b) 119867119863 = 2










0

5

4

8

00

02

04

06

10 20 30 40 50 60

00

01

Disp

lace

men

t (m

m)

Displacement

P

Acc (

g)

Time (s)

10 20 30 40 50 60

Time (s)

10 20 30 40 50 60

Time (s)

minus4

minus01

Δ

El-Centro wave 01 g

120590998400

u

(a) 119886max = 01 g

0

30

60

00

04

08

0 20 40 60 80 100

0 20 40 60 80 100

0

5

20 40 60 80 100

00

04

Disp

lace

men

t (m

m)

Displacement

P

Acc (

g)

Time (s)

Time (s)

Time (s)

Start rising

El-Centro wave 04 g

minus04

Δ 120590

998400u

(b) 119886max = 04 g



119879 + 119882119904+ int

1198632

minus1198632

(1199061) 119889119863 sdot 119871 + 119882

119901= int

1198632

minus1198632

(1199062) 119889119863 sdot 119871 + 119873

(1)





1and 119906



119875 = int

1198632

minus1198632

(1199062minus 1199061) 119889119863 sdot 119871 + 119873 minus 119882

119904 (2)



119875 = int

1198632

minus1198632

(1198902minus 1198901) 119889119863 sdot 119871 (3)





int

1198632

minus1198632

(1199062minus 1199061) 119889119863 sdot 119871 = 120588

119908119892119881pipe (4)


00

01

02

03

04

05

Different shaking

Δu

(P8

and P5

)

Test 1-EL 015 g

Test 1-EL 05 g

Test 2-EL 04 g

02minus

01minus

minus03

120590998400

Test 1-Taft 04 g

Test 2-Taft 04 g



1198791015840+ 1198821015840

119904+ int

1198632

minus1198632

(1199061015840

1) 119889119863 sdot 119871 + 119882

119901

= int

1198632

minus1198632

(1199061015840

2) 119889119863 sdot 119871 + 119873

1015840

(5)


Δ119879 = int

1198632

minus1198632


119904 (6)


1and Δ119906

2are excess


(Δ1199062minus Δ1199061)119889119863 sdot 119871 is









1= 120574sat119891(ℎ


is 1199061015840

2= 120574sat119891(ℎ


1015840

1and

1199061015840

2gives

int

1198632

minus1198632

(1199061015840

2minus 1199061015840

1) 119889119863 sdot 119871

= 120574sat sdot int1198632

minus1198632

[119891 (ℎ2) minus 119891 (ℎ

1)] 119889119863 sdot 119871 = 120574sat119881pipe

(7)





119865119904+ 11988210158401015840

119904+ int

1198632

minus1198632

11990610158401015840

1119889119863 sdot 119871 + 119882

119901

= int

1198632

minus1198632

11990610158401015840

2119889119863 sdot 119871 + 119873

10158401015840+ 119898119901119886

(8)



1 11990610158401015840

211988210158401015840

119904 and119873

10158401015840 are the same as 11990610158401 1199061015840

21198821015840

119904 and119873



1198632

minus1198632


lowast119873 (9)






119904and Δ

lowast119873 are



Time (s)

00

25

50Fo

rce (

kN) Shaking

EL 01g

minus25

0 10 20 30 40 50

(a)

0

Forc

e (kN

)

Shaking

EL 015 g

minus15

minus 45

minus30

0 10 20 30 40 50Time (s)

(b)

0 10 20 30 40 50

0

160

Shaking

Forc

e (kN

)

EL 05 g

minus 160

minus 320

Time (s)

(c)


0 20 40 60 80 100 120 140 160

02

06

05

09

08

00

01

03

04

07

10

HD = 05 HD = 2

EL-01 gZ-015 g

Z-01 g



Δ

ΔT

120590998400 (P5)

u


and excitation


119904

H

T + WS

u1

u2

2 Wp

N




119865119904= 119891119901[119863

119867times (

119867

119863+ 05)

2

] 1205901015840

119867119863119871 (10)

where 1205901015840





H

+

2 WP

f1(h

f2(h)

)

W998400s

u9984001

u9984002

f(h) is the

the burialdepth of

pipe surface

function of

T998400

N998400


0 20 40 60 80 100 120 140 160 180 200

0

100

200

300

Time (s)

Forc

e (kN

)

ΔTΔU

ΔP

sat minus w)Vpipe

minus100

minus200

minus300

(120574 120574




1205901015840

119867= 1205901015840

1198670minus Δ119906 (11)


H

Wpmpa

Fs

(decreased during

shaking)u9984009984001

u9984009984002N998400998400

W998400998400s






0

6

0 10 20 30 40 50

a(m

s)

a

minus6

minus12

Time (s)

(a)

0

2

4

6

0 10 20 30 40 50

aeff

aef

f(m

s2)

Time (s)

(b)

00

01

02

03

0 10 20 30 40 50

V

V

(ms

)

minus01

Time (s)

(c)

0 10 20 30 40 50

0

45

90

Disp

lace

men

t (m

m)


minus45

Time (s)

(d)


5 Conclusions







Acknowledgments


References
































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












1cm

Rigid container

DuxsealSpoke


Load cell


Connecting rod

25 cm 175 cm 20 cm

29 cm

A0

P3

P1

P2

E4

A4A3

A6

A2

A7 E6P5

A5

A1

P4 E2E1

E3 E6

P58 cm

4 cm

2 cm

8 cm

7 cm

1 2

Shaking direction

(a) Test 1

1cm



Shaking direction

Connecting rod

A0

A5

8 cm

4 cm

4 cm

25 cm 175 cm

32 cm

20 cm

8 cm

8 cm

1 2


P3

P1

P2

A4A3

A6

A2

A1

A7P4E2E1

E3 E6P6

E5E4P5

(b) Test 2










Test 1

Noise

30





Test 2

Noise

30







3 Results of Tests





1015840


1015840







00

03

00

03

0 200 400

00

01

P1

P5

Acc (

g)

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

minus01

Δ120590

998400u

Δ 120590

998400u

El-Centro wave 01 g

(a) 119886max = 01 g

00

05

10

00

05

10

0 200 400

00

04

P1

P5

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

minus04

El-Centro wave 04 g

Acc (

g)Δ

120590998400

uΔ

120590998400

u

(b) 119886max = 04 g






0 400 800

000

015

Acc (

g)

Time (s)

minus015

00

03

P3

0 400 800

Time (s)

Δ 120590

998400u

00

03

P4

0 400 800

Time (s)

Δ 120590

998400u


(a) 119886max = 015 g

00

05

10

00

05

10

0 400 800

00

05

P3

P4

Time (s)

0 400 800

Time (s)

0 400 800

Time (s)

minus05

El-Centro wave 05 g

Acc (

g)Δ

120590998400

uΔ

120590998400

u

(b) 119886max = 05 g






00

05

10

00

05

10

00

05

10

0 200 400

00

01

P3

P4

P6

Acc (

g)

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

minus01

Δ

El-Centro wave 01 g

120590998400

uΔ

120590998400

uΔ

120590998400

u

(a) 119886max = 01 g

00

05

10

00

05

10

00

05

10

0 200 400

00

04

P3

P4

P6

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

minus04

El-Centro wave 04 g

Acc (

g)Δ

120590998400

uΔ

120590998400

uΔ

120590998400

u

(b) 119886max = 04 g





0

3

6

0

0

3

6

3

0 50 100 150 200

0 50 100 150 200

000

E1 E4

E2 E5

Incr

emen

t of e

arth

pre

ssur

e (kN

)In

crem

ent o

f ear

th p

ress

ure (

kN)

Incr

emen

t of e

arth

pre

ssur

e (kN

)

E3 E6

Acc (

g)

Time (s)

Time (s)

0 50 100 150 200

Time (s)

0 50 100 150 200

Time (s)

minus3

minus3

minus6

minus015

015


(a) 119886max = 015 g

0

11

0

11

0

6

12

0 200 400 600 800

0 200 400 600 800

00

04

Time (s)

Time (s)

0 200 400 600 800

Time (s)

0 200 400 600 800

Time (s)

minus6

minus12

minus04

minus11

minus11

El-Centro wave 05g

E1 E4

E2 E5

E3 E6

Incr

emen

t of e

arth

pre

ssur

e (kN

)In

crem

ent o

f ear

th p

ress

ure (

kN)

Incr

emen

t of e

arth

pre

ssur

e (kN

)Ac

c (g)

(b) 119886max = 05 g



0

30

60

90

00

04

08

12

0 10 20 30 40 50 60 70 80 90 100

00

04

Disp

lace

men

t (m

m)

Displacement

P5

Acc (

g)

Time (s)

0 10 20 30 40 50 60 70 80 90 100

Time (s)

0 10 20 30 40 50 60 70 80 90 100

Time (s)

Start rising

Still rising

minus30

minus04

Δ

Taft wave 04 g

120590998400

u

(a) 119867119863 = 05

0

30

60

90

00

04

08

0 20 40 60 80 100

00

04

Stop rising

Disp

lace

men

t (m

m)

Displacement

Start rising

P5

Acc (

g)

Time (s)

0 20 40 60 80 100

Time (s)

0 20 40 60 80 100

Time (s)

minus30

minus04

Taft wave 04 g

Δ 120590

998400u

(b) 119867119863 = 2










0

5

4

8

00

02

04

06

10 20 30 40 50 60

00

01

Disp

lace

men

t (m

m)

Displacement

P

Acc (

g)

Time (s)

10 20 30 40 50 60

Time (s)

10 20 30 40 50 60

Time (s)

minus4

minus01

Δ

El-Centro wave 01 g

120590998400

u

(a) 119886max = 01 g

0

30

60

00

04

08

0 20 40 60 80 100

0 20 40 60 80 100

0

5

20 40 60 80 100

00

04

Disp

lace

men

t (m

m)

Displacement

P

Acc (

g)

Time (s)

Time (s)

Time (s)

Start rising

El-Centro wave 04 g

minus04

Δ 120590

998400u

(b) 119886max = 04 g



119879 + 119882119904+ int

1198632

minus1198632

(1199061) 119889119863 sdot 119871 + 119882

119901= int

1198632

minus1198632

(1199062) 119889119863 sdot 119871 + 119873

(1)





1and 119906



119875 = int

1198632

minus1198632

(1199062minus 1199061) 119889119863 sdot 119871 + 119873 minus 119882

119904 (2)



119875 = int

1198632

minus1198632

(1198902minus 1198901) 119889119863 sdot 119871 (3)





int

1198632

minus1198632

(1199062minus 1199061) 119889119863 sdot 119871 = 120588

119908119892119881pipe (4)


00

01

02

03

04

05

Different shaking

Δu

(P8

and P5

)

Test 1-EL 015 g

Test 1-EL 05 g

Test 2-EL 04 g

02minus

01minus

minus03

120590998400

Test 1-Taft 04 g

Test 2-Taft 04 g



1198791015840+ 1198821015840

119904+ int

1198632

minus1198632

(1199061015840

1) 119889119863 sdot 119871 + 119882

119901

= int

1198632

minus1198632

(1199061015840

2) 119889119863 sdot 119871 + 119873

1015840

(5)


Δ119879 = int

1198632

minus1198632


119904 (6)


1and Δ119906

2are excess


(Δ1199062minus Δ1199061)119889119863 sdot 119871 is









1= 120574sat119891(ℎ


is 1199061015840

2= 120574sat119891(ℎ


1015840

1and

1199061015840

2gives

int

1198632

minus1198632

(1199061015840

2minus 1199061015840

1) 119889119863 sdot 119871

= 120574sat sdot int1198632

minus1198632

[119891 (ℎ2) minus 119891 (ℎ

1)] 119889119863 sdot 119871 = 120574sat119881pipe

(7)





119865119904+ 11988210158401015840

119904+ int

1198632

minus1198632

11990610158401015840

1119889119863 sdot 119871 + 119882

119901

= int

1198632

minus1198632

11990610158401015840

2119889119863 sdot 119871 + 119873

10158401015840+ 119898119901119886

(8)



1 11990610158401015840

211988210158401015840

119904 and119873

10158401015840 are the same as 11990610158401 1199061015840

21198821015840

119904 and119873



1198632

minus1198632


lowast119873 (9)






119904and Δ

lowast119873 are



Time (s)

00

25

50Fo

rce (

kN) Shaking

EL 01g

minus25

0 10 20 30 40 50

(a)

0

Forc

e (kN

)

Shaking

EL 015 g

minus15

minus 45

minus30

0 10 20 30 40 50Time (s)

(b)

0 10 20 30 40 50

0

160

Shaking

Forc

e (kN

)

EL 05 g

minus 160

minus 320

Time (s)

(c)


0 20 40 60 80 100 120 140 160

02

06

05

09

08

00

01

03

04

07

10

HD = 05 HD = 2

EL-01 gZ-015 g

Z-01 g



Δ

ΔT

120590998400 (P5)

u


and excitation


119904

H

T + WS

u1

u2

2 Wp

N




119865119904= 119891119901[119863

119867times (

119867

119863+ 05)

2

] 1205901015840

119867119863119871 (10)

where 1205901015840





H

+

2 WP

f1(h

f2(h)

)

W998400s

u9984001

u9984002

f(h) is the

the burialdepth of

pipe surface

function of

T998400

N998400


0 20 40 60 80 100 120 140 160 180 200

0

100

200

300

Time (s)

Forc

e (kN

)

ΔTΔU

ΔP

sat minus w)Vpipe

minus100

minus200

minus300

(120574 120574




1205901015840

119867= 1205901015840

1198670minus Δ119906 (11)


H

Wpmpa

Fs

(decreased during

shaking)u9984009984001

u9984009984002N998400998400

W998400998400s






0

6

0 10 20 30 40 50

a(m

s)

a

minus6

minus12

Time (s)

(a)

0

2

4

6

0 10 20 30 40 50

aeff

aef

f(m

s2)

Time (s)

(b)

00

01

02

03

0 10 20 30 40 50

V

V

(ms

)

minus01

Time (s)

(c)

0 10 20 30 40 50

0

45

90

Disp

lace

men

t (m

m)


minus45

Time (s)

(d)


5 Conclusions







Acknowledgments


References
































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Test 1

Noise

30





Test 2

Noise

30







3 Results of Tests





1015840


1015840







00

03

00

03

0 200 400

00

01

P1

P5

Acc (

g)

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

minus01

Δ120590

998400u

Δ 120590

998400u

El-Centro wave 01 g

(a) 119886max = 01 g

00

05

10

00

05

10

0 200 400

00

04

P1

P5

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

minus04

El-Centro wave 04 g

Acc (

g)Δ

120590998400

uΔ

120590998400

u

(b) 119886max = 04 g






0 400 800

000

015

Acc (

g)

Time (s)

minus015

00

03

P3

0 400 800

Time (s)

Δ 120590

998400u

00

03

P4

0 400 800

Time (s)

Δ 120590

998400u


(a) 119886max = 015 g

00

05

10

00

05

10

0 400 800

00

05

P3

P4

Time (s)

0 400 800

Time (s)

0 400 800

Time (s)

minus05

El-Centro wave 05 g

Acc (

g)Δ

120590998400

uΔ

120590998400

u

(b) 119886max = 05 g






00

05

10

00

05

10

00

05

10

0 200 400

00

01

P3

P4

P6

Acc (

g)

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

minus01

Δ

El-Centro wave 01 g

120590998400

uΔ

120590998400

uΔ

120590998400

u

(a) 119886max = 01 g

00

05

10

00

05

10

00

05

10

0 200 400

00

04

P3

P4

P6

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

minus04

El-Centro wave 04 g

Acc (

g)Δ

120590998400

uΔ

120590998400

uΔ

120590998400

u

(b) 119886max = 04 g





0

3

6

0

0

3

6

3

0 50 100 150 200

0 50 100 150 200

000

E1 E4

E2 E5

Incr

emen

t of e

arth

pre

ssur

e (kN

)In

crem

ent o

f ear

th p

ress

ure (

kN)

Incr

emen

t of e

arth

pre

ssur

e (kN

)

E3 E6

Acc (

g)

Time (s)

Time (s)

0 50 100 150 200

Time (s)

0 50 100 150 200

Time (s)

minus3

minus3

minus6

minus015

015


(a) 119886max = 015 g

0

11

0

11

0

6

12

0 200 400 600 800

0 200 400 600 800

00

04

Time (s)

Time (s)

0 200 400 600 800

Time (s)

0 200 400 600 800

Time (s)

minus6

minus12

minus04

minus11

minus11

El-Centro wave 05g

E1 E4

E2 E5

E3 E6

Incr

emen

t of e

arth

pre

ssur

e (kN

)In

crem

ent o

f ear

th p

ress

ure (

kN)

Incr

emen

t of e

arth

pre

ssur

e (kN

)Ac

c (g)

(b) 119886max = 05 g



0

30

60

90

00

04

08

12

0 10 20 30 40 50 60 70 80 90 100

00

04

Disp

lace

men

t (m

m)

Displacement

P5

Acc (

g)

Time (s)

0 10 20 30 40 50 60 70 80 90 100

Time (s)

0 10 20 30 40 50 60 70 80 90 100

Time (s)

Start rising

Still rising

minus30

minus04

Δ

Taft wave 04 g

120590998400

u

(a) 119867119863 = 05

0

30

60

90

00

04

08

0 20 40 60 80 100

00

04

Stop rising

Disp

lace

men

t (m

m)

Displacement

Start rising

P5

Acc (

g)

Time (s)

0 20 40 60 80 100

Time (s)

0 20 40 60 80 100

Time (s)

minus30

minus04

Taft wave 04 g

Δ 120590

998400u

(b) 119867119863 = 2










0

5

4

8

00

02

04

06

10 20 30 40 50 60

00

01

Disp

lace

men

t (m

m)

Displacement

P

Acc (

g)

Time (s)

10 20 30 40 50 60

Time (s)

10 20 30 40 50 60

Time (s)

minus4

minus01

Δ

El-Centro wave 01 g

120590998400

u

(a) 119886max = 01 g

0

30

60

00

04

08

0 20 40 60 80 100

0 20 40 60 80 100

0

5

20 40 60 80 100

00

04

Disp

lace

men

t (m

m)

Displacement

P

Acc (

g)

Time (s)

Time (s)

Time (s)

Start rising

El-Centro wave 04 g

minus04

Δ 120590

998400u

(b) 119886max = 04 g



119879 + 119882119904+ int

1198632

minus1198632

(1199061) 119889119863 sdot 119871 + 119882

119901= int

1198632

minus1198632

(1199062) 119889119863 sdot 119871 + 119873

(1)





1and 119906



119875 = int

1198632

minus1198632

(1199062minus 1199061) 119889119863 sdot 119871 + 119873 minus 119882

119904 (2)



119875 = int

1198632

minus1198632

(1198902minus 1198901) 119889119863 sdot 119871 (3)





int

1198632

minus1198632

(1199062minus 1199061) 119889119863 sdot 119871 = 120588

119908119892119881pipe (4)


00

01

02

03

04

05

Different shaking

Δu

(P8

and P5

)

Test 1-EL 015 g

Test 1-EL 05 g

Test 2-EL 04 g

02minus

01minus

minus03

120590998400

Test 1-Taft 04 g

Test 2-Taft 04 g



1198791015840+ 1198821015840

119904+ int

1198632

minus1198632

(1199061015840

1) 119889119863 sdot 119871 + 119882

119901

= int

1198632

minus1198632

(1199061015840

2) 119889119863 sdot 119871 + 119873

1015840

(5)


Δ119879 = int

1198632

minus1198632


119904 (6)


1and Δ119906

2are excess


(Δ1199062minus Δ1199061)119889119863 sdot 119871 is









1= 120574sat119891(ℎ


is 1199061015840

2= 120574sat119891(ℎ


1015840

1and

1199061015840

2gives

int

1198632

minus1198632

(1199061015840

2minus 1199061015840

1) 119889119863 sdot 119871

= 120574sat sdot int1198632

minus1198632

[119891 (ℎ2) minus 119891 (ℎ

1)] 119889119863 sdot 119871 = 120574sat119881pipe

(7)





119865119904+ 11988210158401015840

119904+ int

1198632

minus1198632

11990610158401015840

1119889119863 sdot 119871 + 119882

119901

= int

1198632

minus1198632

11990610158401015840

2119889119863 sdot 119871 + 119873

10158401015840+ 119898119901119886

(8)



1 11990610158401015840

211988210158401015840

119904 and119873

10158401015840 are the same as 11990610158401 1199061015840

21198821015840

119904 and119873



1198632

minus1198632


lowast119873 (9)






119904and Δ

lowast119873 are



Time (s)

00

25

50Fo

rce (

kN) Shaking

EL 01g

minus25

0 10 20 30 40 50

(a)

0

Forc

e (kN

)

Shaking

EL 015 g

minus15

minus 45

minus30

0 10 20 30 40 50Time (s)

(b)

0 10 20 30 40 50

0

160

Shaking

Forc

e (kN

)

EL 05 g

minus 160

minus 320

Time (s)

(c)


0 20 40 60 80 100 120 140 160

02

06

05

09

08

00

01

03

04

07

10

HD = 05 HD = 2

EL-01 gZ-015 g

Z-01 g



Δ

ΔT

120590998400 (P5)

u


and excitation


119904

H

T + WS

u1

u2

2 Wp

N




119865119904= 119891119901[119863

119867times (

119867

119863+ 05)

2

] 1205901015840

119867119863119871 (10)

where 1205901015840





H

+

2 WP

f1(h

f2(h)

)

W998400s

u9984001

u9984002

f(h) is the

the burialdepth of

pipe surface

function of

T998400

N998400


0 20 40 60 80 100 120 140 160 180 200

0

100

200

300

Time (s)

Forc

e (kN

)

ΔTΔU

ΔP

sat minus w)Vpipe

minus100

minus200

minus300

(120574 120574




1205901015840

119867= 1205901015840

1198670minus Δ119906 (11)


H

Wpmpa

Fs

(decreased during

shaking)u9984009984001

u9984009984002N998400998400

W998400998400s






0

6

0 10 20 30 40 50

a(m

s)

a

minus6

minus12

Time (s)

(a)

0

2

4

6

0 10 20 30 40 50

aeff

aef

f(m

s2)

Time (s)

(b)

00

01

02

03

0 10 20 30 40 50

V

V

(ms

)

minus01

Time (s)

(c)

0 10 20 30 40 50

0

45

90

Disp

lace

men

t (m

m)


minus45

Time (s)

(d)


5 Conclusions







Acknowledgments


References
































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










00

03

00

03

0 200 400

00

01

P1

P5

Acc (

g)

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

minus01

Δ120590

998400u

Δ 120590

998400u

El-Centro wave 01 g

(a) 119886max = 01 g

00

05

10

00

05

10

0 200 400

00

04

P1

P5

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

minus04

El-Centro wave 04 g

Acc (

g)Δ

120590998400

uΔ

120590998400

u

(b) 119886max = 04 g






0 400 800

000

015

Acc (

g)

Time (s)

minus015

00

03

P3

0 400 800

Time (s)

Δ 120590

998400u

00

03

P4

0 400 800

Time (s)

Δ 120590

998400u


(a) 119886max = 015 g

00

05

10

00

05

10

0 400 800

00

05

P3

P4

Time (s)

0 400 800

Time (s)

0 400 800

Time (s)

minus05

El-Centro wave 05 g

Acc (

g)Δ

120590998400

uΔ

120590998400

u

(b) 119886max = 05 g






00

05

10

00

05

10

00

05

10

0 200 400

00

01

P3

P4

P6

Acc (

g)

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

minus01

Δ

El-Centro wave 01 g

120590998400

uΔ

120590998400

uΔ

120590998400

u

(a) 119886max = 01 g

00

05

10

00

05

10

00

05

10

0 200 400

00

04

P3

P4

P6

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

minus04

El-Centro wave 04 g

Acc (

g)Δ

120590998400

uΔ

120590998400

uΔ

120590998400

u

(b) 119886max = 04 g





0

3

6

0

0

3

6

3

0 50 100 150 200

0 50 100 150 200

000

E1 E4

E2 E5

Incr

emen

t of e

arth

pre

ssur

e (kN

)In

crem

ent o

f ear

th p

ress

ure (

kN)

Incr

emen

t of e

arth

pre

ssur

e (kN

)

E3 E6

Acc (

g)

Time (s)

Time (s)

0 50 100 150 200

Time (s)

0 50 100 150 200

Time (s)

minus3

minus3

minus6

minus015

015


(a) 119886max = 015 g

0

11

0

11

0

6

12

0 200 400 600 800

0 200 400 600 800

00

04

Time (s)

Time (s)

0 200 400 600 800

Time (s)

0 200 400 600 800

Time (s)

minus6

minus12

minus04

minus11

minus11

El-Centro wave 05g

E1 E4

E2 E5

E3 E6

Incr

emen

t of e

arth

pre

ssur

e (kN

)In

crem

ent o

f ear

th p

ress

ure (

kN)

Incr

emen

t of e

arth

pre

ssur

e (kN

)Ac

c (g)

(b) 119886max = 05 g



0

30

60

90

00

04

08

12

0 10 20 30 40 50 60 70 80 90 100

00

04

Disp

lace

men

t (m

m)

Displacement

P5

Acc (

g)

Time (s)

0 10 20 30 40 50 60 70 80 90 100

Time (s)

0 10 20 30 40 50 60 70 80 90 100

Time (s)

Start rising

Still rising

minus30

minus04

Δ

Taft wave 04 g

120590998400

u

(a) 119867119863 = 05

0

30

60

90

00

04

08

0 20 40 60 80 100

00

04

Stop rising

Disp

lace

men

t (m

m)

Displacement

Start rising

P5

Acc (

g)

Time (s)

0 20 40 60 80 100

Time (s)

0 20 40 60 80 100

Time (s)

minus30

minus04

Taft wave 04 g

Δ 120590

998400u

(b) 119867119863 = 2










0

5

4

8

00

02

04

06

10 20 30 40 50 60

00

01

Disp

lace

men

t (m

m)

Displacement

P

Acc (

g)

Time (s)

10 20 30 40 50 60

Time (s)

10 20 30 40 50 60

Time (s)

minus4

minus01

Δ

El-Centro wave 01 g

120590998400

u

(a) 119886max = 01 g

0

30

60

00

04

08

0 20 40 60 80 100

0 20 40 60 80 100

0

5

20 40 60 80 100

00

04

Disp

lace

men

t (m

m)

Displacement

P

Acc (

g)

Time (s)

Time (s)

Time (s)

Start rising

El-Centro wave 04 g

minus04

Δ 120590

998400u

(b) 119886max = 04 g



119879 + 119882119904+ int

1198632

minus1198632

(1199061) 119889119863 sdot 119871 + 119882

119901= int

1198632

minus1198632

(1199062) 119889119863 sdot 119871 + 119873

(1)





1and 119906



119875 = int

1198632

minus1198632

(1199062minus 1199061) 119889119863 sdot 119871 + 119873 minus 119882

119904 (2)



119875 = int

1198632

minus1198632

(1198902minus 1198901) 119889119863 sdot 119871 (3)





int

1198632

minus1198632

(1199062minus 1199061) 119889119863 sdot 119871 = 120588

119908119892119881pipe (4)


00

01

02

03

04

05

Different shaking

Δu

(P8

and P5

)

Test 1-EL 015 g

Test 1-EL 05 g

Test 2-EL 04 g

02minus

01minus

minus03

120590998400

Test 1-Taft 04 g

Test 2-Taft 04 g



1198791015840+ 1198821015840

119904+ int

1198632

minus1198632

(1199061015840

1) 119889119863 sdot 119871 + 119882

119901

= int

1198632

minus1198632

(1199061015840

2) 119889119863 sdot 119871 + 119873

1015840

(5)


Δ119879 = int

1198632

minus1198632


119904 (6)


1and Δ119906

2are excess


(Δ1199062minus Δ1199061)119889119863 sdot 119871 is









1= 120574sat119891(ℎ


is 1199061015840

2= 120574sat119891(ℎ


1015840

1and

1199061015840

2gives

int

1198632

minus1198632

(1199061015840

2minus 1199061015840

1) 119889119863 sdot 119871

= 120574sat sdot int1198632

minus1198632

[119891 (ℎ2) minus 119891 (ℎ

1)] 119889119863 sdot 119871 = 120574sat119881pipe

(7)





119865119904+ 11988210158401015840

119904+ int

1198632

minus1198632

11990610158401015840

1119889119863 sdot 119871 + 119882

119901

= int

1198632

minus1198632

11990610158401015840

2119889119863 sdot 119871 + 119873

10158401015840+ 119898119901119886

(8)



1 11990610158401015840

211988210158401015840

119904 and119873

10158401015840 are the same as 11990610158401 1199061015840

21198821015840

119904 and119873



1198632

minus1198632


lowast119873 (9)






119904and Δ

lowast119873 are



Time (s)

00

25

50Fo

rce (

kN) Shaking

EL 01g

minus25

0 10 20 30 40 50

(a)

0

Forc

e (kN

)

Shaking

EL 015 g

minus15

minus 45

minus30

0 10 20 30 40 50Time (s)

(b)

0 10 20 30 40 50

0

160

Shaking

Forc

e (kN

)

EL 05 g

minus 160

minus 320

Time (s)

(c)


0 20 40 60 80 100 120 140 160

02

06

05

09

08

00

01

03

04

07

10

HD = 05 HD = 2

EL-01 gZ-015 g

Z-01 g



Δ

ΔT

120590998400 (P5)

u


and excitation


119904

H

T + WS

u1

u2

2 Wp

N




119865119904= 119891119901[119863

119867times (

119867

119863+ 05)

2

] 1205901015840

119867119863119871 (10)

where 1205901015840





H

+

2 WP

f1(h

f2(h)

)

W998400s

u9984001

u9984002

f(h) is the

the burialdepth of

pipe surface

function of

T998400

N998400


0 20 40 60 80 100 120 140 160 180 200

0

100

200

300

Time (s)

Forc

e (kN

)

ΔTΔU

ΔP

sat minus w)Vpipe

minus100

minus200

minus300

(120574 120574




1205901015840

119867= 1205901015840

1198670minus Δ119906 (11)


H

Wpmpa

Fs

(decreased during

shaking)u9984009984001

u9984009984002N998400998400

W998400998400s






0

6

0 10 20 30 40 50

a(m

s)

a

minus6

minus12

Time (s)

(a)

0

2

4

6

0 10 20 30 40 50

aeff

aef

f(m

s2)

Time (s)

(b)

00

01

02

03

0 10 20 30 40 50

V

V

(ms

)

minus01

Time (s)

(c)

0 10 20 30 40 50

0

45

90

Disp

lace

men

t (m

m)


minus45

Time (s)

(d)


5 Conclusions







Acknowledgments


References
































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 400 800

000

015

Acc (

g)

Time (s)

minus015

00

03

P3

0 400 800

Time (s)

Δ 120590

998400u

00

03

P4

0 400 800

Time (s)

Δ 120590

998400u


(a) 119886max = 015 g

00

05

10

00

05

10

0 400 800

00

05

P3

P4

Time (s)

0 400 800

Time (s)

0 400 800

Time (s)

minus05

El-Centro wave 05 g

Acc (

g)Δ

120590998400

uΔ

120590998400

u

(b) 119886max = 05 g






00

05

10

00

05

10

00

05

10

0 200 400

00

01

P3

P4

P6

Acc (

g)

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

minus01

Δ

El-Centro wave 01 g

120590998400

uΔ

120590998400

uΔ

120590998400

u

(a) 119886max = 01 g

00

05

10

00

05

10

00

05

10

0 200 400

00

04

P3

P4

P6

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

minus04

El-Centro wave 04 g

Acc (

g)Δ

120590998400

uΔ

120590998400

uΔ

120590998400

u

(b) 119886max = 04 g





0

3

6

0

0

3

6

3

0 50 100 150 200

0 50 100 150 200

000

E1 E4

E2 E5

Incr

emen

t of e

arth

pre

ssur

e (kN

)In

crem

ent o

f ear

th p

ress

ure (

kN)

Incr

emen

t of e

arth

pre

ssur

e (kN

)

E3 E6

Acc (

g)

Time (s)

Time (s)

0 50 100 150 200

Time (s)

0 50 100 150 200

Time (s)

minus3

minus3

minus6

minus015

015


(a) 119886max = 015 g

0

11

0

11

0

6

12

0 200 400 600 800

0 200 400 600 800

00

04

Time (s)

Time (s)

0 200 400 600 800

Time (s)

0 200 400 600 800

Time (s)

minus6

minus12

minus04

minus11

minus11

El-Centro wave 05g

E1 E4

E2 E5

E3 E6

Incr

emen

t of e

arth

pre

ssur

e (kN

)In

crem

ent o

f ear

th p

ress

ure (

kN)

Incr

emen

t of e

arth

pre

ssur

e (kN

)Ac

c (g)

(b) 119886max = 05 g



0

30

60

90

00

04

08

12

0 10 20 30 40 50 60 70 80 90 100

00

04

Disp

lace

men

t (m

m)

Displacement

P5

Acc (

g)

Time (s)

0 10 20 30 40 50 60 70 80 90 100

Time (s)

0 10 20 30 40 50 60 70 80 90 100

Time (s)

Start rising

Still rising

minus30

minus04

Δ

Taft wave 04 g

120590998400

u

(a) 119867119863 = 05

0

30

60

90

00

04

08

0 20 40 60 80 100

00

04

Stop rising

Disp

lace

men

t (m

m)

Displacement

Start rising

P5

Acc (

g)

Time (s)

0 20 40 60 80 100

Time (s)

0 20 40 60 80 100

Time (s)

minus30

minus04

Taft wave 04 g

Δ 120590

998400u

(b) 119867119863 = 2










0

5

4

8

00

02

04

06

10 20 30 40 50 60

00

01

Disp

lace

men

t (m

m)

Displacement

P

Acc (

g)

Time (s)

10 20 30 40 50 60

Time (s)

10 20 30 40 50 60

Time (s)

minus4

minus01

Δ

El-Centro wave 01 g

120590998400

u

(a) 119886max = 01 g

0

30

60

00

04

08

0 20 40 60 80 100

0 20 40 60 80 100

0

5

20 40 60 80 100

00

04

Disp

lace

men

t (m

m)

Displacement

P

Acc (

g)

Time (s)

Time (s)

Time (s)

Start rising

El-Centro wave 04 g

minus04

Δ 120590

998400u

(b) 119886max = 04 g



119879 + 119882119904+ int

1198632

minus1198632

(1199061) 119889119863 sdot 119871 + 119882

119901= int

1198632

minus1198632

(1199062) 119889119863 sdot 119871 + 119873

(1)





1and 119906



119875 = int

1198632

minus1198632

(1199062minus 1199061) 119889119863 sdot 119871 + 119873 minus 119882

119904 (2)



119875 = int

1198632

minus1198632

(1198902minus 1198901) 119889119863 sdot 119871 (3)





int

1198632

minus1198632

(1199062minus 1199061) 119889119863 sdot 119871 = 120588

119908119892119881pipe (4)


00

01

02

03

04

05

Different shaking

Δu

(P8

and P5

)

Test 1-EL 015 g

Test 1-EL 05 g

Test 2-EL 04 g

02minus

01minus

minus03

120590998400

Test 1-Taft 04 g

Test 2-Taft 04 g



1198791015840+ 1198821015840

119904+ int

1198632

minus1198632

(1199061015840

1) 119889119863 sdot 119871 + 119882

119901

= int

1198632

minus1198632

(1199061015840

2) 119889119863 sdot 119871 + 119873

1015840

(5)


Δ119879 = int

1198632

minus1198632


119904 (6)


1and Δ119906

2are excess


(Δ1199062minus Δ1199061)119889119863 sdot 119871 is









1= 120574sat119891(ℎ


is 1199061015840

2= 120574sat119891(ℎ


1015840

1and

1199061015840

2gives

int

1198632

minus1198632

(1199061015840

2minus 1199061015840

1) 119889119863 sdot 119871

= 120574sat sdot int1198632

minus1198632

[119891 (ℎ2) minus 119891 (ℎ

1)] 119889119863 sdot 119871 = 120574sat119881pipe

(7)





119865119904+ 11988210158401015840

119904+ int

1198632

minus1198632

11990610158401015840

1119889119863 sdot 119871 + 119882

119901

= int

1198632

minus1198632

11990610158401015840

2119889119863 sdot 119871 + 119873

10158401015840+ 119898119901119886

(8)



1 11990610158401015840

211988210158401015840

119904 and119873

10158401015840 are the same as 11990610158401 1199061015840

21198821015840

119904 and119873



1198632

minus1198632


lowast119873 (9)






119904and Δ

lowast119873 are



Time (s)

00

25

50Fo

rce (

kN) Shaking

EL 01g

minus25

0 10 20 30 40 50

(a)

0

Forc

e (kN

)

Shaking

EL 015 g

minus15

minus 45

minus30

0 10 20 30 40 50Time (s)

(b)

0 10 20 30 40 50

0

160

Shaking

Forc

e (kN

)

EL 05 g

minus 160

minus 320

Time (s)

(c)


0 20 40 60 80 100 120 140 160

02

06

05

09

08

00

01

03

04

07

10

HD = 05 HD = 2

EL-01 gZ-015 g

Z-01 g



Δ

ΔT

120590998400 (P5)

u


and excitation


119904

H

T + WS

u1

u2

2 Wp

N




119865119904= 119891119901[119863

119867times (

119867

119863+ 05)

2

] 1205901015840

119867119863119871 (10)

where 1205901015840





H

+

2 WP

f1(h

f2(h)

)

W998400s

u9984001

u9984002

f(h) is the

the burialdepth of

pipe surface

function of

T998400

N998400


0 20 40 60 80 100 120 140 160 180 200

0

100

200

300

Time (s)

Forc

e (kN

)

ΔTΔU

ΔP

sat minus w)Vpipe

minus100

minus200

minus300

(120574 120574




1205901015840

119867= 1205901015840

1198670minus Δ119906 (11)


H

Wpmpa

Fs

(decreased during

shaking)u9984009984001

u9984009984002N998400998400

W998400998400s






0

6

0 10 20 30 40 50

a(m

s)

a

minus6

minus12

Time (s)

(a)

0

2

4

6

0 10 20 30 40 50

aeff

aef

f(m

s2)

Time (s)

(b)

00

01

02

03

0 10 20 30 40 50

V

V

(ms

)

minus01

Time (s)

(c)

0 10 20 30 40 50

0

45

90

Disp

lace

men

t (m

m)


minus45

Time (s)

(d)


5 Conclusions







Acknowledgments


References
































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










00

05

10

00

05

10

00

05

10

0 200 400

00

01

P3

P4

P6

Acc (

g)

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

minus01

Δ

El-Centro wave 01 g

120590998400

uΔ

120590998400

uΔ

120590998400

u

(a) 119886max = 01 g

00

05

10

00

05

10

00

05

10

0 200 400

00

04

P3

P4

P6

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

0 200 400

Time (s)

minus04

El-Centro wave 04 g

Acc (

g)Δ

120590998400

uΔ

120590998400

uΔ

120590998400

u

(b) 119886max = 04 g





0

3

6

0

0

3

6

3

0 50 100 150 200

0 50 100 150 200

000

E1 E4

E2 E5

Incr

emen

t of e

arth

pre

ssur

e (kN

)In

crem

ent o

f ear

th p

ress

ure (

kN)

Incr

emen

t of e

arth

pre

ssur

e (kN

)

E3 E6

Acc (

g)

Time (s)

Time (s)

0 50 100 150 200

Time (s)

0 50 100 150 200

Time (s)

minus3

minus3

minus6

minus015

015


(a) 119886max = 015 g

0

11

0

11

0

6

12

0 200 400 600 800

0 200 400 600 800

00

04

Time (s)

Time (s)

0 200 400 600 800

Time (s)

0 200 400 600 800

Time (s)

minus6

minus12

minus04

minus11

minus11

El-Centro wave 05g

E1 E4

E2 E5

E3 E6

Incr

emen

t of e

arth

pre

ssur

e (kN

)In

crem

ent o

f ear

th p

ress

ure (

kN)

Incr

emen

t of e

arth

pre

ssur

e (kN

)Ac

c (g)

(b) 119886max = 05 g



0

30

60

90

00

04

08

12

0 10 20 30 40 50 60 70 80 90 100

00

04

Disp

lace

men

t (m

m)

Displacement

P5

Acc (

g)

Time (s)

0 10 20 30 40 50 60 70 80 90 100

Time (s)

0 10 20 30 40 50 60 70 80 90 100

Time (s)

Start rising

Still rising

minus30

minus04

Δ

Taft wave 04 g

120590998400

u

(a) 119867119863 = 05

0

30

60

90

00

04

08

0 20 40 60 80 100

00

04

Stop rising

Disp

lace

men

t (m

m)

Displacement

Start rising

P5

Acc (

g)

Time (s)

0 20 40 60 80 100

Time (s)

0 20 40 60 80 100

Time (s)

minus30

minus04

Taft wave 04 g

Δ 120590

998400u

(b) 119867119863 = 2










0

5

4

8

00

02

04

06

10 20 30 40 50 60

00

01

Disp

lace

men

t (m

m)

Displacement

P

Acc (

g)

Time (s)

10 20 30 40 50 60

Time (s)

10 20 30 40 50 60

Time (s)

minus4

minus01

Δ

El-Centro wave 01 g

120590998400

u

(a) 119886max = 01 g

0

30

60

00

04

08

0 20 40 60 80 100

0 20 40 60 80 100

0

5

20 40 60 80 100

00

04

Disp

lace

men

t (m

m)

Displacement

P

Acc (

g)

Time (s)

Time (s)

Time (s)

Start rising

El-Centro wave 04 g

minus04

Δ 120590

998400u

(b) 119886max = 04 g



119879 + 119882119904+ int

1198632

minus1198632

(1199061) 119889119863 sdot 119871 + 119882

119901= int

1198632

minus1198632

(1199062) 119889119863 sdot 119871 + 119873

(1)





1and 119906



119875 = int

1198632

minus1198632

(1199062minus 1199061) 119889119863 sdot 119871 + 119873 minus 119882

119904 (2)



119875 = int

1198632

minus1198632

(1198902minus 1198901) 119889119863 sdot 119871 (3)





int

1198632

minus1198632

(1199062minus 1199061) 119889119863 sdot 119871 = 120588

119908119892119881pipe (4)


00

01

02

03

04

05

Different shaking

Δu

(P8

and P5

)

Test 1-EL 015 g

Test 1-EL 05 g

Test 2-EL 04 g

02minus

01minus

minus03

120590998400

Test 1-Taft 04 g

Test 2-Taft 04 g



1198791015840+ 1198821015840

119904+ int

1198632

minus1198632

(1199061015840

1) 119889119863 sdot 119871 + 119882

119901

= int

1198632

minus1198632

(1199061015840

2) 119889119863 sdot 119871 + 119873

1015840

(5)


Δ119879 = int

1198632

minus1198632


119904 (6)


1and Δ119906

2are excess


(Δ1199062minus Δ1199061)119889119863 sdot 119871 is









1= 120574sat119891(ℎ


is 1199061015840

2= 120574sat119891(ℎ


1015840

1and

1199061015840

2gives

int

1198632

minus1198632

(1199061015840

2minus 1199061015840

1) 119889119863 sdot 119871

= 120574sat sdot int1198632

minus1198632

[119891 (ℎ2) minus 119891 (ℎ

1)] 119889119863 sdot 119871 = 120574sat119881pipe

(7)





119865119904+ 11988210158401015840

119904+ int

1198632

minus1198632

11990610158401015840

1119889119863 sdot 119871 + 119882

119901

= int

1198632

minus1198632

11990610158401015840

2119889119863 sdot 119871 + 119873

10158401015840+ 119898119901119886

(8)



1 11990610158401015840

211988210158401015840

119904 and119873

10158401015840 are the same as 11990610158401 1199061015840

21198821015840

119904 and119873



1198632

minus1198632


lowast119873 (9)






119904and Δ

lowast119873 are



Time (s)

00

25

50Fo

rce (

kN) Shaking

EL 01g

minus25

0 10 20 30 40 50

(a)

0

Forc

e (kN

)

Shaking

EL 015 g

minus15

minus 45

minus30

0 10 20 30 40 50Time (s)

(b)

0 10 20 30 40 50

0

160

Shaking

Forc

e (kN

)

EL 05 g

minus 160

minus 320

Time (s)

(c)


0 20 40 60 80 100 120 140 160

02

06

05

09

08

00

01

03

04

07

10

HD = 05 HD = 2

EL-01 gZ-015 g

Z-01 g



Δ

ΔT

120590998400 (P5)

u


and excitation


119904

H

T + WS

u1

u2

2 Wp

N




119865119904= 119891119901[119863

119867times (

119867

119863+ 05)

2

] 1205901015840

119867119863119871 (10)

where 1205901015840





H

+

2 WP

f1(h

f2(h)

)

W998400s

u9984001

u9984002

f(h) is the

the burialdepth of

pipe surface

function of

T998400

N998400


0 20 40 60 80 100 120 140 160 180 200

0

100

200

300

Time (s)

Forc

e (kN

)

ΔTΔU

ΔP

sat minus w)Vpipe

minus100

minus200

minus300

(120574 120574




1205901015840

119867= 1205901015840

1198670minus Δ119906 (11)


H

Wpmpa

Fs

(decreased during

shaking)u9984009984001

u9984009984002N998400998400

W998400998400s






0

6

0 10 20 30 40 50

a(m

s)

a

minus6

minus12

Time (s)

(a)

0

2

4

6

0 10 20 30 40 50

aeff

aef

f(m

s2)

Time (s)

(b)

00

01

02

03

0 10 20 30 40 50

V

V

(ms

)

minus01

Time (s)

(c)

0 10 20 30 40 50

0

45

90

Disp

lace

men

t (m

m)


minus45

Time (s)

(d)


5 Conclusions







Acknowledgments


References
































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

3

6

0

0

3

6

3

0 50 100 150 200

0 50 100 150 200

000

E1 E4

E2 E5

Incr

emen

t of e

arth

pre

ssur

e (kN

)In

crem

ent o

f ear

th p

ress

ure (

kN)

Incr

emen

t of e

arth

pre

ssur

e (kN

)

E3 E6

Acc (

g)

Time (s)

Time (s)

0 50 100 150 200

Time (s)

0 50 100 150 200

Time (s)

minus3

minus3

minus6

minus015

015


(a) 119886max = 015 g

0

11

0

11

0

6

12

0 200 400 600 800

0 200 400 600 800

00

04

Time (s)

Time (s)

0 200 400 600 800

Time (s)

0 200 400 600 800

Time (s)

minus6

minus12

minus04

minus11

minus11

El-Centro wave 05g

E1 E4

E2 E5

E3 E6

Incr

emen

t of e

arth

pre

ssur

e (kN

)In

crem

ent o

f ear

th p

ress

ure (

kN)

Incr

emen

t of e

arth

pre

ssur

e (kN

)Ac

c (g)

(b) 119886max = 05 g



0

30

60

90

00

04

08

12

0 10 20 30 40 50 60 70 80 90 100

00

04

Disp

lace

men

t (m

m)

Displacement

P5

Acc (

g)

Time (s)

0 10 20 30 40 50 60 70 80 90 100

Time (s)

0 10 20 30 40 50 60 70 80 90 100

Time (s)

Start rising

Still rising

minus30

minus04

Δ

Taft wave 04 g

120590998400

u

(a) 119867119863 = 05

0

30

60

90

00

04

08

0 20 40 60 80 100

00

04

Stop rising

Disp

lace

men

t (m

m)

Displacement

Start rising

P5

Acc (

g)

Time (s)

0 20 40 60 80 100

Time (s)

0 20 40 60 80 100

Time (s)

minus30

minus04

Taft wave 04 g

Δ 120590

998400u

(b) 119867119863 = 2










0

5

4

8

00

02

04

06

10 20 30 40 50 60

00

01

Disp

lace

men

t (m

m)

Displacement

P

Acc (

g)

Time (s)

10 20 30 40 50 60

Time (s)

10 20 30 40 50 60

Time (s)

minus4

minus01

Δ

El-Centro wave 01 g

120590998400

u

(a) 119886max = 01 g

0

30

60

00

04

08

0 20 40 60 80 100

0 20 40 60 80 100

0

5

20 40 60 80 100

00

04

Disp

lace

men

t (m

m)

Displacement

P

Acc (

g)

Time (s)

Time (s)

Time (s)

Start rising

El-Centro wave 04 g

minus04

Δ 120590

998400u

(b) 119886max = 04 g



119879 + 119882119904+ int

1198632

minus1198632

(1199061) 119889119863 sdot 119871 + 119882

119901= int

1198632

minus1198632

(1199062) 119889119863 sdot 119871 + 119873

(1)





1and 119906



119875 = int

1198632

minus1198632

(1199062minus 1199061) 119889119863 sdot 119871 + 119873 minus 119882

119904 (2)



119875 = int

1198632

minus1198632

(1198902minus 1198901) 119889119863 sdot 119871 (3)





int

1198632

minus1198632

(1199062minus 1199061) 119889119863 sdot 119871 = 120588

119908119892119881pipe (4)


00

01

02

03

04

05

Different shaking

Δu

(P8

and P5

)

Test 1-EL 015 g

Test 1-EL 05 g

Test 2-EL 04 g

02minus

01minus

minus03

120590998400

Test 1-Taft 04 g

Test 2-Taft 04 g



1198791015840+ 1198821015840

119904+ int

1198632

minus1198632

(1199061015840

1) 119889119863 sdot 119871 + 119882

119901

= int

1198632

minus1198632

(1199061015840

2) 119889119863 sdot 119871 + 119873

1015840

(5)


Δ119879 = int

1198632

minus1198632


119904 (6)


1and Δ119906

2are excess


(Δ1199062minus Δ1199061)119889119863 sdot 119871 is









1= 120574sat119891(ℎ


is 1199061015840

2= 120574sat119891(ℎ


1015840

1and

1199061015840

2gives

int

1198632

minus1198632

(1199061015840

2minus 1199061015840

1) 119889119863 sdot 119871

= 120574sat sdot int1198632

minus1198632

[119891 (ℎ2) minus 119891 (ℎ

1)] 119889119863 sdot 119871 = 120574sat119881pipe

(7)





119865119904+ 11988210158401015840

119904+ int

1198632

minus1198632

11990610158401015840

1119889119863 sdot 119871 + 119882

119901

= int

1198632

minus1198632

11990610158401015840

2119889119863 sdot 119871 + 119873

10158401015840+ 119898119901119886

(8)



1 11990610158401015840

211988210158401015840

119904 and119873

10158401015840 are the same as 11990610158401 1199061015840

21198821015840

119904 and119873



1198632

minus1198632


lowast119873 (9)






119904and Δ

lowast119873 are



Time (s)

00

25

50Fo

rce (

kN) Shaking

EL 01g

minus25

0 10 20 30 40 50

(a)

0

Forc

e (kN

)

Shaking

EL 015 g

minus15

minus 45

minus30

0 10 20 30 40 50Time (s)

(b)

0 10 20 30 40 50

0

160

Shaking

Forc

e (kN

)

EL 05 g

minus 160

minus 320

Time (s)

(c)


0 20 40 60 80 100 120 140 160

02

06

05

09

08

00

01

03

04

07

10

HD = 05 HD = 2

EL-01 gZ-015 g

Z-01 g



Δ

ΔT

120590998400 (P5)

u


and excitation


119904

H

T + WS

u1

u2

2 Wp

N




119865119904= 119891119901[119863

119867times (

119867

119863+ 05)

2

] 1205901015840

119867119863119871 (10)

where 1205901015840





H

+

2 WP

f1(h

f2(h)

)

W998400s

u9984001

u9984002

f(h) is the

the burialdepth of

pipe surface

function of

T998400

N998400


0 20 40 60 80 100 120 140 160 180 200

0

100

200

300

Time (s)

Forc

e (kN

)

ΔTΔU

ΔP

sat minus w)Vpipe

minus100

minus200

minus300

(120574 120574




1205901015840

119867= 1205901015840

1198670minus Δ119906 (11)


H

Wpmpa

Fs

(decreased during

shaking)u9984009984001

u9984009984002N998400998400

W998400998400s






0

6

0 10 20 30 40 50

a(m

s)

a

minus6

minus12

Time (s)

(a)

0

2

4

6

0 10 20 30 40 50

aeff

aef

f(m

s2)

Time (s)

(b)

00

01

02

03

0 10 20 30 40 50

V

V

(ms

)

minus01

Time (s)

(c)

0 10 20 30 40 50

0

45

90

Disp

lace

men

t (m

m)


minus45

Time (s)

(d)


5 Conclusions







Acknowledgments


References
































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

30

60

90

00

04

08

12

0 10 20 30 40 50 60 70 80 90 100

00

04

Disp

lace

men

t (m

m)

Displacement

P5

Acc (

g)

Time (s)

0 10 20 30 40 50 60 70 80 90 100

Time (s)

0 10 20 30 40 50 60 70 80 90 100

Time (s)

Start rising

Still rising

minus30

minus04

Δ

Taft wave 04 g

120590998400

u

(a) 119867119863 = 05

0

30

60

90

00

04

08

0 20 40 60 80 100

00

04

Stop rising

Disp

lace

men

t (m

m)

Displacement

Start rising

P5

Acc (

g)

Time (s)

0 20 40 60 80 100

Time (s)

0 20 40 60 80 100

Time (s)

minus30

minus04

Taft wave 04 g

Δ 120590

998400u

(b) 119867119863 = 2










0

5

4

8

00

02

04

06

10 20 30 40 50 60

00

01

Disp

lace

men

t (m

m)

Displacement

P

Acc (

g)

Time (s)

10 20 30 40 50 60

Time (s)

10 20 30 40 50 60

Time (s)

minus4

minus01

Δ

El-Centro wave 01 g

120590998400

u

(a) 119886max = 01 g

0

30

60

00

04

08

0 20 40 60 80 100

0 20 40 60 80 100

0

5

20 40 60 80 100

00

04

Disp

lace

men

t (m

m)

Displacement

P

Acc (

g)

Time (s)

Time (s)

Time (s)

Start rising

El-Centro wave 04 g

minus04

Δ 120590

998400u

(b) 119886max = 04 g



119879 + 119882119904+ int

1198632

minus1198632

(1199061) 119889119863 sdot 119871 + 119882

119901= int

1198632

minus1198632

(1199062) 119889119863 sdot 119871 + 119873

(1)





1and 119906



119875 = int

1198632

minus1198632

(1199062minus 1199061) 119889119863 sdot 119871 + 119873 minus 119882

119904 (2)



119875 = int

1198632

minus1198632

(1198902minus 1198901) 119889119863 sdot 119871 (3)





int

1198632

minus1198632

(1199062minus 1199061) 119889119863 sdot 119871 = 120588

119908119892119881pipe (4)


00

01

02

03

04

05

Different shaking

Δu

(P8

and P5

)

Test 1-EL 015 g

Test 1-EL 05 g

Test 2-EL 04 g

02minus

01minus

minus03

120590998400

Test 1-Taft 04 g

Test 2-Taft 04 g



1198791015840+ 1198821015840

119904+ int

1198632

minus1198632

(1199061015840

1) 119889119863 sdot 119871 + 119882

119901

= int

1198632

minus1198632

(1199061015840

2) 119889119863 sdot 119871 + 119873

1015840

(5)


Δ119879 = int

1198632

minus1198632


119904 (6)


1and Δ119906

2are excess


(Δ1199062minus Δ1199061)119889119863 sdot 119871 is









1= 120574sat119891(ℎ


is 1199061015840

2= 120574sat119891(ℎ


1015840

1and

1199061015840

2gives

int

1198632

minus1198632

(1199061015840

2minus 1199061015840

1) 119889119863 sdot 119871

= 120574sat sdot int1198632

minus1198632

[119891 (ℎ2) minus 119891 (ℎ

1)] 119889119863 sdot 119871 = 120574sat119881pipe

(7)





119865119904+ 11988210158401015840

119904+ int

1198632

minus1198632

11990610158401015840

1119889119863 sdot 119871 + 119882

119901

= int

1198632

minus1198632

11990610158401015840

2119889119863 sdot 119871 + 119873

10158401015840+ 119898119901119886

(8)



1 11990610158401015840

211988210158401015840

119904 and119873

10158401015840 are the same as 11990610158401 1199061015840

21198821015840

119904 and119873



1198632

minus1198632


lowast119873 (9)






119904and Δ

lowast119873 are



Time (s)

00

25

50Fo

rce (

kN) Shaking

EL 01g

minus25

0 10 20 30 40 50

(a)

0

Forc

e (kN

)

Shaking

EL 015 g

minus15

minus 45

minus30

0 10 20 30 40 50Time (s)

(b)

0 10 20 30 40 50

0

160

Shaking

Forc

e (kN

)

EL 05 g

minus 160

minus 320

Time (s)

(c)


0 20 40 60 80 100 120 140 160

02

06

05

09

08

00

01

03

04

07

10

HD = 05 HD = 2

EL-01 gZ-015 g

Z-01 g



Δ

ΔT

120590998400 (P5)

u


and excitation


119904

H

T + WS

u1

u2

2 Wp

N




119865119904= 119891119901[119863

119867times (

119867

119863+ 05)

2

] 1205901015840

119867119863119871 (10)

where 1205901015840





H

+

2 WP

f1(h

f2(h)

)

W998400s

u9984001

u9984002

f(h) is the

the burialdepth of

pipe surface

function of

T998400

N998400


0 20 40 60 80 100 120 140 160 180 200

0

100

200

300

Time (s)

Forc

e (kN

)

ΔTΔU

ΔP

sat minus w)Vpipe

minus100

minus200

minus300

(120574 120574




1205901015840

119867= 1205901015840

1198670minus Δ119906 (11)


H

Wpmpa

Fs

(decreased during

shaking)u9984009984001

u9984009984002N998400998400

W998400998400s






0

6

0 10 20 30 40 50

a(m

s)

a

minus6

minus12

Time (s)

(a)

0

2

4

6

0 10 20 30 40 50

aeff

aef

f(m

s2)

Time (s)

(b)

00

01

02

03

0 10 20 30 40 50

V

V

(ms

)

minus01

Time (s)

(c)

0 10 20 30 40 50

0

45

90

Disp

lace

men

t (m

m)


minus45

Time (s)

(d)


5 Conclusions







Acknowledgments


References
































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

5

4

8

00

02

04

06

10 20 30 40 50 60

00

01

Disp

lace

men

t (m

m)

Displacement

P

Acc (

g)

Time (s)

10 20 30 40 50 60

Time (s)

10 20 30 40 50 60

Time (s)

minus4

minus01

Δ

El-Centro wave 01 g

120590998400

u

(a) 119886max = 01 g

0

30

60

00

04

08

0 20 40 60 80 100

0 20 40 60 80 100

0

5

20 40 60 80 100

00

04

Disp

lace

men

t (m

m)

Displacement

P

Acc (

g)

Time (s)

Time (s)

Time (s)

Start rising

El-Centro wave 04 g

minus04

Δ 120590

998400u

(b) 119886max = 04 g



119879 + 119882119904+ int

1198632

minus1198632

(1199061) 119889119863 sdot 119871 + 119882

119901= int

1198632

minus1198632

(1199062) 119889119863 sdot 119871 + 119873

(1)





1and 119906



119875 = int

1198632

minus1198632

(1199062minus 1199061) 119889119863 sdot 119871 + 119873 minus 119882

119904 (2)



119875 = int

1198632

minus1198632

(1198902minus 1198901) 119889119863 sdot 119871 (3)





int

1198632

minus1198632

(1199062minus 1199061) 119889119863 sdot 119871 = 120588

119908119892119881pipe (4)


00

01

02

03

04

05

Different shaking

Δu

(P8

and P5

)

Test 1-EL 015 g

Test 1-EL 05 g

Test 2-EL 04 g

02minus

01minus

minus03

120590998400

Test 1-Taft 04 g

Test 2-Taft 04 g



1198791015840+ 1198821015840

119904+ int

1198632

minus1198632

(1199061015840

1) 119889119863 sdot 119871 + 119882

119901

= int

1198632

minus1198632

(1199061015840

2) 119889119863 sdot 119871 + 119873

1015840

(5)


Δ119879 = int

1198632

minus1198632


119904 (6)


1and Δ119906

2are excess


(Δ1199062minus Δ1199061)119889119863 sdot 119871 is









1= 120574sat119891(ℎ


is 1199061015840

2= 120574sat119891(ℎ


1015840

1and

1199061015840

2gives

int

1198632

minus1198632

(1199061015840

2minus 1199061015840

1) 119889119863 sdot 119871

= 120574sat sdot int1198632

minus1198632

[119891 (ℎ2) minus 119891 (ℎ

1)] 119889119863 sdot 119871 = 120574sat119881pipe

(7)





119865119904+ 11988210158401015840

119904+ int

1198632

minus1198632

11990610158401015840

1119889119863 sdot 119871 + 119882

119901

= int

1198632

minus1198632

11990610158401015840

2119889119863 sdot 119871 + 119873

10158401015840+ 119898119901119886

(8)



1 11990610158401015840

211988210158401015840

119904 and119873

10158401015840 are the same as 11990610158401 1199061015840

21198821015840

119904 and119873



1198632

minus1198632


lowast119873 (9)






119904and Δ

lowast119873 are



Time (s)

00

25

50Fo

rce (

kN) Shaking

EL 01g

minus25

0 10 20 30 40 50

(a)

0

Forc

e (kN

)

Shaking

EL 015 g

minus15

minus 45

minus30

0 10 20 30 40 50Time (s)

(b)

0 10 20 30 40 50

0

160

Shaking

Forc

e (kN

)

EL 05 g

minus 160

minus 320

Time (s)

(c)


0 20 40 60 80 100 120 140 160

02

06

05

09

08

00

01

03

04

07

10

HD = 05 HD = 2

EL-01 gZ-015 g

Z-01 g



Δ

ΔT

120590998400 (P5)

u


and excitation


119904

H

T + WS

u1

u2

2 Wp

N




119865119904= 119891119901[119863

119867times (

119867

119863+ 05)

2

] 1205901015840

119867119863119871 (10)

where 1205901015840





H

+

2 WP

f1(h

f2(h)

)

W998400s

u9984001

u9984002

f(h) is the

the burialdepth of

pipe surface

function of

T998400

N998400


0 20 40 60 80 100 120 140 160 180 200

0

100

200

300

Time (s)

Forc

e (kN

)

ΔTΔU

ΔP

sat minus w)Vpipe

minus100

minus200

minus300

(120574 120574




1205901015840

119867= 1205901015840

1198670minus Δ119906 (11)


H

Wpmpa

Fs

(decreased during

shaking)u9984009984001

u9984009984002N998400998400

W998400998400s






0

6

0 10 20 30 40 50

a(m

s)

a

minus6

minus12

Time (s)

(a)

0

2

4

6

0 10 20 30 40 50

aeff

aef

f(m

s2)

Time (s)

(b)

00

01

02

03

0 10 20 30 40 50

V

V

(ms

)

minus01

Time (s)

(c)

0 10 20 30 40 50

0

45

90

Disp

lace

men

t (m

m)


minus45

Time (s)

(d)


5 Conclusions







Acknowledgments


References
































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










00

01

02

03

04

05

Different shaking

Δu

(P8

and P5

)

Test 1-EL 015 g

Test 1-EL 05 g

Test 2-EL 04 g

02minus

01minus

minus03

120590998400

Test 1-Taft 04 g

Test 2-Taft 04 g



1198791015840+ 1198821015840

119904+ int

1198632

minus1198632

(1199061015840

1) 119889119863 sdot 119871 + 119882

119901

= int

1198632

minus1198632

(1199061015840

2) 119889119863 sdot 119871 + 119873

1015840

(5)


Δ119879 = int

1198632

minus1198632


119904 (6)


1and Δ119906

2are excess


(Δ1199062minus Δ1199061)119889119863 sdot 119871 is









1= 120574sat119891(ℎ


is 1199061015840

2= 120574sat119891(ℎ


1015840

1and

1199061015840

2gives

int

1198632

minus1198632

(1199061015840

2minus 1199061015840

1) 119889119863 sdot 119871

= 120574sat sdot int1198632

minus1198632

[119891 (ℎ2) minus 119891 (ℎ

1)] 119889119863 sdot 119871 = 120574sat119881pipe

(7)





119865119904+ 11988210158401015840

119904+ int

1198632

minus1198632

11990610158401015840

1119889119863 sdot 119871 + 119882

119901

= int

1198632

minus1198632

11990610158401015840

2119889119863 sdot 119871 + 119873

10158401015840+ 119898119901119886

(8)



1 11990610158401015840

211988210158401015840

119904 and119873

10158401015840 are the same as 11990610158401 1199061015840

21198821015840

119904 and119873



1198632

minus1198632


lowast119873 (9)






119904and Δ

lowast119873 are



Time (s)

00

25

50Fo

rce (

kN) Shaking

EL 01g

minus25

0 10 20 30 40 50

(a)

0

Forc

e (kN

)

Shaking

EL 015 g

minus15

minus 45

minus30

0 10 20 30 40 50Time (s)

(b)

0 10 20 30 40 50

0

160

Shaking

Forc

e (kN

)

EL 05 g

minus 160

minus 320

Time (s)

(c)


0 20 40 60 80 100 120 140 160

02

06

05

09

08

00

01

03

04

07

10

HD = 05 HD = 2

EL-01 gZ-015 g

Z-01 g



Δ

ΔT

120590998400 (P5)

u


and excitation


119904

H

T + WS

u1

u2

2 Wp

N




119865119904= 119891119901[119863

119867times (

119867

119863+ 05)

2

] 1205901015840

119867119863119871 (10)

where 1205901015840





H

+

2 WP

f1(h

f2(h)

)

W998400s

u9984001

u9984002

f(h) is the

the burialdepth of

pipe surface

function of

T998400

N998400


0 20 40 60 80 100 120 140 160 180 200

0

100

200

300

Time (s)

Forc

e (kN

)

ΔTΔU

ΔP

sat minus w)Vpipe

minus100

minus200

minus300

(120574 120574




1205901015840

119867= 1205901015840

1198670minus Δ119906 (11)


H

Wpmpa

Fs

(decreased during

shaking)u9984009984001

u9984009984002N998400998400

W998400998400s






0

6

0 10 20 30 40 50

a(m

s)

a

minus6

minus12

Time (s)

(a)

0

2

4

6

0 10 20 30 40 50

aeff

aef

f(m

s2)

Time (s)

(b)

00

01

02

03

0 10 20 30 40 50

V

V

(ms

)

minus01

Time (s)

(c)

0 10 20 30 40 50

0

45

90

Disp

lace

men

t (m

m)


minus45

Time (s)

(d)


5 Conclusions







Acknowledgments


References
































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Time (s)

00

25

50Fo

rce (

kN) Shaking

EL 01g

minus25

0 10 20 30 40 50

(a)

0

Forc

e (kN

)

Shaking

EL 015 g

minus15

minus 45

minus30

0 10 20 30 40 50Time (s)

(b)

0 10 20 30 40 50

0

160

Shaking

Forc

e (kN

)

EL 05 g

minus 160

minus 320

Time (s)

(c)


0 20 40 60 80 100 120 140 160

02

06

05

09

08

00

01

03

04

07

10

HD = 05 HD = 2

EL-01 gZ-015 g

Z-01 g



Δ

ΔT

120590998400 (P5)

u


and excitation


119904

H

T + WS

u1

u2

2 Wp

N




119865119904= 119891119901[119863

119867times (

119867

119863+ 05)

2

] 1205901015840

119867119863119871 (10)

where 1205901015840





H

+

2 WP

f1(h

f2(h)

)

W998400s

u9984001

u9984002

f(h) is the

the burialdepth of

pipe surface

function of

T998400

N998400


0 20 40 60 80 100 120 140 160 180 200

0

100

200

300

Time (s)

Forc

e (kN

)

ΔTΔU

ΔP

sat minus w)Vpipe

minus100

minus200

minus300

(120574 120574




1205901015840

119867= 1205901015840

1198670minus Δ119906 (11)


H

Wpmpa

Fs

(decreased during

shaking)u9984009984001

u9984009984002N998400998400

W998400998400s






0

6

0 10 20 30 40 50

a(m

s)

a

minus6

minus12

Time (s)

(a)

0

2

4

6

0 10 20 30 40 50

aeff

aef

f(m

s2)

Time (s)

(b)

00

01

02

03

0 10 20 30 40 50

V

V

(ms

)

minus01

Time (s)

(c)

0 10 20 30 40 50

0

45

90

Disp

lace

men

t (m

m)


minus45

Time (s)

(d)


5 Conclusions







Acknowledgments


References
































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










H

+

2 WP

f1(h

f2(h)

)

W998400s

u9984001

u9984002

f(h) is the

the burialdepth of

pipe surface

function of

T998400

N998400


0 20 40 60 80 100 120 140 160 180 200

0

100

200

300

Time (s)

Forc

e (kN

)

ΔTΔU

ΔP

sat minus w)Vpipe

minus100

minus200

minus300

(120574 120574




1205901015840

119867= 1205901015840

1198670minus Δ119906 (11)


H

Wpmpa

Fs

(decreased during

shaking)u9984009984001

u9984009984002N998400998400

W998400998400s






0

6

0 10 20 30 40 50

a(m

s)

a

minus6

minus12

Time (s)

(a)

0

2

4

6

0 10 20 30 40 50

aeff

aef

f(m

s2)

Time (s)

(b)

00

01

02

03

0 10 20 30 40 50

V

V

(ms

)

minus01

Time (s)

(c)

0 10 20 30 40 50

0

45

90

Disp

lace

men

t (m

m)


minus45

Time (s)

(d)


5 Conclusions







Acknowledgments


References
































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

6

0 10 20 30 40 50

a(m

s)

a

minus6

minus12

Time (s)

(a)

0

2

4

6

0 10 20 30 40 50

aeff

aef

f(m

s2)

Time (s)

(b)

00

01

02

03

0 10 20 30 40 50

V

V

(ms

)

minus01

Time (s)

(c)

0 10 20 30 40 50

0

45

90

Disp

lace

men

t (m

m)


minus45

Time (s)

(d)


5 Conclusions







Acknowledgments


References
































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Documents

Research Article Uplifting Behavior of Shallow Buried Pipe ...downloads.hindawi.com/journals/tswj/2014/838546.pdf · Model Pipe. e model pipes are made of aluminum tube, with a density