study on soil spring model for pipe and silty clay

Research ArticleStudy on Soil Spring Model for Pipe and Silty Clay InteractionBased on Physical Model Test

Liyun Li 12 Junyan Han1 and Xiangjian Wang2

1Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education Beijing University of TechnologyBeijing 100124 China2Institute of Engineering Mechanics China Earthquake Administration Harbin 150080 China

Correspondence should be addressed to Liyun Li llyun5921sinacom

Received 28 July 2020 Revised 5 February 2021 Accepted 22 February 2021 Published 5 March 2021

Academic Editor Patrice Berthod

Copyright copy 2021 Liyun Li et al(is is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

(e previous soil spring model cannot describe the nonlinear characteristics of soil in elastic stage and there are someshortcomings in the selection of soil spring parameters in some published codes Meanwhile the literatures about the springmodel for pipe and silty clay interaction are rare (us a series of pipe-silty clay interaction tests are conducted and somecorresponding experimental results are obtained (e effects of soil properties pipe diameter and embedment depth on thehorizontal resistance of soil are studied Based on the experimental results the failure modes of soil are analysed and a formula tocalculate the peak resistance of soil and the corresponding displacement to peak resistance are proposed Finally a method todescribe the nonlinear spring stiffness coefficient of silty clay is recommended

1 Introduction

In the analysis and design of buried pipeline soil springmodelis often adopt to describe the action of soil on the pipeline inwhich the soil around pipeline is equivalent to a three-di-mensional soil spring and many fruits have been obtainedbased on the soil spring model [1ndash10] For the transverse soil-pipe interaction it is common practice to idealize the re-sistance displacement curve into a linear elastic-perfectlyplastic model represented by two straight lines as shown inFigure 1 so that the properties of soil spring can be deter-mined by getting the peak soil resistance and its corre-sponding displacement In the past forty years a great deal ofstudies has been in progress on the two parameters oftransverse soil spring Audibert et al [11] discussed thebinding force of soil to pipeline in pipe-soil interactionTrautmann and OrsquoRourke [12] conducted a model test ofpipe-sand interaction and suggested a method for deter-mining the parameters of transverse soil spring in sandy soilYimsiri et al [13] analysed the lateral and upward pipemovements at different embedment conditions in order tofind the solution for the peak force and to investigate its

transition from shallow to deep failure mechanism Guo et al[14] discussed the sensitivity of influencing factors of pipe-soilinteraction in sandy soil by the finite element method andanalysed the influence of buried depth and pipe diameter onvalue of soil spring parameters Badv and Daryani [15] in-vestigated the response of buried pipelines in sand totransverse PGD with particular attention to the peak forcesexerted on the pipe Liu et al [16] carried out some modeltests on the restraint effect of sand on buried pipelines in finesand of Bohai region for revealing the exertion process of soilresistance during vertical horizontal and axial movement ofpipelines in sand Jung et al [17] simulated the lateral forceversus displacement relationship of pipelines under plane-strain conditions in both dry and partially saturated sand anddiscussed the relationship between the maximum lateral forceand pipe depth in dense sand Based on Trautmannrsquos ex-perimental work [12] Li et al [18] analysed the sensitivity ofinfluencing factors of pipe-sand interaction by the numericalmethod and proposed an empirical formula to get the ulti-mate bearing capacity of sand under large-depth Robert et al[19] studied the lateral load-displacement behaviour ofpipelines in partially saturated sand Concerning the study of

HindawiAdvances in Materials Science and EngineeringVolume 2021 Article ID 2838605 18 pageshttpsdoiorg10115520212838605

pipe-soil interaction in clayey soil Oliveira et al [20] carriedout the centrifuge physical model test of pipe-soft clay in-teraction and proposed a method for calculating the ultimatebearing capacity of soft clay when the pipeline moved lat-erally Liu et al [21ndash23] conducted a series of pipe-soil in-teractionmodel tests on soft clay in Bohai region analyzed thefailure mode of the soil and proposed a formula for calcu-lating the peak resistance of soil

All the above studies assumed that the soil around thepipe is an ideal elastic-plastic material which is inconsistentwith the nonlinear characteristics of the elastic mechanicalsegment of soil material Moreover most of the previousstudies focused on sand (ere are few studies on pipe-soilinteraction in clayey soil and the research object of pipe-clayinteraction is only on saturated soft clay In the constructionof directly buried pipelines in Beijing region the backfillinginto the trench is usuallymade of claymaterials such as clayeysilt silty clay or clay which are taken from the constructionarea(ese clayeymaterials aremostly above the groundwaterlevel and belong to unsaturated soils (e matrix suctionamong solid liquid and gas phases in soils makes theproperties of unsaturated soils significantly different fromthose of saturated soils and dry soils Few studies publishedfocus on the effect of moisture content in clayey soil on pipe-soil interaction Besides the Code for Seismic Design ofOutdoor Water Supply Drainage and Gas (ermal Engi-neering in China [24] and American Lifelines Alliance [25]recommended the same method for calculating the peakbearing capacity of clayey soil but there are differences in theunit of soil parameters which need to be checked In view ofthe above discussion the authors carried out some physicalmodel tests of pipe-soil interaction with the silty clay inBeijing region Based on the experimental results the authorsdiscuss the determination of key parameters of soil spring andthe mathematical description of soil spring coefficient inorder to provide an experimental basis for the laying ofpipelines in silty clay site in Beijing region

2 Physical Model Tests

Figure 2 shows the photo of experiment device in which thetest container is welded by steel plate with the size of

1000mmtimes 500mmtimes 1100mm (lengthtimeswidthtimes height) Aplexiglass observation window of 900mmtimes 700mm isarranged on the front panel of container for observing thedeformation and failure process of soil during test (ere aretwo parallel vertical joints on the right panel of the containerfor the steel strand to pass through(e actuator and the testpipe are connected by two steel strands and the force andthe movement are automatically recorded via the actuatoracquisition system Figure 3 shows the connection betweenthe steel strand and the test pipe

(e test pipes are steel tubes with the length of 490mm(e diameter of the pipes are the four common sizes in pipeengineering which are 30mm 60mm 102mm and140mm respectively (e test results of 60mm diameterpipe are as the benchmark to analyse the influence of pipediameter on the horizontal resistance of soil

(e test soil is the typical silty clay in Beijing region Itsplastic limited moisture content is 15 liquid limitedmoisture content is 29 and natural moisture content is16 Four soil samples reconstituted by controlling themoisture content and dry unit weight of the soil are in stiffhard plastic and plastic state respectively (e measuredcohesive force and measured internal friction angle of thesesoil samples are listed in Table 1 which are obtained by statictriaxial test As shown in Table 1 the change of cohesiveforce and internal friction angle of silty clay is in goodagreement with those in literature [26] that is the cohesiveforce and internal friction angle decreases with the increaseof water content in silty clay

(e test cases are shown in Table 2 of which the first tofourth cases are to analyse the effect of the depth-diameterratio (HD) and the soil properties on the test results and thefifth case is to investigate the effect of pipe diameter

During the tests the Earth pressure acting on the pipewall is also monitored Since there is only the upstreamsurface of pipe interacting with soil in the test process sevenEarth pressure sensors are arranged at 30deg intervals on theupstream surface of pipe which interacts with soil (eFlexiForce sensor produced by Tekscan company a kind ofthin film pressure sensor is used to measure the Earthpressure on pipe in test Figure 4 shows the location ofpressure sensors on pipe and a photo of thin film pressuresensor (e thin film Earth pressure sensor consists of acircular pressure sensing area a flat wire and a pin (e pinis connected with the data acquisition system through aconnecting wire (e thin film Earth pressure sensor is a

Fm

F

Sm S

Figure 1 General soil spring model

Model test of pipe-soil interaction

Test container

Actuator

Steel strands

Figure 2 Model test device

2 Advances in Materials Science and Engineering

(a) (b)

Figure 3 Connection between the steel strand and the test pipe (a) Fixing device of the steel strand on the test pipe (b) Schematic diagramof the fixed steel strand

Table 1 Parameters of soil property

Sample Dry unit weight cd (kNm3) Moisture content ω () Plastic index Ip Cohesive force c (kPa) Internal friction angle φ (deg)

I 160 10

14

1610 121II 16 1364 102III 170 20 503 88IV 16 649 233

Table 2 Test cases

CaseTest soil

Diameter of tube (mm) Depth-diameter ratio HD Loading modeSample Consistency state

1 I Stiff 60 1 3 5 710

Lateral displacement loading2 II Hard plastic 60 1358103 III Plastic 60 1345674 IV Hard plastic 60 1357105 IV Hard plastic 3060102140 3Note H indicates the distance from the upper surface of soil to the axis of tube D means the outer diameter of tube all the same as below

(a) (b)

Figure 4 Monitoring of Earth pressure (a) Location of the pressure sensor on the pipe (b) (in film pressure sensor

Advances in Materials Science and Engineering 3

piezoelectric sensor and the relationship between pressureand current is linear (us the Earth pressure acting on thepipe can be obtained by changing the current value

(e test process is as follows

Stage 1 According to the dry unit weight of soildesigned for test the total mass of soil required iscalculated and then a sufficient mass of soil withcorresponding moisture content is made for standbyStage 2 (e compacted soil of 045m thick is laid in thetest container to ensure that there is enough soil underpipe to reduce the influence of the bottom boundary ontest results In order to ensure the uniformity of thecompacted soil the soil of 045m thick is evenly dividedinto 9 layers for compaction After each layer of soil iscompacted the soil surface shall be scratched to ensurethat it is rough enough and then the next layer of soil islaidStage 3 Place the test pipe at the specified location inthe test container (as shown in Figure 5)Stage 4 Lay the remaining soil to the design height inthe same way as aboveStage 5 Connect the actuator and steel strand andadjust the actuator to ensure that the test pipe is pulledhorizontally (en start the actuator and pull thepipeline horizontally with speed of 05mms record thesoil resistance and the displacement of the pipe at eachmoment via the actuator acquisition system and takethe images of the whole test process with a camera

In order to ensure the consistency of the undrained shearstrength between each layer of silty clay three stages werecarried out in the test

Stage 1 prepare test soil with designed moisturecontent (1) (e soil is air-dried and the moisturecontent of the soil is measured every day When themoisture content is lower than 10 the air drying isstopped (2) (e amount of water required for test soilwith designed water content is calculated (3)According to the calculated amount of water the soil ismixed with airless water When mixing the amount ofsoil taken out each time is not more than 30 kg therequired water is sprayed into water mist with pressurespout and the soil is constantly turned to ensure theuniformity of water in soil (4) (e moisture content ofthe prepared soil sample is measured to ensure that itmeets the test requirementsStage 2 test the undrained shear strength standard ofclay with different dry unit weight (1) According to therequirements of triaxial test the weight of soil withdesigned dry weight is calculated (2) Soil samples fortriaxial test are prepared (3) Triaxial test is carried outand the undrained shear strength of clay with differentdry unit weights is obtainedStage 3 prepare the model test according to the ex-perimental design (1)(e height mark line on the glasswindow of the test container is drawn (2)(e weight ofeach clay layer according to the designed dry unit

weight and moisture content is calculated (3) (e soilis compacted to set height for each soil layer (4) (esurface of the compacted soil is roughened and thenthe next layer of soil is laid on it (5) Repeat (3) to (4)until the design height is reached

Meanwhile when filling the soil layer where the test pipeis located the 05D thick soil layer is filled and compactedfirstly and then a semicircular trench with diameter of 10Dis excavated at the designed position of pipe and the testpipe is put into the trench After that the subsequent soillayers are filled It should be noted that the soil around thepipe is compacted with compaction tools close to the sidewall of the pipe with light load andmultiple compaction andthe filling of the soil layer above the pipe shall be carried outwith light load and multiple compaction so as to minimizethe influence of the pipe on the lower soil layer

3 Reliability Verification of Experiment

In order to check the reliability of the experimental resultsthe physical model tests in this paper are simulated by usingABAQUS finite element software (e influence of modelscale on experimental results is analysed and the physicalmodel test results are corrected

31 Numerical Modelling Method During the tests the de-formation of soil belongs to plane strain problem (ereforethe two-dimensional model is used for numerical simulationIn order to ensure the accuracy of numerical calculation andsufficient calculation efficiency the following principles areadopted to mesh the elements the element size of the soilunder the pipe is 003mtimes 006m and the element size infront of and above the pipe is 0015mtimes 0015m As we knowthe area of pipe-soil interaction is the key domain of nu-merical calculation so the element size in this area is locallyrefined to 0005mtimes 0005m Figure 6 presents the elementmesh of a numerical model

(e boundary of the numerical model is treated byconstraining the displacement of nodes on the truncatedboundary that is the horizontal and vertical displacementsof nodes on the upper surface of the model are not restrictedthe displacements on the bottom of model are frozen andonly the normal horizontal movement of nodes on the otherrest surface are prohibited

(e element of CPE4R is a kind of self-contained ele-ment type in ABAQUS which represents quadrilaterallinear-reduced integral plane strain element (is elementtype can also obtain more accurate results when the elementis distorted which is suitable for the plane strain problem(erefore the element of CPE4R is selected for soil

Because the deformation of the steel pipe is very small inthe test it can be regarded as a rigid body so the rigidelement of R2D2 which is a two-dimensional linear discreterigid element with infinite stiffness in ABAQUS is chosen tomesh the pipe

(e contact between the pipe and soil is set by penaltyfunction and hard contact method and the friction coeffi-cient is 02 according to the work of literature [27]


In terms of constitutive relation the constitutive rela-tionship of soil is described by theMohrndashCoulombmodel inwhich the major parameters are cohesion force frictionangle dilatancy angle elastic modulus Poisonrsquos ratio anddensity

(1) Dilatancy Angle (e soil used in this test is remoldedsoil and the dilatancy of soil is very small So thevalue of the dilatancy angle is determined as followswhen friction angle φlt 30deg ψ 0 and when frictionangle φgt 30deg ψ φminus 30

(2) Elastic Modulus (e empirical calculation formulaof elastic modulus of cohesive soil proposed by Ou[28] is adopted

Ei C0 times η times Su (1)

in which C0 is related to the over consolidation ratio(OCR) of soil which is taken as 10 in this paper η isrelated to the plasticity index of soil which is taken as800 in this paper and Su is the undrained shearstrength of soil

(3) Cohesion Force and Friction Angle (e cohesionforce and the internal friction angle of test soil areobtained by static triaxial test of which the stressenvironment is different from that of plane strainstate (erefore based on the data obtained from thephysical model test the parameters of cohesion andinternal friction angle are inversed and the cohesionforce and internal friction angle obtained from in-version are employed in the numerical simulation

It is considered that the pipe has been buried for a longtime and the pipe-soil system has reached the equilibriumstate therefore only the initial geo-stress of the pipe-soilmodel before the horizontal tensile test is balanced in nu-merical simulation (e specific numerical implementationis as follows(e vertical downward gravity load is applied tothe pipe-soil model and the stress field under gravity iscalculated (en the obtained stress field is applied to thepipe-soil model in reverse (e reverse applied stress fieldand gravity load make the pipe-soil model in a state of initialstress existence but no initial deformation that is to achievethe initial stress balance After that a displacement is directlyapplied to the pipe and the loading displacement is 015mwhich is consistent with the physical model test (e dy-namic explicit algorithm is used in the numerical calcula-tion so it is necessary to reduce the loading speed as much aspossible to reduce the influence of inertial force in order tosimulate the quasi-static test process of the pipe-soil in-teraction model After the calculation the relationship be-tween the reaction force and displacement on pipe isextracted

Figure 7 compares the experimental results and thenumerical results of soil with dry unit weight of 16 kNm3

and moisture content of 16 under HD 1 3 5 respec-tively As shown in Figure 7(a) the soil resistance dis-placement curve is basically consistent in the initial loadingstage under HD 1 However the numerical results aregreater than the physical experimental results in the post-peak stage and the most relative error is 30 However inFigure 7(b) the soil resistance displacement curve is basi-cally consistent in the postpeak stage and the most relative

078

m

1m

Figure 6 Element meshes of a numerical model

(a) (b)

Figure 5 Place the test pipe at the designated position (a) Side view of pipe placement (b) Top view of pipe placement


error is 33 under HD 3 Different from that of HD 1and HD 3 there are some errors between the numericalresults and the experimental results in the initial stage andthe postpeak stage when HD 5 (as shown in Figure 7(c))but the maximum error is only 25 Figure 7 indicates thatthe soil resistance displacement curve obtained from nu-merical simulation and physical model test is basicallyconsistent under different depth diameter ratios and thedisplacement corresponding to peak resistance and peakresistance is in good agreement

In order to reveal the influence of the model scale on theresults and check the reliability of the physical test theboundary effect of the model is analysed by using the nu-merical model established in this paper Figure 8 gives theresistance displacement curves of soil under different dis-tances between the pipe and truncated boundary in which

the diameter of the pipe is 60mm the depth diameter ratioHD equals 5 the dry unit weight of soil is 16 kNm3 and themoisture content of soil is 16 (e results mean that thedistance between the pipe and the rear boundarythe bottomboundary has little effect on the results but the distancebetween the pipe and the front boundary has a great in-fluence on the results From Figure 8 when the distancebetween the front boundary and pipe axis is greater than055 the calculation results have good convergence and thetest results do not need to be corrected when the distancebetween the pipe axis and the front boundary is less than055m the results need to be corrected According to thenumerical calculation results the physical experimentalresults are corrected (e correction coefficient is shown inTable 3 in which the correction coefficient is obtained bycomparing the maximum resistance from the numerical

Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)

0

1

2

3

4

5

6

7

8

9

10

2 4 6 8 10 12 14 160Horizontal movement of pipe S (cm)

Physical model testNumerical simulation

(a)


Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)

0

2

4

6

8

10

12

14

16

18

20


(b)

Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)



0

5

10

15

20

25

30

35

(c)

Figure 7 Load displacement curve under different HD (a) HD 1 (b) HD 3 (c) HD 5


simulation of far boundary to that from the simulation of theactual model test (e discussion of the following results isbased on the corrected experimental data

4 Results and Discussion

41 Resistance Displacement Curve Figure 9 shows the re-sistance displacement curves of the soil around the pipe withdifferent depth-diameter ratios at D 60mm Figures 9(a)ndash

9(d) demonstrate the variation of soil lateral resistance withmovement of the pipe in case 1 2 3 and 4 respectively (evertical coordinate is the horizontal soil resistance on thepipe of per unit length and the abscissa coordinate isthe horizontal movement of the pipe(e arrow on the curvepoints to the peak soil resistance of each curve

As shown in Figure 9 the exertion process of soil re-sistance is different in different cases In case 1 the form ofthe resistance-displacement curves under different depth-

Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)

0

5

10

15

20

25

30

35

40


Lr = 02mLr = 04mLr = 06m

(a)

Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)

0

5

10

15

20

25

30

35

40


Lb = 045mLb = 028mLb = 018m

(b)

Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)

0

5

10

15

20

25

30

35

40


Lf = 10mLf = 03mLf = 045m

Lf = 055mLf = 065m

(c)

Figure 8 Resistance displacement curves under different boundary distances in which the diameter of tube is 60mm the depth diameterratio HD equals 5 the dry unit weight of soil is 16 kNm3 and the moisture content of soil is 16 (a) (e rear boundary (b) (e bottomboundary (c) (e front boundary


Table 3 Correction factor of test results

CaseParameters of soil property

Diameter of tube (mm)Depth-diameter ratio HD

Dry unit weight cd (kNm3) Moisture content ω () 1 3 5 6 7 8 10

1 16 10 60 1 1 1 mdash 1 094 0902 16 16 60 1 1 1 mdash mdash 093 0913 16 20 60 1 1 1 1 097 095 mdash4 17 16 60 1 1 1 mdash 1 mdash 0925 17 16 3060102140 mdash 1 mdash mdash mdash mdash mdash

0 2 4 6 8 10 12 14 16 18 20 22 24

Case 1

Horizontal movement of pipe S (cm)

Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)

0

10

20

30

40

50

60

70

HD = 1HD = 3

HD = 5HD = 7

(a)

0 2 4 6 8 10 12 14 16 18 20 22 24

Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)


Case 2

0

10

20

30

40

50

60

70

HD = 1HD = 3 HD = 8

HD = 5

(b)

Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)

0 2 4 6 8 10 12 14 16 18 20 22 24Horizontal movement of pipe S (cm)

0

10

20

30

40

50

60

70

Case 3

HD = 1HD = 3HD = 4

HD = 5HD = 6HD = 7

(c)

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14 16 18 20 22 24

Hor

izon

tal s

oil r

esist

ance

F (k

Nm

) Case 4


HD = 1HD = 3

HD = 5HD = 7

(d)

Figure 9 Relationship between lateral soil resistance and deformation (a) Case 1 (b) Case 2 (c) Case 3 and (d) Case 4


diameter ratios is the same (e soil resistance increaseslinearly with the movement of the pipe and decreasesgradually or remains stable after reaching the peak value(ehorizontal movement of the pipe corresponding to the peakvalue of soil resistance is almost the same However theresistance-displacement curves in other three cases aredifferent which show that the soil resistance increasesrapidly and nonlinearly in the initial stage then increasesslowly and the value of soil resistance decreases slightly orremains stable after reaching the peak value When thedepth-diameter ratio is less than 70 the peak resistancepoint in the curve can be marked clearly but while thedepth-diameter ratio exceeds 70 the soil resistance still doesnot reach the peak value even the movement of pipe reaches20 cm

(ese above phenomena may be due to the change of theconsistency and ductility of silty clay caused by the moisturecontent in soil When the moisture content is 10 the siltyclay is in a stiff state the faction of binding water among thesoil particles is obvious and the compressibility of soil isweak When the soil in front and above the pipe reaches thefailure state the bearing capacity of soil reaches the peakvalue and the failure of soil represents as brittle failuremode With the increase of moisture content the boundwater film among soil particles thickens gradually the co-hesion among soil particles weakens the soil is in a hard-plastic or plastic state and the compressibility enhances(efailure of the soil in front and above the pipe characterizes aslocal shear failure (erefore there is no obvious peak valueof soil resistance-displacement curve

Figure 10 shows the soil resistance-displacement curve ofcase 5 when HD 3 which indicates that the soil resistanceincreases with the increase of pipe diameter and the increasefactor is proportional to the pipe diameter However thedisplacement corresponding to the maximum soil resistanceis almost the same except for the test atD 30mmWe thinkthat the reason for this phenomenon is as follows whenHDis constant the pressure of overlying soil on the pipe in-creases with the increase of pipe diameter which leads to theincrease of soil resistance in the test However the inter-action area between the pipe and soil also increases with theincrease of pipe diameter and the failure mode of soilaround the pipe changes from shear failure of soil cut by thepipe to compression failure of soil squeezed by the pipe (edisplacement of the pipe under compression is larger thanthat under shear but the displacement is controlled by themechanical properties of soil around the pipe

42 Failure Mode of Soil Mass (e test results show that thefailure modes of the soil around the pipe vary with the increaseof the buried depth of pipe (1) When the depth-diameter ratioof the pipe is small the horizontal movement of the pipe cancause soil deformation in a certain range above the pipe to reachthe surface of soil (at is pipe movement leads to vertical andoblique cracks in the soil around the pipe the cracks continue toexpand and eventually reach the surface of soil mass and awedge-shaped failure body forms At this moment the bearingcapacity of soil mass reaches its peak We call this failure mode

ldquoshallow-buried failurerdquo(e peak resistance emerges clearly onthe soil resistance-displacement curves and the pipe dis-placement corresponding to the peak resistance is small (ereason for this phenomenon is that the buried depth of the pipeis shallow the Earth pressure acting on pipewall is very low andthe overlying soil cannot restrict the expansion of cracks in thesoil around the pipe Figure 11(a) shows the photograph and thenumerical simulation result of soil failure behind the pipe whenD 60mm and HD 1 which is a typical ldquoshallow-buriedfailurerdquo mode (2)With the increase of the depth-diameter ratioof the pipe the crack propagation in the soil around the pipe islimited and no obvious soil deformation appears on the surfaceof soil mass Finally the soil mass is cut directly by the pipewhich can be called ldquodeep-buried failurerdquo (ere is no peakresistance point of soil observed on the soil resistance-dis-placement curves or the pipe movement is large when the peaksoil resistance occurs(e reason is that with the increase of thedepth-diameter ratio of the pipe the overburden Earth pressureon the pipe increases and the Earth pressure on the pipeprevents the propagation of cracks which is manifested as thepipe extrudes the soil in front of it Figure 11(b) provides thephotograph and the numerical result of soil deformation andfailure behind the pipe at D 60mm and HD 7 which ischaracterized by ldquodeep-buried failurerdquo mode

43 Distribution of Earth Pressure on the Pipe (e failuremodes of soil mass can be proved with the distribution ofEarth pressure on the pipe Figure 12 presents the distri-butions of Earth pressure on upstream surface of the pipe ofdifferent cases Due to the close contact between the thin filmpressure sensor and the pipe wall during tests the Earthpressure in the direction of pipe movement is the largestFigure 12 demonstrates that the Earth pressure acting on thepipe increases with the increase ofHD but the distributionsof Earth pressure on the pipe wall under different cases arenot consistent

0

10

20

30

40

50

60

70


Hor

izon

tal s

oil r

esist

ance

F (k

Nm

) HD = 3

D =30mmD = 60mm

D = 102mmD = 140mm

Figure 10 Resistance displacement curves of soil with differentdiameters


Figure 12(a) shows the distribution of Earth pressure ofcase 1 in which the dry unit weight of soil is 16 kNm3 andmoisture content is 10 As shown in Figure 12(a) themaximum Earth pressure appears at 90deg of the upstreamsurface of pipe as HD ranges from 1 to 7 but when HDequals 8 and 10 themaximumEarth pressure appears at 120degand 60deg of the upstream surface of the pipe which meansthat the pipe tends to move towards 120deg or 60deg of theupstream surface of the pipe (e reason may be that the soilis stiff and brittle and the soil homogeneity in the two HDconditions is not very good due to some reasons in thepreparation of tests (e soil damage occurs first in thedirection of 120deg or 60deg of the upstream surface of the piperespectively resulting in the maximum Earth pressureappearing at 120deg or 60deg of the upstream surface of the pipe

Figure 12(b) shows the distribution of Earth pressure ofcase 2 in which the dry unit weight of soil is 16 kNm3 andmoisture content is 16 From Figure 12(b) the maximumEarth pressure appears at 60deg of the upstream surface of thepipe when HD equals 1 which indicates that the overburdenEarth pressure above the pipe is not enough to limit themovement of the pipe With the destruction of the soil abovethe pipe the pipe moves slant up In other buried depths themaximum Earth pressure appears at 90deg of the upstreamsurface of the pipe but the pressure on the upper part of thepipe increases rapidly It shows that the upward and forward

movement of the pipe still leads to greater pressure althoughthe overburden Earth pressure above the pipe restricts thepropagation of cracks in the soil around the pipe

Figure 12(c) shows the distribution of Earth pressure ofcase 3 in which the dry unit weight of soil is 16 kNm3 andmoisture content is 20 Figure 12(c) indicates that themovement direction of the pipe is well controlled the maxi-mum Earth pressure appears at 90deg of the upstream surface ofthe pipe and the Earth pressure distribution is basicallysymmetrical With the increase of HD the value of Earthpressure increases but when HD exceeds 70 the growth rateof Earth pressure in the moving direction slows down

Figure 12(d) shows the distribution of Earth pressure ofcase 4 in which the dry unit weight of soil is 17 kNm3 andmoisture content is 16 Figure 12(d) demonstrates that theEarth pressure at 90deg of the upstream surface of the pipe is thelargest and the Earth pressure at the upper part of the pipe ishigher than that at the lower part With the increase of HDthe rule of Earth pressure in 90deg of the upstream surface of thepipe varying with HD is shown as follows when HD is lessthan 70 the Earth pressure increases rapidly when HD isgreater than 70 the increase becomes smaller when HD isgreater than 150 the increase increases again

According to the distribution of Earth pressure acting onthe pipe because the upper surface of site is free the pipemoves upward and forward and the Earth pressure

Pipe

Damaged surface

U Magnitude+9884e ndash 02

+9060e ndash 02

+8236e ndash 02

+7413e ndash 02

+6589e ndash 02

+5765e ndash 02

+4942e ndash 02

+4118e ndash 02

+3295e ndash 02

+2471e ndash 02

+1647e ndash 02

+8236e ndash 03

+0000e + 00

(a)

Pipe

Surface upli


+9324e ndash 02

+8476e ndash 02

+7629e ndash 02

+6781e ndash 02

+5933e ndash 02

+5086e ndash 02

+4238e ndash 02

+3390e ndash 02

+2543e ndash 02

+1695e ndash 02

+8476e ndash 03

+0000e + 00

(b)

Figure 11 Soil failure modes in which the left picture is experimental photo and the right picture is the numerical result (a) D 60mmHD 1 (b) D 60mm HD 7


distribution around the pipe shows that the Earth pressure atthe upper part of pipe is greater than that at the lower partWith the increase of buried depth of the pipe the constraintof soil on the pipe increases and the failure mode of soilmass changes from ldquoshallow-buried failurerdquo to ldquodeep-buriedfailurerdquo As shown in Figure 12 with the increase of dry unitweight the soil becomes more and more dense and itsability to resist deformation and failure becomes stronger sothe Earth pressure acting on the pipe is greater(emoisturecontent has a certain influence on the failure of soil mass buthas little effect on the value of Earth pressure

44 Peak Resistance of Soil Mass (Fm) According to thefailure mode of soil around the pipe when the pipe movesPeng [29] used the limit equilibrium method of soil toanalyse the peak resistance of soil in pipe-soil interaction andsuggested using the passive Earth pressure formula to obtainthe peak resistance of soil when the pipeline moves hori-zontally In order to study the pipe-soft clay interaction inthe buckling process of submarine pipelines based on Pengrsquosworks [29] Wang [30] suggested using formula (2) tocalculate the horizontal peak resistance of soft clay con-sidering the cohesion effect of clay

0 20

40

60

80

100

120

140

160180

Eart

h pr

essu

re (k

Pa)

350300250200150100

500

50100150200250300350

HD = 10HD = 8HD = 7

HD = 5HD = 3HD = 1

(a)

030

60

90

120

150180

HD = 3HD = 1

Eart

h pr

essu

re (k

Pa)

HD = 10HD = 8HD = 5

350300250200150100

500

50100150200250300350

(b)

030

60

90

120

150180

Eart

h pr

essu

re (k

Pa)

350300250200150100

500

50100150200250300350

HD = 8HD = 7HD = 6HD = 5

HD = 4HD = 3HD = 1

(c)

030

60

90

120

150180

Eart

h pr

essu

re (k

Pa)

1000

800

600

400

200

0

200

400

600

800

1000

HD = 20HD = 15HD = 10

HD = 7HD = 5HD = 3

(d)

Figure 12 Distribution of Earth pressure on upstream surface of the pipe (a) Case 1 (b) Case 2 (c) Case 3 and (d) Case 4


Fm B212

c H1 + D( 11138572Kp + 2c H1 + D( 1113857

Kp

11139691113876 1113877 (2)

where Fm presents the horizontal peak resistance of soilsubjected to unit length pipe section unit kNm B2 204(H1D)minus 05 is a dimensionless correction coefficientKp tan2(45 +φ2) is the passive Earth pressure coefficient cis cohesive force of soil unit kPa φ is internal friction angleof soil unit degree (deg) c is the natural unit weight ofoverlying soil c (1 + ω)cd unit kNm

3 D is pipe di-ameter unit m andH1 is thickness of covering soil unit m

Essentially the methods proposed by Peng [29] and Wang[30] suppose that the soil in front of the pipe is in the passivecritical state when the soil destroy due to the interaction be-tween the pipe and soil and the peak resistance of the soil iscalculated by modifying the passive Earth pressure (e passiveEarth pressure formula has clear physical meaning but theEarth pressure distribute forms on pipe and retaining wall aredifferent so the calculation results of passive Earth pressureneed to be revisedWangrsquosmethod [30] is proposed for soft clayand its applicability to silty clay in Beijing region will be vali-dated through test Because the assumption of buried depthH inour tests is different from Wangrsquos work [30] formula (2) istransformed into formula (3) to calculate the peak resistance ofsilty clay

Fm B12

c H +D

21113874 1113875

2Kp + 2c H +

D

21113874 1113875

Kp

11139691113890 1113891 (3)

where B is a dimensionless correction coefficient and Hindicates the distance from the ground surface to the centreof pipe Other symbols are the same as formula (2)

Next we will discuss the parameter B in formula (3)Figure 13 shows the relationship between the dimensionless

correction coefficientB and the depth-diameter ratioHD of thepipe in which B is the ratio of the peak resistance of soilobtained from tests to the calculated passive Earth pressure Itcan be seen from Figure 13 that the value of B can be fitted by aformula similar to that in formula (2) as shown in formula (4)but the fitting parameters a and b are affected by the consistencystate and the dry unit weight of soil around the pipe (eparameter a increases with the increase of dry unit weight ofsoil but decreases first and then increases with the increase ofwater content when the dry unit weight of soil is constant (atis when the moisture content is less than the plastic limitedmoisture content the parameter a decreases with the increase ofthe moisture content otherwise the parameter a increases withthe increase of the moisture content(e parameter b decreasesapproximately linearly with the increase of moisture contentthe dry unit weight of soil has little effect on it (e values of aand b can be determined from formulae (5) and (6)

B aH

D1113874 1113875

b

(4)

a a1 + b1ω + c1ω2

1113872 1113873c

(1 + ω)cw

1113888 1113889

d1

(5)

b a2 + b2ω (6)

where c is the natural unit weight of overlying soil unit kNm3 cω is the unit weight of water unit kNm3 ω is themoisture content and a1 b1 c1 d1 a2 and b2 are fittingparameters

Based on the experimental results of 60mm diameterpipe the parameters in formulae (5) and (6) are obtainedthat is a1 000917 b1 minus0126 c1 0478 d1 11433a2 0187 and b2 minus120 Figure 14(a) shows the compar-ison between the parameter a calculated from the formula(5) and that obtained from the experiments which indicatesthat the coincidence is very good Figure 14(b) presents theresult of the comparison between the parameter b calculatedfrom formula (6) and that obtained from experiments whichdemonstrates that the fitting effect is also very good

After the above six parameters related to the moisturecontent and the dry unit weight of soil are determined thepeak soil resistance on the buried pipe can be calculated withformulae (3)ndash(6)

Now using the experimental results of case 5 to verifythe applicability and investigate the accuracy of the proposedmethod Figure 15 shows the comparison of the experi-mental data with the calculated results from formula (3) inthis paper Pengrsquos method [29] Wangrsquos method [30] andALAmethod [25] As can be seen from Figure 15 the resultsobtained from formula (3) and the corresponding param-eters in this paper are in the best agreement with the ex-perimental results (e results of the ALA method [25] areslightly higher than the experimental results (e resultsobtained from Pengrsquos method [29] are much smaller thanexperimental results because the influence of cohesion be-tween clay particles is not considered (e results obtainedfrom Wangrsquos method [30] are much higher than experi-mental results (e reason is that Wangrsquos method [30] is forsaturated soft clay in Bohai region Although the form ofcorrection coefficient B2 is similar to that in this paperWangrsquos method [30] does not consider the influence ofmoisture content and dry unit weight of soil on the B2 valueMoreover the grain composition and structure of saturatedsoft clay in Bohai region are different from that of silty clay in

D = 60mm

B = 05417 (HD)00559

B = 064737 (HD)ndash006351

B = 02733 (HD)006002

B = 025073 (HD)001275

2 4 6 80 10HD

02

03

04

05

06

07

B

Case 1Case 2

Case 3Case 4

Figure 13 Relations between B and HD


Beijing region (erefore Wangrsquos method [30] cannot beemployed directly to the silty clay in Beijing region

In order to further verify the applicability of formula (3) thepipe-soil interaction is numerically calculated under differentHD 1 3 5 7 in which the site consists of soil IV as shown inTable 1 and the pipe diameter is 90mm(e numerical methodused has been described previously Figure 16(a) shows the soilresistance displacement curve calculated by the numericalmethod Figure 16(b) presents the peak resistance is obtained byformula (3) ALA method [25] and numerical calculationwhich indicates that the results obtained by formula (3) is ingood agreement with the numerical results the ALA method[25] overestimates the horizontal binding force on the pipewhen the depth-diameter ratio is less than 3 and underestimatesthe horizontal binding force on the pipe while the depth-di-ameter ratio is greater than 3

From the above analysis formula (3) proposed in thispaper is based on the pipe-soil interaction test of silty clay inBeijing region takes into account the variation of correctioncoefficient B with soil moisture content and dry unit weightand is suitable for calculating the horizontal peak resistanceof silty clay in Beijing region However it is noted thatexperimentally determined parameters required for themodel are necessary when applying this method to othercohesive soil areas

45 Displacement Corresponding to Peak Resistance (Sm)Figure 17(a) describes the relationship between Sm and HD(e abscissa represents the depth-diameter ratio HD and theordinate represents the displacement Sm corresponding to thepeak resistanceWe find that the displacement Sm increases withthe increase of the depth-diameter ratio of the pipe except forcase 1 As mentioned above the reason for this phenomenon isthat the soil is in a stiff state in case 1 the compressibility of thesoil is poor and the resistance provided by the soil rapidlyreaches the peak value during pipe movement In the otherthree cases with the increase of moisture content of the soil thetest soil is in the hard plasticplastic state and it has a strongcompressibility thus the displacement Sm increases with theincrease of the depth-diameter ratio Meanwhile as shown inFigure 10 the diameter of the pipe has little effect on thedisplacement corresponding to the peak resistance

Based on the above discussion the following suggestionsare given When the moisture content is less than the plasticlimited moisture content ie ωle 15 in this paper thedisplacement corresponding to the peak resistance is pro-posed to be 30mm when the moisture content is greaterthan the plastic limited moisture content the displacementcorresponding to the peak resistance is determined fromformula (7) Figure 17(b) compares the results calculatedfrom formula (7) with the experimental results which in-dicates that formula (7) can well represent the change of Sm

070

065060055050045040035030025

a

1012

1416

1820

ω ()

200195

190185

180175 γ (k

Nm3 )D = 60mm

Experimental fitting resultsFormula calculation results

(a)

D = 60mm

ndash016

ndash012

ndash008

ndash004

000

004

008

012

016

b

8 12 16 20 24 28 324ω ()

Experimental fitting results Formula calculation results

(b)

Figure 14 Comparison between the result via formula and test result (a) Variation of parameter a with ω and c (b) Relationship betweenparameter b and ω

HD = 3

0

20

40

60

80

100

120

Peak

resis

tanc

e of s

oil m

ass F

m (k

Nm

)

40 80 120 1600Pipe diameter D (mm)

Experimental dataFormula (3)Wangrsquos method

ALA methodPengrsquos method

Figure 15 Comparison of model test results and formula results inwhich HD 3


Sm

D 00037 times

H

D1113874 1113875

3242+ 048 (7)

46 Soil Spring Coefficient As mentioned above it is cus-tomary to simplify the resistance-displacement curve of soilbefore the peak resistance reached to the linear relationshipshown in Figure 1 (us the whole resistance-displacement

curve can obtained after determining the peak resistance ofsoil and the corresponding displacement (is treatmentmethod cannot describe the nonlinear characteristics of theprefailure deformation of the soil around the pipe Figures 9and 10 show that the resistance-displacement curve (F-Scurve) of the soil around the pipe can be fitted with thehyperbola shown in formula (8) (erefore following thededuction idea of Duncan and Chang model of soil [31] anonlinear expression of the soil spring coefficients of the

Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)

0

10

20

30

40

50

60

70

80

90

100


HD = 1HD = 3

HD = 5HD = 7

(a)

10

20

30

40

50

60

70

80

90

Peak

resis

tanc

e of s

oil m

ass F

m (K

Nm

)

D = 90mm1 2 3 4 5 6 7 8 90

HD

Numerical calculationFormula (3)ALA method

(b)

Figure 16 (e comparison of formula (3) to the ALA method (a) Soil resistance displacement curve calculated by the numerical method(b) (e peak resistance obtained by formula (3) ALA method and numerical calculation

S m (m

m)

0

25

50

75

100

125

150

175

200

1 2 3 4 5 6 7 8 90HD

Case1Case2

Case3Case4

(a)

S mD

0

1

2

3

4

5

1 2 3 4 5 6 7 8 90HD

Case2Case3Case4

(b)

Figure 17 Plot of Sm versus HD (a) Experimental data (b) Comparison between the results calculated from formula (7) and the ex-perimental results


pipe-soil interaction is constructed as shown in formula (9)or (10)

F S

a + bS (8)

in which a 1(FS)i 1Ki is the reciprocal of initial stiffnesscoefficient of soil spring and b 1Fult Fult is the soil re-sistance corresponding to asymptotic line

Kt Ki 1 minus Rf

F

Fm

1113890 1113891

2

(9)

Kt 1

Ki 1Ki( 1113857 + RfSFm1113872 11138731113872 11138732 (10)

in which Kt is tangent stiffness coefficient of soil spring Kiindicates the initial stiffness coefficient of soil spring Rfdenotes the damage ratio and Rf FmFult

Figure 18 shows the change of the initial stiffness co-efficient of soil springKi and of the damage ratio Rf followingthe depth-diameter ratioHD As shown in Figure 18(a) theinitial stiffness coefficient of soil spring Ki decreases with theincrease of HD but the relationship curves are differentunder different site conditions which means that the initialstiffness coefficient of soil spring Ki is affected by thepressure of overlying soil and the depth-diameter ratio HD(erefore formula (11) is suggested to describe the rela-tionship among them

Ki kK

H

D1113874 1113875pa

cH

pa

1113888 1113889

nK

(11)

in which pa means atmospheric pressure value andpa 1014 kPa c is the natural unit weight of overlying soiland kK and nK are test parameters which may be deter-mined readily from the results of a series of tests by plottingthe values of Ki(paHD) against cHpa on log-log scalesand fitting a straight line to the data as shown inFigure 19(a)

Similarly the relationship among the damage ratio Rfthe overburden pressure cH and the depth-diameter ratioHD are obtained

Rf kR

H

D1113874 1113875

cH

pa

1113888 1113889

nR

(12)

in which kRand nR are test parameters which may be de-termined readily from the results of a series of tests as shownin Figure 19(b)

(e fitting curves of Ki and Rf are shown in Figure 18and the above parameters obtained from the experiments arelisted in Table 4 As can be seen from Table 4 the parameternK and nR are less than zero and the parameters kK and nK

decrease with the increase of moisture content and increaseswith the increase of dry unit weight However there is noobvious change rule in kR and nR (e bottom row of Table 4gives the fitting parameters based on all data which take intoaccount the effects of soil dry unit weight moisture content

K ip

a

0

20

40

60

80

100

120

3 6 9 12 150HD

Data from Case 3Data from Case 4Fitting curve for Case 1 (data from Case 1)Fitting curve for Case 2 (data from Case 2)

Data from Case 1Data from Case 2

Fitting curve for Case 3(data from Case 3)

Fitting curve for Case 1 (all data)Fitting curve for Case 2 (all data) Fitting curve for Case 3 (all data)Fitting curve for Case 4 (all data)

Fitting curve for Case 4 (data from Case 4)

(a)

Rf

04

08

12

16

20

3 6 9 12 150HD






(b)

Figure 18 Fitting curve of Ki and Rf (a) Ki versus HD (b) Rf versus HD


of soil and depth-diameter ratio HD (e value of AdjR-Square indicates that the fitting from formulae (11) and(12) have high accuracy

(e tangent stiffness coefficient of soil spring in theprocess of pipe-soil interaction can be determined fromformula (9) or (10) after the peak resistance of soil is ob-tained from formulae (3)minus(6) based on formulae (11) and(12) and Table 4

5 Conclusions

(e process of soil resistance in horizontal movement ofpipe is studied based on physical model tests of soil-pipeinteraction in silty clay field in Beijing region in which someinfluence factors are considered such as pipe diameters soilconsistency state dry unit weight and depth-diameter ratio(e paper focuses on the failure modes of soil the peakresistance of soil the corresponding displacement to peakresistance and the nonlinear property of silty clay spring

When the moisture content of soil is lower than theplastic limited moisture content the horizontal resistance-displacement curve of soil before the peak resistance reached

is approximately linear and the displacement correspondingto the peak resistance is very small about 30mm and is notaffected by the change of depth-diameter ratio When themoisture content of soil is higher than the plastic limitedmoisture content the soil resistance increases quickly at firstthen gradually becomes gentle the displacement corre-sponding to the peak resistance increases gradually with theincreasing of the depth-diameter ratio

(e failure modes of soil under deep buried conditionand shallow buried condition of the pipe are different (eALA method can be used to estimate the peak soil resistanceof silty clay sites in Beijing region when the depth-diameterratio is less than or equal to 3 but the results are slightlyoverestimated and Wangrsquos method cannot be applied di-rectly to the silty clay in Beijing region A method for de-termining the peak resistance of silty clay in Beijing region isproposed

(e nonlinear properties of silty clay spring can bedescribed from formulae (9) or (10)

(e displacement expression given by formula (7) isobtained from the condition of 60mm pipe diameter whichneeds to be verified for other pipe diameter conditions

log

(Ki(p aH

D))

ndash02

00

02

04

06

08

10

12

14

16

ndash20 ndash18 ndash16 ndash14 ndash12 ndash10 ndash08ndash22log (γHpa)

Data from Case 1Fitting curve for Case 1Data from Case 2Fitting curve for Case 2Data from Case 3

Fitting curve for Case 3Data from Case 4Fitting curve for Case 4Fitting curve for all data

(a)lo

g (R

f(H

D))




ndash14

ndash12

ndash10

ndash08

ndash06

ndash04

ndash02

00

02

(b)

Figure 19 Fitting process curve (a)Ki(paHD) versus cHpa (b)Rf(HD) versus cHpa

Table 4 Parameters for describing nonlinear spring of soil

Case Dry unit weight (kNm3) Moisture content () kK nK kR nR

Adj R-SquareKi Rf

1 16 10 00700 minus13799 000546 minus11620 09637 095612 16 16 00094 minus19226 000335 minus13358 09426 097953 16 20 00013 minus25312 000564 minus11463 09559 096134 17 16 00503 minus13856 000469 minus12599 09830 09810

For all data 00148 minus17598 000465 minus12267 08952 09672


Data Availability

All data models and code generated or used during thestudy are included within the article

Conflicts of Interest

(e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

(e authors acknowledge the Scientific Research Fund ofInstitute of Engineering Mechanics China EarthquakeAdministration (Grant no 2018D09) and National NaturalScience Foundation of China (Grant no 51808018) for thefinancial assistance that made this investigation possible

References

[1] B Dadfar M Hesham El Naggar andM Nastev ldquoOvalizationof steel energy pipelines buried in saturated sands duringground deformationsrdquo Computers and Geotechnics vol 69pp 105ndash113 2015

[2] T Sheldon H Sezen and I Moore ldquoBeam-on-Springsmodeling of jointed pipe culvertsrdquo Journal of Performance ofConstructed Facilities vol 30 no 2 Article ID 040150022016

[3] V E Melissianos G P Korakitis C J Gantes andG D Bouckovalas ldquoNumerical evaluation of the effectivenessof flexible joints in buried pipelines subjected to strike-slipfault rupturerdquo Soil Dynamics and Earthquake Engineeringvol 90 pp 395ndash410 2016

[4] V E Melissianos D Vamvatsikos and C J Gantes ldquoPer-formance-based assessment of protection measures for buriedpipes at strike-slip fault crossingsrdquo Soil Dynamics andEarthquake Engineering vol 101 pp 1ndash11 2017

[5] S Hamzeh and J Vahid ldquoIntensity measures for the as-sessment of the seismic response of buried steel pipelinesrdquoBulletin of Earthquake Engineering vol 14 pp 1265ndash12842016

[6] X Liu H Zhang K Wu M Xia Y Chen and M LildquoBuckling failure mode analysis of buried X80 steel gaspipeline under reverse fault displacementrdquo EngineeringFailure Analysis vol 77 pp 50ndash64 2017

[7] B Dezhkam and A Z Nouri ldquoDynamic response of nano-particle-water pipes buried in the soil subjected to far-faultearthquake using numerical methodrdquo Soil Dynamics andEarthquake Engineering vol 113 pp 174ndash179 2018

[8] X Liu H Zhang B Wang et al ldquoLocal buckling behavior andplastic deformation capacity of high-strength pipe at strike-slip fault crossingrdquo Metals vol 8 no 22 2018

[9] Z Zhong S Wang M Zhao X Du and L Li ldquoPerformanceof ductile iron push-on joints rehabilitated with CIPP linerunder repetitive and seismic loadingsrdquo Soil Dynamics andEarthquake Engineering vol 115 pp 776ndash786 2018

[10] Y S Hsu ldquoFinite element approach of the buried pipeline ontensionless foundation under random ground excitationrdquoMathematics and Computers in Simulation vol 169pp 149ndash165 2020

[11] J M E Audibert and K J Nyman ldquoSoil restraint againsthorizontal motion of pipesrdquo Journal of the GeotechnicalEngineering Division vol 103 no 12 pp 1119ndash1142 1977

[12] C H Trautmann T D OrsquoRourfce and F H Kulhawy ldquoUpliftforce-displacement response of buried piperdquo Journal ofGeotechnical Engineering vol 111 no 9 pp 1061ndash1076 1985

[13] S Yimsiri K Soga K Yoshizaki G R Dasari andT D OrsquoRourke ldquoLateral and upward soil-pipeline interac-tions in sand for deep embedment conditionsrdquo Journal ofGeotechnical and Geoenvironmental Engineering vol 130no 8 pp 830ndash842 2004

[14] P J Guo and D F E Stolle ldquoLateral pipe-soil interaction insand with reference to scale effectrdquo Journal of Geotechnicaland Geoenvironmental Engineering vol 131 no 3 pp 338ndash349 2005

[15] K Badv and KE Daryani ldquoAn investigation into the upwardand lateral soil-pipeline interaction in sand using finite dif-ference methodrdquo Iranian Journal of Science and TechnologyTansaction B Engineering vol 34 no B4 pp 433ndash445 2010

[16] R Liu SW Yan HBWang et al ldquoModel tests on soil restraintto pipelines buried in sandrdquo Chinese Journal of GeotechnicalEngineering vol 33 no 4 pp 559ndash565 2011 in Chinese

[17] J K Jung T D OrsquoRourke and N A Olson ldquoLateral soil-pipeinteraction in dry and partially saturated sandrdquo Journal ofGeotechnical and Geoenvironmental Engineering vol 139no 12 pp 2028ndash2036 2013

[18] LY Li and JL Li ldquoUltimate soil bearing capacity of lateralpipeline-sand interactionrdquo Journal of Beijing University ofTechnology vol 42 no 6 pp 933ndash938 2016 in Chinese

[19] D J Robert K Soga T D OrsquoRourke et al ldquoLateral load-displacement behavior of pipelines in unsatuarated sandsrdquoJournal of Geotechnical and Geoenvironmental Engineeringvol 142 no 11 2016

[20] J Oliveira M Almeida M Almeida et al ldquoPhysical modelingof lateral clay-pipe interactionrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 136 no 7 pp 950ndash9562009

[21] R Liu S Z Guo H B Wang et al ldquoSoil resistance acting onburied pipelines in Bohai Bay soft clayrdquo Chinese Journal ofGeotechnical Engineering vol 35 no 5 pp 961ndash967 2013 inChinese

[22] R Liu S Yan and XWu ldquoModel test studies on soil restraintto pipeline buriedin Bohai soft clayrdquo Journal of PipelineSystems Engineering and Practice vol 4 no 1 pp 49ndash562013

[23] R Liu P Basu and H Xiong ldquoLaboratory tests and thermalbuckling analysis for pipes buried in Bohai soft clayrdquo MarineStructures vol 43 pp 44ndash60 2015

[24] GB50032-2003 ldquoCode of seismic design of outdoor watersupply sewerage gas and heating engineeringrdquo Ministry ofConstruction of the Peoplersquos Republic of China BeijingChina 2003

[25] American Lifelines Alliance ldquoGuidelines for the design ofburied steel piperdquo Federal Emergency Management Agency(FEMA) Washington DC USA 2001 httpwwwamericanlifelinesallianceorg

[26] C G Zhang and H J Zhang ldquoExperiment study on therelationship between water content and shear strength pa-rameters of silty clayrdquo Journal of North China Institute ofScience and Technology vol 2 pp 27ndash29 2011 in Chinese

[27] L Li X Liu X Du et al ldquoAnalysis on numerical simulationmodel for seismic response of a buried pipelinerdquo EarthquakeEngineering and Engineering Dynamics vol 35 no 6pp 106ndash113 2015 in Chinese

[28] Z Y Ou ldquoAnalysis and design theory and practice of deepexcavation engineeringrdquo Science and technology books CoLtd Taipei China 2002 in Chinese


[29] L C Peng ldquoStress analysis methods for underground pipe-linesrdquo Pipeline Industry vol 47 no 5 pp 65ndash74 1978

[30] H B Wang ldquoStudy on the interaction between soil andsubmarine pipeline in lateral buckling moderdquo M Eng thesisTianjin University Tianjin China 2010

[31] J M Duncan and C Y Chang ldquoNonlinear analysis of stressand strain in soilsrdquo Journal of Soil Mechanics and FoundationsDivision ASCE vol 96 no SM5 pp 1629ndash1653 1970


pipe-soil interaction in clayey soil Oliveira et al [20] carriedout the centrifuge physical model test of pipe-soft clay in-teraction and proposed a method for calculating the ultimatebearing capacity of soft clay when the pipeline moved lat-erally Liu et al [21ndash23] conducted a series of pipe-soil in-teractionmodel tests on soft clay in Bohai region analyzed thefailure mode of the soil and proposed a formula for calcu-lating the peak resistance of soil

All the above studies assumed that the soil around thepipe is an ideal elastic-plastic material which is inconsistentwith the nonlinear characteristics of the elastic mechanicalsegment of soil material Moreover most of the previousstudies focused on sand (ere are few studies on pipe-soilinteraction in clayey soil and the research object of pipe-clayinteraction is only on saturated soft clay In the constructionof directly buried pipelines in Beijing region the backfillinginto the trench is usuallymade of claymaterials such as clayeysilt silty clay or clay which are taken from the constructionarea(ese clayeymaterials aremostly above the groundwaterlevel and belong to unsaturated soils (e matrix suctionamong solid liquid and gas phases in soils makes theproperties of unsaturated soils significantly different fromthose of saturated soils and dry soils Few studies publishedfocus on the effect of moisture content in clayey soil on pipe-soil interaction Besides the Code for Seismic Design ofOutdoor Water Supply Drainage and Gas (ermal Engi-neering in China [24] and American Lifelines Alliance [25]recommended the same method for calculating the peakbearing capacity of clayey soil but there are differences in theunit of soil parameters which need to be checked In view ofthe above discussion the authors carried out some physicalmodel tests of pipe-soil interaction with the silty clay inBeijing region Based on the experimental results the authorsdiscuss the determination of key parameters of soil spring andthe mathematical description of soil spring coefficient inorder to provide an experimental basis for the laying ofpipelines in silty clay site in Beijing region

2 Physical Model Tests

Figure 2 shows the photo of experiment device in which thetest container is welded by steel plate with the size of

1000mmtimes 500mmtimes 1100mm (lengthtimeswidthtimes height) Aplexiglass observation window of 900mmtimes 700mm isarranged on the front panel of container for observing thedeformation and failure process of soil during test (ere aretwo parallel vertical joints on the right panel of the containerfor the steel strand to pass through(e actuator and the testpipe are connected by two steel strands and the force andthe movement are automatically recorded via the actuatoracquisition system Figure 3 shows the connection betweenthe steel strand and the test pipe

(e test pipes are steel tubes with the length of 490mm(e diameter of the pipes are the four common sizes in pipeengineering which are 30mm 60mm 102mm and140mm respectively (e test results of 60mm diameterpipe are as the benchmark to analyse the influence of pipediameter on the horizontal resistance of soil

(e test soil is the typical silty clay in Beijing region Itsplastic limited moisture content is 15 liquid limitedmoisture content is 29 and natural moisture content is16 Four soil samples reconstituted by controlling themoisture content and dry unit weight of the soil are in stiffhard plastic and plastic state respectively (e measuredcohesive force and measured internal friction angle of thesesoil samples are listed in Table 1 which are obtained by statictriaxial test As shown in Table 1 the change of cohesiveforce and internal friction angle of silty clay is in goodagreement with those in literature [26] that is the cohesiveforce and internal friction angle decreases with the increaseof water content in silty clay

(e test cases are shown in Table 2 of which the first tofourth cases are to analyse the effect of the depth-diameterratio (HD) and the soil properties on the test results and thefifth case is to investigate the effect of pipe diameter

During the tests the Earth pressure acting on the pipewall is also monitored Since there is only the upstreamsurface of pipe interacting with soil in the test process sevenEarth pressure sensors are arranged at 30deg intervals on theupstream surface of pipe which interacts with soil (eFlexiForce sensor produced by Tekscan company a kind ofthin film pressure sensor is used to measure the Earthpressure on pipe in test Figure 4 shows the location ofpressure sensors on pipe and a photo of thin film pressuresensor (e thin film Earth pressure sensor consists of acircular pressure sensing area a flat wire and a pin (e pinis connected with the data acquisition system through aconnecting wire (e thin film Earth pressure sensor is a

Fm

F

Sm S

Figure 1 General soil spring model

Model test of pipe-soil interaction

Test container

Actuator

Steel strands

Figure 2 Model test device


(a) (b)




I 160 10

14

1610 121II 16 1364 102III 170 20 503 88IV 16 649 233

Table 2 Test cases

CaseTest soil


1 I Stiff 60 1 3 5 710


(a) (b)



























078

m

1m


(a) (b)






Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)

0

1

2

3

4

5

6

7

8

9

10



(a)


Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)

0

2

4

6

8

10

12

14

16

18

20


(b)

Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)



0

5

10

15

20

25

30

35

(c)








Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)

0

5

10

15

20

25

30

35

40


Lr = 02mLr = 04mLr = 06m

(a)

Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)

0

5

10

15

20

25

30

35

40


Lb = 045mLb = 028mLb = 018m

(b)

Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)

0

5

10

15

20

25

30

35

40


Lf = 10mLf = 03mLf = 045m

Lf = 055mLf = 065m

(c)








0 2 4 6 8 10 12 14 16 18 20 22 24

Case 1


Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)

0

10

20

30

40

50

60

70

HD = 1HD = 3

HD = 5HD = 7

(a)

0 2 4 6 8 10 12 14 16 18 20 22 24

Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)


Case 2

0

10

20

30

40

50

60

70

HD = 1HD = 3 HD = 8

HD = 5

(b)

Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)


0

10

20

30

40

50

60

70

Case 3

HD = 1HD = 3HD = 4

HD = 5HD = 6HD = 7

(c)

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14 16 18 20 22 24

Hor

izon

tal s

oil r

esist

ance

F (k

Nm

) Case 4


HD = 1HD = 3

HD = 5HD = 7

(d)









0

10

20

30

40

50

60

70


Hor

izon

tal s

oil r

esist

ance

F (k

Nm

) HD = 3

D =30mmD = 60mm

D = 102mmD = 140mm









Pipe

Damaged surface


+9060e ndash 02

+8236e ndash 02

+7413e ndash 02

+6589e ndash 02

+5765e ndash 02

+4942e ndash 02

+4118e ndash 02

+3295e ndash 02

+2471e ndash 02

+1647e ndash 02

+8236e ndash 03

+0000e + 00

(a)

Pipe

Surface upli


+9324e ndash 02

+8476e ndash 02

+7629e ndash 02

+6781e ndash 02

+5933e ndash 02

+5086e ndash 02

+4238e ndash 02

+3390e ndash 02

+2543e ndash 02

+1695e ndash 02

+8476e ndash 03

+0000e + 00

(b)





0 20

40

60

80

100

120

140

160180

Eart

h pr

essu

re (k

Pa)

350300250200150100

500

50100150200250300350

HD = 10HD = 8HD = 7

HD = 5HD = 3HD = 1

(a)

030

60

90

120

150180

HD = 3HD = 1

Eart

h pr

essu

re (k

Pa)

HD = 10HD = 8HD = 5

350300250200150100

500

50100150200250300350

(b)

030

60

90

120

150180

Eart

h pr

essu

re (k

Pa)

350300250200150100

500

50100150200250300350

HD = 8HD = 7HD = 6HD = 5

HD = 4HD = 3HD = 1

(c)

030

60

90

120

150180

Eart

h pr

essu

re (k

Pa)

1000

800

600

400

200

0

200

400

600

800

1000

HD = 20HD = 15HD = 10

HD = 7HD = 5HD = 3

(d)



Fm B212

c H1 + D( 11138572Kp + 2c H1 + D( 1113857

Kp

11139691113876 1113877 (2)




Fm B12

c H +D

21113874 1113875

2Kp + 2c H +

D

21113874 1113875

Kp

11139691113890 1113891 (3)




B aH

D1113874 1113875

b

(4)

a a1 + b1ω + c1ω2

1113872 1113873c

(1 + ω)cw

1113888 1113889

d1

(5)

b a2 + b2ω (6)





D = 60mm

B = 05417 (HD)00559

B = 064737 (HD)ndash006351

B = 02733 (HD)006002

B = 025073 (HD)001275

2 4 6 80 10HD

02

03

04

05

06

07

B

Case 1Case 2

Case 3Case 4








070

065060055050045040035030025

a

1012

1416

1820

ω ()

200195

190185

180175 γ (k

Nm3 )D = 60mm


(a)

D = 60mm

ndash016

ndash012

ndash008

ndash004

000

004

008

012

016

b

8 12 16 20 24 28 324ω ()


(b)


HD = 3

0

20

40

60

80

100

120

Peak

resis

tanc

e of s

oil m

ass F

m (k

Nm

)






Sm

D 00037 times

H

D1113874 1113875

3242+ 048 (7)



Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)

0

10

20

30

40

50

60

70

80

90

100


HD = 1HD = 3

HD = 5HD = 7

(a)

10

20

30

40

50

60

70

80

90

Peak

resis

tanc

e of s

oil m

ass F

m (K

Nm

)

D = 90mm1 2 3 4 5 6 7 8 90

HD


(b)


S m (m

m)

0

25

50

75

100

125

150

175

200

1 2 3 4 5 6 7 8 90HD

Case1Case2

Case3Case4

(a)

S mD

0

1

2

3

4

5

1 2 3 4 5 6 7 8 90HD

Case2Case3Case4

(b)




F S

a + bS (8)


Kt Ki 1 minus Rf

F

Fm

1113890 1113891

2

(9)

Kt 1

Ki 1Ki( 1113857 + RfSFm1113872 11138731113872 11138732 (10)



Ki kK

H

D1113874 1113875pa

cH

pa

1113888 1113889

nK

(11)



Rf kR

H

D1113874 1113875

cH

pa

1113888 1113889

nR

(12)




K ip

a

0

20

40

60

80

100

120

3 6 9 12 150HD






(a)

Rf

04

08

12

16

20

3 6 9 12 150HD






(b)





5 Conclusions







log

(Ki(p aH

D))

ndash02

00

02

04

06

08

10

12

14

16




(a)lo

g (R

f(H

D))




ndash14

ndash12

ndash10

ndash08

ndash06

ndash04

ndash02

00

02

(b)




Adj R-SquareKi Rf




Data Availability




Acknowledgments


References


































(a) (b)




I 160 10

14

1610 121II 16 1364 102III 170 20 503 88IV 16 649 233

Table 2 Test cases

CaseTest soil


1 I Stiff 60 1 3 5 710


(a) (b)



























078

m

1m


(a) (b)






Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)

0

1

2

3

4

5

6

7

8

9

10



(a)


Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)

0

2

4

6

8

10

12

14

16

18

20


(b)

Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)



0

5

10

15

20

25

30

35

(c)








Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)

0

5

10

15

20

25

30

35

40


Lr = 02mLr = 04mLr = 06m

(a)

Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)

0

5

10

15

20

25

30

35

40


Lb = 045mLb = 028mLb = 018m

(b)

Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)

0

5

10

15

20

25

30

35

40


Lf = 10mLf = 03mLf = 045m

Lf = 055mLf = 065m

(c)








0 2 4 6 8 10 12 14 16 18 20 22 24

Case 1


Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)

0

10

20

30

40

50

60

70

HD = 1HD = 3

HD = 5HD = 7

(a)

0 2 4 6 8 10 12 14 16 18 20 22 24

Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)


Case 2

0

10

20

30

40

50

60

70

HD = 1HD = 3 HD = 8

HD = 5

(b)

Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)


0

10

20

30

40

50

60

70

Case 3

HD = 1HD = 3HD = 4

HD = 5HD = 6HD = 7

(c)

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14 16 18 20 22 24

Hor

izon

tal s

oil r

esist

ance

F (k

Nm

) Case 4


HD = 1HD = 3

HD = 5HD = 7

(d)









0

10

20

30

40

50

60

70


Hor

izon

tal s

oil r

esist

ance

F (k

Nm

) HD = 3

D =30mmD = 60mm

D = 102mmD = 140mm









Pipe

Damaged surface


+9060e ndash 02

+8236e ndash 02

+7413e ndash 02

+6589e ndash 02

+5765e ndash 02

+4942e ndash 02

+4118e ndash 02

+3295e ndash 02

+2471e ndash 02

+1647e ndash 02

+8236e ndash 03

+0000e + 00

(a)

Pipe

Surface upli


+9324e ndash 02

+8476e ndash 02

+7629e ndash 02

+6781e ndash 02

+5933e ndash 02

+5086e ndash 02

+4238e ndash 02

+3390e ndash 02

+2543e ndash 02

+1695e ndash 02

+8476e ndash 03

+0000e + 00

(b)





0 20

40

60

80

100

120

140

160180

Eart

h pr

essu

re (k

Pa)

350300250200150100

500

50100150200250300350

HD = 10HD = 8HD = 7

HD = 5HD = 3HD = 1

(a)

030

60

90

120

150180

HD = 3HD = 1

Eart

h pr

essu

re (k

Pa)

HD = 10HD = 8HD = 5

350300250200150100

500

50100150200250300350

(b)

030

60

90

120

150180

Eart

h pr

essu

re (k

Pa)

350300250200150100

500

50100150200250300350

HD = 8HD = 7HD = 6HD = 5

HD = 4HD = 3HD = 1

(c)

030

60

90

120

150180

Eart

h pr

essu

re (k

Pa)

1000

800

600

400

200

0

200

400

600

800

1000

HD = 20HD = 15HD = 10

HD = 7HD = 5HD = 3

(d)



Fm B212

c H1 + D( 11138572Kp + 2c H1 + D( 1113857

Kp

11139691113876 1113877 (2)




Fm B12

c H +D

21113874 1113875

2Kp + 2c H +

D

21113874 1113875

Kp

11139691113890 1113891 (3)




B aH

D1113874 1113875

b

(4)

a a1 + b1ω + c1ω2

1113872 1113873c

(1 + ω)cw

1113888 1113889

d1

(5)

b a2 + b2ω (6)





D = 60mm

B = 05417 (HD)00559

B = 064737 (HD)ndash006351

B = 02733 (HD)006002

B = 025073 (HD)001275

2 4 6 80 10HD

02

03

04

05

06

07

B

Case 1Case 2

Case 3Case 4








070

065060055050045040035030025

a

1012

1416

1820

ω ()

200195

190185

180175 γ (k

Nm3 )D = 60mm


(a)

D = 60mm

ndash016

ndash012

ndash008

ndash004

000

004

008

012

016

b

8 12 16 20 24 28 324ω ()


(b)


HD = 3

0

20

40

60

80

100

120

Peak

resis

tanc

e of s

oil m

ass F

m (k

Nm

)






Sm

D 00037 times

H

D1113874 1113875

3242+ 048 (7)



Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)

0

10

20

30

40

50

60

70

80

90

100


HD = 1HD = 3

HD = 5HD = 7

(a)

10

20

30

40

50

60

70

80

90

Peak

resis

tanc

e of s

oil m

ass F

m (K

Nm

)

D = 90mm1 2 3 4 5 6 7 8 90

HD


(b)


S m (m

m)

0

25

50

75

100

125

150

175

200

1 2 3 4 5 6 7 8 90HD

Case1Case2

Case3Case4

(a)

S mD

0

1

2

3

4

5

1 2 3 4 5 6 7 8 90HD

Case2Case3Case4

(b)




F S

a + bS (8)


Kt Ki 1 minus Rf

F

Fm

1113890 1113891

2

(9)

Kt 1

Ki 1Ki( 1113857 + RfSFm1113872 11138731113872 11138732 (10)



Ki kK

H

D1113874 1113875pa

cH

pa

1113888 1113889

nK

(11)



Rf kR

H

D1113874 1113875

cH

pa

1113888 1113889

nR

(12)




K ip

a

0

20

40

60

80

100

120

3 6 9 12 150HD






(a)

Rf

04

08

12

16

20

3 6 9 12 150HD






(b)





5 Conclusions







log

(Ki(p aH

D))

ndash02

00

02

04

06

08

10

12

14

16




(a)lo

g (R

f(H

D))




ndash14

ndash12

ndash10

ndash08

ndash06

ndash04

ndash02

00

02

(b)




Adj R-SquareKi Rf




Data Availability




Acknowledgments


References


























































078

m

1m


(a) (b)






Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)

0

1

2

3

4

5

6

7

8

9

10



(a)


Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)

0

2

4

6

8

10

12

14

16

18

20


(b)

Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)



0

5

10

15

20

25

30

35

(c)








Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)

0

5

10

15

20

25

30

35

40


Lr = 02mLr = 04mLr = 06m

(a)

Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)

0

5

10

15

20

25

30

35

40


Lb = 045mLb = 028mLb = 018m

(b)

Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)

0

5

10

15

20

25

30

35

40


Lf = 10mLf = 03mLf = 045m

Lf = 055mLf = 065m

(c)








0 2 4 6 8 10 12 14 16 18 20 22 24

Case 1


Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)

0

10

20

30

40

50

60

70

HD = 1HD = 3

HD = 5HD = 7

(a)

0 2 4 6 8 10 12 14 16 18 20 22 24

Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)


Case 2

0

10

20

30

40

50

60

70

HD = 1HD = 3 HD = 8

HD = 5

(b)

Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)


0

10

20

30

40

50

60

70

Case 3

HD = 1HD = 3HD = 4

HD = 5HD = 6HD = 7

(c)

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14 16 18 20 22 24

Hor

izon

tal s

oil r

esist

ance

F (k

Nm

) Case 4


HD = 1HD = 3

HD = 5HD = 7

(d)









0

10

20

30

40

50

60

70


Hor

izon

tal s

oil r

esist

ance

F (k

Nm

) HD = 3

D =30mmD = 60mm

D = 102mmD = 140mm









Pipe

Damaged surface


+9060e ndash 02

+8236e ndash 02

+7413e ndash 02

+6589e ndash 02

+5765e ndash 02

+4942e ndash 02

+4118e ndash 02

+3295e ndash 02

+2471e ndash 02

+1647e ndash 02

+8236e ndash 03

+0000e + 00

(a)

Pipe

Surface upli


+9324e ndash 02

+8476e ndash 02

+7629e ndash 02

+6781e ndash 02

+5933e ndash 02

+5086e ndash 02

+4238e ndash 02

+3390e ndash 02

+2543e ndash 02

+1695e ndash 02

+8476e ndash 03

+0000e + 00

(b)





0 20

40

60

80

100

120

140

160180

Eart

h pr

essu

re (k

Pa)

350300250200150100

500

50100150200250300350

HD = 10HD = 8HD = 7

HD = 5HD = 3HD = 1

(a)

030

60

90

120

150180

HD = 3HD = 1

Eart

h pr

essu

re (k

Pa)

HD = 10HD = 8HD = 5

350300250200150100

500

50100150200250300350

(b)

030

60

90

120

150180

Eart

h pr

essu

re (k

Pa)

350300250200150100

500

50100150200250300350

HD = 8HD = 7HD = 6HD = 5

HD = 4HD = 3HD = 1

(c)

030

60

90

120

150180

Eart

h pr

essu

re (k

Pa)

1000

800

600

400

200

0

200

400

600

800

1000

HD = 20HD = 15HD = 10

HD = 7HD = 5HD = 3

(d)



Fm B212

c H1 + D( 11138572Kp + 2c H1 + D( 1113857

Kp

11139691113876 1113877 (2)




Fm B12

c H +D

21113874 1113875

2Kp + 2c H +

D

21113874 1113875

Kp

11139691113890 1113891 (3)




B aH

D1113874 1113875

b

(4)

a a1 + b1ω + c1ω2

1113872 1113873c

(1 + ω)cw

1113888 1113889

d1

(5)

b a2 + b2ω (6)





D = 60mm

B = 05417 (HD)00559

B = 064737 (HD)ndash006351

B = 02733 (HD)006002

B = 025073 (HD)001275

2 4 6 80 10HD

02

03

04

05

06

07

B

Case 1Case 2

Case 3Case 4








070

065060055050045040035030025

a

1012

1416

1820

ω ()

200195

190185

180175 γ (k

Nm3 )D = 60mm


(a)

D = 60mm

ndash016

ndash012

ndash008

ndash004

000

004

008

012

016

b

8 12 16 20 24 28 324ω ()


(b)


HD = 3

0

20

40

60

80

100

120

Peak

resis

tanc

e of s

oil m

ass F

m (k

Nm

)






Sm

D 00037 times

H

D1113874 1113875

3242+ 048 (7)



Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)

0

10

20

30

40

50

60

70

80

90

100


HD = 1HD = 3

HD = 5HD = 7

(a)

10

20

30

40

50

60

70

80

90

Peak

resis

tanc

e of s

oil m

ass F

m (K

Nm

)

D = 90mm1 2 3 4 5 6 7 8 90

HD


(b)


S m (m

m)

0

25

50

75

100

125

150

175

200

1 2 3 4 5 6 7 8 90HD

Case1Case2

Case3Case4

(a)

S mD

0

1

2

3

4

5

1 2 3 4 5 6 7 8 90HD

Case2Case3Case4

(b)




F S

a + bS (8)


Kt Ki 1 minus Rf

F

Fm

1113890 1113891

2

(9)

Kt 1

Ki 1Ki( 1113857 + RfSFm1113872 11138731113872 11138732 (10)



Ki kK

H

D1113874 1113875pa

cH

pa

1113888 1113889

nK

(11)



Rf kR

H

D1113874 1113875

cH

pa

1113888 1113889

nR

(12)




K ip

a

0

20

40

60

80

100

120

3 6 9 12 150HD






(a)

Rf

04

08

12

16

20

3 6 9 12 150HD






(b)





5 Conclusions







log

(Ki(p aH

D))

ndash02

00

02

04

06

08

10

12

14

16




(a)lo

g (R

f(H

D))




ndash14

ndash12

ndash10

ndash08

ndash06

ndash04

ndash02

00

02

(b)




Adj R-SquareKi Rf




Data Availability




Acknowledgments


References





































Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)

0

1

2

3

4

5

6

7

8

9

10



(a)


Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)

0

2

4

6

8

10

12

14

16

18

20


(b)

Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)



0

5

10

15

20

25

30

35

(c)








Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)

0

5

10

15

20

25

30

35

40


Lr = 02mLr = 04mLr = 06m

(a)

Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)

0

5

10

15

20

25

30

35

40


Lb = 045mLb = 028mLb = 018m

(b)

Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)

0

5

10

15

20

25

30

35

40


Lf = 10mLf = 03mLf = 045m

Lf = 055mLf = 065m

(c)








0 2 4 6 8 10 12 14 16 18 20 22 24

Case 1


Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)

0

10

20

30

40

50

60

70

HD = 1HD = 3

HD = 5HD = 7

(a)

0 2 4 6 8 10 12 14 16 18 20 22 24

Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)


Case 2

0

10

20

30

40

50

60

70

HD = 1HD = 3 HD = 8

HD = 5

(b)

Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)


0

10

20

30

40

50

60

70

Case 3

HD = 1HD = 3HD = 4

HD = 5HD = 6HD = 7

(c)

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14 16 18 20 22 24

Hor

izon

tal s

oil r

esist

ance

F (k

Nm

) Case 4


HD = 1HD = 3

HD = 5HD = 7

(d)









0

10

20

30

40

50

60

70


Hor

izon

tal s

oil r

esist

ance

F (k

Nm

) HD = 3

D =30mmD = 60mm

D = 102mmD = 140mm









Pipe

Damaged surface


+9060e ndash 02

+8236e ndash 02

+7413e ndash 02

+6589e ndash 02

+5765e ndash 02

+4942e ndash 02

+4118e ndash 02

+3295e ndash 02

+2471e ndash 02

+1647e ndash 02

+8236e ndash 03

+0000e + 00

(a)

Pipe

Surface upli


+9324e ndash 02

+8476e ndash 02

+7629e ndash 02

+6781e ndash 02

+5933e ndash 02

+5086e ndash 02

+4238e ndash 02

+3390e ndash 02

+2543e ndash 02

+1695e ndash 02

+8476e ndash 03

+0000e + 00

(b)





0 20

40

60

80

100

120

140

160180

Eart

h pr

essu

re (k

Pa)

350300250200150100

500

50100150200250300350

HD = 10HD = 8HD = 7

HD = 5HD = 3HD = 1

(a)

030

60

90

120

150180

HD = 3HD = 1

Eart

h pr

essu

re (k

Pa)

HD = 10HD = 8HD = 5

350300250200150100

500

50100150200250300350

(b)

030

60

90

120

150180

Eart

h pr

essu

re (k

Pa)

350300250200150100

500

50100150200250300350

HD = 8HD = 7HD = 6HD = 5

HD = 4HD = 3HD = 1

(c)

030

60

90

120

150180

Eart

h pr

essu

re (k

Pa)

1000

800

600

400

200

0

200

400

600

800

1000

HD = 20HD = 15HD = 10

HD = 7HD = 5HD = 3

(d)



Fm B212

c H1 + D( 11138572Kp + 2c H1 + D( 1113857

Kp

11139691113876 1113877 (2)




Fm B12

c H +D

21113874 1113875

2Kp + 2c H +

D

21113874 1113875

Kp

11139691113890 1113891 (3)




B aH

D1113874 1113875

b

(4)

a a1 + b1ω + c1ω2

1113872 1113873c

(1 + ω)cw

1113888 1113889

d1

(5)

b a2 + b2ω (6)





D = 60mm

B = 05417 (HD)00559

B = 064737 (HD)ndash006351

B = 02733 (HD)006002

B = 025073 (HD)001275

2 4 6 80 10HD

02

03

04

05

06

07

B

Case 1Case 2

Case 3Case 4








070

065060055050045040035030025

a

1012

1416

1820

ω ()

200195

190185

180175 γ (k

Nm3 )D = 60mm


(a)

D = 60mm

ndash016

ndash012

ndash008

ndash004

000

004

008

012

016

b

8 12 16 20 24 28 324ω ()


(b)


HD = 3

0

20

40

60

80

100

120

Peak

resis

tanc

e of s

oil m

ass F

m (k

Nm

)






Sm

D 00037 times

H

D1113874 1113875

3242+ 048 (7)



Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)

0

10

20

30

40

50

60

70

80

90

100


HD = 1HD = 3

HD = 5HD = 7

(a)

10

20

30

40

50

60

70

80

90

Peak

resis

tanc

e of s

oil m

ass F

m (K

Nm

)

D = 90mm1 2 3 4 5 6 7 8 90

HD


(b)


S m (m

m)

0

25

50

75

100

125

150

175

200

1 2 3 4 5 6 7 8 90HD

Case1Case2

Case3Case4

(a)

S mD

0

1

2

3

4

5

1 2 3 4 5 6 7 8 90HD

Case2Case3Case4

(b)




F S

a + bS (8)


Kt Ki 1 minus Rf

F

Fm

1113890 1113891

2

(9)

Kt 1

Ki 1Ki( 1113857 + RfSFm1113872 11138731113872 11138732 (10)



Ki kK

H

D1113874 1113875pa

cH

pa

1113888 1113889

nK

(11)



Rf kR

H

D1113874 1113875

cH

pa

1113888 1113889

nR

(12)




K ip

a

0

20

40

60

80

100

120

3 6 9 12 150HD






(a)

Rf

04

08

12

16

20

3 6 9 12 150HD






(b)





5 Conclusions







log

(Ki(p aH

D))

ndash02

00

02

04

06

08

10

12

14

16




(a)lo

g (R

f(H

D))




ndash14

ndash12

ndash10

ndash08

ndash06

ndash04

ndash02

00

02

(b)




Adj R-SquareKi Rf




Data Availability




Acknowledgments


References







































Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)

0

5

10

15

20

25

30

35

40


Lr = 02mLr = 04mLr = 06m

(a)

Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)

0

5

10

15

20

25

30

35

40


Lb = 045mLb = 028mLb = 018m

(b)

Hor

izon

tal r

esist

ance

of s

oil t

o pi

pe F

(kN

)

0

5

10

15

20

25

30

35

40


Lf = 10mLf = 03mLf = 045m

Lf = 055mLf = 065m

(c)








0 2 4 6 8 10 12 14 16 18 20 22 24

Case 1


Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)

0

10

20

30

40

50

60

70

HD = 1HD = 3

HD = 5HD = 7

(a)

0 2 4 6 8 10 12 14 16 18 20 22 24

Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)


Case 2

0

10

20

30

40

50

60

70

HD = 1HD = 3 HD = 8

HD = 5

(b)

Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)


0

10

20

30

40

50

60

70

Case 3

HD = 1HD = 3HD = 4

HD = 5HD = 6HD = 7

(c)

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14 16 18 20 22 24

Hor

izon

tal s

oil r

esist

ance

F (k

Nm

) Case 4


HD = 1HD = 3

HD = 5HD = 7

(d)









0

10

20

30

40

50

60

70


Hor

izon

tal s

oil r

esist

ance

F (k

Nm

) HD = 3

D =30mmD = 60mm

D = 102mmD = 140mm









Pipe

Damaged surface


+9060e ndash 02

+8236e ndash 02

+7413e ndash 02

+6589e ndash 02

+5765e ndash 02

+4942e ndash 02

+4118e ndash 02

+3295e ndash 02

+2471e ndash 02

+1647e ndash 02

+8236e ndash 03

+0000e + 00

(a)

Pipe

Surface upli


+9324e ndash 02

+8476e ndash 02

+7629e ndash 02

+6781e ndash 02

+5933e ndash 02

+5086e ndash 02

+4238e ndash 02

+3390e ndash 02

+2543e ndash 02

+1695e ndash 02

+8476e ndash 03

+0000e + 00

(b)





0 20

40

60

80

100

120

140

160180

Eart

h pr

essu

re (k

Pa)

350300250200150100

500

50100150200250300350

HD = 10HD = 8HD = 7

HD = 5HD = 3HD = 1

(a)

030

60

90

120

150180

HD = 3HD = 1

Eart

h pr

essu

re (k

Pa)

HD = 10HD = 8HD = 5

350300250200150100

500

50100150200250300350

(b)

030

60

90

120

150180

Eart

h pr

essu

re (k

Pa)

350300250200150100

500

50100150200250300350

HD = 8HD = 7HD = 6HD = 5

HD = 4HD = 3HD = 1

(c)

030

60

90

120

150180

Eart

h pr

essu

re (k

Pa)

1000

800

600

400

200

0

200

400

600

800

1000

HD = 20HD = 15HD = 10

HD = 7HD = 5HD = 3

(d)



Fm B212

c H1 + D( 11138572Kp + 2c H1 + D( 1113857

Kp

11139691113876 1113877 (2)




Fm B12

c H +D

21113874 1113875

2Kp + 2c H +

D

21113874 1113875

Kp

11139691113890 1113891 (3)




B aH

D1113874 1113875

b

(4)

a a1 + b1ω + c1ω2

1113872 1113873c

(1 + ω)cw

1113888 1113889

d1

(5)

b a2 + b2ω (6)





D = 60mm

B = 05417 (HD)00559

B = 064737 (HD)ndash006351

B = 02733 (HD)006002

B = 025073 (HD)001275

2 4 6 80 10HD

02

03

04

05

06

07

B

Case 1Case 2

Case 3Case 4








070

065060055050045040035030025

a

1012

1416

1820

ω ()

200195

190185

180175 γ (k

Nm3 )D = 60mm


(a)

D = 60mm

ndash016

ndash012

ndash008

ndash004

000

004

008

012

016

b

8 12 16 20 24 28 324ω ()


(b)


HD = 3

0

20

40

60

80

100

120

Peak

resis

tanc

e of s

oil m

ass F

m (k

Nm

)






Sm

D 00037 times

H

D1113874 1113875

3242+ 048 (7)



Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)

0

10

20

30

40

50

60

70

80

90

100


HD = 1HD = 3

HD = 5HD = 7

(a)

10

20

30

40

50

60

70

80

90

Peak

resis

tanc

e of s

oil m

ass F

m (K

Nm

)

D = 90mm1 2 3 4 5 6 7 8 90

HD


(b)


S m (m

m)

0

25

50

75

100

125

150

175

200

1 2 3 4 5 6 7 8 90HD

Case1Case2

Case3Case4

(a)

S mD

0

1

2

3

4

5

1 2 3 4 5 6 7 8 90HD

Case2Case3Case4

(b)




F S

a + bS (8)


Kt Ki 1 minus Rf

F

Fm

1113890 1113891

2

(9)

Kt 1

Ki 1Ki( 1113857 + RfSFm1113872 11138731113872 11138732 (10)



Ki kK

H

D1113874 1113875pa

cH

pa

1113888 1113889

nK

(11)



Rf kR

H

D1113874 1113875

cH

pa

1113888 1113889

nR

(12)




K ip

a

0

20

40

60

80

100

120

3 6 9 12 150HD






(a)

Rf

04

08

12

16

20

3 6 9 12 150HD






(b)





5 Conclusions







log

(Ki(p aH

D))

ndash02

00

02

04

06

08

10

12

14

16




(a)lo

g (R

f(H

D))




ndash14

ndash12

ndash10

ndash08

ndash06

ndash04

ndash02

00

02

(b)




Adj R-SquareKi Rf




Data Availability




Acknowledgments


References







































0 2 4 6 8 10 12 14 16 18 20 22 24

Case 1


Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)

0

10

20

30

40

50

60

70

HD = 1HD = 3

HD = 5HD = 7

(a)

0 2 4 6 8 10 12 14 16 18 20 22 24

Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)


Case 2

0

10

20

30

40

50

60

70

HD = 1HD = 3 HD = 8

HD = 5

(b)

Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)


0

10

20

30

40

50

60

70

Case 3

HD = 1HD = 3HD = 4

HD = 5HD = 6HD = 7

(c)

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14 16 18 20 22 24

Hor

izon

tal s

oil r

esist

ance

F (k

Nm

) Case 4


HD = 1HD = 3

HD = 5HD = 7

(d)









0

10

20

30

40

50

60

70


Hor

izon

tal s

oil r

esist

ance

F (k

Nm

) HD = 3

D =30mmD = 60mm

D = 102mmD = 140mm









Pipe

Damaged surface


+9060e ndash 02

+8236e ndash 02

+7413e ndash 02

+6589e ndash 02

+5765e ndash 02

+4942e ndash 02

+4118e ndash 02

+3295e ndash 02

+2471e ndash 02

+1647e ndash 02

+8236e ndash 03

+0000e + 00

(a)

Pipe

Surface upli


+9324e ndash 02

+8476e ndash 02

+7629e ndash 02

+6781e ndash 02

+5933e ndash 02

+5086e ndash 02

+4238e ndash 02

+3390e ndash 02

+2543e ndash 02

+1695e ndash 02

+8476e ndash 03

+0000e + 00

(b)





0 20

40

60

80

100

120

140

160180

Eart

h pr

essu

re (k

Pa)

350300250200150100

500

50100150200250300350

HD = 10HD = 8HD = 7

HD = 5HD = 3HD = 1

(a)

030

60

90

120

150180

HD = 3HD = 1

Eart

h pr

essu

re (k

Pa)

HD = 10HD = 8HD = 5

350300250200150100

500

50100150200250300350

(b)

030

60

90

120

150180

Eart

h pr

essu

re (k

Pa)

350300250200150100

500

50100150200250300350

HD = 8HD = 7HD = 6HD = 5

HD = 4HD = 3HD = 1

(c)

030

60

90

120

150180

Eart

h pr

essu

re (k

Pa)

1000

800

600

400

200

0

200

400

600

800

1000

HD = 20HD = 15HD = 10

HD = 7HD = 5HD = 3

(d)



Fm B212

c H1 + D( 11138572Kp + 2c H1 + D( 1113857

Kp

11139691113876 1113877 (2)




Fm B12

c H +D

21113874 1113875

2Kp + 2c H +

D

21113874 1113875

Kp

11139691113890 1113891 (3)




B aH

D1113874 1113875

b

(4)

a a1 + b1ω + c1ω2

1113872 1113873c

(1 + ω)cw

1113888 1113889

d1

(5)

b a2 + b2ω (6)





D = 60mm

B = 05417 (HD)00559

B = 064737 (HD)ndash006351

B = 02733 (HD)006002

B = 025073 (HD)001275

2 4 6 80 10HD

02

03

04

05

06

07

B

Case 1Case 2

Case 3Case 4








070

065060055050045040035030025

a

1012

1416

1820

ω ()

200195

190185

180175 γ (k

Nm3 )D = 60mm


(a)

D = 60mm

ndash016

ndash012

ndash008

ndash004

000

004

008

012

016

b

8 12 16 20 24 28 324ω ()


(b)


HD = 3

0

20

40

60

80

100

120

Peak

resis

tanc

e of s

oil m

ass F

m (k

Nm

)






Sm

D 00037 times

H

D1113874 1113875

3242+ 048 (7)



Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)

0

10

20

30

40

50

60

70

80

90

100


HD = 1HD = 3

HD = 5HD = 7

(a)

10

20

30

40

50

60

70

80

90

Peak

resis

tanc

e of s

oil m

ass F

m (K

Nm

)

D = 90mm1 2 3 4 5 6 7 8 90

HD


(b)


S m (m

m)

0

25

50

75

100

125

150

175

200

1 2 3 4 5 6 7 8 90HD

Case1Case2

Case3Case4

(a)

S mD

0

1

2

3

4

5

1 2 3 4 5 6 7 8 90HD

Case2Case3Case4

(b)




F S

a + bS (8)


Kt Ki 1 minus Rf

F

Fm

1113890 1113891

2

(9)

Kt 1

Ki 1Ki( 1113857 + RfSFm1113872 11138731113872 11138732 (10)



Ki kK

H

D1113874 1113875pa

cH

pa

1113888 1113889

nK

(11)



Rf kR

H

D1113874 1113875

cH

pa

1113888 1113889

nR

(12)




K ip

a

0

20

40

60

80

100

120

3 6 9 12 150HD






(a)

Rf

04

08

12

16

20

3 6 9 12 150HD






(b)





5 Conclusions







log

(Ki(p aH

D))

ndash02

00

02

04

06

08

10

12

14

16




(a)lo

g (R

f(H

D))




ndash14

ndash12

ndash10

ndash08

ndash06

ndash04

ndash02

00

02

(b)




Adj R-SquareKi Rf




Data Availability




Acknowledgments


References








































0

10

20

30

40

50

60

70


Hor

izon

tal s

oil r

esist

ance

F (k

Nm

) HD = 3

D =30mmD = 60mm

D = 102mmD = 140mm









Pipe

Damaged surface


+9060e ndash 02

+8236e ndash 02

+7413e ndash 02

+6589e ndash 02

+5765e ndash 02

+4942e ndash 02

+4118e ndash 02

+3295e ndash 02

+2471e ndash 02

+1647e ndash 02

+8236e ndash 03

+0000e + 00

(a)

Pipe

Surface upli


+9324e ndash 02

+8476e ndash 02

+7629e ndash 02

+6781e ndash 02

+5933e ndash 02

+5086e ndash 02

+4238e ndash 02

+3390e ndash 02

+2543e ndash 02

+1695e ndash 02

+8476e ndash 03

+0000e + 00

(b)





0 20

40

60

80

100

120

140

160180

Eart

h pr

essu

re (k

Pa)

350300250200150100

500

50100150200250300350

HD = 10HD = 8HD = 7

HD = 5HD = 3HD = 1

(a)

030

60

90

120

150180

HD = 3HD = 1

Eart

h pr

essu

re (k

Pa)

HD = 10HD = 8HD = 5

350300250200150100

500

50100150200250300350

(b)

030

60

90

120

150180

Eart

h pr

essu

re (k

Pa)

350300250200150100

500

50100150200250300350

HD = 8HD = 7HD = 6HD = 5

HD = 4HD = 3HD = 1

(c)

030

60

90

120

150180

Eart

h pr

essu

re (k

Pa)

1000

800

600

400

200

0

200

400

600

800

1000

HD = 20HD = 15HD = 10

HD = 7HD = 5HD = 3

(d)



Fm B212

c H1 + D( 11138572Kp + 2c H1 + D( 1113857

Kp

11139691113876 1113877 (2)




Fm B12

c H +D

21113874 1113875

2Kp + 2c H +

D

21113874 1113875

Kp

11139691113890 1113891 (3)




B aH

D1113874 1113875

b

(4)

a a1 + b1ω + c1ω2

1113872 1113873c

(1 + ω)cw

1113888 1113889

d1

(5)

b a2 + b2ω (6)





D = 60mm

B = 05417 (HD)00559

B = 064737 (HD)ndash006351

B = 02733 (HD)006002

B = 025073 (HD)001275

2 4 6 80 10HD

02

03

04

05

06

07

B

Case 1Case 2

Case 3Case 4








070

065060055050045040035030025

a

1012

1416

1820

ω ()

200195

190185

180175 γ (k

Nm3 )D = 60mm


(a)

D = 60mm

ndash016

ndash012

ndash008

ndash004

000

004

008

012

016

b

8 12 16 20 24 28 324ω ()


(b)


HD = 3

0

20

40

60

80

100

120

Peak

resis

tanc

e of s

oil m

ass F

m (k

Nm

)






Sm

D 00037 times

H

D1113874 1113875

3242+ 048 (7)



Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)

0

10

20

30

40

50

60

70

80

90

100


HD = 1HD = 3

HD = 5HD = 7

(a)

10

20

30

40

50

60

70

80

90

Peak

resis

tanc

e of s

oil m

ass F

m (K

Nm

)

D = 90mm1 2 3 4 5 6 7 8 90

HD


(b)


S m (m

m)

0

25

50

75

100

125

150

175

200

1 2 3 4 5 6 7 8 90HD

Case1Case2

Case3Case4

(a)

S mD

0

1

2

3

4

5

1 2 3 4 5 6 7 8 90HD

Case2Case3Case4

(b)




F S

a + bS (8)


Kt Ki 1 minus Rf

F

Fm

1113890 1113891

2

(9)

Kt 1

Ki 1Ki( 1113857 + RfSFm1113872 11138731113872 11138732 (10)



Ki kK

H

D1113874 1113875pa

cH

pa

1113888 1113889

nK

(11)



Rf kR

H

D1113874 1113875

cH

pa

1113888 1113889

nR

(12)




K ip

a

0

20

40

60

80

100

120

3 6 9 12 150HD






(a)

Rf

04

08

12

16

20

3 6 9 12 150HD






(b)





5 Conclusions







log

(Ki(p aH

D))

ndash02

00

02

04

06

08

10

12

14

16




(a)lo

g (R

f(H

D))




ndash14

ndash12

ndash10

ndash08

ndash06

ndash04

ndash02

00

02

(b)




Adj R-SquareKi Rf




Data Availability




Acknowledgments


References








































Pipe

Damaged surface


+9060e ndash 02

+8236e ndash 02

+7413e ndash 02

+6589e ndash 02

+5765e ndash 02

+4942e ndash 02

+4118e ndash 02

+3295e ndash 02

+2471e ndash 02

+1647e ndash 02

+8236e ndash 03

+0000e + 00

(a)

Pipe

Surface upli


+9324e ndash 02

+8476e ndash 02

+7629e ndash 02

+6781e ndash 02

+5933e ndash 02

+5086e ndash 02

+4238e ndash 02

+3390e ndash 02

+2543e ndash 02

+1695e ndash 02

+8476e ndash 03

+0000e + 00

(b)





0 20

40

60

80

100

120

140

160180

Eart

h pr

essu

re (k

Pa)

350300250200150100

500

50100150200250300350

HD = 10HD = 8HD = 7

HD = 5HD = 3HD = 1

(a)

030

60

90

120

150180

HD = 3HD = 1

Eart

h pr

essu

re (k

Pa)

HD = 10HD = 8HD = 5

350300250200150100

500

50100150200250300350

(b)

030

60

90

120

150180

Eart

h pr

essu

re (k

Pa)

350300250200150100

500

50100150200250300350

HD = 8HD = 7HD = 6HD = 5

HD = 4HD = 3HD = 1

(c)

030

60

90

120

150180

Eart

h pr

essu

re (k

Pa)

1000

800

600

400

200

0

200

400

600

800

1000

HD = 20HD = 15HD = 10

HD = 7HD = 5HD = 3

(d)



Fm B212

c H1 + D( 11138572Kp + 2c H1 + D( 1113857

Kp

11139691113876 1113877 (2)




Fm B12

c H +D

21113874 1113875

2Kp + 2c H +

D

21113874 1113875

Kp

11139691113890 1113891 (3)




B aH

D1113874 1113875

b

(4)

a a1 + b1ω + c1ω2

1113872 1113873c

(1 + ω)cw

1113888 1113889

d1

(5)

b a2 + b2ω (6)





D = 60mm

B = 05417 (HD)00559

B = 064737 (HD)ndash006351

B = 02733 (HD)006002

B = 025073 (HD)001275

2 4 6 80 10HD

02

03

04

05

06

07

B

Case 1Case 2

Case 3Case 4








070

065060055050045040035030025

a

1012

1416

1820

ω ()

200195

190185

180175 γ (k

Nm3 )D = 60mm


(a)

D = 60mm

ndash016

ndash012

ndash008

ndash004

000

004

008

012

016

b

8 12 16 20 24 28 324ω ()


(b)


HD = 3

0

20

40

60

80

100

120

Peak

resis

tanc

e of s

oil m

ass F

m (k

Nm

)






Sm

D 00037 times

H

D1113874 1113875

3242+ 048 (7)



Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)

0

10

20

30

40

50

60

70

80

90

100


HD = 1HD = 3

HD = 5HD = 7

(a)

10

20

30

40

50

60

70

80

90

Peak

resis

tanc

e of s

oil m

ass F

m (K

Nm

)

D = 90mm1 2 3 4 5 6 7 8 90

HD


(b)


S m (m

m)

0

25

50

75

100

125

150

175

200

1 2 3 4 5 6 7 8 90HD

Case1Case2

Case3Case4

(a)

S mD

0

1

2

3

4

5

1 2 3 4 5 6 7 8 90HD

Case2Case3Case4

(b)




F S

a + bS (8)


Kt Ki 1 minus Rf

F

Fm

1113890 1113891

2

(9)

Kt 1

Ki 1Ki( 1113857 + RfSFm1113872 11138731113872 11138732 (10)



Ki kK

H

D1113874 1113875pa

cH

pa

1113888 1113889

nK

(11)



Rf kR

H

D1113874 1113875

cH

pa

1113888 1113889

nR

(12)




K ip

a

0

20

40

60

80

100

120

3 6 9 12 150HD






(a)

Rf

04

08

12

16

20

3 6 9 12 150HD






(b)





5 Conclusions







log

(Ki(p aH

D))

ndash02

00

02

04

06

08

10

12

14

16




(a)lo

g (R

f(H

D))




ndash14

ndash12

ndash10

ndash08

ndash06

ndash04

ndash02

00

02

(b)




Adj R-SquareKi Rf




Data Availability




Acknowledgments


References




































0 20

40

60

80

100

120

140

160180

Eart

h pr

essu

re (k

Pa)

350300250200150100

500

50100150200250300350

HD = 10HD = 8HD = 7

HD = 5HD = 3HD = 1

(a)

030

60

90

120

150180

HD = 3HD = 1

Eart

h pr

essu

re (k

Pa)

HD = 10HD = 8HD = 5

350300250200150100

500

50100150200250300350

(b)

030

60

90

120

150180

Eart

h pr

essu

re (k

Pa)

350300250200150100

500

50100150200250300350

HD = 8HD = 7HD = 6HD = 5

HD = 4HD = 3HD = 1

(c)

030

60

90

120

150180

Eart

h pr

essu

re (k

Pa)

1000

800

600

400

200

0

200

400

600

800

1000

HD = 20HD = 15HD = 10

HD = 7HD = 5HD = 3

(d)



Fm B212

c H1 + D( 11138572Kp + 2c H1 + D( 1113857

Kp

11139691113876 1113877 (2)




Fm B12

c H +D

21113874 1113875

2Kp + 2c H +

D

21113874 1113875

Kp

11139691113890 1113891 (3)




B aH

D1113874 1113875

b

(4)

a a1 + b1ω + c1ω2

1113872 1113873c

(1 + ω)cw

1113888 1113889

d1

(5)

b a2 + b2ω (6)





D = 60mm

B = 05417 (HD)00559

B = 064737 (HD)ndash006351

B = 02733 (HD)006002

B = 025073 (HD)001275

2 4 6 80 10HD

02

03

04

05

06

07

B

Case 1Case 2

Case 3Case 4








070

065060055050045040035030025

a

1012

1416

1820

ω ()

200195

190185

180175 γ (k

Nm3 )D = 60mm


(a)

D = 60mm

ndash016

ndash012

ndash008

ndash004

000

004

008

012

016

b

8 12 16 20 24 28 324ω ()


(b)


HD = 3

0

20

40

60

80

100

120

Peak

resis

tanc

e of s

oil m

ass F

m (k

Nm

)






Sm

D 00037 times

H

D1113874 1113875

3242+ 048 (7)



Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)

0

10

20

30

40

50

60

70

80

90

100


HD = 1HD = 3

HD = 5HD = 7

(a)

10

20

30

40

50

60

70

80

90

Peak

resis

tanc

e of s

oil m

ass F

m (K

Nm

)

D = 90mm1 2 3 4 5 6 7 8 90

HD


(b)


S m (m

m)

0

25

50

75

100

125

150

175

200

1 2 3 4 5 6 7 8 90HD

Case1Case2

Case3Case4

(a)

S mD

0

1

2

3

4

5

1 2 3 4 5 6 7 8 90HD

Case2Case3Case4

(b)




F S

a + bS (8)


Kt Ki 1 minus Rf

F

Fm

1113890 1113891

2

(9)

Kt 1

Ki 1Ki( 1113857 + RfSFm1113872 11138731113872 11138732 (10)



Ki kK

H

D1113874 1113875pa

cH

pa

1113888 1113889

nK

(11)



Rf kR

H

D1113874 1113875

cH

pa

1113888 1113889

nR

(12)




K ip

a

0

20

40

60

80

100

120

3 6 9 12 150HD






(a)

Rf

04

08

12

16

20

3 6 9 12 150HD






(b)





5 Conclusions







log

(Ki(p aH

D))

ndash02

00

02

04

06

08

10

12

14

16




(a)lo

g (R

f(H

D))




ndash14

ndash12

ndash10

ndash08

ndash06

ndash04

ndash02

00

02

(b)




Adj R-SquareKi Rf




Data Availability




Acknowledgments


References


































Fm B212

c H1 + D( 11138572Kp + 2c H1 + D( 1113857

Kp

11139691113876 1113877 (2)




Fm B12

c H +D

21113874 1113875

2Kp + 2c H +

D

21113874 1113875

Kp

11139691113890 1113891 (3)




B aH

D1113874 1113875

b

(4)

a a1 + b1ω + c1ω2

1113872 1113873c

(1 + ω)cw

1113888 1113889

d1

(5)

b a2 + b2ω (6)





D = 60mm

B = 05417 (HD)00559

B = 064737 (HD)ndash006351

B = 02733 (HD)006002

B = 025073 (HD)001275

2 4 6 80 10HD

02

03

04

05

06

07

B

Case 1Case 2

Case 3Case 4








070

065060055050045040035030025

a

1012

1416

1820

ω ()

200195

190185

180175 γ (k

Nm3 )D = 60mm


(a)

D = 60mm

ndash016

ndash012

ndash008

ndash004

000

004

008

012

016

b

8 12 16 20 24 28 324ω ()


(b)


HD = 3

0

20

40

60

80

100

120

Peak

resis

tanc

e of s

oil m

ass F

m (k

Nm

)






Sm

D 00037 times

H

D1113874 1113875

3242+ 048 (7)



Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)

0

10

20

30

40

50

60

70

80

90

100


HD = 1HD = 3

HD = 5HD = 7

(a)

10

20

30

40

50

60

70

80

90

Peak

resis

tanc

e of s

oil m

ass F

m (K

Nm

)

D = 90mm1 2 3 4 5 6 7 8 90

HD


(b)


S m (m

m)

0

25

50

75

100

125

150

175

200

1 2 3 4 5 6 7 8 90HD

Case1Case2

Case3Case4

(a)

S mD

0

1

2

3

4

5

1 2 3 4 5 6 7 8 90HD

Case2Case3Case4

(b)




F S

a + bS (8)


Kt Ki 1 minus Rf

F

Fm

1113890 1113891

2

(9)

Kt 1

Ki 1Ki( 1113857 + RfSFm1113872 11138731113872 11138732 (10)



Ki kK

H

D1113874 1113875pa

cH

pa

1113888 1113889

nK

(11)



Rf kR

H

D1113874 1113875

cH

pa

1113888 1113889

nR

(12)




K ip

a

0

20

40

60

80

100

120

3 6 9 12 150HD






(a)

Rf

04

08

12

16

20

3 6 9 12 150HD






(b)





5 Conclusions







log

(Ki(p aH

D))

ndash02

00

02

04

06

08

10

12

14

16




(a)lo

g (R

f(H

D))




ndash14

ndash12

ndash10

ndash08

ndash06

ndash04

ndash02

00

02

(b)




Adj R-SquareKi Rf




Data Availability




Acknowledgments


References







































070

065060055050045040035030025

a

1012

1416

1820

ω ()

200195

190185

180175 γ (k

Nm3 )D = 60mm


(a)

D = 60mm

ndash016

ndash012

ndash008

ndash004

000

004

008

012

016

b

8 12 16 20 24 28 324ω ()


(b)


HD = 3

0

20

40

60

80

100

120

Peak

resis

tanc

e of s

oil m

ass F

m (k

Nm

)






Sm

D 00037 times

H

D1113874 1113875

3242+ 048 (7)



Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)

0

10

20

30

40

50

60

70

80

90

100


HD = 1HD = 3

HD = 5HD = 7

(a)

10

20

30

40

50

60

70

80

90

Peak

resis

tanc

e of s

oil m

ass F

m (K

Nm

)

D = 90mm1 2 3 4 5 6 7 8 90

HD


(b)


S m (m

m)

0

25

50

75

100

125

150

175

200

1 2 3 4 5 6 7 8 90HD

Case1Case2

Case3Case4

(a)

S mD

0

1

2

3

4

5

1 2 3 4 5 6 7 8 90HD

Case2Case3Case4

(b)




F S

a + bS (8)


Kt Ki 1 minus Rf

F

Fm

1113890 1113891

2

(9)

Kt 1

Ki 1Ki( 1113857 + RfSFm1113872 11138731113872 11138732 (10)



Ki kK

H

D1113874 1113875pa

cH

pa

1113888 1113889

nK

(11)



Rf kR

H

D1113874 1113875

cH

pa

1113888 1113889

nR

(12)




K ip

a

0

20

40

60

80

100

120

3 6 9 12 150HD






(a)

Rf

04

08

12

16

20

3 6 9 12 150HD






(b)





5 Conclusions







log

(Ki(p aH

D))

ndash02

00

02

04

06

08

10

12

14

16




(a)lo

g (R

f(H

D))




ndash14

ndash12

ndash10

ndash08

ndash06

ndash04

ndash02

00

02

(b)




Adj R-SquareKi Rf




Data Availability




Acknowledgments


References


































Sm

D 00037 times

H

D1113874 1113875

3242+ 048 (7)



Hor

izon

tal s

oil r

esist

ance

F (k

Nm

)

0

10

20

30

40

50

60

70

80

90

100


HD = 1HD = 3

HD = 5HD = 7

(a)

10

20

30

40

50

60

70

80

90

Peak

resis

tanc

e of s

oil m

ass F

m (K

Nm

)

D = 90mm1 2 3 4 5 6 7 8 90

HD


(b)


S m (m

m)

0

25

50

75

100

125

150

175

200

1 2 3 4 5 6 7 8 90HD

Case1Case2

Case3Case4

(a)

S mD

0

1

2

3

4

5

1 2 3 4 5 6 7 8 90HD

Case2Case3Case4

(b)




F S

a + bS (8)


Kt Ki 1 minus Rf

F

Fm

1113890 1113891

2

(9)

Kt 1

Ki 1Ki( 1113857 + RfSFm1113872 11138731113872 11138732 (10)



Ki kK

H

D1113874 1113875pa

cH

pa

1113888 1113889

nK

(11)



Rf kR

H

D1113874 1113875

cH

pa

1113888 1113889

nR

(12)




K ip

a

0

20

40

60

80

100

120

3 6 9 12 150HD






(a)

Rf

04

08

12

16

20

3 6 9 12 150HD






(b)





5 Conclusions







log

(Ki(p aH

D))

ndash02

00

02

04

06

08

10

12

14

16




(a)lo

g (R

f(H

D))




ndash14

ndash12

ndash10

ndash08

ndash06

ndash04

ndash02

00

02

(b)




Adj R-SquareKi Rf




Data Availability




Acknowledgments


References



































F S

a + bS (8)


Kt Ki 1 minus Rf

F

Fm

1113890 1113891

2

(9)

Kt 1

Ki 1Ki( 1113857 + RfSFm1113872 11138731113872 11138732 (10)



Ki kK

H

D1113874 1113875pa

cH

pa

1113888 1113889

nK

(11)



Rf kR

H

D1113874 1113875

cH

pa

1113888 1113889

nR

(12)




K ip

a

0

20

40

60

80

100

120

3 6 9 12 150HD






(a)

Rf

04

08

12

16

20

3 6 9 12 150HD






(b)





5 Conclusions







log

(Ki(p aH

D))

ndash02

00

02

04

06

08

10

12

14

16




(a)lo

g (R

f(H

D))




ndash14

ndash12

ndash10

ndash08

ndash06

ndash04

ndash02

00

02

(b)




Adj R-SquareKi Rf




Data Availability




Acknowledgments


References




































5 Conclusions







log

(Ki(p aH

D))

ndash02

00

02

04

06

08

10

12

14

16




(a)lo

g (R

f(H

D))




ndash14

ndash12

ndash10

ndash08

ndash06

ndash04

ndash02

00

02

(b)




Adj R-SquareKi Rf




Data Availability




Acknowledgments


References


































Data Availability




Acknowledgments


References


































study on soil spring model for pipe and silty clay

Documents