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ARTICLE

Uplift soilpipe interaction in granular soil

Jai K. Jung, Thomas D. O'Rourke, and Nathaniel A. Olson

Abstract:Soilpipeline interaction for uplift in granular soil is evaluated by means of a two-dimensional, finite element (FE)

continuum modelwith a MohrCoulomb (MC) yield surface for peak strength, a strain-softening relationship tied to critical void

conditions, and an equivalent modulus that is consistent with soil deformation at maximum uplift resistance. The model

accounts for soil migration beneath the pipe through FE mesh adjustment coordinated with upward pipe displacement. A

systematic comparison of modelresultswith multiplefull-scale testmeasurementsof pipein dry sand showexcellent agreement

both with respect to maximum force and forcedisplacement relationships, including post-peak performance. The relationship

between peak upward force and pipe depth is developed for various sand densities, all of which show maximum force at a

depth-to-diameter ratio of 30. Hyperbolic and bilinear models for vertical upward force versus displacement are presented. The

analytical approach described in this paper benefits from its adaptation to MC strength selection available in many commercial

software packages.

Key words: pipeline, MohrCoulomb, finite element analyses, soilpipeline interaction, upward movement, earthquake.

Rsum :Linteraction soltuyau, responsable du soulvement dans un sol granulaire, est value alaide dun modle continupar lments finis (EF) en deux dimensions avec une surface de rupture a la rsistance au pic de MohrCoulomb (MC), une

relation dadoucissement des dformations lie aux conditions critiques des vides, et un module quivalent consistant avec les

dformations du sol ala rsistance maximale au soulvement. Le modle tient compte de la migration du sol sous le tuyau par

desajustementsde maillage desEF en lien avec lesdplacements vers le haut du tuyau.Les rsultats du modleont tcompars

systmatiquement avec des mesures provenant de nombreux essais a lchelle relle de tuyau dans du sable sec, et les modli-

sations et mesures dmontrent une excellente concordance en termes de la force maximale et des relations forcedplacement,

incluant la performance post-pic. La relation entre la force au pic vers le haut et la profondeur du tuyau est dveloppe pour

plusieurs densits de sable. Pour toutes les densits values, la force maximale se retrouve a un ratio profondeur-diamtre de

30. Des modles hyperboliques et bilinaires de force de soulvement vertical versus le dplacement sont prsents. Lapproche

analytique dcrite dans cet article est facilite par son adaptation au critre de rsistance MC disponible dans plusieurs logiciels

commerciaux. [Traduit par la Rdaction]

Mots-cls : tuyau, MohrCoulomb, analyses par lments finis, interaction soltuyau, mouvement vers le haut, sisme.

IntroductionThis paper focuses on the uplift behavior of underground pipe-

lines. The characterization of uplift behavior is important for

modeling soilpipeline interaction in response to settlementscaused by earthquake-induced liquefaction, landslides, and nor-

mal faulting. Pipeline uplift in response to ground deformationnot only applies to earthquakes, but also occurs in response to

floods, landslides, tunneling, deep excavations, and subsidence

triggeredby dewatering andmining (O'Rourke 2010). Upliftbehav-ior involves material nonlinearities with significant soil yielding

under large vertical displacement of the pipe. Such behavior also

involves nonlinear geometric behavior as soil migrates from aposition above to below the pipe in response to relative upward

movement.Previous research investigations (e.g.,Yimsiri et al. 2004;Klar

et al. 2005;Vorster et al. 2005;O'Rourke 2010;Chou et al. 2011;Xie

et al. 2012)used continuum models to address the complexities ofsoilpipeline interaction under permanent ground deformation.

Pipeline uplift behavior is similarly modeled in this work with

continuum finite element (FE) models. Plane strain conditions aresimulated so that the analytical results can be compared directly

with the results of large-scale experiments on the uplift displace-

ment of pipe in granular soil as provided by Trautmann andO'Rourke (1983).

One of the objectives of this study is to work with relativelysimple models for soil behavior that are readily accessible in oradaptable to commercially available software. If a relativelysimple model is shown to provide good results, it will benefitfrom the ease of use with a number of different software pack-ages. An elastoplastic model was adopted with MohrCoulomb(MC) strength parameters, a nonassociated flow rule based onthe smooth triple symmetric ellipse function proposed byMenetrey and Willam (1995),and a strain-softening model de-veloped byRobert and Soga (2009)on the basis of direct shear(DS) test results.

The paper describes the MC and strain-softening model in con-junction with DS test results and the conversion of DS to plane

strain strength parameters. The method of selecting a strain-compatible modulus is explained, based on a hyperbolic represen-tation of stress versus strain consistent with peak soil strengthmobilized at maximum upward pipe force. The method for FEmesh adjustment is described that accounts for soil migrationbeneath the pipe during upward pipe displacement. The analyti-cal results are compared with multiple full-scale test measure-ments of pipe in dry sand. The relationship between peak upward

Received 27 September 2012. Accepted 23 April 2013.

J.K. Jung.Virginia Polytechnic Institute of Technology, Blacksburg, VA, USA.T.D. O'Rourke.Cornell University, Ithaca, NY, USA.N.A. Olson.Stephens Associates Consulting Engineers, Brentwood, NH, USA.

Corresponding author:Jai K. Jung (e-mail: [email protected]).

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Can. Geotech. J.50: 744753 (2013)dx.doi.org/10.1139/cgj-2012-0357 Published at www.nrcresearchpress.com/cgj on 29 April 2013.

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force and pipe depth is developed for various sand densities, andhyperbolic and bilinear models for vertical upward force versusdisplacement are presented for use in the analytical models mostfrequently used in current design methods.

Finite element model and soil strength properties

Many constitutive models for soil behavior (e.g., MohrCoulomb, DruckerPrager, Modified DruckerPrager/Cap, Cam-Clay, and Nor-Sand) are available. As previously discussed, theauthors selected an elastoplastic model with an MC yield surfacedue to its simplicity and extensive use in soilstructure interac-tion analyses (Ellis and Springman, 2001;Hu and Pu 2003;Yimsiriet al. 2004;Sun et al. 2006;Robert and Soga 2009). In addition, anMC strength model is easy to apply in many commercial softwarepackages (e.g., ABAQUS, FLAC, and PLAXIS).

The elasto-plastic MC model used in this work requires thefollowing principal input parameters: (i) soil strength as ex-

pressed by the plane strain peak friction angle (ps-p), (ii) peakdilation angle (p), and (iii) the secant soil modulus (E) at a strain

compatible with the maximum uplift pipe load. Each input pa-rameter is discussed under a separate subheading that follows.

Plane strain soil strength parametersTo account for soil behavior under plane strain conditions it is

necessary to define the MC yield surface in terms ofps-p. Thisfriction angle can be obtained from DS tests by recognizing thecoaxiality between incremental strain and stress, and using thehorizontal plane of the DS apparatus as the direction of zerolinear strain. Davis (1968) first recognized and described theseconditions to derive a relationship that has been confirmed sub-sequently by numerous researchers (e.g.,Bolton 1986;Jewell andWroth 1987;Lings and Dietz 2004;O'Rourke 2010), as follows:

(1) sinps-p tands-p

cosp (sinp) (tan

ds-p)

in whichds-pis the DS peak friction angle.Figure 1 shows a Mohr circle of stress at peak DS and plane

strain shear for dry sand. In the figure, N, ds-p, and ps-p arenormal stress, direct shear peak shear stress, and plane strainpeak shear stress, respectively. Given that the DS test failure planecoincides with zero extension and that incremental stress andstrain are coaxial,pis oriented at pwith respect to the verticalradius of the Mohr circle at (1 +

3)/2, where

1 and

3are themajor and minor principal stress, respectively, andps-p is definedat the point of maximum obliquity with respect to the Mohrcircle.

To make use ofeq. (1), one needs to determine ds-p and p.Olson (2009)performed numerous DS tests to determine strengthand dilatancy properties of Cornell University (CU) Filter sandused byTrautmann and O'Rourke (1983) in large-scale tests ofsoilpipe interaction under vertical upward movement. The testsoil was an angular to subangular glaciofluvial sand, character-ized by a mean grain size, D50= 0.59 mm, and the coefficient ofcurvature,Cc= 1.26. The grain-size distribution curve for the sand

is shown inFig. 2,with an inset photo of the sand particles. Thesand is classified as poorly graded sand (SP) according to the Uni-fied Soil Classification System (ASTM 2011). For various dry unit

weights, d,Olson (2009)plotted

ds-pand pfor CU Filter sand as

shown inFig. 3.The linear regression equations for ds-pand pversusdare provided in the figure.

As dilatancy is diminished by increasing confining stress, it is

necessary to characterize the relationship between p and

N.

Olson (2009) provided data for p versus

N from DS tests that

were normalized with respect to a reference stress N = 2.1 kPaand plotted in Fig. 4. The nonlinear regression equation forp/p@N Ref.(wherep@N Ref. is the dilation angle at the referencestress) is presented in the figure. The pvalues fromFigs. 3and4

was used to obtain ds-p, using the relationship provided byLingsand Dietz (2004)as

(2) tands-p sincrit sinp

cosp

in whichcritis critical friction angle.Olson (2009)reported

crit

for CU Filter sand as 38.6.

Secant soil modulusImplicit in using an elastoplastic model to predict upward soil

pipe behavior at maximum pipe load is the selection of a Young'smodulus that is strain-compatible with the level of stress in thesoil at peak pipe load. The secant modulus (Esec) of sand is relatedto the fraction of the peak soil strength mobilized at maximumlateral pipe force.Duncan and Chang (1970)have shown that the

stressstrain curve of sand can be approximated by hyperbola as

(3)

(1

3)a b

where is strain anda andbare defined inFig. 5.In the figure,Eiis the initial tangent modulus and (1

3)ultis the asymptoticvalue of the principal stress difference at infinite strain. The stress

difference at the peak lateral pipe force, (1

3)f, is expressed as

(4) (1

3)f Rf(

1

3)ult

whereRfis a reduction factor. The value ofRf= 0.9 reported byTrautmann and O'Rourke (1983)was used in this study. Assuming

that is the fraction of the peak soil strength mobilized at maxi-mumupward pipe force,Jung (2010) related thesecantmodulus to(E

) as

(5) E (1 Rf)Ei

Fromeq. (5), Esecassociated with any percentage of the maxi-mum stress level can be calculated from the initial tangent mod-ulus. Finiteelement simulations of lateral pipe movement in sandwere used to estimate the relationship betweenEi andEsec at peakpipe load. As the maximum lateral pipe force is independent ofthe Youngs modulus, E, FE results can be used without a prioriknowledge ofE to determine. The appropriate value ofEseccan

Fig. 1. Mohr circle for stress at peak direct shear and plane strain

shear in dry sand.=, effective stress; =, effective shear stress;

p, effective peak shear stress.

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then be chosenfrom thehyperbolic model,using from initial FEsimulations.

Janbu (1963) proposed the relationship betweenEi,and

3 asEi =

Kpa(

3/pa)n, in which Kis a constant, pa is atmospheric pressure,

andn is an exponent determining the rate of variation ofEiwith

3.Duncan and Chang (1970) andWong and Duncan (1974) sum-

marizedKand n values obtained from triaxial tests on sand, andreported mid-range values ofKand n equal to 800 and 0.55, re-spectively, for dense sand.Jung (2010) performed a series of FEsimulations for vertical pipe movement to show 0.91 0.98,from which = 0.94 was selected for analysis. Values of secant soilmodulus at a strain compatible with the maximum lateral pipeload are summarized inTable 1for each depth-to-diameter ratio,

Hc/D, whereHcis the depth from the soil surface to the center ofthe pipe andD is the external diameter of the pipe. The modulusis a function of confining stress and changes with depth as E

increases from 4002800 kPa and 7005200 kPa for medium andvery dense dry CU filter sand, respectively, for Hc/D= 1.513.

Strain-softening behaviorTo represent strain-softening, the model proposed by

Anastasopoulos et al. (2007) was used to diminish linearly both

ps-pand pto residual values ofcritand 0, respectively, from the

plastic strain atps-pto the plastic strain atcrit, using the resultsof DS testing as

(6) fp

dxp dxy

H

dxf dxp

dFE

where fp is the the plastic strain atcrit; dxy, dxp, and dxfare the DS

test horizontal displacements at yield, peak strength, and critat

Fig. 2. CU Filter sand: (a) photo and (b) particle-size distribution (afterOlson 2009).

Fig. 3. pand

ds-pversusdfor dry CU Filter sand at

N= 2.1 kPa

(afterOlson 2009).n, number of data points; r2, coefficient of

determination.

Fig. 4. Plot ofp/p@N Ref.versus

Natd= 16.5 kN/m3.

Fig. 5. Hyperbolic stressstrain curve (afterDuncan and Chang

1970).

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which full softening occurs, respectively; His the thickness of theDS specimen, anddFEis the FE element size. The FE element size,dFE, in the refined part of the finite element mesh was taken as20d50, where d50 is themedian grain size. This thickness comparesfavorably with the shear band thickness as reported by severalinvestigators as 820d50(e.g.,Roscoe 1970;Vardoulakis and Graf1985;Muhlhaus and Vardoulakis 1987;Huang et al. 2002). A FOR-TRAN subroutine developed byRobert and Soga (2009) to applythe Anastasopoulos et al. (2007) model in the MC model inABAQUS was used in the two-dimensional (2D) FE simulations.

Finite element modeling

FE analyses were run with a semi-infinite soil medium usinginfinite elements as developed by Zienkiewicz et al. (1983).Figure 6shows the typical geometry of the model used for simu-lating vertical upward soilpipe interaction. In the model, eight-node biquadratic, plane strain, quadrilateral, reduced integrationelements (element type CPE8R) are used to represent the soilaround the pipe from A to B, and from the surface to C. Five-nodequadratic, plane strain, one-way infinite quadrilateral elements(element type CINPE5R) are used to represent the semi-infinitesoil. Theinfinite elements areattached to CPE8Relements andare1.3 m in width. The infinite elements at the base of the model are1.3 m in height. The pipe was modeled as a rigid cylinder withoutsider diameter of 102 mm. The interface between the soil and

pipe has a friction angle of 0.6ds-p. To promote numerical stabil-

ity, allsimulations were performed with a nominal cohesion, cps =0.10.3 kPa. Sensitivity analyses were performed with different

c

psvalues to show that the range ofc

ps = 0.10.3 kPahad negligibleeffect on theresults. Theinterface interaction is modeled throughsurface-based contact, in which separation and slip between soiland pipe are allowed. A refined mesh was used within a distanceof approximately two pipe diameters from the center of the pipe.The thickness of the elements within the refined mesh was takenasthe shear band thickness of12 mm, which isconsistentwiththerupture zone observed during DS tests (Roscoe 1970;VardoulakisandGraf 1985; Muhlhaus and Vardoulakis 1987; Huang et al.2002).Approximately 1500 to 5000 elements were used in the meshes tosimulate differentHc/Dconditions. Geostatic loading was appliedto the soil and pipe at the beginning of the analysis under Ko =1 condition, where Ko is the initial horizontal to vertical stressratio. Sensitivity studies for Ko showed that the maximum forcechanged approximately 3% and the computational time increasedapproximately 10 times when Ko changed from 1 to 0.3. Upwardpipe movement wasimposed as a vertical upwarddisplacement ofall pipe nodes.

In the FE model, vertical effective stress at the horizontal pipecenterline (vc), shown inFig. 6,is taken as

N. Characterizingpinterms ofa singlevc is a simplification that does not account for

variablep and

ps-pwith depth or linkpwith the appropriate

N

at any given depth. Jung et al. (2012) performed a series of FE

simulations for layered soil in whichp and

ps-pwere varied withdepth, and the analytical results were compared with those usingp and

ps-p linked to a singlevertical stress at the pipe centerline.The comparisons showed only 0.2%3.3% difference in the peaklateral forces for a wide range of depths. Thus, characterizing p

andps-pin terms of a single

vcis used, due to its simplicity andstraightforward characterization of soil strength.

The soil displacements measured for vertical upward pipemovements in the medium CU Filter sand at shallow depth(Trautmann and O'Rourke 1983)show that the soil above the pipewas pushed upward and outward, as the pipe was displaced verti-cally. The soil at the sides moved downward and flowed into thevoid created under the pipe, in much the same manner as de-scribed byKananyan (1966)for uplift tests on disks. Soil displace-ment during the large-scale tests was obtained by measuringmovement of 150 mmlongby 6 mm diameter wooden dowels thatwere placed normal to the side of the test box. The large-scale testbox was constructed with a glass window through which measure-ments were made (Trautmannand O'Rourke 1983). The measurementswere performed fortests inmediumtovery densesand(ps-p = 43.8 and

48.6, respectively) for 1.5 Hc/D 13.The average maximum upward ground surface displacement

for eight tests was 25% of the pipe displacement with a range of10%to 45% of the pipe placement. In contrast, the surface displace-ment from finite element analysis (FEA) was approximately equalto the vertical pipe movement. As a consequence, the simulationwas modified to be consistent with the observed soil movementduring the tests. Figure 7 shows the deformed shape of the FEmesh for medium sand at Hc/D = 1.5. The surface elements thatheaved more than 25% of the pipe displacement were removed tobe consistent with the observed surface displacement. This reduc-tion was accomplished by exercising the Remove option inABAQUS during three to four steps of the simulation. As illus-trated later in the paper by comparisons of model results withparticle image velocimetry (PIV) measurements, the analytical

simulations are able to replicate soil displacement fields andshear zone formation at both peak and post-peak conditions ofupward pipe movement. Although the modified numerical modelis not able to account fully for soil that moves into the void be-neath the pipe, it is able to simulate zones of distributed shearabove the pipe that generate forces restricting upward pipe move-ment. The reduction of surface elements in the analyses reducessoil weight while replicating shear transfer mechanisms consis-tent with those observed experimentally and thus captures thepost-peak loss of resistance to vertical movement in the full-scaletests.

In contrast to the conditions for relatively lowHc/D, FEA with-out surface modification forHc/D= 8 and 13 provided results con-sistent with the experimental data, including agreement with

Table 1. Summary of secant soil modulus for up-

ward pipe movement.

Soil Hc/D E(kPa)

Medium dry CU

Filter sand

1.513 4002800

Very dense dry

CU Filter sand

1.513 7005200

Fig. 6. Geometry of the numerical analysis for upward pipe

movement test.

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observed surface displacements. To identify the smallest Hc/Dwhere FEA without modification compares favorably with exper-imental data, a series of simulations was performed to comparethe maximum dimensionless vertical upward movement force,

NqVU-fea=Fpeak/(dHcDL), with themeasured maximum dimension-less vertical upward movement force, NqVU-m. In this equation,

Fpeakis peak force, L is length of the pipe, and d,Hc, andD havebeen defined previously.

Figure 8shows the percentage difference between NqVU-mandNqVU-feawith respect toNqVU-mversusHc/D. The FEAs without mod-ification overpredictNqVU-mat relatively shallow depths (Hc/D = 1.5and4) by 17%42%,whereas theFEAs without modification predict

NqVU-mreasonably well for greater depths. The percentage differ-ence betweenNqVU-mandNqVU-fea for both mediumand very densesand is less than 10%NqVU-mfor Hc/D= 5.5. Therefore, the modifi-cation process was not required for Hc/D 5.5.

Comparison of analytical and experimental results

The analytical results are compared with large-scale test resultsreported by Trautmann and O'Rourke (1983). Dry glaciofluvialsand was used in the tests with unit weights of 16.4 and17.7 kN/m3, and depth-to-diameter ratios of 1.5, 4, 8, and 13. Alltests were performed with 102 mm diameter pipe. The soilstrength properties associated with each series of tests are sum-marized inTable 2.Average values ofdas well as

ps-pand paregiven. The preponderance of the measurements obtained by

Trautmann and O'Rourke (1983)show a clear peak load. For testswith no clear peak, the procedure used by Trautmann andO'Rourke (1983)by fitting the data to a hyperbolic curve and se-

Fig. 7. Example of deformed shape of FE analysis for vertical

upward pipe movement test after modification process.

Fig. 8. Comparisons of vertical upwardNqVU-mandNqVU-fea in medium

and very dense CU Filter sand using the unmodified (regular) FE

analysis.

Table 2. Summary of dry CU Filter sand strength parameters.

Density

d(kN/m3)

ds-p

()

ps-p

()

p()

Full-scale

test results

Medium 16.4 36.0 43.8 4.0 Trautmann and

O'Rourke (1983)Very dense 17.7 40.6 48.6 10.9 Trautmann and

O'Rourke (1983)

Fig. 9. Comparisons ofNqVU-fea andNqVU-mfor vertical upward

movement.

Fig. 10. Summary plot of vertical upward pipe movement NqVUversusHc/D.F, force.

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lecting peak force as the product of the hyperbolic asymptotemultiplied by a reduction factor, Rf= 0.9, was used.

Figure 9 showsNqVU-feaplotted with respect toNqVU-m. There areexcellent agreements between NqVU-feaand NqVU-m, with 88% of

NqVU-feawithin 10% ofNqVU-m.Figure 10compares the FE resultsand 2-D test measurements ofTrautmann and O'Rourke (1983), inwhich the vertical upward dimensionless force (NqVU) is plotted asa function of the dimensionless depth. Nonlinear regression lines

are plotted for the experimental data and numerical results. Ingeneral, the FEA results overpredict measured force by 5%13%,with an average difference of 7.7%. Also plotted inFig. 10are dataexpressed in dimensionless terms from centrifuge tests reportedbyDickin (1994)for sand with grain size characteristics and unitweight, d = 16 kN/m

3, similar to those of the sand used byTrautmann and O'Rourke (1983) for the medium sand (d =16.4 kN/m3) results plotted inFig. 10.The maximum dimension-less upward forces predicted by FE simulation and those obtainedbyDickin (1994)compare very well.

As an additional check, the velocity fields determined by PIVand photogrammetry for pipe uplift tests reported byCheuk et al.(2008)andWhite et al. (2008)for pipe in dense sand with Hc/D= 3are compared with the analytical results for very dense Cornell

Filter sand (d= 17.7 kN/m3) forHc/D= 4.Figures 11aand11bshow

the incremental displacement fields for pipe movement at peakuplift force from FE simulations and the pipe uplift tests, respec-tively.Figures 11cand 11dprovide a similar comparison for post-peak conditions when the pipe movement, , is 0.4D to 0.5D.Incremental vector displacements are normalized by the upwardpipe movement between the movement at peak resistance, peak,and 0.5D, which are scaled by a factor of 5 for better visualization.

The FEA incremental displacements from peak resistance to 0.4Dpipe movement are also scaled by a factor of 5. The FEA displace-ments are confined to 0.4Dto eliminate the effects of local meshinstability at higher values. The displacement fields at peak upliftresistance show similarly sized zones of distributed shear (A) thatcurve outward towards the surface (B), and have similar averageangles of inclination of 18 with respect to vertical, as defined byCheuk et al. (2008).The post-peak displacement fields show simi-lar shear bands that have narrowed above the pipe (C), accompa-nied by downward rotational displacement zones (D) of similardimensions at thepipe level.From an examination of thedisplace-ment fields,Cheuk et al. (2008) concluded that normality is vio-lated, thus requiring a nonassociated flow rule when modelingthe soilpipe interaction. The FEA model in this study uses the

Fig. 11. Comparison of analytical and measured incremental displacement fields for (a) FE simulation at peak load, (b) experiment at peak

load(Cheuk et al. 2008), (c) FE simulation at 0.4Dpipe movement, and (d) experiment at 0.5Dpipe movement (Cheuk et al. 2008).

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nonassociated flow rule proposed byMenetrey and Willam (1995).The comparisons indicate that the FEA model is able to replicatethe experimental displacement fields and shear zone dimensionsin a favorable manner. The model results in post-peak shear bandformation that matches the experimental measurements even assoil is removed from the surface during modeling to account forthe effects of sand migration beneath the pipe.

Comparisons of FEA with measured force versus displacementplots areprovidedin Figs. 12 and 13 for mediumand very dense CUFilter sand, respectively. The vertical upward pipe forces areshown as dimensionless force F= = F/(dHcDL), and upward pipedisplacements are shown as dimensionless displacement Z==Z/D,in whichFis force andZ is the relative vertical upward displace-ment between pipe and soil. The results from modified numerical

simulations for shallow depth show sudden changes in the post-peak behavior as elements on the top surface were removed fromthe FE mesh. The irregular pattern of the upward forces matchesthat of the full-scale test measurements. Overall, the predictedforcedisplacement behavior from the FEA compares very wellwith the measured data in terms of peak force and post-peakbehavior, with analytical peak forces within 10% of the measuredones.

Maximum vertical upward force versus pipe depth

To explore further NqVUversus Hc/D for vertical upward pipemovement, FEAs were performed for Hc/D varying from 5.5 to100 for medium, dense, and very dense dry sand as characterizedinTable 2.In the case of dense sand, dis taken as 17.1 kN/m

3 and

other input parameters are obtained with the procedures de-

scribed earlier.

Comparisons of vertical upwardNqVUversusHc/Dfor medium,

dense, and very dense sandare shown in Fig. 14.The values ofNqVUwere determined as described previously. The FE simulations of

vertical upward pipe movement show thatNqVUreaches its max-

imum of 14, 17, and 20 for medium, dense, and very dense sand,

respectively, atHc/D = 30. A reviewof the FEresults forD =900mm

also show that, at depths ofHc/D= 30, the upward reaction force

attains its maximum value, after which there is a very small force

reduction at greater depth due to reduction in dilation angle with

increased confining stress. Similar trends are reported byYimsiri

et al. (2004)for lateral pipe movement.

Force versus displacement relationships for

one-dimensional modeling of soilpipe interaction

Pipeline analysis for soilstructure interaction under permanent

ground deformation is often performed with one-dimensional

(1-D) FE models to represent the pipe and soil force versus

displacement relationships that are mobilized by various types

of ground movement. The force versus displacement relation-

ships for upward ground movement (qz) can be represented

by a rectangular hyperbola for the nonline ar characterization

of qz or by a simple bilinear relationship between force and

displacement (Trautmann and O'Rourke 1983; ASCE 1984;

Trautmann et al. 1985).

Fig. 12. Vertical upward dimensionless force versus displacement curves for medium CU Filter sand.

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To represent the rectangular hyperbola curve for theqz rela-tionship, FE simulations for differentHc/D and dwere performed.The results were plotted on the dimensionless transformed axesformedbyq=/z= andz= in Fig. 15, as proposed byKondner (1963) andTrautmann and O'Rourke (1983). In thefigure, q= = (F/dHcDL)/NqVU,z== (z/D)/(zmf/D), wherez is the vertical upward displacement andzmfis the upward displacement at which NqVU is mobilized. Thelinear regression, provided in the figure, was fitted to the trans-formed data to determine the constants a and b for the generalform of the hyperbola,F=z/(a +bz), from which the representative

hyperbolic model for vertical upward pipe movement was foundto be

(7) q z

0.1 0.88z

Fig. 13. Vertical upward dimensionless force versus displacement curves for very dense CU Filter sand.

Fig. 14. Summary plot ofNqVUversusHc/Dfor vertical upward pipemovement.

Fig. 15. q=/z=versusz

=plot.

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The results of FE simulations of upward pipe displacement,including those presented inFigs. 12and13,are plotted in dimen-sionless form inFig. 16.Equation(7) is also plotted in the figure.Based on the experimental data,Trautmann and O'Rourke (1983)reported a representative hyperbola relationships for vertical up-ward pipe movement asq==z=/(0.07 + 0.93z=), which is plotted as adashdot line inFig. 16 for comparison. Equation (7) comparesfavorably with the expression reported by Trautmann andO'Rourke (1983).The displacements at the maximum force from

thesimulations were normalized with respect toHc and expressedaszmf/HcinFig. 17for variousHc/D. As shown in the figure, repre-sentative values of zmf/Hc are 1.3%, 1.1%, and 1.0% for medium,dense, and very dense sand, respectively. The displacement zmffrom Fig. 17 can be used with eq. (7) to obtain the hyperbolicrelationships for vertical upward pipe movement.

Some computer programs use a bilinear force versus displace-ment relationship to model soil behavior as shown inFig. 16.Thebilinear force versus displacement model consists of an initiallinear portion with slope K70 that intersects the nonlinear forceversus displacement relationship at 70% of the maximum force.This method of estimatingK70was proposed byThomas (1978) andused byTrautmann and O'Rourke (1983).

Figure 18shows values ofz70/Hc for simulated vertical upwardpipe movement, where z70 is the displacement corresponding to

70% of maximum force for the bilinear relationship. As shown inthe figure, representative values ofz70/Hcare 0.4%, 0.3%, and 0.2%for medium, dense, and very dense sand, respectively. The repre-sentative value forz70/Hccan be used to computeK70as

(8) K70 0.7NqVU(Hc/z70)

Trautmann and O'Rourke (1983) reported a representative valueofz70/Hc= 0.003, or 0.3%, for all sand densities, which is similar tothe simulation values. Usingeq. (8)and the values ofz70/HcfromFig. 18, K70 for various pipe diameters, depths, and soil unitweights can be obtained and used for modeling soilpipeline in-teraction.

Conclusions

An elastoplastic constitutive model using MohrCoulomb (MC)strength parameters, a nonassociated flow rule, and a strain-softeningsubroutine is used to representsoil behavior for upwardpipe movement. Planestrain strength parameters converted fromdirect shear (DS) test results are used in the model and the con-version process is explained. The model accounts for reduced di-latancy and peak angle of shear strength with increased depth.The method for the selection of an appropriate strain-compatiblemodulus is described, based on a hyperbolic representation ofstress versus strain consistent with peak soil strength mobilizedat maximum upward pipe force. To account for soil migration

beneath the pipe during upward movement, the finite element(FE) mesh is adjusted. Large-scale test results are compared withthe simulation results to validate and qualify the soilstructureinteraction modeling. The predicted maximum dimensionlessforces from FE analyses match very well with those from large-scale tests for various dry sand densities and depths. Moreover,the displacement fields and shear zone dimensions for both peakand post-peak uplift load conditions compare favorably withthose measured byCheuk et al. (2008) andWhite et al. (2008)withPIV methods. The favorable comparisons between the analyticalresults and the experimental evidence from multiple sources in-dicatethat themodelingapproachis sufficiently robust to analyzemany different granular soils, pipe diameters, and pipe-depth-to-diameter ratios, including those at large depths. The modeling

Fig. 16. qzrelationships for 1-D modeling of soilpipeline

interaction for vertical upward pipe movement.

Fig. 17. zmf/HcversusHc/Dplots for vertical upward pipe movement.

Fig. 18. z70/HcversusHc/Dplots for vertical upward pipe movement.

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process is used to characterize the peak upward force as a func-tion of pipe depth. The results show that the dimensionless verti-cal upward force reaches its maximum value of approximately14,17, and 20 for medium, dense, and very dense sand, respectively,at a depth-to-diameter ratio of 30. The results of FE simulationsare used to construct hyperbolic and bilinear relationships for theforce versus displacement response during upward pipe move-ment. The relationships from the simulation compare favorably

with the expression from the large-scale test data for both cases.

AcknowledgementsThe work on which this paper was based was supported by the

George E. Brown, Jr. Network for Earthquake Engineering Simu-lation (NEES) Program of the National Science Foundation (NSF)under Grant No. CMMI-1041498. Any opinions, findings, and con-clusions or recommendations expressed in this material are thoseof the authors and do not necessarily reflect the views of the NSF.The authors acknowledge Drs. Soga, Anastasopoulos, and Robertfor their assistance in programming the FORTRAN subroutine.

ReferencesAnastasopoulos, I., Gazetas, G., Bransby, M .F., Davies, A., and El Nahas, M.C.R.

2007. Fault rupture propagation through sand: finite-element analysis andvalidation through centrifuge experiments. Journal of Geotechnical

and Geoevironmental Engineering,133(8): 943958. doi:10.1061/(ASCE)1090-0241(2007)133:8(943).

ASCE. 1984. Guidelines for the seismic design of oil and gas pipeline systems.Committee on Gas and Liquid Fuel Lifelines, American Society of Civil Engi-neers, Reston, Va.

ASTM. 2011. Standard practice for classification of soils for engineering purposes(Unified Soil Classification System). ASTM standard D2487. American Societyfor Testing and Materials, West Conshohocken, Pa.

Bolton, M.D. 1986. The strength and dilatancy of sands. Gotechnique, 36(1):6578. doi:10.1680/geot.1986.36.1.65.

Cheuk, C.Y., White, D.J., and Bolton, M.D. 2008. Uplift Mechanisms of pipesburied in sand. Journal of Geotechnical and Geoenvironmental Engineering,134(2): 154163. doi:10.1061/(ASCE)1090-0241(2008)134:2(154).

Chou, J.C., Kutter, B.L., Travasarou, T., and Chacko, J.M. 2011. Centrifuge model-ing of seismically induced uplift for the BART Transbay Tube. Journal ofGeotechnical and Geoenvironmental Engineering, 137(8): 754765. doi:10.1061/(ASCE)GT.1943-5606.0000489.

Davis, E.H. 1968. Theories of plasticity and the failure of soil masses. In Soilmechanics, selected topics. Edited byI.K. Lee. Butterworth, London.

Dickin, E.A. 1994. Uplift resistance of buried pipelinesin sand. Soils and Foun-dations,34(2): 4148. doi:10.3208/sandf1972.34.2_41.

Duncan, J.M., and Chang, C.-Y. 1970. Nonlinear analysis of stress and strain insoils. Journal of the Soil Mechanics and Foundations Division, ASCE, 96(5):16291653.

Ellis, E.A., and Springman, S.M. 2001. Modelling of soil-structure interaction fora piled bridge abutment in plane strain FEM analyses. Computers andGeotechnics,28(2): 7998. doi:10.1016/S0266-352X(00)00025-2.

Hu, L., and Pu, J.L. 2003. Application of damage model for soilstructure inter-face. Computers and Geotechnics, 30(2): 165183. doi:10.1016/S0266-352X(02)00059-9.

Huang,W., Nbel,K., andBauer, E. 2002. Polar extensionof a hypoplastic modelfor granularmaterials with shear localization. Mechanics of Materials, 34(9):563576. doi:10.1016/S0167-6636(02)00163-1.

Janbu, N. 1963. Soil compressibility as determined by oedometer and triaxialtests.In Proceedings,European Conference on Soil Mechanics & FoundationsEngineering, Wiesbaden, Germany. Vol. 1, pp. 1925.

Jewell, R.A., and Wroth, C.P. 1987. Direct shear tests on reinforced sand. Go-technique,37(1): 5368. doi:10.1680/geot.1987.37.1.53.

Jung, J.K. 2010. Soil-pipe interaction under plane strain conditions. Ph.D. thesis,Cornell University, Ithaca, N.Y.

Jung, J.K., Koo, D., and Zhang, K. 2012. Verification of the pipe depth dependentmodel using a finite element analysis. Tunneling and Underground Space

Technology. dx.doi:10.1016/j.tust.2012.02.024. [Posted online ahead of print24 April 2012.]

Kananyan, A.S. 1966. Experimental investigation of the stability of bases ofanchor foundations. Soil Mechanics and Foundation Engineering,3(6): 387392. doi:10.1007/BF01702954.

Klar, A., Vorster, T.E.B., Soga, K., andMair,R.J. 2005. Soilpipe interaction dueto

tunnelling: comparison between Winkler and elastic continuum solutions.Gotechnique,55(3): 461466. doi:10.1680/geot.2005.55.6.461.

Kondner, R.L. 1963. Hyperbolic stress-strain response: cohesive soils. Journal ofthe Soil Mechanics and Foundations Division, ASCE, 89(SM1): 115143.

Lings, M.L., and Dietz, M.S. 2004. An improved direct shear apparatus for sand.Gotechnique,54(4): 245256. doi:10.1680/geot.2004.54.4.245.

Menetrey,P., andWillam, K.J. 1995. Triaxial failure criterionfor concrete anditsgeneralization. ACI Structural Journal,92(3): 311318.

Muhlhaus, H.B., and Vardoulakis, I. 1987. The thickness of shear bands in gran-ular materials. Gotechnique,37(3): 271283. doi:10.1680/geot.1987.37.3.271.

Olson, N.A. 2009. Soil performance for large scale soil-pipeline tests. Ph.D. the-sis, Cornell University, Ithaca, N.Y.

O'Rourke, T.D. 2010. Geohazards and large, geographically distributed systems.Rankine Lecture. Gotechnique, 60(7): 505543. doi:10.1680/geot.2010.60.7.505.

Robert, D.J., and Soga, K. 2009. Simulations of soil-pipeline interactions in un-saturated soils. Report to Tokyo Gas Co. Ltd., Cambridge University.

Roscoe, K.H. 1970. The influence of strains in soil mechanics. 10th Rankine

Lecture. Gotechnique,20(2): 129170. doi:10.1680/geot.1970.20.2.129.Sun, D., Yao, Y.-P., and Matsuoka, H. 2006. Modification of critical state models

by Mohr-Coulomb criterion. Mechanics Research Communications, 33(2):217232. doi:10.1016/j.mechrescom.2005.05.006.

Thomas, H.G. 1978. Discussion of Soil restraint against horizontal motion ofpipes by J.M.E. Audibert and K.J. Nyman. Journal of the Geotechnical Engi-neering Division, ASCE,104(GT9): 12141216.

Trautmann, C .H., and O'Rourke, T.D. 1983. Behavior of p ipe in dry sand underlateral and uplift loading. Geotechnical Engineering Report 83-7, Cornell

University, Ithaca, N.Y.Trautmann, C.H., O'Rourke, T.D., and Kulhawy, F.H. 1985. Uplift force-

displacement response of buried pipe. Journal of Geotechnical Engineering,111(9): 10611076. doi:10.1061/(ASCE)0733-9410(1985)111:9(1061).

Vardoulakis, I., and Graf, B. 1985. Calibration of constitutive models for granularmaterials using data from biaxial experiments. Gotechnique, 35(3): 299317. doi:10.1680/geot.1985.35.3.299.

Vorster, T.E.B., Klar, A., Soga, K., and Mair, R.J. 2005. Estimating the effects oftunneling on existing pipelines. Journal of Geotechnical and Geoenviron-mental Engineering, 131(11): 13991410. doi:10.1061/(ASCE)1090-0241(2005)131:11(1399).

White, D.J., Cheuk, C.Y, and Bolton, M.D. 2008. The Uplift resistance of pipes andplateanchors buried in sand.Gotechnique, 58(10):771779. doi:10.1680/geot.2008.3692.

Wong, K.S., a nd Duncan, J.M. 1974. Hyperbolic stress-strain parameters for non-linear finite element analyses of stresses of stresses and movements in soilmasses. Report No. TE-74-3, University of California, Department of CivilEngineering, Berkeley, Calif.

Xie, X., Symans, M.D., O'Rourke, M.J., Abdoun, T.H., O'Rourke, T.D., Palmer, M.C.,and Stewart, H.E. 2012. Numerical modeling of buried HDPE pipelines sub-

jected to normal faulting: a case study. Earthquake Spectra. [In press.]Yimsiri, S., Soga, K., Yoshizaki, K., Dasari, G.R ., and O'Rourke, T.D. 2004. Lateral

and upward soil-pipeline interactions in sand for deep embedment condi-tions. Journal of Geotechnical and Geoenvironmental Engineering, 130(8):830842. doi:10.1061/(ASCE)1090-0241(2004)130:8(830).

Zienkiewicz, O.C., Emson, C., and Bettess, P. 1983. A novel boundary infiniteelement. International Journal for Numerical Methods in Engineering, 19(3):393404. doi:10.1002/nme.1620190307.

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Published by NRC Research Press