Datta - 1999 - Seismic Response of Buried Pipelines a State-Of-The-Art Review

Nuclear Engineering and Design 192 (1999) 271284

Seismic response of buried pipelines: a state-of-the-artreview

T.K. Datta *Department of Ci6il Engineering, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India

Abstract

A state-of-the-art review of the seismic response of buried pipelines is presented. The review includes modeling ofsoilpipe system and seismic excitation, methods of response analysis of buried pipelines, seismic behavior of buriedpipelines under different parametric variations, seismic stresses at the bends and intersections of network of pipelines.pipe damage in earthquakes and seismic risk analysis of buried pipelines. Based on the review, the future scope ofwork on the subject is outlined. 1999 Elsevier Science S.A. All rights reserved.

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1. Introduction

The seismic behavior of buried pipelines andpiping systems is quite different from that of theabove-ground structures in many respects, suchas: The horizontal inertia forces, which comprise

the main factor affecting the design of above-ground structures, are largely resisted by thesurrounding soil in the case of buried pipelines.

For above-ground structures, the foundation isusually assumed to follow the ground motionand, therefore, the relevant response is dis-placement relative to the foundation. In thecase of buried pipelines, the relative movementbetween the pipe and the surrounding soil isresponsible for inducing stresses at the joints.

The ground motion is considered to be coher-ent for most over-ground structures, while forburied pipelines it is considered as incoherentbecause of the phase difference between differ-ent stations and the change in shape due to thevariation of soil properties along the pipeline.

The damage of one over-ground structure isgenerally restricted to that structure alone, butthe damage at a certain location within a net-work of pipelines will affect other portions ofthe system.Field observations and various studies indicate

that major seismic hazards to buried pipeline sys-tems are: (1) excessive axial and bending stressesand deformations in pipelines created mainly bythe phase difference and change of wave shapebetween different points along the pipeline; (2)large displacements resulting from the fault move-ment during an earthquake if the pipeline crossesa major fault; and (3) landslides and buoyancycaused by soil liquefaction.

* Tel.: 91-11-686-7754; fax: 91-11-686-2037.E-mail address: [email protected] (T.K. Datta)

0029-5493:99:$ - see front matter 1999 Elsevier Science S.A. All rights reserved.

PII: S0029 -5493 (99 )00113 -2

T.K. Datta : Nuclear Engineering and Design 192 (1999) 271284272

Damage and disruption of buried pipelinescaused by an earthquake may have severe effectson civil life since it may lead to loss of vitalservices, communications and transportation sys-tems. As a consequence, the seismic behavior ofthese structures has been investigated by manyresearchers. A number of issues are involved inthe study of seismic analysis and behavior ofburied pipelines. They include: (1) modeling ofseismic excitation and soilpipe system; (2) evalu-ation of seismic stresses in the pipelines; (3)stresses at the junctions and bends; (4) pipelinestresses due to fault movement and soil liquefac-tion; (5) pipeline damage in earthquakes; and (6)vulnerability of pipelines to seismic hazards. Inthis paper, a state-of-the-art review on seismicresponse and behavior of buried pipelines, ad-dressing the above issues, is presented.

2. Modeling of soilpipe system and seismicexcitation

With the postulation that the soil does not loseits integrity during the design earthquake, thebasic concept governing the response of under-ground pipelines is that the soil is stiff comparedto the structure. Therefore, the earthquake defor-mation is imposed on the structure, which mustconform to this deformation. These deformationsare of two typescurvature and shearing. Theformer represents the direct imposition of the soilcurvature on the structure, which must have thecapacity to absorb the resulting strains. The latterrepresents the lag of soil in response to the baseacceleration imparted to it through the bedrock.It is important for the designer to recognize thatthe effect of the earthquake on undergroundpipelines is the imposition of an arbitrary defor-mation which can not be changed by strengthen-ing the structure (so long as the soil is stiffer thanthe structure). The structural design criterion is,therefore, a provision of sufficient ductility toabsorb the imposed deformation without losingthe capacity to carry static loads, rather than acriterion for resisting inertial loads at a specifiedstress level.

It should also be recognized that the absoluteamplitude of the earthquake displacement may belarge, but this displacement is spread over a longlength. Therefore, the ratio of the earthquakedistortion is generally small, and usually withinthe elastic deformation capacity of the structure.If it can be established that the maximum defor-mation imposed by the earthquake will not strainthe structure beyond the elastic range, no furtherprovision to resist the deformation is required. Ifcertain joints are strained into the plastic range,the ductility of such joints should be investigated.

Soilstructure interaction becomes importantwhen the soil stiffness is comparable to the pipeli-nes stiffness. Under such a condition, a rigorousdynamic analysis for the soilstructure system isrequired. Seismic response analysis of buriedpipelines is a complex phenomenon includingthree-dimensional dynamic analysis of the soilstructure system under multipoint seismic excita-tion and treatment of non-homogeneousnon-linear:linear viscoelastic medium. A rigorousanalysis satisfying all these conditions is almostimpossible; therefore, different degrees of simplifi-cations are made to obtain a good estimate of theresponse quantities of interest. The level of sim-plification depends upon the response quantitiesof interest, and it primarily governs the type ofmodeling of the system. Different types of model-ing of the underground pipelines are available,starting from extremely simple to complex three-dimensional modeling of the soilstructure sys-tem. Accordingly, the method of analysis varies.

The simplest model of buried pipelines is theone in which no soilstructure interaction is ac-counted for. The structure is assumed to followthe deformation of the ground. When the soilstructure interaction is considered, models thathave been widely used are shown in Figs. 14.Fig. 1 shows the model of a beam on elasticsprings (they may be also in axial direction) torepresent long buried pipelines in which bendingand axial deformations are of main concern. Ashell model for a large diameter buried pipeline isshown in Fig. 2. The shell model is assumed to beresting within a viscoelastic medium. In Fig. 3, thecross-section of a large diameter buried pipeline isshown. This is a plane-strain model of the struc-

T.K. Datta : Nuclear Engineering and Design 192 (1999) 271284 273

Fig. 1. Beam model in elastic foundation.

Fig. 3. Plane-strain model.

seismic waves. The possibility of the cross-sectionbuckling is also investigated using this model. Inthe hybrid model shown in Fig. 4, the interiorregion (R1) is modeled by the finite elementmethod (FEM), while the outer region (R2) ismodeled by the half space continuum. A plane-strain model is adopted for both regions. Conti-nuity of displacement and strain is maintained atthe interface boundaries between the two regions.

Many analyses of buried pipelines have beendone with P, S or Rayleigh waves with grounddisplacement modeled as harmonic functions.Waves propagated parallel to the long axis of thepipelines tend to enforce a corresponding sinu-soidal transverse distortion on the structure forS-waves. S-waves traveling at right angles to thestructure tend to move it back and forth longitu-dinally, and may tend to pull it loose at zones of

ture. Fig. 4 shows a hybrid model for a cylindricaltunnel. This type of model is applicable for largediameter pipelines.

In Fig. 1, the spring represents the soil stiffness.The soil damping and stiffness are calculated sep-arately and are included in the mathematicalmodel by equivalent springs and dampers. Theshell model shown in Fig. 2 provides both periph-eral and longitudinal stresses in the structure dueto earthquake waves incident at an angle with thelongitudinal axis of the structure as well as at anangle with one of the principal axes of the shellcross-section. The shell model is also capable ofpredicting the buckling failure of the structure.The plane-strain model, as shown in Fig. 3, iswidely used whenever the hoop stress and theradial displacement are to be obtained due to

Fig. 4. Hybrid model.Fig. 2. Shell model.


abrupt transition in soil conditions, where waveproperties may vary. Diagonally impinging wavessubject different parts of the pipeline to out-of-phase displacements. This results in a longitudinalcompression-rarefaction wave that travels alongthe structure. Seismic shear waves may have anyinclination, but observations indicate that wavescausing displacements in a horizontal plane usu-ally have the greatest amplitude; the amplitude ofvertical waves is generally one-half to two-thirdsas great as that of the corresponding horizontalwaves. The velocity of propagation of shear wavesdecreases with decreased rigidity of the rock orsoil. Correspondingly, the amplitude of the vibra-tion increases as the medium becomes softer.

For buried pipelines, the ground motion be-comes incoherent because of the phase differencebetween two points and change of wave shapealong the structure. Therefore, the single responsespectrum is not applicable for such long systems.For such cases, the time history of ground acceler-ation:displacement is useful for the deterministicseismic response analysis with assumed directionand velocity of wave propagation. For non-deter-ministic analysis, the randomness of ground mo-tion is mostly characterized by a power spectraldensity function (PSDF) of ground displacement:acceleration. Clough and Penzien (1975) and oth-ers considered the strong ground motion as awhite-noise process of limited duration. However,a stationary filtered white-noise of limited dura-tion is found to be more representative of actualground motion. The phase difference betweenground motions at two points is considered bydefining a correlation function involving the sepa-ration distance between the two pointsthe shearwave velocity and the frequency of ground mo-tion. For non-stationary random ground motion,it is generally modeled as a uniformly modulatednon-stationary random process. Various types ofmodulating functions are used to model differenttypes of non-stationarity.

3. Methods of analysis

Depending upon different types of model andresponse quantities of interest, different methods

of analysis have been presented by researchers toobtain the seismic response of buried pipelines.Methods of analysis existing in the literature varyfrom simplified analysis to complex three-dimen-sional finite element methods. Available methodsof analysis can be grouped under the categoriesdiscussed in the following sections.

3.1. Analysis without considering soilstructureinteraction

Deformations in long structures are createdmainly due to the phase difference (time lag) andthe change of wave shape between different sta-tions along the structure. Newmark and Rosen-blueth (1971) presented simplified methods forcalculating the pipe deformations under the as-sumptions that (1) inertia forces and soilpipeinteraction are neglected (i.e. the pipe and soilmove together exactly), and (2) earthquake excita-tion may be modeled as a travelling wave havingconstant wave shape (i.e. the time history of twostations along the propagation path differs onlyby time lag). Using these assumptions, they ob-tained the free field strain and curvature. In thecase of a general angle of incidence of the earth-quake wave, Hindy and Novak (1979) proposedother expressions for free field strain and curva-ture due to two types of waves, namely P-wavesand S-waves. Kuesel (1969) applied this methodto the seismic design of the San Franciscosubway.

Shah and Chu (1974) developed a simplifiedapproach for determining seismic stresses. Thesimplified modeling and the formulae derived arebased on Newmarks values of seismic strain forburied pipelines. The formulae include bendingmoment and shear force for (1) straight elements(2) bends and (3) T-junctions. The approximateformulae are not valid for the ratio of wavelengthto length of the element less than 3p:4.

3.2. Quasi static analysis with soilstructureinteraction

In this analysis, the soil deformations arematched by a combination of pipe deformationsand relative deformations of joints. Using this


approach, upper bounds of axial pipe strain andpipe curvature at a particular point are obtainedby Newmark and Rosenblueth (1971) and Halland Newmark (1977) by neglecting the relativedeformations at the joints (i.e. the pipe is assumedto be flexible with respect to the soil). Upperbounds of the relative displacements and relativerotations at the joints are given by Wang et al.(1979) by ignoring the pipe segment deformations(i.e. the pipe is rigid with respect to the soil).Assuming that the soil displacement in the axialdirection is matched only by the joint displace-ment and no slippage occurs between the pipe andthe soil, Wang et al. (1979) and Nelson andWeidlinger (1979) presented two analyses for theaxial displacement of long segmented buriedpipelines due to traveling waves. The analysisused the approach of a beam on an elastic foun-dation (Fig. 1), and the straight pipeline is mod-eled by a set of rigid segments connected byflexible joints represented by elastic springs anddashpots. In another study, Wang et al. (1982)used a model in which pipe segments have finitestiffness in the axial direction (semi-rigid). Conse-quently, the soil strain is matched by the combi-nation of pipe strain and the relative displacementof joints. They derived expressions for the pipestrain ratio and the relative joint displacementratio. Nelson and Weidlinger (1979) developed aninterference response spectrum (IR spectrum), inwhich any particular ordinate represents the abso-lute maximum axial out-of-phase response be-tween two adjacent joints due to the incoherentground motion resulting from the phase delay.The IR spectrum was constructed by neglectingpipe joint stiffness and damping. Nelson andWeidlinger (1979) also used the IR spectrum todefine the amplification factor for the displace-ment of joints of buried pipelines. The idealiza-tion of a buried pipeline as a beam on an elasticfoundation in axial and lateral direction was usedby Kubo et al. (1979) to realize one formula forcalculating the normal stresses, using the axialstresses caused by the axial deformations and thatcaused by bending deformations. Novak andHindy (1980) modified the equations given byHindy and Novak (1979) by introducing reduc-tion factors accounting for the effect of soilpipe

interaction to obtain a quasi static analysis. Sing-hal and Zuroff (1990) proposed a quasi staticanalysis, using the theory of beam on elasticfoundation, to obtain the response of buriedframed structure with flexible joints under earth-quake excitation.

3.3. Dynamic analysis by considering the theoryof beam on elastic foundation

Considering the pipeline as a long continuous(without joints) system, a spring supportedlumped mass model for such pipes was employedby Hindy and Novak (1979). A deterministicanalysis of the response (both axial and lateral) ofburied pipelines to fully correlated travelingwaves, described by a single time history travel-ling along the pipe axis, was performed. Thesoilpipe interaction was incorporated by aspring dashpot system whose reactions werederived from the static and dynamic continuumtheories. They also obtained the effect of pipejoints on the response by modifying the axialstiffness matrix of the pipe to incorporate theaxial stiffness of the joints. A similar analysis wascarried out by Yuan and Walker (1970) andWong and Weidlinger (1983). Using a spring sup-ported beam model (Fig. 1), Hindy and Novak(1980) obtained the response of buried pipelinefor random ground motion characterized by aPSDF and a cross-spectral density function. Thesoil reactions were derived from the static anddynamic continuum theories and modal spectralanalysis was employed to evaluate the pipe re-sponse in both axial and lateral directions. Dattaand Mashaly (1986) extended the work of Hindyand Novak (1980) to incorporate the effect ofcross terms of soil stiffness and damping matricesin the stochastic seismic analysis of buriedpipelines.

3.4. Analysis by considering shell theory withsoilstructure interaction

Most of the work done on the seismic responseof buried pipelines used the beam theory. How-ever, in such a theory the displacements are un-coupled and the beam model (Fig. 1) can not


describe the buckling and fracture phenomena.These phenomena are best described by a shellmodel which gives displacements in the three di-rections. In the response analysis of buried pipeli-nes due to traveling waves, the pipe has beenmodeled as a thin isotopic elastic cylindrical shellin a viscoelastic medium. Muleski et al. (1979a,b)used the Flugge bending theory of shell to developthree decoupled equilibrium equations giving thedisplacement in three directions due to axialground motion. Datta et al. (1981) and OLearyand Datta (1985a) proposed axisymmetrical andthree-dimensional analysis (respectively) for thedynamic response of buried pipelines to incidentcompressional waves (S and P) traveling along thepipeline, with low frequencies and long wave-lengths. Wong et al. (1986) and Luco and Barnes(1994) also carried out an analysis of pipeline byshell theory.

3.5. Analysis using dynamic plane-strain modelwith soilstructure interaction

Wong et al. (1986) demonstrated the impor-tance of considering the effect of pipeline motionin modifying the free field ground motion into thepipeline analysis. The pipeline modeled as contin-uous beams or cylindrical shells on an elasticfoundation do not consider this effect and as aresult the full soilstructure interaction effect ismissing in such idealization. OLeary and Datta(1985b), Datta et al. (1984), Wong et al. (1986)and Takada and Tanabe (1987) studied this fullsoilpipe interaction problem in three-dimen-sional response behavior of pipelines. The pipelinewas subjected to plane body and surface wavesmoving at an arbitrary angle to the axis of thepipeline in a semi-infinite medium. The equationsof elasto-dynamics governing the motion of thepipe and surrounding ground were solved usingcylindrical eigen functions. The solution outsidethe pipeline was expressed as the sum of a com-plete expansion in terms of outgoing waves satis-fying the boundary conditions on the free groundsurface and the incident waves (Fig. 3). Thistechnique enabled the outer solution to bematched with a finite element representation in-side for the structure (if needed). An exact method

of solution involving series expansion of incidentand reflected SH waves of cylindrical wave func-tion was presented bv Lee and Trifunac (1979) forcircular tunnels (or big diameter pipelines). Itused Hankel functions of the second kind in theseries expansion for the scattered and diffractedwaves (reflected wave function). The differentialequation of the total wave was solved under theboundary conditions imposed for the wholestructure.

3.6. FEM analysis

Dynamic stresses and displacements of a cylin-drical tunnel (or big diameter pipeline) embeddedin a semi-infinite elastic medium were analyzedfor P, SV and Rayleigh wave by Wong et al.(1985) and Masso and Attalla (1984). The prob-lem was considered as one of plane strain, inwhich the wave propagates perpendicular to thelongitudinal axis of infinitely long tunnel. A nu-merical technique that combines the finite elementmethod with the eigen function expansion wasused. The eigen function expansion of the freefield displacement and the scattered wave dis-placement was used outside the boundary of thecircular region of the soiltunnel system. Insidethe boundary, a finite element representation ofthe soilstructure system was adopted (Fig. 4).The continuity of displacement and truncationwas imposed at the boundary.

3.7. Analysis of buried pipeline response to faultmo6ement and soil liquefaction

The large abrupt differential ground motion onan active fault represents one of the most severeearthquake effects on a buried pipeline crossingsuch a fault. The assessment of fault hazardsrequires information about: (1) location of thefault and the total width of the zone; (2) themagnitude and direction of the expected displace-ments and their type (horizontal or vertical); (3)geometry of the fault plane; and (4) the magni-tude of the causative earthquake and its returnperiod. Newmark and Hall (1975) developed aprocedure for analyzing the effect of large faultmovements on buried pipelines. They related the


soil-slip friction on the pipe to the earth pressureat rest (neglecting the passive soil pressure), andthe pipe elongation was calculated using thesmall-deflection theory. A simple expression waspresented by the authors for calculating the longi-tudinal strain. Kennedy et al. (1977b) modeledthe pipeline as a flexible cable deforming into asingle curvature approaching asymptotically tothe undeformed portion. The pipe strain was cal-culated using the large-deflection theory consider-ing a uniform passive earth pressure. Wang andYeh (1985) presented a refined analysis procedurefor calculating the elongation of buried pipelinescrossing either strike-slip or reverse strike-slipfaults using the large-deflection theory. One halfof the deformed pipe was assumed to be a curvedsegment of constant curvature and a semi-infinitesegment on an elastic foundation. The modelinvolved the bending rigidity of the pipe, shearforce at the inflection point, and non-uniformpassive soil pressure, as well as the soil friction onthe pipe surface and tensile forces in the pipesections.

Soil liquefaction due to earthquakes of highintensity and long duration is likely to occurwhen the soil consists of loose uniform small-sizeparticles and becomes saturated. The assessmentof liquefaction hazards requires: (1) a qualitativeanalysis that shows the susceptibility of differentsoil conditions to liquefaction; (2) determinationof whether the anticipated strong earthquake(which has 10% probability of occurrence) islikely to induce liquefaction; and (3) determina-tion of the length of the zone, the vertical andhorizontal soil displacements, as well as thestrength, density and viscosity of the soil. Onlyvery limited and approximate work has been doneon the analysis of pipeline response to soil lique-faction. An approximate estimation of pipe dis-placement was proposed by Kennedy et al.(1977a) for pipelines buried within liquefiable soil.

Kennedy et al. (1977a), Wang and Yeh (1985),Newmark and Hall (1975), Wang and ORourke(1977) and Ariman and Muleski (1981) recom-mended that the following considerations accountfor the design of buried pipelines crossing activefaults or running within liquefiable soil: (1) avoid-ance of placing the anchors, sharp bends or pipe

junction within a distance of at least 200 ft oneither side of the fault line to allow pipe move-ment in all directions; (2) shallow burial (35 ft)with side slopes of 45 or less using cover andback-fill from materials that have lower shearstrength; (3) use of thick-walled pipe withoutabrupt change in the thickness to reduce thestrain concentration; (4) use of ductile steel, high-quality welding and flexible joints to preventstrain concentration and enable the pipe to toler-ate large deformation; (5) allowing fault crossingangle between 40 and 90 (the angle which placesthe pipe in tension); (6) anchoring the pipeagainst uplift or enhancing the pipe in concrete;(7) use of smaller diameter pipes in parallel in-stead of one large diameter pipe; and (8) providefail safe systems at fault and liquefaction zones(such as blow-off valves and reservoirs).

4. Seismic parametric behavior of buried pipelines

The seismic response of buried pipelines de-pends upon a number of factors. As a result,parametric studies leading to the seismic behaviorof buried pipelines have been conducted by differ-ent investigators. Some of the important results ofthe studies are reported below.

Shah and Chu (1974) observed that, if soilstructure interaction is ignored, then larger rela-tive displacement at the bend results in higherbending stress. Relative displacement between theelement and the surrounding soil increases withan increase in particle velocity and decreases withan increase in wave velocity. Relative displace-ment for a straight element forms an upperbound for all cases. Therefore. this relative dis-placement should be used for finding bendingmoments and shear forces in all cases for conser-vative estimate.

Datta et al. (1984) showed that response of thepipe increases with the increase in the frequencyof P and SV waves with zero angle of incidence.For other angles of incidence, the hoop stressmay decrease with the increase in frequency insome cases. The pattern of stresses is depicted inFig. 5. The hoop stress also depends upon theburial depth differently for different waves.


Fig. 5. Axial stresses for different angles of incidence.

Wong et al. (1985) reported that the tunnel (orlarge diameter pipelines) behavior in rock and softsoil are quite different. The hoop stress increaseswith frequency initially and then decreases. If thesurrounding soil is soft, the maximum stress isreached at a lower frequency. The dependence ofstress on the angle of incidence is found to bequite different between P and SV waves, andbetween soft and rock medium.

Hindy and Novak (1979) obtained the responseof buried pipelines crossing an interface betweentwo types of soils having different stiffnesses. Thehighest stresses are found close to the boundary.Takada (1977) studied the effect of pipe slippageon the response behavior of buried pipelines. Theauthor recommended that flexible joints are neces-sary to absorb the sliding strain to assure earth-quake resistance by harmonizing the pipeline tothe behavior of the ground.

The effect of pipe insulation, representing theactual condition (where the pipe is usually sur-rounded by back-fill material), was studied byHindy and Novak (1980). They found that thepipe insulation results in reduction of pipestresses. This result was confirmed by Datta et al.(1984) using the shell model.

Datta and Mashaly (1986, 1988) observed thatabout six or seven modes are sufficient for accu-rate analysis of both axial and lateral responses ofburied pipelines. The increase of radius and wallthickness of the pipe reduces both axial and bend-ing stresses. Structural damping may be ignored

compared to soil damping for calculating theresponses. The stresses near the pipe ends areenhanced due to the pipe end conditions. Thedegree of enhancement and the distance overwhich the effect of end restraint prevails dependupon the pipe end conditions. The axial andbending stresses at the fixed ends are about 10.3and 54 times more than those in the middle. Forpinned ends, they are greatly magnified over cer-tain length near the ends as shown in Fig. 6(Datta and Mashaly, 1988). The pipe stresses inthe middle are independent of end conditions andremain constant over a substantial portion in themiddle as shown in Fig. 7 (Datta and Mashaly,

Fig. 6. Distribution of RMS bending stresses along thepipeline.


Fig. 7. Longitudinal stresses in the buried pipeline.

earthquake shaking caused breakage of main andservice lines, while the direct seismic shakingforces crushed and sheared the pipes, broke thebells and pulled the mechanical joints apart.

Observed failures due to several earthquakessince 1920 in Japan with magnitude greater than 7showed that the damage by pipelines was mostlycaused by direct seismic shaking. In the 1964Niigata earthquake, liquefaction had occurredand caused most of the failures. The types offailure due to these earthquakes were similar tothose observed during the San Fernando andAlaska earthquakes.

After reviewing the data obtained from theobservation of damage due to past earthquakes,Wang and ORourke (1977) concluded that: (1)the damage occurred least in bed-rock, moder-ately in course-grained soils and most frequentlyin fine-grained soil; (2) most damage occurred insoils with response frequency between 3.5 and 4.5Hz; (3) the damage increased for steel and castiron water pipes of small diameters, but for claysewer pipes the trend was reversed; (4) the belland spigot joints with lead or cement caulkingwere vulnerable to earthquake effects and thearc-welded pipes rarely failed at the girth welds;and (5) asbestoscement pipes were generallymore susceptible to seismic damage. The weldedsteel pipes behaved best.

The study by Katayama et al. (1975) on theeffect of ground motion intensity during the 1971San Fernando earthquake showed that the num-ber of failures per kilometer seemed to be linearlyproportional to the maximum ground acceleration(loglog scale). This result was consistent with thedata of several earthquakes (Tokyo, Managua,Fukui). Katayama et al. (1977) also studied theeffect of ground condition and complexity on thedamage of buried pipelines due to the 1923 Kantoearthquake. It was observed that the damage in-dex was greater for complex ground propertiesand for very soft soil. In another study,Shinozuka and Kawakami (1977) observed agood correlation between the surface strain andthe damage index. An excellent state-of-art reviewof the damage of buried pipelines under seismicexcitation was presented by Ariman and Muleski(1981).

1986). However, a minimum length of pipe is tobe considered in the analysis for each type of endconditions in order to realize this result. Theembedment depth has little effect upon thestresses. The pipe stresses are reduced by about15% for shallow burial, and it becomes almostconstant for embedment depth more than 30times the radius of the pipeline. Further, existenceof fluid inside the pipe does not significantlyinfluence the response unless sloshing effect be-comes important.

5. Analysis of pipeline damage

Review of past earthquake damage records(quantitative analysis) and typical modes of fail-ure (qualitative analysis) enables designers to es-tablish performance criteria to develop amethodology that minimizes the probability ofsystem failure.

Observations from the 1971 San Fernandoearthquake showed that pipelines with rigid jointsfailed more than those with flexible joints; mostdamage was due to seismic shaking. The majorfailure mechanisms were crushing, flexural failureof pipe sections, pull-out and shear failure at thejoints. Failures due to buckling were particularlydominant in the pipelines crossing a fault. Theyoccurred due to compressive forces generated bythe earthquake.

In the 1964 Alaska earthquake, it was observedthat buried pipelines were destroyed completely inlandslides. The differential settlement due to


It was also observed that the effect of thespatial correlation of ground motion has consider-able effect on both stresses and displacement re-sponses. The cross terms in soil damping andstiffness have considerable effect on the frequen-cies and mode shapes of the pipeline but they donot have much influence on stresses and displace-ments. This is because of the fact that the soilpipe system is so stiff that the inertia effectbecomes negligible and quasi static responsegoverns.

6. Intersection stresses and network effect

Mashaly and Datta (1989a,b), ORourke et al.(1982) and Singhal and Meng (1983) investigatedthe intersection stresses in buried pipelines. It wasshown that the intersection stresses in the buriedpipelines depend upon a number of factors suchas the type of intersection. angle of intersection ofthe pipes. the ratio of the diameters of the inter-secting members and the angle of incidence of theearthquake. Branches perpendicular to the direc-tion of wave propagation have less stresses thanthe other branches. Further, axial stresses aremuch less than the bending stresses near the pipeintersection. For a single straight segment ofpipeline, an opposite trend is observed. Generally.the intersection stresses are much higher than thestresses in the middle of branches: the amplifica-tion depends on the type of intersection, the angleof incidence of earthquake and the ratio betweenthe diameters of the intersecting pipes. Typicalstresses at the pipe intersection are shown in Fig.8. The variation of intersection stresses with theangle of wave propagation for an L intersection isshown in Fig. 9 (Mashaly and Datta, 1989a).

Shinozuka et al. (1979) have given conservativevalues for the stresses at significant curvaturesand at pipe intersections, obtained by multiplyingthe stresses in straight segments by a factor Bwhich ranges between 1 and 3. ORourke et al.(1982) studied the effects of the propagation oftransverse seismic wave (S-wave) at junctions in aburied pipeline network. They found that therotation in the straight pipe will be reduced if thepipe junction exists. Shah and Chu (1974) devel-

Fig. 8. Intersection stresses.

oped a set of simplified expressions for calculatingthe relative displacement between the soil and thepipe, and shearing force and bending moment atthe pipe intersection. Singhal and Meng (1983)analyzed pipe stresses as a quasi-static problemusing the idealization of beam on elastic founda-tion and using static loads acting at differentportions of the network. Results obtained bySinghal and Meng (1983) and ORourke et al.(1982) showed that very large bending stresses

Fig. 9. Variation of intersection stresses with angle of inci-dence (branch A2).


occur at the pipe intersections, and the networkeffect extends to a distance ranging between pr0and 40 r0 (where r0 is the radius of the pipeline).

7. Seismic risk analysis of buried pipelines

Seismic risk analysis of a buried pipeline systemis a methodology developed to minimize the prob-ability of system breakdown and reduce the lossesfrom damage due to future earthquakes. Seismicrisk analysis requires the evaluation of the proba-bility of pipeline system unserviceability underdifferent levels of earthquake intensity to whichthis system is subjected during its lifetime. Thereare many approaches to conduct the seismic riskanalysis, such as: (1) analysis for reliability of thenetwork system; (2) analysis for seismic hazardlosses; (3) vulnerability analysis; and (4) analysisfor system performance.

Taleb Agha (1977) employed the reliability andnetwork theories to conduct a seismic risk analy-sis of transportation lifelines. He developedschemes to find the probability of partial networkfailure due to a given set of ground shaking. Erelet al. (1977) and Oppenheim (1979) developed arelationship between the number of failures (N)per kilometer of pipeline and peak ground accel-eration or earthquake intensity. The damage con-ditions represented by N was translated into thesystem performance. The system performance wasconverted into losses and subsequently integratedover the probability density function of earth-quake occurrence to obtain the annual expectedloss. Oppenheim (1977) presented a direct numeri-cal procedure using the Monte Carlo method tosimulate the failure of different lifeline links withthe magnitude of the earthquake and its expectedannual probability of occurrence. In the method,the ground acceleration at each link due to eachincremental earthquake magnitude was calculatedand compared with the link resistance. For eachsignificant link failure, the performance of thesystem in terms of losses was evaluated and totalexpected annual hazard losses were obtained bynumerical summation.

Campbell et al. (1979) presented a methodologyfor assessing the reliability of the lifeline in terms

of its effectiveness to meet certain minimum per-formance standards during and after an earth-quake. These standards consider different risks tothe community. Mohammadi and Ang (1982)conducted a seismic hazard analysis for lifelinesystems subjected to severe ground shaking. Theyobtained the annual probability of failure of eachlink of the system assuming uniform seismicity.The probability of system failure was obtained bymodeling the lifeline using network approach.Whitman and Hein (1977) presented a method forseismic risk analysis of water pipeline systems ofshallow burial. In this analysis, a damage (unser-viceability) probability matrix (DPM) was estab-lished for each segment using an appropriatedefinition for damage state in terms of systemunserviceability. The elements of the DPM werederived by combining two matrices. The first onedescribed the probability that each earthquakeintensity would produce different levels of failure,and the other indicated the probabilities that eachlevel of soil site failure would produce differentdamage states.

Despang and Shah (1982) proposed a methodfor quantitative evaluation of seismic damage andrisk of lifelines and infrastructural systems. In thisanalysis, the seismic damage was measured interms of global response, which includes manymeasurements of physical damage and calibra-tions of the level of serviceability after the damag-ing event. Assuming that the response levelsrespond as a Poisson stochastic process, the prob-ability of n occurrences during a time T0 of systemglobal response larger than a certain value, G, isobtained. The reliability is evaluated from theconditional probability of the occurrence of thestate of G. Atkinson et al. (1982) proposed amethod for seismic risk analysis of buried pipeli-nes assuming that the seismic waves are fullycorrelated and travelling along the pipe axis withsurface Rayleigh wave. The axial stress was ob-tained by neglecting the soilpipe interaction.

Shinozuka et al. (1979) developed a methodol-ogy for the seismic risk analysis of water transmis-sion systems. The damage states were defined bysome levels of axial pipe strain which were calcu-lated considering ground shaking, fault movementand soil liquefaction. The probability of different


damage states was calculated for every combina-tion of soil condition and earthquake intensityconsidering the pipe strain as a Gaussian randomvariable. These probabilities were tabulated inDPMs as presented by Whitman and Hein (1977).Mashaly and Datta (1989c) described a procedurefor seismic risk analysis of the component seg-ment of the general network system of buriedpipelines. The concept of DPM was used to ob-tain an estimation of the annual probability ofoccurrence of different damage states. The re-sponse of the pipeline was obtained by using themethod of random vibration analysis.

8. Conclusions

A state-of-the-art review of the seismic behaviorof buried pipelines is presented. It also includesinformation on the estimation of pipe damagecaused by seismic forces and the consequent seis-mic risk analysis. The review shows that consider-able research has been carried out on thedetermination of pipe response to traveling (deter-ministic) seismic waves; in particular, many sim-plified formulae have been developed to obtainseismic stresses produced in the pipeline. Compar-atively much less attention has been paid to theevaluation of pipe stresses for random earthquakeinputs and for network systems crossing activefaults. Specifically, the stresses at the intersectionof network systems under random seismic condi-tions, which are important for seismic risk analy-sis, have not received much attention. It is feltthat more investigations are necessary on the fol-lowing subjects in order to formulate rationaldesign procedures and to obtain realistic assess-ment of seismic risks involved in the designs:1. Network effect on the stresses in the pipeline

with special reference to the evaluation of thestresses at pipeline intersections produced byrandom ground motion.

2. Experimental and field data procurement andanalysis to establish realistic behavior of soilpipe interactive forces, behavior of pipe joints,and actual strain and deformation patterns inthe pipe produced by ground motion.

3. Evaluation of stresses produced in large di-ameter pipes due to random ground motioncaucing buckling and fracture failures.

4. Stresses induced in the pipeline network sys-tem produced by fault movements and inpipelines passing through very soft and liquefi-able soil.

5. Qualitative and quantitative evaluation ofdamages in buried pipelines based on the in-formation available from more recent earth-quakes, and consequent seismic risk analysisof pipeline network systems.

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Datta - 1999 - Seismic Response of Buried Pipelines a State-Of-The-Art Review