Numerical analysis of buried steel pipelines under earthquake excitations

Transcription

1 Numerical analyi of buried teel pipeline under earthquake excitation Miad Saberi, Amir Mahdi Halabian & Mahmood Vafaian Department of Civil Engineering Ifahan Univerity of Technology, Ifahan, Iran. ABSTRACT The performance of buried pipe i affected by eimic wave propagation and it incidence due to out-of phae induction motion. In thi tudy, three dimenional finite element model have been employed to evaluate the effect of bend angle and oil mechanical propertie on eimic repone of buried pipe in bent area. In thee model, beam and nonlinear pring element were ued to imulate pipe and oil-pipe interaction, repectively. Furthermore, a uitable boundary condition ha been ued to imulate far field effect more cloely. The travelling of eimic wave wa aumed to be parallel to a pipe leg, cauing time lag in vibration of different point of model. The influence of geometrical parameter uch a diameter-to-thickne ratio and embedment ratio on elbow train were alo conidered. Reult indicated that a direct relationhip exit between oil tiffne and axial train due to maller lippage. Diameter-to-thickne i a definitive ratio for axial train of bend while effect of the embedment ratio i mall. RÉSUMÉ Emiion de tremblant onde ont due d'impoer de movement d'hor de la phae qu'affecter ur le inhumé pipeline performance. Dan cette recherche, effet d'angle de courbe tube et le mécanique propriété du ol a été. ur la frémiment répone de inhumé tube utiliation d'éxecution modèle de limitée en troi dimenion étudiée performance. Dan la umentionné modèle pour la portraitite de tube et interaction du ol- pipe ont appliquée le trait élement et le reort element, en ordre. Aui pour la précie modéliation d'effet de loin terme et utilizé aux équivalente limite condition. Emiion d,onde et uppoé parallèlement à l'une de courbe branche en ce qu, et créée latence de la phae dan la vibration de différente partie de modèle.l'impact de géométrique parameter comme le diameter au groeur de tube et l'inhumé profondeur ur le courbette de tuyau region ont examine d'autre ca dan cette etude. L'Analye de réultat indique qu'en raion de plu ba glier dan le ol qu'a une plu dureté, la répone de tube ont plu dan ce ol. Aui plu effet de diameter au groeur de tube comparé avec l'inhumé profondeur ur le courbette valeur, autre réultat que ont conidéré. 1 INTRODUCTION Pipeline are ued in different area like natural ga tranportation, ewage ytem, water upply, petroleum tranport and indutrial ector. With the improvement of economy and urbanization, the damage of pipeline ytem everely affected life and manufacture; hence more extenive attention i required with regard to pipeline ytem. Permanent ground movement and tranient ground deformation are major eimic hazard which affect the behaviour of buried pipe. Tranient ground deformation are generated through the wave propagation in oil. The effect of thi phenomenon on the repone of buried pipe (epecially in bent area due to tre concentration and larger train) wa tudied in thi paper. Over the lat three decade variou invetigator have tudied the eimic performance of pipeline and have propoed everal analytical and numerical method to quantify the pipe repone under wave propagation. The oldet and implet analytical method wa baed on the aumption that the maximum axial train of buried traight pipeline wa equal to the maximum train of the urrounding oil (Newmark 1967). In relation to Newmark aumption, another cloed form olution wa developed, indicating that effect of inertia force on dynamic repone of traight pipe are negligible (Takahahi and Sakurai 1969). The tudy on traight buried pipe wa advanced (Shinozuka and Koike 1979; O'Rourke and El Hamdi 1988) in order to imulate the interaction of oil and pipe more accurately where oil i modeled a linear elatic or elato-platic pring. The behavior of buried pipe with elbow ha alo attracted attention by everal reearcher. According to Shah and Chu (1979), Shinozuka and Koike (1979) and Goodling (1983) variou cloed form olution for evaluation of pipe repone in their bent area were developed uing beam on elatic foundation theory. Alo, referring to Kouretzi et al. (26) another analytical formulation to invetigate the buried pipeline under incident hear wave ha been developed. In parallel, numerical method have been alo employed to analyze the traight buried pipeline and different reult were extracted (Takada and Tanabe 1987; Takada and Katagiri 1995; Halabian et al. 28; Vazoura et al. 21). Evaluation of train in bent region (Ogawa and Koike 21) and a quai tatic reearch on embedded pipe with right angle elbow (O'Rourke and Mclaughlin 23, 29) are intance of numerical invetigation on buried bent pipeline. According to the literature, mot of

2 reearch ha been focued on peudo-tatic analye and le attention ha been paid to numerical time hitory tudie on behavior of buried elbow pipe. In the preent reearch, the effect of bend angle, burial depth, and diameter to thickne ratio (D/t) on the pipe deformation and induced train were examined for aumed pipe model buried in different oil. loading can be imulated by nonlinear pring employed in thi paper. Since nonlinear pring act only in compreion, therefore, to take the oil-pipe interaction into account properly, the pring were impoed to the model in both ide of the pipeline (Figure 2). Table 2. Material propertie of andy oil. 2 3D FEM NUMERICAL MODELING In order to get inight into the non-linear behavior of buried pipeline in the elbow area and to examine the affecting parameter uch a the pipe dimenion and elbow geometry, ome three dimenional (3D) finite element model (FEM) were developed. In thee 3D FE model, the pipe wa modeled uing beam element, while Winkler theory wa adopted to take oil-pipe interaction into account. The burial depth (H) and elbow radiu were aumed 1.5m from the ground urface to the pipeline center and 3d, repectively; in which d i the pipe diameter. The mechanical propertie for the pipe taken from API-5L (American Petroleum Intitute 2) are ummarized in Table 1. Unit weight (KN/m3) Internal friction angle φ (degree) Friction angle between pipe and oil (degree) Average hear wave velocity V S(m/) Looe and Soil type Medium and Dene and Table 1. Mechanical propertie of pipe. Table 3. Material propertie of clayey oil. Pipe type Diameter (mm) Thickne (mm) Ma denity (Kg/m 3 ) Soft clay Soil type Medium clay Stiff clay Steel- API-X Unit weight (KN/m3) Elaticity modulu E(GPa) Poion ratio (υ) Yield Stre σ y (MPa) Ultimate Stre σ u (MPa) Shear trength S u (Kpa) N Average hear wave velocity V S(m/) In thi tudy, andy and clayey oil with different trength propertie were aumed a burial domain for pipe elbow. Table 2 and 3, how the characteritic of andy and clayey oil ued in FE modeling. It can be expected that oil-pipe interaction have a fundamental influence on pipe repone againt incident wave. Adopting Winkler theory, the urrounding oil ha been imulated by a number of nonlinear pring element around the pipe in three perpendicular direction. ALA (American Lifeline Alliance 21, 25) tandard wa employed to expre the load diplacement relation for nonlinear pring. The axial, tranvere horizontal and tranvere vertical oil bilinear force-diplacement relationhip (t-x, p-y, and q-z curve) are hown in Figure 1, in which t u, p u and q u are the maximum oil force in oil-pipe interface and x u, y u and z u are the correponding diplacement. The oil-pipe lip a well a oil hardening in cyclic Figure1. The force-diplacement behaviour of oil pring. 2.1 Modeling of Far Field and Input Ground Motion To reach an accurate imulation, the length of each elbow leg hould be taken to be infinite. However, due to computational problem, the modeling of the pipeline

3 Figure 2. Schematic arrangement of the oil pring around the pipe and boundary condition. with thi aumption could be time conuming and therefore a different aumption for the far field hould be conidered. Accordingly, the part of the pipe, which i located on both ide of the elbow, aumed to have only axial elongation and can be modeled uing beam element upported by pring element repreenting the pipe-oil interaction. The far end of thee part of the pipeline are aumed to have fixed boundary, a in thi region the pipe experience very mall axial train. To avoid the error analyi caued by the forced boundary (intead of uing fixed boundary at the end of the beam egment of the pipeline) the equivalent boundary condition propoed by Takada et al. (24) wa adopted in thi tudy. They aumed that the lateral deformation of pipe far from the elbow part do not affect the elbow part and only the longitudinal friction exited. The friction force along the traight part of the pipe temming from axial force can be divided into two part: (a) The tatic friction, (b) the lip friction. The tatic and liding oil friction are expreed by Eq. 1 and 2, repectively: f = Ku [1 ] Where, f i the tatic oil friction per unit length, u i the relative diplacement between the oil and the pipe, and K i the tiffne of oil pring along axial direction. f =.75πDHγ µ = Ku [2 ] In Eq. 2, f i the liding oil friction per unit length, D i the pipe diameter, H i burial depth, γ i the weight denity of urrounding oil, µ i the frictional coefficient, and u i yield relative diplacement between the oil and the pipe. The total axial deformation of the buried pipe ( L) under axial force F i equivalent to a nonlinear elongated pring force. The relationhip between axial force F and longitudinal extenion L i indicated by Eq. 3: F( L) = 3EAf 2 U L 1 2EAf ( L U ) 4 L U U 2 σ ya U L + 2Ef 4 Where E i the oil modulu of elaticity, A i the pipe cro ection area, and σ y i the yield tre of the pipe material. 3D elbow pipeline model introduced in thi tudy were ubjected to different earthquake excitation to examine the effect of wave propagation on their behavior. The ground motion characteritic including the frequency content, the oil hear wave velocity, and the Peak Ground Acceleration were given in Table 4. In thi tudy, to highlight the everity of the ground motion, the pipe aumed to be buried in oil with hear wave velocitie, which correpond to the elected ground motion ite. The record were alo choen in a way uch that the frequency content of each individual record matche the pipeline-oil ytem frequencie. A material damping ratio equal to 4% of critical damping ha alo been conidered. It include Rayleigh type damping with α and β coefficient for ma and tiffne proportional damping, repectively. Modal analyi wa performed to dicover the mode with important contribution. Therefore, the aforeaid coefficient have been computed through the reult obtained from the analyi. Table 4. Characteritic of input ground motion. Earthquake Station Shear wave velocity, V (m/) [3 ] Peak Ground Acceleration (g) Chichi CHY41 V< Chichi CHY28 18 <V< Chichi CHY8 36 <V<

4 Northridge Montebello-Bluff Rd V< Northridge LA-Centinela St 18 <V< Northridge Santa Monica City Hall 36 <V< NUMERICAL RESULTS OF PARAMETRIC STUDY There i no conenu on the minimum required modeled length of pipe leg _in far ditance with the elbow_ to analyzing the bend. Thu, in order to evaluate the influence of the boundary condition on the pipeline repone, a number of model with variou length with far field boundary condition have been analyzed. The length of traight part of the pipeline wa evaluated uing ome preliminary analye and the reult howed if the end boundary condition i aumed to be fixed, 8D i a ufficient length for accurate evaluation of the elbow repone. The preliminary analye alo tated the 4D i the cae when the axial pring i ued a the end boundary condition. In thi tudy to optimize the cot of computation, the length of 4D for the traight part of the model along with equivalent boundary wa employed. In the current paper, a number of numerical model of buried elbow pipe with different geometrie were developed to ae the magnitude of train induced in the elbow region a well a the pipe-oil lippage. The effect of geometrical propertie uch a bend angel, the diameter to thickne ratio (D/t) and the embedment ratio (H/D) were invetigated throughout a comprehenive tudy. The travelling of eimic wave wa aumed to be parallel to one of the pipe leg (Figure 2). Thi aumption caue time lag in vibration of different point of the model. It i noteworthy that all the parameter variation, determined in the following ection, were evaluated uing the mentioned characteritic of the pipe model in Section 2.1 a the bae model. The axial train value were normalized by the yield trength (ε y) of the pipe material which i aumed to be Effect of Bend Angle In thi ection the effect of elbow angle on elbow axial train, which have different oil type, were invetigated. The reult were preented in Figure 3. The variation of elbow angle were aumed to be 9 to 18 in the preent tudy. A it can be een from Figure 3, the value of axial train induced in the elbow area tend to Figure 3. Effect of elbow angle on maximum axial train in bend for variou urrounding oil (H=1.5m, D=.4m, t=.95m); (a) Chichi earthquake, (b) Northridge earthquake. Figure 4. Effect of D/t ratio on maximum axial train at elbow of buried pipe in different oil (H=1.5m); a) and, Chichi earthquake, b) clay, Chichi earthquake, c) and, Northridge earthquake, d) clay, Northridge earthquake. (to be continued)

5 c) d) Figure 4. (Continue) be increaing bend angle around 135 in mot of cae tudied here. Furthermore, the train repone of buried teel pipe increaed in tiffer oil in which the yielding occurred. 3.2 Effect of Apect Ratio on Pipe Strain The effect of diameter-to-thickne ratio (D/t) on elbow train wa alo examined. A 9 elbow wa elected to be tudied in thi ection. In andy oil, an increae of D/t ratio lead to a growth in induced axial train in the pipe bend. Coheion propertie ignificantly affect the behavior of embedded piping ytem in coheive oil. The dicuion above are upported by Figure 4. A it can be een the maximum induced train in the elbow i inverely proportional to the D/t ratio for tiff clay and directly proportional for oft clay. 3.3 Effect of Embedment Ratio In order to examine the effect of embedment ratio (buried depth (H) to pipe diameter (D)), on maximum axial train in the elbow, a oil-pipe ytem with 9 bend wa elected. Other characteritic of the pipeline ytem are according to Table 1. A indicated in Figure 5, the H/D ratio ha a light influence on the maximum c) d) Figure 5. Effect of embedment ratio on maximum axial train at elbow of buried pipe in different oil (D=.4m, t=.95m); a) and, Chichi earthquake, b) clay, Chichi earthquake, c) and, Northridge earthquake, d) clay, Northridge earthquake.

6 train repone compared to the other mentioned parameter in the previou ection. However, further invetigation into the reult illutrated that there i a direct dependency between train repone in the bend and embedment ratio for buried pipeline in noncoheive oil. The coheion propertie affect the behavior of the buried pipe in coheive oil a it wa tated earlier. For coheive oil, again, a changing trend imilar to the D/t effect on the elbow train i oberved. In other word, raie in the embedment ratio reult in a decreae in the elbow train for buried pipe in tiff clay, while the reult in oft clay are different. 3.4 Pipe-Soil Slippage Figure 6, how the maximum axial relative diplacement of the pipeline ytem with variou bend angle ubjected to different earthquake ground motion. The effect of oil type on lippage of the pipe in oil wa alo conidered. A oberved from Figure 6, the bend angle correponding to maximum axial train (Section 3.1) generally lead to minimum lippage between pipe and oil. Furthermore, particular emphai i placed on the pipe lippage in ofter oil. A it wa hown in the reult, the oil with low tiffne experience more lip compared to tiffer oil. In tiff oil, the diplacement of pipe and ground are roughly equal, o the minimum lippage value are obtained in high tiffne oil. Accordingly in mot cae, the maximum axial train at elbow area occurred in tiff oil, a illutrated in previou ection. In addition, the value of lip in andy oil are larger than clayey oil becaue the relative diplacement between oil and pipe i nearly prevented by coheion propertie. 4 CONCLUSIONS A parametric evaluation of buried pipeline with elbow ubjected to earthquake excitation wa performed by the time hitory analyi. The effect of oil propertie, bend angle, pipe diameter to thickne ratio, and embedment ratio on repone characteritic (e.g. the maximum axial train in bend and pipe-oil relative diplacement) were analyzed. Following can be dicued a concluion: Increaing the urrounding oil tiffne raie the train repone of pipe in bent region becaue of approximately imilar deformation of oil and pipe. The majority of maximum axial train value occurred in vicinity of 135 elbow angle. The elbow train repone of buried pipe are more enitive to combination of D/t ratio and oil type. Increaing the embedment ratio up to practical limit would have no ignificant effect on the reult. The bend angle correponding to maximum axial train generally lead to minimum lippage between c) d) Figure 6. Effect of oil type and different elbow angle on maximum relative diplacement between oil and pipe under earthquake loading (H=1.5m, D=.4m, t=.95m); a) and, Chichi earthquake, b) clay, Chichi earthquake, c) and, Northridge earthquake, d) clay, Northridge earthquake.

7 pipe and oil. In addition, decreaing the urrounding oil tiffne raie the value of lippage between the oil and the pipe. The value of axial train in buried pipe under wave propagation exceed the yield limit in ome cae but do not reach the ultimate trength. 5 REFRENCES American Lifeline Alliance (ALA). 21 (with addenda through 25). Guideline for The Deign of Buried Steel Pipe, American Society of Civil Engineering (ASCE). American Lifeline Alliance (ALA). 21 (with addenda through 25). Seimic Guideline for Water Pipeline, American Society of Civil Engineering (ASCE). American Petroleum Intitute (API). 2. Specification for Line Pipe, API Specification 5L, Forty-Second Edition, American Petroleum Intitute. Bowle, J.E Foundation Analyi and Deign, The McGraw-Hill Companie. Committee on Ga and Liquid Fuel Lifeline American Society of Civil Engineer. Guideline for The Seimic Deign of Oil and Ga Pipeline Sytem, Technical Council on Lifeline Earthquake Engineering, ASCE, New York. Goodling, E.C Buried Piping An Analyi Procedure Update, Proceeding International Sympoium on Lifeline Earthquake Engineering, Portland, Oregon, ASME, PVP-77, pp Halabian, A.M. Hokmabadi, T. Hahemolhoeini, S.H. 28. Numerical Study on Soil-HDPE Pipeline Interaction Subjected to Permanent Ground Deformation, The 14 th World Conference on Earthquake Engineering, Beijing, China. Liu, A.I. Hu, Y.X. Zhao, F.X. Li, X.J. Takada, S. Zhao, L. 24. An Equivalent-Boundary Method for The Shell Analyi of Buried Pipeline Under Fault Movement, ACTA SEISMOLOGICA SINICA, Vol. 17, pp Mclaughlin, P.M. O`Rourke, M. 23. Seimic Repone and Behavior of Buried Continuou Piping Sytem Containing Elbow, Doctoral Thei, Renelaer Polytechnic Intitute. Mclaughlin, P. M. O`Rourke, M. 29. Strain in Pipe Elbow Due To Wave Propagation Hazard, Lifeline Earthquake Engineering in a Multi hazard Environment, ASCE, pp Newmark, N.M Problem in Wave Propagation in Soil and Rock, Proceeding International Sympoium on Wave Propagation and Dynamic Propertie of Earth Material, Univerity of New Mexico, Albuquerque, pp O`Rourke, M.J. Liu, X Repone of Buried Pipeline Subject to Earthquake Effect, Multidiciplinary Center for Earthquake Engineering Reearch (MCEER), Monograph No. 3. Pacific Earthquake Engineering Reearch Center (PEER). Sakurai, A. Takahahi, T Dynamic Stre of Underground Pipeline During Earthquake, Proceeding of the Fourth World Conference on Earthquake Engineering, Chilean Aociation on Seimology and Earthquake Engineering, Santiago, Chile, pp Shah, H. Chu, S Seimic Analyi of Underground Structural Element, Journal of the Power Diviion, ASCE, July, Vol. 1, No. PO1, pp Shinozuka, M. Koike, T Etimation of Structural Strain in Underground Lifeline Pipe, Lifeline Earthquake Engineering-Buried Pipeline, Seimic Rik, and Intrumentation, PVP-34, ASME, pp Vazoura, P. Karamano, S.A. Dakoula, P. 21. Finite element analyi of buried teel pipeline under trike-lip fault diplacement. Soil Dynamic and Earthquake Engineering, Vol. 3, pp