A SHELL MODEL WITH AN EQUIVALENT BOUNDARY FOR BURIED PIPELINES UNDER THE FAULT MOVEMENT

Transcription

1 13 th World onference on Earthquake Engineering Vancouver,.., anada ugut 1-6, 2004 Paper No. 613 SHE MODE WITH N EQUIVENT OUNDRY FOR URIED PIPEINES UNDER THE FUT MOVEMENT i-wen IU 1, Shiro TKD 2 and Yu-Xian HU 3 SUMMRY new hell model with an equivalent boundary i preented for etimating the repone of a buried pipeline under large fault movement. The length of affected pipeline under the fault movement i uually too long for a hell-mode calculation becaue of the limitation of memory and time of computer. In thi tudy, only the pipeline egment near fault i modeled with platic hell element in order to conider the effect of local buckling and large ection deformation. The material property of the pipeline egment far away from the fault i conidered a elatic and nonlinear pring element at the equivalent boundarie are obtained and applied at the end of the hell model. t lat, the failure performance of two water teel pipeline with large diameter at fault croing in Kocaeli Earthquake and Ji-Ji Earthquake are tudied with the propoed hell model conidering the different local oil condition on two ide of the fault. INTRODUTION Several implified deign method have been propoed to obtain the maximum tre or train in pipeline croing an earthquake active fault. literature review i hown in Fig.1. Uually, the pipe i modeled a a cable (Newmark-Hall[1], Kennedy[2]) or a beam(wang[3],iu-hu[4]) in thee method. The beam model conidered the bending tiffne of the pipe which wa neglected in the cable model. fter a number of evere earthquake in thee year, for example, the 1995 Kobe Earthquake in Japan, the 1999 Ji-Ji Earthquake in Taiwan and the 1999 Kocaeli Earthquake in Turkey, it ha been noticed that the huge deformation in the pipe ection alway create the very large amount of train in pipeline, and then caue cracking or fracture in the pipe body. Since it i difficult for the cable or beam model to analyze the large deformation in the pipe croing ection, the hell FEM model ha been propoed in the analyi of a pipeline croing the fault. The theoretical method how that the length of affected pipeline under the fault movement i uually larger than 200m, it i too long for a hell-fem-model calculation becaue of the limitation of memory and time of computer. To reduce the calculation time, only the pipe egment (about 30*D) near the fault wa modeled with hell element in the beginning, the fixed boundary wa adopted at two end of the pipe. ut thi way would bring the error to the analyi reult becaue of the forced boundary. ater, a beam-hell hybrid FEM wa propoed to avoid adding thi manmade boundary. In thi tudy, the pipe 1 itant Reearcher, Intitute of Geophyic, E, eijing, hina. liuaiwen@hotmail.com 2 Profeor, Kobe Univerity, Kobe, Japan. Takada@kobe-u.ac.jp 3 Profeor, Intitute of Geophyic, E, eijing, hina. huyuxian@public.bta.net.cn

2 egment near the fault i alo modeled with platic hell element in order to conider the effect of local buckling and large ection deformation. For the pipeline egment far away from the fault, the material property of the pipe i conidered a elatic and nonlinear pring element at the equivalent boundarie are obtained and can be eaily applied to the end of hell FEM model. Since only the pipe egment near fault i modeled with platic hell element, the needed memory and calculation time for thi hell FEM model with equivalent boundary are reduced. (a)able Model 1 (Newmark-Hall, 1975) : f line (b)able Model 2 (Kennedy 1977) : f Pp line rc line (c)eam Model (Wang, 1998, iu-hu, 2000): f Pp eam on an elatic foundation antilever eam Fig.1 iterature review of the theoretical method In 1999, there were two catatrophic earthquake, Ji-Ji Earthquake in Taiwan and Kocaeli Earthquake in Turkey. In both of thee two earthquake, the damage of water teel pipeline with large-diameter are reported (Table.1 ). onidering that the large-diameter pipeline uually take a very important role in the water upply pipeline network, the failure performance of thee two pipe are tudied with the hell FEM propoed by thi paper.

3 (a) Shell-eam Hybrid FEM Model Soil Spring Element (K1) Soil Spring Element (K2) eam Element (200m) Shell Element (30*D) eam Element (200m) (b) Shell FEM Model with Equivalent oundary(thi Study) K1 K2 Equivalent oundary(ke) Shell Element (30*D) Equivalent oundary(ke) Fig. 2 Shell FEM model for an pipe croing the fault Table 1 Damage cae of two water upply pipe with large-diameter ae Earthquake Type diplacement Pipe Soil condition on the two ide of fault 1 Kocaeli Earthquake Nearly trike-lip Φ=2.2m t=18mm 2 Ji-Ji Earthquake Revere lip ateral offet: 1.70m xial horten: 2.47m Vertical: 0.0m ateral offet: 6.87 m xial horten: 1.51m Vertical lifted: 3m Φ=2.0 m t=20mm EQUIVENT OUNDRY FOR THE SHE FEM MODE Soil on one ide of the fault i much ofter than that on the other ide. Same oil condition on both ide. aed on the ettlement experiment of buried pipeline, the relative diplacement of oil and pipe in lateral direction become very mall when the pipe i far enough to the fault line, and there i only the oil friction along the axial direction. The pipe keep in a traight line and move along with the local oil.

4 Friction(N/m) f K u0 Elongation(m) N(x) f (x) O N 1 f F X 1 Static Soil Friction Fig. 3 Equivalent boundary for a buried pipeline hown in Fig.3, when the buried pipe egment i far enough to the fault line, the axial train of point and (ε and ε ) caued by F in the axial direction would be: ε = 0, ε = F / E (1) Where i the area of pipe ection and E i the elatic tiffne of the pipe material. It i noticed that the length of thi pipeline egment i not fixed and dependent on the value of F. The pipe egment can be divided into two part: O and O. For the pipe egment O, there i no lide happened between the oil and the pipe, the tatic oil friction f(x) along O i aumed increaing with the ditance to Point (x): f ( x) = f x 0 x 1 (2) 1 2 Sliding Soil Friction f = 0.75π DZγµ = Ku0 (3) where, f: the oil friction per unite length along pipeline, D: the diameter of pipe, Z: the buried depth, γ: the denity of urrounding oil; µ: the frictional coefficient, u 0 : the yield diplacement for the pipe to tart to lide in the oil, K: the tiffne of axial oil pring. The relationhip between the axial force (N(x)) and the elongation ( (x)) of the pipe for any point at the pipe egment O could be obtained by: 1/ 6 2 / 3 N( x) = 3Ef / 2u0 ( x) (4) t Point O, Equation (4) become: 1/ 6 2 / 3 N1 = 3Ef / 2u0 u0 = 3Ef u0 / 2 (5) t the point O, the pipe begin to lide in the urrounding oil, the liding oil friction (f ) doe not change along the pipe egment O. The length of O ( 2 ) can be calculated by: 2 = ( F N1 ) f (6) Then, the relationhip between the axial force (N 2 ) and the elongation ( ) of point could be obtained by the following equation: 2 1 N( x) F 3 = + = + dx ε 0 xdx u u (7) E 1 Ef Noticed that the material property of the pipe egment hould be elatic, the elongation ( ) i conditioned by: 2 σ u0 (8) 2Ef 4 where σ 1 i the yield tre of the pipe material.

5 ombing Equation (4) and (7), the relationhip of the force (F) and the elongation ( ) could be expreed a: 3Ef 1/ 6 2 / 3 u0 0 u0 2 F( ) = 2 (9) 1 σ f E u0 u0 < + u0 4 2Ef 4 When the fault diplacement i large enough, u 0 /4 <<, Equation (9) can be implified a: F( ) = (2 f E) (10) Equation (10) can alo be obtained when the tatic oil friction i ignored and only the liding oil friction i conidered. In fact, thi aumption i alo taken in Kennedy method. Equation (10) i eay to be thought a an expreion for the force-diplacement curve of a nonlinear pring, it can be the equivalent boundary of the hell FEM model for a buried pipeline under the fault movement. PERFORMNE OF THMES WTER PIPEINE IN KOEI ERTHQUKE Kocaeli Earthquake (Mw 7.4) occurred on the North natolian fault in the northwetern Turkey on ugut 17, The Thame Water 2200 mm diameter butt-welded teel pipeline i a raw water pipeline from Yuvacik Dam to Kullar water treatment plant, covering a ditance of 5.5 km. The water pipeline croe the Sapanca Segment of the North natolian fault and wa damaged at the fault croing (Eidinger[5]). Within a few day after the earthquake, thi Φ2.2m pipe wa expoed in the area of the fault to allow a better undertanding of the nature and extent of damage to the pipe. manhole wa cut into the pipeline at the excavation to allow for acce and emptying of the pipeline. Damage wa oberved at three location: Point, Point and Point. hown in Fig.4, a mall urface leak wa oberved in the pipe at point near the fault croing; a ignificant leak occurred at point and the minor leak happened at the bend of pipe (point ). It hould be noticed that the location of three main wrinkle are not ymmetrically paced around the fault. The wrinkle at point i very near the fault offet and other at point and on the other ide are more ditant from the fault offet. Thi trongly ugget that the oil on the ide with wrinkle and i much ofter than the oil on the other ide with wrinkle. To account for the aymmetric pattern of oil propertie along the length of the pipeline, 50% of the tranvere oil pring on the rigid oil ide i adopted for that on the oft oil ide. It i clear that the amount of fault offet impoed on the pipeline wa large enough to initiate the wrinkle of the pipeline. The location of two cloet oberved wrinkle (Point and Point ) are what would be expected due to high bending moment in the pipeline. The quetion i why the third wrinkle occurred. aed on Eidinger report, thi damage cae i numerical imulated uing the hell FEM model with the equivalent boundary. onidering the effect of pipe-water interaction, the thickne of the pipe adopted in the analytical model i 0.028m. The reult i hown in Fig.5. hown in Fig.5, the repone of the whole pipeline i agreed with the real damage performance of Thame water pipeline. It i very clear that three buckling point occurring in the pipeline. uckling point i very near the fault croing on the rigid oil ide. The other (Point and ) are located on the oft oil ide. The compreion train of Point i the larget of three buckling point, agreeing with the ignificant leak oberved at Point. lthough the compreion train of Point i the mallet, about 4.3%, it i alo larger than the theoretical train (0.0098) to reach the onet of wrinkle, thi i why the minor leak at Point wa oberved.

6 Fig.4 Performance of Thame Water Pipeline at the fault croing Soft Soil Side Rigid Soil Side Fig.5 Numerical Simulation for Thame Water Pipeline

7 Fig.6 how why and how the third buckling point occurred. uckling point and occur at the beginning of fault movement. They can be thought a two hinge in the pipeline. The pipe egment between thee two hinge behavior like a rigid beam. With the increae of fault diplacement, thi pipe egment would rotate around the hinge (Point and ) under the compreion loading. ecaue the different oil condition on two ide of the fault, the lateral diplacement of point on the oft oil ide become larger than the lateral fault movement, therefore the third buckling point occur. Soft Soil Side Soft Soil Side Rigid Soil Side Rigid Soil Side Fig.6 Repone of Thame water pipeline with the increae of fault movement PERFORMNE OF SHIGNG WTER PIPEINE IN JI-JI ERTHQUKE Ji-Ji Earthquake (Mw 7.6) truck Taiwan on Sep. 21, Shigang water pipe i near Shigang dam, which wa alo damaged in Ji-Ji earthquake. The revere-lip fault movement caued 3m vertical diplacement, 6.5m horizontal diplacement in North, and 2.7 m horizontal diplacement in Wet. aed on the pipeline network map, the lateral diplacement of Shigang pipeline i about 6.87 meter; the axial diplacement i about meter and the vertical uplifted diplacement i 3m. The pipeline with 2.0 m for the diameter and 0.02 m for the thickne wa buried about 3.4m. Different from the Thame Water pipeline, the oil condition on one ide of the fault i ame with the other. The reult of hell FEM analyi for thi damage cae i hown in Fig. 7. It i hown that two buckle are ymmetrically located on two ide of the fault and the maximum compreion train i about 14%.

8 (a) Photo of Damaged Pipe: (b) Deformed pipe ection: Fig. 7 Performance of the Shigang water pipeline ONUSIONS hell FEM model with an equivalent boundary i propoed to etimate the repone of a buried pipeline under large fault movement. With the equivalent boundary, only the pipeline egment near fault hould be modeled with platic hell element in order to conider the effect of local buckling and large ection deformation. The performance of Thame Water pipe in Kocaeli Earthquake i a typical damage cae for different oil condition on both ide of the fault. One of the main buckling point i very near the fault offet on the ide with more rigid oil. If the fault diplacement i large enough, the third buckling point may occur on the oft oil ide further from the fault. The performance of Shigang Water pipe in the 1999 Ji-Ji Earthquake i another type of damage cae with two main buckling point ymmetrically located on two ide of fault. REFERENES 1. Newmark N.M., Hall W.J. Pipeline deign to reit large fault diplacement. Proceeding of U. S. National onference on Earthquake Engineering, EERI, 1975, n rbor, Kennedy R.P.,et al. movement effect on buried oil pipeline. Tranportation Engineering J.1977; SE, 103: Wang.. R. et al. Parametric tudy of buried pipeline due to large fault movement. Proceeding of Third hina-japan-us Trilateral Sympoium on EE, Kunmin, hina, 1998: IU.W., HU Y.X. et al. Repone of buried pipeline in large fault movement. Proceeding of Sixth International onference of Seimic Zonation, EERI, Eidinger J. Performance of Thame Water 2.2 meter diameter teel pipe at north natolian fault croing. G&E Report , 2001.