A SIMPLIFIED ESTIMATION METHOD OF ELASTO-PLASTIC DEFORMATIONS OF BURIED PIPELINES CAUSED BY LATERAL SPREADING DUE TO LIQUEFACTION

Transcription

1 SIMPIFIE ESTIMTION METHO OF ESTO-PSTI EFORMTIONS OF URIE PIPEINES USE Y TER SPREING UE TO IQUEFTION S TK 1, T SUZUKI, T KOIKE 3, J UENO 4, Y OGW 5, N HOSOKW 6, T KITNO 7 nd T KUWJIM 8 SUMMRY Practical method to estimate the structural strains of buried ielines under lateral sreading in the liquefied ground is roosed. Two different atterns of ground deformations at sloe and revetment are selected as the tyical lateral sreading modes. The shell/beam hybrid model is used to analyse the inelastic behaviour of buried ies, using the FEM code of QUS. For the ractical formulation conforming to those FEM results, the lastic limit analysis method is adoted to deal with the lastic behaviours of ieline systems. Finally, a simlified design formula is deduced to evaluate the deflection angle of the bend corner in the ieline system, from which the structural strain can be estimated with the relationshi between the maximum structural strain and deflection angle of the bend. INTROUTION iquefaction hazard is observed along the revetment of the reclamation area or alluvial grounds with a slight sloe near riversides. ateral sreading in the liquefied ground often causes several meters of large ground dislacements, so that the ieline crossing these areas may be deformed inelastically or might be buckled or torn out. There are many theoretical and numerical techniques to evaluate the inelastic behaviours of the ieline and its bending ortions, while there are not any simlified design formula to rovide the non-linear structural strain or its equivalent value such as a deflected angle. The roosed method 1) is based on the lastic limit analysis 5), while the alicability of the modelling and its analytical technique is assessed for the simlified design formula with FEM analysis 3) which was also verified with the full-scale test results of bend ies. The simlified design formula develoed herein can rovide the deflection angle of bend ie which is effective as a ractical measure to estimate the large inelastic structural behaviours of the buried ielines and their geometrical elements. Numerical study is devoted to assessing the alicability of the roosed method.. IQUEFTION HZR.1 Tyical Patterns of Ground Movement by ateral Sreading Many ielines might be installed in a reclamation area or along the shoreline, while major trunk lines basically cannot escae the river crossing or geotechnically hazardous grounds. In the liquefaction hazard area, a certain Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe, Jaan, takada@kobe-u.ac.j Toyo University, Kujirai Nakanodai, Kawagoe ity, Saitama, Jaan, suzuki@eng.toyo.ac.j Kawasaki Steel o.,351 Naganuma-cho,Inage-ku, hiba, Jaan, koike@kawasaki-steel.co.j Konoikegumi o., Kita Kyuhoji-cho, huou-ku, Osaka, Jaan, ueno_ji@konoike.co.j Osaka Gas o., 4-1- Hirano-cho, huou-ku, Osaka, Jaan, yasuo-ogawa@osakagas.co.j Tokyo Gas o., Shibaura, Minato-ku, Tokyo, Jaan, naoyuki@tokyo-gas.co.j Toho Gas o., Sakurada-cho, tsuta-ku, Nagoya, Jaan, kitano@tohogas.co.j Sumitomo Metal Industries o., Kitahama, huou-ku, Osaka, Jaan, kuwaijma-tks@aw.sumikin.co.j

2 stretch of the ieline is often installed in the sloe area, in which a straight ie or bend corner may exerience a large ground movement caused by lateral sreading of the liquefied ground as shown in Fig.1. One may also have a ieline to be arallely installed along the revetment, where the liquefaction-induced ground movement causes large bending deflection of bend ie esecially in the corner ortion.. Sloe irection of ground movement Pieline Pieline end ie Revetment (1)Straight ie ()end in the sloe ortion (3)end at the revetment Fig.1 Tyical atterns of ground movement under lateral sreading resulting from liquefaction hazard. The 1995 Hyogoken-Nanbu Earthquake and other recent events rovide many information on the ground dislacement for various geotechnical conditions. Since there are many varieties in the size of the liquefied ground, certain values are selected as an aroximate estimation of the tyical size of the liquefied ground in this study; m, m and m. One may also adot two ground movement modes, sloe tye and revetment tye, as the tyical lateral sreading resulting from the liquefaction hazard. lthough it is difficult to estimate the ground dislacement of both tyes, there are roosed some simle formulae as shown in the following way. (1)The ground dislacement in the sloe area Hamada and Wakamatsu ) roose the aroximate formula to redict the maximum ground dislacement in the sloe area which is liquefied during the earthquake in the following way. δ max = H θ N where δ max : the maximum ground dislacement (m); : arameter to redict the ground dislacement, a value of 15 to be recommended; H : the thickness of the ground (m) which is in the liquefaction; θ : the angle of the sloe (%) which is estimated at the surface of the ground; and N : the modified SPT value which is given by N = 1.7 N σ v ' +.7 (1) and N and σ v are the actual SPT value of the site and the effective vertical soil stress of the ground, resectively. ()The ground dislacement in the revetment ased on the observation and emirical results of the 1995 Hyogoken-Nanbu Earthquake, the aroximate formula to redict the maximum ground dislacement at the revetment is roosed by Iai 4) δ max = α H () eam model where Η and α are the height of the revetment (m) and a arameter which is recommended by Iai 4) for each tye of the revetment.. FEM nalysis of end Pies for Various Ground islacement Patterns eam model Shell model..1fem nalysis comared with exerimental results When a large ground dislacement is alied to buried ielines, inelastic behaviours of ie material and soil-ie interaction must be taken into Fig. Shell-beam hybrid model of ie segment with a bend

3 consideration. FEM analysis technique is used to estimate these inelastic structural behaviour. FEM code of QUS is adoted herein, where a shell/beam hybrid model as shown in Fig. is introduced. The alicability of this modeling is assessed with the exerimental result of the full-scale tests of bend ies, with which inward and outward bending tests 3) given in Table 1 are conducted. The bend ortion and its some stretch of straight ie ortion are modeled with 4 nodes shell elements and others are formed with beam elements, while the stress and strain curve of ie material is also modeled with the data of Table 1. Fig.3 shows the relationshi between the bending angle and axial and hoo strains of the non-buried bend ie, in which the bending angle of bend ie is defined as the tangential angle at the connected ortion of bend and straight ie. oth results of FEM analysis and exeriments show good coincidence u to 8 degree for outward bending and 4 degree and the more for inward bending. This difference between the outward and inward bending suggests that the flexibility of bend ie is more remarkable in the inward bending than in the outward bending. If the bending angle of bend ie is estimated, one may obtain the maximum strain from the bending angle through the relationshi between the bending angle and maximum strain of Fig.3. Maximum axial strain (%) 15 5 FEM Exeriment Maximum hoo strain (%) 15 5 FEM Exeriment ending angle (degree) ending angle (degree) (1) Outward bending () Inward bending Fig.3 Numerical results of the maximum strain and bending angle comaring with the exeriments. Table 1 Numerical conditions (1) Table Numerical conditions () (1)FEM code ()FEM element (3)Pie dimensions ITEM (4)Internal ressure (5)Material characteristics iameter Thickness urvature end angle Yield stress Hardening coeff. ESRIPTION QUS Ver nodes shell element 6 mm 15.1 mm 3 x iameter 9 degree 9.1 MPa 54 N/mm 1 N/mm ITEM Parameter γ for moment of bend ie ength of liquefaction area Maximum ground dislacement ESRIPTION 1.7 (inward) 1.57 (outward) m 7 m ritical soil reaction forces er unit length s cr.6 N/mm.. end ie deformations with lastic hinges under lateral sreading (1)Sloe tye Fig.5(1) shows the analytical conditions of bend ie installed in the liquefied ground of the sloe area. The maximum ground movement is δ max, and the ground strain is assumed to be constant over the liquefied area. s shown in Fig.5(1), these two ie configurations generate tyical ie deformations; inward bending(left-hand side) and outward bending(right-hand side). Fig.5() exresses the results of FEM analysis, which suggests the ossibility of lastic hinge formations at three oints near the bend. ased on this observation, lastic hinge models as shown in Fig.5(3) are introduced in this analysis. The oints 1 and 1 are located in the vicinity of bend, while the distance of 1 and 1 are derived in the following section. 3

4 E tensioncomression deformed original 1 Pin joint 1 Plastic hinge E tensioncomression (1)nalytical conditions ()FEM simulated results (3)Plastic hinge models Fig.5 Structural models for bend ie in the sloe area. ()Revetment tye Fig.6(1) shows the analytical conditions of bend ie installed in the liquefied ground along the shoreline. s shown in Fig.6(), these two ie configurations generate tyical ie deformations; inward bending(left-hand side) and outward bending (right-hand side). ased on this observation of FEM results of Fig.6(), lastic hinge models as shown in Fig.6(3) are also introduced in this analysis. deformed original original 1 Pin joint 1 Plastic hinge E deformed deformed E original (1)nalytical conditions ()FEM simulated results (3)Plastic hinge models Fig.6 Structural models for bend ie along the shoreline. 3. PRTI FORMUTIONS 3.1 Plastic imit nalysis General Formulation When a ieline asses through the liquefied area as shown in Fig.7(1), the most severe relative dislacement occurs at the liquefied and non-liquefied boundary area. Since the bend corner, on the other hand, installed at 4

5 the liquefied area as shown in Fig.7() behaves as a fixed oint, the large relative dislacement can also initiate from the bend ortion. For the simlified analytical formulation, one may introduce the following assumtions; (1)a ieline near the non-liquefied ground behaves as a beam loaded by soil reaction force, while the other ie ortion moves coincidently with a ground dislacement. ()the oint at which the ie moves coincidently with a ground dislacement is modeled as a fixed oint which is, however, movable erendicularly to the ie axis u to the ground dislacement. iquefied area iquefied area Non-liquefied area Soil reaction Non-liquefied area Soil reaction Ground movement δ Ground movement δ (1)Pie crossing boundary ()end ortion Fig.7 nalytical models of buried ielines assing through the liquefied ground. ƒð s ƒð y ƒã Fig.8 Stress-strain curve of steel ie. Steel ie shows the bi-linear stress-strain curve as shown in Fig.8. fter yielding, the ie can behave as a beam which can rotate with lastic moment M. The small ground movement roduces the elastically linear soil ressure to the ie, while, after the soil ressure exceeds the critical value of s cr as shown in Fig.9, the soil ressure is limitted to be equal to the assive soil ressure. The soil ressure er unit length is given with a ie diameter by = s cr (3) In general, the equation of motion of the buried ie can be exressed with a bending rigidity EI of the ie; s cr k ƒ u Fig.9 Soil reaction characteristics. x=-l x= x=l x (1)lying forces at the liquefaction boundary. ƒâ EI d 4 w dx 4 = x l (1)Pie crossing boundary model Fig.(1) shows the model of ie crossing boundary, in which the boundary condition is given in the following; (4) x ƒâ x =, w () = δ, d w () dx = ; x = l, w (l) = δ, dw (l) dx (5) When the end moment at the fixed oint reaches the lastic moment, the ie dislacement and its interval of both ends are, resectively, given by δ = 5 3 M EI, l = l = M )end ortion model The bend ortion model in Fig.() follows the equation (), in which two lastic hinges are generated accordingly to the rogressive ground dislacements. The ie dislacement and its interval of both ends when the first hinge occurs at x= are given by = x= x=l ()lying forces at the bend ortion. Fig. Structural models for ie beam analysi (6) 5

6 δ 1 = 3 8 x =, w () =, dw () = ; x = l, w (l) = δ, dw (l) with the boundary conditions of = (8) dx dx The ie dislacement and its interval of both ends at the second hinge aearing at x=l is exressed as δ = 3 M EI γ M EI, l 1 = 3, l = M γ M dw (l) with the boundary conditions of x = w () = M() = - M ; x = l w (l) = δ = () dx (7) (9) 3.1.Formulation for Straight Pieline Using the results of Section 3.1.1, the ie deflection angle under large ground dislacement is given for elastic and lastic conditions, resectively. Fig.11 shows two tyical models of straight ie crossing the liquefied area. The ie deflection angles for both cases are estimated at the liquefied and non-liquefied boundary oint in Fig.11. W ateral sreading iquefied area W ateral sreading iquefied area (1) Elastic range of δ < cr The ie deflection angle is given by P FSoil ressure P FSoil ressure θc = δ λ where cr = 5 3 M EI, () Plastic range of δ > cr The ie deflection angle is given by θ c = arctan δ λ = 4 K 4EI (11) (1) (13) δ Pie deflection Pie deflection (1)Triangular soil distribution. ()Rectangular soil distribution. Fig.11 Straight ie deflections under lateral sreading δ = W M with the intervals of for triangular soil distribution and = for rectangular soil distribution 3.1.3Formulation for end Pies The numerical results of FEM analysis in the section.. exress that the lastic deflection of bend ortion can be estimated with three-lastic-hinge models. Fig.1 is a general configuration of bend ie deflection with three lastic hinges when a large ground dislacement in the liquefied area makes δ and δ for ie segments and. Since the original angle of the bend is α and the angle of the deformed bend is θ y, the deflected angle of the bend ie is given as the difference of these angles. θ = θ y - α (14) in which the deflected angle θ y is derived from the following way. 6

7 ' ƒ 1 θ 1 y δ δ ' ' θ x ƒ À Fig.1 end ie deformation with three lastic hinges. The ground dislacements at the oints and are given with the directional angle β of the ground movement: δ = δ sin α + β, δ = δ sin α - β (15) The deflected angles, θ x and θ y, of the bend can be estimated based on the geometrical relationshi in the following way; tanθ x = δ - δ sinα 1sinα - δ + δ cosα ; sinθ y = '' 1 = 1 1 δ - δ sin α + 1 sinα - δ + δ cosα where '' = δ - δ sin α + 1sinα - δ + δ cos α and, 1 = γ M (17) (16) and the arameter γ is introduced to obtain the lastic moment of the bend ie from that of straight ie. In the revious section.. one may discuss about four different tyes of bend deflections which are the inward and outward deflections in the sloe and the revetment. These four deflected modes can be evaluated with inserting their corresonding β in Fig.1 as follows. β = ;the sloe model (inward bending mode) β = π - α ; the revetment model(inward bending mode) β =π ; the sloe model(outward bending mode) β = 3π ; the revetment mode(outward bending mode) - α 3. ase Study The numerical results of the roosed simlified calculation formula are comared with the shell /beam hybrid FEM analysis. The ie dimensions and geotechnical arameters to be used herein are shown in Tables 1 and. Fig.13 shows the deflected angle of bend ie for liquefied ground dislacements in the four different cases. The solid line is FEM results, while the line with symbol is the result of the roosed method. oth lines show good corresondence. When one may obtain the relationshi between the deflected angle and the ground dislacement, the maximum strain of the bend ie can be estimated from the diagram of Fig.3 which should be furnished as the database for the conversion from the deflected angle to the maximum strain of the bend ie. 7

8 eflected angle of bend (degree) FEM analysis Proosed method Sloe Model (Inward ending) Ground dislacement (m) eflected angle of bend (degree) FEM analysis Proosed method Revetment Model (Inward ending) Ground dislacement (m) eflected angle of bend (degree) FEM analysis Proosed method Sloe Model (Outward ending) Ground dislacement (m) eflected angle of bend (degree) FEM analysis Proosed method Revetment Model (Outward ending) Ground dislacement (m) Fig.13 ending angles of bend ortions under lateral sreading. 4. ONUSIONS The simlified design formula to estimate the deflection angle of the ieline having a bend ortion under the lateral sreading in the liquefied ground is develoed, in which the lastic limit analysis method is adoted. The result of the simlified formula shows the good coincidence with the FEM analysis. KNOWEGEMENT This study was conducted during fiscal 1996 to 1998 by Jaan Gas ssociation, as art of the Investigation for Gas Pieline Protection against iquefaction rogram (fiscal 1996 through ), commissioned by the Ministry of International Trade and Industry s (MITI) gency of Natural Resources and Energy. We would like to exress our gratitude to all related arties, including MITI staff, and each member of the Secial ommittee on Investigation for Gas Pieline Protection against iquefaction (headed by r. Tsuneo Katayama, general manager of the Science and Technology gency s National Research Institute for isaster Prevention), for their kind assistance in our study. REFERENES 1)Takada, S.,T.Suzuki, T.Koike, Y.Ogawa, K.Yoshizaki, T.Kitano and J.Miyauchi[1998]: Practical formula of elasto-lastic deformation of buried ielines caused by lateral sreading in the liquefied ground, th Jaan Earthquake Engineering Simosium, )Hamada, M. and K.Wakamatsu[1996]: iquefaction, ground deformation and their caused damage to structures, secial reort on the 1995 Hyogoken-Nanbu earthquake - investigation into damage to civil engineering structures -,JSE. 3)Takada,S., Y.Ogawa, K.Yoshizaki, T.Kitano and T.Kuwajima[1998]: large-scale deformation analysis technique for buried ies exosed to lateral dislacement due to liquefaction, 11th Euroean onference on Earthquake Engineering. 4)Iai,S., K.Ii, T.Morita and Y.Sato[1997]: The revetment dislacement of the liquefied ground observed from the earthquakes, nd Hanshin-waji Secial onference, )Neal,.G.[197]:Plastic Methods of Structural nalysis, HPMN & H T,