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Buckling failure mode analysis of buried X80 steel gas pipeline under reverse fault displacement
Engineering Failure Analysis 77 (2017) 50–64
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Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal
Buckling failure mode analysis of buried X80 steel gas pipeline under reverse fault displacement Xiaoben Liu a,⁎, Hong Zhang a,b,⁎⁎, Kai Wu a, Mengying Xia a, Yanfei Chen a, Meng Li a a b
College of Mechanical and Transportation Engineering, China University of Petroleum, Beijing 102249, China China University of Petroleum (Beijing) Karamay Campus, Karamay 834000, China
a r t i c l e
i n f o
Article history: Received 2 March 2016 Received in revised form 22 June 2016 Accepted 27 February 2017 Available online 01 March 2017 Keywords: Buried X80 steel gas pipeline Reverse fault Buckling failure modes Finite element method Critical fault displacement
a b s t r a c t High strength steel pipeline is widely used in long distance transportation of natural gas. These pipelines are vulnerable under active faults in strong seismic areas. The buckling failure modes of high strength X80 gas pipeline crossing reverse fault were analyzed systematically in this paper. Based on the nonlinear finite element method, a pipe-elbow hybrid model was developed for buckling failure analysis of X80 steel pipeline under reverse fault displacement. The pipe soil interaction relationship was simulated by a series of elastic-plastic soil springs. The nonlinearity of pipe material and large deformation were also considered. The non-linear stabilization algorithm was selected due to the convergence of the numerical model. Engineering parameters used in the Second West to East Gas Pipeline in China were selected in this study. Typical features for beam buckling and local buckling failure in the proposed numerical model were derived. Based on a series of parametric studies, the influences of the fault displacement, fault dip angle, pipe wall thickness, buried depth of pipe and soil conditions on the buckling failure modes were discussed in detail. The proposed methodology can be referenced for failure analysis and strength evaluation of pipelines subjected to reverse fault displacement. © 2017 Elsevier Ltd. All rights reserved.
1. Introduction Buried steel pipeline is a main option for long distance transportation of natural gas. In recent years, several large diameter and high pressure pipelines, which are applied for long distance transportation, have been constructed in China, such as the West to East Gas Pipelines. The complicated geological environment around these pipelines makes them vulnerable by a series of nature geological disasters. Active fault is one of the most dangerous hazards [1]. Fault displacements will cause large axial and bending strain in the pipe, probably resulting in rupture and buckling failure of pipelines. Newmark [2] and Kennedy [3] did some pioneering work for the mechanical analysis of pipeline under fault displacement. Wang and Yeh [4], Karamitros et al. [5], and Trifonov [6] proposed some enhanced analytical strain analysis methods. Though various analytical methods have been proposed above, they are all based on several assumptions and can only calculate the tensile strain. Numerical simulation is the most effective tool to analyze the pipeline under compression. Takada [7] developed a beam-shell hybrid finite element model to study the relationship between the maximum strain and bent angle. A. W. Liu [8] proposed an ⁎ Corresponding author. ⁎⁎ Corresponding author at: College of Mechanical and Transportation Engineering, China University of Petroleum, Beijing 102249, China. E-mail addresses: [email protected] (X. Liu), [email protected] (H. Zhang).
http://dx.doi.org/10.1016/j.engfailanal.2017.02.019 1350-6307/© 2017 Elsevier Ltd. All rights reserved.
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equal boundary shell model to decrease the model dimension. Karamitros et al. [9] improved Takada's hybrid model by simulating pipe soil interaction with a series of soil springs. M. Liu [10] conducted some case studies of pipelines under fault displacement with pipe soil interaction simulated by soil springs. Xie [11] proved that both pipe and shell element model can predict reliable pipe strain by comparing with experimental results derived by DaHa [12]. X. B. Liu [13,14] proposed a strain prediction model for X80 pipeline crossing strike-slip fault under compression and bending based on numerical results. More recently, some advanced numerical simulation tools have been used recently in the study of complex mechanical behavior of buried steel pipelines crossing active faults. Vazouras et al. [15,16,17] studied the local buckling failure and strain reaction of X65 and X80 steel pipeline under strike-slip fault displacement. Trifonv et al. [18] developed a 3D numerical model with two different types of fault representation for stress and strain analysis. Uckan et al. [19] derived the critical length of pipeline under strike-slip fault with interaction angle of 90°. Zhang J. [20,21]. studied the local buckling behavior of X65 steel pipeline under strike-slip and reverse fault displacement. Zhao L. et al. [22] discussed the failure modes of X60 steel pipelines under reverse fault displacement with different dip angles. Joshi et al. [23] studied the beam buckling failure of X65 steel pipeline. Although the buckling behavior of steel pipelines has been discussed more or less in above researches, none of them considered the buckling behavior of high strength X80 steel pipelines under reverse fault displacement, which is commonly faced in actual engineering cases [24]. To fill this gap, buckling failure modes of high strength X80 steel gas pipeline under reverse fault was studied systematically in this paper. Typical engineering parameters used in the Second West to East Gas Pipeline in China, the longest X80 gas pipeline in the world, were adopted. A suitable hybrid finite element model with high efficiency algorithm was established for buckling analysis. Typical features for both beam and local buckling of X80 steel pipeline were investigated. The relationships between the failure modes were obtained. What's more, effects of the dip angle, pipe wall thickness, soil properties and buried depth on the failure modes of X80 pipeline were derived quantitatively. This study can provide a reference for the design and safety evaluation for high strength gas pipelines under reverse fault displacement. 2. Pipe material property The stress-strain relationship of high strength X80 pipe steel used in the Second West to East Gas Pipeline is round-house type and has no plastic plateau [25]. The elasto-plasticity of the pipe steel was described by Ramberg-Osgood model [26], and the expression of this relationship is as follows. ε¼
r σ α σ 1þ E 1 þ r σs
ð1Þ
where, E is initial elastic modulus; ε is strain; σ is stress, MPa; σS is yield stress; α and r are parameters of the Ramberg-Osgood model. For X80 pipe steel used in the Second West to East Gas Pipeline Project, E = 2.07 × 106 MPa, σS = 530 MPa, α = 15.94, r = 15.95. The true stress-strain curve is shown in Fig. 1. 3. Pipe-soil interaction model Buried gas pipelines are surrounded by soils, and the pipe soil interaction relationship can be simulated by discrete nonlinear soil springs in the directions of axial, lateral, and vertical, as shown in Fig. 2. Based on numerous experiment studies and engineering data, ALA-ASCE guideline [27] proposed the force-displacement relationship of soil springs for buried steel pipelines, in which all the force-displacement relationships are elastic-perfectly plastic and can be defined by two parameters, i.e., the maximum soil
Fig. 1. True stress-strain curve for X80 pipe steel of the Second West to East Gas Pipeline Project in China.
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Fig. 2. Sketch for the pipe-soil interaction described by non-linear soil springs [27].
resistance per unit length and the soil yield displacement, as illustrated in Fig. 3. This model was widely used for simulating pipe soil interaction in strain or stress analysis of buried pipe structures under fault displacement in a series of studies [5,8,10,11,13,14,19,23,28]. In this model, Tu, Pu, Qu and Qd represent the maximum soil resistance per unit length in three directions. Δp, Δt, Δqd and Δqu represent the yield displacement. Note that the soil springs in the axial and lateral direction are symmetric. However, the soil spring in the vertical direction is not. Because the buried depth of the pipeline is much less than the depth of the ground beneath the pipeline, the maximum soil resistance of the vertical uplift soil spring Qu is much less than the maximum soil resistance of the vertical bearing soil spring Qd. Typical parameters in the Second West to East Gas Pipeline were also adopted in this study. The buried depth of pipeline is 1.5 m. The pipeline is buried in medium sandy soil with the internal friction angle of 35°, and the effective unit weight of soil is 18 kN/m3. Fusion bonded epoxy widely used as pipe coating in industry is also adopted in this study. According to the ALA guideline [27], the maximum soil resistance per unit length and the mobilizing soil displacements of soil springs can be derived as in Table 1. 4. Numerical analysis 4.1. Finite element modeling When a pipeline crosses a reverse fault, the fault displacement on the pipeline can be calculated by three parameters, the fault displacement δ, crossing angle between the pipeline and the fault β and fault dip angle φ. Joshi et al. [23] derived that, the axial displacement of pipeline induced by the reverse fault peaks when the crossing angle β equals 90°, so does the compressive strain. Thus the pipeline is the most likely to occur buckling. So in this study, the pipeline is assumed to be at a crossing angle of 90°. Under this circumstance, the fault displacement and pipe deformation can be described as Fig. 4. When the reverse fault occurs, the hanging wall goes upwards while the foot wall goes downwards. The finite element model for buried pipeline under reverse fault displacement was developed using the commercial finite element software ABAQUS (Version 6.11) [28]. Fig. 5(a) shows the geometry and element dimension of the model. Based on preliminary analyses, the pipe length of 1200 m was considered to be sufficient for this study [13,14]. The pipe is divided into two parts. Part A is the 200-meter-long pipe near the fault, and part B is the remaining 1000-long pipe in the two sides. The pipes in part A are modeled using by elbow elements (ELBOW 32) in ABAQUS. Elbow elements appear as beams but are actually shells with quite complex deformation patterns allowed. There are 20 integration points in the middle surface around the cross section, as shown in Fig. 5(b). So element ELBOW 31 is capable to consider the ovality of pipe section caused by fault displacement to
Fig. 3. Force-displacement relationship for soil springs: (a) lateral (b) axial (c) vertical [27].
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Table 1 Soil spring properties used in the numerical analysis. Soil spring type
Maximum soil resistance force per unit length (kN/m)
Yield displacement (mm)
Axial Lateral Vertical uplift Vertical bearing
42 460 64 2140
3 11 3.16 121.9
obtain accurate deformation of the pipeline in axial direction near the fault; all elbow elements are set to be 0.1 m long. The pipes in part B are modeled by using pipe elements (PIPE 31), whose length is 1 m. Accordingly, the total pipeline consists of 2000 elbow elements and 1000 pipe elements. The nonlinear soil springs used to describe the pipe-soil interaction are modeled by using the pipe soil elements (PSI 34) in ABAQUS [29]. A PSI element has 4 nodes. Two of them are connected to soil nodes, and the rest to pipe nodes. So the model has 3000 PSI elements and 3001 soil nodes corresponding to elbow and pipe elements. In this model, the numerical analysis was conducted in two steps: the pressure loading step and the fault movement step. In the pressure loading step, all soil nodes of PSI elements were constrained and internal pressure was imposed on elbow and pipe elements. In the fault movement step, the soil nodes in foot wall side were also constrained, and a displacement load δ was applied to the soil nodes in hanging wall side to simulate fault displacement. In the numerical analysis, the fault displacement δ is divided into two components, one in the axial direction of the pipeline, δx = δcosφ, and the other in the vertical direction of the pipeline, δy = δsinφ. In the numerical analysis, all parameters were selected from actual design cases in the Second West to East Gas Pipeline Project. The diameter and wall thickness of pipe are 1219 mm and 22 mm, respectively. Considering safety factor equals 0.72 [30] and the minimum wall thickness of the whole pipeline is 18.4 mm, the operating pressure of the Second West to East Gas pipeline is 12 MPa, decided by the equation Pmax = 0.72× (2σst/D). 4.2. Solution algorithms for nonlinear buckling analysis of pipeline under reverse fault displacement The nonlinear buckling of pipeline under reverse fault displacement is geometrical and material non-linear. The loaddisplacement response of this kind of problem may take on the negative stiffness [29]. Some algorithms were used in previous studies for solving this kind of problem. Jin L. et al. [31] used arc-length algorithm in the study of post buckling analysis of buried steel pipelines under reverse fault displacement. Liu P. F. et al. [32] proved that both non-linear stabilization algorithm and arclength algorithm are suitable for the limit load-bearing analysis of deflected steel pipeline. Joshi et al. [23] analyzed the strain reaction of pipeline subjected to reverse fault motion by a nonlinear quasi-static solution method. The nonlinear quasi-static method is useful for the convergence of this problem, but the calculation process will cost too much time. Above all, non-linear stabilization algorithm is a suitable choice for the buckling analysis in this study. The finite element equation of the non-linear stabilization algorithm [29] is :
½K ½u þ ½C ½u ¼ ½ F
ð2Þ
where [K] is the stiffness matrices, [C] is the damping matrices, [u] is the displacement matrices, [F] is the load matrices. In the nonlinear bucking analysis, when [K] becomes a negative stiffness matrix, the damping matrices [C] induced will be large enough to prevent the instantaneous collapse. And by checking up the total energy dissipated due to stabilization to be a negligibly small one compared to the total energies in deformation, a reasonable solution can be obtained. The X80 pipe steel gas pipeline crossing a reverse fault with a dip angle of 30°was analyzed to discuss the difference between the arc-length algorithm and the non-linear stabilization algorithm. The trend of the maximum vertical displacement of pipeline
Fig. 4. Sketch of pipeline deformation under reverse fault displacement.
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Fig. 5. Finite element model for buried pipeline subjected to reverse fault displacement.
umax with the fault displacement δ were used to monitor the beam buckling behavior of the pipeline. The position of maximum vertical displacement umax in the pipe has been illustrated in Fig. 4. Fig. 6 shows the relationship between umax and δ with two algorithms. It is obvious that numerical results are almost the same for these two methods. If δ b 1.84 m, umax changes slowly with δ. If δ N 1.84 m, umax changes abruptly with δ. So the pipeline occurs beam buckling when δ = 1.84 m. Both non-linear stabilization algorithm and arc-length algorithm can simulate the buckling behavior. But note that the non-linear stabilization algorithm only costs half of the time of the arc-length algorithm does, as shown in Table 2. 4.3. Validation of the proposed finite element model Experimental results for steel pipelines obtained by Rofooei et al. [33,34] were used here to validate the accuracy of the proposed finite element model. The soil spring parameters were obtained by sand properties used in the experiment. The true stressstrain curve of the API-5L Grade B material used in the experiment was also adopted. Other main parameters used are listed in Table 3. Because the length of the experiment is limited, the FE model was revised with respect to the length. Thus, the pipe length was redefined to be 8 m and the pipe was modeled by elbow elements, whose size was set to be the same as adopted by Rofooei et al. [34] in his Simplified finite element model. The numerical results by the proposed model were compared with the experiment, simplified and detailed finite element model results derived by Rafooei et al. [34], as show in Fig. 7. It can be demonstrated that the proposed model results match better with the experimental results than simplified numerical model results by Rafooei et al. [34] based on pipe elements for both the invert strain and the crown strain in the pipe. While the proposed model results do not match as well with the experimental results as the detailed finite element results by Rafooei et al. [34] based on pipe elements. The reason is that elbow elements used in our model can simulate the oval deformation of the pipe but cannot simulate the local buckling. Rafooei et al. [34] used the simplified FE model for comprehensive parametric analysis from an engineering point of view, because the maximum compressive strain obtained from the simple FE analysis is slightly larger than the experimental and detailed FE results. Thus, the proposed model is also suitable for the buckling analysis of buried steel pipelines under reverse faulting.
Fig. 6. Trends of umax with δ at dip angle of 30° with different algorithms.
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Table 2 CPU time for two algorithms.
CPU time/S
Arc-length algorithm
Non-linear stabilization algorithm
6462.5
2964.7
5. Results and discussion A series of numerical studies were investigated in this section to study the influence of some main factors on the buckling behavior of X80 steel pipelines under reverse fault displacement, including the fault dip angle, pipe wall thickness, buried depth of pipeline, native and backfill soil properties. 5.1. Determination method of the buckling failure modes There are two buckling failure modes when a pipe subjected to compression. The first one is local buckling failure and the other one is beam buckling failure. The buckling behaviors are analyzed in detail in this section. In the proposed pipe-elbow hybrid model, the beam buckling behavior can be derived directly by analyzing the relationship between max vertical displacement umax and fault displacement δ. However, the wrinkling of the pipe wall can't be simulated by elbow elements. According to previous researches [14,23], the local buckling in shell mode in this study was predicted based on the value of maximum compressive strain in the pipeline. The critical compressive strain εcrit for the onset of local buckling with formation of wrinkles and reduction of load carrying capacities has been studied by a series of researchers. Gresnigt A. M. [35] first proposed Eq. (3), and it has been adopted by CSA Z662 specification [36]. By comparing different formulas of the ultimate compressive strain of local buckling in the standards of Norway, Canada, Japan etc., Eq. (3) is more reasonable for its concern about the influence of internal pressure [37]. As the prediction from the CSA equation is conservative, it is widely used in both academia and industry [14,15,25,27,34]. σ 2 t −0:0025 þ 3000 h εcrit ¼ 0:5 E D
ð3Þ
where the hoop stress σh depends on the level of internal pressure p: 8 pD > > ; < 2t σh ¼ > > : 0:4σ s ;
pD ≤0:4 2tσ s pD N0:4 2tσ s
ð4Þ
where σs is yield stress; t is pipe wall thickness; D is pipe diameter. When the calculated maximum compressive strain in the pipeline εmax is larger than the critical strain εcrit, the pipe can be considered as occurring local buckling at this position. When εmax is beyond εcrit, the strain results can just give a variation tendency, which has no actual meaning With D = 1219 mm, t = 18.4 mm, p = 12 MPa, the critical compressive strain of the X80 gas pipeline under operating pressure is 0.98%. As shown in Fig. 6, with the dip angle of 30°, when the fault displacement δ = 1.84 m, the maximum vertical displacement of the pipe umax increases abruptly, and the pipeline occurs beam buckling. Three cases of different δ around 1.84 m were compared here to analyze the beam buckling behavior. Three fault displacements are δ = 1.74 m, 1.84 m and 1.94 m. Fig. 8 shows the distribution of the vertical displacement value of the pipe u along the pipeline near the fault trace. It can be obtained that when δ increases from 1.74 m to 1.84 m, the maximum vertical displacement umax increases slowly from 1.06 m to 1.26 m. But when δ increases from 1.84 m to 1.94 m, umax increases abruptly from 1.26 m to 2.21 m. According to the obvious instability of the pipeline displacement, it can be demonstrated that the pipeline occurs beam buckling). As shown in Fig. 4, if a pipeline is subjected to reverse fault displacement, the top of the pipeline in foot wall side and the bottom of the pipeline in hanging wall side will be under compression. And because the soil force of the vertical uplift soil spring is much less than that of the vertical bearing soil spring, the compressive strain of the pipe will peak at the bottom of the pipeline in the hanging wall side. Fig. 9 illustrates the distribution of the axial strain at the bottom of the pipeline ε near the fault. Similar to Fig. 8 when δ increases from 1.74 m to 1.84 m, the maximum axial compressive strain εmax increases from −0.89% to −1.2%. While δ increases from 1.84 m to 1.94 m, εmax increases abruptly from −1.2% to −3.0%. Although the strain results have no real Table 3 Parameters of the experiment (adapted from Rofooei et al. [33]). Pipe diameter
Pipe wall thickness
Buried depth of pipe
Fault dip angle
Fault displacement
D(mm) 114.3
t(mm) 4.4
H(m) 1
φ(°) 61
δ(mm) 600
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Fig. 7. Experimental and numerical strain distribution along the pipe.
meaning when εmax is larger than 0.98%, the tendency of the strain results can also reflect the beam buckling process, so it is also briefly analyzed here. Comparing Fig. 8 with Fig. 9, the characteristics when pipeline occurs beam buckling can be derived. When a gas pipeline buckles in beam mode, it will change to a form of “Ω”, which will induce an abrupt vertical displacement for the pipe segments at the top of the deformed pipeline, as position A shown in Fig. 8. The abrupt deformation in the vertical direction in a short length of pipe will then induce a large bending strain, which will make a large axial compressive strain eventually, as position A shown in Fig. 9. When δ = 1.84 m, the maximum compressive strain in the pipe εmax equals to 1.2%, which is a bit larger than the critical compressive strain 0.98%. So the pipe occurs local buckling somewhere before the beam buckling occurs. It can be calculated that when δ = 1.77 m, εmax = 0.98%, the pipe occurs local buckling failure at this fault displacement. Three cases of different δ around 1.77 m were also studied here to analyze the performance of the pipeline when local buckling occurs and beam buckling doesn't occur. The conditions of δ = 1.71 m, 1.77 m and 1.83 m are considered. As illustrated in Figs. 10 and 11, both the vertical displacement and the axial strain of the pipeline change uniformly before and after local buckling failure occurs. In conclusion, when an X80 steel pipeline subjects to reverse fault displacement, two buckling failure modes have different influences on the pipe. The beam buckling failure will lead to instability in the pipeline near the fault, and large vertical displacement and compressive strain will be induced. The local buckling failure will cause wrinkling in the locality of the pipe, which is dangerous for the pipeline, but it has small effect on the global deformation of the pipeline. 5.2. Influence of dip angle on the buckling failure modes 5.2.1. Beam buckling failure analysis of pipeline at different dip angles The influence of dip angle on the buckling failure model was analyzed in detail in this section. Six dip angles were considered: 15°, 30°, 45°, 60°, 75°, 90°. Fig. 12 illustrates the relationship of the maximum vertical displacement umax with the fault displacement δ at different dip angles.
Fig. 8. Distribution of u near the fault with a dip angle of 30° when beam buckling occurs.
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Fig. 9. Distribution of ε near the fault with a dip angle of 30° when beam buckling occurs.
As shown in Fig. 12(a), when dip angle φ ∈ [15°, 60°], the relationship between umax and δ is nonlinear. When δ increases to a certain value, there will be an abrupt increase of umax. And a smaller dip angle causes a more abrupt increase. For example, when φ = 15°, umax changes vertically after δ exceeds 2.38 m. While φ = 60°, umax only changes a little faster with δ after δ exceeds 2.04 m. From Fig. 12(b); when φ ∈ [75°, 90°], the relationship between umax and δ is almost linear, especially when φ = 90°. When umax increases abruptly with δ, it can be demonstrated that the pipeline occurs beam buckling. Table 4 lists the critical fault displacement δcb for beam buckling failure at different fault dip angles. Figs. 13–15 show the distribution of the pipe vertical displacement u and axial strain ε with three dip angles (15°, 45°, 60°) along the pipeline near the fault. Comparing with Figs. 8 and 9, some important conclusions can be derived. When the dip angle is small (φ ≤ 45°), the uplift of the pipeline caused by beam buckling is obvious, and an abrupt increase of the vertical displacement is induced right after the pipeline buckles in beam mode, as shown in Figs. 13(a), 8 and 14(a). The abrupt increase of u will also induce a large bend in the pipe near the fault and lead to an abrupt increase of the compressive strain in the pipeline, as shown in Figs. 13(b), 9 and 14(b). And when the dip angle becomes smaller, the abrupt increase of u and ε is more obvious. When the dip angle equals to 60°, there is no obvious difference for the trends of u and ε after beam buckling. When a pipeline occurs beam buckling, it deforms in a form of “Ω”, and the maximum compressive strain will concentrate at the top of the deformed pipeline, like position A in Fig. 9. The distance of the strain concentration position from the fault Lb is around 10 m (7.1 m in Fig. 13, 8.8 m in Fig. 8, 9.9 m in Fig. 14(b), 10 m in Fig. 15(b)). 5.2.2. Local buckling failure analysis of pipeline at different dip angles In this study, the local buckling failure analysis of pipe is based on the comparison of the maximum compressive strain εmax with the critical compressive strain εcrit. When |εmax | N |εcrit |, the pipeline occurs local buckling. Fig. 16 illustrates the relationship between the maximum compressive strain εmax and the fault displacement δ at different dip angles. As shown in Fig. 16(a), εmax increases regularly with δ at first, and when beam buckling occurs it increases abruptly. The trend of εmax varies with different dip angles. When φ b 45°, εmax reaches εcrit before the beam buckling occurs, which means the local buckling failure occurs before beam buckling failure does. And a larger dip angle induces a larger compressive strain under this kind of condition. When φ = 45°, εmax reaches εcrit at the same fault displacement as the beam buckling failure occurs, which
Fig. 10. Distribution of u near the fault with a dip angle of 30° when local buckling occurs.
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Fig. 11. Distribution of ε near the fault with a dip angle of 30°when local buckling occurs.
Fig. 12. Relationship between umax and δ at different dip angles.
means the beam buckling failure and local buckling failure occur at the same fault displacement. As shown in Fig. 16(b), when φ ≥ 60°, a larger dip angle induces a smaller compressive strain, and the maximum compressive strain with a dip angle φ = 90° is much smaller than other angles. Similar to the condition φ b 45°, when φ = 60°, the local buckling failure occurs before beam buckling. While φ ≥75°, only the local buckling failure occurs. Table 5 lists the critical fault displacement δcs for local buckling failure at different dip angles. X80 steel pipeline is the most likely to occur local buckling at a dip angle of 45°, and the critical fault displacement is 1.74 m. When dip angle equals to 90°, the critical fault displacement is 6.0 m, which is much larger than other dip angles. The local buckling position is also listed in Table 5. In general, the local buckling position is not far away from the fault. 5.3. Influence of pipe wall thickness on the buckling failure modes 5.3.1. Beam buckling failure analysis of pipeline with different pipe wall thicknesses When dip angle φ=45°, the high strength gas pipeline under reverse fault displacement is the most at risk. Under this condition, the influence of pipe wall thickness is discussed here. The pipe wall thickness is selected according to the Second West to Table 4 Critical fault displacement for beam buckling failure at different dip angles. Dip angle φ(°)
Critical fault displacement for beam buckling failure δcb (m)
15 30 45 60 75 90
2.38 1.84 1.74 2.04 No beam buckling No beam buckling
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Fig. 13. Reaction for the pipeline near fault with a dip angle of 15° when beam buckling occurs.
Fig. 14. Reaction for the pipeline near fault with a dip angle of 45° when beam buckling occurs.
East Gas Pipeline Project, and the values are 18.4 mm, 22 mm, 26.4 mm and 33 mm. They are used in the X80 steel gas pipeline in different risk level areas [32]. Fig. 17 illustrates the relationship between the max vertical displacement umax and fault displacement δ with different pipe wall thicknesses. It can be derived that, with the increase of the wall thickness t, the critical fault displacement for beam buckling δcb also increases. Four values are 1.69 m, 1.74 m, 1.87 m and 2.02 m. After beam buckling occurring, the strain concentration position will be a little further from the fault as the wall thickness increases. The values are 7.7 m, 9.9 m, 12.3 m and 15.6 m.
Fig. 15. Reaction for the pipeline near fault with a dip angle of 60° when beam buckling occurs.
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Fig. 16. Relationship between εmax and δ at different dip angles.
5.3.2. Local buckling failure analysis of pipeline with different pipe wall thickness The local buckling is also predicted by the comparison between the maximum axial compressive strain and critical compressive strain. According to Eq. (3), the wall thickness t has an influence on the critical compressive strain εcrit. εcrit increases with the increase of t. It equals to 0.84%, 0.98%, 1.16% and 1.44% with respect to the wall thickness of 18.4 mm, 22 mm, 26.4 mm and 33 mm. Fig. 18 shows the relationship between the maximum compressive strain εmax and fault displacement δ with different pipe wall thicknesses. The critical fault displacement of local buckling δcs for these four cases can be obtained as 1.16 m, 1.76 m, 1.95 m and 2.16 m. The local buckling position from the fault Ls can also be derived as 0.6 m, 6.0 m, 10.4 m and 14.0 m. By comparing the critical fault displacement δcs with δcb, it has been found that, when t b 22 mm, the local buckling failure occurs before beam buckling failure does; when t ≥ 22 mm, the beam buckling failure occurs before local buckling failure occurs. If local buckling failure occurs first, the failure position is near the fault, otherwise, the failure position is a little further away from the fault. 5.4. Influence of the buried depth of pipeline on the buckling failure modes 5.4.1. Beam buckling failure analysis of pipeline at different buried depths Fig. 19 shows the relationship between the max vertical displacement umax and fault displacement δ with different buried depths. Three values for the buried depth to the top of the pipe H were selected for the analysis, as 1.5 m, 1.8 m and 2.1 m. According to the ALA-ASCE guideline [27], the buried depth of pipeline has an influence on the property of the soil springs used to simulate the pipe-soil interaction. When the buried depth is larger, the maximum force for the axial soil spring and vertical soil springs will be larger. From the calculated numerical results, some conclusions can be drawn. When H reaches to 1.5 m, the critical fault displacement for beam buckling failure δcb is 1.74 m. When H varies to 1.8 m and 2.1 m, the results of the critical fault displacement for beam buckling failure δcb are the same as 1.90 m. After beam buckling occurs, the distances of the strain concentration position from the fault Lb for three buried depths are 10.0 m, 6.5 m and 4.9 m with respect to the buried depths of 1.5 m, 1.8 m and 2.1 m. 5.4.2. Local buckling failure analysis of pipeline at different buried depths Fig. 20 illustrates the relationship between the maximum compressive strain εmax and fault displacement δ at different buried depths. It can be derived that εmax increases with the increase of buried depth H before beam buckling failure occurs in the pipeline. But once the beam buckling occurs the maximum compressive strain of all cases increase abruptly, thus the difference becomes negligible. The critical fault displacement for local buckling δcs of three buried depths (1.5 m, 1.8 m and 2.1 m) are 1.76 m, 1.33 m and 1.15 m. So the X80 steel pipeline is more vulnerable with a larger buried depth. The distance from the fault Ls for the local buckling can be obtained from numerical results. They are 6.0 m, 1.0 m and 0.9 m for the buried depth of 1.5 m, 1.8 m and 2.1 m. So the local buckling failure position is closer to the fault with a larger buried depth. Table 5 Critical fault displacement and buckling position for local buckling failure at different dip angles. Dip angle φ(°)
Critical fault displacement for local buckling failure δcs (m)
Buckling position distance from fault Ls (m)
15 30 45 60 75 90
2.10 1.77 1.74 1.87 2.13 6
2.0 4.9 6.0 5.2 1.5 1.1
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Fig. 17. Relationship between umax and δ with different pipe wall thickness.
5.5. Influence of the soil conditions on the buckling failure modes 5.5.1. Beam buckling failure analysis of pipeline with different soil conditions In the above sections of this paper, the pipeline was assumed to be buried in medium sandy soils. Here three kinds of native and backfill soil types were discussed: 1. both the native and backfill soil are medium sandy soils; 2. both the native and backfill
Fig. 18. Relationship between εmax and δ with different pipe wall thickness.
Fig. 19. Relationship between umax and δ at different buried depth.
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Fig. 20. Relationship between εmax and δ at different buried depths.
soil are medium cohesive soils; 3. the native soil is medium cohesive soil and the backfill soil is the medium sandy soil. The property of the sandy soil is the same as the previous study. The coefficient of the cohesion of the medium cohesive soil is 80 kPa, the internal friction angle is 20°, and the effective unit weight of soil is 18 kN/m3. Fig. 21 shows the relationship between the max vertical displacement umax and fault displacement δ with three different soil types. It can be derived that, when δ b 0.7 m, umax increases linearly with δ for all three cases discussed above, and there is negligible difference between them. The max vertical displacement umax of the pipeline buried in cohesive soil increases abruptly with the increase of δ after δ = 0.7 m, while umax of the pipeline buried in other two kinds of soil conditions keep increasing linearly. When δ N 1.8 m, umax of the pipeline buried in sandy soil and native cohesive soil with backfill sandy soil increase abruptly with the increase of δ. So the critical fault displacement for beam buckling δcb for three different kinds of soil can be derived as Table 6. It is obvious that the beam buckling is much easier to occur in the pipeline buried in cohesive soil than those buried in sandy soil. But if the backfill of the pipeline buried in cohesive soil is replaced by sandy soil, the critical fault displacement δcb will become almost the same as the pipeline buried in sandy soil.
5.5.2. Local buckling failure analysis of pipeline with different types of native and backfill soil Fig. 22 illustrates the relationship between the maximum compressive strain εmax and fault displacement δ with different soil conditions. The pipeline buried in cohesive soil has much larger max compressive strain than those buried in other two soil conditions. The critical fault displacement for local buckling δcs of three different soil conditions (sandy soil, cohesive soil and native cohesive soil with backfill sandy soil) are 1.75 m, 0.5 m, 1.75 m. So the pipeline buried in cohesive soil is much more vulnerable. The distance for the local buckling from the fault Ls can be obtained as 9.6 m, 1.5 m, 9.0 m. Hence the local buckling failure position of pipeline buried in cohesive soil is almost at the fault trace.
Fig. 21. Relationship between umax and δ with different soil types.
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Table 6 Critical fault displacement for beam buckling failure with different soil types. Surrounding soil type
Critical fault displacement for beam buckling failure δcb (m)
Sandy soil Cohesive soil Native cohesive soil with backfill sandy soil
1.7 0.7 1.7
6. Conclusion In this paper, the buckling failure modes of high strength X80 steel gas pipeline under reverse fault were studied. A pipeelbow hybrid model was established considering the non-linearity of the pipe material, pipe soil interaction and large deformation. The non-linear stabilization algorithm was selected to simulate the buckling phenomenon of the pipe. The typical features of both beam and local buckling failure were analyzed in detail. From numerical results, the influence of the fault displacement, fault dip angle, pipe diameter-to-thickness ratio, buried depth of pipe and soil conditions of buried pipe on the buckling failure modes have been discussed in detail, and the following conclusions can be drawn: 1. The buckling failure analysis problem of high strength pipeline under reverse fault is highly non-linear. The non-linear stabilization algorithm is a proper option for solving this kind of problem, for it has much higher efficiency than arc-length algorithm. 2. When both buckling failure modes occur in the pipeline, if the pipe occurs beam buckling first, the occurrence of local buckling will be immediately following. But if the local buckling occurs first, there is negligible influence on the total deformation of the pipeline, it will cause wrinkling in the locality of the pipe, which is dangerous for the pipeline. And the failure position of beam buckling is further away from the fault trace than that of local buckling. 3. If the dip angle φ b 75°, both beam buckling failure and local buckling failure will occur in the pipe. If φ ≥ 75°, only the local buckling failure will occur. The critical fault displacements for both buckling failure modes have their minimal values with φ =45°, and peak with φ= 90°. When dip angle φ N 75°, the pipeline is at less risk of buckling failure. 4. If the pipe wall thickness t b 22 mm, the local buckling failure occurs first in the pipeline ahead of beam buckling failure, and the pipe performs more like shell. When t ≥ 22 mm, the beam buckling failure occurs ahead of local buckling failure and the pipeline performs more like a beam. The critical fault displacement for beam buckling failure increases with the increase of the buried depth of pipeline, while the critical fault displacement for local buckling failure decreases with the increase of the buried depth of pipeline. 5. The critical fault displacements of pipelines buried in sandy soil are much larger than those in cohesive soil for both beam and local buckling failure. By using sandy soil as backfill for native cohesive soil, the critical fault displacement will increase up to almost the same value of that for native sandy soil. Therefore, using sand as backfill soil is an effective way to prevent the buckling of pipelines.
Acknowledgements The work was financially supported by CNPC Fund for Science and Technology Special Project under Grant No. 2012E-2801-01, National Natural Science Foundation of China (Grant No. 51309236), the Opening Fund of State Key Laboratory of Ocean Engineering (Shanghai Jiao Tong University) (Grant No. 1314), Opening Fund of State Key Laboratory of Hydraulic Engineering Simulation and Safety (Tianjin University) (Grant No. HESS-1411), Opening Fund of State Key Laboratory of Coastal and Offshore Engineering
Fig. 22. Relationship between εmax and δ with different soil types.
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(Dalian University of Technology) (Grant No. LP1507), Science Foundation of China University of Petroleum, Beijing (Grant No. 2462015YQ0403 and 2462015YQ0408).
References [1] M.J. O'Rourke, X. Liu, Seismic Design of Buried and Offshore Pipelines, Multidisciplinary Center for Earthquake Engineering Research, University at Buffalo, Buffalo, New York, 2011. [2] N.M. Newmark, W.J. Hall, Pipeline design to resist large fault displacement, Proceedings of the US National Conference on Earthquake Engineering, University of Michigan, Ann Arbor, 1975. [3] R.P. Kennedy, A.M. Chow, R.A. Williamson, Fault movement effects on buried oil pipeline, Transp. Eng. J. Am. Soc. Civil. Eng. 103 (1977) 617–633. [4] L.R.L. Wang, Y.H. Yeh, A refined seismic analysis and design of buried pipeline for fault movement, Earthq. Eng. Struct. Dyn. 13 (1985) 75–96. [5] D.K. Karamitros, G.D. Bouckovalas, G.P. Kouretzis, Stress analysis of buried steel pipelines at strike-slip fault crossings, Soil Dyn. Earthq. Eng. 27 (2007) 200–211. [6] O.V. Trifonov, V.P. Cherniy, A semi-analytical approach to a nonlinear stress–strain analysis of buried steel pipelines crossing active faults, Soil Dyn. Earthq. Eng. 30 (2010) 1298–1308. [7] S. Takada, N. Hassani, K. Fukuda, A new proposal for simplified design of buried steel pipes crossing active faults, Earthq. Eng. Struct. Dyn. 30 (2001) 1243–1257. [8] A.W. Liu, Y.X. Hu, F.X. Zhao, S. Takada, An equivalent-boundary method for the shell analysis of buried pipelines under fault movement, Acta Seismol. Sin. 17 (2004) 150–156. [9] D.K. Karamitros, G.D. Bouckovalas, G.P. Kouretzis, An analytical method for strength verification of buried steel pipelines at normal fault crossings, Soil Dyn. Earthq. Eng. 31 (2011) 452–1464. [10] M. Liu, Y.Y. Wang, Z. Yu, Response of pipelines under fault crossing, Proceedings of International Offshore and Polar Engineering Conference, Vancouver, BC, Canada, 2008. [11] X. Xie, M.D. Symans, M.J. O'Rourke, T.H. Abdoun, T.D. O'Rourke, Numerical modeling of buried HDPE pipelines subjected to strike-slip faulting, J. Earthq. Eng. 15 (2011) 1273–1296. [12] D. Ha, Evaluation of Ground Rupture Effect on Buried HDPE PipelinesPHD Thesis Department of Civil and Environmental Engineering, Rensselaer Polytechnic Institute, 2007. [13] X.B. Liu, H. Zhang, Strain prediction of X80 steel pipeline at strike-slip fault under compression combined with bending, Proceedings of the 2015 ASME Pressure Vessels & Piping Conference, Boston, USA, 2015. [14] X.B. Liu, H. Zhang, Y.S. Han, et al., A semi-empirical model for peak strain prediction of buried X80 steel pipelines under compression and bending at strike-slip fault crossings, J. Nat. Gas Sci. 32 (2016) 465–475. [15] P. Vazouras, S.A. Karamanos, P. Dakoulas, Finite element analysis of buried steel pipelines under strike-slip fault displacements, Soil Dyn. Earthq. Eng. 30 (2010) 1361–1376. [16] P. Vazouras, S.A. Karamanos, P. Dakoulas, Mechanical behavior of buried steel pipes crossing active strike-slip faults, Soil Dyn. Earthq. Eng. 41 (2012) 164–180. [17] P. Vazouras, P. Dakoulas, S.A. Karamanos, Pipe–soil interaction and pipeline performance under strike–slip fault movements, Soil Dyn. Earthq. Eng. 72 (2015) 48–65. [18] O.V. Trifonov, Numerical stress-strain analysis of buried steel pipelines crossing active strike-slip faults with an emphasis on fault modeling aspects, J. Pip. Sys. Eng. Prac. 6 (2014) 04014008. [19] E. Uckan, B. Akbas, J. Shen, W. Rou, F. Paolacci, M. O'Rourke, A simplified analysis model for determining the seismic response of buried steel pipes at strike-slip fault crossings, Soil Dyn. Earthq. Eng. 75 (2015) 55–65. [20] J. Zhang, Z. Liang, C.J. Han, Buckling behavior analysis of buried gas pipeline under strike-slip fault displacement, J. Nat. Gas Sci. Eng. 21 (2014) 921–928. [21] J. Zhang, Z. Liang, C.J. Han, Numerical simulation of buckling behavior of the buried steel pipeline under reverse fault displacement, Mech. Sci. 6 (2015) 203–210. [22] L. Zhao, H. Tang, X. Peng, X. Li, Failure modes of steel buried pipeline crossing reverse fault, J. Bas. Sci. Eng. S1 (2010). [23] S. Joshi, A. Prashant, A. Deb, S.K. Jain, Analysis of buried pipelines subjected to reverse fault motion, Soil Dyn. Earthq. Eng. 31 (2011) 930–940. [24] D. Lower, Mark, Strain-Based Design Methodology of Large Diameter Grade X80 LinepipePhD diss. University of Tennessee, 2014http://trace.tennessee.edu/utk_ graddiss/2769. [25] Petrochina Company Limited, Guideline for Strain-based Design in Seismic Area and Active Fault Crossing of the Second West-east Natural Gas Transportation Pipeline Project. Q/SY GJX 0136-2008, Beijing, 2008. [26] W. Ramberg, W.R. Osgood, Description of stress-strain curves by three parameters, Tech. Rep. Arch. Image Libr. 902 (1943). [27] American Lifelines Alliance, Guidelines for the Design of Buried Steel Pipe, American Society of Civil Engineers, US, 2001. [28] X.B. Liu, H. Zhang, M. Li, et al., Effects of steel properties on the local buckling response of high strength pipelines subjected to reverse faulting, J. Nat. Gas Sci. 33 (2016) 378–387. [29] ABAQUS, ‘User's Manual’, Version 6.11. Dassault Systemes. Hebbit, Karlsson and Sorensen Inc, 2011. [30] ASME, Gas Transmission and Distribution Piping Systems, American Society of Mechanical Engineers, 2007. [31] L. Jin, H.J. Li, Nonlinear response analysis of buried pipeline crossing thrust fault, J. Disa. Prev. Mitig. Eng. 30 (2010) 130–134. [32] P.F. Liu, J.Y. Zheng, B.J. Zhang, P. Shi, Failure analysis of natural gas buried X65 steel pipeline under deflection load using finite element method, Mater. Des. 31 (2010) 1384–1391. [33] F.R. Rofooei, H.H. Jalali, K.A.A. Nader, M. Alavi, Full-scale laboratory testing of buried pipelines subjected to permanent ground displacement caused by reverse faulting, Proceedings of the 15th World Conference on Earthquake Engineering, Lisboa, Portugal, 24–28 September, 2012 (Paper No. 4381). [34] F.R. Rofooei, H.H. Jalali, K.A.A. Nader, et al., Parametric study of buried steel and high density polyethylene gas pipelines due to oblique-reverse faulting, Can. J. Civ. Eng. 42 (2015) 178–189. [35] A.M. Gresnigt, Plastic design of buried steel pipelines in settlement areas, Heron 31 (1987) 1–113. [36] Canadian Standards Association, Oil and Gas Pipeline SystemsCSA Z662-07, Canada 2007. [37] P. Li, Y. Tao, J. Zhou, A study of the ultimate compressive strain of local buckling in strain-based design of pipelines, Nat. Gas Ind. 33 (2013) 101–107.
Contents lists available at ScienceDirect
Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal
Buckling failure mode analysis of buried X80 steel gas pipeline under reverse fault displacement Xiaoben Liu a,⁎, Hong Zhang a,b,⁎⁎, Kai Wu a, Mengying Xia a, Yanfei Chen a, Meng Li a a b
College of Mechanical and Transportation Engineering, China University of Petroleum, Beijing 102249, China China University of Petroleum (Beijing) Karamay Campus, Karamay 834000, China
a r t i c l e
i n f o
Article history: Received 2 March 2016 Received in revised form 22 June 2016 Accepted 27 February 2017 Available online 01 March 2017 Keywords: Buried X80 steel gas pipeline Reverse fault Buckling failure modes Finite element method Critical fault displacement
a b s t r a c t High strength steel pipeline is widely used in long distance transportation of natural gas. These pipelines are vulnerable under active faults in strong seismic areas. The buckling failure modes of high strength X80 gas pipeline crossing reverse fault were analyzed systematically in this paper. Based on the nonlinear finite element method, a pipe-elbow hybrid model was developed for buckling failure analysis of X80 steel pipeline under reverse fault displacement. The pipe soil interaction relationship was simulated by a series of elastic-plastic soil springs. The nonlinearity of pipe material and large deformation were also considered. The non-linear stabilization algorithm was selected due to the convergence of the numerical model. Engineering parameters used in the Second West to East Gas Pipeline in China were selected in this study. Typical features for beam buckling and local buckling failure in the proposed numerical model were derived. Based on a series of parametric studies, the influences of the fault displacement, fault dip angle, pipe wall thickness, buried depth of pipe and soil conditions on the buckling failure modes were discussed in detail. The proposed methodology can be referenced for failure analysis and strength evaluation of pipelines subjected to reverse fault displacement. © 2017 Elsevier Ltd. All rights reserved.
1. Introduction Buried steel pipeline is a main option for long distance transportation of natural gas. In recent years, several large diameter and high pressure pipelines, which are applied for long distance transportation, have been constructed in China, such as the West to East Gas Pipelines. The complicated geological environment around these pipelines makes them vulnerable by a series of nature geological disasters. Active fault is one of the most dangerous hazards [1]. Fault displacements will cause large axial and bending strain in the pipe, probably resulting in rupture and buckling failure of pipelines. Newmark [2] and Kennedy [3] did some pioneering work for the mechanical analysis of pipeline under fault displacement. Wang and Yeh [4], Karamitros et al. [5], and Trifonov [6] proposed some enhanced analytical strain analysis methods. Though various analytical methods have been proposed above, they are all based on several assumptions and can only calculate the tensile strain. Numerical simulation is the most effective tool to analyze the pipeline under compression. Takada [7] developed a beam-shell hybrid finite element model to study the relationship between the maximum strain and bent angle. A. W. Liu [8] proposed an ⁎ Corresponding author. ⁎⁎ Corresponding author at: College of Mechanical and Transportation Engineering, China University of Petroleum, Beijing 102249, China. E-mail addresses: [email protected] (X. Liu), [email protected] (H. Zhang).
http://dx.doi.org/10.1016/j.engfailanal.2017.02.019 1350-6307/© 2017 Elsevier Ltd. All rights reserved.
X. Liu et al. / Engineering Failure Analysis 77 (2017) 50–64
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equal boundary shell model to decrease the model dimension. Karamitros et al. [9] improved Takada's hybrid model by simulating pipe soil interaction with a series of soil springs. M. Liu [10] conducted some case studies of pipelines under fault displacement with pipe soil interaction simulated by soil springs. Xie [11] proved that both pipe and shell element model can predict reliable pipe strain by comparing with experimental results derived by DaHa [12]. X. B. Liu [13,14] proposed a strain prediction model for X80 pipeline crossing strike-slip fault under compression and bending based on numerical results. More recently, some advanced numerical simulation tools have been used recently in the study of complex mechanical behavior of buried steel pipelines crossing active faults. Vazouras et al. [15,16,17] studied the local buckling failure and strain reaction of X65 and X80 steel pipeline under strike-slip fault displacement. Trifonv et al. [18] developed a 3D numerical model with two different types of fault representation for stress and strain analysis. Uckan et al. [19] derived the critical length of pipeline under strike-slip fault with interaction angle of 90°. Zhang J. [20,21]. studied the local buckling behavior of X65 steel pipeline under strike-slip and reverse fault displacement. Zhao L. et al. [22] discussed the failure modes of X60 steel pipelines under reverse fault displacement with different dip angles. Joshi et al. [23] studied the beam buckling failure of X65 steel pipeline. Although the buckling behavior of steel pipelines has been discussed more or less in above researches, none of them considered the buckling behavior of high strength X80 steel pipelines under reverse fault displacement, which is commonly faced in actual engineering cases [24]. To fill this gap, buckling failure modes of high strength X80 steel gas pipeline under reverse fault was studied systematically in this paper. Typical engineering parameters used in the Second West to East Gas Pipeline in China, the longest X80 gas pipeline in the world, were adopted. A suitable hybrid finite element model with high efficiency algorithm was established for buckling analysis. Typical features for both beam and local buckling of X80 steel pipeline were investigated. The relationships between the failure modes were obtained. What's more, effects of the dip angle, pipe wall thickness, soil properties and buried depth on the failure modes of X80 pipeline were derived quantitatively. This study can provide a reference for the design and safety evaluation for high strength gas pipelines under reverse fault displacement. 2. Pipe material property The stress-strain relationship of high strength X80 pipe steel used in the Second West to East Gas Pipeline is round-house type and has no plastic plateau [25]. The elasto-plasticity of the pipe steel was described by Ramberg-Osgood model [26], and the expression of this relationship is as follows. ε¼
r σ α σ 1þ E 1 þ r σs
ð1Þ
where, E is initial elastic modulus; ε is strain; σ is stress, MPa; σS is yield stress; α and r are parameters of the Ramberg-Osgood model. For X80 pipe steel used in the Second West to East Gas Pipeline Project, E = 2.07 × 106 MPa, σS = 530 MPa, α = 15.94, r = 15.95. The true stress-strain curve is shown in Fig. 1. 3. Pipe-soil interaction model Buried gas pipelines are surrounded by soils, and the pipe soil interaction relationship can be simulated by discrete nonlinear soil springs in the directions of axial, lateral, and vertical, as shown in Fig. 2. Based on numerous experiment studies and engineering data, ALA-ASCE guideline [27] proposed the force-displacement relationship of soil springs for buried steel pipelines, in which all the force-displacement relationships are elastic-perfectly plastic and can be defined by two parameters, i.e., the maximum soil
Fig. 1. True stress-strain curve for X80 pipe steel of the Second West to East Gas Pipeline Project in China.
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Fig. 2. Sketch for the pipe-soil interaction described by non-linear soil springs [27].
resistance per unit length and the soil yield displacement, as illustrated in Fig. 3. This model was widely used for simulating pipe soil interaction in strain or stress analysis of buried pipe structures under fault displacement in a series of studies [5,8,10,11,13,14,19,23,28]. In this model, Tu, Pu, Qu and Qd represent the maximum soil resistance per unit length in three directions. Δp, Δt, Δqd and Δqu represent the yield displacement. Note that the soil springs in the axial and lateral direction are symmetric. However, the soil spring in the vertical direction is not. Because the buried depth of the pipeline is much less than the depth of the ground beneath the pipeline, the maximum soil resistance of the vertical uplift soil spring Qu is much less than the maximum soil resistance of the vertical bearing soil spring Qd. Typical parameters in the Second West to East Gas Pipeline were also adopted in this study. The buried depth of pipeline is 1.5 m. The pipeline is buried in medium sandy soil with the internal friction angle of 35°, and the effective unit weight of soil is 18 kN/m3. Fusion bonded epoxy widely used as pipe coating in industry is also adopted in this study. According to the ALA guideline [27], the maximum soil resistance per unit length and the mobilizing soil displacements of soil springs can be derived as in Table 1. 4. Numerical analysis 4.1. Finite element modeling When a pipeline crosses a reverse fault, the fault displacement on the pipeline can be calculated by three parameters, the fault displacement δ, crossing angle between the pipeline and the fault β and fault dip angle φ. Joshi et al. [23] derived that, the axial displacement of pipeline induced by the reverse fault peaks when the crossing angle β equals 90°, so does the compressive strain. Thus the pipeline is the most likely to occur buckling. So in this study, the pipeline is assumed to be at a crossing angle of 90°. Under this circumstance, the fault displacement and pipe deformation can be described as Fig. 4. When the reverse fault occurs, the hanging wall goes upwards while the foot wall goes downwards. The finite element model for buried pipeline under reverse fault displacement was developed using the commercial finite element software ABAQUS (Version 6.11) [28]. Fig. 5(a) shows the geometry and element dimension of the model. Based on preliminary analyses, the pipe length of 1200 m was considered to be sufficient for this study [13,14]. The pipe is divided into two parts. Part A is the 200-meter-long pipe near the fault, and part B is the remaining 1000-long pipe in the two sides. The pipes in part A are modeled using by elbow elements (ELBOW 32) in ABAQUS. Elbow elements appear as beams but are actually shells with quite complex deformation patterns allowed. There are 20 integration points in the middle surface around the cross section, as shown in Fig. 5(b). So element ELBOW 31 is capable to consider the ovality of pipe section caused by fault displacement to
Fig. 3. Force-displacement relationship for soil springs: (a) lateral (b) axial (c) vertical [27].
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Table 1 Soil spring properties used in the numerical analysis. Soil spring type
Maximum soil resistance force per unit length (kN/m)
Yield displacement (mm)
Axial Lateral Vertical uplift Vertical bearing
42 460 64 2140
3 11 3.16 121.9
obtain accurate deformation of the pipeline in axial direction near the fault; all elbow elements are set to be 0.1 m long. The pipes in part B are modeled by using pipe elements (PIPE 31), whose length is 1 m. Accordingly, the total pipeline consists of 2000 elbow elements and 1000 pipe elements. The nonlinear soil springs used to describe the pipe-soil interaction are modeled by using the pipe soil elements (PSI 34) in ABAQUS [29]. A PSI element has 4 nodes. Two of them are connected to soil nodes, and the rest to pipe nodes. So the model has 3000 PSI elements and 3001 soil nodes corresponding to elbow and pipe elements. In this model, the numerical analysis was conducted in two steps: the pressure loading step and the fault movement step. In the pressure loading step, all soil nodes of PSI elements were constrained and internal pressure was imposed on elbow and pipe elements. In the fault movement step, the soil nodes in foot wall side were also constrained, and a displacement load δ was applied to the soil nodes in hanging wall side to simulate fault displacement. In the numerical analysis, the fault displacement δ is divided into two components, one in the axial direction of the pipeline, δx = δcosφ, and the other in the vertical direction of the pipeline, δy = δsinφ. In the numerical analysis, all parameters were selected from actual design cases in the Second West to East Gas Pipeline Project. The diameter and wall thickness of pipe are 1219 mm and 22 mm, respectively. Considering safety factor equals 0.72 [30] and the minimum wall thickness of the whole pipeline is 18.4 mm, the operating pressure of the Second West to East Gas pipeline is 12 MPa, decided by the equation Pmax = 0.72× (2σst/D). 4.2. Solution algorithms for nonlinear buckling analysis of pipeline under reverse fault displacement The nonlinear buckling of pipeline under reverse fault displacement is geometrical and material non-linear. The loaddisplacement response of this kind of problem may take on the negative stiffness [29]. Some algorithms were used in previous studies for solving this kind of problem. Jin L. et al. [31] used arc-length algorithm in the study of post buckling analysis of buried steel pipelines under reverse fault displacement. Liu P. F. et al. [32] proved that both non-linear stabilization algorithm and arclength algorithm are suitable for the limit load-bearing analysis of deflected steel pipeline. Joshi et al. [23] analyzed the strain reaction of pipeline subjected to reverse fault motion by a nonlinear quasi-static solution method. The nonlinear quasi-static method is useful for the convergence of this problem, but the calculation process will cost too much time. Above all, non-linear stabilization algorithm is a suitable choice for the buckling analysis in this study. The finite element equation of the non-linear stabilization algorithm [29] is :
½K ½u þ ½C ½u ¼ ½ F
ð2Þ
where [K] is the stiffness matrices, [C] is the damping matrices, [u] is the displacement matrices, [F] is the load matrices. In the nonlinear bucking analysis, when [K] becomes a negative stiffness matrix, the damping matrices [C] induced will be large enough to prevent the instantaneous collapse. And by checking up the total energy dissipated due to stabilization to be a negligibly small one compared to the total energies in deformation, a reasonable solution can be obtained. The X80 pipe steel gas pipeline crossing a reverse fault with a dip angle of 30°was analyzed to discuss the difference between the arc-length algorithm and the non-linear stabilization algorithm. The trend of the maximum vertical displacement of pipeline
Fig. 4. Sketch of pipeline deformation under reverse fault displacement.
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Fig. 5. Finite element model for buried pipeline subjected to reverse fault displacement.
umax with the fault displacement δ were used to monitor the beam buckling behavior of the pipeline. The position of maximum vertical displacement umax in the pipe has been illustrated in Fig. 4. Fig. 6 shows the relationship between umax and δ with two algorithms. It is obvious that numerical results are almost the same for these two methods. If δ b 1.84 m, umax changes slowly with δ. If δ N 1.84 m, umax changes abruptly with δ. So the pipeline occurs beam buckling when δ = 1.84 m. Both non-linear stabilization algorithm and arc-length algorithm can simulate the buckling behavior. But note that the non-linear stabilization algorithm only costs half of the time of the arc-length algorithm does, as shown in Table 2. 4.3. Validation of the proposed finite element model Experimental results for steel pipelines obtained by Rofooei et al. [33,34] were used here to validate the accuracy of the proposed finite element model. The soil spring parameters were obtained by sand properties used in the experiment. The true stressstrain curve of the API-5L Grade B material used in the experiment was also adopted. Other main parameters used are listed in Table 3. Because the length of the experiment is limited, the FE model was revised with respect to the length. Thus, the pipe length was redefined to be 8 m and the pipe was modeled by elbow elements, whose size was set to be the same as adopted by Rofooei et al. [34] in his Simplified finite element model. The numerical results by the proposed model were compared with the experiment, simplified and detailed finite element model results derived by Rafooei et al. [34], as show in Fig. 7. It can be demonstrated that the proposed model results match better with the experimental results than simplified numerical model results by Rafooei et al. [34] based on pipe elements for both the invert strain and the crown strain in the pipe. While the proposed model results do not match as well with the experimental results as the detailed finite element results by Rafooei et al. [34] based on pipe elements. The reason is that elbow elements used in our model can simulate the oval deformation of the pipe but cannot simulate the local buckling. Rafooei et al. [34] used the simplified FE model for comprehensive parametric analysis from an engineering point of view, because the maximum compressive strain obtained from the simple FE analysis is slightly larger than the experimental and detailed FE results. Thus, the proposed model is also suitable for the buckling analysis of buried steel pipelines under reverse faulting.
Fig. 6. Trends of umax with δ at dip angle of 30° with different algorithms.
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Table 2 CPU time for two algorithms.
CPU time/S
Arc-length algorithm
Non-linear stabilization algorithm
6462.5
2964.7
5. Results and discussion A series of numerical studies were investigated in this section to study the influence of some main factors on the buckling behavior of X80 steel pipelines under reverse fault displacement, including the fault dip angle, pipe wall thickness, buried depth of pipeline, native and backfill soil properties. 5.1. Determination method of the buckling failure modes There are two buckling failure modes when a pipe subjected to compression. The first one is local buckling failure and the other one is beam buckling failure. The buckling behaviors are analyzed in detail in this section. In the proposed pipe-elbow hybrid model, the beam buckling behavior can be derived directly by analyzing the relationship between max vertical displacement umax and fault displacement δ. However, the wrinkling of the pipe wall can't be simulated by elbow elements. According to previous researches [14,23], the local buckling in shell mode in this study was predicted based on the value of maximum compressive strain in the pipeline. The critical compressive strain εcrit for the onset of local buckling with formation of wrinkles and reduction of load carrying capacities has been studied by a series of researchers. Gresnigt A. M. [35] first proposed Eq. (3), and it has been adopted by CSA Z662 specification [36]. By comparing different formulas of the ultimate compressive strain of local buckling in the standards of Norway, Canada, Japan etc., Eq. (3) is more reasonable for its concern about the influence of internal pressure [37]. As the prediction from the CSA equation is conservative, it is widely used in both academia and industry [14,15,25,27,34]. σ 2 t −0:0025 þ 3000 h εcrit ¼ 0:5 E D
ð3Þ
where the hoop stress σh depends on the level of internal pressure p: 8 pD > > ; < 2t σh ¼ > > : 0:4σ s ;
pD ≤0:4 2tσ s pD N0:4 2tσ s
ð4Þ
where σs is yield stress; t is pipe wall thickness; D is pipe diameter. When the calculated maximum compressive strain in the pipeline εmax is larger than the critical strain εcrit, the pipe can be considered as occurring local buckling at this position. When εmax is beyond εcrit, the strain results can just give a variation tendency, which has no actual meaning With D = 1219 mm, t = 18.4 mm, p = 12 MPa, the critical compressive strain of the X80 gas pipeline under operating pressure is 0.98%. As shown in Fig. 6, with the dip angle of 30°, when the fault displacement δ = 1.84 m, the maximum vertical displacement of the pipe umax increases abruptly, and the pipeline occurs beam buckling. Three cases of different δ around 1.84 m were compared here to analyze the beam buckling behavior. Three fault displacements are δ = 1.74 m, 1.84 m and 1.94 m. Fig. 8 shows the distribution of the vertical displacement value of the pipe u along the pipeline near the fault trace. It can be obtained that when δ increases from 1.74 m to 1.84 m, the maximum vertical displacement umax increases slowly from 1.06 m to 1.26 m. But when δ increases from 1.84 m to 1.94 m, umax increases abruptly from 1.26 m to 2.21 m. According to the obvious instability of the pipeline displacement, it can be demonstrated that the pipeline occurs beam buckling). As shown in Fig. 4, if a pipeline is subjected to reverse fault displacement, the top of the pipeline in foot wall side and the bottom of the pipeline in hanging wall side will be under compression. And because the soil force of the vertical uplift soil spring is much less than that of the vertical bearing soil spring, the compressive strain of the pipe will peak at the bottom of the pipeline in the hanging wall side. Fig. 9 illustrates the distribution of the axial strain at the bottom of the pipeline ε near the fault. Similar to Fig. 8 when δ increases from 1.74 m to 1.84 m, the maximum axial compressive strain εmax increases from −0.89% to −1.2%. While δ increases from 1.84 m to 1.94 m, εmax increases abruptly from −1.2% to −3.0%. Although the strain results have no real Table 3 Parameters of the experiment (adapted from Rofooei et al. [33]). Pipe diameter
Pipe wall thickness
Buried depth of pipe
Fault dip angle
Fault displacement
D(mm) 114.3
t(mm) 4.4
H(m) 1
φ(°) 61
δ(mm) 600
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Fig. 7. Experimental and numerical strain distribution along the pipe.
meaning when εmax is larger than 0.98%, the tendency of the strain results can also reflect the beam buckling process, so it is also briefly analyzed here. Comparing Fig. 8 with Fig. 9, the characteristics when pipeline occurs beam buckling can be derived. When a gas pipeline buckles in beam mode, it will change to a form of “Ω”, which will induce an abrupt vertical displacement for the pipe segments at the top of the deformed pipeline, as position A shown in Fig. 8. The abrupt deformation in the vertical direction in a short length of pipe will then induce a large bending strain, which will make a large axial compressive strain eventually, as position A shown in Fig. 9. When δ = 1.84 m, the maximum compressive strain in the pipe εmax equals to 1.2%, which is a bit larger than the critical compressive strain 0.98%. So the pipe occurs local buckling somewhere before the beam buckling occurs. It can be calculated that when δ = 1.77 m, εmax = 0.98%, the pipe occurs local buckling failure at this fault displacement. Three cases of different δ around 1.77 m were also studied here to analyze the performance of the pipeline when local buckling occurs and beam buckling doesn't occur. The conditions of δ = 1.71 m, 1.77 m and 1.83 m are considered. As illustrated in Figs. 10 and 11, both the vertical displacement and the axial strain of the pipeline change uniformly before and after local buckling failure occurs. In conclusion, when an X80 steel pipeline subjects to reverse fault displacement, two buckling failure modes have different influences on the pipe. The beam buckling failure will lead to instability in the pipeline near the fault, and large vertical displacement and compressive strain will be induced. The local buckling failure will cause wrinkling in the locality of the pipe, which is dangerous for the pipeline, but it has small effect on the global deformation of the pipeline. 5.2. Influence of dip angle on the buckling failure modes 5.2.1. Beam buckling failure analysis of pipeline at different dip angles The influence of dip angle on the buckling failure model was analyzed in detail in this section. Six dip angles were considered: 15°, 30°, 45°, 60°, 75°, 90°. Fig. 12 illustrates the relationship of the maximum vertical displacement umax with the fault displacement δ at different dip angles.
Fig. 8. Distribution of u near the fault with a dip angle of 30° when beam buckling occurs.
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Fig. 9. Distribution of ε near the fault with a dip angle of 30° when beam buckling occurs.
As shown in Fig. 12(a), when dip angle φ ∈ [15°, 60°], the relationship between umax and δ is nonlinear. When δ increases to a certain value, there will be an abrupt increase of umax. And a smaller dip angle causes a more abrupt increase. For example, when φ = 15°, umax changes vertically after δ exceeds 2.38 m. While φ = 60°, umax only changes a little faster with δ after δ exceeds 2.04 m. From Fig. 12(b); when φ ∈ [75°, 90°], the relationship between umax and δ is almost linear, especially when φ = 90°. When umax increases abruptly with δ, it can be demonstrated that the pipeline occurs beam buckling. Table 4 lists the critical fault displacement δcb for beam buckling failure at different fault dip angles. Figs. 13–15 show the distribution of the pipe vertical displacement u and axial strain ε with three dip angles (15°, 45°, 60°) along the pipeline near the fault. Comparing with Figs. 8 and 9, some important conclusions can be derived. When the dip angle is small (φ ≤ 45°), the uplift of the pipeline caused by beam buckling is obvious, and an abrupt increase of the vertical displacement is induced right after the pipeline buckles in beam mode, as shown in Figs. 13(a), 8 and 14(a). The abrupt increase of u will also induce a large bend in the pipe near the fault and lead to an abrupt increase of the compressive strain in the pipeline, as shown in Figs. 13(b), 9 and 14(b). And when the dip angle becomes smaller, the abrupt increase of u and ε is more obvious. When the dip angle equals to 60°, there is no obvious difference for the trends of u and ε after beam buckling. When a pipeline occurs beam buckling, it deforms in a form of “Ω”, and the maximum compressive strain will concentrate at the top of the deformed pipeline, like position A in Fig. 9. The distance of the strain concentration position from the fault Lb is around 10 m (7.1 m in Fig. 13, 8.8 m in Fig. 8, 9.9 m in Fig. 14(b), 10 m in Fig. 15(b)). 5.2.2. Local buckling failure analysis of pipeline at different dip angles In this study, the local buckling failure analysis of pipe is based on the comparison of the maximum compressive strain εmax with the critical compressive strain εcrit. When |εmax | N |εcrit |, the pipeline occurs local buckling. Fig. 16 illustrates the relationship between the maximum compressive strain εmax and the fault displacement δ at different dip angles. As shown in Fig. 16(a), εmax increases regularly with δ at first, and when beam buckling occurs it increases abruptly. The trend of εmax varies with different dip angles. When φ b 45°, εmax reaches εcrit before the beam buckling occurs, which means the local buckling failure occurs before beam buckling failure does. And a larger dip angle induces a larger compressive strain under this kind of condition. When φ = 45°, εmax reaches εcrit at the same fault displacement as the beam buckling failure occurs, which
Fig. 10. Distribution of u near the fault with a dip angle of 30° when local buckling occurs.
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Fig. 11. Distribution of ε near the fault with a dip angle of 30°when local buckling occurs.
Fig. 12. Relationship between umax and δ at different dip angles.
means the beam buckling failure and local buckling failure occur at the same fault displacement. As shown in Fig. 16(b), when φ ≥ 60°, a larger dip angle induces a smaller compressive strain, and the maximum compressive strain with a dip angle φ = 90° is much smaller than other angles. Similar to the condition φ b 45°, when φ = 60°, the local buckling failure occurs before beam buckling. While φ ≥75°, only the local buckling failure occurs. Table 5 lists the critical fault displacement δcs for local buckling failure at different dip angles. X80 steel pipeline is the most likely to occur local buckling at a dip angle of 45°, and the critical fault displacement is 1.74 m. When dip angle equals to 90°, the critical fault displacement is 6.0 m, which is much larger than other dip angles. The local buckling position is also listed in Table 5. In general, the local buckling position is not far away from the fault. 5.3. Influence of pipe wall thickness on the buckling failure modes 5.3.1. Beam buckling failure analysis of pipeline with different pipe wall thicknesses When dip angle φ=45°, the high strength gas pipeline under reverse fault displacement is the most at risk. Under this condition, the influence of pipe wall thickness is discussed here. The pipe wall thickness is selected according to the Second West to Table 4 Critical fault displacement for beam buckling failure at different dip angles. Dip angle φ(°)
Critical fault displacement for beam buckling failure δcb (m)
15 30 45 60 75 90
2.38 1.84 1.74 2.04 No beam buckling No beam buckling
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Fig. 13. Reaction for the pipeline near fault with a dip angle of 15° when beam buckling occurs.
Fig. 14. Reaction for the pipeline near fault with a dip angle of 45° when beam buckling occurs.
East Gas Pipeline Project, and the values are 18.4 mm, 22 mm, 26.4 mm and 33 mm. They are used in the X80 steel gas pipeline in different risk level areas [32]. Fig. 17 illustrates the relationship between the max vertical displacement umax and fault displacement δ with different pipe wall thicknesses. It can be derived that, with the increase of the wall thickness t, the critical fault displacement for beam buckling δcb also increases. Four values are 1.69 m, 1.74 m, 1.87 m and 2.02 m. After beam buckling occurring, the strain concentration position will be a little further from the fault as the wall thickness increases. The values are 7.7 m, 9.9 m, 12.3 m and 15.6 m.
Fig. 15. Reaction for the pipeline near fault with a dip angle of 60° when beam buckling occurs.
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Fig. 16. Relationship between εmax and δ at different dip angles.
5.3.2. Local buckling failure analysis of pipeline with different pipe wall thickness The local buckling is also predicted by the comparison between the maximum axial compressive strain and critical compressive strain. According to Eq. (3), the wall thickness t has an influence on the critical compressive strain εcrit. εcrit increases with the increase of t. It equals to 0.84%, 0.98%, 1.16% and 1.44% with respect to the wall thickness of 18.4 mm, 22 mm, 26.4 mm and 33 mm. Fig. 18 shows the relationship between the maximum compressive strain εmax and fault displacement δ with different pipe wall thicknesses. The critical fault displacement of local buckling δcs for these four cases can be obtained as 1.16 m, 1.76 m, 1.95 m and 2.16 m. The local buckling position from the fault Ls can also be derived as 0.6 m, 6.0 m, 10.4 m and 14.0 m. By comparing the critical fault displacement δcs with δcb, it has been found that, when t b 22 mm, the local buckling failure occurs before beam buckling failure does; when t ≥ 22 mm, the beam buckling failure occurs before local buckling failure occurs. If local buckling failure occurs first, the failure position is near the fault, otherwise, the failure position is a little further away from the fault. 5.4. Influence of the buried depth of pipeline on the buckling failure modes 5.4.1. Beam buckling failure analysis of pipeline at different buried depths Fig. 19 shows the relationship between the max vertical displacement umax and fault displacement δ with different buried depths. Three values for the buried depth to the top of the pipe H were selected for the analysis, as 1.5 m, 1.8 m and 2.1 m. According to the ALA-ASCE guideline [27], the buried depth of pipeline has an influence on the property of the soil springs used to simulate the pipe-soil interaction. When the buried depth is larger, the maximum force for the axial soil spring and vertical soil springs will be larger. From the calculated numerical results, some conclusions can be drawn. When H reaches to 1.5 m, the critical fault displacement for beam buckling failure δcb is 1.74 m. When H varies to 1.8 m and 2.1 m, the results of the critical fault displacement for beam buckling failure δcb are the same as 1.90 m. After beam buckling occurs, the distances of the strain concentration position from the fault Lb for three buried depths are 10.0 m, 6.5 m and 4.9 m with respect to the buried depths of 1.5 m, 1.8 m and 2.1 m. 5.4.2. Local buckling failure analysis of pipeline at different buried depths Fig. 20 illustrates the relationship between the maximum compressive strain εmax and fault displacement δ at different buried depths. It can be derived that εmax increases with the increase of buried depth H before beam buckling failure occurs in the pipeline. But once the beam buckling occurs the maximum compressive strain of all cases increase abruptly, thus the difference becomes negligible. The critical fault displacement for local buckling δcs of three buried depths (1.5 m, 1.8 m and 2.1 m) are 1.76 m, 1.33 m and 1.15 m. So the X80 steel pipeline is more vulnerable with a larger buried depth. The distance from the fault Ls for the local buckling can be obtained from numerical results. They are 6.0 m, 1.0 m and 0.9 m for the buried depth of 1.5 m, 1.8 m and 2.1 m. So the local buckling failure position is closer to the fault with a larger buried depth. Table 5 Critical fault displacement and buckling position for local buckling failure at different dip angles. Dip angle φ(°)
Critical fault displacement for local buckling failure δcs (m)
Buckling position distance from fault Ls (m)
15 30 45 60 75 90
2.10 1.77 1.74 1.87 2.13 6
2.0 4.9 6.0 5.2 1.5 1.1
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Fig. 17. Relationship between umax and δ with different pipe wall thickness.
5.5. Influence of the soil conditions on the buckling failure modes 5.5.1. Beam buckling failure analysis of pipeline with different soil conditions In the above sections of this paper, the pipeline was assumed to be buried in medium sandy soils. Here three kinds of native and backfill soil types were discussed: 1. both the native and backfill soil are medium sandy soils; 2. both the native and backfill
Fig. 18. Relationship between εmax and δ with different pipe wall thickness.
Fig. 19. Relationship between umax and δ at different buried depth.
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Fig. 20. Relationship between εmax and δ at different buried depths.
soil are medium cohesive soils; 3. the native soil is medium cohesive soil and the backfill soil is the medium sandy soil. The property of the sandy soil is the same as the previous study. The coefficient of the cohesion of the medium cohesive soil is 80 kPa, the internal friction angle is 20°, and the effective unit weight of soil is 18 kN/m3. Fig. 21 shows the relationship between the max vertical displacement umax and fault displacement δ with three different soil types. It can be derived that, when δ b 0.7 m, umax increases linearly with δ for all three cases discussed above, and there is negligible difference between them. The max vertical displacement umax of the pipeline buried in cohesive soil increases abruptly with the increase of δ after δ = 0.7 m, while umax of the pipeline buried in other two kinds of soil conditions keep increasing linearly. When δ N 1.8 m, umax of the pipeline buried in sandy soil and native cohesive soil with backfill sandy soil increase abruptly with the increase of δ. So the critical fault displacement for beam buckling δcb for three different kinds of soil can be derived as Table 6. It is obvious that the beam buckling is much easier to occur in the pipeline buried in cohesive soil than those buried in sandy soil. But if the backfill of the pipeline buried in cohesive soil is replaced by sandy soil, the critical fault displacement δcb will become almost the same as the pipeline buried in sandy soil.
5.5.2. Local buckling failure analysis of pipeline with different types of native and backfill soil Fig. 22 illustrates the relationship between the maximum compressive strain εmax and fault displacement δ with different soil conditions. The pipeline buried in cohesive soil has much larger max compressive strain than those buried in other two soil conditions. The critical fault displacement for local buckling δcs of three different soil conditions (sandy soil, cohesive soil and native cohesive soil with backfill sandy soil) are 1.75 m, 0.5 m, 1.75 m. So the pipeline buried in cohesive soil is much more vulnerable. The distance for the local buckling from the fault Ls can be obtained as 9.6 m, 1.5 m, 9.0 m. Hence the local buckling failure position of pipeline buried in cohesive soil is almost at the fault trace.
Fig. 21. Relationship between umax and δ with different soil types.
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Table 6 Critical fault displacement for beam buckling failure with different soil types. Surrounding soil type
Critical fault displacement for beam buckling failure δcb (m)
Sandy soil Cohesive soil Native cohesive soil with backfill sandy soil
1.7 0.7 1.7
6. Conclusion In this paper, the buckling failure modes of high strength X80 steel gas pipeline under reverse fault were studied. A pipeelbow hybrid model was established considering the non-linearity of the pipe material, pipe soil interaction and large deformation. The non-linear stabilization algorithm was selected to simulate the buckling phenomenon of the pipe. The typical features of both beam and local buckling failure were analyzed in detail. From numerical results, the influence of the fault displacement, fault dip angle, pipe diameter-to-thickness ratio, buried depth of pipe and soil conditions of buried pipe on the buckling failure modes have been discussed in detail, and the following conclusions can be drawn: 1. The buckling failure analysis problem of high strength pipeline under reverse fault is highly non-linear. The non-linear stabilization algorithm is a proper option for solving this kind of problem, for it has much higher efficiency than arc-length algorithm. 2. When both buckling failure modes occur in the pipeline, if the pipe occurs beam buckling first, the occurrence of local buckling will be immediately following. But if the local buckling occurs first, there is negligible influence on the total deformation of the pipeline, it will cause wrinkling in the locality of the pipe, which is dangerous for the pipeline. And the failure position of beam buckling is further away from the fault trace than that of local buckling. 3. If the dip angle φ b 75°, both beam buckling failure and local buckling failure will occur in the pipe. If φ ≥ 75°, only the local buckling failure will occur. The critical fault displacements for both buckling failure modes have their minimal values with φ =45°, and peak with φ= 90°. When dip angle φ N 75°, the pipeline is at less risk of buckling failure. 4. If the pipe wall thickness t b 22 mm, the local buckling failure occurs first in the pipeline ahead of beam buckling failure, and the pipe performs more like shell. When t ≥ 22 mm, the beam buckling failure occurs ahead of local buckling failure and the pipeline performs more like a beam. The critical fault displacement for beam buckling failure increases with the increase of the buried depth of pipeline, while the critical fault displacement for local buckling failure decreases with the increase of the buried depth of pipeline. 5. The critical fault displacements of pipelines buried in sandy soil are much larger than those in cohesive soil for both beam and local buckling failure. By using sandy soil as backfill for native cohesive soil, the critical fault displacement will increase up to almost the same value of that for native sandy soil. Therefore, using sand as backfill soil is an effective way to prevent the buckling of pipelines.
Acknowledgements The work was financially supported by CNPC Fund for Science and Technology Special Project under Grant No. 2012E-2801-01, National Natural Science Foundation of China (Grant No. 51309236), the Opening Fund of State Key Laboratory of Ocean Engineering (Shanghai Jiao Tong University) (Grant No. 1314), Opening Fund of State Key Laboratory of Hydraulic Engineering Simulation and Safety (Tianjin University) (Grant No. HESS-1411), Opening Fund of State Key Laboratory of Coastal and Offshore Engineering
Fig. 22. Relationship between εmax and δ with different soil types.
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(Dalian University of Technology) (Grant No. LP1507), Science Foundation of China University of Petroleum, Beijing (Grant No. 2462015YQ0403 and 2462015YQ0408).
References [1] M.J. O'Rourke, X. Liu, Seismic Design of Buried and Offshore Pipelines, Multidisciplinary Center for Earthquake Engineering Research, University at Buffalo, Buffalo, New York, 2011. [2] N.M. Newmark, W.J. Hall, Pipeline design to resist large fault displacement, Proceedings of the US National Conference on Earthquake Engineering, University of Michigan, Ann Arbor, 1975. [3] R.P. Kennedy, A.M. Chow, R.A. Williamson, Fault movement effects on buried oil pipeline, Transp. Eng. J. Am. Soc. Civil. Eng. 103 (1977) 617–633. [4] L.R.L. Wang, Y.H. Yeh, A refined seismic analysis and design of buried pipeline for fault movement, Earthq. Eng. Struct. Dyn. 13 (1985) 75–96. [5] D.K. Karamitros, G.D. Bouckovalas, G.P. Kouretzis, Stress analysis of buried steel pipelines at strike-slip fault crossings, Soil Dyn. Earthq. Eng. 27 (2007) 200–211. [6] O.V. Trifonov, V.P. Cherniy, A semi-analytical approach to a nonlinear stress–strain analysis of buried steel pipelines crossing active faults, Soil Dyn. Earthq. Eng. 30 (2010) 1298–1308. [7] S. Takada, N. Hassani, K. Fukuda, A new proposal for simplified design of buried steel pipes crossing active faults, Earthq. Eng. Struct. Dyn. 30 (2001) 1243–1257. [8] A.W. Liu, Y.X. Hu, F.X. Zhao, S. Takada, An equivalent-boundary method for the shell analysis of buried pipelines under fault movement, Acta Seismol. Sin. 17 (2004) 150–156. [9] D.K. Karamitros, G.D. Bouckovalas, G.P. Kouretzis, An analytical method for strength verification of buried steel pipelines at normal fault crossings, Soil Dyn. Earthq. Eng. 31 (2011) 452–1464. [10] M. Liu, Y.Y. Wang, Z. Yu, Response of pipelines under fault crossing, Proceedings of International Offshore and Polar Engineering Conference, Vancouver, BC, Canada, 2008. [11] X. Xie, M.D. Symans, M.J. O'Rourke, T.H. Abdoun, T.D. O'Rourke, Numerical modeling of buried HDPE pipelines subjected to strike-slip faulting, J. Earthq. Eng. 15 (2011) 1273–1296. [12] D. Ha, Evaluation of Ground Rupture Effect on Buried HDPE PipelinesPHD Thesis Department of Civil and Environmental Engineering, Rensselaer Polytechnic Institute, 2007. [13] X.B. Liu, H. Zhang, Strain prediction of X80 steel pipeline at strike-slip fault under compression combined with bending, Proceedings of the 2015 ASME Pressure Vessels & Piping Conference, Boston, USA, 2015. [14] X.B. Liu, H. Zhang, Y.S. Han, et al., A semi-empirical model for peak strain prediction of buried X80 steel pipelines under compression and bending at strike-slip fault crossings, J. Nat. Gas Sci. 32 (2016) 465–475. [15] P. Vazouras, S.A. Karamanos, P. Dakoulas, Finite element analysis of buried steel pipelines under strike-slip fault displacements, Soil Dyn. Earthq. Eng. 30 (2010) 1361–1376. [16] P. Vazouras, S.A. Karamanos, P. Dakoulas, Mechanical behavior of buried steel pipes crossing active strike-slip faults, Soil Dyn. Earthq. Eng. 41 (2012) 164–180. [17] P. Vazouras, P. Dakoulas, S.A. Karamanos, Pipe–soil interaction and pipeline performance under strike–slip fault movements, Soil Dyn. Earthq. Eng. 72 (2015) 48–65. [18] O.V. Trifonov, Numerical stress-strain analysis of buried steel pipelines crossing active strike-slip faults with an emphasis on fault modeling aspects, J. Pip. Sys. Eng. Prac. 6 (2014) 04014008. [19] E. Uckan, B. Akbas, J. Shen, W. Rou, F. Paolacci, M. O'Rourke, A simplified analysis model for determining the seismic response of buried steel pipes at strike-slip fault crossings, Soil Dyn. Earthq. Eng. 75 (2015) 55–65. [20] J. Zhang, Z. Liang, C.J. Han, Buckling behavior analysis of buried gas pipeline under strike-slip fault displacement, J. Nat. Gas Sci. Eng. 21 (2014) 921–928. [21] J. Zhang, Z. Liang, C.J. Han, Numerical simulation of buckling behavior of the buried steel pipeline under reverse fault displacement, Mech. Sci. 6 (2015) 203–210. [22] L. Zhao, H. Tang, X. Peng, X. Li, Failure modes of steel buried pipeline crossing reverse fault, J. Bas. Sci. Eng. S1 (2010). [23] S. Joshi, A. Prashant, A. Deb, S.K. Jain, Analysis of buried pipelines subjected to reverse fault motion, Soil Dyn. Earthq. Eng. 31 (2011) 930–940. [24] D. Lower, Mark, Strain-Based Design Methodology of Large Diameter Grade X80 LinepipePhD diss. University of Tennessee, 2014http://trace.tennessee.edu/utk_ graddiss/2769. [25] Petrochina Company Limited, Guideline for Strain-based Design in Seismic Area and Active Fault Crossing of the Second West-east Natural Gas Transportation Pipeline Project. Q/SY GJX 0136-2008, Beijing, 2008. [26] W. Ramberg, W.R. Osgood, Description of stress-strain curves by three parameters, Tech. Rep. Arch. Image Libr. 902 (1943). [27] American Lifelines Alliance, Guidelines for the Design of Buried Steel Pipe, American Society of Civil Engineers, US, 2001. [28] X.B. Liu, H. Zhang, M. Li, et al., Effects of steel properties on the local buckling response of high strength pipelines subjected to reverse faulting, J. Nat. Gas Sci. 33 (2016) 378–387. [29] ABAQUS, ‘User's Manual’, Version 6.11. Dassault Systemes. Hebbit, Karlsson and Sorensen Inc, 2011. [30] ASME, Gas Transmission and Distribution Piping Systems, American Society of Mechanical Engineers, 2007. [31] L. Jin, H.J. Li, Nonlinear response analysis of buried pipeline crossing thrust fault, J. Disa. Prev. Mitig. Eng. 30 (2010) 130–134. [32] P.F. Liu, J.Y. Zheng, B.J. Zhang, P. Shi, Failure analysis of natural gas buried X65 steel pipeline under deflection load using finite element method, Mater. Des. 31 (2010) 1384–1391. [33] F.R. Rofooei, H.H. Jalali, K.A.A. Nader, M. Alavi, Full-scale laboratory testing of buried pipelines subjected to permanent ground displacement caused by reverse faulting, Proceedings of the 15th World Conference on Earthquake Engineering, Lisboa, Portugal, 24–28 September, 2012 (Paper No. 4381). [34] F.R. Rofooei, H.H. Jalali, K.A.A. Nader, et al., Parametric study of buried steel and high density polyethylene gas pipelines due to oblique-reverse faulting, Can. J. Civ. Eng. 42 (2015) 178–189. [35] A.M. Gresnigt, Plastic design of buried steel pipelines in settlement areas, Heron 31 (1987) 1–113. [36] Canadian Standards Association, Oil and Gas Pipeline SystemsCSA Z662-07, Canada 2007. [37] P. Li, Y. Tao, J. Zhou, A study of the ultimate compressive strain of local buckling in strain-based design of pipelines, Nat. Gas Ind. 33 (2013) 101–107.