Response Analysis of Buried Pipeline Subjected to Fault Movements
Zhongliang Jiao1, Jian Shuai2 and Kejiang Han3
1 Ph.D. Student, Faculty of Petroleum Engineering, China University of Petroleum; No 18, Fuxue Road, Changping, Beijing 102249; Email: [email protected]; Tel: 13488730821 2 Professor, Faculty of Mechanical and Electronic Engineering, China University of Petroleum; No 18, Fuxue Road, Changping, Beijing 102249; Email: [email protected]; Tel: 01089733772 3 Ph.D. Student, Faculty of Petroleum Engineering, China University of Petroleum; No 18, Fuxue Road, Changping, Beijing 102249; Email: [email protected]; Tel: 01089733391 ABSTRACT As an important factor to safe operation of pipelines, seismic faults may cause them to fail with tension rupture or buckling failure. This paper presents a detailed analysis of pipelines using the shell finite element method, considering depth, backfill soil properties and pipeline-soil nonlinear interaction. Conclusions are attained as follows: crossing angle of pipeline and fault is a sensitive factor which easily causes pipeline tensile rupture or buckling failure. Compactness of backfill soil cannot be ignored in theoretical analysis and engineering design. The stress, strain and displacement have a regular distribution, and elliptic phenomenon along pipeline is also needed to be considered. KEYWORDS Fault movements; Buried pipeline; Pipeline-Soil Interaction; Shell Model; Response Analysis INTRODUCTION Fault movement is an important factor in the safety operation of pipelines. The pipelines may be failed with tension rupture or buckling failure according to the type of fault movement. Such as the San Fernando earthquake in 1971 made California's buried pipeline and drainage pipeline suffered great destruction with 450 pipeline fractures. In 1976, the Beijing-Qinhuangdao line was confronted with four damage incidents due to the Tangshan earthquake, those 4 damages are all tensile failure or shear destruction by the fault movement. Scholars home and abroad have experienced more researches on buried pipelines. Newmark proposed a simplified calculation method ignoring the inertia of pipeline (Newmark & Hal, 1975). Kennedy extended the pioneering work of Newmark, by taking into large deflection theory (Kennedy et al., 1977). In the 1990s, Wang
Ruliang considered bending stiffness of pipeline and transverse action of soil around pipeline, and simplified pipeline far away the fault as elastic foundation beam (Wang & Yeh, 1985). Meanwhile, shell model and finite element method are introduced to the analysis of buried pipeline. Feng Qimin (2000) considered pipeline-soil interaction and material nonlinearity of pipeline and soil, and analyzed buried pipeline as a shell structure. Liu Aiwen analyzed the response characteristics of pipeline on both sides of the fault with asymmetrical deformation with shell finite element method (Liu et al., 2002). Researches of buried pipeline had experienced from simple beam model based on linear elastic analysis to plate and shell finite element model and contact method based on nonlinear theory. This paper discusses the mechanical model of buried pipeline under fault movement by setting up the model of pipeline-soil interaction. Response characteristics of pipeline subjected to fault movement is analyzed in detail, the influence factors such as crossing angle and compactness of backfill soil are also discussed. FINITE ELEMENT MODEL Based on the previous research results of buried pipelines, this paper present a detailed analysis of pipeline with shell finite element method, considering depth, backfill soil properties and pipeline-soil nonlinear interaction. The key technologies are as follows:
Model of Pipeline-Soil Interaction. Extended Drucker-Prager model is adopted in this analysis. The contact interactions between pipeline and soil is decomposed into normal contact and tangent contact, normal contact is used for lateral load to pipeline, and tangent contact for axial frictional force to pipeline. Both the normal contact and tangent contact militate while pipeline and soil are closed together, and disappear while separated.
Equivalent Boundary Condition. Within a certain distance from fault, there exists relative displacement between pipeline and soil. But far away from fault, relative displacement between pipeline and soil is small, the transverse force by soil can be ignored, so the pipeline is only subjected to axial friction by soil and axial force by itself. In order to reduce the memory and time of computers, this paper deals with boundary conditions at the two ends of pipeline based on equivalent boundary method (Liu et al., 2004) proposed by Liu Aiwen.
Set strike-slip fault as analysis example, in order to analyze the response of pipeline subjected to different crossing angle of pipeline and fault, slip amount and compactness of backfill soil, some parameters of model are fixed such as operating pressure, steel grade and dimension of pipeline. RESPONSE ANALYZING OF PIPELINE The crossing angle of pipeline and fault is set as 90° for an example, the Mises stress nephogram of pipeline is shown in Figure 1, it is shown that Mises stresses distribute symmetrical about the fault, and maximum stress is about 2m from the fault. Two points are selected at the bent location as shown in Figure 1, as the stress change
trend of those two points, the Mises stress increase with the slip amount. There is existing a phenomenon that stress of point B have a valley value (Figure 2), it's because that the axial stress is composed of tension-compression stress and bending stress, and bending stress occupies leading position at that step.
A
B
0.0 0.5 1.0 1.5 2.0 2.5 3.00
100200300400500600
Pt.A Pt.BM
ises
Stre
ss(M
Pa)
Slip-Amount(m)
low stress at Pt.B
Figure 1. Mises stress distribution Figure 2. Stress change trend of point A and B
Through point A, path A is selected along the pipeline, and Mises stress along the path A with different slip amount is plotted as Figure 3. It is shown that Mises stress is symmetric distributing about fault, increasing with the enlargement of slip amount. But the stress isn't symmetric while the slip amount is 0.5m because of the bending compressive stress, which is similar as pre-discussed.
Figure 3. Stress distribution of path A with different slip amount
The stress at inner and outer surface is different because of the combined effect of internal pressure and external force of soil. The crossing angle of pipeline and fault is set as 90° for an example, in order to analyze the stress distribution of the cross section of pipeline, a coordinate is determined as shown in Figure 1. The Mises stress inner and outer surface of pipeline is shown as Figure 4, the horizontal axis is the angle of location on the cross section. The different valve (angel of 0° or 360°) of inner and outer surface is small, but the absolute value is over 500MPa, higher than other regions, the pipeline has been yield in those regions. In the other side of pipeline (angle of 180°), the Mises stress is slight lower, and the pipeline is compressed in this region, so tensile stress is some certainly offset, but Mises stress inner is higher that outer surface. At upper and lower of the section (angel of 90° or 270°), Mises stress outer is higher 100MPa than inner. To summarize, because of the bending of the pipeline, the Mises stress inner and outer of pipeline is different.
L o c a t io n Figure 4. Mises stress distribution at cross section of pipeline
Set the crossing angle of pipeline and fault of 90° as example, relative displacement of cross section is plotted as Figure 5.
-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
Previous Following
Figure 5. Relative displacement of pipeline As shown in Figure 5, the pipeline moves horizontal with the soil, but vertical only about 0.05m, pipeline move upward because of the smaller load of the backfill soil. Meanwhile, elliptic phenomenon of pipeline is obvious because of transverse shear of soil. The pipeline is horizontal compressed seriously by soil, so the radial displacement of the cross section is obvious horizontal but slightly vertical. Radial Displacement along Cross Section is plotted as Figure 6. It is shown that radial displacement is about -7.5mm horizontal and 5.3mm vertical. According to strain based design criterion in DNV-OS-F101, ellipticity limit of pipeline is 3%, in this calculation examples, the ellipticity is expressed as
max min
max min
670.54 645.12 2 3.87% 3.0%670.54 645.1
D DD Dθ
− −⎛ ⎞ ⎛ ⎞Δ = = = >⎜ ⎟⎜ ⎟+ +⎝ ⎠⎝ ⎠
Where θΔ is ellipticity, maxD is maximum diameter of pipeline, and minD is minimum diameter of pipeline. The ellipticity in the example has exceeded the design limit in DNV-OS-F101, so in the pipeline design, ellipticity of pipeline subjected to fault movement need to be considered.
The crossing angle of pipeline and fault plays an important role to pipeline' damage. Pipeline may fail with tension rupture or buckling failure, according to the change of crossing angle, so scholars home and abroad have done a lot of research on the crossing angle. When the crossing angle of pipeline and fault is less than 90°(as shown in Figure 7-a), pipeline is tensile and firstly yielded at about certainty distance from the fault plane, the yield region then rapidly extends to fault plane and finally resulting in the whole pipeline yield. When the crossing angle is about 90°, yield region retain at two side of fault plane, and pipeline is also tensile because that two fault body is separating. When the crossing angle is greater than 90°(as shown in Figure 7-b), the pipeline is compressed, pipeline yields at the besides of fault plane, and yields region retain at the same position, different from the situation when the crossing angle is less than 90°.
(a) Crossing angel: 45° (b) Crossing angel: 135°
Figure 7. Nephogram of mises stress with different slip amount In order to analyze the influence of slip amount to pipeline failure, slip amount is changed from 0.5m to 1m, Mises stress distribution of path A is shown in Figure 8. With the increasing of slip amount, Mises stress of pipeline with different crossing angle all raise correspondingly, and stress distribution become progressively symmetrical about fault plane. Under the same slip amount, the maximum Mises stress along the pipeline is least when the crossing angle is 90°, so this is the proposal crossing angle for the pipeline subjected to fault.
Figure 8. Influence of slip amount to stress distribution
When the compactness of backfill soil is changed, stress distribution of pipeline is shown in Figure 9. The constraint exerted to pipeline by soil will be changed according to the compactness of backfill soil, the maximum stress of pipeline become less with the decreasing compactness of backfill soil. So in order to improve pipeline's earthquake resistant capability, compactness of backfill soil needs to be decreased.
L o c a tio n a lo n g P ip e lin e (m ) Figure 9. Influence of backfill soil to stress distribution of pipeline
CONCLUSIONS Response analysis of buried pipelines subjected to strike-slip faults is presented and the stress distribution of pipelines under different situations is discussed. The paper also discusses the large deformation failure mode of pipelines as a hollow cylindrical shell. Some conclusions are as follows:
Axial stress of pipeline is composed of bending stress and tensile stress. Under different situation, both the bending stress and tensile stress may play an important role, so axial stress of pipeline is widely distributed correspondingly.
The crossing angle of pipeline and fault is important to the response of pipeline, the crossing angle directly determine the failure mode of pipeline. To sum up, 90° is the proposal crossing angle for the pipeline.
The pipeline is extruded and sheared by soil, the elliptic phenomenon of pipeline is obvious, and so the elliptic phenomenon should not be neglected in the pipeline design.
The compactness of backfill soil is also an important factor in the pipeline design, properly selecting of backfill soil will be propitious to improving of pipeline's earthquake resistant capability.
REFERENCES DNV-OS-F101: Submarine pipeline systems. (2000). DET NORSKE VERITAS. Kennedy, R.P., Chow, A.W. and Williamson, R.A. (1977). "Fault Movement Effects
on Buried Oil Pipeline." J. Transportation Engineering, 617-633. Liu, A.W., Zhang, S.L. and Hu, Y.X. (2002). "A Method for Analyzing Response of
Buried Pipeline due to Earthquake Fault Movement." J. Earthquake Engineering and Engineering Vibration, 22-27.
Liu, A.W., Hu, Y.X. and Zhao, F.X. (2004). "An Equivalent-Boundary Method for the Shell Analysis of Buried Pipelines under Fault Movement." J. ACTA Seismologica Sinica, 150-156.
Newmark, N.M. and Hall, W.J. (1975). "Pipeline Design to Resist Large Fault Displacement." C. Proceedings of U.S. National Conference on Earthquake Engineering. University of Michigan, Ann Arbor, 416-425.
Wang, R.L. and Yeh, Y. (1985). "Refined Seismic Analysis and Design of Buried Pipeline for Fault Movement." J. Earthquake Engineering and Structural Dynamics, 75-96.
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