تحلیل غیرخطی اثرات گسلش سطحی بر لوله های مدفون با استفاده از روش تفاضل محدود و نیوتن چندمتغیره

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی دکتری مهندسی زلزله، پژوهشکده مهندسی ژئوتکنیک، پژوهشگاه بین المللی زلزله شناسی و مهندسی زلزله، تهران، ایران

2 استادیار، پژوهشکده مهندسی ژئوتکنیک، پژوهشگاه بین المللی زلزله شناسی و مهندسی زلزله، تهران، ایران

3 استاد، پژوهشکده مدیریت خطر پذیری و بحران، پژوهشگاه بین المللی زلزله شناسی و مهندسی زلزله، تهران، ایران

چکیده

بررسی گسیختگی‌های خطوط لوله مدفون پس از وقوع زمین‌لرزه‌های شدید نشان داده است که یکی از علل عمده در خرابی‌های این سازه‌های خطی ناشی از اثر گسلش سطحی بوده است. بنابراین، در صورت طراحی و اجرای مناسب خطوط لوله مدفون، جابه‌جایی ماندگار زمین ناشی از حرکت گسل سنگ بستر موجب گسیختگی این دست از لوله‌ها نخواهد شد. به‌منظور بررسی رفتار لوله‌های مدفون در برابر جابه‌جایی ناشی از گسلش، در این مقاله یک روش عددی با ترکیب تکنیک‌های تفاضل محدود و نیوتن چند مجهولی توسعه داده شده است. روش ارائه‌شده رفتار غیرخطی لوله و فنرهای جایگزین خاک، و کرنش­های بزرگ را به‌صورت هم‌زمان در مدل تیر- فنر در نظر می‌گیرد. همچنین، به‌منظور مدل‌سازی دقیق‌تر برش، از مدل تیر تیموشنکو برای مدل‌سازی لوله استفاده شده است. اعتبارسنجی روش ارائه‌شده با نتایج یک آزمایش سانتریفیوژ و یک مدل‌سازی عددی اجزای محدود صورت گرفته است. روش ذکر شده با استفاده از یکسری پارامترهای ساده و تلاش محاسباتی پایین‌تر پاسخ‌های مناسبی را ارائه کرده است. همچنین، نتایج تأثیر عرض ناحیه گسلی روی رفتار یک لوله فولادی مدفون تحت گسلش نرمال 70 درجه در انتهای مقاله ارائه شده است. این نتایج به‌طورکلی نشان‌دهنده‌ی افزایش کرنش کششی، لنگر خمشی و انحنای لوله با کاهش عرض ناحیه گسلش بوده‌اند.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Nonlinear Analysis of the Surface Faulting Effects on the Buried Pipelines: the Application of the Combination of Finite Difference and Multivariable Methods

نویسندگان [English]

  • Hamid Tohidifar 1
  • Mojtaba Moosavi 2
  • Mohammad Kazem Jafari 3
1 Ph.D. Student, Geotechnical Engineering Research Center, International Institute of Earthquake Engineering and Seismology (IIEES), Tehran, Iran
2 Assistant Professor, Geotechnical Engineering Research Center, International Institute of Earthquake Engineering and Seismology (IIEES), Tehran, Iran
3 Professor, Earthquake Risk Management Research Center, International Institute of Earthquake Engineering and Seismology (IIEES), Tehran, Iran
چکیده [English]

In current modern cities, the use of buried pipelines in the conveying of vital fluids such as water, oil, and gas have become very important. Investigations on the behavior of the buried pipelines after the occurrence of the severe earthquakes have indicated that one of the primary sources of the failures of these kinds of linear structures were due to surface fault rupture. Therefore, if the buried pipelines are designed and implemented correctly, the permanent ground displacement due to the movement of the bedrock fault will not lead to such rupture of the pipes. On this basis, different researchers have concentrated their studies on investigating the interaction of pipe and soil during the permanent ground displacement. Due to the difficulty and cost of laboratory tests on this phenomenon, the number of available experimental data is very few. On the other hand, analytical studies have various limitations and complexities that have made it difficult for engineers to use these methods. In addition, numerical methods used to study the interaction of pipes and faults are mostly prepared for academic environments. These numerical approaches usually need the knowledge of soil or pipe advanced constitutive models and require the familiarity with mathematical parameters necessary for the convergence of the computational efforts.
In order to investigate the behavior of buried pipes against faulting displacement, in this paper, a numerical method has been developed by combining finite difference and Newton multivariable techniques. The equilibrium equation of forces in x and y directions along with the equilibrium equation of bending moment for an infinite section of the pipe under the influence of the displaced soil pressure has been obtained first. Then the system of equations for all of the discretized nodes of a pipeline has been solved using the proposed hybrid method. The proposed method simultaneously considers the nonlinear behavior of pipes, soil equivalent springs, and large strains in the beam-spring model. In addition, to more precisely assess the shear factor in the beam behavior, the Timoshenko beam model has been applied to model the pipe.
The validity of the proposed method has been performed using the results of a laboratory centrifuge test on HDPE pipe and 90° normal fault. In addition, this hybrid method is also validated with the results of a finite element numerical analysis on 70° normal fault and API5L-X65 oil transfer pipe. Comparison of the obtained results for different parameters such as longitudinal strains, settlement, and flexural bending of the pipes shows that the presented numerical method is very suitable in predicting the interaction behavior of pipes against dip-slip faults. At the same time, a lower computational effort has been required to arrive in the final answers. In addition, using the proposed numerical method, the effect of fault zone width with values equal to 0.001, 10, 30, 60, and 100 m on the behavior of a pipeline against a normal 70-degree fault has been investigated. The results of this study show that increasing the width of the fault zone significantly reduces the amount of tensile strain in the pipes. Also, increasing the width of the fault zone causes the pipe to rupture from two different points, while in the small fault width equal to 0.001 m, the pipe failure occurs only at one point. Maximum bending moment and pipe curvature also increased with decreasing fault width.

کلیدواژه‌ها [English]

  • Surface Faulting
  • Buried Pipeline
  • Numerical Modeling
  • Finite difference method
  • Multivariable Newton Method
  • Nonlinear behavior
  1. Youd, T. (1973) Ground Movements in Van Norman Lake Vicinity During San Fernando Earthquake, California Earthquake of February 9. US Department of Commerce, 197-206.
  2. Ariman, T. and Muleski, G.E. (1981) A review of the response of buried pipelines under seismic excitations. Earthquake Engineering and Structural Dynamics, 9, 133-152.
  3. Oka, S. and O'Rourke, T. (1996) Damage of gas facilities by great Hanshin earthquake and restoration process.  Japan-US Workshop on Earthquake Resistant Design of Lifeline Facilities and Countermeasures Against Soil Liquefaction, 6, National Center for Earthquake Engineering Research, 111-126.
  4. O'Rourke, M.J. and Liu, X. (2012) Seismic Design of Buried and Offshore Pipelines, Buffalo, NY, USA. Multidisciplinary Center for Earthquake Engineering Research, University at Buffalo.
  5. Miyajima, M. and Hashimoto, T. (2001) Damage to water supply system and surface rupture due to fault movement during the 1999 Ji-Ji earthquake in Taiwan. Fourth International Conference on Recent Advances in Geotechnical Earthqauke Engineering and Soil Dynamics, University of Missouri-Rolla, Paper No. 10-45.
  6. Kim, J., Nadukuru, S.S., Pour-Ghaz, M., Lynch, J.P., Michalowski, R.L., Bradshaw, A.S., Green, R.A., and Weiss W.J. (2012) Assessment of the behavior of buried concrete pipelines subjected to ground rupture: experimental study. Journal of Pipeline Systems Engineering and Practice, 3, 8-16.
  7. O'rourke, T.D. (2010) Geohazards and large, geographically distributed systems. Géotechnique, 60, 505-543.
  8. Wham, B.P., Argyrou, C., O'Rourke, T.D., Stewart, H.E., and Bond T.K. (2016) PVCO pipeline performance under large ground deformation. Journal of Pressure Vessel Technology, 139,  011702-011708.
  9. Saiyar, M., Ni, P., Take, W., and Moore, I. (2016) Response of pipelines of differing flexural stiffness to normal faulting. Géotechnique, 66, 275-286.
  10. Ha, D., Abdoun, T.H., O’Rourke, M.J., Symans, M.D., O’Rourke, T.D., Palmer, M.C., and Stewart, H.E. (2008) Centrifuge modeling of earthquake effects on buried high-density polyethylene (HDPE) pipelines crossing fault zones. Journal of Geotechnical and Geoenvironmental Engineering, 134, 1501-1515.
  11. Ni, P., Moore, I., and Take, W. (2017) Distributed fibre optic sensing of strains on buried full-scale PVC pipelines crossing a normal fault. Géotechnique, 68, 1-17.
  12. Rojhani, M., Moradi, M., Galandarzadeh, A., and Takada, S. (2012) Centrifuge modeling of buried continuous pipelines subjected to reverse faulting. Canadian Geotechnical Journal, 49, 659-670.
  13. Karamitros, D., Bouckovalas, G., Kouretzis, G., and Gkesouli, V. (2011) An analytical method for strength verification of buried steel pipelines at normal fault crossings. Soil Dynamics and Earthquake Engineering, 31, 1452-1464.
  14. Karamitros, D.K., Bouckovalas, G.D., and Kouretzis, G.P. (2007) Stress analysis of buried steel pipelines at strike-slip fault crossings. Soil Dynamics and Earthquake Engineering, 27, 200-211.
  15. Newmark, N.M. and Hall, W.J. (1975) Pipeline design to resist large fault displacement. Proceedings of US National Conference on Earthquake Engineering, 416-425.
  16. Kennedy, R.P., Chow, A., and Williamson, R.A. (1977) Fault movement effects on buried oil pipeline. Transportation Engineering Journal of the American Society of Civil Engineers, 103, 617-633.
  17. Trifonov, O.V. and Cherniy, V.P. (2010) A semi-analytical approach to a nonlinear stress–strain analysis of buried steel pipelines crossing active faults. Soil Dynamics and Earthquake Engineering, 30, 1298-1308.
  18. Wang, L.R.-L. and Yeh, Y.-H. (1985) A refined seismic analysis and design of buried pipeline for fault movement. Earthquake Engineering & Structural Dynamics, 13, 75-96.
  19. Melissianos, V.E. and Gantes, C.J. (2017) Numerical modeling aspects of buried pipeline-fault crossing. Computational Methods in Earthquake Engineering, Springer, 1-26.
  20. Joshi, S., Prashant, A., Deb, A., and Jain, S.K. (2011) Analysis of buried pipelines subjected to reverse fault motion. Soil Dynamics and Earthquake Engineering, 31, 930-940.
  21. Ni, P., Moore, I.D., and Take, W.A. (2018) Numerical modeling of normal fault-pipeline interaction and comparison with centrifuge tests. Soil Dynamics and Earthquake Engineering, 105,  127-138.
  22. Xie, X., Symans, M.D., O'Rourke, M.J., Abdoun, T.H., O'Rourke, T.D., Palmer, M.C., and Stewart, H.E. (2013) Numerical modeling of buried HDPE pipelines subjected to normal faulting: a case study. Earthquake Spectra, 29, 609-632.
  23. Rofooei, F.R., Jalali, H.H., Attari, N.K.A., Kenarangi, H., and Samadian, M. (2015) Parametric study of buried steel and high density polyethylene gas pipelines due to oblique-reverse faulting. Canadian Journal of Civil Engineering, 42, 178-189.
  24. Jalali, H.H., Rofooei, F.R., Attari, N.K.A., and Samadian, M. (2016) Experimental and finite element study of the reverse faulting effects on buried continuous steel gas pipelines. Soil Dynamics and Earthquake Engineering, 86, 1-14.
  25. Erami, M.H., Miyajima, M., Kaneko, S., Toshima, T., and Kishi, S. (2015) Pipe–soil interaction for segmented buried pipelines subjected to dip faults. Earthquake Engineering and Structural Dynamics, 44, 403-417.
  26. ALA (2005) Seismic Guidelines for Water Pipelines. American Lifelines Alliance.
  27. ASCE (1984) Guidelines for the Seismic Design of Oil and Gas Pipeline Systems. American Society of Civil Engineers, Committee on Gas Liquid Fuel Lifelines.
  28. Demirci, H.E., Bhattacharya, S., Karamitros, D., and Alexander, N. (2018) Experimental and numerical modelling of buried pipelines crossing reverse faults. Soil Dynamics and Earthquake Engineering, 114,  198-214.
  29. Tohidifar, H., Jafari, M.K., and Moosavi, M. (2020) Downwards force-displacement response of buried pipelines during dip-slip faulting in sandy soil. Canadian Geotechnical Journal, 58(3), 377-397.
  30. Timoshenko, S.P. and Gere J.M. (2009) Theory of Elastic Stability. Courier Corporation.
  31. Gere, J. and Timoshenko, S. (1997) Mechanics of Materials. PWS-KENT Publishing Company.
  32. Wierzbicki, T. (2013) 2.080J Structural Mechanics, in, MIT OpenCourseWare, Massachusetts Institute of Technology.
  33. Timoshenko, S.P. (1921) LXVI. On the correction for shear of the differential equation for transverse vibrations of prismatic bars. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 41, 744-746.
  34. Hosseini-Ara, R., Mirdamadi, H.R., Khademyzadeh, H., and Mostolizadeh, R. (2012) Stability analysis of carbon nanotubes based on a novel beam model and its comparison with Sanders shell model and molecular dynamics simulations. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 34, 126-134.
  35. Cowper, G.R. (1966) The shear coefficient in timoshenko’s beam theory. Journal of Applied Mechanics, 33,  335-340.
  36. Ha, D., Abdoun, T.H., O’Rourke, M.J., Symans, M.D., O’Rourke, T.D., Palmer, M.C., and Stewart, H.E. (2008) Buried high-density polyethylene pipelines subjected to normal and strike-slip faulting—a centrifuge investigation. Canadian Geotechnical Journal, 45,  1733-1742.
  37. Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P. (2007) Numerical Recipes 3rd Edition: The Art of Scientific Computing. Cambridge University Press.