Elastic Buckling of Thin-Walled Liners Encased in Partially Grouted Pipelines under External Pressure
Publication: Journal of Structural Engineering
Volume 146, Issue 4
Abstract
In this study, the pressure-displacement equilibrium path and the elastic buckling pressure were formulated analytically for a thin-walled circular liner encased in a partially grouted pipeline–liner system. Numerical verification was conducted in the plane strain condition assuming a frictionless interface between the pipeline and the liner. Nonlinear equilibrium equations were developed to obtain the theoretical solutions by employing the principle of minimum potential energy and admissible displacement functions of the liner selected for different pipeline–liner contact conditions. The external pressure increases proportionally with displacement to an initial limit when the liner is not restrained by the pipeline, varies slightly to a lower bound due to geometrical nonlinearity, suddenly increases again to the critical buckling due to pipeline confinement, and finally decreases rapidly in the postbuckling stage. The confinement effect on the buckling pressure of the liner, defined by a ratio of the critical and initial pressures, decreases with an increase of void thickness between the liner and the pipeline. The analytical solution in critical buckling pressure differed from the numerical result by less than 6%. Both the analytical and numerical predictions were consistent with other available closed-form solutions in special cases.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
Financial support for this study was provided in part by the Department of Civil, Architectural, and Environmental Engineering through Robert W. Abbett endowment funds.
References
Allen, H. G., and P. S. Bulson. 1980. Background to buckling. London: McGraw-Hill.
Bakeer, R. M., M. E. Barber, S. E. Pechon, J. E. Taylor, and S. Chunduru. 1999. “Buckling of HDPE liners under external uniform pressure.” J. Mater. Civ. Eng. 11 (4): 353–361. https://doi.org/10.1061/(ASCE)0899-1561(1999)11:4(353).
Boot, J. C. 1998. “Elastic buckling of cylindrical pipe linings with small imperfections subjected to external pressure.” Tunnelling Underground Space Technol. 12 (1): 3–15. https://doi.org/10.1016/S0886-7798(98)00018-2.
Boot, J. C., A. A. Javadi, and I. L. Torpova. 2004. “The structural performance of polymeric linings for nominally cylindrical gravity pipes.” Thin Walled Struct. 42 (8): 1139–1160. https://doi.org/10.1016/j.tws.2004.03.004.
Boot, J. C., M. M. Naqvi, and J. E. Gumbel. 2014. “A new method for the structural design of flexible liners for gravity pipes of egg-shaped cross section: Theoretical considerations and formulation of the problem.” Thin Walled Struct. 85 (Dec): 411–418. https://doi.org/10.1016/j.tws.2014.09.001.
Chang, C. S., and D. H. Hodges. 2009. “Stability studies for curved beams.” J. Mech. Mater. Struct. 4 (7–8): 1257–1270. https://doi.org/10.2140/jomms.2009.4.1257.
Chunduru, S., M. E. Barber, and R. M. Bakeer. 1996. “Buckling behavior of polyethylene liner system.” J. Mater. Civ. Eng. 8 (4): 201–206. https://doi.org/10.1061/(ASCE)0899-1561(1996)8:4(201).
El-Sawy, K., and I. D. Moore. 1998. “Stability of loosely fitted liners used to rehabilitate rigid pipes.” J. Struct. Eng. 124 (11): 1350–1357. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:11(1350).
Glock, D. 1977. “Überkritisches Verhalten eines starr ummautelten Kreisrohres bei Wasserdruck von aussen und Temperaturdehnung. (Critical behavior of liners of rigid pipeline under external water pressure and thermal expansion.)” [In German.] Der Stahlbau 46 (7): 212–217.
Guo, Z., D. S. Jeng, H. Zhao, W. Guo, and L. Wang. 2019. “Effect of seepage flow on sediment incipient motion around a free spanning pipeline.” Coast. Eng. 143 (Jan): 50–62. https://doi.org/10.1016/j.coastaleng.2018.10.012.
Kang, Y. J., and C. H. Yoo. 1994. “Thin-walled curved beams. II: Analytical solutions for buckling of arches.” J. Eng. Mech. 120 (10): 2102–2125. https://doi.org/10.1061/(ASCE)0733-9399(1994)120:10(2102).
Karnovsky, I. A. 2012. Theory of arches structures. New York: Springer.
Li, K., Z. Guo, L. Wang, and H. Jiang. 2019a. “Effect of seepage flow on shields number around a fixed and sagging pipeline.” Ocean Eng. 172 (Jan): 487–500. https://doi.org/10.1016/j.oceaneng.2018.12.033.
Li, Z., F. Tang, Y. Chen, Y. Tang, and G. Chen. 2019b. “Elastic and inelastic buckling of thin-walled steel liners encased in circular host pipes under external pressure and thermal effects.” Thin Walled Struct. 137 (Apr): 213–223. https://doi.org/10.1016/j.tws.2018.12.044.
Li, Z., F. Tang, Y. Chen, and J. Zheng. 2019c. “Material distribution optimization of functionally graded arch subjected to external pressure under temperature rise field.” Thin Walled Struct. 138 (May): 64–78. https://doi.org/10.1016/j.tws.2019.01.034.
Li, Z., Y. Tang, F. Tang, Y. Chen, and G. Chen. 2018. “Elastic buckling of thin-walled polyhedral pipe liners encased in a circular pipe under uniform external pressure.” Thin Walled Struct. 123 (Feb): 214–221. https://doi.org/10.1016/j.tws.2017.11.019.
Li, Z., L. Wang, Z. Guo, and H. Shu. 2012. “Elastic buckling of cylindrical pipe linings with variable thickness encased in rigid host pipes.” Thin Walled Struct. 51 (Feb): 10–19. https://doi.org/10.1016/j.tws.2011.11.003.
Li, Z., J. Zheng, and Y. Chen. 2019d. “Nonlinear buckling of thin-walled FGM arch encased in a rigid confinement subjected to external pressure.” Eng. Struct. 186 (May): 86–95. https://doi.org/10.1016/j.engstruct.2019.02.019.
Li, Z., J. Zheng, Q. Sun, and H. He. 2019e. “Nonlinear structural stability performance of pressurized thin-walled FGM arches under temperature variation field.” Int. J. Non Linear Mech. 113 (Jul): 86–102. https://doi.org/10.1016/j.ijnonlinmec.2019.03.016.
Omara, A. M., L. K. Guice, W. T. Straughan, and F. A. Akl. 1997. “Buckling models of thin circular pipes encased in rigid cavity.” J. Eng. Mech. 123 (12): 1294–1301. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:12(1294).
Omara, A. M., L. K. Guice, W. T. Straughan, and F. A. Akl. 2000. “Instability of thin pipes encased in oval rigid cavity.” J. Eng. Mech. 126 (4): 381–388. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:4(381).
Pi, Y. L., and M. A. Bradford. 2010. “Nonlinear in-plane elastic buckling of shallow circular arches under uniform radial and thermal loading.” Int. J. Mech. Sci. 52 (1): 75–88. https://doi.org/10.1016/j.ijmecsci.2009.10.011.
Rueda, F., A. Marquez, J. L. Otegui, and P. M. Frontini. 2016. “Buckling collapse of HDPE liners: Experimental set-up and FEM simulations.” Thin Walled Struct. 109 (Dec): 103–112. https://doi.org/10.1016/j.tws.2016.09.011.
Rueda, F., J. P. Torres, M. Machado, P. M. Frontini, and J. L. Otegui. 2015. “External pressure induced buckling collapse of high density polyethylene (HDPE) liners: FEM modeling and predictions.” Thin Walled Struct. 96 (Nov): 56–63. https://doi.org/10.1016/j.tws.2015.04.035.
Simitses, G. J., and D. H. Hodges. 2006. Fundamentals of structural stability. New York: Elsevier.
Timoshenko, S. P., and J. M. Gere. 1961. Theory of elastic stability. 2nd ed. New York: McGraw-Hill.
Vasilikis, D., and S. A. Karamanos. 2009. “Stability of confined thin walled steel cylinders under external pressure.” Int. J. Mech. Sci. 51 (1): 21–32. https://doi.org/10.1016/j.ijmecsci.2008.11.006.
Wang, J. H., and A. Koizumi. 2017. “Experimental investigation of buckling collapse of encased liners subjected to external water pressure.” Eng. Struct. 151 (Nov): 44–56. https://doi.org/10.1016/j.engstruct.2017.08.008.
Wang, J. H., A. Koizumi, and D. J. Yuan. 2016. “Theoretical and numerical analyses of hydrostatic buckling of a noncircular composite liner with arched invert.” Thin Walled Struct. 102 (May): 148–157. https://doi.org/10.1016/j.tws.2016.01.021.
Wang, J. H., M. Nakano, Z. H. Shi, and A. Koizumi. 2013. “Buckling of encased liner under external pressure and the effects of voids in backfilling grout.” In Vol. 3 of Shell Structures: Theory and Applications-Proc., 10th SSTA 2013 Conf., 259–262. London: CRC Press.
Information & Authors
Information
Published In
Copyright
©2020 American Society of Civil Engineers.
History
Received: Jul 9, 2018
Accepted: Sep 3, 2019
Published online: Feb 7, 2020
Published in print: Apr 1, 2020
Discussion open until: Jul 7, 2020
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.