Technical Notes
Jul 11, 2022

Buried Pipeline Subjected to Underground Blast Load: Closed-Form Analytical Solution

Publication: International Journal of Geomechanics
Volume 22, Issue 9

Abstract

The current study derives a closed-form analytical solution of buried pipeline subjected to underground blast load. The solution is derived considering Euler Bernoulli’s beam resting on viscoelastic foundation. In viscoelastic foundation, shear interactions between individual Winkler springs are considered. Soil pressure on the pipeline resulting from the self-weight of the soil above the buried pipeline is also incorporated in the present analysis. The finite sine–Fourier transform is employed to obtain the solution for the governing differential equation. The proposed formulation is validated with the results obtained from the past centrifuge model test, finite-element-based three-dimensional (3D) numerical analysis and simplified analytical study. Further, a parametric study is performed to obtain the impact of trinitrotoluene (TNT) charge weight, standoff distance, damping ratio, and flexural rigidity of the pipe-on-pipe response. From the results of the parametric study, it is noticed that peak pipe deformation increases with increasing the TNT charge weight and decreases with increasing the magnitude of standoff distance, damping ratio, and flexural rigidity of the pipe. The proposed formulation can be adopted in the initial design stage for rapid estimation of buried pipe responses subjected to underground blast load.

Get full access to this article

View all available purchase options and get full access to this article.

Data Availability Statement

Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request (MATLAB code).

References

Abedi, A. S., and N. Hataf. 2019. “Analytical solution of the dynamic response of piles under blast waves.” Iran. J. Sci. Technol. Trans. Civ. Eng. 43 (4): 727–734. https://doi.org/10.1007/s40996-018-0216-y.
Abedi, A. S., N. Hataf, and A. Ghahramani. 2016. “Analytical solution of the dynamic response of buried pipelines under blast wave.” Int. J. Rock Mech. Min. Sci. 88: 301–306. https://doi.org/10.1016/j.ijrmms.2016.07.014.
ALA (American Lifelines Alliance). 2001. Guidelines for the design of buried steel pipe. Reston, VA: ASCE, (with addenda through February 2005).
Basu, D., and N. S. V. Kameswara Rao. 2013. “Analytical solutions for Euler-Bernoulli beam on visco-elastic foundation subjected to moving load.” Int. J. Numer. Anal. Methods Geomech. 37 (8): 945–960. https://doi.org/10.1002/nag.1135.
Bulson, P. S. 2003. Explosive loading of engineering structures. London: Taylor & Francis.
Chakraborty, T. 2016. “Analysis of hollow steel piles subjected to buried blast loading.” Comput. Geotech. 78: 194–202. https://doi.org/10.1016/j.compgeo.2016.05.015.
Chaudhuri, C. H., and D. Choudhury. 2020a. “Effect of earthquake induced transverse permanent ground deformation on buried continuous pipeline using winkler approach.” In Geo-Congress 2020: Geotechnical Earthquake Engineering and Special Topics, Geotechnical Special Publication 318, edited by J. P. Hambleton, R. Makhnenko, and A. S. Budge, 274–283. Reston, VA: ASCE.
Chaudhuri, C. H., and D. Choudhury. 2020b. “Buried pipeline subjected to seismic landslide: A simplified analytical solution.” Soil Dyn. Earthquake Eng. 134: 106155. https://doi.org/10.1016/j.soildyn.2020.106155.
Chaudhuri, C. H., and D. Choudhury. 2021a. “Semi-analytical solution for buried pipeline subjected to horizontal transverse ground deformation.” J. Pipeline Syst. Eng. Pract. 12 (4): 04021038. https://doi.org/10.1061/(ASCE)PS.1949-1204.0000541.
Chaudhuri, C. H., and D. Choudhury. 2021b. “Buried pipeline subjected to static pipe bursting underneath: A closed-form analytical solution.” Géotechnique 1–10. https://doi.org/10.1680/jgeot.20.p.167.
De, A., A. Niemiec, and T. F. Zimmie. 2017. “Physical and numerical modeling to study effects of an underwater explosion on a buried tunnel.” J. Geotech. Geoenviron. Eng. 143 (5): 04017002. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001638.
De, A., and T. F. Zimmie. 2006. “Modeling of surface blast effects on underground structures.” In GeoCongress 2006: Geotechnical Engineering in the Information Technology Age, edited by D. J. DeGroot, J. T. DeJong, D. Frost, and L. G. Baise. Reston, VA: ASCE.
De, A., T. F. Zimmie, and K. E. Vamos. 2005. “Centrifuge experiments to study surface blast effects on underground pipelines.” In Pipelines 2005: Optimizing Pipeline Design, Operations, and Maintenance in Today’s Economy, edited by C. Vipulanandan and R. Ortega, 362–370. Reston, VA: ASCE.
Jayasinghe, L. B., D. P. Thambiratnam, N. Perera, and J. H. A. R. Jayasooriya. 2013. “Computer simulation of underground blast response of pile in saturated soil.” Comput. Struct. 120: 86–95. https://doi.org/10.1016/j.compstruc.2013.02.016.
Jayasinghe, L. B., H. Y. Zhou, A. T. C. Goh, Z. Y. Zhao, and Y. L. Gui. 2017. “Pile response subjected to rock blasting induced ground vibration near soil-rock interface.” Comput. Geotech. 82: 1–15. https://doi.org/10.1016/j.compgeo.2016.09.015.
Jiang, N., T. Gao, C. Zhou, and X. Luo. 2018. “Effect of excavation blasting vibration on adjacent buried gas pipeline in a metro tunnel.” Tunnelling Underground Space Technol. 81: 590–601. https://doi.org/10.1016/j.tust.2018.08.022.
Kangarlou, K. 2013. “Mechanics of blast loading on the head models in the study of traumatic brain injury.” Nationalpark-Forschung In Der Schweiz (Switz. Res. Park J.) 102 (11): 1571–1581.
Karlos, V., and G. Solomos. 2013. Calculation of blast loads for application to structural components. Luxembourg: Publications Office of the European Union.
Kumar, R., D. Choudhury, and K. Bhargava. 2014. “Response of shallow foundation in rocks subjected to underground blast loading using FLAC3D.” Disaster Adv. 7 (2): 64–71.
Muleski, G. E., and T. Ariman. 1985. “A shell model for buried pipes in earthquakes.” Int. J. Soil Dyn. Earthquake Eng. 4 (1): 43–51. https://doi.org/10.1016/0261-7277(85)90035-X.
Nourzadeh, D., S. Takada, and K. Bargi. 2010. “Response of buried pipelines to underground blast loading.” In Proc., 5th Civil Engineering Conf., in the Asian Region and Australasian Structural Engineering Conf., 233. Barton, ACT, Australia: Engineers Australia.
Roy, J., A. Kumar, and D. Choudhury. 2018. “Natural frequencies of piled raft foundation including superstructure effect.” Soil Dyn. Earthquake Eng. 112: 69–75. https://doi.org/10.1016/j.soildyn.2018.04.048.
Shim, H. 1996. “Response of piles in saturated soil under blast loading.” Ph.D. thesis, Dept. of Civil, Environmental, and Architectural Engineering, Univ. of Colorado.
Smith, P., and J. Hetherington. 1994. Blast and ballistic loading of structures. London: Taylor & Francis.
Sun, L. 2001. “A closed-form solution of a Bernoulli-Euler beam on a viscoelastic foundation under harmonic line loads.” J. Sound Vib. 242 (4): 619–627. https://doi.org/10.1006/jsvi.2000.3376.
Sun, L. 2002. “A closed-form solution of beam on viscoelastic subgrade subjected to moving loads.” Comput. Struct. 80 (1): 1–8. https://doi.org/10.1016/S0045-7949(01)00162-6.
Sun, L. 2003. “An explicit representation of steady state response of a beam on an elastic foundation to moving harmonic line loads.” Int. J. Numer. Anal. Methods Geomech. 27 (1): 69–84. https://doi.org/10.1002/nag.263.
Tiwari, R., T. Chakraborty, and V. Matsagar. 2017. “Dynamic analysis of tunnel in soil subjected to internal blast loading.” Geotech. Geol. Eng. 35 (4): 1491–1512. https://doi.org/10.1007/s10706-017-0189-9.
Tiwari, R., T. Chakraborty, and V. Matsagar. 2020. “Analysis of curved tunnels in soil subjected to internal blast loading.” Acta Geotech. 15 (2): 509–528. https://doi.org/10.1007/s11440-018-0694-x.
Wang, L., J. Ma, Y. Zhao, and Q. Liu. 2013. “Refined modeling and free vibration of inextensional beams on the elastic foundation.” J. Appl. Mech. 80 (4): 041026. https://doi.org/10.1115/1.4023032.
Wu, Y., and Y. Gao. 2015. “Analytical solutions for simply supported viscously damped double-beam system under moving harmonic loads.” J. Eng. Mechanics. 141 (7): 04015004. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000900.
Yin, J.-H. 2000. “Comparative modeling study of reinforced beam on elastic foundation.” J. Geotech. Geoenviron. Eng. 126 (3): 265–271. https://doi.org/10.1061/(ASCE)1090-0241(2000)126:3(265).
Yu, H., C. Cai, Y. Yuan, and M. Jia. 2017. “Analytical solutions for Euler-Bernoulli beam on pasternak foundation subjected to arbitrary dynamic loads.” Int. J. Numer. Anal. Methods Geomech. 41 (8): 1125–1137. https://doi.org/10.1002/nag.2672.
Zhang, J., H. Zhang, L. Zhang, and Z. Liang. 2020. “Buckling response analysis of buried steel pipe under multiple explosive loadings.” J. Pipeline Syst. Eng. Pract. 11 (2): 04020010. https://doi.org/10.1061/(ASCE)PS.1949-1204.0000431.
Zhaohua, F., and R. D. Cook. 1983. “Beam elements on two-parameter elastic foundations.” J. Eng. Mech. 109 (6): 1390–1402. https://doi.org/10.1061/(ASCE)0733-9399(1983)109:6(1390).

Information & Authors

Information

Published In

Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 22Issue 9September 2022

History

Received: Jun 30, 2021
Accepted: Mar 7, 2022
Published online: Jul 11, 2022
Published in print: Sep 1, 2022
Discussion open until: Dec 11, 2022

Permissions

Request permissions for this article.

Authors

Affiliations

Ph.D. Research Scholar, Dept. of Civil Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India. ORCID: https://orcid.org/0000-0003-2434-9461. Email: [email protected]
Prof. T. Kant Chair Professor and Head, Dept. of Civil Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India (corresponding author). ORCID: https://orcid.org/0000-0002-2331-7049. Email: [email protected]

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.

Cited by

  • Dual-Beam Mathematical Model for Mechanical Response of Buried Pipeline and Pavement Structures Subjected to Ground Subsidence, Journal of Pipeline Systems Engineering and Practice, 10.1061/JPSEA2.PSENG-1462, 14, 4, (2023).
  • Mechanical Analyses of Underground Pipelines Subjected to Ground Subsidence Considering Soil-Arching Effect, Journal of Pipeline Systems Engineering and Practice, 10.1061/JPSEA2.PSENG-1405, 14, 2, (2023).
  • Upheaval Buckling Resistance of Pipelines Buried in Unsaturated Clay Backfills, International Journal of Geomechanics, 10.1061/IJGNAI.GMENG-7546, 23, 5, (2023).
  • Dynamic analysis of buried pipeline with and without barrier system subjected to underground detonation, Defence Technology, 10.1016/j.dt.2023.02.017, (2023).

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share