Skip to main content
Log in

Seismic Vulnerability Assessment of an Unanchored Circular Storage Tank Against Elephant’s Foot Buckling

  • Original Paper
  • Published:
Journal of Vibration Engineering & Technologies Aims and scope Submit manuscript



Seismic vulnerability assessment of liquid containing storage tanks is the most vital relevance for industrial plants and society safety to endure damage during impending earthquakes. Because such systems also play an essential role in the public lifeline and also ensure continued use in emergencies. Furthermore, considering that the material contained in individual plants could be hazardous, requisite precautions have paramount importance against undesired leakage. The high internal pressure and axial forces exerted by the liquid in the steel tanks near the tank wall bottom produce elastic–plastic buckling, also known as Elephant’s Foot Buckling (EFB). As far as the authors are aware, no study has been carried out that involves a critical assessment and comparison of IDA and truncated IDA-based EFB failure criterion. This study provides insight into incremental dynamic analysis (IDA) and truncated IDA-based seismic evaluation of cylindrical unanchored steel storage tanks by employing a developed pressure-based surrogate modeling approach. For this purpose, probability-based seismic assessment of a representative sample is considered based on IDA and truncated IDA approaches to identify the potential of the EFB failure and to explore potential enhancements in the sophisticated structural analysis model to prevent the hazardous effects of impending earthquakes.


Due to the significance of industrial plants for public safety and benefit, the structural response evaluation methods for different types of storage tanks have been widely reported. In the literature, the most comprehensive analytical assessment methodology is the IDA approach, in which nonlinear time-history analyses are considered in the finite element analysis model to assess the structural model’s seismic performance.


To generate fragility curves, both IDA approaches are employed, taking into consideration and ignoring uncertainty of material properties. The values of the two methods-based fragility curves approach each other as the magnitude of dispersion increases.


The two fragility curves give the probability of failures close to each other as the dispersion amount increases while considering the uncertainty of the material properties. In addition, fragility curves generated based on the truncated IDA have been found to give a higher probability of failure, up to 32.5 percent. When compared to the IDA-based fragility curves, the truncated IDA-based fragility curves were found to be on the conservative side.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others


  1. Bektaş N (2020) Reliability based seismic assessment of unanchored circular steel storage tanks (MSc Thesis). Izmir Institute of Technology

    Google Scholar 

  2. Chen JZ (2010) Generalized sdof system for dynamic analysis of concrete rectangular liquid storage tanks (PhD Thesis). Ryerson University

    Google Scholar 

  3. Christovasilis IP (2006) Seismic analysis of liquefied natural gas tanks (MSc Thesis). State University of New York, Buffalo

    Google Scholar 

  4. D’Amico M (2018) Seismic fragility and dynamic behavior of atmospheric cylindrical steel tanks (PhD Thesis). University of Bologna, Bologna

    Google Scholar 

  5. Yazıcı G (2008) Sismik yalıtımlı düşey silindirik sıvı depolarının deprem yükleri altındaki davranışının incelenmesi (PhD Thesis). Istanbul Technical University

    Google Scholar 

  6. Rammerstorfer FG, Scharf K, Fisher FD (1990) Storage tanks under earthquake loading. Appl Mech Rev 43(11):261–282

    Article  Google Scholar 

  7. Uckan E, Akbas B, Paolacci F, Shen J, Abalı E (2015) Earthquake protection of liquid storage tanks by sliding isolation bearings. In: Proceedings of the ASME 2015 Pressure Vessels and Piping Conference. Volume 8: Seismic Engineering. Boston, Massachusetts, USA. V008T08A008. ASME.

    Book  Google Scholar 

  8. API 650 (2007) Welded steel tanks for oil storage, 11th edn. American Petroleum Institute.

    Google Scholar 

  9. CEN (European Committee for Standardization) (2006) EN 1998-4 Eurocode 8: design of structures for earthquake resistance—Part 4: Silos, tanks and pipelines. European Committee for Standardization, Belgium

  10. New Zealand Society for Earthquake Engineering (NZSEE) (2009) Seismic design of storage tanks. Recommendations of a study group of the New Zealand Society for Earthquake Engineering, New Zealand Society for Earthquake Engineering, Wellington, New Zealand

  11. American Lifelines Alliance (ALA) (2001) Seismic fragility formulations for water systems: Part 1—guideline. American Society of Civil Engineers (ASCE), Federal Emergency Management Agency (FEMA)

    Google Scholar 

  12. American Lifelines Alliance (ALA) (2001) Seismic fragility formulations for water systems: Part 2—appendices. American Society of Civil Engineers (ASCE), Federal Emergency Management Agency (FEMA)

    Google Scholar 

  13. Phan HN, Paolacci F and Alessandri S (2016) Fragility analysis methods for steel storage tanks in seismic prone areas. In: ASME 2016 Pressure Vessels and Piping Conference (p. 9). Vancouver, British Columbia, Canada.

  14. Colombo JI, Almazán JL (2019) Simplified 3D model for the uplift analysis of liquid storage tanks. Eng Struct 196:109278.

    Article  Google Scholar 

  15. Malhotra PK (2010) Seismic analysis of structures and equipment. Springer.

  16. Hernandez-Hernandez D, Larkin T, Chouw N (2021) Impact of the excitation frequencies on wall stresses in a storage tank. Eng Struct 244:112775.

    Article  Google Scholar 

  17. Phan HN, Paolacci F, Nguyen VM, Hoang PH (2021) Ground motion intensity measures for seismic vulnerability assessment of steel storage tanks with unanchored support conditions. J Pressure Vessel Technol 143(6):061904.

    Article  Google Scholar 

  18. Vathi M and Karamanos SA (2015) Effects of base uplifting on the seismic response of unanchored liquid storage tanks. In Pressure Vessels and Piping Conference. 55072:183–190. American Society of Mechanical Engineers.

  19. Hernandez-Hernandez D, Larkin T and Chouw N (2019) Simultaneous effect of uplift and soil-structure interaction on seismic performance of storage tanks. In: VII International Conference on Eartquake Geotechnical Engineering. Rome, Italy, pp 2851–2858

  20. Ozdemir Z, Souli M, Fahjan YM (2010) Application of nonlinear fluid–structure interaction methods to seismic analysis of anchored and unanchored tanks. Eng Struct 32(2):409–423.

    Article  Google Scholar 

  21. Ormeño M, Larkin T, Chouw N (2015) The effect of seismic uplift on the shell stresses of liquid-storage tanks. Earthquake Eng Struct Dynam 44(12):1979–1996.

    Article  Google Scholar 

  22. Bakalis K, Vamvatsikos D, Fragiadakis M (2017) Seismic risk assessment of liquid storage tanks via a nonlinear surrogate model. Earthquake Eng Struct Dynam 46(15):2851–2868.

    Article  Google Scholar 

  23. Ormeño M, Larkin T, Chouw N (2019) Experimental study of the effect of a flexible base on the seismic response of a liquid storage tank. Thin-Walled Struct 139:334–346.

    Article  Google Scholar 

  24. Hernandez-Hernandez D, Larkin T, Chouw N (2021) Shake table investigation of nonlinear soil–structure–fluid interaction of a thin-walled storage tank under earthquake load. Thin-Walled Struct 167:108143.

    Article  Google Scholar 

  25. Ghaemmaghami A (2010) Dynamic time-history response of concrete rectangular liquid storage tanks (PhD Thesis). Ryerson University, Toronto, Canada.

    Google Scholar 

  26. Systèmes D (2019) Abaqus analysis user’s manual. Simulia Corp, Providence

    Google Scholar 

  27. Karim AA (2008) Vibration analysis of circular cylindrical liquid storage tanks using finite element technique (PhD Thesis). University of Basrah

    Google Scholar 

  28. Phan HN, Paolacci F, Alessandri S (2019) Enhanced seismic fragility analysis of unanchored steel storage tanks accounting for uncertain modeling parameters. J Pressure Vessel Technol.

    Article  Google Scholar 

  29. Sobhan MS, Rofooei FR, Attari NKA (2017) Buckling behavior of the anchored steel tanks under horizontal and vertical ground motions using static pushover and incremental dynamic analyses. Thin-Walled Struct 112:173–183.

    Article  Google Scholar 

  30. Phan HN, Paolacci F, Corritore D, Alessandri S (2018) Seismic vulnerability analysis of storage tanks for oil and gas industry. Pipeline Sci Technol 2(1):55–65.

    Article  Google Scholar 

  31. Erkmen B (2017) Evaluation of code provisions for seismic performance of unachored liquid storage tanks. In: COMPDYN 2017—Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, pp 1700–1710. Rhodes island.

  32. Ormeno M, Larkin T, Chouw N (2012) Influence of uplift on liquid storage tanks during earthquakes. Coupled Syst Mech 1(4):311–324.

    Article  Google Scholar 

  33. Di Carluccio A, Fabbrocino G (2012) Some remarks on the seismic demand estimation in the context of vulnerability assessment of large steel storage tank facilities. ISRN Civ Eng 1–12.

    Article  Google Scholar 

  34. Vathi M, Pappa P and Karamanos SA (2013) Seismic response of unanchored liquid storage tanks. In: ASME 2013 pressure vessels and piping conference. Volume 8: Seismic Engineering. Paris, France.

  35. Çelik Aİ, Köse MM, Akgül T, Alpay AC (2018) Directional-deformation analysis of cylindrical steel water tanks subjected to El-Centro earthquake loading. Sigma J Eng Nat Sci 36(4):1033–1046

  36. Çelik Aİ, Köse MM (2020) Dynamic buckling analysis of cylindrical steel water storage tanks subjected to Kobe earthquake loading. Steel Construct 13(2):128–138.

    Article  Google Scholar 

  37. Haroun MA (1983) Vibration studies and tests of liquid storage tanks. Earthquake Engng Struct Dyn 11(2):179–206

    Article  Google Scholar 

  38. Haroun MA, Housner GW (1981) Earthquake response of deformable liquid storage tanks. ASME. Appl Mech 48(2):411–418.

    Article  Google Scholar 

  39. Malhotra PK (1992) Seismic response of uplifting liquid storage tanks (PhD Thesis). Rice University. Houston, Texas, USA.

    Google Scholar 

  40. Malhotra PK and Veletsos AS (1994) Uplifting response of unanchored liquid-storage tanks. Journal of Structural Engineering-American Society of Civil Engineers, 120(12):3525–3547.

  41. Vathi M and Karamanos SA (2015) Simplified model for the seismic performance of unanchored liquid storage tanks. In Pressure Vessels and Piping Conference (Vol. 56987, p. V005T09A014). American Society of Mechanical Engineers.

  42. Cortes G, Prinz GS, Nussbaumer A, Koller MG (2012) Cyclic demand at the shell-bottom connection of unanchored steel tanks. In: 15th World Conference on Earthquake Engineering

  43. Phan HN, Paolacci F (2018) Fluid-structure interaction problems: an application to anchored and unanchored steel storage tanks. In 16th European Conference on Earthquake Engineering (p. 10). Thessaloniki. arXiv preprint arXiv:1805.00679

  44. Merino Vela RJ, Brunesi E, Nascimbene R (2019) Seismic Assessment of an industrial frame-tank system: development of fragility functions. Bull Earthquake Eng 17:2602. (Springer Netherlands)

    Article  Google Scholar 

  45. Bakalis K, Fragiadakis M and Vamvatsikos D (2015) Surrogate modeling of liquid storage tanks for seismic performance design and assessment. In: COMPDYN 2015 5th ECCOMAS thematic conference on computational methods in structural dynamics and earthquake engineering, 15–15, Crete Island, Greece.

  46. Bakalis K, Vamvatsikos D (2015) Direct performance based seismic design for liquid storage tanks. SECED 2015 Conference: Earthquake Risk and Engineering towards a Resilient World, Cambridge UK

  47. Bakalis K, Vamvatsikos D and Fragiadakis M (2015) Seismic fragility assessment of steel liquid storage tanks. American Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication) PVP, 8, 1–8.

  48. Çelik Aİ, Köse MM, Akgül T, Apay AC (2019) Effects of the shell thickness on the directional deformation and buckling on the cylindrical steel water tanks under the Kobe earthquake loading. Sakarya Univ J Sci. 23(2):269–281.

    Article  Google Scholar 

  49. Virella JC, Godoy LA, Suarez LE (2005) Effect of pre-stress states on the impulsive modes of vibration of cylindrical tank-liquid systems under horizontal motions. J Vib Control 11(9):1195–1220.

    Article  MATH  Google Scholar 

  50. Jaiswal OR, Jain SK (2005) Modified proposed provisions for aseismic design of liquid storage tanks: Part II—commentary and examples. J Struct Eng 32(4):297–310

    Google Scholar 

  51. Kotrasova K, Kormanikova E (2017) The study of seismic response on accelerated contained fluid. Adv Math Phys 1–9.

    Article  MathSciNet  MATH  Google Scholar 

  52. Van Rossum G (2007) Python programming language. In: USENIX Ann Tech Conf 41(1):1–36

    Google Scholar 

  53. Meng X, Li X, Xu X, Zhang J, Zhou W, Zhou D (2019) Earthquake response of cylindrical storage tanks on an elastic soil. J Vibr Eng Technol 7(5):433–444.

    Article  Google Scholar 

  54. Phan HN, Paolacci F, Corritore D, Tondini N and Bursi OS (2019) A kriging-based surrogate model for seismic fragility analaysis of unanchored storage tanks. In: ASME 2019 Pressure Vessels & Piping Conference. San Antonio, Texas, USA.

  55. Bakalis K, Karamanos SA (2021) Uplift mechanics of unanchored liquid storage tanks subjected to lateral earthquake loading. Thin-Walled Struct 158(October 2020):107145.

    Article  Google Scholar 

  56. Tsipianitis A, Tsompanakis Y, Psarropoulos PN (2020) Impact of dynamic soil–structure interaction on the response of liquid-storage tanks. Front Built Environ 6(140):18.

    Article  Google Scholar 

  57. Meskouris K, Butenweg C, Hinzen K-G, Höffer R (2019) Structural dynamics with applications in earthquake and wind engineering (Second Edi.). Springer, Germany.

    Book  Google Scholar 

  58. Bakalis K, Kazantzi AK, Vamvatsikos D, Fragiadakis M (2019) Seismic performance evaluation of liquid storage tanks using nonlinear static procedures. J Pressure Vessel Technol Trans ASME.

    Article  Google Scholar 

  59. Rotter JM (1985) Local inelastic collapse of pressurised thin cylindrical steel shells under axial compression. ASCE J Struct Eng 116(7):1955–1970

    Article  Google Scholar 

  60. Rotter JM, Seide P (1987) On the design of unstiffened shells subjected to an axial load and internal pressure. In: Proceedings of the ECCS Colloquium on Stability on Plate and Shell Structures. Ghent University, pp 539–548

  61. Bakalis K, Vamvatsikos D, Fragiadakis M (2014) Surrogate modelling and sensitivity analysis of steel liquid storage tanks. In: 8th Hellenic National Conference of Steel Structures. Tripoli, Greece, 2-4 October

  62. Baltas C (2004) Nonlinear seismic response of circular pressed reservoirs (MSc Thesis). Istituto Universitario di Studi Superiori, Università degli Studi di Pavia

  63. Vamvatsikos D (2002) Seismic performance, capacity and reliability of structures as seen through incremental dynamic analysis (PhD Thesis). Standford University, Stanford, USA

    Google Scholar 

  64. Applied Technology Council (2009) Quantification of building seismic performance factors. US Department of Homeland Security, FEMA

  65. Vamvatsikos D, Cornell CA (2002) Incremental dynamic analysis. Earthquake Eng Struct Dyn 31(3):491–514.

    Article  Google Scholar 

  66. Baker JW (2015) Efficient analytical fragility function fitting using dynamic structural analysis. Earthq Spectra 31(1):579–599.

    Article  Google Scholar 

  67. Wilson AW, Phillips AR, Motter CJ, Lee JY, Dolan JD (2021) Seismic loss analysis of buildings with post-tensioned cross-laminated timber walls. Earthq Spectra 37(1):324–345.

    Article  Google Scholar 

  68. Bakhshi A, Soltanieh H (2019) Development of fragility curves for existing residential steel buildings with concentrically braced frames. Scientia Iranica 26(4A):2212–2228.

    Article  Google Scholar 

  69. PEER NGA Database (2020) Pacific earthquake engineering research center. University of California, Berkeley.

  70. Bravo-Haro MA, Liapopoulou M, Elghazouli AY (2020) Seismic collapse capacity assessment of SDOF systems incorporating duration and instability effects. Bull Earthq Eng 18(7):3025–3056.

    Article  Google Scholar 

  71. Martineau MO, Lopez AF, Vielma JC (2020) Effect of earthquake ground motion duration on the seismic response of a low-rise RC building. Adv Civ Eng 2020:1–12.

    Article  Google Scholar 

  72. Baker JW (2013) Trade-offs in ground motion selection techniques for collapse assessment of structures, Vienna Congress on Recent Advances in Earthquake Engineering and Structural Dynamics, Vienna, Austria

  73. D-Amico M, Buratti N (2019) Observational seismic fragility curves for steel cylindrical tanks. J Pressure Vessel Technol. 141(1).

    Article  Google Scholar 

  74. Bakalis K (2018) Seismic performance assessment of industrial facility atmospheric liquid storage tanks (PhD Thesis). National Technical University of Athens, Athens, Greece

    Google Scholar 

  75. Salzano E, Iervolino I, Fabbrocino G (2003) Seismic risk of atmospheric storage tanks in the framework of quantitative risk analysis. J Loss Prev Process Ind 16(5):403–409.

    Article  Google Scholar 

  76. Chikhi A, Djermane M (2017) Dynamic buckling of cylindrical storage tanks during earthquake excitations. Asian J Civ Eng 18(4):607–620.

    Article  Google Scholar 

  77. Alessandri S, Caputo AC, Corritore D, Giannini R, Paolacci F, Phan HN (2018) Probabilistic risk analysis of process plants under seismic loading based on Monte Carlo simulations. J Loss Prevent Process Indust 53:136–148.

    Article  Google Scholar 

  78. Jerath S, Lee M (2015) Stability analysis of cylindrical tanks under static and earthquake loading. J Civ Eng Architect 9(1):72–79.

    Article  Google Scholar 

  79. Cimellaro GP, Reinhorn AM, Bruneau M, Rutenberg A (2006) Multi-dimentional fragility of structures: formulation and evaluation. Multidisciplinary Center for Earthquake Engineering Research, vol 123. Buffalo, New York

    Google Scholar 

  80. Tsipianitis A and Tsompanakis Y (2017) Seismic vulnerability assessment of base-isolated liquid fuels tanks. In Proceedings of 12th International Conference on Structural Safety and Reliability (ICOSSAR). Vienna, Austria

  81. Jalayer F (2003) Direct probabilistic seismic analysis: implementing non-linear dynamic assessments (PhD Thesis). Stanford University. Retrieved from.

  82. Auad GA, Almazán JL (2017) Nonlinear vertical-rocking isolation system: application to legged wine storage tanks. Eng Struct 152:790–803.

    Article  Google Scholar 

  83. HAZUS (2001) Earthquake loss estimation methodology. National Institute of Building Science, Risk Management Solution, Menlo Park, California, USA

    Google Scholar 

  84. Porter K (2015) A beginner’s guide to fragility, vulnerability, and risk. Encyclopedia Earthquake Eng 235–260.

    Article  Google Scholar 

  85. Ibarra LF and Krawinkler H (2005) Global collapse of frame structures under seismic excitations (No. 152) (p 324). Stanford: John A. Blume Earthquake Engineering Center. Retrieved from

  86. Porter K, Hamburger R, Kennedy R (2007) Practical development and application of fragility functions. Struct Eng Res Front 1–16.

    Article  Google Scholar 

  87. Capanna I, Cirella R, Aloisio A, Alaggio R, Di Fabio F, Fragiacomo M (2021) Operational modal analysis, model update and fragility curves estimation, through truncated incremental dynamic analysis, of a masonry belfry. Buildings 11(3):120.

    Article  Google Scholar 

  88. Eaton JW, Bateman D and Hauberg S (1997) Gnu octave. Network theory, London, p 42

  89. Phan HN, Paolacci F, Corritore D, Akbas B, Uckan E, Shen JJ (2016) Seismic vulnerability mitigation of liquefied gas tanks using concave sliding bearings. Bull Earthq Eng 14:3283–3299.

    Article  Google Scholar 

  90. Federal Emergency Management Agency (FEMA) (2018) Seismic performance assessment of buildings: volume 1—methodology. Rep. No. FEMA P-58-1

  91. Phan HN and Paolacci F (2016) Efficient intensity measures for probabilistic seismic response analysis of anchored above-ground liquid steel storage tanks. In: ASME 2016 Pressure Vessels and Piping Conference, vol 5, pp 1–10.

Download references


This research received no external funding.

Author information

Authors and Affiliations



Conceptualization: NB and EA; investigation: NB; writing—original draft preparation: NB; writing—review and editing: NB and EA; supervision: EA. All authors have read and agreed to the published version of the manuscript.

Corresponding author

Correspondence to Engin Aktaş.

Ethics declarations

Conflicts of Interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bektaş, N., Aktaş, E. Seismic Vulnerability Assessment of an Unanchored Circular Storage Tank Against Elephant’s Foot Buckling. J. Vib. Eng. Technol. 11, 1661–1678 (2023).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: