Abstract
In this paper, we describe the computational framework of a novel method for solving the challenging problem of probabilistic finite elements. The method is called Improved Dynamic Bounds (IDB) and was developed recently to improve the efficiency of the dynamic bounds. The IDB is used in finite element numerical models to calculate time-dependent failure analyses of structures. In applications, the IDB can speed up the overall simulation process by several orders of magnitude. In applications controlled by two influential variables (e.g, two-dimensional problem), the computational efficiency is improved by a factor of 769 according to Rajabalinejad (2009). Applications of IDB indicate the method is most efficient for problems where the number of influential variables are limited. This is often the case for geotechnical and coastal flood defence systems. The IDB method is applied in this paper to the 17th Street Flood Wall, a component of the flood defence system (levee infra-structure) that failed during the Hurricane Katrina, to calculate the failure probability of an I-wall.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
These sets become gradually available during the Monte Carlo simulations.
An efficient criterion is essential to rank variables for the IDB method.
The rank correlation shows that variables 3, 8, and 4 are the most influential variables and this sequence may change when the structure’s response becomes nonlinear at the high water level, W.L. = +8 ft (2.4 m).
The variation of soil parameters was assumed to estimate the reliability of this structure; this assumption affects the calculated probability of failure.
References
Brinkgreve RBJ (ed) (2002) Plaxis, finite element code for soil and rock analyses, vol 2D-version 8. A.A. Balkema Publishers, a member of Swets & Zeitlinger Publishers, The Netherlands, Delft
Demirbilek Z, Lin L, Mark D (2008) Numerical modeling of storm surges in chesapeake bay. Int J Ecol Dev 10(S08):24–39
Link LE, Jaeger JJ, Stevenson J, Stroupe W, Mosher RL, Martin D, Garster JK, Zilkoski DB, Ebersole BA, Westerwink JJ (2006) Performance evaluation of the New Orleans and Southeast Louisiana hurricane protection system: draft final report of the interagency performance evaluation task force, vol 1. United States Army Corps of Engineers (USACE), vol 1e9
Rajabalinejad M (2009) Reliability methods for finite element models, i ed. IOS Press, Amsterdam, The Netherlands
Rajabalinejad M, Kanning W, van Gelder P, Vrijling JK, van Baars S (2007) Probabilistic assessment of the flood wall at 17th street canal, New Orleans, risk, reliability and societal safety 1–3:2227–2234
Rajabalinejad M, van Gelder P, Vrijling J (2008a) Probabilistic finite elements with dynamic limit bounds: a case study: 17th street flood wall, New Orleans. In: Prakash S (ed) 6th international conference on case histories in geotechnical engineering, vol I, Missouri University of Science and Technology, Rolla, MO, USA
Rajabalinejad M, van Gelder P, Vrijling JK (2008b) Improved dynamic limit bounds in Monte carlo simulations. In: 49th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, vol I of American Institute of Aeronautics and Astronautics, American Institute of Aeronautics and Astronautics, Schaumburg, IL, USA
Rajabalinejad M (2010) Bayesian Monte Carlo method. Reliability Eng Syst Saf 95(10):1050–1060
Rajabalinejad M, Mahdi T (2010) The inclusive and simplified forms of Bayesian interpolation for general and monotonic models using Gaussian and Generalized Beta distributions with application to Monte Carlo simulations. Nat Hazards. doi:10.1007/s11069-010-9560-3
Rajabalinejad M, Van Gelder P, Mahdi T (2010a) Stochastic methods for safety assessment of the flood defence system in the Scheldt Estuary of the Netherlands. Nat Hazards. doi:10.1007/s11069-010-9563-0
Rajabalinejad M, van Gelder P, Demirbilek Z, Mahdi T.-F, Vrijling JK (2010b) Application of the dynamic bounds method in the safety assessment of flood defences, a case study: 17th street flood wall, New Orleans. Georisk: assessment and management of risk for engineered systems and geohazards. doi:10.1080/17499510903416170
Team ILI (2006) Investigation of the performance of the New Orleans flood protection systems in hurricane Katrina, Technical Report Chap. 8, Berkely University, Berkely (May 22, 2006)
Triebel H (1978) Interpolation theory, function spaces. differential operators, North-Holland
USACE-c (2006) Orleans and Southeast Louisiana hurricane protection system, vol III The hurricane protection system, Technical Report 378, U.S. Army Corps of Engineers, Report of the Interagency Performance Evaluation Task Force (June 2006)
USACE-e (2006) Orleans and Southeast Louisiana hurricane protection system, vol V, The performance levees and floodwalls, Technical Report 86, U.S. Army Corps of Engineers, Report of the Interagency Performance Evaluation Task Force (June 2006)
van Gelder P (2009) Reliability analysis of flood defence systems. Technical report T07-09-20, Technical University Delft, Delft. http://www.floodsite.net
Acknowledgments
The information used in this research for the 17th Street Flood Wall project was obtained from various publications available on Internet and study reports downloaded from different Web sites. ZD was supported by the NavSys Program during this research and would like to thank Program Managers Jeff Lillycrop and Eddie Wiggins for their support. Permission to publish this information was granted by the Chief, U.S. Army Corps of Engineers.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rajabalinejad, M., Demirbilek, Z. & Mahdi, T. Determination of failure probabilities of flood defence systems with improved dynamic bounds method. Nat Hazards 55, 95–109 (2010). https://doi.org/10.1007/s11069-010-9561-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11069-010-9561-2