Plane Strain versus Axisymmetric Modeling of Convex Levees
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 141, Issue 4
Abstract
The Natomas basin is a 21,450-ha area north of downtown Sacramento, California. The developed area relies on levees for flood protection along its perimeter. The western boundary is a 29.9-km-long levee that protects the area from flooding by the Sacramento River. Since its construction over a century ago, this levee has experienced a myriad of performance issues. From 2008 to 2011, a team of engineers completed design and construction of remedial measures with the objective of ending the historic performance issues. Along one stretch, the Sacramento River and levee make a sharp bend at a constant levee radius of approximately 515 m. During the design processes, the levee was analyzed using a two-dimensional plane strain model despite this relatively sharp convex bend. This paper presents a review of the plane strain and axisymmetric formulations in which it is shown that the radial (horizontal) scale of the axisymmetric formulation is not arbitrary and requires additional planning by the modeler. A comparison of the results (seepage gradients and computed factor of safety for stability) from numerical modeling of levees using plane strain and axisymmetric formulations through the use of a case history is then presented. The computed gradients for the convex axisymmetric case are higher than those computed using a plane strain formulation. For the cross sections used in this study, the increase is greater than previously reported. Moreover, the increase is not systematic and is unique to each cross section.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The lead author was a senior technical lead for Kleinfelder during this project and acknowledges the many engineers from 20 offices who worked long hours on this fast-paced project. The authors wish to thank Mr. John Bassett, Director of Engineering for the Sacramento Area Flood Control Agency, for use of data from this project, and Ms. Mary Perlea (USACE), Mr. Ray Costa (Consultant), and Dr. Panos Kiousis (Colorado School of Mines) for their valuable comments. We also acknowledge the SREL levee design team, including Kleinfelder, MBK Engineers, and HDR Engineering, Inc., for their cooperation in this work.
References
CADWR (California Department of Water Resources). (2009). “Proposed interim levee design criteria for urban and urbanizing area state-federal project levees.” Third Draft.
CADWR (California Department of Water Resources). (2012). “Urban levee design criteria, May 2012.” 〈http://www.water.ca.gov/floodsafe/leveedesign/ULDC_May2012.pdf〉 (Sep. 22, 2014).
Code of Federal Regulations. (1986). 10(65.10).
Code of Federal Regulations. (2001). 10(65.2).
Connor, J. J., and Brebbia, C. A. (1976). Finite element techniques for fluid flow, Newnes-Butterworths, Boston.
Du, R., and Merry, S. M. (2014). “The effect of the waterside boundary condition on the seepage and slope stability analyses of the Natomas levees—A case study.” Proc., Geocongress 2014 (GSP 234), M. Abu-Farsakh, X. Yu, and L. R. Hoyos, eds., ASCE, Reston, VA, 1511–1524.
GeoStudio 2007 Analysis Software, version 7.11, Build 5051 [Computer software]. Geo-Slope International, Calgary, AB, Canada.
Geostudio 2012 Analysis Software, version 8.0.10.6504 [Computer software]. Geo-Slope International, Calgary, AB, Canada.
Inci, G. (2008). “3D effects on flood protection levees—Plain strain versus axisymmetric modelling.” Proc., 12th Int. Conf. of Int. Association for Computer Methods and Advances in Geomechanics (IACMAG), Curran Associates, Red Hook, NY, 3820–3826.
Kleinfelder. (2009a). “Draft geotechnical basis of design report, Sacramento river east levee, SREL 3 (reaches 10 through 15).” Natomas Levee Improvement Program, Sacramento and Sutter, CA.
Kleinfelder. (2009b). “Draft geotechnical data report, Sacramento river east levee, SREL 3 (reaches 10 through 15).” Natomas Levee Improvement Program, Sacramento and Sutter, CA.
MBK Engineers. (2008). “Supplemental report for the design water surface profile for the Natomas levee improvement program.” Sacramento Area Flood Control District.
Merry, S. M., and Du, R. (2014). “Plane strain versus axisymmetric modeling of the Natomas levees—A case study.” Proc., Geocongress 2014 (GSP 234), M. Abu-Farsakh, X. Yu, and L. R. Hoyos, eds., ASCE, Reston, VA, 1542–1556.
Rao, S. S. (1999). The finite element method in engineering, 3rd Ed., Butterworths-Heinemann, Boston.
Reclamation District 1000. (2013). “Floods.” 〈http://www.rd1000.org/floods.php〉 (Sep. 22, 2014).
Reddy, J. N. (1993). An introduction to the finite element method, 2nd Ed., McGraw-Hill, Hightstown, NJ.
SAFCA (Sacramento Area Flood Control Agency). (2014). “Sacramento area flood history.” 〈http://www.safca.org/history.html〉 (Sep. 22, 2014).
Spencer, E. (1967). “A method of analysis of the stability of embankments assuming parallel interslice forces.” Geotechnique, 17(1), 11–26.
U.S. Army Corps of Engineers (USACE). (2010). “Engineering and design—USACE process for the national flood insurance program (NLIP) levee system evaluation.”, Washington, DC.
Information & Authors
Information
Published In
Journal of Geotechnical and Geoenvironmental Engineering
Volume 141 • Issue 4 • April 2015
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Aug 16, 2013
Accepted: Oct 31, 2014
Published online: Dec 9, 2014
Published in print: Apr 1, 2015
Discussion open until: May 9, 2015
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.