Seismic Design of Rocking Shallow Foundations: Displacement-Based Methodology
Publication: Journal of Bridge Engineering
Volume 19, Issue 11
Abstract
This paper proposes a direct displacement-based design (DDBD) methodology for seismic design of rocking shallow foundations for ordinary bridges under earthquake loads. A multilinear model is developed to represent the backbone curve of the nonlinear moment-rotation behavior. In addition, a new empirical relationship is proposed that correlates the initial rotational stiffness to the moment capacity of a rocking foundation; this correlation is proposed as an alternative to calculation of stiffness based upon elasticity theory. In the proposed design procedure, a bridge system consisting of a deck mass, a rocking foundation, and a damped elastic column is integrated into a single element from which the equivalent linear damping and period can be determined. The DDBD methodology uses the equivalent system damping and period along with a design displacement response spectrum to determine the seismic displacement demand. The approach is checked by comparing displacements predicted by this method to those computed using nonlinear time-history analyses. The methodology also includes provisions to determine footing dimensions to obtain acceptable performance in terms of foundation settlement and lateral sliding. The DDBD methodology is further illustrated with a design example.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The project was supported by the National Science Foundation (NSF) Network for Earthquake Engineering Simulation Research (NEESR) Grant 0936503 and the Pacific Earthquake Engineering Research Center (PEER) Transportation Research Program under the “Last Hurdles for Rocking Foundations for Bridges” project. The authors are grateful to CALTRANS collaborators M. Mahan, T. Shantz, F. Alameddine, and M. Desalvatore for their constructive suggestions during the project; K. Johnson for helping to process the data used in Figs. 1–5, and J. G. Tom of Advanced Geomechanics Pty. Ltd. for his useful comments on early drafts of this paper. Professors M. Aschheim and T. Hutchinson also contributed feedback and ideas that facilitated the development of concepts presented in this paper. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the collaborators and sponsors.
References
AASHTO. (2010). AASHTO LRFD bridge design specifications, 6th Ed., Washington, DC.
Allotey, N., and El Naggar, H. M. (2003). “Analytical moment–rotation curves for rigid foundations based on a Winkler model.” Soil. Dyn. Earthquake Eng., 23(5), 367–381.
Anastasopoulos, I., Gazetas, G., Loli, M., Apostolou, M., and Gerolymos, N. (2010). “Soil failure can be used for seismic protection of structures.” Bull. Earthquake Eng., 8(2), 309–326.
Applied Technology Council (ATC). (2005). “Improvement of nonlinear static seismic analysis procedures.” Rep. Prepared for the Dept. of Homeland Security, FEMA, FEMA 440, Redwood City, CA.
ASCE. (2000). “Prestandard and commentary for the seismic rehabilitation of buildings.” Rep. Prepared for FEMA, FEMA 356, Reston, VA.
ASCE. (2007). Seismic rehabilitation of existing buildings, 41-06, Reston, VA.
Baker, J. W., Lin, T., Shahi, S., and Jayaram, N. (2011). “New ground motion selection procedures and selected motions for the PEER transportation research program.” Pacific Earthquake Engineering Research Center Rep. No. 2011/03, Berkeley, CA.
Blandon, C. A., and Priestley, M. J. N. (2005). “Equivalent viscous damping equations for direct displacement based design.” J. Earthquake Eng., 9(SI 2), 257–278.
CALTRANS. (2010). Seismic design criteria, Sacramento, CA.
CALTRANS. (2012). “Caltrans ARS Online (v1.0.4).” 〈http://dap3.dot.ca.gov/shake_stable〉.
Chatzigogos, C. T., Figini, R., Pecker, A., and Salencon, J. (2011). “A macroelement formulation for shallow foundations on cohesive and frictional soils.” Int. J. Numer. Anal. Methods Geomech., 35(8), 902–931.
Chopra, A. K., and Goel, R. K. (2001). “Direct displacement-based design: use of inelastic vs. elastic design spectra.” Earthquake Spectra, 17(1), 47–64.
Deng, L. (2012). “Centrifuge modeling, numerical analyses, and displacement-based design of rocking foundations.” Ph.D. dissertation, Dept. Civil and Environmental Engineering, Univ. of California, Davis, Davis, CA.
Deng, L., and Kutter, B. L. (2012). “Characterization of rocking shallow foundation using centrifuge model tests.” Earthquake Eng. Struct. Dynam., 41(5), 1043–1060.
Deng, L., Kutter, B. L., and Kunnath, S. K. (2012a). “Centrifuge modeling of bridge systems designed for rocking foundations.” J. Geotech. Geoenviron. Eng., 335–344.
Deng, L., Kutter, B. L., and Kunnath, S. K. (2012b). “Probabilistic seismic performance of rocking-foundation and hinging-column bridges.” Earthquake Spectra, 28(4), 1423–1446.
Dwairi, H. M., and Kowalsky, M. J. (2006). “Implementation of inelastic displacement patterns in direct displacement-based design of continuous bridge structures.” Earthquake Spectra, 22(3), 631–662.
Dwairi, H. M., Kowalsky, M. J., and Nau, J. M. (2007). “Equivalent damping in support of direct displacement-based design.” J. Earthquake Eng., 11(4), 512–530.
European Committee for Standardization (CEN). (2005). “Eurocode 8: Design of structures for earthquake resistance—Part 2: Bridges.” EN 1998-2, Brussels, Belgium.
Gajan, S., and Kutter, B. L. (2008). “Capacity, settlement, and energy dissipation of shallow footings subjected to rocking.” J. Geotech. Geoenviron. Eng., 1129–1141.
Gazetas, G. (1991). “Foundation vibrations.” Foundation engineering handbook, H. Y. Fang, ed., Van Nostrand Reinhold, New York.
Housner, G. W. (1963). “The behavior of inverted pendulum structures during earthquakes.” Bull. Seismol. Soc. Am., 53(2), 403–417.
Jacobsen, L. S. (1930). “Steady forced vibration as influenced by damping.” Trans. Am. Soc. Mech. Eng. (ASME), 52(1), 169–181.
Jara, M., and Casas, J. R. (2006). “A direct displacement-based method for the seismic design of bridges on bi-linear isolation devices.” Eng. Struct., 28(6), 869–879.
Johnson, K. E. (2012). “Characterization of test results of rocking shallow foundations using a multi-linear hysteretic model.” M.S. report, Dept. of Civil and Environmental Engineering, Univ. of California, Davis, Davis, CA.
Kelly, T. E. (2009). “Tentative seismic design guidelines for rocking structures.” Bull. New Zealand Soc. Earthquake Eng., 42(4), 239–274.
Kowalsky, M. J., Priestley, M. J. N., and McRae, G. A. (1994). “Displacement based design of RC bridge columns.” Proc., 2nd Int. Workshop Seismic Design of Bridges, New Zealand Society for Earthquake Engineering, Wellington, New Zealand, 1, 138–163.
Kumar, J., and Rao, V. B. K. M. (2002). “Seismic bearing capacity factors for spread foundation.” Geotechnique, 52(2), 79–88.
Meyerhof, G. G. (1963). “Some recent research on the bearing capacity of foundations.” Can. Geotech. J., 1(1), 16–26.
Negro, P., Paolucci, R., Pedretti, S., and Faccoili, E. (2000). “Large scale soil-structure interaction experiments on sand under cyclic loading.” Proc., 12th World Conf. Earthquake Eng., International Association for Earthquake Engineering, Tokyo.
Ni, P. (2013). “Effects of soil-structure interaction on direct displacement-based assessment procedure of multi-span reinforced concrete bridges.” Eur. J. Environ. Civ. Eng., 17(7), 507–531.
Ni, P., Petrini, L., and Paolucci, R. (2013). “Direct displacement-based assessment with nonlinear soil–structure interaction for multi-span reinforced concrete bridges.” Struct. Infrastruct. Eng., in press.
Pais, A., and Kausel, E. (1988). “Approximate formulas for dynamic stiffnesses of rigid foundations.” Soil. Dyn. Earthquake Eng., 7(4), 213–227.
Paolucci, R., Figini, R., and Petrini, L. (2013). “Introducing dynamic non-linear soil-foundation-structure interaction effects in displacement-based seismic design.” Earthquake Spectra, 29(2), 475–496.
Paolucci, R., Shirato, M., and Yilmaz, M. T. (2008). “Seismic behavior of shallow foundations: shaking table experiments vs. numerical modeling.” Earthquake Eng. Struct. Dynam., 37(4), 577–595.
Pecker, A., Paolucci, R., Chatzigogos, C., Correia, A., and Figini, R. (2013). “The role of non-linear dynamic soil-foundation interaction on the seismic response of structures.” Bull. Earthquake Eng., in press.
Priestley, M. J. N., Calvi, G. M., and Kowalsky, M. J. (2007). Displacement-based seismic design of structures, IUSS Press, Pavia, Italy.
Salgado, R. (2008). Engineering of foundations, McGraw Hill, New York.
Smith-Pardo, J. P. (2012). “Design aids for simplified nonlinear soil–structure interaction analyses.” Eng. Struct., 34, 572–580.
Standards New Zealand. (2004). Structural design actions, NZS 1170.5: 2004, Wellington, New Zealand.
Stewart, J. P., et al. (2013). “Soil-structure interaction for building structures.” ATC-83, Rep. Prepared for the Applied Technology Council, Redwood City, CA.
Wang, S., Kutter, B. L., Chacko, J., Wilson, D. W., Boulanger, R. W., and Abghari, A. (1998). “Nonlinear seismic soil-pile structure interaction.” Earthquake Spectra, 14(2), 377–396.
Information & Authors
Information
Published In
Journal of Bridge Engineering
Volume 19 • Issue 11 • November 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Mar 25, 2013
Accepted: Feb 24, 2014
Published online: Mar 27, 2014
Discussion open until: Aug 27, 2014
Published in print: Nov 1, 2014
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.