Use of Exact Solutions of Wave Propagation Problems to Guide Implementation of Nonlinear Seismic Ground Response Analysis Procedures
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 133, Issue 11
Abstract
One-dimensional nonlinear ground response analyses provide a more accurate characterization of the true nonlinear soil behavior than equivalent-linear procedures, but the application of nonlinear codes in practice has been limited, which results in part from poorly documented and unclear parameter selection and code usage protocols. In this article, exact (linear frequency-domain) solutions for body wave propagation through an elastic medium are used to establish guidelines for two issues that have long been a source of confusion for users of nonlinear codes. The first issue concerns the specification of input motion as “outcropping” (i.e., equivalent free-surface motions) versus “within” (i.e., motions occurring at depth within a site profile). When the input motion is recorded at the ground surface (e.g., at a rock site), the full outcropping (rock) motion should be used along with an elastic base having a stiffness appropriate for the underlying rock. The second issue concerns the specification of viscous damping (used in most nonlinear codes) or small-strain hysteretic damping (used by one code considered herein), either of which is needed for a stable solution at small strains. For a viscous damping formulation, critical issues include the target value of the viscous damping ratio and the frequencies for which the viscous damping produced by the model matches the target. For codes that allow the use of “full” Rayleigh damping (which has two target frequencies), the target damping ratio should be the small-strain material damping, and the target frequencies should be established through a process by which linear time domain and frequency domain solutions are matched. As a first approximation, the first-mode site frequency and five times that frequency can be used. For codes with different damping models, alternative recommendations are developed.
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Acknowledgments
Financial support for this work was provided by PEER Lifelines project No. UNSPECIFIED2G02, which is sponsored by the Pacific Earthquake Engineering Research Center’s Program of Applied Earthquake Engineering Research of Lifeline Systems. The PEER Lifelines program, in turn, is supported by the State Energy Resources Conservation and Development Commission and the Pacific Gas and Electric Company. This work made use of Earthquake Engineering Research Center’s Shared Facilities supported by the National Science Foundation under Award No. NSFEEC-9701568. In addition, the support of the California Department of Transportation’s PEARL program is acknowledged. This project has benefited from the helpful suggestions of an advisory panel consisting of Drs. Yousef Bozorgnia, Susan Chang, I. M. Idriss, Steven Kramer, Faiz Makdisi, Geoff Martin, Lelio Mejia, Tom Shantz, Walter Silva, and Joseph Sun.
DEEPSOIL development was supported in part by the Earthquake Engineering Research Center’s Program of the National Science Foundation under Award No. NSFEEC-9701785; the Mid-America Earthquake Center. 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 National Science Foundation.
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Information & Authors
Information
Published In
Journal of Geotechnical and Geoenvironmental Engineering
Volume 133 • Issue 11 • November 2007
Pages: 1385 - 1398
Copyright
© 2007 ASCE.
History
Received: Jul 11, 2006
Accepted: Feb 6, 2007
Published online: Nov 1, 2007
Published in print: Nov 2007
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